THE 
 COAL MINERS' POGKETBOOK 
 
McGraw-Hill BookCompany 
 
 Electrical World The Engineering andMining Journal 
 Engineering Record Engineering News 
 
 Railway Age Gazette American Machinist 
 
 Signal Engineer AraaicanEngneer 
 
 Electric Railway Journal Coal Age 
 
 Metallurgical and Chemical Engineering Power 
 
COAL MINERS' 
 POCKETBOOK 
 
 FOEMEELY THE 
 
 COAL AND METAL MINERS' POCKETBOOK 
 
 PRINCIPLES, RULES, 
 FORMULAS AND TABLES 
 
 ELEVENTH EDITION 
 REVISED, ENLARGED, AND ENTIRELY RESET 
 
 McGRAW-HILL BOOK COMPANY, INC, 
 
 239 WEST 39TH STREET. NEW YORK 
 
 LONDON: HILL PUBLISHING CO., LTD. 
 
 6 & 8 BOUVERIE ST., E. C. 
 
 1916 
 
COPYRIGHT, 1916, BY THE 
 MCGRAW-HILL BOOK COMPANY, INC. 
 
 COPYRIGHT, 1901, 1905, BY THE 
 INTERNATIONAL TEXTBOOK COMPANY 
 
 COPYRIGHT, 1890, 1893, 1900, BY THE 
 COLLIERY ENGINEER COMPANY 
 
 ENTERED AT STATIONERS' HALL, LONDON 
 
 All Rights Reserved 
 
PREFACE TO ELEVENTH EDITION 
 
 Perhaps the most important change in the present edition 
 of this book, is the omission of matter pertaining strictly to ore 
 mining, in order that the space formerly occupied by it, and a 
 large amount in addition, might be devoted to coal mining. 
 In consequence of this, the publishers have deemed it wise to 
 change the title from "The Coal and Metal Miners' Pocket- 
 book," to " The Coal Miners' Pocketbook." It is believed that 
 the pocketbook will still prove of interest and value to all men 
 engaged ^ in mining, as well as to many in other branches of 
 engineering, but it seemed no longer possible, within the limits 
 of a compact handbook, to cover both fields in full detail. 
 
 The present edition represents a thorough revision. Not 
 only have material changes been made throughout the text, but 
 substantial additions to many sections, which bring the work up 
 to date, and, it is hoped, increase its usefulness. 
 
 The subjects of Weights and Measures and Mathematics 
 have been entirely rewritten and greatly enlarged. The depart- 
 ment on Surveying has been expanded to include Leveling with 
 the aneroid barometer, so much of Railroad Surveying as is 
 necessary at mines, and Determination of the Meridian, both 
 by solar and pole-star observations; and to it have been added 
 some practical notes on Surveying, as ordinarily practised in 
 flat seams. Under the heading of Mechanics, Strength of Mate- 
 rials, etc., will be found very complete tables of specific gravi- 
 ties and weights of various substances per cubic foot. The de- 
 partment on Concrete Construction is entirely new and complete 
 and is of timely interest. Hydrostatics and Hydraulics have 
 been enlarged by the addition of entirely new tables. Pump 
 Machinery now includes centrifugal pumps. The department 
 on Fuels has been practically rewritten and now contains the 
 best formulas for calculating the heating values of coals from 
 their proximate and ultimate analyses, as well as very complete 
 tables of analyses of American and foreign coals. The notes 
 upon Prospecting include the newer types of drilling machinery. 
 The matter on-Mine Timbering is practically new and includes 
 notes on the preservation of timber, steel timbers, etc. The 
 subject of Flushing Culm has been brought up to date with 
 numerous examples drawn from recent practice. The sub- 
 jects of Explosives and Mining Machines have been rewritten 
 on the lines of modern practice. Under Hoisting and Haulage 
 will be found much entirely new matter on gasoline and storage- 
 battery motors, and the subject of Tracklaying has been entirely 
 rewritten. The subject of the Treatment of Injured Persons is 
 now up to date, and the Glossary has been enlarged. 
 
 Those who use this book are kindly and earnestly requested 
 to advise us of any errors or omissions they may note and to 
 offer suggestions for the betterment of subsequent editions. 
 
 394012 
 
CONTENTS 
 
 (For detailed Index, see back of volume. See also Glossary of Mining Terms 
 page 1102.) 
 
 WEIGHTS AND MEASURES 
 Linear Measure. Surveyor's Linear Measure, 1; Decimals of an Inch and 
 
 Millimeters for Each ^64 In., Table, 2; Decimals of a Foot for Each 
 
 fa In., Table, 4, 5. 
 
 Measures of Surface. Square Measure, 3; Surveyor's Square Measure, 3. 
 Measures of Weight. Troy, 4; Apothecaries', 4; Avoirdupois, 5. 
 Measures of Volume. Masonry, 6; Brickwork, 6; Shipping, 7; Liquid 
 
 (U. S.), 7; Dry (U. S.), 7; Relation Between Volumes and Weights 
 
 of Water, U. S. Liquid Measure, 8; Equivalent Weights and Volumes 
 
 of Water, 8. 
 Angular, or Circular, Measure. Laying off Right Angles, 9; Ratio of Sides 
 
 of Right- Angled Triangle, Table, 9; Laying off an Angle With a Tape, 
 
 Measures of Time. Longitude and Time, 10. 
 
 The Metric System. Metric Measures of Length, 11; Of Surface, 11; Of 
 
 Weight, 12; Of Volume, 12; Of Capacity, 12; Equivalents of Volume, 
 
 Weight of Water, and Capacity, 12. 
 Conversion Factors. Metric to United States, 13; United States to Metric, 
 
 14. 
 
 Weights and Measures of Great Britain and Colonies. Imperial Measure, 
 Both Liquid and Dry, 15. 
 
 Money. United States Currency, 16; Standard United States Coins, 16: 
 Currency of Great Britain, 16; Foreign Monetary Systems and 
 Equivalents in United States Gold, 17; Values of Foreign Coins, 18. 
 
 MATHEMATICS 
 
 Arithmetic. Mathematical and Other Commonly Used Signs and Abbrevia- 
 tions, 18, 19; Common Fractions, 19; Decimals, 20; Formulas, 20; 
 Proportion, or Cause and Effect, 21; Percentage, 22; Interest, 23; 
 Trade Discount, 23; Reciprocals, 23; Arithmetical Progression, 24; 
 Geometrical Progression, 25; Involution, 25; First Nine Powers of 
 First Nine Numbers, Table, 26; Evolution, 26; To Find the Square 
 Root of a Number, 26; To Find the Cube Root of a Number, 27: 
 Finding the Fourth and the Fifth Root of a Number, 28; Table of 
 Fifth Powers, 28.; Simple Method of Extracting Roots, 29. 
 
 Logarithms. Exponents, 29; Rule for Characteristics, 30; Finding the Loga- 
 rithm of a Number, 30; To Find a Number Whose Logarithm is 
 Given, 31; Multiplication by Logarithms, 32; Division by Logarithms, 
 33; Involution by Logarithms, 34; Evolution by Logarithms, 34; 
 Solution of Equations by Logarithms, 36. 
 
 Geometry. Principles, 36; Problems in Geometrical Construction, 38-43. 
 
 Mensuration of Surfaces. Triangles, 43; Parallelograms, 44; Trapezoids, 
 44; Trapeziums, 45; Polygons, 45; Names and Relations of Regular 
 Polygons, Table, 46; Circles, 48; Rings, 49; Sectors, 49; Circular 
 Segments, 49; Ellipse, 50. 
 
 Mensuration of Solids. Values Used in Formulas, 50; Prismoid and Pris- 
 moidal Formula, 50; Regular Polyhedrons, 50; Regular Polyhedrons 
 Whose Edges are Unity, 51; The Sphere, 51; Spherical Segments, 52; 
 Spherical Zones, 52; Cylindrical Rings, 52; Parallelepipeds, 52 
 Cylinders, 53; The Pyramid, 53; The Wedge, 53; The Cone, 53. 
 
viii CONTENTS 
 
 Plane Trigonometry. Definitions, 54; Fundamental Relations, 55; Signs of 
 Trigonometric Functions, 55; Functions of Angles Between 90 and 
 180, 55; Functions of 90+ A, 55; Functions of 180 -A and of 
 180 + A, 55; Functions of (A + B) and of (A-B), 56; Func^ns 
 of 2A and of \iA., 56; Sums and Differences of Functions, 56; Solution 
 of Right- Angled Triangles, 56; Relations Between Angles and Sides of 
 Right-Angled Triangles, 57; Solution of Oblique-Angled Triangles, 
 57; Practical Examples, 58. 
 
 SURVEYING 
 
 The Compass. General Description, 60; Compass Adjustments, 60; Using 
 the Compass, 61; Magnetic Variation, 61; Reading the Vernier, 62; 
 Field Notes for an Outside Compass Survey, 62. 
 
 The Transit. General Description, 62; Transit Verniers, 63; Transit Tele- 
 scope, 64; Transit Adjustments, 64. 
 
 Chain, Steel Tape, and Pins. 65. 
 
 Transit Surveying. Reading Angles, 67; Making a Survey With a Transit, 
 67; Meridians, or Base Lines, 67; Monuments, 68; Outside Surveys, 
 68; Preliminary Work, 68; Angular Measurements, 69; Distance 
 Measurements, 70; Locating Corners, Etc., 70; Keeping Notes, 71; 
 Transit Notes, 71; Closing Surveys, 72. 
 
 Leveling. Description of Instruments, 73; Level Adjustments, 73: Using 
 the Level, 74; Field Work, 75; Level Notes, 75; Proof of Calculations, 
 76; Trigonometric Leveling, 76. 
 
 Connecting Outside and Inside Work Through Shafts and Slopes. Survey- 
 ing Shafts, 77; The T-Square Method, 81; Check Methods, 81; Sur- 
 veying Slopes or Inclined Shafts, 82; Bent Plumb-Line Method, 82; 
 Method by a Single Wire in the Slope, 82. 
 
 Underground, or Mine, Surveying. Introduction, 83; Flat Work, 83; 
 Stations, 84; Sighting, 85; Centers, 86; Placing Stations on Line, 86; 
 Placing Sights, 87; Surveying and Note Keeping, 88; Level Notes, 
 90; Pitching Work, 90; Stations, 90; Surveying Methods, 91; Locating 
 Pillars for Surface Support, 92; Mine Corps, 92; Care of Instruments, 
 92. 
 
 Traversing and Mapping. Traversing, 93; Traversed Survey Notes, Table, 
 94; Errors in Closure, 94; Balancing Surveys, 95; Locating Special 
 Work, 95; Mapping, 95; Laying Off a Map, 95; Mapping the Field 
 Notes, 97; Coloring a Map, 98. 
 
 Determination of Meridian. Latitude and Longitude, 99; Celestial Sphere, 
 99; Reference Circles, 99; Time, 100; Civil Time and Astronomical 
 Time, 100; Longitude and Time, 101; Relation Between Time and 
 Longitude, 101; Standard Time, 101; To Change Standard Time Into 
 Local Time and Vice Versa, 101; Determination by Observing Polaris 
 at Culmination, 101; Field Work, 101; Local Mean Astronomical 
 Time of Upper Culmination of Polaris, Table, 102; Time of Culmina- 
 tion of Polaris, 103; Determination by Observing Polaris at Elonga- 
 tion, 103; Making the Observation and Marking the Meridian, 103; 
 Azimuths of Polaris at Elongation, Table, 104; Determination by 
 Solar Observation, 105; Formula for Azimuth of the Sun, 105; Values 
 of 5 and <f>, 105; Determination of Latitude, and Corrections for Alti- 
 tude, 105; Approximate Determination of Latitude from Polaris, 105; 
 Latitude by Solar Observation, 106; Corrections for Altitude, 106; 
 Sun's Parallax in Altitude to be Applied to All Measured Altitudes 
 of the Sun, Table, 106; Corrections for Observation of the Sun for 
 Azimuth, 106; Mean Refraction to be Applied to All Measured Alti- 
 tudes, Table, 107. 
 
 Railroad Surveying. Definitions of Circular Curves, 109; Geometry of Cir- 
 cular Curves, 109; Elements and Methods of Laying Out a Circular 
 Curve, 110; Relation Between Radius and Deflection Angle, 110; 
 Tangent Distance, 110; Laying Out a Curve With a Transit, 110; 
 Table of Radii and Deflections, 111; Tangent and Chord Deflec- 
 tions, 112; Special Values of Chord and Tangent Deflection, 113; 
 Application of Chord and Tangent Deflection, 113; Middle Ordinate, 
 113; To Determine Degree of Curve from Middle Ordinate, 113; 
 
CONTENTS ix 
 
 Rules for Measuring the Radius of a Curve, 114; Other Ordinates 
 114; Field Notes for Curves, 115; Earthwork, 115; Cuts and Fills 
 115; Slope Ratio, 115; Width of Excavations and Embankments, 116- 
 Grade Profile, 116; Slope Stakes, 117; Form of Notes in Cross-Section 
 Work, 118; Railroad Location, 119; Preliminary Estimate, 119; Loca- 
 tion, 120; Curvature, 120; Compensation for Curvature, 120; Final 
 Grade Lines, 121; Vertical Curves, 1 22j Vertical Curve at a Spur, 122 : 
 Vertical Curve at a Sag, 124; Curved Track, 124; Curving Rails, 124; 
 Middle Ordinates for Curving Rails, Table, 125; Turnouts, 125; 
 Switches, 125; Frogs and Guard-Rails, 126; Frog Angle and Frog 
 Number, 126; Guard-Rails, 127; Radius and Lead of a Turnout for 
 Stub Switches, 127; Dimensi9nsof Stub-Switch Turnouts, Table, 127; 
 Turnout Dimensions for Point Switches, 128; Dimensions of Point- 
 Switch Turnouts, Table, 128; Turnouts From the Outer Side of a 
 Curved Track, 129; Turnout From the Inner Side of a Curved Track, 
 130; Connecting Curves, 130; Cross-Overs, 130; Cross-Over Between 
 Two Parallel Straight Tracks, 130; Another Form, 131; Laying Out 
 Turnouts, 131; To Lay Out a Stub Switch, 131; To Lay Out a Point 
 Switch, 132; Switch Timbers, 133; Practical Method of Laying Out 
 Sharp Curves in a Mine, 133. 
 
 Stadia Surveying. Definition, 134; Reduction of Inclined Sights, 135; Use 
 of Stadia, 136; Stadia Reduction Tables, 137-139. 
 
 Barometric Leveling. General, 140; Barometric Formulas, 141; Barometric 
 Elevations, Table, 142; Corrections for Temperature and Humidity, 
 Table, 143; Use of Barometer, 143; Care of the Barometer, 144. 
 
 Practical Problems in Surveying. 144-148. 
 
 MECHANICS 
 
 Elements of Mechanics. General Law, 149; Levers, 149; Wheel and Axle 
 150; Inclined Plane, 151; To Find Weight Required to Balance Any 
 Weight on Any Inclined Plane, 151; Screw, 151; Wedge, 151; Pulley, 
 152; Combinations of Pulleys, 152; Differential Pulley, 152. 
 
 Falling Bodies. 153. 
 
 Work. 153. 
 
 Composition and Resolution of Forces. Parallelogram of Forces, 154; Reso- 
 lution of Forces, 154. 
 
 Moments of Forces. 154. 
 
 Center of Gravity. Definitions, 155; Of Solids, 156. 
 
 Moment of Inertia. Table, 157; Principles, 158. 
 
 Radius of Gyration. 158. 
 
 Section ^odulus and Moment of Resistance. 159. 
 
 Friction. Coefficient of Friction, 159; Angle of Friction, 160; Angle of 
 Repose, 160; Coefficients of Friction and Angles of Repose for 
 Masonry Materials, Table, 160; Rolling Friction, 160; Coefficients 
 of Friction, Angles of Repose, and Weights of Earth, Table, 161; 
 Coefficients and Angles of Friction for Miscellaneous Materials, 
 Table, 161; Rolling Friction for Different Roadway Surfaces, Table, 
 162; Coefficients of Friction in Axles, Table, 152; Frictional Resist- 
 ance of Shafting, 162; Friction of Mine Cars, 163; Summary of 
 Friction Tests on Old-Style Mine-Car Wheels, Table, 164} On 
 Self-Oiling Mine-Car Wheels, Table, 165; Ball and Roller Bearings, 
 166; Lubrication, 166; Lubricant Tests, 168; Best Lubricants for 
 Different Purposes (Thurston), 169. 
 
 STRENGTH OF MATERIALS 
 
 Definitions. 169; Average Ultimate Strengths of Metals, in Pounds per 
 
 Square Inch Table, 170; Of Woods, in Pounds per Square Inch, 
 
 Table, 171. 
 Simple, or Direct Stress. Formula for Simple Stress, 172; Important 
 
 Applications of Formulas for Direct Stress, 172; Shearing and Bear- 
 
 ,-g Values of Rivets, in Pounds, Table, 173. 
 
x . CONTENTS 
 
 Beams. Reactions, 175; External Shear and Bending Moment, 175; Design- 
 ing of Beams, 176- Formulas for Maximum Shear and Bending Mo- 
 ments of Beams, Table, 177; Stiffness, 178; Formulas for Deflection 
 of Beams, Table, 179. 
 
 Columns. Values of Ki (Rankine's Formula), Table, 180; Constants for 
 the Straight-Line and Euler's Formulas, Table, 180; Safe Loads for 
 Hollow, Cylindrical, Cast-Iron Columns, Table, 181; Euler's For- 
 mula, 182; Formula for Wooden Columns, 182. 
 
 Combined Stresses. Bending Combined With Compression or Tension, 
 182; Strength of Hemp and Manila Ropes and of Chains, 183; Ulti- 
 mate Resistance and Proof Tests of Chain Cables, Table, 183. 
 
 Practical Problems in the Strength of Beams and Props. 184; Table of 
 Constants for Seasoned Timber, 184; Crushing Loads of Well- 
 Seasoned American Woods, Table, 185; Safe Loads Uniformly 
 Distributed for Standard and Special I-Beams, Table, 186; Iron and 
 Steel Beams, 187. 
 
 CONCRETE 
 
 Cementing Materials. Definitions, 187; Limes, 188; Cements, 188; 
 Properties of Cements, 188; Average Weights of Hydraulic Cements, 
 189; Sand and Its Mixtures, 189; Properties of Sand, 190; Prepara- 
 tion of Sand, 191 ; Lime and Cement Mortars, 191 ; Materials 
 Required per Cubic Yard of Mortar, Table, 192; Properties and Uses 
 of Cement Mortars, 193; Tensile Strength of Cement Mortars, 
 Table, 193; Retempering of Mortar, 194; Laying Mortar in Freezing 
 Weather, 194; Shrinkage of Mortars, 194; Grouting, 194. 
 
 Cement Testing. Field Inspection and Sampling, 195; Sampling, 195; 
 Purpose and Classification of Tests, 195: Primary Tests, 196; Tests 
 for Soundness, 196; For Tensile Strength, 198: Percentage of Water 
 for Standard Sand Mortar, Table, 199; Sand for Mortar Tests, 199; 
 Briquets, 200; Testing Machines, 200: Results of Tensile-Strength 
 Tests, 201; Tensile Strength of Cement Briquets, 201; Secondary Tests, 
 202; Tests for Time of Setting, 202; For Fineness, 203; For Specific 
 Gravity, 203; Tests of Natural and Slag Cements, 204. 
 
 Cement Specifications. Specifications for Portland Cement, 204; Require- 
 ments for High-Grade Cements, Table, 205. 
 
 Plain Concrete. Definitions and Terms, 206; Aggregates Other Than Sand, 
 206; Size of Aggregates, 206; Selection of Aggregates, 207; Propor- 
 tioning of- Ingredients, 207; Effect on Strength and Imperviousness, 
 207; Proportioning by Weights, 207; Compressive Strength of Con- 
 ' crete Made of Different-Sized Stones, Table, 208; Usual Proportions 
 of Materials, 208; Water for Concrete, 209; Destructive Agencies, 209; 
 Effect of Fire on Concrete, 210; Effect of Mine Water, 210; Expan- 
 si9n and Contraction, 211; Effect of Thermal Changes, 211; Effect of 
 Vibration, 211; Working Stresses and Strength Values, 211; Con- 
 crete Mixtures, 211; Methods of Measuring Ingredients, 211; Aver- 
 age Ultimate Crushing Strength of Concrete, Table, 212; Fuller's 
 Rule for Quantities, 212; Working of Concrete, 212; Mixing, 212; 
 Retempering, 213; Concreting at High Temperatures, 213; In 
 Freezing Weather, 213; Joining of Old Concrete With New, 213. 
 
 Elements of Steel Reinforcement. Principles of Construction, 214; Parts 
 of Steel Reinforcement, 214; Members to Resist Lines of Failure, 215; 
 Areas and Weights of Square and Round Bars, Table, 216; Rein- 
 f9rcing Materials, 217; Plain Bar Iron, 217; Bars of Special Construc- 
 tion, 217; Square-Twisted Bars, 217; Corrugated Bar, 217; Kahn 
 Trussed Bar, 218; Expanded Metal, 218; Woven Wire, 218; Floor 
 Systems, 218. 
 
 Form Work. Construction and Finish, 220; Forms for Floor Systems, 220; 
 Common Types of Form Work, 220; Forms Constructed of Plank, 
 221; Wall Forms With Wire Ties, 221 ; Wall-Form Construction 
 With Clamp Bolts, 222; Clamping Devices and Plank Holders for 
 Wall Forms, 223 ; Braces for Wall Forms, 223. 
 
 Concrete Mixers. 223. 
 
CONTENTS xi 
 
 Concrete Structures. Tank Tower of Reinforced Concrete, 223; Rein- 
 forced- Concrete Retaining Walls, 226; High Retaining Walls, 226; 
 Conduits, 226; Coal Breakers in Reinforced Concrete, 227; Con- 
 crete Coal Pockets, 229; Concrete Shaft Lining, 230-233. 
 
 MASONRY 
 
 Materials of Construction. Stone, 234; Strength of Stone, 234; Crushing 
 Strength and Modulus of Rupture of Building Stone, 234; Minimum 
 Safe-Bearing Values of Masonry Materials, 234; Ultimate Unit 
 Crushing Strength of Various Stones and Stone Masonry Piers, Table, 
 235; Of Brick Masonry Piers, Table, 235; Absorptive Power of 
 Stone, 236; Durability of Stone, 236; Brick, 236; Size and Weight, 
 236; Weight and Strength, 236; Requisites for Good Brick, 236. 
 
 WIRE ROPES 
 
 General Description. Wire- Rope Materials, 237; Construction of Wire 
 Ropes, 238; Lay of Ropes, 238. 
 
 Hoisting Ropes. Round Ropes, 239; Non-Spinning Ropes, 240; Flattened- 
 Strand Ropes, 240; Scale Ropes, 240; Flat Ropes, 241; Taper 
 Ropes, 241. 
 
 Haulage Ropes. 6X7 Ropes, 241; Flattened-Strand Ropes, 242; Scale 
 Ropes, 242. 
 
 Ropes for Miscellaneous Purposes. For Cableways, 242; For Suspension 
 Bridges, 213; Derrick Ropes, 243; Hawsers, 243. 
 
 Rope Drums and Fastenings. Fastening Rope to Drum, 244; Rope Sockets, 
 244. 
 
 Wire-Rope Tables. Sizes and Strengths of Standard Hoisting Ropes, 246; 
 Of Patent, Flattened-Strand Hoisting Ropes, 247; Of Flat Hoisting 
 Ropes, 248; Of Standard 6X7 Haulage Ropes, 248; Galvanized 
 Steel Cables for Suspension Bridges, 248; Sizes and Strengths of 
 Patent, Flattened-Strand Haulage Ropes, 249; Cast-Steel Locked- 
 Wire Cable, 249; Tramway or Smooth-Coil Cable, 249; Galvanized 
 Iron and Steel Running Rope, 250; Galvanized Steel Hawsers, 250; 
 Galvanized Steel Mooring Lines, 250. 
 
 Wire-Rope Calculations. Working Load, 251; Proper Working Load, 253; 
 Starting Stress on Rope, Table, 253; On Hoisting Rope, 254; Stress 
 of Rope on Planes, 254; On Inclined Planes, 254; Relative Effect 
 of Various Sized Sheaves or Drums on Life of Wire Ropes, 254; 
 Cast-Steel Ropes for Inclines, Table, 254; Cast-Steel Hoisting Ropes, 
 Table, 255; Iron Hoisting Ropes, Table, 255. 
 
 Care of Wire Ropes. Ordinary Method of Splicing, 255; Rapid Method, 
 256; Wear of Wire Ropes, 257; Inspection, 257; Lubrication, 257; 
 General Precautions, 258. 
 
 Cableways and Tramways. Cableways, 258. 
 
 Wire-Rope Tramways. Single Tramways, 260; Double, 261. 
 
 Glossary of Rope Terms. 262. 
 
 POWER TRANSMISSION 
 
 Transmission by Wire Ropes. General, 264; Value of Coefficients, Table, 
 265; Minimum Diameters of Sheaves, Table, 266; Sheaves, 266; 
 Power Transmitted. 266; Table of Constants for Ropes on Different 
 Materials 267' Horsepower That May Be Transmitted by a Steel 
 Rope Making a Single Lap on Wood-Filled Sheaves, Table, 267. 
 
 Transmission by Hemp Rope. General, 268; Horsepower of Manila 
 Ropes, Table, 269. 
 
 Line Shafting. Constants, Table, 270; Maximum Distance Between Bear- 
 ings, Table, 270; Horsepower Shafting Will Transmit, Table, 271. 
 
 Belt Pulleys. Solid and Split Pulleys, 271; Wooden Pulleys, 272; Driving 
 and Driven Pulleys, 272; Diameter and Speed of Driver, 272; O 
 Driven, 272. 
 
xii CONTENTS 
 
 Belting. Sag of Belts, 273; Speed, 273; Horsepower, 273; Allowable 
 Effective Pull, Table, 174; Lacing, 274; Care and Use, 274; Flapping, 
 275. 
 
 SPECIFIC GRAVITY, WEIGHT, AND OTHER PROPERTIES OF 
 
 MATERIALS 
 Definitions. 275. 
 
 Specific Gravity of Common Substances. Of Minerals and Earths, 276; 
 Of Metals, 277; Of Liquids, 277; Of Gases and Vapors, 277; Of 
 " Dry Woods, 278; Of Miscellaneous Substances, 278. 
 
 Average Weight of Various Substances. Weight of 1 Cu. Ft. of Various 
 Metals, 278; Of Various Woods, When Dry, 279; Of Philippine 
 Woods, When Dry, 281; Of Australian Woods, When Dry, 281; Of 
 Indian Woods, 282; Of American Timbers, 283; Of 1 Sq. Ft. of 
 Building Materials, 283; Of 1 Cu. Ft. of Building Materials, 284; 
 of Miscellaneous Materials, 284-285. 
 
 Properties of Coal. Specific Gravity of American Coals, 286: Weights and 
 Measurements of Coal, 287; Average Weight and Bulk of American 
 Coals, 288; Specific Gravities of Various Coals, 288; Weight of Sus- 
 quehanna Coal Co.'s White Ash Anthracite, 288; Contents of Hori- 
 zontal Coal Seams, 289; Sizes of Prepared Anthracite, 289; Cubic 
 Feet in 1 T. of Anthracite Broken in Trade Sizes, 290; Weights of 
 English and French Coals, 290. 
 
 Wire and Sheat-Metal Gauges. Table, 291; Standard Decimal Gauge, 292. 
 
 Miscellaneous Tables. Weight of Wrought-Iron Bolt Heads, Nuts, and 
 Washers, 292; Of Sheets and Plates of Steel, Wrought Iron, Copper, 
 and Brass, 293; Of Cast-Iron Pipe per Ft., in Pounds, 294; Contents 
 of Cylinders or Pipes for 1 Ft. in Length, 295: Standard Dimensions 
 of Wrought-Iron Welded Pipes, 296; Strength of Metals per Square 
 Inch, 296; Standard and Extra-Gauge Steel Boiler Tubes, 297; 
 Standard Lap-Welded Charcoal-Iron Boiler Tubes, 297; Weight of 
 Wrought Iron, 298; Diameter and Number of Wood Screws. 298; 
 Spikes and Nails, 299; Weight of 100 Bolts With Square Heads and 
 Nuts, 299; Proportions of the United States Standard Screw Threads, 
 Nuts, and Bolt Heads, 300; Weight of 1 Lin. Ft. of Flat Wrought 
 Iron, 301. 
 
 Timber and Board Measure. Timber Measure, 301; Table of Quarter 
 Girths, 302; Board Measure, 302; Table of Board Feet, 302. 
 
 HYDROSTATICS 
 
 General. Equilibrium of Liquids, 303; Pressure of Liquids on Surfaces, 303; 
 To Find Pressure Exerted by Quiet Water Against Side of Gangway or 
 Heading, 304; Pressure Against Dams, Etc., 304; Distribution of 
 Pressure, 304; Transmission of Pressure Through Water, 305; To 
 Find Pressure on Plane Surface at Any Given Depth of Water, 305; 
 Pressure at Different Vertical Depths, Table, 305; Pressure of Water 
 in Pipes, 306; Thickness of Pipe for Different Heads and Pressures, 
 306; Wooden Pipe, 306; Standard Sizes of Wood Pipe, 307; Compres- 
 sibility of Liquids, 307. 
 
 HYDRAULICS 
 
 Definitions. To Find Theoretical Velocity of Jet of Water, 307; To Find 
 Theoretical Quantity of Water Discharged in Given Time, 308; 
 Flow of Water Through Orifices, 308; Coefficient of Contraction, of 
 Velocity, of Discharge, 308; Suppression of Contraction, 308. 
 
 Gauging Water. Miners' Inch, 309; Duty of Miners' Inch, Table, 309; 
 Duty or Work Performed by a Miners' Inch of Water, 310; Sluice 
 Head, 310; Gauging by V Notch, 311; Discharge of Water Through 
 a Right-Angled V Notch, Table, 311; Gauging by Weirs, 312; 
 Coefficient of Discharge for Weirs with End Contractions, Table, 313; 
 Without End Contractions, Table, 313; Discharge per Minute for 
 Each Inch in Length of Weir for Depths From 1-8 In. to 25 In., 314. 
 
 Conversion Factors. 314. 
 
CONTENTS xiii 
 
 Flow of Water in Open Channels. Ditches, 315; Safe Bottom Velocity, 315- 
 Safe Bottom and Mean Velocities of Streams, Table, 315; Resistance* 
 of Soils to Erosion by Water, 316; Carrying Capacity of Ditches, 316 ; 
 Grade, 316; Influence of Depth on Ditch, 316; Measuring the Flow 
 of Water in Channels, 317; Coefficient of Roughness Under Various 
 Conditions, 317; Flow in Brooks and Rivers, 317. 
 
 Flumes. Grade and Form, 318; Connection With Ditches, 319; Trestles 
 319; Curves, 319; Waste Gates, 319; Flow of Water Through 
 Flumes, 319. 
 
 Tunnels. 319. 
 
 Flow Through Pipes. Hydraulic Gradient, 320; Flow in Pipes, 320; 
 Eytelwein's Formula for Delivery of Water in Pipes, 321; Hawksley's 
 Formula, 321 ; Neville's General Formula, 321 ; Comparison of 
 Formulas, 321; Value of C in Darcy's Formula, 322; Loss of Head in 
 Pipe by Friction, 322; Friction of Knees and Bends, 323; Relative 
 Quantities of Water Delivered in 24 Hours, in 1 Hour, and in 1 Minute, 
 Table, 323; Actual Amount, or 80% of the Theoretical Flow, in 
 Pipes From 1 In. to 30 In. Diameter, Table, 324; Loss of Head by 
 Friction, Table, 325-326. 
 
 Reservoirs. 327. 
 Mine Dams. 327. 
 
 Outside Dams. Wooden Dams, 328; Abutments and Discharge Gates, 
 328; Spillways, or Waste Ways, 329; Stone Dams, 329; Earth Dams, 
 329; Irrigation Quantity Tables, 330; Refuse Dams, 331; Wing 
 Dams, 331; Masonry and Concrete Dams, 331. 
 
 Water-Power. Theoretical Efficiency, 331; Horsepower of a Running 
 Stream, 331; Current Motors, 332; Utilizing Power of Waterfall, 
 332. 
 
 Pump Machinery. Classification of Pumps, 333; Cornish, 333; Simple and 
 Duplex, 333; Speed of Water Through Valves, Pipes, and Pump 
 Passages, 334; Ratio of Steam and Water Cylinders in a Direct- 
 Acting Pump, 335; Piston Speed of Pumps, 335; Strokes for Piston 
 Speed of 100 Ft. per Min., Table, 335; Boiler Feed-Pumps, 335; 
 Theoretical Capacity of Pumps and Horsepower Required to Raise 
 Water, 336; Ratios of Areas to Diameters of Steam and Water Cylin- 
 ders, Table, 336-337; Depth of Suction, 338; Suction Lift of Pumps 
 at Different Altitudes, Table, 338; Theoretical Horsepower Required 
 to Raise Water to Different Heights, Table, 339; Amount of Water 
 Raised by a Single-Acting Lift Pump, 340; Capacity of Pumps, 
 Table, 340; Pump Valves, 341; Power Pumps, 341; Electrically 
 Driven, 342; Theoretical Consumption of Electric Current for Pump- 
 ing Water per 1,000 Gal., Table, 342; Precautions Necessary With 
 Electrically Driven Mine Pumps, 343; Centrifugal Pumps, 343; Dis- 
 charge of Pumps at Various Piston Speeds, Table, 344; Pumps for 
 Special Purposes, 346; Sinking Pumps, 346; For Acid Waters, 346; 
 Pump Foundations, 346; Pump Management, 346; Miscellaneous 
 Forms of Water Elevators, 349; Jet Pump, 349; Vacuum Pump, 349; 
 Air-Lift Pumps, 349; Water Buckets, 350; Siphons, 351. 
 
 HEAT AND FUELS 
 
 Heat. Thermometers, 352; Comparison of Thermometer Scales, 353; Abso- 
 lute Zero, 353; British Thermal Unit, 353; Calorie, 354; Pound 
 Calorie, 354; Equivalence of Heat Units, 354; Mechanical Equiva- 
 lent of Heat, 354; Expansion by Heat, 354; Equivalent Temperatures 
 by the Fahrenheit and Centigrade Thermometers, Table, 355; Equiva- 
 lent Temperatures by the Centigrade and Fahrenheit Thermometers, 
 Table, 357; Coefficients of Linear Expansion per 1 P., 359; Conduc- 
 tion of Heat, 359; Relative Heat Conductivities of Metals, 359; 
 Radiation of Heat, 359; Specific Heat, 360; Specific Heat of Water 
 at Various Temperatures, 360; Specific Heats of Solids, 360; Of 
 Liquids, 361; Of Gases, 361; Sensible and Latent Heat, 361; Melting 
 Points and Latent Heat of Fusion of Metals, Table, 362 ; Boiling Point 
 of Water at Various Altitudes, Table, 363; Combustion, 363. 
 
xiv CONTENTS 
 
 FUELS 
 
 Fuels in General. 365. 
 
 Wood as Fuel. Weights per Cord of Dry Wood Arranged According to Fuel 
 Values, 366; Weight of Coal Equivalent to 1 Cord of Air-Dried Wood, 
 366; Composition and Calorific Value per Pound of Wood, 366. 
 
 Peat as Fuel. 367. 
 
 Coal. Constituents, 368: Changes in Chemical Composition from Wood to 
 Anthracite, 368; Classification of Coals, 370; Classification Based on 
 Their Content of Fixed Carbon and Volatile Matter, 371 ; Anthracite, 
 371; Semianthracite, 372; Semibituminous, 372; Bituminous, 372; 
 Subbituminous, 372: Lignite, 373; Gas Coals, 373; Domestic, 373; 
 Blacksmith, or Smithing, 374; Steam Coals, 374; Coking, 374; 
 Yield of Coke, 376; Pishel's Test for Coking Qualities of Coal, 377; 
 Non-Coking Coals, 378; Fat and Dry, or Lean, 378; Free-Burning 
 Coal, 378; Cannel, 378, Splint, 378; Proximate Analysis of Coal, 378; 
 Sampling, 378; Moisture, 379; Volatile Combustible Matter, 379; 
 Ash, 379; Fixed Carbon, 379; Sulphur (Eschka's Method), 379; 
 Forms of Reporting Analyses, 379; Coal 114 from Sewell Seam, 
 McDonald, W. Va., Table, 380; Analyses of Typical Coals, 381 ; 
 Proximate and Ultimate Analyses and Heating Values of American 
 Coals, Table, 382-385; Proximate Analyses and Heating Values of 
 Pennsylvania Anthracites, Table, 386; Proximate Analyses of Mis- 
 cellaneous American Coals, Table, 387; Proximate Analyses and 
 Heating Values of Canadian Coals, Table, 388-389; Proximate 
 Analyses of Alaskan Coals, Table, 390; Of Foreign Coals, Table, 391; 
 Determination of Heating Value of Coal from a Proximate Analysis, 
 392; Kent's Method, 392; Approximate Heating Value of Coals, 392; 
 Method of Lord and Haas, 392; Value of K for Various Coals, 393; 
 Determination of Heating Value of Coal from an Ultimate Analysis, 
 394 ; Dulong's Formula, 394. 
 
 Petroleum as Fuel. Composition of Crude Petroleum, 395; Flash Point 
 and Firing Point, 395; Ultimate Analyses of Crude Petroleum, Table, 
 396; Calorific Value of Fuel Oil, 396; Comparative Value of C9al and 
 Oil as Fuel, Table, 397; Advantages and Disadvantages of Oil Fuel, 
 397. 
 
 Gaseous Fuels. Kinds of Gas, 398; Analyses and Heating Values of Vari- 
 ous Gases, Table, 398; Blast-Furnace Gases, 398; Analyses of 
 Natural, Producer, and Coke-Oven Gases, Table, 399; Heating 
 Value of Gases at 32 F., 400; Natural Gas, 400; By-Product Gas, 
 401; Coke-Oven Gas, 402; Coal Gas, 402; Analyses of Gas Coals, 
 Table, 403; Water Gas, 403; Producer Gas, 404; Quantity of Gas 
 Produced per Pound of Fuel in an Up- Draft Pressure Producer, 
 Table, 404; Yield and Heat Value of Gas per Ton of Fuel as Fired in 
 an tip-Draft Pressure Producer, Table, 405- Gas Producers, 405; 
 Typical Analyses by Volume of Producer Gas, Table, 405. 
 
 BOILERS 
 
 Steam. Properties of Steam, 406; Saturated Steam, 406; Properties of 
 Saturated Steam, Table, 407; Use of Steam Table, 408; Superheated 
 Steam, 409; Quality of Steam, 410; Moisture in Steam, 410; Heat in 
 Wet Steam, 410; Flow of Steam, 410; Weight of Steam Discharged, 
 410; Weight Delivered per Minute Through 100 Ft. of Pipe with 1 Lb. 
 Drop of Pressure, Table, 411; Resistance of Elbows and Valves, 411; 
 Steam Pipes for Engines, 412. 
 
 Boiler Piping. Principal Considerations, 412; Materials for Pipes, 412; Ex- 
 pansion Joints, 412; Expansion Bends, 413; Arrangement of Piping, 
 413. 
 
 Boiler Fittings. Safety Valves, 414; Weight of Ball for Lever Safety Valve, 
 414; Position of Ball, 414; Roper's Safety Valve Rules, 414; Area of 
 Safety Valve, 415; Location, 415; Fusible Plugs, 415; Location, 415; 
 Connection of Steam Gauge, 416; Blow-Offs, 416; Blow-Off Cocks 
 and Valves, 417; Protection of Blow-Off Pipe, 417. 
 
 Furnace Fittings. Bridge Wall, 417; Fixed Grates, 417; Dead Plate, 418; 
 Objection to Stationary Grate Bars, 418; Shaking Grates, 418; 
 
CONTENTS xv 
 
 Classes of Mechanical Stokers, 418; Overfeed Stoker, 418; Underfeed 
 Stoker, 419. 
 
 Covering for Boilers, Steam Pipes, Etc. Losses by Radiation, 419; Loss of 
 Heat from Steam Pipes, Table, 420; Conducting Power of Various 
 Substances, 421; Relative Value of Non-Conductors, 421, 
 
 Boiler Feeding and Feedwater. Injectors, 422; Classification, 422; Advan- 
 tages and Disadvantages, 422; Size, 422; Water Delivered by In- 
 jectors, Table, 422; Water Required per Minute to Feed Boilers, 
 Table, 423; Location of Injector, 423; Steam Supply to Injector, 423; 
 Injector Troubles, 423; Incrustation and Corrosion, 424; Impurities 
 in Feedwater, 425; Formation of Scale, 425; Danger of Scale, 425; 
 Scale Containing Lime, 425; Kerosene as Scale Remover, 425; Re- 
 moval by Chipping, 426; Removal of Mud, 426; Internal Corrosion, 
 426; Pitting or Honeycombing, 426; Grooving, 426; External Corro- 
 sion, 426; Lamination, 426; Overheating, 427; Prevention of Incrusta- 
 tion and Corrosion, 427; Scale-Forming Substances and Their Reme- 
 dies, 427; Use of Zinc in Boilers, 428; Testing of Feedwater, 428; 
 Purification of Feedwater, 428; By Settlement, 428; By Filtration, 
 428; By Chemicals, 428; Treatment for Sulphate of Lime, 429; Quan- 
 tity of Chemicals to Use, 429; Use of Carbonate of Soda, 429; Of Tri- 
 sodium Phosphate, 429; Neutralization of Acids, 429; Purification by 
 Heat, 429; Feedwater Heating, 430; Types of Exhaust-Steam Feed- 
 water Heaters, 430; Selection of Heater, 430. 
 
 Boiler Trials. Purposes, 430; Observations During Trial, 430; Weighing 
 the Coal, 431; Measurement of Feedwater, 431; Standard of Boiler 
 Horsepower, 431; Equivalent Evaporation, 431; Factors of Evapora- 
 tion, 431; Table of Same, 432; Boiler Efficiency, 433; Standard Code, 
 433. 
 
 Boiler Management. Filling Boilers, 433; Preparation, 433; Height of 
 Water, 433; Escape of Air, 433; Management of Fires When Starting, 
 434; Precautions, 434; Starting, 434; Value of Slow Fires, 434; Trying 
 the Fittings, 434; Connecting Boilers, 434; Cutting Boiler Into Service, 
 434; Connecting Boilers to Main, 434; Changing Over, 434; Equal- 
 izing the Feed, 435; Firing With Solid Fuel, 435; Cleaning of Fires, 
 435; Uniform Steam Pressure, 436; Desirability, 436; Maintenance, 
 436; Keeping Water Level Constant, 436; Priming and Foaming, 436; 
 Evidences of Priming, 437; Foaming, 437; Shutting Down and Start- 
 ing Up 437; Preparations for Shutting Down, 437; Starting the Fires, 
 437; Blowing Down, 438; Care of Boilers, 438; Safety Valves, 438; 
 Pressure Gauge, 438; Water Level, 438; Gauge-Cocks and Water 
 Gauges, 438; Feed-Pump or Injector, 438; Low Water, 438; Blisters 
 and Cracks, 438; Fusible Plugs, 438; Firing, 438; Cleaning, 438; 
 Hot Feedwater, 439; Foaming, 439; Air Leaks, 439; Blowing Off, 439; 
 Leaks, 439; Filling Up, 439; Dampness, 439; Galvanic Action, 439; 
 Rapid Firing, 439; Standing Unused. 439; Repair of Coverings, 439; 
 General Cleanliness, 439. 
 
 Boiler Inspection. Nature of Inspection, 439; External Inspection, 440; 
 Preparation, 440; Inspection of Externally Fired Boilers, 440; In- 
 spection of Internally Fired Boilers, 440; Inspection of New Boilers, 
 440; Internal Inspection, 440; Preparation, 440; Inspection of Loco- 
 motive-Type Boilers, 441; Flues and Combustion Chambers. 441; In- 
 spection of Vertical Boilers, 441; Inspection of Fittings, 441. 
 
 Selection of Boilers. General Requirements, 441; Liability to Explosion 
 442; Durability, 443; Repairs, 443; Facility for Removal of Scale and 
 for Inspection, 443; Water and Steam Capacity, 443; Water Circu- 
 lation, 444; Ratio of Heating Surface to Horsepower and to Grate 
 Area, Table, 444; Heating Surface, 444; Probable Maximum Work 
 of a Plain Cylindrical Boiler of 120 Sq. Ft. Heating Surface and 12 
 Sq. Ft. Grate Surface, Table, 445. 
 
 Chimneys. Products of Combustion, 446; Weight of Air, Water Vapor, and 
 Saturated Mixtures at Different Temperatures, Table, 447; Oxygen 
 and Air Required for the Combustion of Carbon, Hydrogen. Etc., 
 Table, 447; Temperature of Ignition of Various Fuels, 448; iempera- 
 ture of Fire 449' Heat and Products of Combustion of Burning 
 Carbon Table, 449; Estimation of Air Supply, 451; Production and 
 
xvi CONTENTS 
 
 Measurement of Draft, 451; Erection of Chimneys, 452; Height and 
 Area of Chimneys, 452; Maximum Combustion Rate, 453; Forced 
 Draft, 453; Size of Chimneys and Horsepower of Boilers, Table, 454. 
 
 STEAM ENGINES 
 
 Principles and Requirements. Clearance, 454; Cut-Off, 455; Ratio of Ex- 
 pansion, 455; Mean Effective Pressure, 455; Constants Used in Calcu- 
 lating Mean Effective Pressure, 456; Horsepower, 456; Finding the 
 Indicated Horsepower, 456; Stating Sizes of Engines, 457; Mechanical 
 Efficiency, 458; Piston Speed, 458; Allowance for Area of Piston Rod, 
 458; Cylinder Ratios, 458. 
 
 Condensers. Surface Condensers, 459; Cooling Water for Surface Con- 
 denser, 459; Injection Water for Jet Condenser, 460. 
 
 Engine Management. Starting and Stopping, 460; Warming Up, 460; Oil 
 and Grease Cups, 461; Starting and Stopping Non-Condensing Slide- 
 Valve Engine, 461; Condensing Slide-Valve Engine, 461; Simple Cor- 
 liss Engine, 461; Compound Slide- Valve Engine, 462; Compound 
 Corliss Engine, 463. 
 
 Pounding of Engines. Faulty Bearings, 463; Pounding in Cylinders, 464; 
 Improper Valve Setting, 464; Reversal of Pressure, 464; Insufficient 
 Lead, 465; Pounding at Crosshead, 465; In Air Pump, 465; In Circu- 
 lating Pump, 465; Hot Bearings, 465; Dangerous Heating, 466; Re- 
 fitting Cut Bearing, 466; Newly Fitted Bearings, 466; Faulty Brasses, 
 466; Edges of Brasses Pinching Journal, 467; Hot Bearings Due to 
 Faulty Oiling, 467; Grit in Bearings, 468; Overloading of Engine, 468; 
 Engine Out of Line, 468; Effect of External Heat on Bearings, 468; 
 Springing of Bedplate, 468; Springing or Shifting of Pillow-Block, 469. 
 
 Steam Turbines. Types, 469; Steam Consumption, 469; Comparison of 
 Turbines and Engines, 470; Steam Consumption per Hour of Tur- 
 bines, 470; Finding Horsepower of Turbines, 470; Turbine Troubles, 
 470; Operation of Turbines, 471; Economy of Turbine, 472; Care of 
 Gears in De Laval Turbines, 472. 
 
 Rules for Stationary Engineers. 473. 
 
 COMPRESSED AIR 
 
 Classification and Construction of Compressors. Theory of Air Compres- 
 sion, 475; Construction of Compressors, 475; Rating, 475; Efficiencies 
 at Different Altitudes, Table, 476; Cooling, 476. 
 
 Transmission of Air in Pipes. 476^ 
 
 Losses in the Transmission of Compressed Air. Cause of Loss, 478; Loss 
 of Pressure, in Pounds per Square Inch, by Flow of Air in Pipes 1,000 
 Ft. Long, Table, 482; Friction of Air in Pipes, 482; Loss by Friction in 
 Elbows, 483. 
 
 Design, Operation, and Installation of Air Compressors. Design for avoid- 
 ing Explosions, 483; Installation of Compressor, 483; Operation, 484. 
 
 ELECTRICITY 
 
 Practical Units. Strength of Current, 484; Electromotive Force, 485; Re- 
 sistance, 485; Ohm's Law, 485; Electric Power, 485; Electrical Ex- 
 pressions and Their Equivalents, 486. 
 
 Circuits. Series, 486; Parallel, 487. 
 
 Resistances in Series and Multiple. In Series, 488; In Parallel, 488; Shunt, 
 488. 
 
 Electric Wiring (Conductors). Materials, 488; Properties of Annealed Cop- 
 per Wire; American, or Brown & Sharpe, Gauge, Table, 489; Wire 
 Gauge, 490; Carrying Capacity of Copper Cables, Table, 490; Com- 
 parison of Properties of Aluminum and Copper, 490; Estimation of 
 Resistance, 491; Breaking Strength of Copper and Aluminum Wires 
 and Cables, Table, 491. 
 
 Calculation of Wires for Electric Transmission. Direct-Current Circuits, 
 492; Insulated Wires, 494; Weather-Proof Line Wire (Roebling's), 
 Table, 494. 
 
CONTENTS xvii 
 
 Current Estimates. Incandescent Lamps, 494; Arc Lamps, 495; Motors 
 495; Current Required for Direct- Current Motors, Table, 496; Con- 
 ductors for Electric- Haulage Plants, 496. 
 
 Dynamos and Motors. Direct- Current Dynamos, 497; Factors Determin- 
 ing Electromotive Force Generated, 500; Field Excitation of Dyna- 
 mos, 500; Direct-Current Motors, 501; Principles of Operation, 501; 
 Speed Regulation of Motors, 503; Connections for Continuous-Cur- 
 rent Motors, 504; Alternating-Current Dynamos, 506; Uses of Multi- 
 phase Alternators, 507; Alternating-Current Motors, 508; Selection 
 of Induction Motors for Mine Use, 509; Installation and Care of 
 Induction Motors, 511. 
 
 Transformers. 513. 
 
 Electric Signaling. Batteries, 514; Elements of Primary Batteries, Table, 
 515; Bell Wiring, 516; Annunciator System, 517; Diagrams for Wiring 
 Systems, 517-523. 
 
 Dynamo and Motor Troubles. Sparking at Brushes, 523; Brush Faults, 523; 
 Commutator Faults, 524; Heating of Armature, Field Coil, and Bear- 
 ings, 524; Noise, 525; Regulation of Speed, 526; Motor Stops, Fails 
 to Start, or Runs Backwards or Against the Brushes, 526; Failure of 
 Dynamo to Generate, 527; Reversed Residual Magnetism, 527; 
 Short Circuits, 527; Field Coils Opposed to One Another, 527; Open 
 Circuit, 527; Overloaded Dynamos, 528; Miscellaneous Troubles, 528; 
 Weak Magnetic Field, 528; Excessive Current in Armature Due to 
 an Overload, 528; Armature Faults, 528; General Precautions, 528. 
 
 General Rules for Handling Electricity. 529-531. 
 
 INTERNAL-COMBUSTION ENGINES 
 
 Definitions and Principles. Internal- Combustion Engines, 532; Single- and 
 Double- Acting Engines, 532; Gasoline-Engine Cycles, 532; Four- 
 Cycle Engines, 532; Two-Cycle Engines, 533; Application of Four- 
 Cycle Principle, 533; Graphic Representation of Four-Stroke Cycle, 
 533; Application of Two- Cycle Principle, 534. 
 
 Gas-Engine Fuels. Gaseous Fuels, 536; Alcohol, 536; Gasoline, 536; 
 Kerosene, 537; Fuel, or Compound, Oils, 537; Rating of Oil and 
 Gasoline, 537; Baum6 Hydrometer, 537; Comparative Value of 
 Liquid Fuels: Specific Gravities Corresponding to Baum6 Readings 
 for Liquids Lighter Than Water, Table, 538. 
 
 Types of Internal- Combustion Engines. Internal- Combustion Engines at 
 Mines, 538; Stationary Gas Engines, 540; Haulage- Motor Gasoline 
 Engines, 540. 
 
 Carburetion and Ignition. Carbureters for Constant-Speed Engines, 541; 
 For Variable-Speed Engines, 541; Make-and-Break Ignition, 542; 
 Jump-Spark Ignition, 542; Requirements of Spark Plugs, 544. 
 
 Operation of Internal-Combustion Engines. Engine Starters, 545; Start- 
 ing the Engine, 545; Stopping, 545; Lubrication, 546. 
 
 Engine Troubles and Remedies. Hot Bearings, 547; Misfiring, 547; 
 Back Firing, 547; Preignition, 548; Carbureter Troubles, 548; 
 Compression Troubles, 548. 
 
 PROSPECTING 
 
 Outfit and Methods. Outfit Necessary, 549; Plan of Operations, 549. 
 
 Coal -Bearing Formations. Outcrops, 550; Formations Likely to Contain 
 Coal, 550; Geological Chart for the United States, 551; Faults, 553. 
 
 Exploration by Drilling or Bore Holes. Earth Augers, 553; Percussion 
 Drills, 554; Percussion Core Drill, Cost of Well Drilling, 554; Core 
 Drills, 554; Selecting the Machine, 555; Size of Tools, 555; Dia- 
 mond-Drilling, 555; Calyx Drilling, 556; Prospecting for Petroleum, 
 Natural Gas, and Bitumen, 557; Construction of Geological Maps and 
 Cross- Sections, 557; To Obtain Dip and Strike From Bore-Hole Rec- 
 ords, 558; Sampling and Estimating the Amount of Mineral Avail- 
 able, 559; Diagram for Reporting on Coal Lands, 560-563. 
 
xviii CONTENTS 
 
 MINING 
 
 General and Financial Considerations. Relation Between Investment and 
 Cost of Production, 564 ; Relative Cost of Different Types of Open- 
 ing, 564; Cost of Production as Affected by Type of Opening, 564. 
 
 Location of Surface Plant. Grades, 565; Length and Number of Sidings. 565; 
 Mining Plant, 566; Mining Village, 566; Coke Ovens, 566. 
 
 Location of Mine Opening. Flat Seams, 567; Seams of Moderate Dip, 568; 
 Of High Dip, 568; Method of Working, 568. 
 
 Drifts. 568. 
 
 Tunnels. Through Loose Ground, 569; Forepoling, 569; Wedging, 570; 
 
 Tunnels Through Rock, 571; Arrangement of Drill Holes, 571; 
 
 American and European Practice, 571; Conical Center Cut, 572; 
 
 The Billy White Cut, 573; Square-Cut Drillinp and Blasting, 574; 
 
 Side Cut in Heading, 574; Special Arrangement for Throwing 
 
 Broken Rock from Face, 575. 
 
 Slopes. Safety Appliances, 575; Data Concerning Well-Known Shafts 
 Table, 576-577. 
 
 Shafts. Introduction, 578; Form of Shaft, 578; Compartments, 578; Size, 
 578; Width, 578; Length, 579; Sinking Tools and Appliances, 580; 
 Buckets, 580; Bucket Guides, 580; Dumping Buckets, 581; Engines 
 and Boilers, 581; Sinking Head Frame, 581; Shaft Coverings, 582; 
 Ventilation and Lighting, 583; Sinking Through Firm Ground, 583; 
 Preliminary Operations, 583; Sinking Through Earth and Loose 
 Rock, 583; Through Rock, 584; Long-Hole, or Continuous-Hole, 
 Method, 585; Sinking in Swelling Ground, 586; Sinking Through 
 Running Ground, 586; Draining the Ground, 586; Piling, 586; Fore- 
 poling, 587; Shoes for Shaft Sinking, 588; Pneumatic Process, 590; 
 Freezing Processes, 591; Cementation Process, 591; Other Methods 
 of Shaft Sinking, 592; Enlarging and Deepening Shafts, 593; Up- 
 raising, 594; Shaft Drainage and Pumping, 596; Water Rings, 596; 
 Coffer Dams, 596; Lodgements, or Basins, 596; Sump, 596. 
 
 Slope and Shaft Bottoms. Slope Bottoms, 596; Vertical Curves, 599; Shaft 
 Bottoms, 599; General Bottom Details, 601; Mine Stables, 601; 
 Pump Room, 602; Engine Room, 602; Lamp Stations, 602; Shanties, 
 603; Manway About the Shaft, 603; Surface Tracks for Slopes and 
 Shafts. 
 
 METHODS OF OPEN WORK 
 
 General. 604; Steam-Shovel Mines, 605. 
 
 METHODS OF CLOSED WORK 
 
 Introductory. General Considerations, 606; General Systems of Mining, 
 607. 
 
 Room-and -Pillar Systems of Mining. Preliminary Considerations, 607; 
 Number of Entries, 607; Size, 609; Distance Between Entries, 610; 
 Direction of Entries in Flat Seams, 610; In Inclined Seams, 611; 
 Alinement and Grade of Entries, 611 ; Rooms in General, 611 ; Double 
 Rooms, 612; Rooms With Extra Entry Pillars, 613; Inclination of 
 Rooms to the Entry, 613; Direction of Rooms as Determined by 
 Cleat, 614; Distance from Center to Center of Rooms or Breasts 
 Measured on Entry or Gangway, Table, 615; Direction of Rooms as 
 Determined by Slips in the Roof, 616; Working Flat Seams, 616; 
 Pittsburg Region, 616; Clearfield, 616; Reynoldsville, 617; West 
 Virginia, 617; George's Creek District, Md., 617; Blossburg Coal 
 Region, Pa., 618; Indiana Coal Mining, 618; Iowa Coal Mining, 618; 
 Steep Rooms, 619; Working Pitching Seams, 619; Difficulties, 619; 
 Working Thick and Gaseous Seams That Run, 620; Thick Non- 
 Gaseous Seams, 621; Small Seams Laying From Horizontal to 10, 
 621; Laying at More Than 10, 622; Buggy Breasts, 622; Chutes, 
 623; Single-Chute Rooms, 624; Double-Chute Rooms, 625; Method 
 Suitable for Use in Inclined Seams, 626; Battery Breasts, 626; 
 Working Contiguous Seams, 629; New Castle, Col., Method, 631; 
 Alabama Methods, 631; Tesla, Cal., Method, 632. 
 
CONTENTS xix 
 
 Pillar -and-Stall Systems of Mining. General, 634; Connellsville Region, 
 635; J. L. Williams' Method, 636. 
 
 Panel System of Mining. Col. Brown's Method, 637. 
 
 Mining and Blasting Coal. Shooting Off the Solid, 638; Precautions in 
 Solid Shooting, 641; Objections, 642; Blasting after Undercutting, 
 642; Combined Undercutting and Solid Shooting, 643; Undercutting 
 in Longwall, 644: Machine Mining, 644; Pick Machines, 644; Chain 
 Machines, 645; Capacity of Coal- Cutting Machines, 646; Longwall 
 Machines, 646; Heading Machines, 647; Machine Mining in Anthra- 
 cite Mines, 648. 
 
 Drawing Pillars -General, 648; Work of Drawing, 650; Delayed Pillar 
 Drawing, 651; Precautions, 651. 
 
 Longwall System of Mining. Systems of Longwall, 652; Considerations 
 Affecting Its Adoption, 653; Roof Pressure, 653; Nature of Coal 
 Seam, 653; Waste, 653; Surface Damage, Water, Gas, Etc., 654: 
 Timber Supply, 654; Labor and Trade Conditions, 654; Longwall 
 Working in Flat Seams, 655; Scotch, or Illinois, Plan, 655; Rectangu- 
 lar Longwall, 656; Longwall Working in Pitching Seams, 657; On 
 Low Inclination, 658; When Inclination is Less Than 40, 658; When 
 Inclination is From 30 to 60, 659; In Steeply Inclined Seams, 661; 
 Special Forms of Longwall Working, 661; In Panels, 661; In Thick 
 Seams, 663; In Inclined Thick Seams, 664; In Contiguous Seams, 
 664; Details of Longwall Working, 664; Starting, 664; Roadways, 
 665, Control of Roof Pressure, 665; Building Pack Walls and Stowing, 
 666; Timbering a Longwall Face, 666. 
 
 EXPLOSIVES AND BLASTING 
 
 Classification of Explosives. Low, 667; High, 667; Sizes of Grains of 
 Black Blasting Powder, Table, 667. 
 
 Explosives for Rock Work. Straight Nitroglycerin Dynamite, 668; Com- 
 positions, Table, 668; Slow, or Low- Freezing, Dynamites, 668; 
 Compositions, Table, 668; Ammonia Dynamites, 668; Composi- 
 tions, Table, 669; Gelatin Dynamites, 669: Compositions, Table, 
 669; Analyses or High Explosives, Table, 669; Comparative 
 Analyses, 670; Products of Combustion, 670; Analyses of Mine Air 
 After Blasting, Table, 670; Comparative Strength of Explosives, 
 670; Results of Tests to Determine Potential Energy and Disruptive 
 and Propulsive Effects of Explosives, Table, 671. 
 
 Explosives for Coal Mines. Classes of Permissible Explosives, 672. 
 
 Care of Explosives. Storing, 673; Thawing Dynamite, 673; Handling 
 Explosives, 674; Precautions When Handling, 675. 
 
 Firing Explosives. Means of Firing Low Explosives, 676; Squibs, 676; 
 Fuse, 676; Electric Squibs, 677; Means of Firing High Explosives, 
 677; Fuse and Caps, 677; Electric Detonators, 677; Delay- Action 
 Detonators, 678; Charging and Firing Explosives With Squibs or 
 With Cap and Fuse, 678; Charging Black Powder and Firing With 
 Squib, 678; Firing With Fuse and Cap, 679; Charging and Firing 
 Dynamite With Cap and Fuse, 680; Precautions When Tamping Ex- 
 plosives, 680; Firing Explosives by Electricity, 681; Charging for 
 Electric Firing, 681; Shot Firing With the Electric Blasting Machine, 
 682; Connecting Wires, 682; Connecting Up and Firing the Blasts, 
 682; Firing With Dry Batteries, 683; Precautions When Firing With 
 the Electric Blasting Machine, 683; Firing From Dynamo, 684; 
 Firing Single Shots From the Surface, 685. 
 
 Substitutes for Blasting in Dry and Dusty Mines. Wedging Down Coal, 
 685; Hydraulic Cartridge, 686; Lime Cartridges, 687; Water Car- 
 tridge, 687. 
 
 General Considerations Affecting Blasting. Definitions, 687; Effect of Free 
 Faces in Mining, 688; Diameter of Shot Holes, 690; Amount and 
 Kind of Explosive, 690. 
 
 SUPPORTING EXCAVATIONS 
 
 Introduction. 692. 
 
 Coal Pillars. General Considerations Affecting Size, 692; Amount of Pillar 
 Coal, 692; Practical Considerations Determining Size, 692; Depth of 
 
xx CONTENTS 
 
 Cover, 693; Weight of Rocks, 694; Crushing Strength of Anthracite, 
 and Table, 694; Of Bituminous Coal, 695; Room, Entry, and Slope 
 Pillars, 695; Load on Pillars, 695; Strength 9f Pillars, 695; Width of 
 Room Pillars, 695; Weight on Pillars at Various Depths, Table, 696; 
 Slope Pillars, 696; Entry Pillars. 697; Shaft Pillars, 697; Pillars in 
 Flat Seams, 697; Rules, Merivale's, Andre's, Wardle's, Pamely's, Min- 
 ing Engineering (London), Poster's, 697; Dron's, Hughes 's, Central 
 Coal Basin, 698; Size of Shaft Pillar Obtained by Use of Several 
 Formulas, Table, 698; Pillars in Inclined Seams, 698; Pillars for Mis- 
 cellaneous Purposes, 699; For Supporting Buildings, Etc., 699; Re- 
 serve Pillars, 699; Chain Pillar, 699; Barrier Pillars, 699; Size of 
 Barrier Pillars to be Left Between Adjoining Properties, 700; Squeeze 
 and Creep, 701; Stopping a Squeeze, 701; Reopening a District Closed 
 by Squeeze, 701. 
 
 Flushing of Culm. 702-705. 
 
 Built-Up Packs and Cribs. Strength, 705; Supporting Strength of Various 
 Forms of Dry Filling, Table, 706. 
 
 Timbering With Wood. Nature of Rock Pressure, 707; Choice of Timber, 
 707; R9om Timbering in Flat Seams, 707; Props, 707; Systematic 
 Timbering, 708; Bad Roofs, 709; Supporting the Face While Under- 
 cutting, 710; Entry Timbering in Flat Seams, 710; Two-Stick Sets, 
 710; Three-Stick Sets, 711; Four-Stick Sets, 711; Room Timbering 
 in Pitching Seams, 712; Undersetting of Props, Table, 712; Entry 
 Timbering in Pitching Seams, 713; Two-Stick Sets, 713; Three-Stick 
 Sets, 714; Shaft Timbering, 715; General Principles, 715; Timbering 
 in Rock, 715; In Loose Dry Material, 716; In Swelling Ground, 717; 
 In Very Wet Ground or Quicksand, 717; Square Frame at Foot of 
 Shaft, 718; Square-Set Timbering, 718; Miscellaneous Forms of Tim- 
 bering, 719. 
 
 Framing Timbers. Limiting Angle of Resistance, 720; Placing Timber Sets, 
 720; Timber Joints, 721. 
 
 Care and Preservation of Timber. Cutting and Storing, 722; Time to Cut. 
 722; Peeling, 722; Seasoning and Storing, 722; Preservation of Mine 
 Timber, 723; Destructive Agencies, 723; General Principles of Timber 
 Preservation, 723; Brush Treatments, 724; Open-Tank Treatments, 
 724; Pressure Treatments, 724; Comparison of Open-Tank and Pres- 
 sure Treatments, 724; Cost of Open-Tank Plant, 725; Cost of Pressure 
 Plant, 725; Cost of Treatment, 725; Cost of Untreated and Treated 
 Loblolly Pme Gangway and Entry Sets Placed by the Philadelphia 
 & Reading Coal & Iron Co., in Cooperation With the Forest Service, 
 Table, 726: Durability of Treated Timbers, 727; Economy in Use of 
 Treated Timbers, 728; Peeled and Treated Loblolly and Shortleaf 
 Pine Gangway Sets Placed in Mines of Philadelphia & Reading Coal 
 & Iron Co., Table, 728; Summary, 729. 
 
 Steel and Masonry Supports. Iron and Steel Props, 730; Cylindrical Cast- 
 iron Props, 730; Steel H-Beam Props, 730; Cast-Iron Posts With 
 I-Beam Caps, 730; Steel Entry Timbers, 730; Standard Forms, 730; 
 Steel Gangway Timbers, Table, 732; Relative Cost of Steel and Wood 
 Timbering, 733; Advantages of Steel Timbering, 735; Preservation of 
 Steel Mine Timbers, 735; Masonry and Iron Shaft Linings, 735; 
 Tubbing, 736; Steel and Concrete Shaft Linings, 737; Steel Sets, 737; 
 Steel Buntons, 738; Concrete and Steel Shaft Linings, 738. 
 
 HOISTING 
 General. 739. 
 
 Hand- and Horse-power Hoists. 739. 
 
 Steam-Power Hoisting Engines. Second-Motion, or Geared, Hoisting 
 Engines, 740; First- Motion, or Direct- Acting, Hoisting Engines, 741. 
 Hoisting Engines Using Other Power Than Steam. Compressed-Air Hoist- 
 ing Engines, 741; Gasoline, 741; Hydraulic, 742; Electric, 742. 
 
 Conical Drums, 
 ting System, 
 
 _. , . , , .JO; Monopol 
 
 System, 751. 
 
CONTENTS xxi 
 
 Calculations for First-Motion Hoisting Engines. General Considerations, 
 751; Forces and Moments in Hoisting, Table, 755. 
 
 Calculations for Second-Motion Hoisting Engines. Standard Sizes of 
 Second- Motion Hoisting Engines, Table, 757; Dimensions, 758. 
 
 HAULAGE 
 
 Resistances to Haulage. Total Resistance, 758; Due to Friction, 758; Due to 
 Curvature, 759; Due to Grade, 760; Grade Equivalents, Table, 761; 
 Resistance Due to Inertia, 762. 
 
 Trackwork. Choice of Grade, 762; Curvature, 763; Rule, 763; Rail Eleva- 
 tion, Table, 764; Table of Rails and Accessories, 764-767; Gauge of 
 Track, 765; Rails, 766; Weight of Rails, in Tons of 2,240 Lb., Required 
 to Lay 1,000 Ft. Single Track, Table, 768; Ties, 768; Sizes and Quan- 
 tities of Spikes, Table, 769; Number of Track Bolts in a Keg of 200 
 Lb., Table, 769; Spaces Between Ends of Rails, Table, 769; Feet, 
 Board Measure, in Mine Ties of Various Lengths, Table, 770; Number 
 of Ties per 1,000 Ft., and per Mile of Track, Table, 770; Entry 
 Switches, 770; Frogs, 771; Room and Branch Switches, 771; Diamond 
 Switch, 773; Notes on Tracklaying, 773. 
 
 Animal Haulage. Selection of Stock, 775; Feeding Mules, 775; Care, 776; 
 Work, 777; Cost of Mule Haulage, 777; Safe Grade, 778. 
 
 Self-Acting Inclines. Tracks, Switches, Etc., 779; Rollers, 779; Ropes, 
 Drums, Barneys, Etc., 779; Grades and Their Effects, 781; Condi- 
 tions Unfavorable to Use of Inclines, 781; Calculations for Self-Acting 
 Inclines, 781; Profile of Inclines, 783. 
 
 Jig Planes. Definition, 783; Calculations, 784. 
 
 Slopes and Engine Planes. Slopes 784; Engine Planes, 785. 
 
 Endless-Rope Haulage. General, 785; General Arrangement of Systems, 
 786; Engines and Drums, 787; Rope- Tightening Arrangements, 788; 
 Grips and Grip Cars, 788; Rollers and Sheaves, 789; Side-Entry 
 Haulage, 789; Overhead, 790; High-Speed, or Reversing, 790; On 
 Inclines, 791; Calculations for Low-Speed, Endless-Rope, Haulage 
 Engines, 791; For High-Speed, 791. 
 
 Tail-Rope Haulage. General Arrangement, 792; Engines, Drums, Etc., 
 793; Sheaves, Rollers, Etc., 794; Comparison of Endless- and Tail- 
 Rope Haulage, 794; Calculations, 795. 
 
 Steam-Locomotive Haulage. Steam Mine Locomotives, 795; Power of 
 Steam Locomotives, 795; Dimensions of Four- Wheel Steam Loco- 
 motives, Table, 796; Speed, 798; Horsepower, 798. 
 
 Compressed -Air Haulage. General, 798: Simple, or Single-Stage, Locomo- 
 tives, 799; Reheating Compressed Air, 799; Compound, or Two-Stage, 
 Locomotives, 799; Dimensions of Single-Stage Compressed- Air 
 Locomotives, Table, 800; Dimensions of Two-Stage Compressed- 
 Air Locomotives, 801; Table, 802; Tractive Power, 803; Locomotive 
 Storage Tanks, 803; Stationary Storage, 804: Standard Steam and 
 Extra-Strong Pipe Used for Compressed-Air Haulage Plants, Table, 
 805; Pipe Lines and Charging Stations, 805; Air Compressors for 
 Haulage Plants, 806; Horsepower Necessary to Compress 100 Cu. Ft. 
 of Free Air, Table, 807. 
 
 Gasoline -Motor Haulage. Construction of Gasoline Locomotives, 807; 
 Hauling Capacity and Fuel Requirements, 808; Cost, 809; Compari- 
 son of Gasoline and Other Types of Haulage Motors, 810; Analyses 
 of Mine Air as Affected by Exhaust of Gasoline Locomotives, Table, 
 811; Volume of CO and CO 2 Discharged by Gasoline Locomotives, 
 in Cubic Feet per Minute, Table, 812; Purification of the Exhaust, 
 814. 
 
 Electric-Locomotive Haulage. General Considerations, 815; Advantages 
 and Disadvantages, 815; Current and Voltage, 816; Electric Genera- 
 tors 816; Classes of Electric Locomotives, 816; Wiring for Electric 
 Haulage, 816; Arrangement of Power Lines, 816; Shape of Trolley 
 Wire, 816; Location of Wires, 817; Trolley Frogs, 817; Resistance of 
 Steel Rails, 817; Sizes of Locomotives, Rails, and Bonds, Table, 818; 
 Resistance of Steel Rails, Table, 818; Bonding, 818; Cross-Bonding, 
 
xxii . CONTENTS 
 
 819; Feeders, 819; Sizes of Wires for Three-Phase Transmission Serv- 
 ice, Table, 821; Voltages Advisable, Table, 821; Direct-Current Loco- 
 motives, 822; Number and Arrangement of Motors, 822; Construction 
 of! Motors, 822; Controllers, 823; Frames, 823; Wheels and Jour- 
 nals, 823; Brakes, 824; Trolleys, 824; Headlights, 824; Capacity of 
 Locomotives, 824; Selection of Motors, 825; Tandem Locomotives, 
 826; Cable-Reel Locomotives, 826; Crab Locomotives, 827; Combina- 
 tion Cable-Reel and Crab Locomotives, 827; Rack-Rail Locomotives, 
 827; Operation of Electric Locomotives, 828; Troubles of Electric 
 Locomotives, 828; Alternating-Current Locomotives, 830; Storage- 
 Battery Locomotives, 830. 
 
 VENTILATION OF MINES 
 
 Chemical and Physical Properties of Gases. Chemistry, 831; Matter and Its 
 Divisions, 831; Classes of Matter, 831; Forms of Matter, 831; Changes 
 in Matter, 832; Symbols and Formulas, 832; Atomicity of Elements, 
 832; Chemical Reactions, 832; Chemical Equations, 832; Atomic 
 Weight, 833; Table of the Elements With Their Symbols and Atomic 
 Weights, 833; Molecular Weight, 834; Formulas and Molecular 
 Weights of Common Gases, Table, 834; Percentage Composition, 834; 
 Weights of Substances Concerned in Reactions, 834; Volumes of Gases 
 Concerned in Reactions, 835; Volumes of Gases When Burned in Air, 
 835; Weight and Volume of Gases in Reactions, 836; Physics of Gases, 
 836; Avogadro's Law, 836; Density of Gases, 836; Density at 32 F. and 
 29.92 In. of Mercury, Table, 837: Specific Gravity, Weight, and Volume 
 of Gases at 32 F. and 29.92 In. of Mercury, Table, 837; Atmos- 
 
 gheric Pressure, 838; Measurement of Atmospheric Pressure, 838; 
 quivalent Heights of Columns of Air, Water, and Mercury, Table, 
 838; Corresponding Mercury and Air Columns, and Pressure per 
 Square Foot for Each Inch of Water Column, Table, 838; Water 
 Column, and Pressure per Square Foot for Each Inch of Mercury 
 Column, Table, 839; Barometers, 839; Relation Between Volume and 
 Temperature of Gases, 840; Between Volume and Pressure, 840; 
 Between Volume, Temperature, and Pressure, 840; Between Weight, 
 Temperature, and Pressure, 841; Weight and Volume of Air and 
 Gases, 841; Volume and Weight of Air at Sea Level at Different 
 Temperatures, Table, 842; Diffusion of Gases, 842; Rates of Diffusion 
 and Transpiration of Gases Compared to Air, Table, 843; Occlusion 
 and Transpiration of Gases, 843; Humidity, 843; Gallons of Water 
 in 100,000 Cu. Ft. of Saturated Air at Temperatures From 20 F. 
 to + 100 F., Table, 844; Psychrometers or Hygrometers, 844. 
 Mine Gases. Atmospheric and Mine Air, 845; Composition of Pure Air, 
 Table, 845; Mine Air, 846; Oxygen, 846; Properties and Sources, 
 846; Effect on Life, 846; On Combustion, 847; Composition of Resid- 
 ual Atmospheres That Extinguish Flame, Table, 847; Absorption of 
 Oxygen by Coal, 848; Nitrogen, 848; Properties and Sources, 848; 
 Effectjfcn Life, 848; On Combustion, 848; Carbon Dioxide, 848; 
 Properties and Sources, 848; Effect on Life, 849; On Combustion, 
 850; Explosive Range of Mixtures of Methane and Carbon Dioxide, 
 Table, 850; Blackdamp, 851; Haldane's Blackdamp Indicator, 851; 
 Carbon Monoxide, 852; Properties and Sources, 852; Effect on Life, 
 853; Explosibility, 855; Detection, 856; Reaction of CO on PIClii, 
 856; Effect on Mice and Canaries, 857; Per Cent, of CO in Air 
 Corresponding to Various Percentages of Saturation of Blood Solu- 
 tion, Table, 858; Methane, 859; Properties and Sources, 859: 
 Pressure of Occluded Gas, Table, 860; Formation, 861; Occurrence 
 in Mines, 861; Effect on Life, 862; Explosibility, 862; Limiting 
 Explosive Mixtures of Various Explosive Gases With Air, Table, 863; 
 Firedamp, 864; Coal From Face, Naomi Mine (Gas Coal, Pittsburgh, 
 Pa., District), Table, 864; Coal From Face, No. 1 North Shaft, 
 Nanticoke, Pa. (Anthracite), Table, 864; Gases Enclosed in the Pores 
 of Coal and Evolved in a Vacuum at 212 P., Table, 865; Analyses 
 of Firedamp, Table, 865; Analyses of Firedamp from Blowers, 
 Table, 866; From Feeders, Table, 866; Gases From An Enclosed 
 Area in an Anthracite Mine, Table, 866; Analyses of Firedamp, Con- 
 nellsville Region, Table, 867; Analyses of Gas From Drill Holes, 
 Table, 867; Combustion Products of Methane, 867; Products of 
 
CONTENTS xxiii 
 
 Explosion of Methane in Air, Table, 867; Effect of Atmospheric 
 Changes on Escape of Firedamp, 868; Afterdamp, 869; Detection of 
 Methane, 870; The Rarer Mine Gases, 870; General Considerations, 
 870; Ethane and Other Paraffin Gases, 870; Ethylene and Other 
 Olefin Gases, 871; Hydrogen, 871; Acetylene, 871; Hydrogen Sul- 
 phide, 871; Sulphur Dioxide, 872; Nitric Oxide and Nitrogen Diox- 
 ide. 872; Effect of Heat and Humidity on Mine Workers, 873. 
 Safety and Of her Lamps. Principle and Origin, 874; Description, 874- 
 Dates of Discovery, 874; Principles, 874; Early Classification, 874; 
 Approved Lamps, 874; Construction, 875; Specifications, 875; 
 Design, 875; Materials, 875; Gauzes, 875; Glasses, 876; Multiple 
 Gauzes, 876; Bonnets, 876; Circulation of Air, 877; Wick Tubes, 
 Wicks, Etc., 877; Igniters, or Relighters, for Safety Lamps, 878- 
 Locks, 878; Oils, 879; Illuminating Power, S80; Table, 880; Testing 
 for Methane, 881; Desirable Features in Lamps for Testing and for 
 General Use, 881; Testing for Gas, 882; Height of Gas Cap, Table. 
 882; Care of Safety Lamps, 883: Cleaning, 883; Assembling, 884- 
 Failure, 884; Relighting Stations, Lamp Houses, Etc., 884; Standard 
 Types of Safety Lamps, 884; Davy, 884; Stephenson, 886: Clanny, 
 886; Evan Thomas, 886; Deflector, 887; Bull's Eye, or Mauchline, 
 887; Marsaut, 887; Mueseler, 887; Ashworth-Hepplewhite-Gray. 
 887; Wolf, 888; Protector, 888; Hailwood, 888; Special Types, 889- 
 Clowes Hydrogen, 889; Stokes Alcohol, 889; Pieler, 890; Chesneau, 
 890; Stuchlick Acetylene, 891; Tombelaine Acetylene, 891; Gas 
 
 William's Methanometer, 894; Aitkin's Indicator, 894; Beard- 
 
 Mackie Sight Indicator, 894; Brigg's Wire Loop, 894; Cuninghame- 
 Cadbury Indicator, 894; Colored Glass Indicators, 895; Forbes, 895; 
 Firedamp Whistle, 895; Hardy Indicator, 895; Shaw Gas- Testing 
 Machine, 895; Hanger and Pescheux Gas-Signaling Apparatus, 896; 
 Low Gas-Signaling Apparatus, 896; Electric Safety Lamps, 896; 
 Points of PDanger, 896; Types, 897; The Ceag Lamp, 897; Special 
 Forms, 898; Cap Lamps, 898; Charging Stations, 899; Acetylene 
 Lamps, 900. 
 
 Explosive Conditions in Mines. Causes, 900; Derangement of Ventilating 
 Current, 901; Sudden Increase 9f Gas, 901; Effect of Coal Dust in 
 Mine Workings, 901; Humidifying the Air Current, 902; Hygrome- 
 ters, 904; Pressure as Affecting Explosive Conditions, 905; Rapid 
 Successi9n of Shots in Close Workings, 906; Quantity of Air Required 
 for Ventilation, 906; Quantity Required by State Laws, 906; Quantity 
 Required for Dilution of Mine Gases, 906; Quantity Required to Pro- 
 duce the Necessary Velocity of Current at the Face, 907; Elements in 
 Ventilation, 907; Horsepower or Power of the Current, 907: Mine 
 Resistance, 907; Velocity of the Air Current, 907; Relation of Power, 
 Pressure, and Velocity, 907; Measurement of Ventilating Currents, 
 907; Of Velocity, 908: Water Gauge, 908: Calculation of Mine 
 Resistance, 909; Table of Various Coefficients of Friction of 
 Air in Mines, 909; Calculation of Power, or Units of Work per 
 Minute, 910; The Equivalent Orifice, 910; P9tential Factor of a Mine, 
 910; Table of Water Gauges for Calculating the Amount of Air 
 Required for Mine Workings, 911; Formulas, 913; Variation of the 
 Elements, 915; Quantity Produced by Two or More Ventilators, 916. 
 
 Distribution of Air in Mine Ventilation. General, 917; Requirements of 
 Law in Regard to Splitting, 918; Practical Splitting of the Air Cur- 
 rent, 918; Natural Division, 918; Calculation of 'Natural Splitting, 
 918; Proportional Division of the Air Current, 919; Box Regulator. 
 919; Door Regulator, 920; Calculation of Pressure for Box Regula- 
 tors, 920; Size of Opening, 920; Size of Opening for a Door Regulator, 
 921; Calculation of Horsepower for Box Regulators, 921; For Door 
 Regulators, 921; Splitting Formulas, 922. 
 
 Methods and Appliances in the Ventilation of Mines. Ascensional Ventila- 
 tion, 925; General Arrangement of Mine Plan, 925; Natural Ventila- 
 tion, 925; Ventilation of Rise and Dip Workings, 926; Influence of 
 Seasons, 926; Furnace Ventilation, 927; Construction of a Mine 
 
xxiv CONTENTS 
 
 Furnace, 927; Air Columns, 927; Inclined Air C9lumns, 928; Calcula- 
 tion of Ventilating Pressure in Furnace Ventilation, 928; Calcula- 
 tion of Motive Column or Air Column, 928; Influence of Furnace 
 Stack, 929; Mechanical Ventilators, 929; Fan Ventilation, 929; Disk 
 Fans, 929; Centrifugal Fans, 930; Exhaust Fans, 930; Force Fans 
 and Blowers, 930; Vacuum System of Ventilation, 930: Plenum 
 System, 930; Comparison of Vacuum and Plenum, 930; Types of 
 Centrifugal Fans, 931; Nasmyth, 931; Biram's Ventilator, 931: 
 Waddle, 932; Schiele, 932; Guibal, 932; Murphy, 933; Capell, 933; 
 Sirocco Fan, 933; Direct-Connected Engines, 934; Other Drives, 
 934; Method of Determining Fan Diameter, 934; To Ascertain Fan 
 Speed Required, 934; Horsepower Needed, 934; Size of Motor, 934; 
 Evase Stack, 934; Maximum Inlet Velocity, 935; Loss at Inlets, 935; 
 Standard Air, 935: Inlet Velocities, 935; Special Fans, 935: Equiva- 
 lent Orifice, 935; Murgue's Formula, 936; Sullivan Reversible Fans, 
 936; Sullivan Fans, Sizes, Weights, Dimensions, Table, 937; Fan 
 Ratings, Tables, 938-940; Table of Capacities, 941; Position of Any 
 Fan, Etc., 941; Manometrical Efficiency, 942- Mechanical Efficiency, 
 942; Fan Construction, 942; Size of Central Orifice, 942; Diameter of 
 Fan, 942; Curvature of Blades, 943; Tapered Blades, 943; Number 
 of Blades, 943; Spiral Casing, 944; Evase Chimney, 944; High- 
 Speed and Low-Speed Motors, 944; Fan Tests, 944; Conducting Air 
 Currents, 944; Doors, 944; Stoppings, 945; Air Bridges, 945; Air 
 Brattice, 945; Curtains, 944. 
 
 MINE FIRES 
 
 Means of Extinguishing. Isolating the Section, 945; Sealing Off Fires, 946; 
 
 Stopping Materials, 946; Unsealing After the Fire Is Out. 947. 
 Spontaneous Combustion. Causes, 948; Coal Storage, 949. 
 
 THE PREPARATION OF COAL 
 
 Crushing Machinery. Object, 949; Cracking Rolls, 949; Corrugated 
 Rolls, 950; Disintegrating Rolls and Pulverizers, 950; Hammers, 950; 
 Miscellaneous Forms of Crushers, 951; Sizing and Classifying 
 Apparatus, 951; Stationary Screens, Grizzlies, Head-Bars, or Plat- 
 form Bars, 951; Shaking Screens, 952; Size of Mesh, Table, 952; 
 Revolving Screens, or Trommels, 952; Speed, 953; Duty of Anthracite 
 Screens, 953; Revolving Screen Mesh for Anthracite, 953; Hydraulic 
 Classifiers, 953; Jeffrey-Robinson Coal Washer, 953; Scaife Trough 
 Washer, 954; Jigs, 954; Stationary Screen Jigs, 954; Heberle Gate, 
 955; Theory of Jigging, 955; Equal Settling Particles, 955; Table of 
 Equal Settling Factors or Multipliers, 956; Interstitial Currents, or 
 Law of Settling Under Hindered Settling Conditions, 956; Interstitial 
 Factors, 957; Acceleration, 957; Suction, 957; Removal of Sulphur 
 From Coal, 957; Preparation of Anthracite, 958; Preparation of 
 Bituminous Coal, 959: Sizes, 959; Method, 960; Screening Area, 961; 
 Shaker Screens for Small Sizes, 961; Screen Feeders, 962; Tipple 
 Design, 962; Washing Bituminous Coal, 962. 
 
 Handling of Material. Anthracite Coal, 962: Weights and Capacities of 
 Standard Steel Buckets, Table, 963; Elevating Capacities of Malle- 
 able Iron Buckets, Table, 963; Conveying Capacities of Flights at 100 
 Ft. per Min., Table, 963; Horsepower for Bucket Elevators, Table, 
 964; Pitch at Which Anthracite Coal Will Run, Table, 964; Horse- 
 powers for Coal Conveyors, Table, 965; Horizontal Pressure Exerted 
 by Bituminous Coal Against Vertical Retaining Walls, Table, 965; 
 By Anthracite, Table, 966; Cost of Unloading Coal, 966; Briqueting, 
 967; Machines, 967; Briqueting of Fuel, 967; Of Flue Dust, 968; 
 Cubic Feet Occupied by 2,000 Pounds of Various Coals, Table, 968. 
 
 SAFETY AND FIRST AID 
 
 Rules for First-Aid Corps. 969: Shock, 970; Burns and Scalds, 970; Heat 
 Prostration, 970; Convulsions, 970; Artificial Respiration, Shafer 
 Method, 970; Sylvester Method, 971; Treatment for Electrical 
 Shock, 972; Rescue From Electrical Contact, 972; Fractures, 973; 
 Drowning, 973. 
 
 Method of Moving Injured Persons. 973. 
 
CONTENTS xxv 
 
 MINE SAFETY 
 
 Safety First. Systematic Timbering, 975; Adequate Supervision, 975; 
 
 Premium System and Company Rules, 976; Safeguarding Machinery, 
 
 978; Protecting from Electricity, 980; Failure of Machine Parts, 980; 
 
 Preventing Mismanipulation of Controlling Devices, 980; Safety 
 
 Practices of the H. C. Frick Coke Co., 982. 
 Mine-Rescue Work. Organization, 984; First Steps, 984; Reversing the 
 
 Air Current, 985; Work of Recovery, 985. 
 Mine-Rescue Apparatus. Breathing Apparatus, 986; Self Rescuer, 987; 
 
 Resuscitation Apparatus, 987. 
 
 NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS 
 Explanation of Tables. 989. 
 Tables of Natural Sines and Cosines, 991-999. 
 Tables of Natural Tangents and Cotangents. 1000-1008. 
 
 LOGARITHMIC TABLES 
 
 Explanation of Tables. 1009; Common Logarithms of Numbers, Table, 
 
 1009. 
 
 Tables of Logarithms of Numbers. 1010-1027. 
 Tables of Logarithms of Trigonometric Functions. 1028-1072. 
 
 TRAVERSE TABLES 
 Directions for Use. 1073. 
 
 Tables of Latitudes and Departures. 1074-1080. 
 Tables of Squares, Cubes, Square and Cube Roots, Circumferences, and 
 
 Areas. 1081-1096. 
 Tables of Circumferences and Areas of Circles From ^4 to 100. 1097-1101. 
 
 GLOSSARY OF MINING TERMS 
 Explanation. 1101. 
 Glossary. 1102-1149. 
 Index. 1151-1172. 
 
The Coal Miners 5 Pocketbook 
 
 WEIGHTS AND MEASURES 
 
 LINEAR MEASURE 
 
 Immediately following each table of weights or of measures is given a table 
 of equivalents showing the relation existing between the different denomina- 
 tions. All figures on the same horizontal line are of equal or equivalent value. 
 
 The United States unit of length, of which unit all other denominations 
 are multiples or submultiples, is the yard, originally derived from the Imperial 
 yard of Great Britain. Since 1893, the United States Bureau of Standards 
 has been authorized to derive the yard from the meter, using the relationship 
 
 established by Congress in the act of July 28, 1866, viz., 1 yard = ^r^ meter. 
 
 12 inches (in.) =1 foot ft. 
 
 3 feet =1 yard yd. 
 
 5.5 yards =1 rod rd. 
 
 40 rods =1 furlong fur. 
 
 8 furlongs =1 mile mi. 
 
 in. ft. yd. rd. fur. mi. 
 
 1 - .083333 = .027778 = .005051 = .000126 = .000016 
 
 12 = 1 = .333333 = .060606 = .001515 = .000189 
 
 36= 3= 1 = . 181818 = .004545 = .000568 
 
 198= 16.5= 5.5= 1 = . 025000 = .003 125 
 
 7,920= 660= 220= 40= 1 = . 125000 
 
 63,360= 5,280= 1,760= 320= 8= 1 
 
 The rod of 16.5 ft., and variously known as the perch or pole, is the same as 
 in surveyor's measure. The furlong is now no longer used. 
 
 The land league of 3 statute mi. is 15,840 ft.; the nautical, or marine, league 
 of 3 geographical mi. is 18,240 ft. 
 
 The nautical, marine, or geographical mile is the & part of 1 of a great 
 circle of a sphere whose surface is equal to the surface of the earth. This is 
 commonly taken as 6,080 ft., but is more accurately 6,080.26 ft., and is 
 equivalent to 1.1516 stat. mi. One statute mile equals .8684 naut. mi. 
 
 The fathom of 6 ft. is used at sea in measuring depths of water, and some 
 times (England) in giving depths of mine shafts. 
 
 The pace is commonly 3 ft. The U. S. military pace is 30 in. 
 
 SURVEYOR'S LINEAR MEASURE 
 
 The surveyor's linear measure is no longer in common use but its denomi- 
 nations are found in descriptions of the boundaries of farms taken from old 
 deeds. Lengths of land lines are now measured and recorded in feet and 
 decimal parts thereof. 
 
 7.92 inches (in.) = 1 link li. 
 
 25 links. . . = 1 rod (16.5 ft.) rd. 
 
 4 rods. .' =1 chain (66 ft.) ch. 
 
 80 chains =1 mile mi. 
 
2 WEIGHTS: A.ND MEASURES 
 
 'in. ' W. ' rd.' ch. mi. 
 
 1 ~ .126263 - .005051." .001263 = .000016 
 
 7.92= 1^:040000 = .010000 =.000125 
 
 198= 25= 1 = . 250000 = .003125 
 
 792= 100= 4= 1 = . 012500 
 
 63,360= 8.000= 320= 80= 1 
 
 Surveyors commonly use the engineer's chain of 50 or 100 ft., the feet being 
 divided into tenths and hundredths. 
 
 The annexed scale shows on one side, proportionately reduced, a scale of 
 tenths. On the other, a scale of twelfths, corresponding to inches. To 
 reduce inches to decimal parts of a foot, find the number of inches and frac- 
 tional parts thereof on the side marked "inches." Opposite, on the scale of 
 
 ft" | 
 
 
 
 * * i fi 
 
 ,,,,,,,, 
 
 rn.^,....,^. 
 
 V,,,^^/IMI| 
 
 1 r^J i 
 
 """i 111 
 
 i ' " ' i ' M ] M 
 
 ^" 
 
 
 1 "i 1 " 'A 
 
 tenths, will be found the decimal part of a foot. Thus, if it is wanted to find 
 the decimal part of a foot represented by 7^ in., find the mark corresponding 
 to 7$ in. on the side marked "inches." Opposite this mark may be read 
 6 tenths, 2 hundredths, and 5 thousandths; or, expressed decimally, .625. 
 This scale may be laid out, full size, upon stiff cardboard and will be found very 
 useful in figuring lengths in construction work. 
 
 DECIMALS OF AN INCH AND MILLIMETERS FOR EACH 1-64TH IN. 
 
 64ths of 
 an Inch 
 
 Decimal 
 Parts of 
 lln. 
 
 Millimeters 
 
 64ths of 
 an Inch 
 
 Decimal 
 Parts of 
 1 In. 
 
 Millimeters 
 
 A 
 
 .015625 
 
 .397 
 
 i 
 
 
 .515625 
 
 13.097 
 
 *"* 
 
 .031250 
 
 .794 
 
 
 
 .531250 
 
 13.494 
 
 _s^ 
 
 .046875 
 
 1.191 
 
 A 
 
 
 .546875 
 
 13.891 
 
 A 
 
 .062500 
 
 1.588 
 
 ! 
 
 
 .562500 
 
 14.288 
 
 JL 
 
 .078125 
 
 1.984 
 
 1 
 
 
 .578125 
 
 14.684 
 
 A 
 
 .093750 
 
 2.381 
 
 1 
 
 
 .593750 
 
 15.081 
 
 J_ 
 
 .109375 
 
 2.778 
 
 1 
 
 1 
 
 .609375 
 
 15.478 
 
 
 .125000 
 
 3.175 
 
 
 
 
 .625000 
 
 15.875 
 
 
 .140625 
 
 3.572 
 
 
 
 .640625 
 
 16.272 
 
 i 
 
 .156250 
 
 3.969 
 
 . 
 
 
 .656250 
 
 16.669 
 
 H 
 
 .171875 
 
 4.366 
 
 
 
 .671875 
 
 17.066 
 
 JL 
 
 .187500 
 
 4.763 
 
 
 
 .687500 
 
 17.463 
 
 if 
 
 .203125 
 
 5.159 
 
 
 
 .703125 
 
 17.859 
 
 A 
 
 .218750 
 
 5.556 
 
 
 
 
 .718750 
 
 18.256 
 
 is. 
 
 .234375 
 
 5.953 
 
 j 
 
 i 
 
 .734375 
 
 18.653 
 
 i 
 
 .250000 
 
 6.350 
 
 
 
 .750000 
 
 19.050 
 
 H 
 
 .265625 
 
 6.747 
 
 
 
 .765625 
 
 19.447 
 
 & 
 
 .281250 
 
 7.144 
 
 
 
 .781250 
 
 19.844 
 
 y 
 
 .296875 
 
 7.541 
 
 
 
 .796875 
 
 20.241 
 
 / 
 
 
 .312500 
 
 7.938 
 
 
 
 .812500 
 
 20.638 
 
 
 
 .328125 
 
 8.334 
 
 
 
 .828125 
 
 21.034 
 
 i 
 
 
 .343750 
 
 8.731 
 
 
 
 .843750 
 
 21.431 
 
 i 
 
 
 .359375 
 
 9.128 
 
 
 
 .859375 
 
 21.828 
 
 i 
 
 
 .375000 
 
 9.525 
 
 
 
 .875000 
 
 22.225 
 
 i 
 
 
 .390625 
 
 9.922 
 
 1 
 
 
 .890625 
 
 22.622 
 
 1 
 
 
 .406250 
 
 10.319 
 
 I 
 
 
 .906250 
 
 23,019 
 
 & 
 
 
 .421875 
 
 10.716 
 
 5 
 
 
 .921875 
 
 23.416 
 
 I 
 
 
 .437500 
 
 11.113 
 
 
 
 .937500 
 
 23.813 
 
 * 
 
 
 .453125 
 
 11.509 
 
 
 
 .953125 
 
 24.209 
 
 & 
 
 
 .468750 
 
 11.906 
 
 
 
 .968750 
 
 24.606 
 
 i 
 
 
 
 .484375 
 
 12.303 
 
 
 
 .984375 
 
 25.003 
 
 * 
 
 .500000 
 
 12.700 
 
 
 
 1.000000 
 
 25.400 
 
WEIGHTS AND MEASURES 3 
 
 MEASURES OF SURFACE 
 
 SQUARE MEASURE 
 
 144 square inches (sq. in.) =1 square foot sq. ft. 
 
 9 square feet =1 square yard sq. yd. 
 
 30.25 square yards - 1 square rod sq. rd. 
 
 40 square rods =1 rood rood. 
 
 4 roods (160 sq. rd.) =1 acre A. or ac. 
 
 640 acres= 1 section =1 square mile sq. mi. 
 
 sq. in. sq.ft. sq. yd. sq. rd. rood A. sq. mi. 
 
 1= .006944= .000772 = .000026 
 
 144= 1= .111 111 = .003673 = .000092 = .000023 
 
 1 ,296 = 9 = 1 = .033058 = .000826 = .000207 
 
 39,204= 272.25= 30.25= 1 = .025000 = .006250 = .000009 
 
 1,568,160= 10,890= 1,210= 40= 1 = . 250000 = .000391 
 
 6,272,640= 43,560= 4,840= 160= 4= 1 = . 001563 
 
 4,014,489,600 = 27,878,400 = 3,097,600 = 102,400= 2,560= 640= 1 
 
 The square rod is also known as the perch. The rood, equal to 40 sq. rd., 
 or 1 A., is obsolete. 640 A. make one section; 320 A., one half-section; 160 A., 
 a quarter section, etc. 36 sections, or 23,040 A., make 1 township (twp.). 
 The areas of small tracts of land, such as city lots, are usually given in square 
 feet and decimals thereof; of larger bodies of land, in acres and decimals of an 
 acre. A square measuring 208.71 ft., or 69.57 yd., on each side contains 
 1 A. 
 
 Squares of 100 sq. ft. or of 1 sq. yd. are used in estimating various kinds of 
 work, such as roofing, lathing, plastering, etc. It is advisable to specify the 
 size of the square in all contracts. 
 
 SURVEYOR'S SQUARE MEASURE 
 
 The surveyor's square measure is practically obsolete in the United States, 
 although its denominations are commonly found in old deeds in describing the 
 area of lands. As lengths of land lines are now generally measured in feet, 
 tenths, and hundredths, areas are commonly expressed in square feet or in 
 acres and in decimal parts thereof. 
 
 62.7264 square inches (sq. in.) =1 square link sq. li. 
 
 625 square links =1 square rod sq. rd. 
 
 16 square rods =1 square chain sq. ch. 
 
 10 square chains =1 acre A. or ac. 
 
 640 acres = 1 section =1 square mile sq. mi. 
 
 36 square miles =1 township tp. or twp. 
 
 sq. in. sq. li. sq. rd. sq. ch. A. sq. mi. 
 
 1= .015942 = .000026 = .000002 
 
 62.7264= 1 = . 001600 = .000100 = .000010 
 
 39 ,204 = 625 = 1 = .062500 = .006250 = .000009 
 
 627,264= 10,000= 16= 1 = . 100000 = .000156 
 
 6,272,640= 100,000= 160= 10= 1 = . 001563 
 
 4,014,489,600 = 64,000,000 = 102,400= 6,400= 640= 1 
 
 1 township = 36 sq. mi. = 23,040 A. =-230,400 sq. ch. = 3.686,400 sq. rd. 
 2,304 ,000,000 sq. li. = 144,521,625,600 sq. in. 
 
 MEASURES OF WEIGHT 
 
 The United States standard of weight is the troy pound of Great Britain 
 from which the avoirdupois pound is derived in the ratio 1 pound avoirdupois 
 = LP^ pound troy. Since 1893, the United States Bureau of Standards has 
 been authorized to derive the pound avoirdupois from the kilogram, using the 
 
4 WEIGHTS AND MEASURES 
 
 relationship established by Congress in the act of July 28, 1866, viz., 1 pound 
 
 avoirdupois = 
 
 kilogram. The weight of the grain in the troy, apothe- 
 
 2.2046 
 caries', and avoirdupois pounds, is the same. 
 
 TROY WEIGHT 
 
 Troy weight is used in weighing gold and silver. 
 
 24 grains (gr.) = 1 pennyweight dwt. 
 
 20 pennyweights =1 ounce oz. 
 
 12 ounces = 1 pound Ib. 
 
 gr. dwt. oz. Ib. 
 
 1 = .041667 = .002083 = .000174 
 
 24= 1 = . 050000 =.004167 
 
 480= 20= 1 = . 083333 
 
 5,760= 240= 12= 1 
 
 1 oz. troy = 1 oz. apothecaries' = 1.09714 oz. avoirdupois 
 1 Ib. troy = 1 Ib. apothecaries' = .82286 Ib. avoirdupois 
 1 oz. avoirdupois = .91146 oz. troy or apothecaries' 
 1 Ib. avoirdupois = 1.21528 Ib. troy or apothecaries' 
 
 APOTHECARIES' WEIGHT 
 
 20 grains (gr.) =1 scruple sc. 
 
 3 scruples .\= 1 dram dr. 
 
 8 drams =1 ounce oz. 
 
 12 ounces = 1 pound Ib. 
 
 DECIMALS OF A FOOT FOR EACH 1-64TH IN. 
 
 Inch 
 
 0" 
 
 "l" 
 
 2" 
 
 3" 
 
 4" 
 
 5" 
 
 6" 
 
 7" 
 
 8" 
 
 9" 
 
 10" 
 
 11" 
 
 
 
 
 
 .0833 
 
 .1667 
 
 .2500 
 
 .3333 
 
 .4167 
 
 .5000 
 
 .5833 
 
 .6667 
 
 .7500 
 
 .8333 
 
 .9167 
 
 
 .0013 
 
 .0846 
 
 .1680 
 
 .2513 
 
 .3346 
 
 .4180 
 
 .5013 
 
 .5846 
 
 .6680 
 
 .7513 
 
 .8346 
 
 .9180 
 
 A 
 
 .0026 
 
 .0859 
 
 .1693 
 
 .2526 
 
 .3359 
 
 .4193 
 
 .5026 
 
 .5859 
 
 .6693 
 
 .7526 
 
 .8359 
 
 .9193 
 
 j_ 
 
 .0039 
 
 .0872 
 
 .1706 
 
 .2539 
 
 .3372 
 
 .4206 
 
 .5039 
 
 .5872 
 
 .6706 
 
 .7539 
 
 .8372 
 
 .9206 
 
 A 
 
 .0052 
 
 .0885 
 
 .1719 
 
 .2552 
 
 .3385 
 
 .4219 
 
 .5052 
 
 .5885 
 
 .6719 
 
 .7552 
 
 .8385 
 
 .9219 
 
 JL 
 
 .0065 
 
 .0898 
 
 .1732 
 
 .2565 
 
 .3398 
 
 .4232 
 
 .5065 
 
 .5898 
 
 .6732 
 
 .7565 
 
 .8398 
 
 .9232 
 
 A 
 
 .0078 
 
 .0911 
 
 .1745 
 
 .2578 
 
 .3411 
 
 .4245 
 
 .5078 
 
 .5911 
 
 .6745 
 
 .7578 
 
 .8411 
 
 .9245 
 
 J_ 
 
 .0091 
 
 .0924 
 
 .1758 
 
 .2591 
 
 .3424 
 
 .4258 
 
 .5091 
 
 .5924 
 
 .6758 
 
 .7591 
 
 .8424 
 
 .9258 
 
 1 
 
 .0104 
 
 .0937 
 
 .1771 
 
 .2604 
 
 .3437 
 
 .4271 
 
 .5104 
 
 .5937 
 
 .6771 
 
 .7604 
 
 .8437 
 
 .9271 
 
 
 
 .0117 
 
 .0951 
 
 .1784 
 
 .2617 
 
 .3451 
 
 .4284 
 
 .5117 
 
 .5951 
 
 .6784 
 
 .7617 
 
 .8451 
 
 .9284 
 
 5 
 
 .0130 
 
 .0964 
 
 .1797 
 
 .2630 
 
 .3464 
 
 .4297 
 
 .5130 
 
 .5964 
 
 .6797 
 
 .7630 
 
 .8464 
 
 .9297 
 
 |i 
 
 .0143 
 
 .0977 
 
 .1810 
 
 .2643 
 
 .3477 
 
 .4310 
 
 .5143 
 
 .5977 
 
 .6810 
 
 .7643 
 
 .8477 
 
 .9310 
 
 JL 
 
 .0156 
 
 .0990 
 
 .1823 
 
 .2656 
 
 .3490 
 
 .4323 
 
 .5156 
 
 .5990 
 
 .6823 
 
 .7656 
 
 .8490 
 
 .9323 
 
 || 
 
 .0169 
 
 .1003 
 
 .1836 
 
 .2669 
 
 .3503 
 
 .4336 
 
 .5169 
 
 .6003 
 
 .6836 
 
 .7669 
 
 .8503 
 
 .9336 
 
 & 
 
 .0182 
 
 .1016 
 
 .1849 
 
 .2682 
 
 .3516 
 
 .4349 
 
 .5182 
 
 .6016 
 
 .6849 
 
 .7682 
 
 .8516 
 
 .9349 
 
 8 
 
 .0195 
 
 .1029 
 
 .1862 
 
 .2695 
 
 .3529 
 
 .4362 
 
 .5195 
 
 .6029 
 
 .6862 
 
 .7695 
 
 .8529 
 
 .9362 
 
 
 .0208 
 
 .1042 
 
 .1875 
 
 .2708 
 
 .3542 
 
 .4375 
 
 .5208 
 
 .6042 
 
 .6875 
 
 .7708 
 
 .8542 
 
 .9375 
 
 H 
 
 .0221 
 
 .1055 
 
 .1888 
 
 .2721 
 
 .3555 
 
 .4388 
 
 .5221 
 
 .6055 
 
 .6888 
 
 .7721 
 
 .8555 
 
 .9388 
 
 J 
 
 .0234 
 
 .1068 
 
 .1901 
 
 .2734 
 
 .3568 
 
 .4401 
 
 .5234 
 
 .6068 
 
 .6901 
 
 .7734 
 
 .8568 
 
 .9401 
 
 if 
 
 .0247 
 
 .1081 
 
 .1914 
 
 .2747 
 
 .3581 
 
 .4414 
 
 .5247 
 
 .6081 
 
 .6914 
 
 .7747 
 
 .8581 
 
 .9414 
 
 JL 
 
 .0260 
 
 .1094 
 
 .1927 
 
 .2760 
 
 .3594 
 
 .4427 
 
 .5260 
 
 .6094 
 
 .6927 
 
 .7760 
 
 .8594 
 
 .9427 
 
 fi 
 
 .0273 
 
 .1107 
 
 .1940 
 
 .2773 
 
 .3607 
 
 .4440 
 
 .5273 
 
 .6107 
 
 .6940 
 
 .7773 
 
 .8607 
 
 .9440 
 
 ii 
 
 .0286 
 
 .1120 
 
 .1953 
 
 .2786 
 
 .3620 
 
 .4453 
 
 .5286 
 
 .6120 
 
 .6953 
 
 .7786 
 
 .8620 
 
 .9453 
 
 H 
 
 .0299 
 
 .1133 
 
 .1966 
 
 .2799 
 
 .3633 
 
 .4466 
 
 .5299 
 
 .6133 
 
 .6966 
 
 .7799 
 
 .8633 
 
 .9466 
 
 I 
 
 .0312 
 
 .1146 
 
 .1979 
 
 .2812 
 
 .3646 
 
 .4479 
 
 .5312 
 
 .6146 
 
 .6979 
 
 .7812 
 
 .8646 
 
 .9479 
 
 II 
 
 .0326 
 
 .1159 
 
 .1992 
 
 .2826 
 
 .3659 
 
 .4492 
 
 .5326 
 
 .6159 
 
 .6992 
 
 .7826 
 
 .8659 
 
 .9492 
 
 33 
 
 .0339 
 
 .1172 
 
 .2005 
 
 .2839 
 
 .3672 
 
 .4505 
 
 .5339 
 
 .6172 
 
 .7005 
 
 .7839 
 
 .8672 
 
 .9505 
 
 H 
 
 .0352 
 
 .1185 
 
 .2018 
 
 .2852 
 
 .3685 
 
 .4518 
 
 .5352 
 
 .6185 
 
 .7018 
 
 .7852 
 
 .8685 
 
 .9518 
 
 ~lS 
 
 .0365 
 
 .1198 
 
 .2031 
 
 .2865 
 
 .3698 
 
 .4531 
 
 .5365 
 
 .61-98 
 
 .7031 
 
 .7865 
 
 .8698 
 
 .9531 
 
 II 
 
 .0378 
 
 .1211 
 
 .2044 
 
 .2878 
 
 .3711 
 
 .4544 
 
 .5378 
 
 .6211 
 
 .7044 
 
 .7878 
 
 .8711 
 
 .9544 
 
 M 
 
 .0391 
 
 .1224 
 
 .2057 
 
 .2891 
 
 .3724 
 
 .4557 
 
 .5391 
 
 .6224 
 
 .7057 
 
 .7891 
 
 .8724 
 
 .9557 
 
 U 
 
 .0404 
 
 .1237 
 
 .2070 
 
 .2904 
 
 .3737 
 
 .4570 
 
 .5404 
 
 .6237 
 
 .7070 
 
 .7904 
 
 .8737 
 
 .9570 
 
 1 
 
 .0417 
 
 .1250 
 
 .2083 
 
 .2917 
 
 .3750 
 
 .4583 
 
 .5417 
 
 .6250 
 
 .7083 
 
 .7917 
 
 .8750 
 
 .9583 
 
WEIGHTS AND MEASURES 5 
 
 gr. sc. dr. oz. lb. 
 
 1 = .050 = .016667 => .002083 = .000174 
 
 20= 1 = . 333333 = .041667 = .003472 
 
 60= 3= 1 = . 125000 = .010417 
 
 480= 24= 8= 1 = . 083333 
 
 5,760= 288= 96= 12= 1 
 
 For equivalents in troy and apothecaries' weights, see under the former. 
 
 AVOIRDUPOIS WEIGHT 
 
 SHORT TON 
 
 27.34375 grains (gr.) =1 dram dr. 
 
 16 drams =1 ounce oz. 
 
 16 ounces =1 pound lb. 
 
 100 pounds =1 hundredweight cwt. 
 
 20 hundredweight \ t + 
 2,000 pounds / = lton... 
 
 gr. dr. oz. lb. cwt. 
 
 1 = .036571 = .002286 = .000143 = .000001 
 27.34375 = 1 = .062500 = .003906 = .000039 = .000002 
 
 437.5 = 16 = 1 = .062500 = .000625 = .00003 1 
 
 7,000= 256= 16= 1 = . 010000 = .000500 
 
 700,000= 25,600= 1,600= 100= 1 = . 050000 
 
 14,000,000 = 512,000= 32,000= 2,000= 20= 1 
 
 The ton of 2,000 lb. is the trade standard of the United States, except in 
 transactions involving anthracite (in Pennsylvania) and certain iron and steel 
 products in bulk. A hundredweight is sometimes known as a quintal and is 
 not uncommonly used among fishermen. The dram is practically obsolete. 
 
 DECIMALS OF A FOOT FOR EACH 1-64TH IN. 
 
 ..T. 
 T. 
 
 Inch 
 
 0" 
 
 1" 
 
 2" 
 
 3" 
 
 4" 
 
 5" 
 
 6" 
 
 7" 
 
 8" 
 
 9" 
 
 10" 
 
 11" 
 
 i 
 
 .0417 
 
 .1250 
 
 .2083 
 
 .2917 
 
 .3750 
 
 .4583 
 
 .5417 
 
 .6250 
 
 .7083 
 
 .7917 
 
 .8750 
 
 .9583 
 
 |i 
 
 .0430 
 
 .1263 
 
 .2096 
 
 .2930 
 
 .3763 
 
 .4596 
 
 .5430 
 
 .6263 
 
 .7096 
 
 .7930 
 
 .8763 
 
 .9596 
 
 Jr 
 
 .0443 
 
 .1276 
 
 .2109 
 
 .2943 
 
 .3776 
 
 .4609 
 
 .5443 
 
 .6276 
 
 .7109 
 
 .7943 
 
 .8776 
 
 .9609 
 
 M 
 
 .0456 
 
 .1289 
 
 .2122 
 
 .2956 
 
 .3789 
 
 .4622 
 
 .5456 
 
 .6289 
 
 .7122 
 
 .7956 
 
 .8789 
 
 .9622 
 
 TS 
 
 .0469 
 
 .1302 
 
 .2135 
 
 .2969 
 
 .3802 
 
 .4635 
 
 .5469 
 
 .6302 
 
 .7135 
 
 .7969 
 
 .8802 
 
 .9635 
 
 fl 
 
 .0482 
 
 .1315 
 
 .2148 
 
 .2982 
 
 .3815 
 
 .4648 
 
 .5482 
 
 .6315 
 
 .7148 
 
 .7982 
 
 .8815 
 
 .9648 
 
 M 
 
 .0495 
 
 .1328 
 
 .2161 
 
 .2995 
 
 .3828 
 
 .4661 
 
 .5495 
 
 .6328 
 
 .7161 
 
 .7995 
 
 .8828 
 
 .9661 
 
 i 
 
 .0508 
 
 .1341 
 
 .2174 
 
 .3008 
 
 .3841 
 
 .4674 
 
 .5508 
 
 .6341 
 
 .7174 
 
 .8008 
 
 .8841 
 
 .9674 
 
 1 
 
 .0521 
 
 .1354 
 
 .2188 
 
 .3021 
 
 .3854 
 
 .4688 
 
 .5521 
 
 .6354 
 
 .7188 
 
 .8021 
 
 .8854 
 
 .9688 
 
 : 
 
 x 
 
 .0534 
 
 .1367 
 
 .2201 
 
 .3034 
 
 .3867 
 
 .4701 
 
 .5534 
 
 .6367 
 
 .7201 
 
 .8034 
 
 .8867 
 
 .9701 
 
 
 
 .0547 
 
 .1380 
 
 .2214 
 
 .3047 
 
 .3880 
 
 .4714 
 
 .5547 
 
 .6380 
 
 .7214 
 
 .8047 
 
 .8880 
 
 .9714 
 
 
 
 .0560 
 
 .1393 
 
 .2227 
 
 .3060 
 
 .3893 
 
 .4727 
 
 .5560 
 
 .6393 
 
 .7227 
 
 .8060 
 
 .8893 
 
 .9727 
 
 
 
 .0573 
 
 .1406 
 
 .2240 
 
 .3073 
 
 .3906 
 
 .4740 
 
 .5573 
 
 .6406 
 
 .7240 
 
 .80-73 
 
 .8906 
 
 .9740 
 
 i 
 
 
 .0586 
 
 .1419 
 
 .2253 
 
 .3086 
 
 .3919 
 
 .4753 
 
 .5586 
 
 .6419 
 
 .7253 
 
 .8086 
 
 .8919 
 
 .9753 
 
 
 i 
 
 .0599 
 
 .1432 
 
 .2266 
 
 .3099 
 
 .3932 
 
 .4766 
 
 .5599 
 
 .6432 
 
 .7266 
 
 .8099 
 
 .8932 
 
 .9766 
 
 h 
 
 .0612 
 
 .1445 
 
 .2279 
 
 .3112 
 
 .3945 
 
 .4779 
 
 .5612 
 
 .6445 
 
 .7279 
 
 .8112 
 
 .8945 
 
 .9779 
 
 i 
 
 .0625 
 
 .1458 
 
 .2292 
 
 .3125 
 
 .3958 
 
 .4792 
 
 .5625 
 
 .6458 
 
 .7292 
 
 .8125 
 
 .8958 
 
 .9792 
 
 % 
 
 
 .0638 
 
 .1471 
 
 .2305 
 
 .3138 
 
 .3971 
 
 .4805 
 
 .5638 
 
 .6471 
 
 .7305 
 
 .8138 
 
 .8971 
 
 .9805 
 
 i 
 
 
 .0651 
 
 .1484 
 
 .2318 
 
 .3151 
 
 .3984 
 
 .4818 
 
 .5651 
 
 .6484 
 
 .7318 
 
 .8151 
 
 .8984 
 
 .9818 
 
 i 
 
 
 .0664 
 
 .1497 
 
 .2331 
 
 .3164 
 
 .3997 
 
 .4831 
 
 .5664 
 
 .6497 
 
 .7331 
 
 .8164 
 
 .8997 
 
 .9831 
 
 i 
 
 
 .0677 
 
 .1510 
 
 .2344 
 
 .3177 
 
 .4010 
 
 .4844 
 
 .5677 
 
 .6510 
 
 .7344 
 
 .8177 
 
 .9010 
 
 .9844 
 
 1 
 
 
 .0690 
 
 .1523 
 
 .2357 
 
 .3190 
 
 .4023 
 
 .4857 
 
 .5690 
 
 .6523 
 
 .7357 
 
 .8190 
 
 .9023 
 
 .9857 
 
 i 
 
 
 
 .0703 
 
 .1536 
 
 .2370 
 
 .3203 
 
 .4036 
 
 .4870 
 
 .5703 
 
 .6536 
 
 .7370 
 
 .8203 
 
 .9036 
 
 .9870 
 
 M 
 
 .0716 
 
 .1549 
 
 .2383 
 
 .3216 
 
 .4049 
 
 .4883 
 
 .5716 
 
 .6549 
 
 .7383 
 
 .8216 
 
 .9049 
 
 .9883 
 
 1 
 
 .0729 
 
 .1562 
 
 .2396 
 
 .3229 
 
 .4062 
 
 .4896 
 
 .5729 
 
 .6562 
 
 .7396 
 
 .8229 
 
 .9062 
 
 .9896 
 
 
 1 
 
 .0742 
 
 .1576 
 
 .2409 
 
 .3242 
 
 .4076 
 
 .4909 
 
 .5742 
 
 .6576 
 
 .7409 
 
 .8242 
 
 .9076 
 
 .9909 
 
 j 
 
 I 
 
 .0755 
 
 .1589 
 
 .2422 
 
 .3255 
 
 .4089 
 
 .4922 
 
 .5755 
 
 .6589 
 
 .7422 
 
 .8255 
 
 .9089 
 
 .9922 
 
 
 1 
 
 .0768 
 
 .1602 
 
 .2435 
 
 .3268 
 
 .4102 
 
 .4935 
 
 .5768 
 
 .6602 
 
 .7435 
 
 .8268 
 
 .9102 
 
 .9935 
 
 
 I 
 
 .0781 
 
 .1615 
 
 .2448 
 
 .3281 
 
 .4115 
 
 .4948 
 
 .5781 
 
 .6615 
 
 .7448 
 
 .8281 
 
 .9115 
 
 .9948 
 
 
 | 
 
 .0794 
 
 .1628 
 
 .2461 
 
 .3294 
 
 .4128 
 
 .4961 
 
 .5794 
 
 .6628 
 
 .7461 
 
 .8294 
 
 .9128 
 
 .9961 
 
 
 \ 
 
 .0807 
 
 .1641 
 
 .2474 
 
 .3307 
 
 .4141 
 
 .4974 
 
 .5807 
 
 .6641 
 
 .7474 
 
 .8307 
 
 .9141 
 
 .9974 
 
 J 
 
 i 
 
 .0820 
 
 .1654 
 
 .2487 
 
 .3320 
 
 .4154 
 
 .4987 
 
 .5820 
 
 .6654 
 
 .7487 
 
 .8320 
 
 .9154 
 
 .9987 
 
 l 
 
 
 
 
 
 
 
 
 
 
 
 
 1.0000 
 
6 WEIGHTS AND MEASURES 
 
 LONG TON 
 The grains, drams, ounces, and pounds are the same as in the short ton. 
 
 16 ounces =1 pound Ib. 
 
 14 pounds =1 stone st. 
 
 2 stones. =1 quarter qr. 
 
 4 quarters =1 hundredweight cwt. 
 
 20 hundredweight = 1 ton (2,240 Ib.) T. 
 
 oz. Ib. st. qr. cwt. T. 
 
 1 = .062500 = .004464 = .002232 = .000558 = .000028 
 
 16= 1 = .071429 = .035714 = .008929 = .000446 
 
 224 = 14 = 1 = .500000 = . 125000 = .006250 
 
 448= 28= 2= 1 = . 250000 = .012500 
 
 1,792= 112= 8= 4= 1 = .050000 
 
 35,840= 2,240= 160= 80= 20= 1 
 
 Short tons multiplied by 1.12 equal long tons. Long tons multiplied by 
 .892857 equal short tons. The long ton is the standard in Great Britain and 
 colonies, except Canada, but its use in the United States is limited. The 
 long ton is used in estimating custom duties. 
 
 MEASURES OF VOLUME 
 
 1,728 cubic inches (cu. in.) =1 cubic foot cu. ft. 
 
 27 cubic feet =1 cubic yard. . ... .cu. yd. 
 
 cu. in. cu. ft. cu. yd. 
 1 = . 000579 = .000021 
 1,728= 1 = . 037037 ' 
 
 46,656= 27= 1 
 
 A cord of wood is 128 cu. ft., or a pile 8 ft. long and 4 ft. high when cut in 
 4-ft. lengths. It is used in estimating amounts of fire and pulp wood, tan- 
 bark, etc. 
 
 A ton (2,240 Ib.) of Pennsylvania anthracite, when broken for domestic 
 use, occupies about 42 cu. ft. of space; bituminous coal about 46 cu. ft.; and 
 coke, about 88 cu. ft. 
 
 A bushel of coal is 80 Ib. in Kentucky, Illinois, and Missouri; 76 Ib. in Penn- 
 sylvania and Montana; and 70 Ib. in Indiana. 
 
 Masonry. A perch of masonry is 24.75 cu. ft., or is a section of wall 16.5 ft. 
 (1 rd. or perch) long, 1.5 ft. thick, and 1 ft. high. It is very frequently taken 
 as 25 cu. ft. Methods and customs of estimating masonry vary locally and it 
 is highly advisable, when preparing contract specifications, to insert in the 
 agreement, upon what basis the measurements are to be made; that is, if by 
 the perch, the number of cubic feet therein. Owing to the confusion in the 
 dimensions of the perch, the term is falling into disuse, and contracts specify 
 measurements either in cubic feet or cubic yards. 
 
 Masonry is measured solid, no deductions being made for corners, which 
 are counted twice, or for openings under 3 ft. in width. This is the custom 
 of the trade and holds in law unless the contract specifies differently. Thus, 
 a foundation wall 1 ft. thick, 8 ft. high, and with outside dimensions of 10 ft. 
 by 12 ft., and with one door opening 2 ft. wide and 8 ft. high, actually contains 
 [(12X2) + (10-1-1)X2]X8-(2X8) = 304 cu. ft. On the trade basis, the 
 door opening is neglected arid the four side walls are counted at their total 
 length (2 of 12 ft., and 2 of 10 ft.), and the wall contains [(12X2) + (10X2)1 
 X8 = 352 cu. ft. 
 
 Brickwork. Brickwork is generally estimated by the thousand bricks 
 laid in the wall, but measurements by the cubic foot and the perch are also 
 used. When making calculations of the volume of walls, etc., to allow for 
 mortar, it is customary to add J in. to the length and thickness of each brick. 
 The following data will be useful in calculating the number of bricks in a wall. 
 For each superficial foot of wall 4 in. in thickness (the width of one brick), 
 allow 7 5 bricks; for a 9-in. wall (the width of two bricks), allow 15 bricks; and 
 so on, estimating 7 bricks for each additional 4 in. in thickness of wall. If 
 brickwork is estimated by the cubic yard, allow 500 bricks to 1 cu. yd. This 
 figure is based on the use of a 8J in. by 4 in. by 2j in. brick, with mortar joints 
 not over f in. thick. If the joints are i in. thick, as in face brickwork, 1 cu. yd. 
 will require about 575 bricks. An allowance of 5% should be made for waste 
 in breakage, etc. 
 
WEIGHTS AND MEASURES 7 
 
 Shipping. The gross tonnage of a ship is its entire internal capacity, cal- 
 culated according to certain rather complicated rules laid down in the Revised 
 Statutes of the United States. The net tonnage of a ship is obtained by deduct- 
 ing from the gross tonnage the space given over to engines, coal, quarters for 
 the crew, etc.; that is, it is the net space available for cargo or paying load. 
 Registered tonnage is the entire internal cubic contents of the vessel divided by 
 100, or 100 cu. ft. equals 1 registered ton. The term gives no idea of the dimen- 
 sions of the vessel, and is merely an arbitrary way of forming some conception 
 of its relative size. 
 
 Displacement is the weight of the volume of water displaced by the hull of 
 a vessel and is often confused with some one of the meanings of tonnage just 
 given. The displacement of a ship naturally varies, depending on the weight 
 of cargo, stores, fuel, etc., aboard. Thus, the displacement of a transatlantic 
 liner will be markedly less on arriving at New York than when leaving 
 England. Displacement is frequently calculated at a normal, or standard, 
 depth of water, to which draft the ship is usually loaded, or for which it was 
 designed; from this is derived the expression, say, "displacement 18,500 T. on 
 23 ft. draft." 
 
 For the purpose of calculating vessel freights, estimating stowage capacity, 
 etc., 1 U. S. shipping ton equals 40 cu. ft. and is equivalent to 32.143 U. S. bu., 
 or 31.16 imp. bu. of England. The British shipping ton is 42 cu. ft. and is 
 equal to 32.719 imp. bu., or 33.75 U. S. bu. 
 
 For weights of various materials see under the heading Specific Gravity. 
 
 LIQUID MEASURE 
 
 By act of Congress the standard of liquid measure is the gallon of 231 cu. in. 
 
 1 gill gi 7.21875 cu. in. 
 
 4 gills = 1 pint pt 28.875 cu. in. 
 
 2 pints =1 quart qt 57.750 cu. in. 
 
 4 quarts =1 gallon gal 231.000 cu. in. 
 
 31.5 gallons =1 barrel bbl 4.211 cu. ft. 
 
 2 barrels =1 hogshead . .hhd 8.422 cu. ft. 
 
 gi. pt. qt. gal. bbl. hhd. 
 
 1 = .250 = .125 = .03125 = .000992 = .000496 
 
 4= 1 = . 500 =.12500 = .003968 = .001984 
 
 8= 2= 1 = . 25000 = .007936 = .003968 
 
 32 = 8-= 4= 1 = . 031746 = .015873 
 
 1,008= 252= 126= 31.5= 1 = . 500000 
 
 2,016= 504= 252= 63= 2= 1 
 
 The U. S. liquid pint, quart, and gallon are equal, respectively, to .85937 
 U. S. dry pint, quart, and gallon. The U. S. dry pint, quart, and gallon are 
 equal, respectively, to 1.16365 U. S. liquid pint, quart, and gallon. 
 
 A box 19 f in. long on each edge contains 1 bbl. 
 
 In approximate calculations, 1 cu. ft. of water may be considered equal to 
 7j gal., and 1 gal. as weighing 8| Ib. 
 
 The capacity of a cylinder in U. S. liquid gallons = square of the diameter, 
 in inches X height, in inches X. 0034 (accurate within 1 part in 100,000). 
 
 The following cylinders contain the given measures very closely: 
 
 Diam. Height 
 Inches Inches 
 
 Gill If 
 
 Pint 3* 
 
 Quart 3 
 
 Diam. Height 
 
 Inches Inches 
 
 Gallon 7 6 
 
 8gal 14 12 
 
 10 gal 14 15 
 
 DRY MEASURE 
 
 By act of Congress the standard of dry measure is the bushel defined as a 
 cylinder 18 in. in diameter, 8 in. deep, and containing 2,150.42 cu. in. 
 
 1 pint 
 
 2 pints 
 
 4 quarts 
 
 2 gallons 
 
 4 pecks 
 
 pt 33.6003125 cu. n 
 
 1 quart. . .qt. 67.200625 cu. n 
 
 268.8025 cu. n 
 
 537.605 cu. n 
 
 2,150.42 cu. n 
 
 1 gallon . .gal 
 
 =1 peck. . . .pk 
 
 =1 bushel . .bu 
 
8 
 
 WEIGHTS AND MEASURES 
 
 pt. qt. gal. pk. bu. 
 
 1 = .500 = .125 = .0625 = .015625 
 
 2= 1 = . 250 =.1250 = .031250 
 
 8= 4 = 1 = . 5000 = .125000 
 
 16= 8= 2= 1 = .250000 
 
 64= 32= 8= 4= 1 
 
 The standard bushel is a struck, or level full, bushel. The heaped bushel 
 is approximately equal to 1J struck bu., the cone, or heap, being not less than 
 6 in. in height. 
 
 The standard bushel is equal to 1.24445, or approximately lj, cu. ft. 
 1 cu. ft. is equal to .80356, or approximately f , bu. 
 
 A cube 3.227 in. on an edge contains 1 pt.; one 4.066 in. on an edge, 1 qt.; 
 one 6.454 in. on an edge, 1 gal.; one 8.131 in. on an edge, 1 pk.; and one 12.908 
 in. on an edge, 1 bu. 
 
 The capacity of a cylinder in U. S. bushels = square of diameter in inches 
 X height in inches X. 0003652. 
 
 There appears to be no standard barrel, dry measure, although one of 
 3 struck bu. is frequently recognized. 
 
 The relation between the dimensions of the units of dry and liquid measure 
 will be found under the former. 
 
 RELATION BETWEEN VOLUMES AND WEIGHTS OF WATER, U. S. 
 LIQUID MEASURE 
 
 The mass of a given volume of water, such as 1 cu. ft. or 1 gal., depends 
 on the conditions under which it is weighed, being less if weighed in air than in 
 a vacuum, at the equator than at the poles, at sea level than at any elevation 
 above, and at higher than at lower readings of either the thermometer or bar- 
 ometer. Reduced from the French measurements made to determine the 
 relations existing between the units of the metric system, the weight in vacuuo 
 of 1 cu. ft. of pure distilled water, free from air, at the temperature of its maxi- 
 mum density (4 C., or 39.3 F.) and under a barometric pressure of 760 milli- 
 meters (29.92 in.) of mercury, at sea level and at the latitude of Paris 
 (48 50' N), is 62.42664 Ib. This is the weight commonly used in pocketbooks 
 and is often given as 62.427 Ib., 62.43 Ib., and even as 62.5 Ib., depending on 
 the degree ol accuracy required. From this, the weight of 1 cu. in. of water 
 under the given conditions may be taken as .036126 Ib., .036 Ib., or even .04 Ib. 
 At other temperatures commonly used in calculations the weight of 1 cu. ft. 
 of water is: at 32 F., 62.418 Ib.; at 62 P., 62.355 Ib.; and at 212 F., 59.846 Ib. 
 
 The following table gives the weight in air of 1 gal. and of 1 cu. ft. of dis- 
 tilled water. These weights are reduced from the French : 
 
 are referred to sea level at the latitude of Paris. 
 or ordinary manner of weighing. 
 
 measurements and 
 They represent the customary 
 
 Temperature Pressure 
 
 4 C. (39.3 F.) . . 760 mm. (29.92 in.) . 
 62 F. (16.7 C.) . .760 mm. (29.92 in.) . 
 62 F. (16.7 C.) . . 30 in. (762.0 mm.) . 
 The following table of equivalents is based upon the weight of 1 cu. ft. of 
 water weighed in air at 39.3 P., and 29.92 in. of mercury, viz.: 62.356562 Ib. 
 avoirdupois. 
 
 Weight of 
 
 1 Gal. 
 
 Pounds 
 
 ..8.33586... 
 
 ..8.32675... 
 
 ..8.32673.. 
 
 Weight of 
 Cu. Ft. 
 Pounds 
 .62.35656 
 
 .62.28844 
 . 62.28827 
 
 EQUIVALENT WEIGHTS AND VOLUMES OF WATER 
 
 Gills 
 
 Pints 
 
 Quarts 
 
 Gallons 
 
 Cubic 
 Inches 
 
 Cubic 
 Foot 
 
 Weight 
 of Water 
 
 
 
 
 
 
 
 Pounds 
 
 1 
 
 .250000 
 
 .125000 
 
 .031250 
 
 7.218750 
 
 .004178 
 
 .260496 
 
 4 
 
 1 
 
 .500000 
 
 .125000 
 
 28.875000 
 
 .016710 
 
 1.041983 
 
 8 
 
 2 
 
 1 
 
 .250000 
 
 57.750000 
 
 .033420 
 
 2.083965 
 
 32 
 
 8 
 
 4 
 
 1 
 
 231 
 
 .133681 
 
 8.335860 
 
 .138528 
 
 .034632 
 
 .017316 
 
 .004329 
 
 1 
 
 .000579 
 
 .036086 
 
 239.376624 
 
 59.844156 
 
 29.922078 
 
 7.480520 
 
 1,728 
 
 1 
 
 62.356562 
 
 3.838836 
 
 .959709 
 
 .479855 
 
 .119964 
 
 27.711598 
 
 .016037 
 
 1 
 
WEIGHTS AND MEASURES 
 
 ANGULAR, OR CIRCULAR, MEASURE 
 
 60 seconds (sec. or ") =1 minute min. or ' 
 
 60 minutes =1 degree deg. or 
 
 360 degrees =1 circumference . . . .cir. 
 
 sec. min. deg. cir. 
 
 1 = .016667 = .000278 = .000008 
 
 60= 1 = . 016667 = .000463 
 
 3,600= 60= 1 = . 002778 
 
 1,296,000= 21,600= 360= 1 
 
 For tables of grades, grade angles, etc., see under the head of Tracklaying. 
 Laying Off Right Angles. Right angles may conveniently 
 be laid off in the field by using the relation existing between 
 the hypotenuse and sides of a right-angled triangle, viz.: The 
 square of the hypotenuse is equal to the sum of the squares 
 of the sides. The commonly used ratio is 3 for the horizontal 
 side, 4 for the vertical side, and 5 for the hypotenuse, or slope. 
 There are many other ratios, such as 8, 15, 17, and the like, a 
 number of which are given in the following table. Likewise, 
 any multiple or submultiple of these ratios may be used. Thus, 
 instead of 3, 4, and 5, f, 1%, or 2 times the proportion may be 
 used, as 1.5, 2, 2.5, or 4.5, 6, 7.5, or 6, 8, and 10, respectively. 
 
 RATIO OF SIDES OF RIGHT-ANGLED TRIANGLE 
 
 Hori- 
 zontal 
 
 Verti- 
 cal 
 
 Slope 
 
 Hori- 
 zontal 
 
 Verti- 
 cal 
 
 Slope 
 
 Hori- 
 zontal 
 
 Verti- 
 cal 
 
 Slope 
 
 3 
 
 4 
 
 5 
 
 12 
 
 16 
 
 20 
 
 18 
 
 24 
 
 30 
 
 4 
 
 3 
 
 5 
 
 12 
 
 9 
 
 15 
 
 20 
 
 15 
 
 25 
 
 6 
 
 8 
 
 10 
 
 14 
 
 48 
 
 50 
 
 20 
 
 48 
 
 52 
 
 7 
 
 24 
 
 25 
 
 15 
 
 8 
 
 17 
 
 24 
 
 32 
 
 40 
 
 8 
 
 6 
 
 10 
 
 15 
 
 20 
 
 25 
 
 24 
 
 18 
 
 30 
 
 8 
 
 15 
 
 17 
 
 15 
 
 36 
 
 39 
 
 24 
 
 45 
 
 51 
 
 9 
 
 12 
 
 15 
 
 16 
 
 12 
 
 20 
 
 24 
 
 7 
 
 25 
 
 10 
 
 24 
 
 26 
 
 16 
 
 30 
 
 40 
 
 25 
 
 60 
 
 65 
 
 Laying Off an Angle With a Tape. It is frequently necessary to lay off 
 other than right angles as, for example, when a cut or two must be taken from 
 
 _- 
 
 tion from which 
 
 Angle Is fumed 
 
 the rib of an entry at a point where a branch entry is to be started, in order that 
 there may be room to place the sights. Suppose it is desired to turn an angle 
 
10 WEIGHTS AND MEASURES 
 
 of 50 to the left. Fasten the end of an ordinary tape at A , then stretch the 
 tape to B a distance of 10 ft., and fasten the 10-ft. mark at B. If the angle is 
 to be turned from an entry, the points A and B can be lined in from the entry 
 sights. Then fasten the 30-ft. mark of the tape at A. This will leave 20 ft. 
 of slack tape between A and B. Find the 19-ft. mark on the" tape, and draw 
 the tape tight from both A and B. The tape line from A to the 19-ft. mark 
 will make an angle of 50 at A with the line A B. If the angle is to the right, 
 
 tape 
 mark; for 30, hold it at the 16' 9|" mark, and similarly for other angles. 
 
 MEASURE OF TIME 
 
 60 seconds (s.) =1 minute min. or m 
 
 60 minutes =1 hour hr. or h 
 
 24 hours = 1 day da. or d 
 
 sec. min. hr. da. 
 
 1 = .016667 = .000278 = .000012 
 
 60= . 1 = . 016667 = .000694 
 
 3,600= 60= 1 = . 041667 
 
 86,400= 1,440= 24= 1 
 
 Solar, astronomical, civil, and standard time are discussed in the chapter 
 on Surveying under the heading Determination of the Meridian. 
 
 LONGITUDE AND TIME 
 
 As the earth makes a complete revolution of 360 upon its axis in 24 hr., 
 degrees, minutes, and seconds of arc, or longitude, may be expressed in hours, 
 minutes, and seconds of time. 
 
 Arc = Time Arc = Time 
 
 360 degrees = 24 hours 1 minute = 4 seconds 
 
 15 degrees = 1 hour 15 seconds = 1 second 
 
 1 degree = 4 minutes 1 second = .0666 + second 
 
 15 minutes = 1 minute 
 
 THE METRIC SYSTEM 
 
 The fundamental unit of the metric system is the meter, which is the unit 
 of length and which was intended to be equal in length to TTnn&rnrff part of the 
 quadrant of the earth, or the distance from the equator to the pole, measured 
 on the meridian of Paris, France. Owing to imperfection in instruments, etc., 
 the length of the arc of 10 that was used in determining the length of the 
 quadrant was not measured with absolute accuracy, so that the meter, as well as 
 the units derived from it, is not of exactly the dimensions it was intended to be. 
 Since its adoption by France in the law of June 22, 1799, the use of the system 
 has become world wide, until the only countries of commercial importance 
 where it is not now in general use are China, Great Britain, Japan, Russia, 
 and the United States. 
 
 While Congress has authority, under Article I of the Constitution, to compel 
 the use of the metric system, it has never done so, contenting itself, under the 
 act of July 28, 1866, with legalizing its use and establishing the relations 
 between the units of the ordinary and the metric systems. By Executive 
 Order of April 5, 1893, the yard and the avoirdupois pound may now be derived 
 from the meter and the kilogram. The ratios established by Congress are 
 1 meter = 39.37 in., and 1 kilogram = 2. 2046 Ib. avoirdupois. As these values 
 are less than the true ones, the yard and the pound thus derived are longer 
 and heavier, respectively, than the true yard and the true pound. 
 
 The names applied to the various denominations of the system are not 
 always those used in France, but are frequently adapted from the names of 
 
WEIGHTS AND MEASURES 11 
 
 the measures that the metric system has displaced. In almost all of these 
 countries the old and replaced systems are still in use, the extent of this usage 
 being, apparently, in inverse ratio to the commercial importance of the country 
 and to the length of time during which the metric system has been in force. 
 
 The original standards of the metric system were a meter and a kilogram 
 of platinum deposited in the Palais des Archives, Paris, at the time of the 
 formal adoption of this system in France. At the second meeting of what is 
 now the International Bureau of Weights and Measures, held in Paris, Sept. 24, 
 1872, the representatives of thirty nations present decided that the standards 
 of the system should be made of an alloy of 90% platinum and 10% iridium, 
 because of its hardness, fine grain, and ability to withstand the action of acids. 
 A number of meters and kilograms were made and the ones corresponding to 
 the original platinum standards are deposited in the permanent headquarters 
 of the bureau, near Paris. Each nation subscribing to the expenses of the 
 bureau received two copies each of the meter and the kilogram, which are 
 known, respectively, as the national prototype meter and kilogram. These are 
 of the same materials and accuracy as the originals. The United States 
 prototypes were received by the President on Jan. 2, 1890, and one of each was 
 selected as a reference standard, while the other is used for working purposes. 
 
 The unit of weight of the metric system is the kilogram, originally intended 
 to be the weight, in vacuuo, of 1 cubic decimeter of pure, distilled water at the 
 temperature of its maximum density, 4 C. (39.3 P.), with the barometer at 
 760 millimeters (29.92 in.) of mercury. As with the meter, this relation is 
 not exact, owing to errors in the original standard. 
 
 The unit of capacity is the liter, which was designed to be the volume of 
 1 kilogram of pure water under the conditions just named. 
 
 The unit of area for land measure is the are, a square 10 meters on the side. 
 Among engineers, superficial dimensions are usually expressed in square centi- 
 meters, square meters, and square kilometers. 
 
 Cubic dimensions are expressed in cubic centimeters, cubic meters, etc. 
 
 Multiples of the various units of the metric system are obtained by prefixing 
 to the names of the units (meter, gram, and liter) the Greek words, deka or 
 deca (10), hekto or heclo (100), kilo (1,000), and myria (10,000). The sub- 
 multiples or divisions are obtained by prefixing to the names of the units, the 
 Latin words deci tfs), centi ( T fo), and milli ddro). 
 
 METRIC MEASURES OF LENGTH 
 
 1 millimeter mm .001 
 
 10 millimeters =1 centimeter. . .cm .01 
 
 10 centimeters. =1 decimeter dm .1 
 
 10 decimeters = 1 meter m 
 
 10 meters =1 dekameter. . . Dm 10 
 
 10 dekameters =1 hektometer . .Hm 100 
 
 10 hektometers =1 kilometer Km l.OCK 
 
 10 kilometers =1 myriameter . . Mm 10,001 
 
 Of these denominations the ones commonly employed are the millimeter, 
 centimeter, meter, and kilometer. The United States Coast and Geodetic 
 Survey, since 1884, has used the value 1 m.= 39.370432 in.; the legal equiva- 
 ent by Act of Congress is 1 m. =39.37 in. 
 
 METRIC MEASURES OF SURFACE 
 
 1 sq. millimeter sq. mm., or mm.* .000001 
 
 100 sq. millimeters. = 1 sq. centimeter . .sq. cm., or cm. 2 
 100 sq. centimeters. = 1 sq. decimeter. . .sq. dm., or dm. 2 
 
 100 sq. decimeters . = 1 sq. meter sq. m., or m. 2 
 
 100 sq. meters = 1 sq. dekameter . .sq. Dm., or Dm. 2 
 
 100 sq. dekameters. = 1 sq. hektometer. . sq. Hm., or Hm. 2 10,000 
 
 100 sq. hektometers = 1 sq. kilometer. . . sq. Km., or Km. 2 l-OOO.OOl 
 100 sq. kilometers. . = 1 sq. myriameter .sq. Mm., or Mm. 2 100,000,001 
 
 The square meter is sometimes known as the centare; the square dekameter 
 as the are; and the square hektometer as the hectare. Farm measurements 
 are generally given in hectares. Engineers use the square millimeter, square 
 centimeter, square meter, and square kilometer. The other denominations 
 are but little used. The square meter, or centare, is a little larger than 
 1 sq. yd.; the hektometer, or hectare, is about 2* A. 
 
12 WEIGHTS AND MEASURES 
 
 METRIC MEASURES OF WEIGHT 
 
 1 milligram mg .001 
 
 10 milligrams =1 centigram ... eg .01 
 
 10 centigrams =1 decigram . . . . dg .1 
 
 10 decigrams =1 gram g 1 
 
 10 grams =1 dekagram . . . Dg 10 
 
 10 dekagrams =1 hektogram . .Hg 100 
 
 10 hektograms =1 kilogram. . . .Kg 1,000 
 
 10 kilograms =1 myriagram. . Mg 10,000 
 
 10 myriagrams =1 quintal Q 100.000 
 
 10 quintals =1 tonne T 1,000,000 
 
 The denominations in common use are the milligram, centigram, gram, 
 
 kilogram (commonly called kilo), and tonne. Commercially, the kilogram is 
 
 divided into halves, quarters, etc. As near as may be determined, 1 Kg. 
 
 = 2.2046223 Ib. avoirdupois. The ratio legalized by Congress is 1 Kg. = 2.20-46 
 
 Ib. avoirdupois. 
 
 METRIC MEASURES OF VOLUME 
 
 1 cubic millimeter cu. mm., or mm. 8 . . .000000001 
 
 1,000 cubic millimeters =1 cubic centimeter. c.c., cc. 3 , or cu. cm.. .000001 
 
 1,000 cubic centimeters = 1 cubic decimeter, .cu. dm., or dm. 3 001 
 
 1,000 cubic decimeters = 1 cubic meter cu. m., or m. 3 1 
 
 The cubic millimeter and cubic decimeter are rarely used. The cubic 
 centimeter is a common unit with chemists, and engineers use the cubic meter 
 in the same way as the cubic yard. 
 
 METRIC MEASURES OF CAPACITY 
 
 1 milliliter ' ml /I 7 " 1 ; .001 
 
 10 milliliters =1 centiliter cl .01 
 
 10 centiliters =1 deciliter dl .\ ' .1 
 
 10 deciliters. . . f =1 liter 1 v" * * 1 
 
 10 liters . = 1 dekaliter, or Dl 10 
 
 1 centistere cs. 
 
 10 dekaliters =1 hektoliter, or HI 100 
 
 1 decistere ds. 
 
 10 hektoliters =1 kiloliter, or Kl 1,000 
 
 1 stere s. 
 
 10 kiloliters =1 myrialiter, or Ml 10,000 
 
 1 dekastere Ds. 
 
 The liter and the milliliter (but in its equivalent form the cubic centimeter) 
 are in use among chemists. Engineers use the liter and kiloliter, the latter 
 being called by its equivalent name, cubic meter. Groceries and the like are 
 purchased by the liter, half liter, and quarter liter, instead of by the decimal 
 parts of a liter. Grain is measured by the stere and by the decistere, the 
 latter being called hektoliter. 
 
 Congress has not established a ratio between the units of the measures of 
 capacity of the metric and ordinary systems. 
 
 EQUIVALENTS OF VOLUME, WEIGHT OF WATER, AND CAPACITY 
 
 Distilled water at 4 C. (39.3 F.) and 760 mm. (29.92 in.) pressure. 
 
 Volume Weight Capacity Ratio 
 
 1 cubic centimeter =1 gram =1 milliliter 1 
 
 10 cubic centimeters =1 decagram =1 centiliter 10 
 
 100 cubic centimeters =1 hektogram =1 deciliter 
 
 1 cubic decimeter =1 kilogram =1 liter 1.000 
 
 10 cubic decimeters =1 myriagram =1 dekaliter 10,000 
 
 100 cubic decimeters =1 quintal =1 hektoliter 100,000 
 
 1 cubic meter/ =1 tonne =1 stere 1,000,000 
 
WEIGHTS AND MEASURES 
 
 13 
 
 LIQUID MEASURE 
 ml. X. 008454 = gi. 
 L XI. 066717 -qt. 
 I.X. 264 179 = gal. 
 HI. X 26.417916 = gal. 
 HI. X. 838664 = bbl. 
 s.X 264.179164 = gal. 
 s.X 8.386640 = bbl. 
 
 MEASURES OF LENGTH 
 mm. X. 039370 = in. 
 cm. X. 393704 = in. 
 cm. X. 032809 = ft. 
 m. X 39. 370432 = in. 
 m. X 3.280869 = ft. 
 m. XI. 093623 = yd. 
 m. X. 000621 = mi. 
 Km. X 3,280.869300 = ft. 
 Km. X 1,093.623100 = yd. 
 Km. X. 621375 = mi. 
 
 MEASURES OF WEIGHT 
 mg.X. 015432 = gr. 
 eg. X. 154324 = gr. 
 eg. X. 000353 = oz. 
 g. XI 5.432356 = gr. 
 g. X. 035274 = oz. 
 g. X. 002205 = lb. 
 Kg. X 35.273957 = oz. 
 Kg. X 2.204622 = lb. 
 Kg. X. 001 102 = short T. 
 tonnes X 1.102311 = short T. 
 tonnes X. 984206 = long T. 
 RELATION OF WEIGHT AND VOLUME 
 
 OF WATER 
 
 cu. cm. X 15.432356 = gr. 
 l.X 2.204622 = lb. (avoir.) 
 cu.m.X 2,204.622341 = lb. 
 cu. m.X 264. 179164 = gal. 
 cu.m.X 8.386640 = bbl. 
 cu. m.X 1.102311 = short T. 
 cu. m. X .984206 = long T. 
 Kg. X 1.056717 = qt. 
 
 CONVERSION FACTORS 
 
 METRIC TO UNITED STATES 
 
 RELATION OF WEIGHT AND VOLUME OF 
 
 WATER Continued 
 Kg. X. 264179 = gal. 
 Kg. X 61.025387 = cu. in. 
 Kg. X. 035316 = cu. ft. 
 
 DRY MEASURE 
 I.X. 908107 = qt. 
 I.X. 028378 = bu. 
 HI. X 22.702686 = gal. 
 HI. X 2.837836 = bu. 
 s.X 227.026857 = gal. 
 s.X 28.378357 = bu. 
 
 MEASURES OF VOLUME 
 ml. X. 061025 = cu. in. 
 cl.X. 610254 = cu. in. 
 dl.X 6. 1025^9 = cu. in. 
 l.X 61. 025387 = cu. in. 
 l.X.035316 = cu. ft. 
 
 ^' } X 3.531562 = cu. ft. 
 ?- L )x 35.315617 = cu. ft. 
 
 S. J 
 
 JP' } XI. 307986 -cu. yd. 
 
 SQUARE MEASURE 
 sq. mm. X. 001550 = sq. in. 
 sq. cm. X.I 55003 = sq. in. 
 sq. m.X 10.764104 = sq. ft. 
 sq. m. XI. 196012 = sq. yd. 
 sq. m.X. 000247 = A. 
 hectares X 2.471098 = A. 
 hectares X .003861 = sq. mi. 
 sq. Km. X 247. 109816 = A. 
 sq. Km. X. 386109 = sq. mi. 
 CUBIC MEASURE 
 cu. cm. X. 061025 = cu. in. 
 cu. dm. X 61.025387 = cu. in. 
 cu. dm. X. 035316 = cu. ft. 
 cu. m. X 35.315617 = cu. ft. 
 cu. m. X 1. 307986 = cu. yd. 
 
 MISCELLANEOUS CONVERSION FACTORS 
 
 cm. per sec. X 1.968522 = ft. per min. 
 cu. cm. per sec. X. 015851 = gal. per 
 
 min. 
 
 cm. per m.X. 12 = in. per ft. 
 m. per Km. X. 10 = ft. per 100 ft. 
 m. per Km. X 5.28 = ft. per mi. 
 m. (depth) per hectare XI. 327697 
 
 = A.-ft. 
 
 Kg. per m.X.671963 = lb. per ft. 
 Kg. per sq. cm. X 14.223084 = Ib. per 
 
 sq. in. 
 
 Kg. per sq. cm. X .967557 = atmos- 
 pheres (14.7 Ib.) per sq. in. 
 Kg. per sq. m.X. 204812 = lb. per sq. 
 
 ft. 
 g. per cu. cm. X. 036126 = lb. per cu. 
 
 in. 
 Kg. per l.X 8.345217 = lb. per gal. 
 
 (liquid) 
 Kg. per cu. m. X .062426 = Ib. per cu. 
 
 ft. 
 
 Kg. per cu. m. X .008345 = Ib. per 
 
 gal. (liquid) 
 francs (fr.) per m.X. 176386 = dollars 
 
 (dol.) per yd. 
 
 fr. per Km. X. 310441 = dol. per mi. 
 fr. per hectare X. 078063 = dol. per A. 
 fr. per Kg. X .087498 = dol. per Ib. 
 fr. per tonne X. 174996 = dol. per T. 
 
 (short) 
 fr. per l.X. 182547 = dol. per qt. 
 
 (liquid) 
 fr. per l.X. 730187 ='dol. per gal. 
 
 (liquid) 
 fr. per 1. X .212419 = dol. per qt. 
 
 (dry) 
 
 fr. per HI. X. 067974 = dol. per bu. 
 fr. per cu. m.X. 147478 = dol. per cu. 
 
 mik's (mk.) per m.X. 217717 = dol. 
 
 per yd. 
 mk. per Km. X. 383182 = dol. per mi. 
 
14 
 
 WEIGHTS AND MEASURES 
 MISCELLANEOUS CONVERSION FACTORS Continued 
 
 mk. per hectare X .096354 = dol. per A. 
 mk. per Kg. X. 108000 = dol. per Ib. 
 mk. per tonne X. 2 16001 = dol. per T. 
 
 (short) 
 mk. per l.X. 225321 = dol. per qt. 
 
 (liquid) 
 mk. per l.X. 901282 = dol. per gal. 
 
 (liquid) 
 mk. per l.X. 262194 = dol. per qt. 
 
 (dry) 
 mk. per HI. X .083902 = dol. per bu. 
 
 mk. per cu. m. X.I 82036 = dol. per 
 
 cu. yd. 
 
 m.-Kg. X 7.233077 = ft.-lb. 
 m.-Kg.X. 009297 = B. T. U. 
 joules X .737308 = ft.-lb. 
 Kw.X 1.341113 = H. P. 
 cheval-vapeurX. 986329 = H. P. 
 PonceletX 1.315105 = H. P. 
 cal.X 3.968320 = 6. T. U. 
 cal. X 3,087.3531 12 = ft.-lb. 
 Gravity (Paris) = 980.90 cm. per sec. 
 
 LIQUID MEASURE 
 gi. XI 18.290925 = ml. 
 qt.X. 946327 = 1. 
 gal. X 3.785310 = 1. 
 gal. X. 037853 = HI. 
 gal. X. 003785 = s. 
 bbl.X 1.192373 = HI. 
 bbLX. 119237 = s. 
 RELATION OF WEIGHT AND VOLUME 
 
 OF WATER 
 
 gr.X. 064799 = cu. cm. 
 Ib. (avoir.) X .453592 = 1. 
 Ib.X. 000454 = cu. m. 
 gal. X. 003785 = cu. m. 
 bbl.X. 119237 = cu. m. 
 short T.X.907185 = cu. m. 
 long T.X 1.016047 = cu. m. 
 qt.X. 946327 = Kg. 
 gal.X3.785310 = Kg. 
 cu. in. X. 01 6387 = Kg. 
 cu. ft.X 28.3 16094 = Kg. 
 
 MEASURES OF LENGTH 
 in. X 25.399780 = mm. 
 in. X 2.539978 = cm. 
 in. X. 025400 = m. 
 ft. X 30.4797260 = cm. 
 ft. X. 304797 = m. 
 ft. X. 000305 = Km. 
 yd. X. 914391 792 = m. 
 yd. X. 00091 4 = Km. 
 mi. X. 001609 = m. 
 mi. X 1.609330 = Km. 
 
 MEASURES OF WEIGHT 
 gr.X 64.798918 = mg. 
 gr.X 6.479892 = eg. 
 gr.X. 064800 = g. 
 oz. X 2,834.952670 = eg. 
 oz.X 28.349527 = g. 
 oz.X. 028350 = Kg. 
 Ib.X 453.592428 = g. 
 
 UNITED STATES TO METRIC 
 
 MEASURES OF WEIGHT Continued 
 Ib.X. 453592 = Kg. 
 short T.X 907. 184856 = Kg. 
 short T.X. 907 185 = tonnes 
 long T. X 1.016047 = tonnes 
 DRY MEASURE 
 qt.Xl. 101191 = 1. 
 gal. X. 044048 = HI. 
 gal. X. 004405 = s. 
 bu.X35.238122 = l. 
 bu.X. 352381 = HI. 
 bu.X. 035238 = s. 
 
 MEASURES OF VOLUME 
 cu. in. X 16.386623 = ml. 
 cu. in. XI. 638662 = cl. 
 cu. in. X.I 63866 = dl. 
 cu. in. X. 016387 = 1. 
 cu. ft.X 28.316094 = 1. 
 
 cu. ft.X. 283161 ={ gj' 
 cu. ft.X. 028316 ^{f 1 ' 
 
 cu. yd. X. 764535 ={f" 1 ' 
 
 SQUARE MEASURE 
 pq. in.X645.148422 = sq. mm. 
 sq. in. X 6.451484 = sq. cm. 
 sq. ft.X. 092901 =sq. m. 
 sq. yd.X.836112 = sq. m. 
 A. X 4,046.787846 = sq. m. 
 A. X .404679 = hectares 
 sq. mi. X 258.994161 = hectares 
 A. X. 004047 = sq. Km. 
 sq. mi. X 2.589942 = sq. Km. 
 
 CUBIC MEASURE 
 cu. in. X 16.386623 = cu. cm. 
 cu. in. X. 016387 = cu. dm. 
 cu. ft. X 28.316094 = cu. dm. 
 cu. ft. X.028316 = cu. m. 
 cu. yd. X. 764534 = cu. m. 
 
 MISCELLANEOUS CONVERSION FACTORS 
 
 ft. per min.X. 507996 = cm. per sec. 
 
 gal. per min. X 63. 088498 = cu. cm. 
 per sec. 
 
 in. per ft.X 8.333333 = cm. per m. 
 
 ft. per 100 ft.X 10.00 = m. per Km. 
 
 ft. per mi. X. 189394 = m. per Km. 
 
 A.-ft.X.753183 = m. (depth) per hec- 
 tare 
 
 Ib. per ft.X 1.488177 = Kg. per m. 
 
 Ib. per sq. in. X. 070309 = Kg. per sq. 
 cm. 
 
 atmospheres (14.7 Ib.) X 1.033539 
 
 = Kg. per sq. cm. 
 Ib. per sq. ft.X 4.882535 = Kg. per 
 
 sq. m. 
 ib. per cu. in. X 27.680653 = g. per cu. 
 
 cm. 
 Ib. per gal. (liquid) X.I 19829 = Kg. 
 
 per 1. 
 Ib. per cu. ft.X 16.018897 = Kg. per 
 
 cu. m. 
 
WEIGHTS AND MEASURES 
 
 15 
 
 Ib. 
 
 = Kg. per cu. m. 
 
 dol. per yd. X 5.669377 = fr. per m. 
 dol. per mi. X 3.221224 = fr. per Km. 
 dol. per A. X 12.810239 = fr.per hectare 
 dol. per Ib.X 11.428835 = fr. per Kg. 
 dol. per T.X 5.714417 = fr. per tonne 
 dol. per qt. (liquid) X 5.478052 = fr. 
 
 MISCELLANEOUS CONVERSION FACTORS Continued 
 gal. (liquid) XI 19.829666 dol. per Ib.X 9.259228 = mk. per Kg. 
 dol. per TX4.629614=mk. per tonne 
 dol. per qt. (liquid) X 4.4381 13 = mk. 
 
 perl, 
 dol. per gal. (liquid) XI. 109530 = mk. 
 
 per 1. 
 dol. per qt. (dry) X 3.813588 = mk. 
 
 per 1. 
 dol. per bu. X 11.918671 = mk. per 
 
 HI. 
 dol. per cu. yd. X 5.4934 13 = mk. per 
 
 cu. m. 
 
 ft.-lb.X. 138254 = m.-Kg. 
 ft.-lb. X 1.356284 = joules 
 ft.-lb.X. 000324 = cal. 
 H. P. X. 745649 = Kw. 
 H. P.X1.013861 = cheval-vapeur 
 H. P. X. 760396 = Poncelet. 
 B. T. U.X 107.561415 = m.-Kg. 
 B. T.U.X. 251995 = cal. 
 
 dol. per gal. (liquid) X 1.369513 = fr. 
 
 dol. per qt. (dry) X 4. 707659 = fr. 
 per 1. 
 
 dol. per bu.X 14.71 1434 = fr. per HI. 
 
 dol. per cu. yd. X 6.780771 = fr. per 
 cu. m. 
 
 dol. per yd.X4.593124 = mk. per m. 
 
 dol. per mi.X2.609677 = mk. per Km. 
 
 dol. per A. X 10.378394 = mk. per hec- 
 tare 
 One dm. = 3.937043 in.; 1 Dk. = 32.808693 ft. or 10.936231 yd.; 1 Hm. 
 
 = 109.362310 yd.; 1 Mm. = 6.213750 mi. The U. S. 5c. piece, or nickel, is 
 
 slightly over 2 cm. across. 
 
 One sq. dm. = 15.500309 sq. in.; 1 sq. Dm. = 119.601151 sq. yd.; 1 sq. Mm. 
 
 = 38.610909 sq. mi., or a little more than 1 township. 
 
 One Q. = 220.462230 Ib.; 1 Mg. = 22.046223 Ib.; 1 Hg. = . 220462 Ib.; the 
 
 Dg. = .35273957 oz. 
 
 The United States 50c. silver coin weighs 12.5 g.; the 25c. coin, 6.25 g.; 
 
 and the lOc. coin, 2.5 g. These weights have been assigned by congressional 
 
 enactment. 
 
 WEIGHTS AND MEASURES OF GREAT BRITAIN AND 
 COLONIES 
 
 The measures of length, of surface, of weight, and of volume, while not 
 absolutely identical, are, for all practical purposes, the same as those of the 
 United States. It should be noted, however, that the United States long ton 
 of 2,240 Ib. is used in Great Britain and all of her colonies, except Canada, 
 where the ton has been fixed by statute at 2,000 Ib. The quarter of 28 Ib. and 
 the stone of 14 Ib. are used to some extent. 
 
 The chief difference between the measures of Great Britain and the United 
 States is to be found in the sizes of the units of dry and liquid measure. The 
 United States liquid gallon is, by Act of Congress, equal to 231 cu. in., and the 
 United States bushel is, by similar enactment, equal to 2,150.42 cu. in., no 
 reference being made to the weight of water contained in either of the measures. 
 They were founded upon the former British wine gallon and the Winchester 
 struck (level full) bushel, respectively, which have not been current in Great 
 Britain since 1825, when they were replaced by the imperial gallon and bushel. 
 By Act of Parliament, the imperial gallon is the volume of 10 Ib. of pure water 
 at 62 F., weighed against brass weights in air at the same temperature and at 
 a barometric pressure of 30 in. of mercury. The imperial bushel is the volume 
 of 80 Ib. of pure water under the preceding conditions. From this, it is apparent 
 that the imperial gill, pint, quart, and gallon, are the same in both the liquid 
 and dry measure. 
 
 Using the value for the weight of 1 cu, ft. of water, 62.28827 Ib., the volume 
 of the imperial gallon is found to be 277.4203 cu. in., and of the imperial btfshel, 
 2,219.3613 cu. in. 
 
 IMPERIAL MEASURE, BOTH LIQUID AND DRY 
 
 Volume Weight of Water 
 
 Cubic Inches Pounds 
 
 8.6694 = .3125 
 
 = 34.6775 = 1.2500 
 
 = 69.3551 = 2.5000 
 
 = 277.4203 = 10.0000 
 
 = 554.8403 = 20.0000 
 
 ...=2,219.3613 =80.0000 
 
 * &* 
 
 4gi.- 
 2pt 
 4 qt 
 
 = 
 
 pt 
 
 qt. 
 
 gal 
 
 . . . . 
 
 2 gal. 
 4pk 
 
 .....= 
 
 e , 
 pk 
 bu 
 
 
16 
 
 WEIGHTS AND MEASURES 
 
 One imp. gal. equals 1.20085 U. S. liquid gal., and 1 imp. bu. equals 1.03206 
 U. S. bu, Likewise, 1 U. S. liquid gal. equals .83267 imp. gal., and 1 U. S. 
 bu. equals .96894 imp. bu. 
 
 MONEY 
 
 UNITED STATES CURRENCY 
 
 Denominations 
 10 mills = 1 cent 
 10 cents = 1 dime 
 10 dimes = 1 dollar 
 10 dollars =1 eagle 
 
 Mill Cent Dime Dol. Eagle 
 
 1= .1= .01= .001= .0001 
 
 10= 1 = .1 = .010= .0010 
 
 100= 10 = 1.0 = .100= .0100 
 
 1,000= 100 = 10.0 = 1.000= .1000 
 
 10,000=1,000 =100.0 =10.000=1.0000 
 
 STANDARD UNITED STATES COINS 
 
 Gold 
 
 Silver 
 
 Denomination 
 
 Value 
 
 Weight 
 Grains 
 
 Denomination 
 
 Value 
 
 Weight 
 Grains 
 
 *Dollar 
 
 $1 00 
 
 258 
 
 *Trade dollar 
 
 $1 00 
 
 420 
 
 Quarter-eagle 
 Three-dollar piece . . 
 Half-eagle 
 
 Eagle 
 
 2.50 
 3.00 
 5.00 
 1000 
 
 64.5 
 
 77.4 
 129.0 
 2580 
 
 Standard silver dol- 
 lar 
 Half-dollar 
 
 1.00 
 .50 
 25 
 
 412.5 
 192.9 
 96 45 
 
 Double eagle 
 
 20.00 
 
 516.0 
 
 Dime 
 
 10 
 
 38 58 
 
 
 
 
 
 
 
 Fineness expresses the proportion of pure metal in 1,000 parts; thus, 
 "900 fine" means that 900 of every 1,000 parts are pure metal. Fineness of 
 U. S. coins = 900 pure metal, 100 alloy; alloy of gold coin is copper or copper 
 and silver, but in no case shall silver exceed one-tenth of total alloy. Alloy 
 of silver coin is copper. 
 
 Weight 
 Piece Grains Contents 
 
 5-cent (nickel) 77.16 75% copper, 25% nickel 
 
 *3-cent 30 75% copper, 25% nickel 
 
 *2-cent 66 95% copper, 5% tin and zinc 
 
 1-cent (copper) 48 95% copper, 5% tin and zinc 
 
 CURRENCY OF GREAT BRITAIN 
 
 Denominations far. d. s. 
 
 4 farthings (far.) =1 penny d 1 = .25= .0208 = .0010 
 
 12 pence =1 shilling s 4=5 1.00= .0833= .0042 
 
 20 shillings =1 pound 48jfc 12.00= 1.0000= .0500 
 
 21 shillings =1 guinea 960 = 240.00 = 20.0000 = 1.0000 
 
 The unit is the pound sterling, valued at $4.8665. English silver is .925 fine; 
 gold, .916|. The larger silver coins are the shilling, the florin or 2s., the 
 crown or 5s., and the half-crown or 2s. 6d. The gold coins are the sovereign 
 or pound, and the half-pound, or 10s. 
 
 Great Britain United States 
 
 1 pound = $4.8665 
 
 1 shilling = .243325 
 
 1 penny = .0202771 
 
 *No longer coined. 
 
 United States Great Britain 
 
 1 cent = .49312 pence 
 
 1 dollar. . . =4 sh. 1.312 pence 
 
 1 dollar =4.109333 shillings 
 
 1 dollar = .205466 pound 
 
WEIGHTS AND MEASURES 17 
 
 FOREIGN MONETARY SYSTEMS AND EQUIVALENTS IN UNITED 
 STATES GOLD 
 
 Argentine 100 centavos = 1 peso 
 
 Austria 100 heller = 1 krone 
 
 Belgium 100 centimes = 1 franc 
 
 Bolivia 100 centavos = 1 boliviano . . 
 
 Bosnia . . 
 
 Brazili 
 
 Bulgaria 
 
 Canada 
 
 Chilei 
 
 China 2 . . 
 
 Colombia 
 
 Costa Rica 
 
 Cuba' 
 
 Denmark ........ 
 
 Ecuador 
 
 Egypt* 
 
 France 
 
 Germany 
 
 Great Britain 
 
 Greece 
 
 Guatemala 1 
 
 Holland. 
 
 100 heller = 1 krone 
 
 1,000 reis = l milreis 
 
 . 100 stotmki = 1 leva 
 
 .100 cents = 1 dollar 
 
 . 100 centavos = 1 peso 
 
 .100parts=l yuan 
 
 . 100 centavos = 1 peso 
 
 . 100 centavos = 1 colon 
 
 . 100 centavos= 1 peso 
 
 . 100 ore = 1 krona 
 
 . 100 centavos = 1 sucre 
 
 . 40 paras = 1 piastre 
 
 . 100 centimes = 1 franc 
 
 . 100 pfennige = 1 mark , 
 
 . 20 shillings = 1 pound 
 
 . 100 lepta = 1 drachma 
 
 . 100 centavos = 1 peso 
 
 100 cents =1 gulden... 
 
 Honduras 1 100 centavos = 1 peso 
 
 India 5 16 annas = 1 rupee. . . 
 
 100 centesimi = 1 lira 
 
 100 sen = 1 yen 
 
 100 centavos = 1 peso 
 
 100 heller =1 krone 
 
 100 cents = 1 gulden 
 
 100 centavos = 1 peso 
 
 100 ore = l krona 
 
 100 centavos = 1 balboa 
 
 100 centavos = 1 peso 
 
 20 chahi = 1 kran 
 
 Isol 
 
 1 peso. 
 
 Uruguay 7 
 
 Venezuela 
 
 Italy 
 
 Japan 
 
 Mexico 
 
 Montenegro 
 
 Netherlands 
 
 Nicaragua 
 
 Norway 
 
 Panama 
 
 Paraguay 
 
 Persia 8 
 
 Peru 100 centavos 
 
 Philippine Islands 100 centavos 
 
 Porto Rico 100 cents = 1 dollar. . . . 
 
 Portugal 1 1,000 reis = 1 milreis 
 
 Roumania 100 bani = 1 leu 
 
 Russia 100 kopecs = 1 rouble 
 
 Salvador 1 100 centavos = 1 peso 
 
 Servia 100 paras = 1 dinar 
 
 Spain 6 100 centavos = 1 peseta 
 
 Sweden 100 ore = 1 krona 
 
 Switzerland 100 centimes = 1 franc 
 
 Turkey 40 paras= 1 piastre 
 
 . 100 centesimos = 1 peso 
 
 . 100 centimes = 1 bolivar 
 
 $ .9647 
 .2026 
 .1929 
 .3893 
 .2026 
 .5463 
 .1929 
 1.0000 
 .3649 
 .4772 
 1.0000 
 1.0000 
 1.0000 
 .2679 
 .4866 
 .0494 
 .1929 
 .2381 
 4.8665 
 .1929 
 .3998 
 .4020 
 .3998 
 .3244 
 .1929 
 .4984 
 .4984 
 .2026 
 .4020 
 .3998 
 .2679 
 1.0000 
 .9646 
 .1704 
 .4866 
 .5000 
 1.0000 
 1.0804 
 .1929 
 .5145 
 .3998 
 .1929 
 .1929 
 .2679 
 .1929 
 .0439 
 .9647 
 
 .1929 
 
 1 The actual currency is either depreciated or inconvertible paper of fluctu- 
 ating value. The values given are for the standard gold coin. 
 
 2 This is the new coinage. The former tael is still largely used. Its value 
 differs from town to town and ranges between $.599 at Shanghai to $.660 at 
 Takau. The Haikwan,/or tael in which customs are payable, is valued at 
 $.667. The Hong Kong and British dollar, valued at $.431, and the Mexican 
 dollar, valued at $.434, circulate widely. 
 
 3 Cuba has no national currency, gold, silver, or paper, relying upon the 
 money of the United States, Great Britain, and Spain for its needs. 
 
 4 The actual standard is the pound sterling of Great Britain. 
 6 Fifteen rupees equal 1 pound sterling. 
 
 6 The values given are for the gold kran and peseta respectively. The 
 actual currency is silver circulating above its metallic value. 
 
 7 The value given is for the silver peso. While under the gold standard, 
 Uruguay has never coined this metal. The standard value of the gold peso 
 is $1.0342. 
 
18 
 
 MATHEMATICS 
 VALUES OF FOREIGN COINS 
 
 Alexander, Bulgaria 
 
 $ 3.8589 
 4 8236 
 
 Groschen, Prussian Poland. 
 Gulden Baden 
 
 $ .0240 
 .4000 
 
 Boliviano, Bolivia 
 Condor Chile 
 
 .9700 
 7 2995 
 
 Imperial, Russia 
 Jirmilik Turkey 
 
 7.7183 
 .8000 
 
 Condor, Colombia and 
 Ecuador 
 
 9.6470 
 
 Kreutzer, Bavaria 
 Libra, Colombia 
 
 .0067 
 4.8665 
 
 
 2 3819 
 
 Libra Ecuador 
 
 4.9429 
 
 
 10 8043 
 
 Libra, Peru 
 
 4.8665 
 
 Crown, Sicily 
 Crown, Spain 
 
 .9600 
 1.9500 
 
 Lira, Turkey 
 Maria Theresa Dollar, Ab- 
 
 4.3960 
 
 Dos, Spain 
 
 3.7084 
 
 yssinia 
 
 .4139 
 
 
 14 5000 
 
 
 3 3000 
 
 Doubloon Chile 
 
 3.6497 
 
 Menelik Dollar, Abyssinia. . 
 
 .4139 
 
 Doubloon, New Grenada. . . 
 Doubloon Spain Mexico 
 
 15.3400 
 15.6500 
 
 Mohur, India 
 Napoleon, France 
 
 7.1050 
 3.8400 
 
 Ducat, Austria, Bohemia, 
 Hamburg, Hanover 
 Ducat Holland . . 
 
 2.2800 
 2.2826 
 
 Peseta, Peru 
 Peso fuerte, Peru. : 
 Pistole, Rome 
 
 .0973 
 .4866 
 3.3700 
 
 
 1.1100 
 
 Pistole Spain 
 
 3 9000 
 
 Ducat, Sweden 
 
 2.2000 
 
 Pound, Egypt 
 
 4.9429 
 
 Escudo, Chile 
 Florin, Austria-Hungary . . 
 Florin, Hanover (gold) . . 
 Florin, Hanover (silver) . . . 
 Florin, Holland 
 Florin Prussia 
 
 1.8248 
 1.9290 
 1.6600 
 .5600 
 .4019 
 .5500 
 
 Real, Peru 
 Rial (Azizi), Morocco 
 Rial (Hassani), Morocco . . 
 Rupee, Persian 
 Sou, France . 
 Sovereign England 
 
 .0486 
 .4000 
 .4663 
 .3750 
 .0100 
 4 8665 
 
 Florin, Silesia 
 Fuange, Siam . . 
 
 .4800 
 .0600 
 
 Toman, Persia 
 
 1.7046 
 
 MATHEMATICS 
 
 MATHEMATICAL AND OTHER COMMONLY USED SIGNS 
 AND ABBREVIATIONS 
 
 = plus, or addition 
 
 = minus, or subtraction 
 
 = plus or minus 
 
 = multiplication 
 
 = division 
 
 = ratio 
 
 f proportion 2 : 3 : : 4 : 6 
 = < or 2:3 = 4:6 shows 
 
 I that 2 is to 3 as 4 is to 6 
 = equality 
 
 V 
 
 = 
 
 square root , 
 
 * 
 
 = 
 
 cube root,, etc. 
 
 , V3 ' 
 
 = 
 
 square root of 3 
 
 ^ 
 
 = 
 
 cube root of 5 
 
 . 72 
 
 == 
 
 7 squared 
 
 8 3 
 
 = 
 
 8 cubed 
 
 a 
 ft 
 
 - 
 
 a/b or c-T-6 
 
 
 _ 
 
 therefore, or hence 
 
 8>7 
 
 = 
 
 8 is greater than 7 
 
 3<5 
 
 n= 
 
 3 is less than 5 
 
 D 
 
 = 
 
 square 
 
 D' 
 
 = square feet 
 
 D" 
 
 = 
 
 square inches 
 
 = round 
 
 signs of aggregation and 
 denote that the numbers 
 
 = enclosed are to be taken 
 together ; as (a + b) X c 
 = 4+3X5 = 35 
 
 = degrees, arc or thermom- 
 eter 
 
 = minutes or feet 
 
 ' = seconds or inches, 30 40' 
 4" is 30 degrees 40 min- 
 utes 4 seconds; 4' 6" is 
 4 feet 6 inches 
 
 = accents to distinguish let- 
 ters as a', a", a"' and 
 read a prime, a second, a 
 third 
 
 are read a sub 1, a sub , and 
 a-subb 
 
 = a to the two-thirds power, 
 or the Cube root of a 
 squared 
 
 =a to the three halves 
 power, or square root of a 
 cubed 
 
MATHEMATICS 
 
 19 
 
 MATHEMATICAL SIGNS AND 
 
 Z = angle 
 
 L . = right angle 
 
 _L = perpendicular to 
 
 log = logarithm 
 
 log sin ( = logarithmic sine, loga- 
 
 log cos l rithmic cosine 
 
 sin = sine 
 
 cos = cosine 
 
 tan = tangent 
 
 cotan = cotangent 
 
 sec = secant 
 
 cosec = cosecant 
 
 versin = versed sine 
 
 coversin =coversed sine 
 
 TT =pi, or ratio of circum- 
 
 ference of circle to diam- 
 eter, 3.14159265 
 
 g = acceleration due to grav- 
 
 ity =32.16 ft. per sec. 
 
 h, m, s = hours, minutes, seconds, 
 6 h 5 m 4 s is 6 hours, 5 min- 
 utes, 4 seconds 
 
 R, or r = radius 
 
 W, or w == weight 
 
 ABBREVIATIONS Continued 
 
 H. P. 
 G. C. D. 
 B. M. 
 c. o. d. 
 
 oo 
 
 2 
 
 I. H. P. 
 B. H. P. 
 
 A. W. G. 
 
 B.W.'G. 
 
 r. p. m. 
 c. p. 
 
 B. T. U. 
 cal 
 
 kw. or \ 
 K. W. / 
 f. o. b. 
 c. i. f. 
 
 D. C. 
 
 A. C. 
 
 : horsepowei 
 
 = greatest common divisor 
 
 = board measure 
 
 = cash on delivery 
 
 = infinity 
 
 = summation , or the sum 
 of a series of terms 
 
 = indicated horsepower 
 
 = brake horsepower 
 
 = American wire gauge, or 
 Brown & Sharpe 
 
 = Birmingham wire gauge 
 
 = revolutions per minute 
 
 = candlepower, or chem- 
 ically pure 
 
 = British thermal units 
 
 = calories 
 
 = kilowatts 
 
 = free on board 
 
 = cost, insurance, freight; 
 
 i. e., included in cost 
 = direct current 
 = alternating current 
 
 ARITHMETIC 
 
 COMMON FRACTIONS 
 
 To Add Fractions. If the fractions are of the same denominator, add 
 together the numerators only. Thus, | + f + | = =ls- 
 
 If they have different denominators, change them to fractions with common 
 denominators, and proceed as before. Thus, $ + i+f = %%+*$+$$ = %% 
 
 To Subtract Fractions. If the fractions are of the same denominator, 
 subtract the lesser numerator from the greater. Thus, jg fg = i*8 = i- 
 
 If they have different denominators, change them to fractions with common 
 denominators, and proceed as before. Thus, I f = f i ii = A- 
 
 To Multiply Fractions. Multiply the numerators together for the numer- 
 ator, and the denominators for the denominator. Thus, $ X fe XI = T?B = T&- 
 
 To Divide Fractions. Invert the divisor and multiply. Thus, to divide 
 & by f the is inverted, and ^i = &Xf = T s- 
 
 To Reduce Compound Fractions to Simple Fractions. Multiply the integer 
 by the denominator of the fraction, add the numerator for the new numerator, 
 and place it over the denominator. 
 
 EXAMPLE. Reduce 5f to a simple fraction. 
 
 SOLUTION. (5 X 3) +2 = 17, the numerator, the fraction is therefore ty. 
 
 To Reduce Simple Fractions to Compound Fractions. Divide the numera- 
 tor by the denominator, and use the remainder as the numerator of the remain- 
 ing fraction. 
 
 EXAMPLE. Reduce *& to a compound fraction. 
 
 SOLUTION. 9)64(7 
 
 6 3 Compound fraction is 7J 
 
 To Reduce Common Fractions to Decimal Fractions. Annex ciphers to the 
 numerator, and divide by the denominator, and point off as many decimal 
 places in the quotient as there are ciphers annexed. 
 EXAMPLE. Reduce A to a decimal fraction. 
 SOLUTION. 1 6 ) 9.0 (.5 6 2 5 
 
 80. 
 100 
 9_6 
 40 
 
 80 
 80 
 
20 MATHEMATICS 
 
 NOTE. Ciphers annexed to a decimal do not increase its value. 1.13 
 is the same as 1.1300. Every cipher placed between the first figure of a 
 decimal and the point divides the decimal by 10. Thus, .13-7- 10 = .013. 
 
 DECIMALS 
 
 Decimals are fractions that have for their denominators 10 or a power 
 of 10, but the denominator is usually omitted. Thus, .1 = ^; .01 = T J ; .001 
 
 = ^' etc ' .0075 
 
 To Add Decimals. Place whole numbers under whole .6 3 
 
 numbers, tenths under tenths, hundredths under hund- 1.0 6 
 
 redths, etc., and add, placing the decimal point in the sum 1 7.9 3 4 2 
 
 directly under the points above. Thus, 1 9.6 3 1 7 
 
 To Subtract Decimals. Arrange the figures as in addi- 5.9 6 9 7 8 
 tion, and proceed as in simple subtraction. Thus, o.2 8694 
 
 2.6 8 2 8 4 
 
 To Multiply Decimals. Proceed as in 4.6 7 5 3 1 (5 decimal places) 
 
 simple multiplication, pointing off as .053 (3 decimal places) 
 
 many decimal places in the result as there 1402593 
 are decimal places in both multiplicand 2337655 
 and multiplier. Thus, .24779143 (8 decimal places) 
 
 To Divide Decimals. Proceed as in simple division, and point off as many 
 decimal places in the quotient as the number of decimal places in the dividend 
 exceeds those in the divisor. 
 
 EXAMPLE 1. Divide 4.756 by 3.3. 
 
 SOLUTION. 3.3 ) 4.7 5 6 ( 1.4 4 1 2 
 
 33 
 
 EXAMPLE 2. Divide .006 by 20. 
 SOLUTION. 2 ).0 6 (.0 3 
 
 .60 
 
 To Reduce Decimals to Common Fractions. Omit the decimal point and 
 use the figures thus obtained for the numerator. The denominator will be 1 
 with as many ciphers attached as there are places after the decimal point and 
 will always be 10 or some multiple thereof. Reduce the fraction thus obtained 
 to its lowest terms. Thus, in the form of a common fraction, the decimal .025 
 
 -m-.-* FORMD1AS 
 
 The term formula, as used in mathematics and in technical books, may be 
 defined as a rule in which symbols are used instead of words; in fact, a formula 
 -may be regarded as a shorthand method of expressing a rule. 
 
 The well-known rule for finding the indicated horsepower of a steam engine 
 may be stated as follows: 
 
 Divide the continued product of the mean effective pressure, in pounds per 
 square inch, the length of the stroke, in feet, the area of the piston, in square inches, 
 and the number of strokes per minute by 83,000; the result will be the horsepower. 
 
 An examination of the rule will show that four quantities (viz., the mean 
 effective pressure, the length of the stroke, the area of the piston, and the 
 number of strokes) are multiplied together, and the result is divided by 33,000. 
 Hence, the rule might be expressed as follows: 
 
 mean effective pressure ^, stroke 
 {n ^^ pgr squ&re inch) X (in feet) ^ 
 
 area of piston v number of strokes . oo nnn 
 (in square inches) X (per minute) ' ddlUUU 
 
MA THEM A TICS 21 
 
 This expression may be shortened by representing each quantity by a 
 single letter, thus: representing horsepower by the letter H, the mean effective 
 pressure m pounds per square inch by P, the length of the stroke in feet by L 
 the area of the piston in square inches by A, the number of strokes per minute 
 by 2V, and substituting these letters for the quantities that they represent 
 the foregoing expression will reduce to 
 
 H _PXLXAXN 
 
 33,000 ' 
 
 a much simpler and shorter expression. This last expression is called a formula 
 It is customary, however, to omit the sign of multiplication between two 
 or more quantities when they are to be multiplied together, or between a 
 number and a letter representing a quantity, it being always understood that 
 when two letters are adjacent with no sign between them, the quantities 
 represented by these letters are to be multiplied. Bearing this fact in mind 
 the formula just given can be further simplified to 
 
 PL A N 
 
 33,000 
 
 PROPORTION, OR CAUSE AND EFFECT 
 
 Ratio is the relation of one number to another as obtained by dividing one 
 by the other. The ratio of 8 to 4 is 8 -4- 4 = 2. 
 
 Simple proportion is the expression of equality between equal ratios; thus, 
 the ratio of 10 to 5 is 2 and the ratio of 4 to 2 is, also, 2. The relations between 
 these are expressed thus, 10 : 5 : : 4 : 2, or as 10 : 5 = 4 : 2. The equality sign ( = ) 
 being easier to write than the double colon ( : : ) is the form commonly used. 
 
 Proportions may also be expressed as fractions. The preceding ratio, 
 
 10 : 5 = 4 : 2, may be written i? = |- 
 
 There are four terms in every proportion. The first and last terms are the 
 extremes, and the second and third terms the means. 
 
 In the ratio 10 : 5 the first term, 10, is the antecedent, and the second term, 5, 
 is the consequent. In the question " If 10 men earn $20, how much will 30 men 
 earn?" which may be expressed in the form 10 : 20 = 30 : y (y representing 
 the unknown amount the 30 men will earn), the number of men, 10 and 30, 
 are the antecedents, or causes, and the sums earned, $20 and y dollars, are the 
 consequents or effects. 
 
 Quantities are in proportion by alternation when antecedent is compared 
 with antecedent and consequent with consequent. Thus, if 10 : 5 = 4 : 2, 
 then 10 : 4 = 5 : 2. 
 
 Quantities are in proportion by inversion when the antecedents are made 
 consequents and the consequents antecedents. Thus, if 10 : 5 = 4 : 2, then 
 5 : 10 = 2 :4. 
 
 In any proportion, the product of the means will equal the product of the 
 extremes. Thus, if 10 : 5 = 4 : 2, then 5X4 = 10X2. 
 
 A mean proportional between two quantities equals the square root of their 
 product. Thus, a mean proportional between 12 and 3 = the square root of 
 12X3, or 6, and the proportion is expressed thus, 12 : 6 = 6 : 3. 
 
 If the two means and one extreme of a proportion are given, the other 
 extreme may be found by dividing the product of the means by the given 
 extreme. Thus, 10 : 5 = 4 : (), then (4X5) -=-10 = 2, and the proportion 
 is 10 : 5 = 4 : 2. This may also be expressed algebraically. If y = the unknown 
 quantity, the proportion is written 10 : 5 = 4 : y. Then 10Xy = 5X4, or Wy 
 = 20 and y = 20-MO = 2, as before. 
 
 If the two extremes and one mean are given, the other mean may be found 
 by dividing the product of the extremes by the given mean. Thus, 10 : ( ) 
 = 4:2, then (10X2) -^4 = 5, and the proportion is 10 : 5 = 4 : 2. This may be 
 expressed algebraically. Thus, 10 : y = 4 : 2, or 10X2 = yX4, or 4y = 20, 
 and y = 20 -f- 4 = 5, as before. 
 
 EXAMPLE. If 6 men load 30 cars in 1 da., how many cars will 10 men load? 
 
 SOLUTION. The antecedents, or causes are the number of men and the 
 consequents, or effects, the number of cars loaded by them. If y represents 
 the unknown number of cars loaded by the 30 men, the proportion may be 
 
 cause effect cause effect 
 
 expressed 6 (men) : 30 (cars) = 10 (men) : y (cars). Prom this, 6Xy = 30X 10, 
 or 6? = 300, and y = 300 -5- 6 = 50, the number of cars loaded by 10 men. 
 
 A compound proportion is one in which one or both of the ratios contains 
 more than one term. The governing principles are as follows: 
 
22 MA THEM A TICS 
 
 1. The product of the simple ratios of the first couplet equals the product 
 of the simple ratios of the second couplet. Thus, (7:}5) = ( : }2) 
 
 -i Z-=A V I 
 
 ~12 X 14~10 X 18' 
 
 2. The product of all the terms in the extremes equals the product of all 
 the terms in the means. Thus, in {7 ! }|} = {Q ! Jg}, 4X7X10X18 = 12 
 
 3. Any term in either extreme equals the product of the means divided 
 by the product of the other terms in the extremes. Thus, in the same pro- 
 
 5X6X12X14 
 portion, 4- 
 
 4. Any term in either mean equals the product of the extremes divided 
 
 by the product of the other terms in the means. Thus, in {2 j |? \ = { 5 j J9 V, 
 5- (4X7X10X18)-*- (6X12X14). 
 
 EXAMPLE 1. If 4 men in 7 da. earn $24, how much can 14 men earn 
 in 12 da.? 
 
 SOLUTION. Here the antecedents, or causes, are the men and the number 
 of days they worked and the consequents, or effects, are the sums of money 
 they earned. If y is considered equal to the second effect, that is, the unknown 
 number of dollars earned by 14 men in 12 da., the proportion is 7 V^) 
 
 : 24 (dollars = J^da? : y ( dollars > From this ' y X 4 X 7 = 24 X 14 X 12, or 28? 
 = 4,032, or y = $144. 
 
 EXAMPLE 2. If 12 men in 35 da. build a wall 140 rd. long, 6 ft. high, how 
 many men can, in 40 da., build a wall of the same thickness 144 rd. long, 
 5 ft. high? 
 
 SOLUTION. Here, the causes are the men and the number of days worked 
 and the effects are the length and height of wall built by them. It is to be 
 noted that the thickness of the wall is not considered as it is the same for each 
 
 set of men. If y is made equal to the unknown number of men, 35 ^a) 
 
 : 6% I"* = 40 Oil? : 5 4 (1 tOi*'* ' From this> I 2 X 35 X 144 X 5 = 140 X 6 X y 
 X40, or 33,600^ = 302,400, or y = 9. 
 
 PERCENTAGE 
 
 Percentage is a process of computation in which the basis of comparison 
 is a hundred. 
 
 Per cent, means by, or on, the hundred. 6 per cent, (also written 6%, or .06) 
 of a quantity means 6 of every hundred in the quantity. 
 
 The base is the amount upon which the percentage is computed. In the 
 case of money at interest, the base is known as the principal. 
 
 The rate, or rate per cent., is the number of hundredths of the base that are 
 to be taken. In monetary transactions, the rate is commonly called interest. 
 
 The percentage is the sum obtained by multiplying the base (or principal) 
 by the rate. In finance, the percentage is always known as the interest. 
 
 The amount is the sum of the base and percentage or, what is the same thing, 
 the sum of the principal and interest. 
 
 To Find the Percentage, Having the Rate and the Base. Multiply the base 
 by the rate expressed in hundredths. Thus 6% of 1,930 is found as follows: 
 1. 930 X. 06 =115.80. 
 
 To Find the Amount, Having the Base and the Rate. Multiply the base 
 by 1 plus the rate. Thus, the amount of $1,930 for 1 yr. at 6% is $ 1, 930 X 1.06 
 = $2,045.80. 
 
 To Find the Base, Having the Rate and the Percentage. Divide the per- 
 centage by the rate. Thus, if the rate is 6% and the percentage is 115.80, the 
 base = 1 15.80 -r- .06 = 1,930. 
 
 To Find the Rate, Having the Percentage and the Base. Divide the per- 
 centage by the base. Thus, if the percentage is 115.80 and the base 1,930, the 
 rate equals 115.80 -5-1,930 = .06, or 6%. 
 
 To Find the Rate,. Having the Amount and Base. Subtract the base from 
 the amount ; this will give the percentage. Divide the percentage by the base 
 to find the rate. Thus, if the amount is $2,045.80 and the base is $1,930, the 
 
MA THEM A TICS 23 
 
 percentage (or interest) is $2,045.80 -$1,930 = $115.80. The rate is then 
 115.80 -M.930 = .06, or 6%. 
 
 Interest. Interest is money paid for the use of money, and may be likened 
 to rent paid for the use of a house by a tenant to his landlord. Interest is 
 figured as a certain per cent, of the money lent; 6% is the prevailing rate in 
 the United States. 
 
 In banks interest is generally figured on the basis of there being 360 da., 
 or 12 mo. 9f 30 da. each, in the year. The following are short rules for calcu- 
 lating 6% interest when 360 da. are taken as l^r.: 
 
 Rule I. Multiply the principal by the number of days and divide by 6,000. 
 
 Rule II. Multiply the principal by the number of months and divide by 200. 
 
 At 6% a year, the interest on $1 for 1 mo. is 3%. 
 
 A note is a written promise to pay a certain sum of money at a certain 
 time and at a certain rate of interest and, usually, at a certain place. The 
 amount of money to be paid is the principal and is often called the face of the 
 note. The discount is the interest on the money for the given time and at the 
 given rate, and is so called because it is deducted (or discounted) in advance. 
 The proceeds is the net amount received; that is, it is the face of the note less the 
 discount (or interest) paid in advance. 
 
 Banks charge interest, as already explained, on the basis of there being 360 
 da. in the year, and for the exact number of days elapsed. N9tes are com- 
 monly made for 1, 2, or 3 mo., or for 30, 60, or 90 da. Thus, if on June 15 
 three sums are borrowed at 1, 2, and 3 mo. time, the notes will be due on the 
 15th day of July, August, and September, respectively. But interest will not 
 be charged for T V B , and \ yr. in the individual cases, but for 30, 61, and 92 da., 
 and these days are ^g, 3%, and $& yr., respectively. On the other hand, should 
 three other sums of money be borrowed on the same day for 30, 60, and 90 da., 
 the notes will fall due on July 15, August 14, and September 13, and interest 
 would be charged for the 30, 60, and 90 da. 
 
 EXAMPLE 1. What is the 'date of payment, discount, and proceeds of a 
 90-da. note, for $150, dated July 27? 
 
 SOLUTION. The date of payment will be 90 da. from July 27,. or on October 
 25, as there are 31 da. each in the months of July and August. The discount 
 will be the interest for 90 da. at 6% , which by rule I is (150X 90) -r 6,000 = $2.25. 
 The proceeds will be $150 -$2.25 = $147.75. 
 
 EXAMPLE 2. What is the date of payment, discount, and proceeds of a 
 3-mo. note for $150, dated July 27? 
 
 SOLUTION. The date of payment is 3 mo. from July 27, or October 27. As 
 the number of days between these dates is 92, by rule I the discount will be (150 
 X 92) -=-6,000 = $2.30. The proceeds will be $150 -$2.30 = $147.70. 
 
 Trade Discount. A discount is an abatement from the price of an article 
 for some consideration, frequently the payment of cash upon the receipt of the 
 goods or material purchased. Discounts are generally expressed as a certain 
 per cent, of the purchase price; therefore, the net, or real, cost of an article is 
 found by multiplying the first cost by 1.00 minus the discount. Thus, if a car- 
 load of corn is billed at $438, with a discount of 5% for cash, the price for 
 immediate payment will be 438X (1.00-.05) =438X.95 = $416.10. 
 
 Discounts are frequently compound or continuous; that is, there are two 
 or more discounts upon the price of an article. Thus, a discount may be 
 quoted as "ten, ten, and fiye." This does not mean that the total discount 
 is the sum of the three single discounts, or 25%; each discount and the 
 resultant net price are figured separately. In the case in queston, if the first 
 cost of the article was $100, the first net cost will be 100 X (1.00- .10 = .90) = $90; 
 the second net cost will be 90 X (1.00 -.10 = .90) = $81; and the third net, or 
 final cost will be 81 X (1.00- .05 = .95) = $76.95. The total discount is, there- 
 fore, $100.00 -$76.95 = $23.05, or 23.05% and.not 25%. 
 
 RECIPROCALS 
 
 The reciprocal of a number is unity, or 1, divided by the number. Thus, 
 the reciprocal of 5 is l-f-5 = .2. Reciprocals are always expressed decimally. 
 The reciprocal of a whole number is entirely decimal, while the reciprocal of 
 a number less than unity is either a whole number or a whole number followed 
 by a decimal. Thus, the reciprocal of .5 is 1 -T- .5 = 2, and the reciprocal of .6 is 
 1-7- .6 = 1.6666+. Reciprocals are used to avoid the labor of division. Thus, 
 the operation represented by 100 -f- 621 may be performed in the ordinary way 
 by long division, or 100 may be multiplied by the reciprocal of 621. Reciprocals 
 of numbers from 1 to 1,000 are given in connection with the table of powers, 
 
24 MATHEMATICS 
 
 etc., near the end of this volume. From this table, the reciprocal of 621 is 
 found to be .001610306, and 100 -v- 621 = 100 X. 001610306 = .1610306. 
 
 Reciprocals of numbers that are multiples or submultiples of those in the 
 table may be obtained directly therefrom by shifting the decimal point. Thus, 
 the reciprocal of 62,100 is rfo of the reciprocal of 621, or .00001610306. The 
 reciprocal of 6.21 is 100 times the reciprocal of 621, or .1613036, and the reci- 
 procal of .0621 is 10,000 times that of 621, or 16.10306. 
 
 Reciprocals of numbers intermediate between those in the table may be 
 found therefrom by interpolation. Thus, the reciprocal of 621.25 is .0016096579, 
 and by shifting the decimal point the reciprocal of 6.2125 is .16096579. 
 
 ARITHMETICAL PROGRESSION 
 
 Quantities are said to be in arithmetical progression when they increase or 
 decrease by a common difference. The following is an increasing series in arith- 
 metical progression: 1, 3, 5, 7, 9, 11, 13; if the figures are read backwards, 
 13, 11, 9, etc., it becomes a decreasing series. In the first series, the first term 
 is 1; the last term 13; the number of terms 7; the common difference 2; and the 
 sum of the terms 49. In any arithmetical progression, 
 Let /= first term; 
 
 I = last, or th term; 
 d = common difference; 
 = number of terms; 
 5 = their sum. 
 
 (1) 
 
 (2) . za 
 
 n = 2l + d^(2 l+ W-8ds 
 
 (3) ,_, 2d 
 
 <-iT (") 
 
 =?fe^ (u> 
 
 (5) ^^ffSr d5) 
 
 (6> : - (16) 
 
 (17) 
 s = ?(2f+(n-l)d] (18) 
 
 n = ^+l (9) ,.W + i^=/> (19) 
 
 d 2 ^ 2d 
 
 n= ^Tl ( 10 > s = ^[2l-(n-l)d] (20) 
 
 EXAMPLE 1. During the last month of the year, the mules at a certain mine 
 used 40 bales of hay. The consumption was 2 bales less than this during 
 November, and similarly less for each month until the first of the year. What 
 was the consumption of hay during January, and how many bales were used 
 during the year? 
 
 SOLUTION. Here w = 12 (mo.), d = 2 (bales), and / = 40 (bales during 
 December). It is required to find / and s. To find /, substituting the various 
 values in formula 6 gives /= 40 (12 1) X 2 = 40 22 = 18 = number of bales 
 used in January. To find's, substituting in formula 20 gives 5 = ^X[2X40 
 -(12-1)X2] = 6X(80-22)=6X58 = 348 bales during the year. It will be 
 noted that / has been found in the first part of the solution and it may be used 
 to find 5 in formula 17 which is more simple than formula 20. 
 
 EXAMPLE 2. A contractor agrees to put down a bore hole for $1 a ft. for 
 the first 100 ft.; $3 a ft. for the second 100 ft.; and $2 a ft. additional for each 
 successive 100 ft. Upon completion of the work he was paid $6,400. How 
 deep was the hole and what was the cost per foot of the last 100 ft.? 
 
 SOLUTION. Here /= 100 (dollars), s = $6,400, and d = 200 (dollars increase 
 in cost per 100 ft.). Using formula 11, 
 
MATHEMATICS 25 
 
 = 200- (2X 100) + V[(2X 100) -200p+ (8X200X6. 400) 
 _ 2X200 ~~ 
 
 __ 200 - 200 + V(200 - 200)2+ 10,240,000 0+ Vp2+ 10,240,000 
 
 400 400 
 
 = A/10,240,000 3,200 
 400 400 
 
 That is, there are 8 sections each 100 ft. deep, or the total depth of the hole is 
 8X100 = 800 ft. By using the value of n, just found, the last term may be 
 determined by means of the simple formula 1. By substitution, the last term 
 = 100+(8-l)X200 = 100 + 1,400= 1,500. That is, the last 100 ft. cost 
 $1,500. or $15 a ft. 
 
 GEOMETRICAL PROGRESSION 
 
 A series of quantities, in which each is derived from that which precedes 
 it, by multiplicaton by a constant quantity, is called a geometrical progression. 
 If the multiplier is a whole number, the progression is styled increasing; if 
 it is a fraction, the progression is styled decreasing. The series 1, 2, 4, 8, 16, 32 
 has 2 for a multiplier, and is an increasing progression. The series 32,16, 8, 4, 2, 
 1, \, i. I. A. T* has \ for a multiplier, and is a decreasing progression. 
 
 The common multiplier in a geometrical progression is called the common 
 ratio; or, briefly, the ratio. 
 Let /= first term; 
 
 J = last term, whose number from / is n; 
 n = number of terms; 
 r = ratio; 
 5 = sum of terms. 
 
 (2) log, 
 
 log 
 
 f=s-r(s-l) (4) r= J=l 
 
 log' "^T" <9) 
 
 n-|fl (5) ,-/ (10) 
 
 EXAMPLE 1. How much will it cost to sink a shaft 1,500ft. deep at the 
 rate of &c. for the first 50 ft.; {c. for the second 50 ft.; c. for the third 50 ft.; 
 and so on at the same rate? 
 
 SOLUTION. In this case,/= ^; n = 30; and r = 2. Substituting in formula 1, 
 I = AX (2)= 33,554,432, and from formula 10 
 
 EXAMPLE 2. At the end of a certain period a mine had produced 126,000 
 T. of coal. The production for the first 6 mo. was 2,000 T., which was doubled 
 each 6 mo. How long had the mine been in operation? 
 
 SOLUTION. In this case, 5 = 126,000; /= 2,000; and r = 2. Using formula 6 
 log rl26.000X(2-l) i 
 
 
 
 mine had been in operation for six periods of 6 mo. each, or for 3 yr. 
 
 INVOLUTION 
 
 Involution is the process of finding any power of a number. The power 
 of a number is the product arising from multiplying the number by itself as 
 many times as is indicated by another number known as the exponent. Thus, 
 4 2 is read four squared, or four to the second power, and is equal to 4X4 = 16. 
 Similarly 5 3 is read five cubed, or five to the third power, and is equal to 5X5X5 
 = 125. Likewise, 2 5 is read two to the fifth power, or the fifth power of two, and 
 is equal to 2X2X2X2X2 = 32. The figures 2, 3, and 5, written to the right 
 and above the numbers are the exponents, 
 
MATHEMATICS 
 FIRST NINE POWERS OF FIRST NINE NUMBERS 
 
 1 
 
 j) 
 
 8 
 
 Jl u, 
 
 E S 
 
 3$ 
 
 3% 
 
 J3 t-. 
 
 w 
 
 3 v 
 
 3 
 a 
 
 
 I 
 
 3 
 O 
 
 II 
 
 Kjfi 
 
 II 
 
 0) ^ 
 
 is 
 
 ."0 
 
 W^ 
 
 Is 
 
 1 
 
 1 
 
 1 
 
 1 
 
 i 
 
 i 
 
 1 
 
 1 
 
 1 
 
 2 
 
 4 
 
 8. 
 
 16 
 
 32 
 
 64 
 
 128 
 
 256 
 
 512 
 
 3 
 
 9 
 
 27 
 
 81 
 
 243 
 
 729 
 
 2,187 
 
 6,561 
 
 19,683 
 
 4 
 
 16 
 
 64 
 
 256 
 
 1,024 
 
 4,096 
 
 16,384 
 
 65,536 
 
 262,144 
 
 5 
 
 25 
 
 125 
 
 625 
 
 3,125 
 
 15.625 
 
 78,125 
 
 390,625 
 
 1,953,125 
 
 6 
 
 30 
 
 216 
 
 1,296 
 
 7,776 
 
 46,656 
 
 279,936 
 
 1,679,616 
 
 10,077,696 
 
 7 
 
 49 
 
 343 
 
 2,401 
 
 16,807 
 
 117,649 
 
 823,543 
 
 5,764,801 
 
 40,353,607 
 
 8 
 
 64 
 
 512 
 
 4,096 
 
 32,768 
 
 262,144 
 
 2,097,152 
 
 16,777,216 
 
 134,217,728 
 
 9 
 
 81 
 
 729 
 
 6,561 
 
 59,049 
 
 531,441 
 
 4,782,969 
 
 43,046,721 
 
 387,420,489 
 
 The power of a number may be obtained by multiplying together any two 
 or more lower powers, the sum of whose exponents is equal to the exponent of 
 the required power. Thus, if n = any number, 9 = n 4 X 8 = wXn 2 Xw 6 = 2 Xw 3 
 X 4 , etc. Similarly, w7 = w 2 X n2Xw 3 = n 2 X 5 , etc. 
 
 A table of squares and cubes is given at the end of this volume. The 
 powers of numbers not in the table may be found by interpolation with suffi- 
 cient accuracy for most purposes. Logarithms afford a rapid method of 
 determining powers. 
 
 EVOLUTION 
 
 ' The root of a number is one of the equal factors of a number. The number 
 of equal factors in any number is indicated by a number known as the index 
 of the root. This index, which is written to the left and a little above the 
 sign \, shows how many factors compose the number, or how many times the 
 root must be multiplied by itself to produce the number. 
 
 To Find the Square Root of a Number: 
 
 Rule. I. Separate the given number into periods of two figures each, begin- 
 ning at the units place. 
 
 n. Find the greatest number whose square is contained in the period on the 
 left; this will be the first figure in the root. Subtract the square of this figure from 
 the period on the left, and to the remainder annex the next period to form a dividend. 
 
 HI. Divide this dividend, omitting the figure on the right, by double the part of 
 the root already found, and annex the quotient to that part, and also to the divisor; 
 then, multiply the divisor thus completed, by the figure of the root last obtained, 
 and subtract the product from the dividend. 
 
 IV. Add the root last found to the last trial divisor to form a new trial divisor. 
 Divide the dividend by this new trial divisor and the quotient will be the next figure 
 of the root, which quotient is to be annexed to the trial divisor to form a new complete 
 divisor. Multiply this last complete divisor by the figure of the root last obtained 
 and subtract from the dividend. 
 
 V. Bring down the next period to form a new dividend and continue 'as before 
 until all the periods have been used. 
 
 VI. // it is desired to carry the root farther, annex periods of two ciphers each, 
 and proceed as before. 
 
 EXAMPLE. Find the square root: (a) of 874.225; (b) of .00874225. 
 SOLUTION. 
 
 (a) 
 
 874.2 2'50 (29.56 7 + 
 
 4 
 
 474 
 
 441 
 
 3322 
 
 2925 
 
 
 59127 
 
 183 
 
 3 
 
 1865 
 
 .0 0'8 7'4 2'2 5 (.0 9 3 5 
 
 
 ~87 
 8J 
 642 
 549 
 9325 
 9325 
 
 
MA THEM A TICS 27 
 
 To Find the Cube Root of a Number: 
 
 Rule. I. Separate the given number into periods of three figures, each begin- 
 ning at the units place. 
 
 II. Find the greatest number whose cube is contained in the period on the left; 
 this will be the first figure in the root. Subtract the cube of this figure from the 
 period on the left, and to the remainder annex the next period to form a dividend. 
 
 HI. Divide this dividend by the partial divisor, which is three times the square 
 of the root already found considered as tens; the quotient is the second figure of the 
 root. 
 
 IV. To the partial divisor add 3 times the product of the second figure of the 
 root by the first, considered as tens, also the square of the second figure; the result 
 will be the complete divisor. 
 
 V. Multiply the complete divisor by the second figure of the root, and subtract 
 the product from the dividend. 
 
 VI. // there are more periods to be brought down, proceed as before, using the 
 part of the root already found, the same as the first figure in the previous process. 
 
 VII. // it is desired to carry the root farther, annex periods of three ciphers 
 each, and proceed as above. 
 
 EXAMPLE. Find the cube root of 12,813,904. 
 
 SOLUTION. 1 2'8 1 3'9 4 ( 2 3 4 
 
 First partial divisor, 3X20' = 1200 4813 
 3X20X3= 180 
 
 32= 9 
 
 First complete divisor = 1389 
 
 Second partial divisor, 3X2302= 1 5 8700 
 
 3X230X4 = 2760 
 
 42 = 16^ 
 
 Second complete divisor = 161476 645904 
 
 A table of squares and cubes is given at the end of this volume by means 
 of which square roots and cube roots may be readily extracted. The roots 
 of numbers whose powers are within the limits of the table, 1,000,000 for 
 squares and 1,000,000,000 for cubes, may be obtained directly, by finding in 
 the proper column, the number whose root is to be extracted and in the column 
 headed Number the root will be found. Thus, if it is desired to extract the 
 cube root of 825,293,672, the number will be found in the column headed Cube, 
 and on the same line in the column headed Number are the figures 938, which 
 is the cube root of the required number. 
 
 Often, by shifting and replacing the decimal point, the roots of numbers 
 not in the table may conveniently be found. The decimal point must be shifted 
 the number of figures there are in a period, two in the case of squares and 
 three in that of cubes. Thus, if it is desired to extract the cube root of 
 14.706125, the decimal point may be shifted either three or six figures (one or 
 two periods) to the right and the cube root of 14,706.125 or of 14,706,125 
 extracted. After the root is extracted, the decimal point must be restored. 
 In the case just given, by shifting the decimal point six places, or two periods, 
 the cube root of 14,706,125 is found to be 245. As there is but one period 
 before the decimal point in the number, there can be but one figure before the 
 decimal point in the root; hence, the root is 2.45. Similarly, in extracting 
 the cube root of .000000100544625 the decimal point and the six ciphers (two 
 periods) may be dropped and the cube root of 100,544,625 extracted. This 
 root is found to be 465. As there are two periods (of three ciphers each) after 
 the decimal point in the number, there must be two ciphers (one for each period) 
 after the decimal point in the root. Hence, the cube root of .000000100544625 
 is .00465. 
 
 The square or cube roots of numbers not in the table may be found, approx- 
 imately, by interpolation. When finding the square root of 874.225, the 
 decimal point may be shifted one period, or two figures, to the right, and the 
 square root of 87'422.50 extracted. This is found to be between the squares 
 of 295 and 296. The interpolation is made as follows: 
 
 Number Root Number Root 
 
 87,616 = 2962 87,422.50 = ? 
 
 87,025 = 2952 - 87,025.00 = 2952 
 
 591 = first difference 397.50 = second difference 
 
28 
 
 MATHEMATICS 
 
 Then, second difference-?- first difference = 397.50 -5- 591 = .656. This is to 
 be added to 295 and the square root of 87,422.50 is found to be 295.656. As 
 the decimal point has been shifted one period to the right it must now be 
 shifted one figure to the left, and the square root of 874.225 is 29.5656. As 
 the true root, 29.5673, is within .0017 of the root found by interpolating in 
 the table, this method is accurate enough for all practical purposes. 
 
 Finding the Fourth and the Fifth Root of a Number. Fourth roots may be 
 found by taking the square root of the square root, that is, by extracting the 
 square root twice. 
 
 Fifth roots are rarely required, and when needed, occur in formulas involving 
 coefficients of friction (k, in problems relating to ventilation, etc.) whose 
 values are uncertain within 50% or more. Under such circumstances, it is 
 apparent that even a very large percentage of error in the fifth root is allow- 
 able. In the vast majority of cases, no error of importance will be introduced 
 by using for the true root the nearest value thereto, taken directly from the 
 table. 
 
 TABLE OF FIFTH POWERS 
 
 No. 
 
 Power 
 
 No. 
 
 Power 
 
 No. 
 
 Power 
 
 No. 
 
 Power 
 
 1.0 
 
 1.00000 
 
 3.3 
 
 391.35393 
 
 5.6 
 
 5,507.31776 
 
 7.9 
 
 30,770.56399 
 
 1.1 
 
 1.61051 
 
 3.4 
 
 454.35424 
 
 5.7 
 
 6,016.92057 
 
 8.0 
 
 32,768.00000 
 
 1.2 
 
 2.48832 
 
 3.5 
 
 525.21875 
 
 5.8 
 
 6,563.56768 
 
 8.1 
 
 34,867.84401 
 
 1.3 
 
 3.71293 
 
 3.6 
 
 604.66176 
 
 5.9 
 
 7,149.24299 
 
 8.2 
 
 37,073.98432 
 
 1.4 
 
 5.37824 
 
 3.7 
 
 693.43957 
 
 6.0 
 
 7,776.00000 
 
 8.3 
 
 39,390.40643 
 
 1.5 
 
 7.59375 
 
 3.8 
 
 792.35168 
 
 6.1 
 
 8,445.96301 
 
 8.4 
 
 41,821.19424 
 
 1.6 
 
 10.48576 
 
 3.9 
 
 902.24199 
 
 6.2 
 
 9,161.32832 
 
 8.5 
 
 44,370.53125 
 
 1.7 
 
 14.19857 
 
 4.0 
 
 1,024.00000 
 
 6.3 
 
 9,924.36543 
 
 8.6 
 
 47,042.70176 
 
 1.8 
 
 18.89568 
 
 4.1 
 
 1,158.56201 
 
 6.4 
 
 10,737.41824 
 
 8.7 
 
 49,842.09207 
 
 1.9 
 
 24.76099 
 
 4.2 
 
 1,306.91232 
 
 6.5 
 
 11,602.90625 
 
 8.8 
 
 52,773.19168 
 
 2.0 
 
 32.00000 
 
 4.3 
 
 1,470.08443 
 
 6.6 
 
 12,523.32576 
 
 8.9 
 
 55,840.59449 
 
 2.1 
 
 40.84101 
 
 4.4 
 
 1,649.16224 
 
 6.7 
 
 13,501.25107 
 
 9.0 
 
 59,049.00000 
 
 2.2 
 
 51.53632 
 
 4.5 
 
 1,845.28125 
 
 6.8 
 
 14,539.33568 
 
 9.1 
 
 62,403.21451 
 
 2.3 
 
 64.36343 
 
 4.6 
 
 2,059.62976 
 
 6.9 
 
 15,640.31349 
 
 9.2 
 
 65,908.15232 
 
 2.4 
 
 79.62624 
 
 4.7 
 
 2,293.45007 
 
 7.0 
 
 16,807.00000 
 
 9.3 
 
 69,568.83693 
 
 2.5 
 
 97.65625 
 
 4.8 
 
 2,548.03968 
 
 7.1 
 
 18,042.29351 
 
 9.4 
 
 73,390.40224 
 
 2.6 
 
 118.81376 
 
 4.9 
 
 2,824.75249 
 
 7.2 
 
 19,349.17632 
 
 9.5 
 
 77,378.09375 
 
 2.7 
 
 143.48907 
 
 5.0 
 
 3,125.00000 
 
 7.3 
 
 20,730.71593 
 
 9.6 
 
 81,537.26976 
 
 2.8 
 
 172.10368 
 
 5.1 
 
 3,450.25251 
 
 7.4 
 
 22,190.06624 
 
 9.7 
 
 85,873.40257 
 
 2.9 
 
 205.11149 
 
 5.2 
 
 3,802.04032 
 
 7.5 
 
 23,730.46875 
 
 9.8 
 
 90,392.07968 
 
 3.0 
 
 243.00000 
 
 5.3 
 
 4,181.95493 
 
 7.6 
 
 25,355.25376 
 
 9.9 
 
 95,099.00499 
 
 3.1 
 
 286.29151 
 
 5.4 
 
 4,591.65024 
 
 7.7 
 
 27,067.84157 
 
 10.0 
 
 100,000.00000 
 
 3.2 
 
 335.54432 
 
 5.5 
 
 5,032.84375 
 
 7.8 
 
 28,871.74368 
 
 
 
 This table may be used in the same way as the table of squares and cubes, to 
 find the fifth roots of intermediate values. It must be remembered that the 
 periods are composed of five figures and that there must be one figure in the 
 root for each such period in the number. 
 
 EXAMPLE. Find the fifth root of 3,827,963,000. 
 
 SOLUTION. By pointing off and inserting a decimal point, the fifth root 
 of 38,279.63 is to be extracted. This is seen to lie between 8.2 and 8.3 and 
 an interpolation, which may be made mentally, shows it to be about midway 
 between these or is 8.25. By restoring the decimal point, the fifth root of the 
 given number is found to be 82.5. As the root, by seven-place logarithms, is 
 found to be 82.5265, this simple approximation is accurate enough for use in 
 those formulas in which fifth roots occur. Should greater accuracy be 
 demanded it is possible to interpolate as follows: 
 
 Number Root Number Root 
 
 39,390.40463 = 8.35 38,279.63000= ? 
 
 37,073.98432 = 8.25 37,073.98432 = 8.25 
 
 2,316.42031 = first difference 1,205.64568 = second difference 
 
 Second difference -5- first difference = 1,205.64568-^2,316.42031 = .5205, which 
 is to be annexed to 8.2, making the root 8.25205. By restoring the decimal 
 point the fifth root of 3,827,963,000 is 82.5205. 
 
MATHEMATICS 29 
 
 Simple Method of Extracting Roots. A simple method of extracting roots 
 where tables are not available and the rules have been forgotten, is based upon 
 Sir Isaac Newton's Method of Approximating the Roots of Higher Equations. 
 The method is based on the fact that any number is composed of as many 
 equal factors as are indicated by the index of the root. Thus, the fifth root is 
 one of the five equal factors of the number and the cube root is one of the three 
 equal factors, and similarly. 
 
 If the number whose root is required is placed equal to n in the case of the 
 cube root, it may be considered that aXbXc = n. When these factors are 
 equal, that is, when a = b = c, the cube root is found. From the given equation, 
 
 aXbXc = n, c= .. If a is made equal to b, and a value is assumed for them 
 
 as near the cube root as possible, the average of the values of a, b, and c, will 
 be nearer the true root than either a or b. This value of c is known as the 
 first approximation, and may be placed equal to a and b to find a new value 
 for c, the average of the three values being the second approximation. These 
 approximations may be carried indefinitely, but with a little practice it will 
 be found that the first approximation answers all practical purposes. 
 
 EXAMPLE 1. Find the cube root of 987,654,321. 
 
 SOLUTION. Pointing off and inserting a decimal point, it is necessary to 
 extract the cube root of 987.654321. If a table of cubes is not available, one 
 should be prepared. The number will be found between 729 = 9 3 and 1,000 
 = 10 3 ; that is, the cube root of the number is between 9 and 10. In this case a 
 XbXc = 987.654321, and when a = b = c, the root is found. An interpolation 
 between the cube roots of 729 and 1 ,000 shows that the cube root of the number 
 is about 9.92. Making a = & = 9.92 and substituting gives 9.92X9.92Xc 
 = 987.654321, from which c= 10.036. The mean of these values is (9.92 
 +9.92 + 10. 036) -5- 3 = 9.95867. This is the first approximate root, which may 
 be placed equal to a and b to find a second approximate root. In the case of the 
 first root, by restoring the decimal point, the cube root of 987,654,321 is found 
 to be 995.867, which is identical with that extracted by means of seven-place 
 logarithms. Such coincidence is unusual, but indicates that by carefully 
 selecting the trial factors, a first approximation answers for all but abstract 
 problems. 
 
 EXAMPLE 2. Find the fifth root of 3,827,963,000. 
 
 SOLUTION. Pointing off and placing a decimal point between the periods 
 gives a XbXcXdXe = 38,279.63. From a table of powers, the fifth root of 
 this number is found to lie between 8 and 9, and an interpolation shows it to 
 be about 8.21. Then 8.21X8.21X8.21X8.21X = 38,279.63. From this e 
 = 8 425 and the mean of the five factors is 8.253. Restoring the decimal point 
 shows that the first approximate fifth root of 3,827,963,000 is 82.53. This may 
 be used for a second approximation, giving 82.5261, but the first should answer 
 any purpose. This method may be compared with that based on the use of 
 tables. 
 
 LOGARITHMS 
 
 EXPONENTS 
 
 By the use of logarithms, the processes of multiplication, division, involu- 
 tion, and evolution are greatly shortened, and some operations may be per- 
 formed that would be impossible without them. Ordinary logarithms cannot 
 be applied to addition and subtraction. A logarithm is the exponent of the 
 power to which a fixed number, called the base, must be raised to produce a 
 given number. 
 
 Although any positive number except 1 can be used as a base and a table 
 of logarithms calculated, but two numbers have ever been employed. For all 
 arithmetical operations (except addition and subtraction) the logarithms used 
 are called the Briggs, or common, logarithms, and the base used is 10. In 
 abstract mathematical analysis, the logarithms used are variously called 
 hyperbolic, Napierian, or natural logarithms, and the base is 2.718281828+ . 
 the common logarithm of any number may be converted into a Napierian 
 logarithm by multiplying the common logarithm by 2.30258509 + , which is 
 usually expressed as 2.3026, and sometimes as 2.3. Only the common system 
 of logarithms will be considered here. 
 
 As in the common system the base is 10, all numbers are to be regarded 
 as powers of 10; therefore, as !Qi = 10. 10*= 100, 10 = 1,000, etc., the logarithms 
 (exponents) of 10, 100, 1,000, etc., are 1, 2, 3, etc., respectively. Similarly, 
 
30 M A THEM A TICS 
 
 as 10-1 = ^5 = .!, 10-2 = T fo = .01, 10-3 = ^3 =.001, etc., the logarithms (expo- 
 nent?) of .1, .01, .001, etc., are -1, -2, -3, etc., respectively. 
 
 From the foregoing, it is seen that while the logarithms of exact powers 
 of 10 and of decimals like, .1, .01, .001, etc., are whole numbers, the logarithms 
 of all other numbers are wholly or in part fractional, the fractional part being 
 expressed decimally. Thus, to produce 20, 10 must have an exponent of 
 approximately 1.30103, or 10 1 ' 30103 = 20, very nearly, the degree of exactness 
 depending on the number of decimal places used. Hence, log 20=1.30103. 
 A logarithm, therefore, usually consists of two parts; a whole number, called 
 the characteristic, and a fraction, called the mantissa. While mantissas are 
 always to be regarded as positive, characteristics may be either positive or 
 negative. From the foregoing, it is apparent that the characteristics of the 
 logarithms of all numbers less than unity are negative, while for numbers 
 greater than unity, they are positive. Negative characteristics are expressed 
 by the sign, , placed above the figures; thus, log .20 = 1.30103. 
 
 Rule for Characteristics. The characteristic of the logarithm of a number 
 equal to or greater than unity is 1 less than the number of digits in the number. 
 In the case of numbers less than unity, the characteristic is determined by the 
 position, with respect to the decimal point, of the first digit in the number. If the 
 first digit is found in the tenths column, the characteristic is 1; if in the hundredths 
 column, it is 2; and similarly; or the characteristic is 1 more than the number of 
 ciphers following the decimal point. 
 
 Log .0005 = 2.69897 Log 5 = .69897 
 
 Log .005 =3.69897 Log 50 =1.69897 ' 
 
 Log .05 =2.69897 Log 500 =2.69897 
 
 Log .5 =1.69897 Log 5,000 =3.69897 
 
 Log 50,000 = 4.69897 
 
 FINDING THE LOGARITHM OF A NUMBER 
 
 A table of logarithms, containing the mantissas of the logarithms from 1 
 to 9,999 to five places of decimals, is given at the end of this volume. The 
 mantissas of logarithms of larger numbers can be found by interpolation. 
 This table depends on the principle that all numbers having the same figures 
 in the same order have the same mantissa, without regard to the position of 
 the decimal point, which affects the characteristic only. This is apparent from 
 an inspection of the table giving the logarithm of 5 and its multiples and 
 submultiples by 10. 
 
 The logarithm of a number having not more than four figures may be found 
 by the following rule: 
 
 Rule. Find the first three significant figures of the number whose logarithm 
 is desired, in the left-hand column; find the fourth figure in the column at the top 
 (or bottom) of the page; and in the column under (or above) this figure, and opposite 
 the first three figures previously found, will be the mantissa or decimal part of the 
 logarithm. The characteristic being found, as previously described, write it at the 
 left of the mantissa, and the resulting expression will be the logarithm of the required 
 number. 
 
 EXAMPLE. Find the logarithm: (a) of 6; (6) of 48; (c) of 300; (d) of 3,717; 
 (e) of .006195. 
 
 SOLUTION. (c) The mantissa of the logarithm of 6 is the same as the 
 mantissa of the logarithm of 600. The mantissa is found in the column 
 headed L. and opposite 600 in the column headed N. (number). The first 
 two figures in the mantissa are not repeated for each number, but are found 
 (in this instance) opposite the number 589, and are 77. The last three numbers 
 are found opposite the figures 600. The complete mantissa is 77815. The 
 characteristic is positive and since the number (6) consists of but one digit, 
 the characteristic is 1 1 = 0, therefore, log 6 = .77815. 
 
 (b) The mantissa of the logarithm of 48 is the same as the mantissa of 
 the logarithm of 480. As before, this is found in the column headed L. 
 and opposite 480 in the column headed N. The mantissa is 68124. As the 
 number is composed of two figures, the characteristic is 2 1 = 1, therefore, 
 log 48 =1.68124. 
 
 - (c) The mantissa of 300 may be taken directly from the table, being found 
 in the column headed L. opposite 300 in the column headed N. The man- 
 tissa is 47712. The characteristic, as the number is composed of three figures, 
 is 3 - 1 = 2, therefore, log 300 = 2.47712. 
 
 (d) First find 371 in the column headed N. On the same horizontal line 
 and in the column headed 7, the last three figures of the mantissa are found 
 
MATHEMATICS 31 
 
 to be *019. This star means that the first two figures of the mantissa are to 
 be found below the horizontal line in which 019 is found and not above, and 
 are 57 and not 56. The entire mantissa becpmes 57019. As the number is 
 composed of four figures, the characteristic is 4 1 = 3; therefore, log 3,717 
 = 3.57019. 
 
 (e) The mantissa of 6,195 is found opposite 619. The first two figures, 
 79, are found in the column headed L. 0, and the last three, 204, in the column 
 headed 5. The entire mantissa is 79204. As the first digit in the number is 
 found in the third decimal place, the characteristic is 5, therefore, log .006195 
 = 3.79204. 
 
 The logarithm of a number consisting of five or more figures may be found 
 by the following rule: 
 
 Rule. I. // the number consists of more than five figures and the sixth figure 
 is 5 or greater, increase the fifth figure by 1 and ivrite ciphers in place of the sixth 
 and remaining figures. 
 
 II. Find the mantissa corresponding to the logarithm of the first four figures, 
 and subtract this mantissa from the next greater mantissa in the table; the remainder 
 is the difference. 
 
 III. Find in the secondary table, headed P. P., a column headed by the same 
 number as that just found for the difference, and in this column, opposite the num- 
 ber corresponding to the fifth figure (or fifth figure increased by 1) of the given 
 number (this figure is always situated at the left of the dividing line of the column), 
 will be found the P. P. (proportional part) for that number. The P. P. thus 
 found is to be added to the mantissa found in II, as in the preceding examples, 
 and the result is the mantissa of the logarithm of the given number, as nearly as 
 may be found with five-place tables. 
 
 To take out the logarithm of a number consisting of more than four figures, 
 it is inexpedient to use more than five figures of the number when using five- 
 place logarithms (the logarithms given at the end of this volume are five-place) . 
 Hence, if the number consists of more than five figures and the sixth figure is 
 less than 5, replace all figures after the fifth with ciphers; if the sixth figure 
 is 5 or greater, increase the fifth figure by 1 and replace the remaining figures 
 with ciphers. Thus, if the number is 31,415,926, find the logarithm of 
 31,416,000; if 31,415,426, find the logarithm of 31,415,000. 
 
 EXAMPLE. Find log 31,416. 
 
 SOLUTION. Find the 'mantissa of the logarithm of the first four figures, as 
 already explained. This is, in the present case, .49707. Now, subtract the 
 number in the column headed 1, opposite 314 (the first three figures of the given 
 number), from the next greater consecutive number, in this case 721, in the 
 column headed 2. 721 707 = 14; this number is called the difference. At 
 the extreme right of the page will be found a sec9ndary table headed P. P., and 
 at the top of one of these columns, in this table, in bold-face type, will be found 
 the difference. It will be noticed that each column is divided into two parts 
 by a vertical line, and that the figures on the left of this line run in sequence 
 from 1 to 9. Considering the difference column headed 14, opposite the 
 number 6 (6 is the last or fifth figure of the number whose logarithm we are 
 taking out) is the number 8.4, which, added to the mantissa just found, dis- 
 regarding the decimal point in the mantissa, gives 49,707 + 8.4 = 49,715.4. 
 Now as 4 is less than 5, it is rejected, giving for the complete mantissa .49715. 
 As the characteristic of the logarithm of 31,416 is 5- 1 = 4, log 31,416 = 4.49715. 
 
 TO FIND A NUMBER WHOSE LOGARITHM IS GIVEN 
 Rule. I. Consider the mantissa first. Glance along the different columns 
 of the table that are headed 0, until the first two figures of the mantissa are found. 
 Then, glance down the same column until the third figure is found (or 1 less than 
 the third figure). Having found the first three figures, glance to the right along the 
 row in which they are situated until the last three figures of the mantissa are found. 
 Then, the number that heads the column in which the last three figures of the man- 
 tissa are found is the fourth figure of the required number, and the first three figures 
 lie in the column headed N, and in the same row in which lie the last three figures 
 of the mantissa. .. .. . . 
 
 H. // the mantissa cannot be found in the table, find the mantissa that is 
 nearest to, but less than, the given mantissa, and which call the next less mantissa. 
 Subtract the next less mantissa from the next greater mantissa in the table to obtain 
 the difference. Also, subtract the next less mantissa from the mantissa of the 
 given logarithm, and call the remainder the P. P. Looking in the secondary table 
 headed P P. for the column headed by the difference just found, find the number 
 opposite the P. P. just found (or the P. P. corresponding most nearly to that just 
 
32 MATHEMATICS 
 
 found); this number is the fifth figure of the required number; the fourth figure 
 will be found at the top of the column containing the next less mantissa, and the 
 first three figures in the column headed N and in the same row that contains the 
 next less mantissa. 
 
 HI. Having found the figures of the number as directed, locate the decimal 
 point by the rules for the characteristic, annexing ciphers to bring the number up 
 to the required number of figures if the characteristic is greater than 1. 
 
 EXAMPLE. Find the number corresponding: (a) to the logarithm 3.56867; 
 (fc) to the logarithm 2.05753. 
 
 SOLUTION. (a) The first two figures of the mantissa are 56; glancing 
 down the column, the third figure, 8 (in connection with 820 )is found opposite 
 370 in the N column. Glancing to the right along the row containing 820, 
 the last three figures of the mantissa, 867, are fpund in the column headed 4; 
 hence, the fourth figure of the required number is 4, and the first three figures 
 are 370, making the figures of the required number 3,704. As the characteristic 
 is 3, there must be 3+1 = 4 figures to the left of the decimal point. Hence, 
 the number is 3,704. 
 
 (ft) The mantissa 05753 is not found in the table. The next less mantissa 
 is found in the column headed 1, opposite the figures 114 in the column 
 headed N; hence, the first four figures are 1,141. The mantissa of log 1141 
 = 05729, and of log 1142 = 05767. The difference is 38. The P. P. (propor- 
 tional part) is the given logarithm the lesser tabular logarithm, or 05753 
 -05729 = 24. Under the head of 38 in the P. P. section, 24 is found between 
 22.8 (opposite 6) and 26.6 (opposite 7). As 24 is nearer the smaller number, 
 the fifth figure of the number is 6, and the entire number is 11,416. As the 
 characteristic is 2, the number is a decimal and there is 2 1 = 1 cipher after 
 the decimal point; hence, the number is .011416. 
 
 MULTIPLICATION BY LOGARITHMS 
 
 The principle on which the process of multiplication by means of logarithms 
 is based is that log 06 = log o+log b. To multiply two or more numbers by 
 using logarithms apply the following rule: 
 
 Rule. Add the logarithms of the several numbers, and the sum will be the 
 logarithm of the product. Find the number corresponding to this logarithm, and 
 the result will be the number sought. 
 
 EXAMPLE 1. Multiply 4.38, 5.217, and 83 together. 
 
 SOLUTION. Log 4.38= .64147 
 
 Log 5.217= .71742 
 
 Log 83 = 1.91908 
 Adding, 3.27797 = log (4.38X5.217X83) 
 
 Number corresponding to 3.27797 is 1,896.6. Hence, 4.38X5.217X83 
 = 1,896. 6,nearly. By actual multiplication, the product is 1,896.58818, show- 
 ing that the result obtained by using logarithms was correct to five 
 
 When adding logarithms, the algebraic sum is always to be found. Hence, 
 if some of the numbers multiplied together are wholly decimal, the algebraic 
 sum of the characteristics will be be the characteristic of the product. It must 
 be remembered that the mantissas are always positive. 
 
 EXAMPLE 2. Multiply 49.82, .00243, 17, and .97 together. 
 
 SOLUTION. 
 
 Log 49.82 = 1.69740 
 Log .00243 = 3.38561 
 Log 17 = 1.23045 
 Log .97 = 1.98677 
 Adding, 0.30023 = log (49.82 X .00243 X 17 X .97) 
 
 Number corresponding to .30023 is 1.9963. Hence, 49. 82 X. 00243X17 
 X. 97 = 1.9963. 
 
 In this case the sum of the mantissas was 2.30023. The integral 2 added 
 to the positive characteristics makes their sum = 2+ 1 + 1 = 4; sum of negative 
 characteristics = 3+1 = 3, whence 4+( 4)=0. If, instead of 17, the number 
 had been .17 in this example, the logarithm of .17 would have been 1.23045, 
 and the sum of the logarithm would have been 2.30023; the product would 
 then have been .019963. 
 

 MATHEMATICS 33 
 
 DIVISION BY LOGARITHMS 
 
 The principle upon which the process of division by means of logarithms 
 is based is that log r = log a log b. 
 
 Rule I. Subtract the logarithm of the divisor from the logarithm of the dividend, 
 and the result will be the logarithm of the quotient. 
 EXAMPLE 1. Divide 6,784.2 by 27.42. 
 SOLUTION. Log 6,784.2 = 3.83150 
 Log 27.42 = 1.43807 
 
 difference = 2.39343 = log (6,784.2 -4- 27.42) 
 
 Number corresponding to 2.39343 is 247.42. Hence, 6,784.2 -=-27.42 
 = 247.42. 
 
 When subtracting logarithms, their algebraic difference is to be found; 
 The operation may sometimes be confusing, because the mantissa is always 
 positive, and the characteristic may be either positive or negative. 
 
 Rule II. When the logarithm to be subtracted is greater than the logarithm 
 from which it is to be taken, or when negative characteristics appear, subtract the 
 mantissa first, and then the characteristic, by changing its sign and adding. 
 EXAMPLE 2. Divide 274.2 by 6,784.2. 
 SOLUTION. Log 274.2 = 2.43807 
 
 Log 6,784.2 = 3.83150 
 2\60657 
 
 First subtracting the mantissa .83150 gives .60657 for the mantissa of the 
 quotient. In subtracting, 1 had to be taken from the characteristic of the 
 minuend, leaving a characteristic of 1. Subtract the characteristic 3 from this, 
 by changing its sign and adding_ 1 3 = 2, the characteristic of the quotient. 
 The number corresponding to 2.60657 is .040417. Hence, 274.2 -i- 6,784.2 
 = .040417. 
 
 EXAMPLE 3. Divide .067842 by .002742. 
 SOLUTION. Log .067842 = 2.83 150 
 
 Log .002742 = 3.43807 
 difference = 1.39343 
 
 As .83150 .43807 = .39343 and 2 + 3 = 1, number corresponding to 1.39343 
 is 24.742. Hence, .067842 + .002742 = 24.742. 
 
 The only case that is likely to cause trouble in subtracting is that in which 
 the logarithm of the minuend has a negative characteristic, or none at all, and 
 a mantissa less than the mantissa of the subtrahend. For example, let it be 
 required to subtract the logarithm 3.74036 from the logarithm 3.55145. The 
 logarithm 3.55145 is equivalent to 3 + .55 145. Now, if both_+l and 1 are 
 added to this logarithm, it will not change its value. Hence, 3.55145= 3 1 
 + 1 + . 55145 = 3 + 1.55145. Therefore, 3.55145-3.74036 = 
 5+1.55145 
 3+ .74036 
 
 difference = 1+ .81109 = 7.81109 
 
 Had the characteristic of the logarithm been 0_instead of 3, the process 
 would have been exactly the same. Thus, .55145 = 1 + 1.55145; hence, 
 1+1.55145 
 3+ .74036 
 
 difference = l+ .81109 = 2.81109 
 EXAMPLE 4. Divide .02742 by 67.842. 
 SOLUTION. Log .02742 = 2.43807 = 3+1.43807 
 Log 67.842 = 1.83150 = 1+ .83150 
 
 difference = 3+ .60657 = 2.60657 
 
 Number corresponding to 2.60657 is .00040417. Hence, .02742 -=- 67.842 
 = .00040417. 
 
 EXAMPLE 5. What is the reciprocal of 3.1416? 
 
 SOLUTION. Reciprocal of 3.1416 = ^J^Q> and Io 8 O4i6 = log 1 ~ log 
 
 3.1416 = -.49715. Since 0= - 1 + 1, 
 
 I +1.00000 
 .49715 
 
 difference = 1+ .50285 = 1.50285 
 Number whose logarithm is 1.50285 is .31831. 
 
34 MATHEMATICS 
 
 INVOLUTION BY LOGARITHMS 
 
 The process of involution by means of logarithms is based on the principle 
 that log an = log a. 
 
 Rule I. Multiply the logarithm of the number by the exponent that denotes 
 the power to which the number is to be raised; the result will be the logarithm of the 
 required power. 
 
 EXAMPLE 1. What is: (a) the square of 7.92? (6) the cube of 94.7? (c) the 
 1.6 power of 512. that is, the value of 512 i: ? 
 
 SOLUTION. (a) Log 7.92 = .89873; exponent of power = 2. Hence, .89873 
 X 2 = 1.79746 = log 7.922. Number corresponding to 1.79746 is 62.727. Hence, 
 7.922 = 62.727, nearly. 
 
 (b) Log 94.7 = 1.97635; 1.97635X3 = 5.92905 = log 94.7". Number corre- 
 sponding to 5.92905 is 849,280, nearly. Hence, 94.7 3 = 849,280, nearly. 
 
 (c) Log 512i- e= 1.6 X log 512 = 1.6X2.70927 = 4.334832, or 4.33483 (when 
 using five-place logarithms) = log 21,619. Hence, 5121-6 = 21,619, nearly. 
 
 Rule II. // the number is wholly decimal, so that the characteristic is negative, 
 multiply the two parts of the logarithm separately by the exponent of the number. 
 If, after multiplying the mantissa, the product has a characteristic, add it, alge- 
 braically, to the negative characteristic multiplied by the exponent, and the result 
 will be the negative characteristic of the required power. 
 
 EXAMPLE 1. 'Raise .0751 to the fourth power. 
 
 SOLUTION. Log; .0751* = 4Xlog .0751=4X2.87564. Multiplying the parts 
 separately, 4X2 = 8 and 4 X. 87564 = 3.50256. Adding the 3 and 8, 3 
 + (-8)= -5; therefore, log .0751* = 3.50256. Number corresponding to this 
 is .00003181. Hence, .0751* = .00003181. 
 
 A decimal may be raised to a power whose exponent contains a decimal 
 as follows: 
 
 EXAMPLE 2. Raise .8 to the 1.21 power. 
 
 SOLUTION. Log .8 f ; 21 = 1.21X1.90309. There are several ways of per- 
 forming the multiplication. 
 
 First Method. Adding the characteristic and mantissa algebraically, the 
 result is -.09691. Multiplying this by 1.21 gives -.1172611, or -.11726, 
 when using five-place logarithms. To obtain a positive mantissa, add +1 
 and -1; whence, log .8- = - 1 + 1 -.11726 = 1.88274. 
 
 Second Method. Multiplying the characteristic and mantissa separately 
 gives 1.21 + 1.09274. Adding characteristic and mantissa algebraically, gives 
 -.11726; then, adding +1 and -1, log .8 1 - 1 = 1.88274. 
 
 Third Method. Multiplying the characteristic and mantissa separately 
 gives 1.21 + 1.09274. Adding the decimal part of the characteristic to the 
 mantissa gives 1 + ( .21 + 1.09274) = 1.88274 = log .8 1 ' 21 . The number corre- 
 sponding to the logarithm 1.88274 = .76338. 
 
 Any one of these methods may be used, but the first or the third is recom- 
 mended. The third saves figures but requires the exercise of more caution 
 than does the first method. Below will be found the entire work of multipli- 
 cation for both .8 1 ' 21 and .8 <21 . 
 
 1.90309 1.90309 
 
 1.21 _ .21 
 
 90309 90309 
 
 180618 180618 
 
 90309 +1.1896489 
 
 -1-.21 
 
 1.9796489, or 1.97965 
 i 1.8827389, or 1.88274 
 
 In the second case, the negative decimal obtained by multiplying 1 and .21 
 was greater than the positive decimal obtained by multiplying .90309 and .21; 
 hence, + 1 and 1 were added, as shown. 
 
 EVOLUTION BY LOGARITHMS 
 
 The process of evolution by logarithms is based on the principle that 
 
 Rule. Divide the logarithm of the number by the index of the root; the result 
 will be the logarithm of the root. 
 
 EXAMPLE. Extract: (a) the square root of 77,851; (b) the cube root of 
 698,970; (c) the 2.4 root of 8,964,300. 
 
MA THEM A TICS 
 
 35 
 
 SOLUTION. (a) Log 77,851 =4.89127; index of root is 2; hence, log V77.851 
 = 4.89 127 -=-2 = 2.44564; number corresponding to this is 279.02. Hence, 
 V77.851 = 279.02, nearly. 
 
 (6) Log %98,970 = 5.84446 -i-3 = 1.94815 = log 88.746; or, ^698,970 
 = 88.746. 
 
 (c) Log 2 '^8,946,300 = 6.95251 -^ 2.4 = 2.89688 = log 788.64; or, 2- >/8,964,300 
 = 788.64, nearly. 
 
 If it is required to extract a root of a number wholly decimal, and the 
 negative characteristic will not exactly contain the index of the root, without 
 a remainder, the following rule may be used: 
 
 Rule. Separate the two parts of the logarithm; add as many units (or parts 
 of a unit) to the negative characteristic as will make it exactly contain the index 
 of the root. Add the same number to the mantissa, and divide both parts by the 
 index The result will be the characteristic and mantissa of the root. 
 
 EXAMPLE 1. Extract the cube root of .0003181. 
 
 *-7vSi^n i log .0003181 4.50256 
 SOLUTION. Log \.0003181 = ^ -- = ^ . 
 
 (1+2 = 6) + (2 + .50256 = 2.50256) 
 
 (6 -5- 3 = 2) +J2.50256 -5- 3 = .834 19) 
 
 or, log -^0003181 = 2.834 19 = log .068263 
 
 Hence, ^.0003181 = .068263 
 
 EXAMPLE 2. Find the value of 1- *>l.0003181. 
 
 T 1 - 4 Vnnrwi5T log- 0003181 3.50256 
 SOLUTION. Log \.0003181 = - ^ - = 1 41 . 
 
 If .23 is added to the characteristic, it will contain 1.41 exactly three 
 
 aCe> [-4+ (-.23) = -4.23] + (.23 + . 50256 = .73256) 
 
 (-4.23 -s-1.41 = 3) + (.73256-^- 1.41 = .51955) 
 or, log 1 ' 4 >/.0003181 = 3.51955 = log .0033079 
 
 Hence, 1 ' 4 V^003181 = . 0033079 
 
 497 X. 0181X762 
 EXAMPLE 3. Solve, by logarithms, 
 
 SOLUTION. 
 
 3 300X6517 
 497 = 2.69636 
 .0181 = 2.25768 
 762 = 2.88195 
 
 Log 
 
 Log 
 Log 
 
 Log product = 3.83599 
 Log 3,300 = 3.51851 
 Log .6517 = 1.81405 
 
 Hence, 
 
 EXAMPLE 
 
 SOLUTION: 
 
 Log product = 3.33256 
 3.83599 - 3.33256 = .50343 = log 3. 1874 
 497 X. 0181X762 
 3,300X.65i7~- d ' 1874: 
 
 Log 504,203 = 5.70260 
 Log 507 = 2.70501 
 
 Log product = 8.40761 
 Log 1.75= .24304 
 Log 71.4 = 1.85370 
 Log 87 = 1.93952 
 
 Log product 
 8.40761 -4.03626 
 
 Hence ' 
 
 3 r 
 
 \ 
 
 L75X74X87 
 
 4.03626 
 
 28 - 65 
 
36 MATHEMATICS 
 
 SOLUTION OF EQUATIONS BY LOGARITHMS 
 
 Logarithms can often be applied to the solution of equations. 
 EXAMPLE 1. Solve the equation 2.43x 5 = "^.0648. 
 
 SOLUTION. Dividing by 2 .43 , x s = ~~r^r Taking the logs of both numbers , 
 
 5 log x - I -log 2.43; 5 log x = -~- -.38561 =1.80193 -.38561 
 
 = 1.41632. Dividing by 5, log x = 1.88326, whence x= .7643. 
 EXAMPLE 2. Solve the equatipn 4.5* = 8. 
 SOLUTION. Taking the logarithms of both numbers, x log 4.5 = log 8, 
 
 whence, x = . g = "65321" Talcm g logarithms again, log * = log .90309 log 
 
 .65321 = 1.95573-1.81505 = .14068, and x= 1.3825. 
 
 REMARKS. Logarithms are particularly useful in those cases when the 
 unknown quantity is an exponent, as in the last example, or when the exponent 
 contains a decimal, as in several instances in the examples already given. 
 Such examples can be solved without the use of logarithms, but the process is 
 very long and somewhat involved, and the arithmetical work required is 
 enormous. To solve the example last given without using the logarithmic 
 table and obtain the value of x correct to five figures will require, perhaps, 
 100 times as many figures as are used in the solution given, and the resulting 
 liability to error will be correspondingly increased; indeed, to confine the work 
 to this number of figures will also require a good knowledge of short-cut methods 
 in multiplication and division, and judgment and skill on the part of the 
 calculator, which can only be acquired by practice and experience. 
 
 Formulas containing quantities affected with decimal exponents are gener- 
 ally of an empiric nature; that is, the constants or exponents or both are given 
 such values as will make the results obtained by the formulas agree with those 
 obtained by experiment. Such formulas occur frequently in works treating 
 on thermodynamics, strength of materials, machine design, etc. 
 
 GEOMETRY 
 
 PRINCIPLES OF GEOMETRY 
 
 1. The sum of all the angles formed on one side of a straight line equals 
 two right angles, or 180. 
 
 2. The sum of all the angles formed around a point equals four right 
 angles, or 360. 
 
 3. When two straight lines intersect each other, the opposite or vertical 
 a/igles are equal. 
 
 4. If two angles have their sides parallel, they are equal. 
 
 5. If two triangles have two sides, and the included angle of the one 
 equal to two sides and the included angle of the other, they are equal in all 
 their parts. 
 
 6. If two triangles have two angles, and the included side of the one equal 
 to two angles and the included side of the other, they are equal in all their parts, 
 
 7. In any triangle, the greater side is opposite the greater angle, and the 
 greater angle is opposite the greater side. 
 
 8. The sum of the lengths of any two sides of a triangle is greater than 
 the length of the third side. 
 
 9. In an isosceles triangle, the angles opposite the equal sides are equal. 
 
 10. In any triangle, the sum of the three angles is equal to two right 
 angles, or 180. 
 
 11. If two angles of a triangle are given, the third may be found by sub- 
 tracting their sum from two right angles, or 180. 
 
 12. A triangle must have at least two acute angles, and can have but one 
 obtuse or one right angle. 
 
 13. In any triangle, a perpendicular let fall from the apex to the base is 
 shorter than either of the two other sides. 
 
 14. If a triangle is equilateral, it is equiangular, and vice versa. 
 
 15. If a straight line from the vertex of an isosceles triangle bisects the base, 
 it bisects the vertical angle and is perpendicular to the base. 
 
 16. If one side of a triangle is extended, the exterior angle thus formed, 
 is equal to the sum of the two interior and opposite angles. 
 
MATHEMATICS 37 
 
 17. If two triangles are mutually equiangular, they are similar and their 
 corresponding sides are proportional. 
 
 18. Triangles that have an angle in each equal, are to one another as the 
 products of the sides including those equal angles. 
 
 19. Similar triangles are to one another as the squares of their corre- 
 sponding sides. 
 
 20. In a right-angled triangle, the square of the hypotenuse is equal to the 
 sum of the squares of the other two sides. 
 
 21. If a triangle is inscribed in a semicircle, one side being a diameter, it 
 is right-angled. 
 
 22. In any parallelogram, the opposite sides are equal; the opposite angles 
 are equal; it is bisected by its diagonals into two equal triangles, and its diag- 
 onals bisect each other. 
 
 23. If the sides of a polygon are produced in regular order, the sum of the 
 exterior angles thus formed is equal to 360. 
 
 24. The sum of the interior angles of a polygon is equal to twice as many 
 right angles as the polygon has sides, less four right angles. For example, the 
 sum of the interior angles of a pentagon is (2X5) 4 = 6 right angles, or 540; 
 of an octagon, (2X8) 4 = 12 right angles, or 1,080, etc. 
 
 25. The diagonals joining the vertices of a regular polygon intersect at 
 the center of the inscribed and circumscribed circles. 
 
 26. The angle at the center subtended by the side of a regular polygon is 
 equal to 360 divided by the number of sides. 
 
 27. Plane figures are similar when they are bounded by the same number 
 of similar sides and their correspondingly situated angles are equal each to each. 
 
 28. The perimeters of similar polygons are to one another as any two 
 corresponding sides; and their areas are to one another as the squares of those 
 sides. 
 
 29. The circle is a polygon of an infinite number of sides. 
 
 30. A circle may be described about or inscribed within any regular 
 polygon. 
 
 31. Through three points not in the same straight line a circle may be made 
 to pass and but one. 
 
 32. The diameter of a circle is greater than any chord. 
 
 33. Any radius that is perpendicular to a chord, bisects the chord and the 
 arc subtended by it. 
 
 34. Arcs and chords of the same circle are proportional to the angles at 
 the center of the circle subtended by them. 
 
 35. Similar arcs are proportional to the radii of their circles. 
 
 36. A tangent to a circle meets it at one point only, and is perpendicular 
 to the radius at that point. 
 
 37. If from a point without a circle tangents are drawn to touch the 
 circle, there are but two such tangents; they are equal, and they make equal 
 angles with the chord joining the points of tangency. 
 
 38. The angle between a tangent and a chord is equal to one-half the angle 
 at the center subtended by the chord. 
 
 39. The perimeters of circles are to one another as any two corresponding 
 dimensions, and their areas are to one another as the squares of such dimensions. 
 
 40. Only five regular polyhedrons are possible; the tetrahedron with four 
 triangular faces; the cube with six square faces; the octahedron with eight 
 triangular faces; the dodecahedron with twelve pentagonal faces; and the 
 icosahedron with twenty triangular faces. 
 
 41. The sum of all the angles of the faces of any polyhedron is equal to 
 four right angles taken as many times as che polyhedron has vertices less two. 
 
 42. The center of any regular polyhedron and of -its circumscribed and 
 inscribed spheres is at the point of intersection of the diagonals joining its 
 opposite vertices. 
 
 43. Solids are similar which are bounded by the same number of similar 
 faces similarly placed, and which have their corresponding polyhedral angles 
 equal. 
 
 44. The areas of the surfaces of similar solids are to one another as the 
 squares of their similar dimensions, and the volumes of similar solids are to 
 one another as the cubes of like dimensions. 
 
 45. The sphere is a regular polyhedron of an infinite number of sides. 
 
 46. A sphere may be described about any regular polyhedron, and its 
 radius is equal to the distance from any vertex to the center; and a sphere 
 may be inscribed within any regular polyhedron, and its radius is equal to the 
 perpendicular distance from the center of any face to the center of the figure. 
 
38 
 
 MA THEM A TICS 
 
 47. Through four points not in the same plane a spherical surface may be 
 made to pass, and but one. 
 
 48. From a point without a sphere two tangents may be drawn to a great 
 circle of the sphere, and but two. 
 
 49. Through a line without a sphere two tangent planes to the surface 
 of the sphere may be drawn, and but two. 
 
 PROBLEMS IN GEOMETRICAL CONSTRUCTION 
 1. To Bisect a Given Straight Line or the Chord or the Arc of a Circle. 
 
 Let AB, Fig. 1, be the given line or chord and ACB the arc of the circle. With A 
 * and B as centers and with a radius greater than one- 
 
 half the line AB or the arc ACB, describe arcs inter- 
 secting at E and F. The line EF will bisect the line, 
 chord, or arc. 
 
 COROLLARY. The line EF will also be perpendicu- 
 lar to the line AB and, when prolonged, will pass 
 through the center of the circle of which ACB is 
 the arc. _ 
 
 2. From a Given Point 
 C, Without a Straight Line 
 _, A B, to Draw a Perpendicular < A 
 
 * IG - * to the Line. From C, Fig. 2, ^ a 
 
 as a center, with a radius greater than the distance 
 from C to AB, describe an arc cutting the line AB 
 at A and B. From A and B as centers and with a 
 radius greater than one-half of AB, describe arcs 
 intersecting at D, and draw the line CD. 
 
 COR. The line CD will bisect that portion of the line 
 the points A and B. 
 
 3. At a Given Point C in a Straight Line AB, 
 to Erect a Perpendicular to That Line. Lay off 
 the points A and B, Fig. 3, equidistant from C, and 
 with A and B as centers and, with a radius greater 
 than one-half AB, describe arcs intersecting at D. 
 The line DC will be perpendicular to AB. 
 
 4. To Erect a Perpen- _ 
 dicular at the End A of a 
 Given Line A B. First 
 
 L 
 
 FIG. 2 
 ncluded between 
 
 FIG. 3 
 
 Method. From any point C, Fig. 4, above the line 
 AB and with a radius AC describe the arc of the circle 
 AD, which also cuts the line AB at B. Connect B 
 and C and prolong the line to intersect the circle at D. 
 
 The line AD will be perpendicular 
 
 to the line AB. 
 
 FIG. 4 
 
 Second Method. From the given point A, Fig. 5, set 
 off a distance AB equal to three parts by any scale. 
 From A and B as centers and with radii equal, respec- 
 tively, to four parts and five parts, draw arcs intersecting 
 at C. The line AC will be the perpendicular required. 
 
 NOTE. This is one of the methods employed for laying 
 off the coordinates on mine maps. 
 
 5. Through a Given 
 
 u Point A, to Draw a Straight 
 
 FIG. 5 Line Parallel to a Given 
 
 Straight Line CD. With A , Fig. 6, as a center 
 
 and with a radius greater than the shortest 
 
 distance from A to the line CD, describe an 
 
 indefinite arc DB. With D as a center and with 
 
 _ ~ the same radius 
 
 D 
 
 FIG. 7 
 
 DA .describe the FlG< 6 
 
 arc AC. With D as a center and with the radius 
 AC describe an arc cutting the arc DB at B, 
 The line AB will be parallel to the line CD. 
 
 6. To Draw a Straight Line Parallel to a 
 Given Line and at a Given Distance From It. 
 
 First Method. Select any two points A and B, Fig. 7, on the given line. With 
 these as centers and with radii equal to the distance apart of the lines de- 
 scribe the arcs C and D. Draw the line CD touching the arcs. 
 
MA THEM A TICS 
 
 39 
 
 1 
 
 * 
 
 f. 
 
 Frc. 9 
 
 Second Method. At any two selected points A and B, Fig. 8, in the given 
 line, erect perpendiculars. With A and B as centers and with a radius equal 
 to the distance apart of the lines, draw arcs of 
 
 circles cutting the perpendiculars at C and D. t c ,/> 
 
 The line CD joining these points of intersec- ~ 
 tion will be parallel to the line AB. 
 
 NOTE. These methods are employed to 
 lay off the coordinates of mine maps. 
 
 7. To Divide a Straight Line Into Any 
 Number of Equal Parts. Let AB, Fig. 9, be 
 
 .a straight line that is to be divided into, say, seven equal parts. Draw 
 the parallel lines AC and BD making any angle with A B, and measure 
 off upon each of them seven equal spaces. Connect the points, 1 and 1 , 2 and 2, 
 etc., by lines. These lines will divide the line A B into seven equal parts. 
 
 Or, but one line AC need be drawn. 
 By connecting 7 and B, the parallel lines 
 drawn through 6,5,4, etc., will divide the 
 line as required. 
 
 B NOTE. This method is available for 
 7 dividing a line into any odd number of 
 parts when no scale of such parts is to be 
 had. Thus, to divide a line, 2J in. long 
 into sevenths, seven i or 5 in., may be laid 
 off along the line AC. The operation will, if 
 properly carried out, divide the 2fc in. into 
 seven equal parts of .3171 in. 
 A line may be divided into proportional parts by this method. Thus to 
 divide the line AB in the ratio of 3 to 4- Lay off the distance A-3 equal to 
 three parts, and the distance 4~7 equal to four parts. The line 3-3 will divide 
 the line AB in the required ratio. 
 
 8. At a Point A on a Given Straight Line AB, 
 to Make an Angle Equal to a Given Angle EFG. 
 From F, Fig. 10, as a center and with any radius FG 
 describe the arc EG. From A as a center and 
 with the same radius, describe the arc CB\ then 
 with a radius equal to the chord EG, describe an 
 arc from B as a center, cutting CB at D, and draw 
 the line AD. The angle BAD will be equal to the 
 
 , angle EFG. 
 
 9. To Draw Angles of 60 and 30. From any point 
 A, Fig. 11, on the line AB and with any radius AB 
 describe the arc BD. With B as a center and with the 
 same radius AB, describe an arc cutting BD at D. The 
 line AD will form an angle DAB with AB equal to 60. 
 The perpendicular DC to the base will form the angle 
 ADC of 30. 
 
 10. To Draw an Angle of 45. 
 Lay off any distance AB, Fig. 12, 
 and at B erect a perpendicular to 
 
 AB. With B as a center and with a radius equal to 
 
 BA describe an arc cutting the perpendicular at C. 
 
 The line AC will form with the line AB an angle CAB 
 
 equal to 45. 
 
 Or, the second method under problem 4 may be used. FIG. 12 
 
 11. To Bisect an Angle ABC. With any radius and 
 
 with B, Fig. 13, as a center, describe an arc cutting the sides at A and C. 
 With A and C as centers, describe arcs of equal 
 radius intersecting at D. The line BD is the 
 bisector, and the angle ABD = angle DEC. 
 
 12. To Bisect an Open Angle (Method by L. L. 
 LOGAN). Let AB and CD, Fig. 14, be the sides of 
 an open angle. With any point O as a center, 
 describe a circle cutting the sides at e,f, g, and h, 
 and with e and /, and g and h as centers and any 
 radius, describe arcs intersecting at k amd /, 
 
 respectively. Draw Ok and Ol and mn. With p and q as centers, and any 
 
 radius, describe arcs intersecting at R and S. The line drawn through RS is 
 
 the required bisector. 
 
 Q 
 
 D 11 
 
 FIG. 13 
 
40 
 
 MATHEMATICS 
 
 13. To Find the Center of a Given Circumference or Arc. First Method. 
 Take any three points A, B, and C, Fig. 15, on the circumference and unite 
 them by lines AB and BC. Bisect these 
 chords by the perpendiculars DO and EO\ 
 their intersection is the center of the circle. 
 
 Second Method. Take any three points A , B, 
 and C, Fig. 16, on the circumference as far 
 apart as convenient. With these three points 
 
 FIG. 14 
 
 FIG. 15 
 
 FIG. 16 
 
 as centers and with the same radius, draw a series of intersecting arcs. The 
 lines GF and DE through these intersections cut one another at the center H 
 of the circle. 
 
 NOTE. This method is employed to describe a circle through any three 
 points not in the same straight line. 
 
 14. To Describe an Arc of a Circle 
 Passing Through Three Given Points 
 When the Center Is Not Available. 
 Let A, B, and C, Fig. 17, be the three 
 points. From A and C as centers and 
 with the radius AC describe the arcs CY 
 and AX. Through the third point B 
 draw the lines CD and AE cutting the 
 arcs. Divide the distance AD into any 
 number of equal parts and lay off 
 similar parts above D on the arc AX. 
 
 Also lay off like parts above and below E on the arc CY. Draw lines CF, CG, 
 etc., and AH, AL, etc. Their intersection, 1, and 2, will be points on the 
 required circle. The curve may be drawn by splines. The smaller the divi- 
 sions of the arcs, the more points will there be given in the arc of the circle. 
 
 15. To Draw a Tangent to a Circle Through a Given Point P in the Circum- 
 ference. Find the center C, Fig. 18, of the circle by any of the methods de- 
 scribed and draw the radial line CD. At P erect a perpendicular AB to this 
 line CD; the perpendicular AB will be tangent to the circle at P. 
 
 FIG. 17 
 
 FIG. 18 
 
 FIG. 19 
 
 16. To Draw Tangents to a Circle From a Point P Without the Circum- 
 ference. First Method. If the center of the circle is not given find it by any 
 method, and draw the line PC, Fig. 19. Bisect this line PC at E, and with the 
 radius EC = PE, describe a circle cutting the given circle at A and B. Con- 
 nect A and P and B and P; the lines AP and BP will be tangent to the circle. 
 
 Second Method. As before, let P, Fig. 20, be the point. Find the center C 
 of the circle and draw the line PCD. With P as a center and with a radius PC, 
 
M A THEM A TICS 
 
 41 
 
 describe the arc FCG. With C as a center and with a radius equal to the 
 diameter DE of the circle, cut this arc at F and G. Draw the lines FC and GC 
 cutting the circle at L and K. Draw the lines PB and PA through L and K 
 respectively; they will be tangents to 
 the circle. 
 
 17. To Draw an Arc of a Circle 
 Tangent to Two Lines Inclined to Each 
 Other, One Point of Tangency B 
 Being Given. Produce the given lines, 
 AB and CD, Fig. 21, until they inter- 
 sect at E. Bisect the angle A EC by 
 the line EF. Draw a perpendicular Fl G- 21 
 
 to the line AB from the point B. Its intersection G with the line EF, the 
 bisector of the angle, is the center of the required arc. The other point of tan- 
 gency may be found by dropping a perpendicular GH upon the line CD. 
 NOTE. If an intersection cannot be reached, use the method described 
 in problem 12, for bisecting the angle. 
 
 18. To Construct a Triangle, the Sides 
 Being Given. Let A B, Fig. 22, be one of the 
 sides. With A as a center and a radius equal 
 to one of the remaining sides describe the arc 
 AC, and with B as a center and a radius equal 
 to the third side describe the arc BC cutting 
 the arc AC at C' Draw the lines AC and 
 BC; then ABC will be the required triangle. 
 
 p IG> 22 
 
 19. To Describe a Circle About a Triangle. Let 
 ABC, Fig. 23, be the triangle. Bisect any two sides 
 as A B and AC at D and E and at these points erect 
 perpendiculars to the sides intersecting at F. With F 
 as a center and with a radius equal to FA = FB = FC, 
 describe the circle ABC. 
 
 20. To Inscribe a Circle in a Triangle. Let ABC, 
 
 Fig. 24, be the given 
 
 triangle. Bisect 
 any two angles, such 
 as A and C, by lines p IG 23 
 
 intersecting at D. 
 
 Drop a perpendicular from D upon any side 
 as DE upon the side AC, and with D as a 
 center and a radius DE, inscribe the circle. 
 21. To Construct a Hexagon Upon a 
 Given Straight Line. Let FE, Fig. 25, be 
 
 FIG. 24 
 
 the given line. From its extremities F and E as 
 
 centers and with the radius FE describe arcs of circles 
 
 intersecting at G. With a radius GE, draw the cir- 
 cumscribing circle EDCBAF. With the same radius 
 
 GE = FE set off upon the circumference of this circle 
 
 the chords ED, DC, CB, and BA. The points so 
 
 found, when joined, will form the required hexagon. 
 NOTE. The side of any hexagon is equal to the 
 
 radius of its circumscribed circle. As the exterior 
 
 angles of a hexagon are each equal to 60, this polygon 
 
 is readily drawn with a straightedge and a 60-30 
 triangle. 
 
 22. To Describe an Octagon Upon a Given Straight 
 Line. Let AH, Fig. 26, be the given line. Produce 
 it in both directions and at A and H erect the perpen- 
 diculars AD and HE. Bisect the angles DAa and 
 EHh with the lines AB and HG. With A and H as 
 centers and with a radius AH equal to the length of 
 the given side describe arcs cutting the bisectors at 
 B and G respectively; AB and HG will be sides of 
 the octagon. Draw BC and GF parallel to DA and 
 EH. Make them equal to AH by cutting them 
 (using B and G as centers) with the arcs of a circle whose 
 From C and F as centers and with a radius equal to AH, 
 
 FIG. 26 
 radius is equal to AH. 
 
 describe arcs of circles intersecting the perpendiculars at D and E. The lines, 
 CD, DE, and EF, joining the points thus determined, complete the octagon. 
 
42 
 
 MATHEMATICS 
 
 NOTE. As the exterior angles of an octagon are each 45, this polygon is 
 
 readily drawn with a straightedge and a 45 triangle. 
 
 23. To Construct an Ellipse, the Axes Being Given. Let AB and CD, 
 
 Fig. 27, be the major and minor axes, respectively, intersecting, bisecting, and 
 perpendicular to each other at P. Using P 
 as a center draw two circles with radii equal, 
 respectively, to one-half the axes, or PA and 
 PC. Prom P, draw any number of random 
 lines, as Pa, Pb, ... P/ to the circumfer- 
 ence of the larger circle and drop perpendic- 
 ulars from the extremities, a, b, . . . f. From 
 the points of intersection, 1, 2, . . . 6, of the 
 lines Pa, Pb, etc., with the smaller circle draw 
 lines parallel to the major axis AB. The 
 points of intersection of these parallels with 
 the verticals previously drawn will be points 
 on the ellipse. This is the most convenient 
 method of drawing an ellipse and is the one 
 used very largely in drafting rooms. It will 
 be noted that more points should be deter- 
 mined where the .direction of the curve is 
 
 FIG. 27 
 
 changing rapidly, as at and near B, than at C where, for a considerable dis- 
 tance on either side of the minor axis, the change in direction is slight. 
 
 The foci of the ellipse may be found by drawing, with C or D as a center 
 and with PA = PB as a radius, arcs of circles cutting the major axis at F and F'. 
 
 There are numerous complicated and inaccurate methods of drawing what 
 is called an approximate ellipse, three of which are given, but they do not 
 compare in simplicity with the exact method given. 
 
 24. To Construct an Approximate Ellipse, the Axes Being Given. 
 Method by Three Centers. Let a, Fig. 28, be the center, be the major, and ae 
 one-half of the minor axis of an ellipse. 
 Draw the rectangle bfgc, and the diagonal 
 line be; at a right angle to the line be, draw 
 line fh cutting the line BB at i. With radius 
 ae, and from a as a center, draw the dotted 
 arc ej, giving the point j on the line BB. 
 From k, which is central between b and j, 
 draw the semicircle bmj, cutting the line 
 A A at I. Draw the radius of the semicircle 
 bmj, cutting fg at n. With radius mn, mark 
 on the line A A, from a as a center, the 
 
 rint o. With radius ho, and from center 
 draw the arc poq. With radius al, and 
 from b and c as centers, draw arcs cutting 
 the arc poq at the points p and q. Draw 
 the lines hpr and hqs, and also the lines pit 
 and qvw. From h as a center, draw that 
 part of the ellipse lying between r and s 
 with radius hr. From p as a center draw 
 
 FIG. 28 
 
 that part of the ellipse lying between r and t with the radius pr. From q, draw 
 the ellipse from s to w . With radius */, from i as a center, draw the ellipse from 
 / to b with radius it, and from v as a center, draw the ellipse from w to c, and 
 one-half the ellipse will be drawn. It will be noted that the whole construc- 
 tion has been performed to find the centers h, p, q, i, and v, and that while v 
 and * may be used to carry the curve around the other side or half of the 
 ellipse, new centers must be provided for h, p, and q; these new centers cor- 
 respond in position to h, p, q. 
 
 INoTE. This method is the one commonly employed 
 to lay off concrete, or masonry arches, etc. 
 Method by Straightedge. On a straightedge, lay off 
 AB, Fig. 29, equal to one-half the shorter axis and AC 
 equal to one-half the longer axis. Determine points 
 in the ellipse by marking positions of A as the point B 
 is moved along the major axis, at the same time the 
 point C being kept in the minor axis. 
 
 Method by Cord. Lay off the axes and find the foci 
 
 FIG. 29 
 
 as described in problem 23. Stick pins at the foci F and F', Fig. 27. To these 
 pins attach a string making its length equal to FC+CF'. The point of a 
 
MATHEMATICS 43 
 
 pencil placed inside the string may be made to describe an ellipse, if the string 
 is kept tightly and uniformly stretched while the pencil is in motion. 
 
 NOTE. This is the method commonly employed to lay off an ellipse upon 
 the ground, as when making garden beds, etc. 
 
 The cord and straightedge methods are theoretically capable of describing 
 a true ellipse. That is, the methods are founded on the mathematical prin- 
 ciples governing the ellipse, but it is not generally possible to manipulate 
 either the string or straightedge so that perfect results may be obtained. 
 
 MENSURATION OF SURFACES 
 
 TRIANGLES 
 
 A triangle is a plane surface bounded by three straight lines. Some of the 
 different kinds of triangles are shown here. 
 
 a, b, c = sides opposite angles A, B, 
 
 andC 
 
 P = perimeter 
 
 h = perpendicular upon base from 
 vertex of angle opposite 
 
 Acute 
 
 Let A, B, C = interior angles 
 A', B', C' exterior angles 
 6 = side called base 
 A = area 
 m = distance from foot of 
 
 h to nearest vertex 
 Angles. A +B + C= 180. A = 180- (B+O, and similarly for B and C. 
 A+A' = 18Q, and similarly for B + B' and. C+C'. A' =180- A, and simi- 
 larly for B' and C. A' + B' + C' = 360. A' = 360 -(B' + C r ), and similarly 
 for B' and C'. A' = B+C; B' = A + C; C' = A+B. 
 
 Perimeter and Sides. P = a+b + c. In all acute-angled triangles, includ- 
 
 ing equilateral, isosceles, and right-angled triangles, any side a= V& 2 +c 2 2bm. 
 
 In an obtuse-angled triangle, the side opposite the obtuse anglea = V6 2 +c 2 +2fci. 
 
 Altitude. In any triangle, the altitude, or perpendicular distance from the 
 
 base to the vertex of the opposite angle, is h= Vc 2 m?. 
 
 Area. In any triangle, the area is equal to the product of the base by 
 
 one-half the altitude, or A = -=-. Any side may be selected as the base. Thus, 
 
 in the obtuse-angled triangle, if the base is the side b, A = ; if the base is the 
 side a, A = -^-. If the length of the three sides is given, let p = one-half the 
 
 sum of the three sides, or p = a+ ^ + -, and A = ^p(p-a)(p-b)(p-c)\ that is, 
 
 the area is equal to the square root of one-half the sum of the sides multiplied by 
 this one-half sum less each one of the sides, respectively. 
 
44 
 
 MATHEMATICS 
 
 Special Cases. Equilateral Triangle. Angle A=B = C-=GO. Side a = b 
 
 = c. Altitude h = side X. 866025. Side = h -h .866025 = h X 1.154701. Side 
 
 = VareaX 1.51967. . Area = side 2 X. 443013. Length of side of square having 
 same area as an equilateral triangle = side of triangle X. 658037. Diameter of 
 circle of same area as an equilateral triangle = side of triangle -5- 1.34677. The 
 perpendicular h bisects the angle B and the side b; and similarly for the other 
 angles and sides. This triangle is also known as the equiangular or 60 triangle. 
 
 Isosceles Triangle. Angle A=C. B = 90 - A or C. Side a = c. The per- 
 pendicular h bisects the angle B and the side b. 
 
 Right- A ngled Triangle. Angle A = 90. Angles B + C = 90. Side a 2 = b 1 + 
 c*, and o= V& 2 +c 2 , b = Va 2 -c 2 , c= Va 2 -R 
 
 For other properties and methods of solving triangles, see under 
 Trigonometry. 
 
 PARALLELOGRAMS 
 
 A parallelogram is a plane figure bounded by four straight lines which are 
 parallel, two and two. Some of the different kinds of parallelograms are 
 shown here. 
 
 A*. 
 
 Square. Four 
 
 equal sides 
 and four right 
 angles 
 
 Rectangle. Four 
 
 right angles 
 and opposite 
 sides equal 
 
 Rhombus. Four 
 equal sides 
 
 and 
 oblique angles 
 
 Rhomboid. Four 
 oblique angles 
 
 and 
 opposite sides equal 
 
 Angles. The sum of the exterior angles = the sum of the interior angles 
 <=A+B+C+D = A'+B'+C r +D' = 36Q. In the square and the rectangle, 
 the four angles are equal and each is 90; in the rhombus and rhomboid, A =C 
 and B = D. In the square and the rhombus, the diagonals are perpendicular 
 to one another and bisect one another and the angles at their opposite 
 extremities. 
 
 Perimeter and Sides. Let the sides be a, b, c, and d, respectively, then the 
 perimeter, P = a+b + c+d. In the square and rectangle, any side = area -?- by 
 an adjacent side. In the rhombus and rhomboid, a side = area -I- by the 
 altitude h. In all four cases, the diagonal d = area-=-by perpendicular p. 
 
 Area. In all cases, the area A = bh = dp. 
 
 Square. Diagonal d = sideX 1.41421. Side = diagonal X .707107. The side 
 of a square equal in area to a given circle = diameter of circle X. 886277. The 
 area of the largest square that may be inscribed in a circle = 2 X radius of circle. 2 
 
 It should be noted that all problems relating to parallelograms, as well as 
 to trapezoids, trapeziums, and regular and irregular polygons, may be solved 
 by resolving these figures into triangles. 
 
 TRAPEZOIDS 
 
 A trapezoid is a plane figure bounded by four straight lines, only two of 
 - "- 1 -- - 1 - 
 
 which are parallel one to the other 
 
 One is shown in the accompanying figure. 
 Angles. The sum of the interior 
 angles = the sum of the exterior angles 
 = 360, or A+B+C+D = A' + B' + C' 
 +D' = 360. A=B': B = A'; C=D f ; D 
 = C'. A = 180-A'; B= 180 - B'; and 
 similarly for C and D. A + B = C' + D'; 
 A+C=B'+D'; A+D = B'+C'; B+C 
 = A'+D'; and similarly for other combi- 
 nations of A, B, C, and D. 
 
 Perimeter. The sides being a, b, c, and 
 1 d, the perimeter P = a+b+c+d. 
 Diagonal. The diagonal d = 2 X area -^ (p+p f ). 
 Area. Case /.Given the two parallel sides a and c and the perpendicular 
 
 distance between them h, A= 
 

 MATHEMATICS 45 
 
 Case II. Given the diagonal d and the perpendiculars upon it p and P'. 
 
 Case III. Given the two parallel sides a and c and the angles adjacent to 
 one of them, A and D, the area, 
 
 _ c 2 a 2 _ (c o)(c+a) sin A sin B 
 
 2 (cot A+cot B)~~ 2 sin (A+B) 
 Case IV. Given all four sides a, b, c, and d. Let c a=f, and 
 
 = 5, then area A = 
 
 TRAPEZIUMS 
 
 A trapezium is a plane figure bounded by four straight lines, no two of which 
 are parallel. 
 
 FIG. 1 
 
 FIG. 2 
 
 Angles. As with trapezoids, the sum of the interior angles = the sum of 
 the exterior angles = 360. Also, A = 180 A', and similarly for B, C, and D. 
 
 Perimeter and Diagonal. The same relations prevail for the perimeter 
 and the diagonal as for trapezoids. 
 
 Area. In the trapezium shown in Fig. 1, A = [b(h+h') + ah+ch']. 
 
 In the trapezium shown in Fig. 2, A - (p-\-p f ). 
 
 POLYGONS 
 
 A polygon is a plane figure bounded by three or more straight lines. Some 
 of the more common forms are shown in Fig. 1. 
 
 Pentagon 
 
 Hexagon 
 
 Heptagon 
 
 Octagon 
 
 FIG. 1 
 
 If all the sides and angles are equal, each to each, the figure is a regular 
 polygon; otherwise it is not. Of the figures previously discussed, the 
 equilateral triangle and the square are regular polygons; the others are 
 irregular. 
 
 In any regular polygon, Fig. 2, let the central angle (AOB = BOC, etc.) =C; 
 let the interior angle (ABC = BCD, etc.) = /; let the exterior angle (A'AB 
 
 = B'BC, etc.) = . Also let R = -= = radius of circumscribed circle, and let r 
 
 = - = radius of inscribed circle = apothem. Likewise, let 5 = length of a side 
 
 as AB, BC, etc., and let N = number of sides. 
 
 Central Angle. The central angle is equal to the exterior angle and is equal 
 
 to 360 divided by the number of sides in the polygon, or C = E = -^-. The 
 sum of either the central or the exterior angles of any polygon is 360. 
 
46 
 
 MATHEMATICS 
 
 Interior Angle. The interior angle is equal to 180 minus either the central 
 the exterior angle, or / = 180 C= 180 E. The sum of all the interior 
 
 
 
 '--,?' 
 
 angles of any polygon is equal to twice as many 
 right angles as the polygon has sides, less four 
 right angles, or 27= (2X-/VX90)-360. 
 
 Diagonals. The diagonals AD, BE, etc., of 
 a regular polygon bisect the interior angles /, 
 bisect one another, intersect at the center of 
 the inscribed and circumscribed circles, divide the 
 polygon into as many isosceles triangles as it has 
 sides; also, they are the diameters D of the cir- 
 cumscribed circle. 
 
 Apothems. The apothems LO, etc., of a 
 regular polygon are perpendicular to the sides. 
 They bisect the sides, the central angles, and 
 one another; divide the fundamental isosceles 
 triangles of the polygon into two equal right 
 angled triangles BLO+CLO = BOC; and are 
 
 the radii r of the inscribed circle. 
 
 Perimeter and Sides. The perimeter of any polygon is equal to the sum 
 
 of the lengths of all its sides. The perimeter of a regular polygon, P = NS. 
 
 Any side, 5= 2^R*=r* = 2R sin = 2r tan = . 
 
 p' 
 
 Area. In any polyg9n, the area is equal to the sum of the areas of the 
 triangles into which it is divided by its diagonals. The area of a regular 
 polygon is equal to the area of one of the fundamental triangles, as AOB, 
 multiplied by the number of sides. ' 
 
 A = Nr z tan = 
 
 Likewise, 
 sin C- 
 
 The accompanying table gives, for the more important regular polygons, 
 the number of sides; the name; the central angle, which equals the exterior 
 angle; the interior angle; the length of the side, in terms of the radius of both 
 the circumscribed and inscribed circles R and r\ and the area, in terms of the 
 side 5 and in terms of the radius of the circumscribed and inscribed circles R 
 and r, respectively. 
 
 NAMES AND RELATIONS OF REGULAR POLYGONS 
 
 *6 
 
 L, 05 
 
 
 Angle 
 
 Side 
 
 Area 
 
 S <U 
 
 13 
 
 . Name 
 
 
 
 
 
 
 
 
 
 
 
 9 
 
 fci 
 
 
 C = E 
 
 7 
 
 R = l 
 
 r=l 
 
 5=1 
 
 R=l 
 
 r = l 
 
 3 
 
 Equilateral 
 
 120 
 
 60 
 
 1.73205 
 
 3.46410 
 
 .43301 
 
 1.29904 
 
 5.19615 
 
 
 Triangle 
 
 
 
 
 
 
 
 
 4 
 
 Square 
 
 90 
 
 90 
 
 1.41421 
 
 2.00000 
 
 1.00000 
 
 2.00000 
 
 4.00000 
 
 5 
 6 
 
 Pentagon 
 Hexagon 
 
 72 
 60 
 
 108 
 120 
 
 1.17557 
 1.00000 
 
 1.45308 
 1.15470 
 
 1.720482.37765:3.63271 
 2.59808 2.59808 3.46608 
 
 7 
 
 Heptagon 
 
 51 25.7' 
 
 128 34.3' 
 
 .86776 
 
 .96315 
 
 3.63391 
 
 2.73641 
 
 3.37106 
 
 8 
 
 Octagon 
 
 45 
 
 135 
 
 .76536 
 
 .82842 
 
 4.82842 
 
 2.82840 
 
 3.31368 
 
 9 
 
 Nonagon 
 
 40 
 
 140 
 
 :68404 
 
 .72794 
 
 6.18183 
 
 2.89253 
 
 3.27573 
 
 10 
 
 Decagon 
 
 36 
 
 144 
 
 .61804 
 
 .64984 
 
 7.69421 
 
 2.93895 
 
 3.24921 
 
 11 
 
 Undecagon 
 
 32 43.6' 
 
 14716.4' 
 
 .56346 
 
 .58724 
 
 9.36581 
 
 2.97341 
 
 3.22972 
 
 12 
 
 Dodecagon 
 
 30 
 
 150 
 
 .51764 
 
 .53590 
 
 11.19615 
 
 3.00000 
 
 3.21538 
 
 EXAMPLE 1. What is the length of the side of a triangle inscribed in a 
 circle of 2 in. radius? 
 
 SOLUTION. Here R = 2 and the side 5 = 2X1.73205 = 3.46410. 
 
 EXAMPLE 2. 'What is the length of the side of a pentagon circumscribed 
 about a circle of 4 in. radius? 
 
 SOLUTION. Here r = 4 and side 5 = 4X1.45308 = 5.81232 in. 
 
 EXAMPLE 3. What is the area of a hexagon whose side is 2 in. long? 
 
 SOLUTION. Here 5 = 2 and area = 5 2 or 4X2.59808=10.39232 sq. in. 
 
 EXAMPLE 4. What is the area of a dodecagon that may be inscribed in a 
 circle of 3 in. radius? 
 
MATHEMATICS 
 
 47 
 
 SOLUTION. In this case, R = 3 and area =R* or 9X3.000000 = 27.000000 
 sq. in. 
 
 EXAMPLE 5. What is the area of a decagon that may be circumscribed 
 about a circle of 4 in. radius? 
 
 SOLUTION. In this case r = 4 and area = r 2 or 16X3.24921 = 51.9874 sq. in. 
 
 EXAMPLE 6. What is the radius of the circle that may be circumscribed 
 about a square whose side is 2 in.? 
 
 SOLUTION. Here R = 2 and it is required to find S. 5 = 2^-1.41421 
 = 1.41421. 
 
 Area of Irregular Polygons. If the figure is bounded by straight lines, to 
 find its area divide it into triangles; the sum of the areas of these will be equal 
 to that of the irregular polygon. This method is commonly used by engineers 
 as a useful check upon the accuracy of the areas obtained by calculation. In 
 many cases the results thus obtained answer every purpose. 
 
 If one or more of the boundaries is an irregular line, as -would be that of the 
 bank of a river, the area may be found by one of several methods. 
 
 First Method. Lei A and E, Fig. 3, 
 be two corners on the river or on any 
 other irregular boundary. Draw the A] 
 lines AF and FE to include as much 
 water on the land side as they exclude 
 
 land on the water side. If the map f _ 
 
 has been platted by means of coordi- B\r -' 
 
 natesi, those of F may be found by 
 measurement, and the area can then be 
 calculated by double latitudes. Or the 
 entire figure may be divided into a 
 series of triangles as shown and the 
 sum of their areas taken as that of the ^ p IG> 3 
 
 Second Method: By Selected Ordinates. Draw perpendiculars on AB, 
 Fig. 4, from the points of the curve at which its direction changes appreciably, 
 and consider the portion of the curve between two consecutive perpendiculars 
 to be a straight line. The figure is then treated as if divided into a number 
 of trapezoids, whose areas can be computed by the rules already given. 
 
 FIG. 4 
 
 Third Method: Trapezoidal Rule. The ordinates are measured at regular 
 intervals d along the line, as shown in Fig. 5. If the end ordinates are a and n 
 
 respectively, the area is A = (~^ + 2fe)<f in which 2fc is the sum of all the 
 
 intermediate ordinates. 
 
 EXAMPLE If the ordinates from the straight line AB to the curved boun- 
 dary DC, are 19, 18, 14, 12, 13, 17, and 23 li., respectively, and are at equal 
 distances of 50 li., what is the area included between the curved boundary and 
 
 the straight line? 
 
 SOLUTION. Area ABCD 
 
 _*- 
 
 1 
 
 -_ 
 2 
 
 
 4 
 
 
 5 
 
 6 
 
 3 
 
 a 
 
 h * 
 
 * 9 
 
 h 2 
 
 '*3 
 
 h 2 
 
 k-d-~ 
 
 1 d 
 
 1 -d 1 cf- 
 
 FIG. 6 
 
 t d 
 
 ld-H 
 
 + 18+14 + 12+13+17) X 50 = 4,750 
 
 ^'Fourth Method: Simpson's Rule. 
 The base line must be divided into an 
 even number of equal parts, as shown 
 in Fig. 6. The area is then equal to A 
 
 = (o+n+42/i2-t-22ft3)^, in which o+n is the sum of the end ordinates; 42fo is 
 four times the sum of all intermediate even-numbered ordinates; and22As is 
 
48 MATHEMATICS 
 
 twice the sum of all intermediate odd-numbered ordinates. This rule is more 
 accurate than the trapezoidal rule. 
 
 EXAMPLE. What is the area A BCD of the polygon, in the example of the 
 Third Method, according to Simpson's rule? 
 
 SOLUTION. A = [19+23+4X (18+12+ 17)+2X (14 + 13)1X^ = 4.733 sq.li. 
 
 Fifth Method. Prepare two drawings upon paper of the same weight and 
 quality, one of the tract of irregular outline and another of about the same 
 size but of a tract whose area is known, both drawings being to the same scale. 
 Cut each out carefully along the boundary and weigh in a chemist's balance 
 sensitive to milligrams (1 mg. = .015 gr., about). The area of the irregular 
 figure may be calculated from the proportion: The unknown area : the known 
 area = the weight of the drawing of the unknown area : the weight of the drawing 
 of the known area. 
 
 Sixth Method. Draw the figure upon cross-section paper. If each of the 
 small squares represents a certain area to the scale of the map, the number 
 of whole squares and fractions thereof within the boundary, when multiplied 
 by the relative area of a single square, will give the area of the figure. 
 
 Seventh Method. If the area of many irregular figures (such as a series of 
 indicator diagrams) is to be determined, a planimeter should be secured. 
 This instrument, of which there are several types, and which may be secured 
 through any dealer in engineer's supplies, affords the most rapid and accurate 
 means for determining the areas of irregular figures. 
 
 NOTE. The accuracy of the results obtained by the use of these approxi- 
 mate methods for determining the areas of _ irregular figures depends almost 
 entirely on the skill and judgment of the engineer. Other things being equal, 
 the smaller the subdivisions (in the method involving ordinates or small squares) 
 the more accurate the results. 
 
 CIRCLES 
 
 A circle is a plane figure bounded by a curved line every point of which is 
 equidistant from an interior point called the center. 
 
 In the formulas relating to circles the letters have the following meanings: 
 capital letters refer to the larger and lower-case letters to the smaller of two 
 circles concerned in the same formula. 
 
 D, d = diameter . L, 1 = length of arc 
 
 R,r= radius C, c = angle at center subtended by 
 
 A , a = area chord or arc 
 
 P, p = circumference = perimeter T, t = thickness of circular ring 
 
 H, h = rise of arc A, B = major and minor axes of 
 
 * = ratio of P to Z> = 3.1416 ellipse 
 
 * = 3.141592653589793238462 a, b = semi-major and semi-minor 
 
 ir 2 = 9.86965 axes 
 
 K, k = length of chord ^ = 1.772453 
 
 /> = ir<f = 3.14164 p p 
 
 2 VTTA= 3.5449 \U 
 2A 4A r=\/--.5642VA 
 
 <f = 2\/^=1.1284VI *- pr - pd 
 
 2~ 4 
 1 = v- = -07960 2 
 
 To Find Diameter of a Circle Equal in Area to a Given Square. Multiply 
 one side of the square by 1.12838. 
 
 To Find Radius of a Circle to Circumscribe a Given Square. Multiply 
 one side by .7071; or take one-half the diagonal. 
 
 To Find Side of a Square Equal in Area to a Given Circle. Multiply the 
 diameter by .88623. 
 
 To Find Side of Greatest Square in a Given Circle. Multiply the diameter 
 by .7071. 
 
 To Find Area of Greatest Square in a Given Circle. Square the radius 
 and multiply by 2. 
 
MA THEM A TICS 
 
 49 
 
 To Find Side of an Equilateral Triangle Equal in Area to a Given Circle. 
 
 Multiply the diameter by 1.3468. 
 
 Circumferences and areas of circles from 1 to 1,000 units in diameter will be 
 found in connection with the table of squares, cubes, etc. A similar table, 
 but for diameters from ^ to 100, increasing by J, is also given at the end of 
 the volume. Circumferences and areas of circles whose diameters are not 
 exactly given in the tables, but are within its limits, may be found by inter- 
 polation. If the diameters are greater than those given in the table, the 
 circumferences and areas may be found by recalling that the former are pro- 
 portional to the diameters and the latter to the squares of the diameters. 
 Thus, the circumference and area of a circle 9,380 units in diameter are 
 respectively 10 and 100 times those of a circle 938 units in diameter. 
 
 Let 5 = area and T 
 
 RINGS 
 
 thickness of a ring. 
 
 2TT 
 
 = A-a = ~~- = .079578(P2- 
 
 - d 2 ) = .785398(D* - 
 
 SECTORS 
 
 A sector is a portion of the surface of a circle included 
 between an arc AEB and two radii OA and OB. 
 
 A = \lr = " = ^- r*C = 28.647823 ~ = .00872666r*C 
 IT C obU C 
 
 180 I 
 if C~ 
 
 10.704732 \ 9; 
 
 The central angle C must be reduced to degrees and 
 decimal parts thereof. 
 
 CIRCULAR SEGMENTS 
 
 A segment is a portion of the surface of a circle in- 
 cluded between an arc NEM and its chord NM. 
 
 Area segment NEM = area sector ONEM area 
 triangle NOM. 
 
 The area of the sector is found from some one of the 
 formulas already given and that of the triangle is 
 found from 
 
 A' = ^(r- K) = \i* sin C= \k cot ~=(k-h)* tan 
 
 Z 
 
 Other formulas are k = 2 ^h(2r-h) = 2r sin - 
 
 h = r- 
 
 -rC- .017453C 
 
 . C 
 Sm 2 
 
 To determine the area of a heading, the upper part of which is the arc of a 
 circle, the width thereof k and the rise of the arc h being given. Find r from the 
 
 formula r - 
 
 8h 
 
 Then find \C from sin - = -. 
 
 The angle found is \C and 
 
 must be multiplied by 2. C is to be expressed in degrees and decimals thereof. 
 The area of the sector ONEM is now found from the formula A = .00872664r 2 C. 
 
 The area of the triangle NM is found from the formula A ' - ^(r K) . Then A 
 
 A' = area segment NEM, which is to be added to that of the lower rectangular 
 portion of the heading. 
 
SO MATHEMATICS 
 
 ELLIPSE 
 
 If A and B are the axes of an ellipse and c and b are the semi-, or half, axes, 
 the area A = 7rc6 = 3.141593 ab = |A = . 785398 A B. 
 
 No simple formula has been developed for finding the perimeter of an 
 ellipse. In terms of the semi-axes, the formula for the perimeter involves the 
 summation of an expanding series of an infinite number of terms: 
 
 i /(a-fly , 1 /(o-&)y 
 
 In an ellipse whose semi-axes are 4 and 3, the values within the brackets 
 become 1 + . 005102041 + .000006507 +.000000033. It is apparent, then, except 
 in cases,. involving great accuracy, that the terms beyond the second may 
 be dropped and the formula for the perimeter of an ellipse may be written, 
 
 P = ir(o+6) s 1 + ! ' This, the correct formula, is fully as simple 
 
 and is, naturally, far more accurate than any of the so-called shorter approxi- 
 mations. 
 
 MENSURATION OF SOLIDS 
 
 VALUES USED IN FORMULAS 
 
 V = volume of solid P = perimeter of base 
 
 5 = area of convex surface p = perimeter of second base or top 
 
 A area of main base R, r, D,d = radius and diameter of main base 
 
 a = area of second base, or top and of secondary base, respec- 
 
 T = area of entire surface = 5+A+a tively; or, radius and diameter 
 
 h = altitude, or perpendicular dis- of a sphere 
 
 tance from base to top / = slant height, or length from base 
 
 to base measured on surface 
 
 PRISMOID AND PRISMOIDAL FORMULA 
 
 A prismoid is any solid having two parallel ends or faces of any shape 
 similar or dissimilar, regular or irregular, provided these ends are united by 
 
 surfaces, whether plane or curved, on 
 which and through every point of which, 
 a straight line may be drawn from one 
 of the parallel ends to the other. It 
 embraces all polyhedrons, parallelepi- 
 peds, prisms, cylinders, cones, pyra- 
 mids, etc., and even the sphere, which 
 may be regarded as a regular polyhe- 
 dron of an infinite number of faces. 
 This is true whether the solids are regular or irregular, right or oblique, and 
 applies to their frustums when cut parallel to the base. 
 The formula for the volume of a prismoid is 
 Tr H(A+4M+B) 
 
 6 
 in which A and B = areas of two ends, respectively; 
 
 M = are"a of section taken midway between ends; 
 H = perpendicular distance between parallel ends. 
 
 This is known as the prismoidal formula, and from it, by making the proper 
 substitutions for A , M, and B, an equation for the volume of any solid may be 
 deduced, provided its form is included in the definition of a trapezoid. Unless 
 the parallel ends are similar polygons, the mid-section M , is not the mean of 
 the sections A and B. This formula is extensively used in calculating exca- 
 vations in railroad work. 
 
 REGULAR POLYHEDRONS 
 
 A polyhedron is a solid contained within any number of plane sides. A 
 regular polyhedron is one whose bounding planes (faces) are regular polygons 
 of the same shape and area, and whose solid (polyhedral) angles are equal 
 each to each. Unless the sphere is considered a regular polyhedron of an 
 
MATHEMATICS 
 
 51 
 
 infinite number of sides, only five regular polyhedrons are possible; these are 
 shown in the accompanying figure. 
 
 Tetrahedron 
 
 Cube 
 
 Octahedron Dodecahedron Icosahedron 
 
 REGULAR POLYHEDRONS WHOSE EDGES ARE UNITY 
 
 Name 
 
 Bounding Polygons 
 
 Surface 
 
 Volume 
 
 Tetrahedron 
 Hexahedron or cube 
 Octahedron 
 Dodecahedron 
 Icosahedron 
 
 4 equilateral triangles 
 6 squares 
 8 equilateral triangles 
 12 pentagons 
 20 equilateral triangles 
 
 1.732051 
 6.000000 
 3.464102 
 20.645729 
 8.660254 
 
 .117851 
 1.000000 
 .471405 
 7.663119 
 2.181695 
 
 The surface of any regular polyhedron is equal to the number of faces 
 multiplied by the area of a single face. It maybe found from the accompanying 
 table by squaring the length of the edge of a face and multiplying this by the 
 number, in the column headed Surface, opposite the name of the polyhedron. 
 Thus, the surface area of an octahedron whose edge is 2 in. long, is 22, or 4X 
 3.464102 = 14.856408 sq. in. 
 
 The volume of any polyhedron may be obtained by taking the sum of the 
 volumes of the pyramids into which it may be divided. There will be as many 
 pyramids as there are faces in the polyhedron and the bases of these pyramids 
 will be the several faces of the polyhedron. The volumes of the regular poly- 
 hedrons may be obtained from the table by multiplying the cube of the length 
 of the edge by the number, in the column headed Volume, opposite the name 
 of the polyhedron concerned. Thus, the volume of a tetrahedron whose edge 
 is 2 in. long, is 2", or 8X .117851 = .942808 cu. in. 
 
 THE SPHERE 
 
 The sphere may be defined as a regular polyhedron of an infinite number of 
 sides; or as a solid generated by the revolution of a semicircle about its diam- 
 eter; or as a solid, every point of whose surface is equi- 
 distant from a fixed interior point called the center. 
 
 A great circle of a sphere is the line formed by the 
 intersection of a plane through the center with the 
 surface of the sphere, as A BCD or AbCc. Its radius 
 
 and diameter r and d are the same as those of the ., -,._ * 
 
 sphere ; its area irR 2 may be placed equal to Z. A * " 
 
 R=\IT- F = . 62035 ^F=\f~- = . 2821 VS 
 
 \4ir \4ir 
 
 p = -v/e^F = 3 8978 %V-- 
 5 = 47^2=12.5664^=-^ 
 
 1.7725 VS=4 
 a 
 
 6 
 
 dZ 
 
52 
 
 MATHEMATICS 
 
 SPHERICAL SEGMENTS 
 
 A spherical segment is that portion of a sphere that is included between its 
 surface and a plane cutting it, as EABCD. If the plane passes through the 
 center, the sphere is divided into two equal parts, each of 
 which is a hemisphere. Let EF = h = height of segment, 
 and r' and d' be the radius and diameter of the basal 
 plane, and R be the radius of the sphere. 
 
 5 = 2irRh = 6.2832Rh 
 
 .7854(^+4^) = Ph 
 
 To this must be added the area of the base, ^d' 2 , if 
 the entire surface is required. 
 
 SPHERICAL ZONES 
 
 A spherical zone is that portion of a sphere that is in- 
 cluded between two parallel intersecting planes. 
 
 Let d be the diameter of the sphere and d f and d" be 
 the diameters AC and ac of the two planes, whose distance 
 apart is EF = h. 
 
 S = PZ " ' "'-'- ' - * 
 
 Vo- 
 
 vdh = surface of sphere X -. 
 
 V-f 
 
 CYLINDRICAL RINGS 
 
 A cylindrical ring is produced by bending a cylinder upon 
 itself. Using the notation in the accompanying figure 
 5 = 4**Rr = 39A78GRr = ir*Dd = 9.8Q97Dd. V = 2v*Rr* 
 
 d-J = 19.7393Kr 2 = ^ Dd* = 2.4674Dd*. 
 
 ^*^fopfMV.'>i'Sftnff ! ''''?:";: .';;. ""'"''.^1 
 
 PARALLELOPIPEDS 
 
 Cube 
 
 Rectangular Prism Rhombohedron Rhombic Prism 
 
 A parallelepiped is a solid bounded by six faces, all of which are parallelo- 
 grams; opposite faces being parallel. In the cube, there are six equal faces 
 and eight equal solid angles; in the rectangular prism, there are three pairs of 
 equal opposite faces and eight equal solid angles; in the rhombqhedron, there are 
 six equal faces and four pairs of equal and diagonally opposite angles; in the 
 rhombic prism, there are three pairs of equal opposite faces and four pairs of 
 equal and diagonally opposite angles. 
 
 .5 = sum of areas of six faces. In the cube and rhombohedron 5 = 6.4. 
 In the two prisms (calling the equal faces A, B, and C) S = 2A+2B+2C. 
 V = Ah\ that is, the volume is equal to the area of any face multiplied by 
 the perpendicular distance to the opposite face. 
 
 In the cube, F = cube of length of one edge. The diagonal 
 joining opposite vertices = an edge X 1.732051. The radius of the 
 inscribed sphere = the edge X .5. The radius of the circumscribed 1 
 sphere = one-half the diagonal joining opposite vertices = the edge 
 X. 866026. 
 
 Frustum of Prism. If a section perpendicular to the edges 
 is a triangle, square, parallelogram, or regular polygon, 
 
 T/ sum of lengths of edges vx , . , . 
 
 V = : r- 5 T - - Xarea of right section 
 
 number of edges 
 
MATHEMATICS 
 
 53 
 
 CYLINDERS 
 
 A cylinder of revolution, which is the common form, is a solid that may be 
 considered to have been generated by the revolution of a parallelogram about 
 one edge. 
 
 S = 2vrh = irdh = Ph. T = 5+2Xarea of base = 
 
 V= area of base X perpendicular height h, or V = Ah 
 -d?h = ~h = 3.1416r2/i = . 
 
 irr*h 
 
 - ~ 
 4 4x 
 
 Frustum of Cylinder. 
 
 Let h = one-half sum of greatest and least heights 
 
 T = 
 
 d 2 +area of elliptic top. 
 
 Hollow Cylinders. The volumes of hollow cylinders, as the 
 quantity of metal in a pipe, may be found by multiplying the area 
 of the ring made by its cross-section by the length of the cylinder. 
 The area of the cross-section may be determined by the formulas 
 given under Rings. 
 
 THE PYRAMID 
 
 A pyramid, Fig. 1, is a solid having for its base a plane figure of any num- 
 ber of sides, and for its sides, plane triangles terminating in 
 a common point, called the apex. 
 
 S = iPJ, and T = %Pl+A, in which P is the perimeter 
 of the base, A its area, and I the slant height. Note that 
 I, Fig. 1, is not measured on an edge, but from the center of 
 one side of the base to the vertex. These formulas apply to 
 the right regular pyramid in which the base is a regular poly- 
 gon and the axis is perpendicular thereto. If the base is not 
 a regular polygon and the pyramid is oblique (the axis is 
 inclined to the base), each triangular side has different p IG 
 
 dimensions. To find S, the sum of the areas of the different 
 triangular sides must be taken, to which must be added the area of the irreg- 
 ular base if T is desired. 
 
 The volume of any pyramid is equal to the area of the 
 base multiplied by one-third the altitude, or V = %Ah. 
 
 Frustum of Regular Pyramid. If A and a and P and p 
 * are the area and perimeter of the lower and upper bases, re- 
 ^ | spectively, of a frustum of a regular pyramid, Fig. 2, 
 
 If the cutting p^lane is inclined to the base or the frus- 
 FIG. 2 * um i s J-hat f an irregular or oblique pyramid, the surface 
 
 area 5 is the sum of the areas of the trapeziums forming the 
 sides, to which must be added the areas of the irregular bases if T is wanted. 
 The volume of the frustum of any pyramid is V = ih(A+a- 
 
 THE WEDGE 
 
 The wedge, whether with a blunt edge 
 as A BCD-abed, or with a sharp edge as 
 ABCD-a'b', is a special form of the trape- 
 zoid, as the ends abed, or a'V are parallel 
 to the base A BCD. In the blunt wedge, 
 V = %fh(m-\-n) and in the sharp wedge 
 V=afnh, as m-O. In the latter case, h 
 = Bb'. 
 
 THE CONE 
 
 A cone, Fig. 1, is a solid generated by a straight line, one end 
 of which passes through a fixed point, called the apex while the 
 other end is free to move around the perimeter of a closed curve, 
 known as the base. Cones are regular when the base is a circle 
 and are right of oblique according as the axis is at right angles 
 to or inclined to the base. 
 
 P The common form of cone, as shown in accompanying 
 
 figure, is the right regular cone of revolution, which may be 
 
54 
 
 MATHEMATICS 
 
 considered to have been generated by the revolution of a right-angled tri- 
 angle about one side. Its base is a circle and its axis is perpendicular to the 
 center of the base. 
 
 The surface of the cone is S 
 
 Thetotal surface, T= irrl 
 
 The volume, 
 
 V = 
 
 vr(l + r) 
 
 1 .0472r 2 /. 
 
 Frustum of Cone. When, as in Fig. 2, the cutting plane 
 is parallel to the base of the cone 
 
 , and T- 
 
 FIG. 1 
 
 PLANE TRIGONOMETRY 
 
 DEFINITIONS 
 
 Plane trigonometry treats of the solution of plane triangles. In every tri- 
 angle there are six parts three sides and three angles. These parts are so 
 related that when three of the parts are given, one being a side, the other parts 
 may be found. 
 
 An angle is measured by the arc included between its sides, the center of 
 the circumference being at the vertex of the angle. 
 
 For measuring angles, the circumference is divided into 360 equal parts, 
 called degrees; each degree is divided into 60 equal parts called minutes; and 
 each minute is divided into 60 equal parts called seconds. Divisions smaller 
 than a second are expressed in decimal parts of that unit; thus, 24.56". 
 
 A. quadrant is one-fourth the circumference of a circle, 
 or 90. 
 
 The complement of an arc is 90 minus the arc; the 
 arc DC, Fig. 1, is the complement of the arc BC, and the 
 angle DOC is the complement of the angle BOC. 
 
 The supplement of an arc is 180 minus the arc; the arc ^ I 
 AE is the supplement of the arc BDE, and the angle AOE 
 is the supplement of the angle BOE. 
 
 In trigonometry, instead of comparing the angles of 
 triangles or the arcs that measure them, the trigonomet- 
 ric functions, known as the sine, cosine, tangent, cotan- 
 gent, secant, and cosecant, are compared. 
 
 The sine of an arc is the perpendicular let fall from one extremity of the 
 arc on the diameter that passes through the other extremity. Thus, CD, 
 
 Fig. 2, is the sine of the arc AC. 
 The cosine of an arc is the 
 sine of its complement ; or it is 
 the distance from the foot of 
 the sine to the center of the 
 circle. Thus, CE or OD equals 
 the cosine of arc AC. 
 
 The tangent of an arc is a 
 line that is perpendicular to 
 the radius at one extremity 
 of an arc and limited by a line 
 passing through the center of 
 the circle and the other ex- 
 tremity . Thus , A T is the tan- 
 gent of AC. 
 
 The cotangent of an arc is 
 equal to the tangent of the 
 c. complement of the arc. Thus, 
 
 BT' is the cotangent of AC. 
 
 The secant of an arc is a line drawn from the center of the circle through 
 one extremity of the arc, and limited by a tangent at the other extremity. 
 Thus, OT is the secant of AC. 
 
MATHEMATICS 55 
 
 The cosecant ot an arc is the secant of the complement of the arc. Thus, 
 OT' is the cosecant of AC. 
 
 The versed sine of an arc is that part of the diameter included between the 
 extremity of the arc and the foot of the sine. DA is the versed sine of AC. 
 
 The coversed sine, is the versed sine of the complement of the arc. Thus, 
 BE is the coversed sine of AC. 
 
 FUNDAMENTAL RELATIONS 
 
 t 
 e 
 sin 2 x-f cos 2 # 
 
 If x is any angle, the fundamental relations that its trigonometric functions 
 sustain to one another are: 
 
 cosec x- 
 
 sec 2 x= 1-f-tan 2 x 
 
 _ - cosec 2 x =1 + cot 2 x 
 
 C ~tanx vers*=l-cos* 
 
 covers x = 1 sin x 
 
 The tangent and cotangent of the same angles are reciprocals of each other; 
 so also are the secant and cosine; and the cosecant and sine. 
 
 The value of the sine and cosine cannot be greater than 1. Tangents 
 and cotangents may have any value from to 00. Secants and cosecants 
 may have any value between 1 and 00. Versed sines and coversed sines may 
 have any value between and 2. 
 
 SIGNS OF TRIGONOMETRIC FUNCTIONS 
 
 The various trigonometric functions have signs; that is, they are + or , 
 depending on the magnitude of the angle. 
 
 Sines and cosecants of angles between and 180 are +; and those of 
 angles between 180 and 360 are -. 
 
 Cosines and secants of angles between and 90 and between 270 and 360 
 are -f-; and those of angles between 90 and 270 are . 
 
 Tangents and cotangents of angles between and 90 and between 180 
 and 270 are + ; and those of angles between 90 and 180 and between 270 
 and 360 are -. 
 
 Versed sines and coversed sines are always + regardless of the magnitude 
 of the angle. 
 
 FUNCTIONS OF ANGLES BETWEEN 90 AND 180 
 
 In the solution of obtuse-angled triangles, it is commonly necessary to 
 have to find the functions of an angle of more than 90. This may readily be 
 done if it is recalled that the sine, etc., of an angle equals the corresponding 
 function of its supplement. Thus 
 
 sine 110 = sine of 70 cosine 110 = cosine 70 
 
 tangent 110 = tangent of 70 cotangent 110 = cotangent 70 
 
 secant 110 = secant of 70 cosecant 110 = cosecant 70 
 
 Thus, if it is desired to find the sine of an angle of 120 30', look for the sine 
 of 180 120 30', or 59 30', and similarly for the other functions. In deal- 
 ing with angles of more than 90 attention should be paid to the sign of the 
 function. 
 
 FUNCTIONS OF 90+ A 
 
 sin (90+A) = cos A cot (90+A) = -tan A 
 
 tan (90+ A) = -cot A sec (90+ A) = -esc A 
 
 cos (90+A) = -sin A esc (90+A)= sec A 
 
 FUNCTIONS OF 180- A AND OF 180+ A 
 
 sin (180- A) = sin A sin (180+ A) = -sin A 
 
 tan (180- A) = -tan A tan (180+A) = tan A 
 
 cos (180- A) = -cos A cos (180 + A) = -cos A 
 
 cot (180- A) = -cot A cot (180+A)= cot A 
 
 sec (180-A) = -sec A sec (180+A) = -sec A 
 
 esc (180- A) = esc A esc (180+A) = -esc A 
 
56 
 
 MATHEMATICS 
 FUNCTIONS OF (A+B) AND OF (A-B) 
 
 sin (A+B) = 
 sin (A-B) = 
 cos (A +B) = 
 cos (A-B) = 
 
 tan(A+B)=* 
 tan (A- 
 
 sin A cos B + cos A sin B 
 sin A cos B cos A sin B 
 cos A cos J3 sin A sin B 
 cos A cos .B+sin A sin J3 
 
 tan A + tan B 
 1-tan A tan B 
 
 tan A tan B 
 1-f-tan A tan B 
 
 FUNCTIONS OF 2A AND OF J. 
 
 sin 2A = 2 sin A cos A 
 
 sin $A = 
 cos 2A = cos 2 A sin 2 A 
 
 cos 2A =2 cos 2 A - 1 cos *A = 
 
 cos 2A = 1 2 sin* A 
 2 tan A 
 
 cos A 
 
 tan 2A = 
 
 1-tan 2 A 
 
 sin A 
 
 SUMS AND DIFFERENCES OF FUNCTIONS 
 
 sin A+sin B = 2 sin 
 sin A sin B = 2 sin 
 cos A+cos B = 2 cos 
 cos A cos B = 2 sin 
 
 (A-B) 
 (A+B) 
 (A-B) 
 (B-A) 
 
 R 
 
 cos B 
 sin (A-B) 
 cos A cos B 
 sin 2 A sin 2 B = sin (A + B) sin 
 cos 2 A - cos 2 B = sin (A + B) sin 
 
 tan A -tan B = 
 
 (A-, 
 [B-. 
 
 cos 2 A - sin 2 B = cos (A + B) cos (A - B) 
 
 Side adjacent 
 
 SOLUTION OF RIGHT-ANGLED TRIANGLES 
 
 There are six parts in every triangle and if 
 three of them are known the other three may be 
 u determined by calculation, provided one of the 
 three known parts is a side. In the case of a right- 
 angled triangle, one of the angles is 90, but 
 two other parts, one of them a side, are necessary 
 . for its solution. Three angles do not determine 
 a triangle, because all triangles whose sides are 
 parallel each to each have the same angles but 
 sides of different length. 
 
 In right-angled triangles, the following rela- 
 tions between the angles and sides prevail: 
 
 cos A 
 
 . = side opposite _ a 
 = hypotenuse ~ c 
 side adjacent _ b 
 hypotenuse c 
 
 A _side opposite _a 
 
 ia,n si 
 
 side adjacent b 
 
 versA=l-- 
 
 cot A = 
 
 sec A 
 
 side adjacent _ b 
 side opposite a 
 hypotenuse _^ 
 side adjacent b 
 . _ hypotenuse _ c 
 side opposite a 
 
 covers A = l - 
 
MA THEM A TICS 
 
 RELATIONS BETWEEN ANGLES AND SIDES OF RIGHT- 
 ANGLED TRIANGLES 
 
 57 
 
 Given 
 
 Required 
 
 Formula 
 
 Given 
 
 Required 
 
 Formula 
 
 a, A 
 
 B,b,c 
 
 {b = a cot A 
 a 
 
 
 
 tan B = -, 
 
 sin A 
 
 a,B 
 
 A,b,c 
 
 !'b = ata.nB 
 C = cosB = aSeC B 
 
 a, b 
 
 A, B, c 
 
 :3? L 
 
 c,A 
 
 B,a,b 
 
 < a = c sin A 
 I b = c cos A 
 
 
 
 sin A - 
 c 
 
 
 
 
 
 
 cos B = - 
 
 
 
 
 a, c 
 
 A,B,b 
 
 c 
 
 
 
 
 
 
 = V(c+o)(c a] 
 b = a cot A 
 
 Area. The area ot a right-angled triangle is equal to one-half the product 
 of the base by the altitude, or area = \ ab. 
 
 The area is also equal to one-half the product of any two sides into the sine 
 of the angle between them. Thus, if the angle A and the sides c and b are given, 
 area=jcfc sin A. 
 
 SOLUTION OF OBLIQUE-ANGLED TRIANGLES 
 
 The following relations between the sides and angles apply to all triangles, 
 but are of particular service in solving those with oblique angles: 
 
 1. The sides of any plane triangle are proportional to the sines of the angles 
 opposite. 
 
 a : b = sin A : sin B 
 a : c = sin A : sin C 
 b : c = sin B : sin C 
 
 2. Any side of a plane triangle equals the sum of the products of each of the 
 other sides into the cosine of the angle that it makes with the first side. 
 
 a = b cos C+c cos B 
 b = a cos C+c cos A 
 c = a cos B + b cos A 
 
 3. The square of any side of a plane triangle equals the sum of the squares 
 of the other two, minus twice their product into the cosine of their included angle. 
 
 2 2 be cos A 
 
 C 2 = c 2 -f-fc 2 2afe cos C 
 
 4. The sum of any two rides of a plane triangle is to their difference, as the 
 tangent of one-half the sum of the angles opposite them is to the tangent of one-half 
 their difference. 
 
 a+b : a-& = tan i(A+J3) : tan $(A-B) 
 a+c : a-c = tan JU+C) : tan $(A-C) 
 b+c : b-c = t&n $(B+C) : tan $(B-C) 
 
58 MATHEMATICS 
 
 5. The cosine of any angle of a plane triangle is equal to the sum of the squares 
 of the adjacent sides minus the square of the side opposite, the whole divided by 
 twice the product of the adjacent sides. 
 
 ros A 
 
 COSA 
 
 2bc 
 
 02 + CZ 
 
 cos B= - n 
 2ac 
 
 6. The area of any plane triangle is equal to one-half the product of any two 
 sides into the sine of the included angle. 
 
 Area = \d> sin A = %ac sin B = \ab sin C 
 
 7. The area of any plane triangle is equal to the square root of the continued 
 product of one-half its perimeter into one-half its perimeter minus each side sep- 
 arately. 
 
 If the perimeter, a+b+c = p, then, 
 
 Area 
 
 PRACTICAL EXAMPLES 
 
 1. Having given two sides and the included angle, to find the other side and 
 
 remaining angles. Let & = 30, c = 20, and A = 38 20'; required a, B, and C. 
 
 Find the angle B from the third formula of the fourth relation, which may 
 
 be transposed to tan KB-C)=tan ^(B+C)X^~. In this B+C=180-A 
 
 = 180-38 20'= 141 40', and (5+0 = 70 50'; B-C is unknown; b + c 
 = 30+20 = 50, and &-c = 30-20 = 10. By substitution, tan JCB-O =2.87700 
 X 8 = .57540. From this $(B - C) = 29 55' (very nearly) , and B - C = 29 55' 
 X2 = 5950'. 
 
 B + C = 141 40' 
 
 B-C = 59 50' 
 
 By addition, 2B =201 30' 
 
 By division, B = 100 45' 
 
 From this A+B = 38 20' +100 45' =139 5', and C=180-(A+B) = 180 
 -139 5' = 40 55'. 
 
 Find the side a from the first formula of the first relation, which may be 
 
 transposed to read, ..x-30X-<.lM. Re- 
 
 member that sin 100 45' = sin (180- 100 45')= sin 79 15'. 
 
 2. Having given two sides and the angle opposite one of them, to find the other 
 side and remaining angles. Let the given parts of the triangle shown in Fig. 1, 
 be A =38 20', 6 = 30, and a = 18.94; from which it is required to find c, B, 
 and C. 
 
 Find the angle B from the first formula of the first relation, which trans- 
 
 posed is sin B = -Xsin A =Xsin 38 20' = X. 62024 = .98245; whence 
 
 1 = 79 15' or 100 45'. Unless the shape of the triangle is actually known 
 it is impossible to tell which of these values of B 
 should be taken. In fact, both of them are correct, 
 as a study of the accompanying figure will show. 
 As only A, b, and a, are fixed, it is apparent that a 
 may occupy either position CB or CB' and yet have 
 the same value, 18.94. Such being the case, the angle 
 at B may be (for the position CB = a' = 18.94) CBA 
 = 79 15', or (for the position CB' = a= 18.94) CB'A 
 = 100 15'. Hence, angle C=180-(A+) =180 
 - (38 20'+79 15') = 180- 117 35' = 62 25', or 
 C=180-(38 20'+100 45') = 180 -.139 5' = 40 55' 
 The side c may now be found from the second formula of the first relation, 
 
 which may be transposed to read c = a . - , and taking the two values of the 
 
 sin A 
 
I 
 
 MATHEMATICS 
 
 Thus two solutions of this triangle are possible; in the first case, B = 79 15', 
 C = 62 25', c = 27.07, and in the second case, =100 45', C = 40 55', c = 20. 
 
 3. Having given two angles and any side, to find the other angle and the other 
 two sides. Let A = 38 20', 5 = 100 45', a = 18.94; to find the remaining 
 angle C and the other sides b and c. 
 
 Find C from the relation C = 180-(A+.B) = 180- (38 20'+100 45') 
 = 180 -139 5' = 40 55'. 
 
 The sides may now be found from the first and second formulas given in 
 the first relation after these have been transposed. 
 
 sin 5 smOO 45' 98245 
 
 4. Having given the three sides to find the three angles. Let a =18.94, 
 b = 30, and c = 20; required the angles A , B, and C. Using the formulas given in 
 the fifth relation to find A and B, then C may be found from C= 180- (A + B). 
 
 tc= 180- (A+B) = 180- (38 20'+ 100 45') =40 55' 
 Note that the angle corresponding to the cosine .18648 is either 79 15' 
 or 100 45'. By referring to the section Signs of Trigonometnc Functions, 
 it will be seen that when the cosine is minus, as it is 
 in this case (-.18648), the angle is between 90 and 
 270; hence, the value B = 100 45' is taken. 
 
 This example is readily solved by the solution of two 
 right-angled triangles, as shown in Fig. 2. Let fall a h, 
 
 perpendicular CD from the opposite vertex C upon the 
 longest side AB dividing it into two segments AD 
 = m andDjB = n. From geometry, m + n : b+a = b ( 
 
 (b+a)(b-a) 
 :m n, and as m +n = c,m n = . 
 
 bining the value of m n thus obtained with that of 
 w + n = c, the values of m and n may be found. In the right-angled triangles 
 ACD and BCD, b and m and a and n, respectively, are given, from which the 
 angles A and B may be calculated; angle C found by subtracting the sum of 
 angles A and B from 180. 
 
 Using the values for the sides, a = 18.94, & = 30, and c = 27.066 
 (30 + 18.94) X (30 - 18.94) 48.94 X 1 1 .06 
 
 m n= 
 
 Then 
 1 
 i 
 
 27.066 
 
 n + n = 27.066 
 w-n= 19.998 
 
 27.066 
 
 m+ = 27.066 
 m-n= 19.998 
 
 By addition 
 
 2w = 47.064 
 w = 23.532 
 
 By subtraction 2n= 7.068 
 n= 3.534 
 
 In the triangle A CD, cos A = = - = .78440. Whence A = 38 20'. 
 
 In the triangle DCB, cos 5 = -= = . 18659. Whence = 79 15'. 
 
 a is.y4 
 
 C = 180 - (A + B) = 180 - 1 17 35' = 62 25' 
 
 Tables of natural and logarithmic trigonometric functions will be found 
 at the end of the volume; each table is preceded by the necessary explanations 
 for its use. 
 
60 SURVEYING 
 
 SURVEYING 
 
 THE COMPASS 
 
 GENERAL DESCRIPTION 
 
 Surveying is an extension of mensuration, and, as ordinarily practiced, 
 may be divided into surface work, or ordinary surveying, and underground 
 work, or mine surveying. With slight modifications, the instruments employed 
 in both are the same, and consist of a compass if the work is of little impor- 
 tance, and accuracy is not required a transit, level, transit and level rods, 
 steel tape or chain, and measuring pins, and sometimes certain accessory instru- 
 ments, as clinometers or slope levels, dipping needles, etc., as will be described 
 later. 
 
 The compass may be either a pocket compass, or a surveyor's compass, 
 and may be used while held in the hand, or upon a tripod. The Jacob's staff, 
 convenient for use on the surface, is useless in the mine. As the compass can- 
 not be sighted accurately on an object, cannot be read closer than 30', except 
 by guess, and may be deflected from its true course as much as 2 or 3 by the 
 iron in the rails or water pipes or by electric currents, it is obvious that bear- 
 ings and angles determined through its use cannot be relied on as being within 
 15' of the truth and they may be very much more in error. As present day 
 surveying requires that any angle be known within 1 min. and in special cases, 
 such as tunnel work, within 30" or even 20" or 15", the compass is now no 
 longer used except, in emergencies, when a transit is not available. However, 
 in driving room necks far enough for the permanent sights, in obtaining a rough 
 idea of the direction of a heading, and, on the surface, in connection with the 
 rerunning of old land lines, the compass has its uses. 
 
 Owing to the length of time taken by the needle to settle so that it can be 
 read, an accurate transit survey can commonly be made in less time than an 
 inaccurate one with the compass. 
 
 COMPASS ADJUSTMENTS 
 
 When adjusting the levels, first bring the bubbles into the center by the 
 pressure of the hand on different parts of the plate, and then turn the compass 
 half way around. Should the bubbles run to the ends of the tubes, those ends 
 are the higher; these should then be lowered by tightening the screws imme- 
 diately under, and loosening those under the lower ends until, by estimation, 
 the error is half removed. The plate should again be leveled and the first 
 operatipn repeated until the bubbles will remain m the center during an entire 
 revolution of the compass. 
 
 The sights may next be tested by observing, through the slits, a fine hair 
 or thread, made exactly vertical by a plumb. Should the hair appear on one 
 side of the slit, the sight must be adjusted by filing off its under surface on 
 the side that seems the higher. 
 
 The needle is adjusted in the following manner: Having the eye nearly in 
 the same plane with the graduated rim of the compass circle, with a small 
 splinter of wood, or a slender iron wire, bring one end of the needle in line 
 with any prominent division of the circle, as the or 90 mark, and notice 
 if the other end corresponds with the degree on the opposite side. If it does, 
 the needle is said to cut opposite degrees; if not, bend the center pin by apply- 
 ing a small brass wrench, furnished with most compasses, about in. below 
 the point of the pin, until the ends of the needle are brought into line with the 
 opposite degrees. Then, holding the needle in the same position, turn the 
 compass half way around, and note whether it now cuts opposite degrees; 
 if not, correct half the error by bending the needle, and the remainder by bend- 
 ing the center pin. The operation must be repeated until perfect reversion 
 is secured in the first position. This being obtained, it may be tried on another 
 quarter of the circle; if any error is there manifested, the correction must be 
 made in the center pin only, the needle being already straightened by the pre- 
 vious operation. When again made to cut, it should be tried on the other 
 quarters of the circle, and corrections made in the same manner until the error 
 is entirely removed, and the needle will reverse in every point of the divided 
 circle. 
 
SURVEYING 61 
 
 USING THE COMPASS 
 
 When using the compass, the surveyor should keep the south end toward 
 his person, and read the bearings from the north end of the needle. In the 
 surveyor's compass the position of the E and W letters on the face of the com- 
 pass are reversed from their natural position, in order that the direction of the 
 sight may be correctly read. 
 
 The compass circle being graduated to |, a little practice will enable the 
 surveyor to read the bearings to quarters estimating with his eye the space 
 bisected by the point of the needle. 
 
 The compass is divided into quadrants, and is placed at the north and 
 south ends; 90 is placed at the E and W marks, and the graduations run right 
 and left from the to 90. When reading the bearing, the surveyor will 
 notice that if the sights are pointed in a NW direction, the north end of the 
 needle, which always points approximately north, is to the right of the front 
 sight or front end of the telescope, and, as the number of degrees is read from 
 it, the letters marking the cardinal points of the compass read correctly. If 
 the E, or east.^mark were on the right side of the circle, a NW course would 
 read NE. This same remark applies to all four quadrants. The compass 
 should always be in a level position. 
 
 If all the corners of a field can be seen from a central point, the survey 
 can be made by setting up at that point, and with one corner as a backsight, 
 taking all the other corners as foresights, and by measuring from this point 
 to all of the corners; or the compass can be set up at any corner and a line of 
 survey run around the field. This latter method is called meandering. Both 
 methods will give the same result when plotted; but the first is much quicker, 
 as the boundaries of a. tract are frequently oyergrown with bushes that must 
 be cleared to allow a sight; while a central point can frequently be found that 
 will allow a free sight to all the corners, and the distance can be measured by 
 tape, or stadia. As the central point is nearer the corners than they are to 
 one another, a shorter distance must be chained or cut in the case of a central 
 set-up. 
 
 MAGNETIC VARIATION 
 
 Magnetic declination, or variation, of the needle is the angle made by the 
 magnetic meridian with the true meridian or true north and south line. It 
 is east or west according as the north end of the needle lies east or west of the 
 true meridian. It is _not constant, but changes from year to year, and, for 
 this reason, in rerunning the lines of a tract of land, from field notes of some 
 years' standing, the surveyor makes an allowance in the bearing of every line 
 by means of a vernier. 
 
 The declination, where a knowledge of it is necessary, should always be 
 determined for the particular place and at the particular time where and when 
 it is needed. Quite a number of the States in cooperation with the United 
 States Coast and Geodetic Survey have established a true meridian by astro- 
 nomical observations at each county seat. Information as to the location, etc., 
 of the monuments marking the meridian may be obtained from the county sur- 
 veyor, the recorder of deeds, or some one else in authority at the county court 
 house. However, the variation thus obtained is only available for use a com- 
 paratively short distance either east or west of the county seat (assuming that 
 the highest accuracy is desired), because on the average, there is in the United 
 States, a change in the value of the declination of 1' per mi. in the foregoing 
 directions. From this, it is apparent that the declination at a place 30 mi. 
 east or west of the county seat will probably vary 30' from that at the monu- 
 ments referred to. This difference of 30' is within the limits between which 
 the compass is ordinarily read. In proceeding north or south from the county 
 seat, the change in declination is very much less than in an east or west direc- 
 tion. If the declination cannot be determined, a note should be made of the 
 date of the survey, with a statement to the effect that the bearings are referred 
 to the magnetic meridian, and these notes should appear on the map and should 
 be incorporated in the deed if the survey was made preliminary to a transfer 
 of property. 
 
 The United States Coast and Geodetic Survey, Washington, District of 
 Columbia, issues from time to time tables and charts showing the declination 
 at many points in the United States and outlying possessions, together with 
 formulas by means of which the declination may be calculated with a high 
 degree of accuracy at future times. These may be obtained from the Super- 
 intendent of the Survey. 
 
62 
 
 SURVEYING 
 
 Reading the Vernier. The compass vernier, shown in the accompanying 
 illustration, is usually so graduated that 30 spaces on it equal 31 on the limb 
 of the instrument and, commonly, there are 15 spaces on each side of the mark. 
 It is read as follows: Note the degrees and half degrees on the limb of the 
 
 instrument. If the space passed 
 beyond the degree or half-degree 
 mark by the zero mark on the 
 vernier is less than one-half the 
 space of | on the limb, the num- 
 ber of minutes is, of course, less 
 than 15, and must be read from the 
 lower row of figures. If the space 
 passed is greater than one-half the 
 spacing on the limb, the upper row of figures must be read. The line on the 
 vernier that exactly coincides with a line on the limb is the mark that denotes 
 the number of minutes. If the index is moved to the right, the minutes are read 
 from the left half of the vernier; if moved to the left, they are read from the 
 right side of the vernier. 
 
 Turning Off the Variation. Moving the vernier to either side, and with it, 
 of course, the compass circle attached, set the compass to any variation by 
 placing the instrument on some well-defined line of the old survey, and by 
 turning the tangent screw (slow-motion screw) until the needle of the compass 
 indicates the same bearing as that given in the old field notes of the original 
 survey. Then screw up the clamping nut underneath the vernier and run all 
 the other lines from the old field notes without further alteration. The read- 
 ing of the vernier on the limb gives the amount of variation since the original 
 survey was made. 
 
 FIELD NOTES FOR AN OUTSIDE COMPASS SURVEY 
 
 Call place of beginning Station 1. 
 
 Stations Bearings Distances 
 
 1-2 N 35 E 270.0 
 
 At 1+ 37 ft. crossed small stream 3 ft. wide. 
 At l-i-116 ft. = first side of road. 
 At 1 + 131 ft. = second side of road. 
 
 At 1 + 137 ft. = blazed and painted pine tree, 3 ft. left, marked for a go-by. 
 Station 2 is a stake at foot of white-oak tree, blazed and painted on four 
 sides for corner. 
 
 2-3 N 83 E 129.0 
 
 Station 3 is a stake-and-stones corner. 
 
 3-4 S 57 E 222.0 
 
 3+64 ft. = center of small stream 2 ft. wide. 
 3 + 196 ft. = white oak go-by, 2 ft. right. 
 Station 4, cut stone corner. 
 
 4-5 S 341 W 355.0 
 
 4+174 ft. =* ledge of sandstone 10 ft. thick, dipping 27 south. 
 
 5-1 N 56i W 323.0 
 
 5+274 ft. = ledge of sandstone 10 ft. thick, dipping 25 south (evidently 
 
 continuation of same ledge as at 4 + 174). 
 Station 1 = place of beginning. 
 
 THE TRANSIT 
 
 GENERAL DESCRIPTION 
 
 The transit is the only instrument that should be used for measuring angles 
 in any survey where accuracy is desired. The advantages of a transit over a 
 vernier compass are mainly due to the use of a telescope. By its use, angles 
 can be measured either vertically or horizontally, and, as the vernier is used 
 throughout, extreme accuracy is secured. 
 
 Fig. 1 shows the interior construction of the sockets of a transit having 
 two verniers to the limb, the manner in which it is detached from its spindle, 
 and how it can be taken apart when desired. The limb b is attached to the 
 main socket c, which is carefully fitted to the conical spindle h, and held in 
 place by the spring catch s. 
 
 The upper plate a, carrying the compass circle, standards, etc., is fastened 
 to the flanges of the socket k, which is fitted to the upper conical surface of the 
 
SURVEYING 
 
 63 
 
 main socket c. The weight of all the parts is supported on the small bearings 
 of the end of the socket, as shown, so as to make as little friction as possible 
 where such parts are be- 
 ing turned as a whole. 
 A small conical cen- 
 ter, in which a strong 
 screw is inserted from 
 below, is brought down 
 firmly on the upper end 
 of the main socket c, 
 thus holding the two 
 plates of the instrument 
 securely together, and, 
 at the same time, allow- 
 ing them to move freely 
 around each other. The 
 steel center pin on which 
 the needle rests is held 
 by the small disk fas- 
 tened to the upper plate 
 by two small screws 
 above the conical cen- 
 ter. The clamp to limb 
 df, with clamp screw, is 
 attached to the main 
 socket. The instrument 
 
 FIG. 1 
 
 is leveled by means of the leveling screws / and placed exactly over a point by 
 means of the shifting center. The plummet is attached to the loop p. 
 
 Transit Verniers. In transits, the limb or plate has two sets of concentric 
 graduations, as shown in part in Fig. 2. The style of marking these gradua- 
 tions may be varied to suit the ideas of the surveyor, but the arrangement 
 shown is a common and a good one. The same point is used for both sets 
 of the graduations and is placed near or under the eye end of the telescope. 
 One set of graduations is continuous from this to 360 toward the left. 
 The other set begins at the same point and increases to 90 at the left, 
 decreases to directly opposite the starting point, increases to 90 at the 
 
 mark at the right; and then decreases by 10 to the starting point. This last 
 set of graduations, known as quadrant graduations, is marked with an N at the 
 point, with E at the 90 point; and similarly with S and W at the second 
 and second 90 points, respectively. Further, as shown, at each marking, 
 the letters N E, S E, S W, or N W are stamped on the plate at its proper quad- 
 rant. Thus the of the continuous graduation is the same as the N on the 
 quadrant graduation, the 90 of the continuous graduation is the same as the E 
 of the quadrant, the 180 of the continuous graduation is the S of the quadrant, 
 and the 270 of the continuous graduation is the W of the quadrant. 
 
 There are two transit 
 verniers; one, known as ver~ 
 nier A, is placed as near as 
 possible under the eye end 
 of the telescope, and the 
 other, known as vernier B, 
 is placed directly opposite. 
 These verniers are double, 
 that is, they read both 
 ways from the mark so 
 that angles deflected either 
 to the right or left may be 
 read. The vernier is com- 
 monly divided so that 30 
 
 spaces on i 
 vernier is 
 
 it are equal to 29 spaces on the limb of the transit. Each division of the 
 , therefore, ^, or, in other words, 1' shorter than the graduations on 
 the limb. In Fig. 2, the reading is S 60 30' E (from the limb) + 13' (from the ver 
 nier) = S 60 43' E. This is the quadrant reading from the inner row of gradu- 
 ations. The continuous vernier (outer row) reading is 119 (from the limb) 
 
64 SURVEYING 
 
 + 17' (from the vernier) = 119 17'. It will be noted that the sum of the two 
 readings is 60 43'+ 119 IT = 180. This summation proves and checks the 
 readings. Had the quadrant reading been N 33 18' E, the continuous vernier 
 should read 33 18'. Had the quadrant reading been S 56 39' W, the con- 
 tinuous vernier should read 180+56 39' = 236 39'; and had the quadrant 
 reading been N 76 29' W, the continuous vernier should read 360 76 19' 
 = 283 31'. In other words, when the continuous vernier reads from to 90, 
 the quadrant reading will be NE; when the continuous is between 90 and 
 180 the quadrant is SE; when the continuous is between 180 and 270 the 
 quadrant is SW; and when the continuous is between 270 and 360 (or 0), 
 the quadrant is NW. 
 
 Transit Telescope. The interior of the telescope is fitted up with a dia- 
 phragm or cross-wire ring to which cross-wires are attached. These cross- 
 wires are either of platinum or are strands of spider web. For inside work, 
 platinum should be used, as spider web is translucent and cannot readily be 
 seen. They are set at right angles to each other and are so arranged that one 
 can be adjusted so as to be vertical and the other horizontal. This diaphragm 
 is suspended in the telescope by four capstan-headed screws, and can be moved 
 in either direction by working the screws with an ordinary adjusting pin. 
 The transit should not be subjected to sudden changes in temperature that 
 may break the cross-hairs. In case of a break, the cross-hair diaphragm 
 must be removed and the broken wire replaced. 
 
 The intersection of the wires forms a very minute point, which, when 
 they are adjusted, determines the optical axis of the telescope, and enables 
 the surveyor to fix it upon an object with the greatest precision. 
 
 The imaginary line passing through the optical axis of the telescope is 
 termed the line of collimation, and the operation of bringing the intersection of 
 the wires into the optical axis is called the adjustment of the line of collimation. 
 
 All screws and movable parts should be covered, so that acid water and dust 
 will be kept out. If this is not done, the mine work will destroy a transit. 
 The vertical circle on the transit may be a full circle or a segment. The for- 
 mer is to be preferred, as it is always ready without intermediate clamp screws. 
 
 TRANSIT ADJUSTMENTS 
 
 The use of a transit tends to disarrange some 9f its parts, which detracts 
 from the accuracy of its work, but in no way injures the instrument itself. 
 Correcting this disarrangement of parts is called adjusting the transit. 
 
 1. To make the level tubes parallel to the vernier plate. Plant the feet of 
 the tripod firmly in the ground. Turn the instrument until one of the levels 
 is parallel to a pair of opposite leveling screws; the other level will be parallel 
 to the other pair. Bring the bubble in each tube to the middle with the pair 
 of leveling screws to which the tube is parallel. Next turn the vernier plate 
 half way around; that is, revolve it through an angle of 180. If the bubbles 
 have remained in the middle of the tubes, the levels are in proper adjustment. 
 If they have not remained so, but have moved toward either end, bring them 
 half way back to the middle of the tubes by means of the capstan-headed screws 
 attached to the tubes, and the rest of the way back by the leveling screws. 
 Again turn the vernier plate through 180, and if the bubbles do not remain 
 at the middle of the tubes, repeat the correction. Sometimes the adjustment 
 is made by one trial, but usually it is necessary to repeat the operation. Each 
 level must be adjusted separately. 
 
 2. To make the line of collimation perpendicular to the horizontal axis that 
 supports the telescope. With the instrument firmly set at A, Fig. 1, and care- 
 fully leveled, sight to a pin or tack set at a point B, about 400 ft. distant, and 
 on level, or nearly level, ground. Reverse the telescope; that is, turn it over on 
 
 its axis until it points in the 
 
 O A '& opposite direction, and set a 
 
 B . u i-^^~^ F point at about the same dis- 
 
 400*~~ C * tance, which will be at D, 
 
 FiG. 1 for example, if this adjust- 
 
 ment needs correction. Un- 
 
 clamp the vernier plate, and, without touching the telescope, revolve the instru- 
 ment about its vertical axis sufficiently far to take another sight upon the 
 point B. Then turn the telescope on its axis and locate a third point, as at C. 
 Measure the distance CD, and at E, one-fourth of the distance from C to D, 
 set the pin or tack. Move the cross-hairs, by means of the capstan-headed 
 screws, until the vertical hair exactly covers the pin at E, being careful to 
 move it in the opposite direction from that in which it appears it should be 
 
SURVEYING 65 
 
 moved. Having done this, and then having reversed the telescope, the line of 
 sight will not be at the point B, but at G, a distance from B equal to CE. Again 
 sight to B, then reverse, and the pin will be at F in the same straight line with 
 A B. It may be necessary to repeat the operation to secure an exact adjustment. 
 
 3. To make the horizontal axis of the telescope parallel to the vernier plate, 
 so that the line of collimation will revolve in a vertical plane. Sight to some point 
 A, Fig. 2, at the top of a building, so that the teleg&ope will be 
 elevated at a large angle. Depress the telescope and set a pin 
 
 on the ground below at a point B. Loosen the clamp, turn over 
 the telescope, and turn the plate around sufficiently far to take 
 an approximately accurate sight upon the point A. Then clamp 
 the instrument and again take an exact sight to the point A. Next 
 depress the telescope, and set another pin on the ground, which 
 will come at C. The distance BC is double the error of adjust- 
 ment. Correct the error by raising or lowering one end of the 
 telescope axis by means of a small screw placed in the standard for 
 that purpose. The amount the screw must be turned is deter- 
 mined only by repeated trials. 
 
 4. To make the axis of the attached level of the telescope parallel 
 to the line of collimation. Drive two stakes at equal distances from 
 the instrument and in exactly opposite directions. Level the plate 
 carefully, and clamp the telescope in a horizontal position, or as p IG 
 nearly so as possible. Sight to a rod placed alternately upon each 
 
 stake, and have the stakes driven down until the rod reading is the same on 
 both stakes. When this condition is reached, the heads of the stakes are at 
 the same level. Then move the instrument beyond one stake and set it up so 
 that it will be in line with both stakes. Level the plate again and elevate or 
 depress the telescope so that, when a sight is taken to the rod held on first 
 one stake and then on the other, the reading will be alike on both. In this 
 position, the line of collimation is level, and the bubble in the level attached 
 to the telescope should stand in the center of the bubble tube. If it does 
 not, bring it to the center by turning the nuts at the ends of the tube, being 
 careful at the same time to keep the telescope in the position that gives equal 
 rod readings on both stakes. 
 
 CHAIN, STEEL TAPE, AND PINS 
 
 The chain is probably the earliest form of distance-measuring instrument. 
 The original surveyor's or Gunters chain, was 66 ft. or 4 rd. in length and was 
 composed of 100 li.,each 7.92 in. long. This form of chain is no longer used, 
 but is useful in preliminary work in locating old corners from descriptions in 
 early deeds where distances are expressed in rods (poles, perches, or chains). 
 The engineer's chain composed of 100 li. each 1 ft. long is also falling into dis- 
 use except for railroad work. Any chain is so liable to abrasion at the numer- 
 ous joints and to bending, that distances measured with it cannot be relied 
 on to be accurate within the limits demanded by modern engineering. A 
 100-ft. chain has 800 wearing surfaces, and should each one of these be worn 
 but T fo in. after several season's work, the chain will be 100 ft. 8 in. (100.67 ft.) 
 in length, and each full 100 ft. measured with it will be recorded as but 99.34 ft. 
 Similarly, bends or kinks shorten the chain so that the distances measured 
 with it are recorded as being too great. 
 
 When used at all, the chain should be made of annealed steel wire, each 
 link exactly 1 ft. in length. The links should be so made as to reduce the liabil- 
 ity to kink to a minimum. All joints should be brazed, and handles at each 
 end of D shape, or modifications of D shape, should be provided. These 
 handles should be attached to short links at eacn end, and the combined length 
 of each of these short links and one handle should be exactly 1 ft. The handles 
 should be attached to the short link in such a manner that the chain may be 
 slightly lengthened or shortened by screwing up a nut at the handle. It should 
 be divided every 10 ft. with a brass tag, on which either the number of points 
 represents the number of tens from the front end, or the number of tens may 
 be designated by figures stamped on the tags. 
 
 When a chain is purchased, one that has been warranted as Correct, U. S. 
 Standard," should be selected, and, before using it, it should be stretched on 
 a level surface, care being taken that it is straight, and no kinks in it, and 
 the extremities marked by some permanent mark. These marks can be used 
 in the future to test the chain. It slumld be tested frequently, and the length 
 kept to the standard as- marked when it was new. 
 
66 SURVEYING 
 
 Ordinarily, the chain should be held horizontally, and if either end is held 
 above the ground, a plumb-bob and line should be used to mark the end of the 
 chain on the ground. If used on a regular slope, the chain may be stretched 
 along the ground, and, by having the amount of inclination, the horizontal 
 and vertical- 1 distances may either be calculated or found in the Traverse Table. 
 
 The steel tape, which has superseded the chain, is simply a ribbon of steel 
 not so high in carbon as to be brittle and liable to snap on a short bend, nor 
 of so soft a steel that it will stretch when strongly pulled. Tapes are made 
 of a standard or exact length at a given temperature, say 60 F., and under a 
 certain tension, say, 15 Ib. At higher temperatures or under greater pull the 
 tape expands, and distances measured with it are less than the true ones. At 
 lower temperatures or under less tension, the tape contracts and distances 
 measured with it are too long. When a tape is hung unsupported between two 
 points it forms a curve, called a catenary, and measures a greater distance 
 between the points than if the tape formed a straight line. However, the 
 apparent shortening of the distance between two points, owing to the tape 
 being subject to more than the normal tension, may be offset by the lengthen- 
 ing of the distance due to sag in the unsupported tape. For every span, there 
 is a corresponding tension where the errors balance, and this tension should 
 be ascertained and used in practice. The errors due to expansion and contrac- 
 tion, arising from changes in temperature, cannot be compensated and must be 
 corrected for in all accurate work. It should be noted that the temperature 
 of the average mine is about 65 and being essentially the same as that at which 
 the tape was graduated, no allowance for expansion or contraction is generally 
 necessary in mine work. 
 
 Steel tapes are of two general kinds, and are commonly named from their 
 length, as a 100-ft. tape, a 400-ft. tape, etc. The 50-ft. and 100-ft. tapes are 
 about | in. wide, coil or wind up in a leather case or upon a small single-handed 
 reel, and, for surveyor's use, are divided throughout their length into feet, 
 tenths, and hundredths. 
 
 The steel tape, proper, is a narrow band of metal about one-third the width 
 of the 100-ft. tape and considerably thicker, which is wound upon a wooden 
 or iron reel like a spool. These tapes may be made in any length, but those 
 400 ft. long appear to be in most general use. The tape is commonly graduated 
 every 5 ft. on brass sleeves soldered upon it. Distances are read to the nearest 
 5 ft. from the tape and intermediate distances measured with a pocket tape 
 graduated in hundredths of a foot. Sometimes before the mark there is an 
 extra set of divisions into feet, the first foot being further divided into tenths. 
 In this case, the scale for determining the hundredths need be very short, say 
 a tenth or two in length. In use, a handle with a swivel joint is fixed in an eye 
 at the end and the tape unwound from the reel for the desired or required 
 distance, but is not removed from the reel unless a distance equal to that of the 
 tape is to be measured many times. In this case, a second handle may be 
 fixed in the eye at the outer end of the tape. 
 
 In order to repair breaks that may occur in the field, clamps are made to 
 hold the broken ends together. Brass sleeves that may be brazed around 
 broken ends by the surveyor or by a competent gunsmith may be purchased. 
 To keep a mark upon the tape for frequent reference, a clip (made by bending 
 sharply upon itself a piece of steel Jm. X3in.) is slipped upon the tape, where 
 it will remain unless subject to considerable force. 
 
 What are known as metallic tapes, are made in lengths of 25, 50, and 100 ft., 
 and are graduated in hundredths of a foot for surveyors and into inches and 
 eighths for mine foremen. These are similar to the 100-ft. steel tape but are 
 made of linen, with threads df copper woven in to overcome the tendency to 
 stretch. One of these tapes, 100 ft. long, is part of every surveying outfit 
 and it should be used, wherever possible, to save the more costly 100-ft. steel 
 tape. The metallic tape answers every purpose in measuring the dimensions 
 of buildings that must appear on the map, the width of small streams, roads, 
 etc., and the distance to a property corner, if it is a nearby tree or other not 
 sharply defined point. 
 
 Pins are now but little used except in those classes of work where the use 
 of the chain is permissible. Pins should be from 15 to 18 in. long, made of 
 tempered-steel wire, and should be pointed at one end, and turned with a ring 
 for a handle. When using a 50-ft. chain, a set of pins should consist of eleven, 
 one of which should be distinguished by some peculiar mark. This should be 
 the last pin stuck by the front chainman. When all eleven pins have been 
 stuck, the front chainman calls "Out! " and the back chainman comes forwards 
 and delivers him the ten pins that he has picked up,, and he notes the out. 
 
SURVEYING 67 
 
 When giving the distance to the transitman, he counts his outs, each of which 
 consists of 500 ft., and adds to their sum the number of fifties as denoted by 
 the pins in his possession, and the odd number of feet and fractional parts of 
 a foot from the last pin to the front end of the chain. Pins cannot be used 
 in underground work as they cannot be stuck in the floor. If the distance 
 to be measured is longer than the tape, a tack is placed in a tie between the 
 stations and a measurement taken t9 it from each station with the dip of the 
 sights. In outside work, a stake with a tack is used for the same purpose, 
 and is lined in with the transit. 
 
 The clinometer, or slope level, is a valuable instrument for side-note work; 
 but it is not accurate enough for a survey, and its place is taken by the ver- 
 tical circle on the transit. There are two styles of clinometer, with a bubble 
 and with a pendulum. The latter is the old-fashioned and more accurate 
 German gradbogen that is used by some old corps. The bubble variety is 
 much more easily rendered worthless by the breaking of the bubble tube, and, 
 in general, is not so accurate as the other style, which consists of a semicircular 
 protractor cut out of thin brass and furnished with hooks at each end, that it 
 can be hung on a stretched string so that the string will pass through the 
 and 180 points. The dip is read by a pendulum swung from the center of the 
 circle. If made sufficiently large, it will readily read to quarter degrees. By 
 inclining the string parallel to the surface and hanging the clinometer, the dip 
 will be obtained. A pocket instrument combining a compass and clinometer 
 can be obtained from any dealer in surveying instruments. 
 
 TRANSIT SURVEYING 
 
 READING ANGLES 
 
 The angle read may be included or deflected. If the transit is set up at 0, 
 and a backsight taken on B and a foresight taken on C, it will be noted that 
 there are two angles made by the line CO with the line BOA , namely the included 
 angle BOC, and the deflected angle AOC. It will be further noted that AOC 
 = 180 BOC, and vice versa. 
 
 Reading the Included Angle. To read the included angle, set the zeros 
 of the vernier and the limb as near together as possible by the eye, clamp the 
 upper plate and bring the zeros into exact coincidence by means of the upper 
 tangent screw. Set the vertical hair approximately upon the backsight, clamp 
 the lower motion, and by the lower tangent screw, make the setting exact. 
 Loosen the upper clamp, set approximately on the foresight, tighten the upper 
 clamp, and by means of the upper tangent screw make the setting exactly. 
 The vernier will read, say 45, which is the included angle 
 BOC. 
 
 Reading the Deflected Angle. -After arranging the 
 verniers as just explained, to read the deflected angle, in- 
 vert the telescope so that the level bubble is above, and 
 set upon the backsight as before. Turn the telescope back 
 to its normal position (this is called plunging the telescope) 
 and sight to the foresight as explained. The vernier will 
 read a right angle of 135. As noted, the sum of the in- 
 cluded and deflected angles must always be 180, and in the case given 45 
 + 135 = 180. 
 
 MAKING A SURVEY WITH A TRANSIT 
 
 Meridians, or Base Lines. Every survey must start from some fixed point 
 and the angles measured in the course thereof must be referred to some line 
 as a base. The nature of the base line depends on the use to which the sur- 
 vey of the property is to be put. When surveying small tracts of land, such 
 as city or town lots, the starting point may be a stake driven into the ground 
 or a corner of the property itself and the base line may be one of the sides of the 
 tract. When surveying farms, it is customary to make one of the property 
 corners the starting point and to use as a base line the magnetic meridian, 
 noting the date on which the survey is made, so that at any subsequent time an 
 allowance may be made for the variation of the needle. When surveying large 
 tracts of land, or even comparatively small ones, upon which mines are to be 
 opened, the starting point is commonly some firmly planted artificial object, 
 and the base line is the true meridian, as determined by astronomical observa- 
 tions on the North Star (Polaris), or on the sun, by methods given under the 
 
68 SURVEYING 
 
 head of Latitude and Longitude. The true meridian is the only invariable 
 base line that can always be determined at any time or place by means of the 
 engineer's transit. 
 
 Monuments. When establishing a reference meridian or base line for 
 any large coal property, it is not customary to place the monuments marking 
 its extremities exactly in the true north-and-south line; in fact, it is not gen- 
 erally possible to do 39. The monuments should be placed where they will 
 not be disturbed by mining operations; where the line of sight between them 
 will not become obstructed by subsequent building operations; and where they 
 will be convenient for use. Hence, monuments should be placed outside the 
 crop line if this comes upon the property so that pillar drawing, followed by set- 
 tling of the surface, will not throw them out of line. If the property is opened 
 by a shaft, one monument may be placed upon that portion of the surface that 
 will be sustained by the shaft pillar, and the other monument or monuments 
 may be placed upon reservations from under which the coal will not be mined, 
 or may be placed entirely outside the boundaries of the property. If no place 
 that will remain undisturbed during the life of the mine can be found for the 
 second monument, sights may be taken to a number of prominent buildings 
 or natural objects within or without the boundaries of the property. The 
 angles made by the lines joining these objects with the monument as a vertex 
 should be repeatedly read, and the mean of the readings taken as the true angle. 
 Reference points so selected will determine the direction of the meridian at 
 any later date, as it is improbable that all of the five or ten reference points will 
 be disturbed or destroyed. 
 
 The cheapest monuments may be made from mine-car axles or from old 
 railroad iron of, say, 60 to 70 Ib. to the yd., cut into lengths of from 4 to 8 ft., 
 depending on the nature of the soil. One end should then be sharpened and 
 the axle or rail driven into the ground until about 6 in. project above the sur- 
 face. A bole is then deeply marked in the top by a center punch and its dis- 
 tance from three or four nearby points is measured. These distances, or 
 references, will enable the monument to be found in event of its being subse- 
 quently covered with dirt. 
 
 Monuments made of rails, unless the ends are driven well below the frost- 
 line, are apt to be moved out of line through the alternate freezing and thaw- 
 ing of the soil; therefore, a better way is to place the monuments in solid, out- 
 cropping rock. In this case, a hole some 12 in. deep is drilled in the rock and 
 a bolt of 1-in. or IJ-in. round iron is leaded into it, the head of the bolt being 
 allowed to project 1 or 2 in. above the rock. The bolt is center-punched the 
 same as would be a rail. Sometimes the projecting end of the bolt is threaded 
 so that a cap may be screwed upon it to protect the center. This is a good plan 
 in damp climates if the monument is intended to last many years. 
 
 Excellent monuments may be made of dressed stone in which a center- 
 punched bolt is set to mark the exact point. The upper foot, in length, of 
 the stone, about 6 in. of which projects above the surface, is dressed square 
 with a side of 6 to 8 in. The lower portion beneath the ground should be as 
 large, and consequently as heavy, as possible. The length should be 4 ft. or 
 more, so that the bottom is set well below the frost line. Concrete monuments 
 are cheaper than stone and may be constructed of any size. They are, of 
 course, built up in a pit of good depth, the center bolt being placed before the 
 cement has had time to set. 
 
 The boundary of a large property may be 5, 10, or more mi. in length. 
 As it is impossible to tell, in advance, when and where new property will be 
 acquired, necessitating an extension of the original survey, it is a most excel- 
 lent plan to set a pair of monuments at intervals of about 1 mi. along the line 
 of the survey. The wooden pegs used as stations in the original survey, will 
 disappear in 12 to 18 mo. or will have been so displaced by the action of frost 
 as to be useless. If two consecutive stations are made of rails placed in the 
 fashion of monuments, they will serve at any future time as a base for the 
 extension of the survey. These permanent stations, as they are frequently 
 called, should be carefully witnessed and referenced. 
 
 OUTSIDE SURVEYS 
 
 Preliminary Work. Before the survey of a property is undertaken, it 
 is highly advisable that the surveyor should go over the ground and familiarize 
 himself with the location of all the corners, roads, streams, houses, outcrops, 
 reservations, and other features that are to appear upon the map. While in 
 some cases a map of the property is furnished the surveyor, it is usually neces- 
 sary for him to prepare one from the deeds to its component tracts as recorded 
 
SURVEYING 69 
 
 at the county seat. A large property is usually made up of from 10 to 100 or 
 more tracts varying in size from a fraction of 1 A. to 100 A. or more. As the 
 surveys found in the deeds were made at widely different dates, the bearing 
 of a line common to two or more properties is commonly different in each deed 
 in which it is mentioned. In such cases, the surveyor should mark on his 
 tracing the different bearings given, as well as the different lengths for each line. 
 With this map, a good pocket compass, and a 100-ft. tape, together with what 
 information may be picked up from residents along the line, the surveyor and 
 his assistant can locate and mark the various corners. 
 
 Angular Measurements. The angular measurements in a survey may be 
 made by one of two methods. In one, the angle at any station is read but 
 once, the method commonly used being known as the continuous vernier; in 
 the other method, the angle at each station is read twice. By the first method, 
 no check on the accuracy of the wprk is afforded until the initial station of the 
 survey is occupied with the transit and the azimuth of the first line redeter- 
 mined, affording what is known as a close. As the bulk of the time in the field 
 is employed in setting up the transit, it would seem but ordinary good sense 
 to repeat or check the angles at each station that the accuracy of the work may 
 be certain as the survey proceeds. In no case should the results of a single- 
 angle survey be accepted as correct until such a close has been made. 
 
 When making a survey by single angles, the procedure is as follows: Set 
 the transit over the monument marking one end of the base line, which is called 
 Sta. 0. Assuming that the base line makes an angle of 48 21' to the right of 
 the meridian, this angle is the azimuth of the base line; and as it is to right 
 of the meridian, its bearing is N 48 21' E. Set off this azimuth on the limb of 
 the transit and focus the vertical hair on the second mounment; the line 
 of collimation of the transit will now be in a line directed N 48 21' E, and 
 if the upper plate is loosened and the instrument set on any distant object, 
 the azimuth and bearing of that point from Sta. 0, may be read from the grad- 
 uated limb. Suppose the sight is taken to Sta. 1 of the survey. If the read- 
 ing on one set of graduations is 326 48', which is the azimuth of the line 0-1, 
 the reading on the other set will be N 33 12' W, which is the bearing of the 
 
 Setting up the instrument over Sta. 1, the vernier is read, to see that it still 
 reads 326 48'. Then invert the telescope so that the level tube is on top, f and 
 by means of the lower motion, take a backsight on Sta. 1. When the telescope 
 is plunged into its normal position (level tube below) , the line of sight is in the 
 line 0-1 produced with an azimuth of 326 48'. Loosen the upper motion 
 and sight on Sta. 2 of the survey. If the azimuth from one set of graduations 
 is, say, 266 10', the bearing from the other set will be S 86 10' W. Continue 
 this work from station to station until the transit finally reoccupies Sta. 0, 
 the monument at one end of the base line. If, now, the azimuth of the base 
 line as determined by reference to the last line of the survey is found to be 
 48 21' as determined astronomically, all of the angles of the survey have been 
 measured correctly, and the survey is said to close in angle. 
 
 When making a survey by double angles at each station, assume that the 
 azimuths of the lines are the same as those just used for illustration and that 
 the transit is set up at Sta. 1. Set the vernier at and take a backsight on 
 Sta. 0. If the upper motion is loosened and the telescope revolved 180 around 
 its vertical axis, the line of sight will be in the line 0-1 produced. Continue 
 revolving the telescope until it is set upon Sta. 2, when it will have been turned 
 to the left of the line 1-0 produced and the angle made by the line 1-2 with this 
 line (0-1 produced) is a deflection angle to the left, or a left angle commonly 
 called. This will be found to be (in the assumed case) 60 38'. Next, set the 
 vernier on the azimuth of the line 0-1, viz.: 326 48' (bearing N 33 12' W), 
 and with the telescope inverted take a backsight upon Sta. 0. Plunge the 
 telescope and by the upper motion set on Sta. 2. The azimuth will be found 
 to be 266 10' (bearing S 86 10' W). As the deflection angle subtracted from 
 the azimuth of the line 0-1 gives the azimuth of the line 1-2, the angles have 
 been correctly read. Thus 326 48' (azimuth) -60 38' (deflection angle) 
 = 266 10' (azimuth line 1-2). Similarly N 33 12' W (bearing line 7 1) 
 +60 38' (left deflection angle) = N 93 50' W = S 86 10' W (bearing of line 
 1-2). 
 
 It is customary to read and record the deflection angle first, and then to read 
 and record the azimuth or bearing. After the main angles by which the sur- 
 vey is continued have been noted, before moving to the next station, all the cor- 
 ners, houses, roads, streams, etc., that can conveniently be reached from the 
 instrument should be located and entered in the notebook. 
 
70 SURVEYING 
 
 Whether the direction of a line of a survey shall be recorded and described 
 by its azimuth or by its bearing is a matter of choice. Few of those for whom 
 the map is chiefly made are familiar with the former term, and the statement 
 that a certain property line or heading has an azimuth of, say, 286 10' does 
 not give them any idea as to its direction ; whereas, every layman understands 
 the meaning of the equivalent bearing, S 86 10' W. For this reason it seems 
 better to give the bearings of lines instead of their azimuths. 
 
 Distance Measurements. A general rule that should not be broken is 
 that all operations necessary to carry on the main line of the survey must be 
 done before anything else is attempted. Therefore, after reading and record- 
 ing the angle between the lines of the survey, and checking it by the method 
 just explained, the distance to the next, or foresight, station must be read. 
 The method of doing this will depend on whether a 100-ft. tape or chain is used, 
 or, as is the better practice, a 400-ft. tape is employed. 
 
 The method of using a chain on level ground has been described. On 
 ground sloping, say, down hill from the instrument, one end of the chain is 
 held at the tack in the stake marking the station, and as much of the tape as 
 can be held horizontal is stretched out in the line to the next station. The end 
 of the horizontal portion of the chain is marked on the ground by dropping 
 a plumb-line from it. The length of this level portion is noted on a piece of 
 paper; the end of the tape held at the plumb-bob in the ground and another 
 length of level tape stretched out and its end marked, and length noted as 
 before. This is kept up until the distance between the stations has been cov- 
 ered, when the sum of the single measurements, is equal to the entire measure- 
 ment. This is a slow, laborious, and generally inaccurate method that has, by 
 mine surveyors, at least, given way to the use of the long steel tape. 
 
 If the distance between stations is less than the length of the tape and the 
 ground is level or uniformly sloping, the end of the tape is held at the tack 
 in the stake at the instrument and the distance to the tack in the foresight stake 
 read, as previously explained. If the ground slopes either up or down hill, 
 the angle of elevation or depression of the slope must be taken and recorded 
 as a plus (+) angle if one of elevation, or as a minus ( ) angle, if one of depres- 
 sion. If the tape has been stretched along a plane surface, as explained, the 
 line of sight when the so-called vertical angle is read must be parallel to the tape. 
 To do this, a sight must be taken at a point on the foresight rod as far above 
 the ground as is the center of the telescope axis at the instrument station. If 
 the ground is not uniformly sloping, the end of the tape is held at the hole 
 marking the end of the horizontal axis of the telescope, and the measurement 
 is made to the tack in the foresight stake. In this case the vertical angle is 
 measured directly, exactly as the horizontal cross-hair cuts the station tack. 
 Distance on slope X cos vertical angle = horizontal distance (1) 
 
 Distance on slope X sin vertical angle = difference in elevation (2) 
 
 The reduction of the slope distances to horizontal ones is made in the office, 
 not in the field. If the elevation of the first survey station is known, that of 
 all the other stations is obtained by adding continuously to it the difference 
 in elevation, as obtained from formula 2. While elevations thus obtained 
 are not so accurate as those secured through the use of leveling instruments, 
 they answer every purpose as a basis for a topographical survey made with the 
 stadia. 
 
 If the distance is greater than the length of the tape, but less than twice 
 as great, say 790 ft., a stake with a tack is placed about half way between the 
 stations and in the line joining them. The distance and vertical angle to the 
 stake are read after making the foresight, and again from the next station, after 
 taking the backsight. The sum of these distances, after reduction to the hori- 
 zontal, is the total distance between the two stations. 
 
 If the distance is greater than two tape lengths, say, 1,000 ft., two stakes 
 must be set. The first stake a may be placed, say, 350 ft. from the instrument, 
 and the second stake b, 350 ft. beyond that. Before moving the transit the 
 distance and vertical angle to a must be read and the transit set up roughly 
 over a and the distance and vertical angle to b read. At the next station and 
 on the backsight, the distance and vertical angle to b must be read. The sum 
 of these three distances reduced to the horizontal is the distance between the 
 stations. 
 
 Locating Corners, Etc. After the main-line angle is read and checked 
 and the distance to the next station measured (or such part of it as is possible 
 without moving the transit) a sight or sights should be taken to any nearby 
 property corner or corners and the azimuth or bearing, as well as the distance 
 and the vertical angle thereto recorded. It should be noted that the deflection 
 
SURVEYING 
 
 71 
 
 angle between the lines joining stations should be read first, as the instru- 
 ment must be properly oriented before corners, etc., can be located and this 
 orientation is secured at each station by using as a backsight for the second 
 reading, the azimuth of the line joining the backsight and instrument stations 
 as determined from the previous set-up. After the corners have been located 
 stadia sights are taken to any houses, streams, roads, topographic features' 
 etc., that should appear upon the map. 
 
 Keeping Notes. The various ways of keeping the main-line and side notes 
 of an outside survey arrange themselves into four groups: (1) The side notes 
 of each sight follow the transit notes of that sight, and on the same paee 
 (2) They are entered in the same book on opposite pages. (3) The transit 
 notes of the whole survey come first, and are followed by the side notes in the 
 same book. (4) Each set of notes has a separate book. 
 
 Of these methods, the second and third are in common use. For a survey 
 made by the methods just explained, the accompanying form of transit notes 
 is the usual one. The columns are headed for station (Sta.), Bearing Anele 
 (deflection angle) which may be either R (right) or L (left), distance (Dist ) 
 and Slope (vertical angle, or pitch). 
 
 TRANSIT NOTES 
 
 
 
 Angle 
 
 
 
 Sta. 
 
 Bearing 
 
 
 Dist. 
 
 Slope 
 
 
 
 
 
 R 
 
 L 
 
 
 
 Mt-Mz 
 Mi-1 
 
 N 48.21 E 
 S 26.30 W 
 
 (Bea 
 
 ring of base 
 21.51 
 
 line) 
 262.83 
 
 4.16 
 
 1-2 
 
 S 67.49 W 
 
 41.19 
 
 
 387.62 
 
 2 18 
 
 2-3 
 
 3-4 
 
 N 86.11 W 
 S 55.28 W 
 
 26.00 
 
 38.21 
 
 316.99 
 365.34 
 
 +0.16 
 + 1.56 
 
 The bearing of the base line, or that joining the two monuments, Mi and 
 M2, is N 48.21 E. It will be noted that the signs and ' are not used, a period 
 serving to separate the degrees and minutes. This saves time. The notes are 
 simple and self-explanatory. The transit is always assumed to be at the sta- 
 tion whose number or letter is given first in the station column. Thus, the 
 instrument is at Sta. Mi, 1, 2, and 3. The foresight follows the instrument 
 station in the same horizontal line. Thus, the foresights to Sta. 1, 2, 3, and 4, 
 are made from Sta. Mi, 1, 2, and 3, respectively. The backsight at Sta. 1 is, 
 of course, Mi, at Sta. 2, it is 1, and similarly. It should be noted at Sta. Mi, 
 when the vernier is set for the purpose of taking the azimuth or bearing of the 
 line 1-2, that the setting S 48.21 W and not N 48.21 E is used. This is because 
 the line M^-Mi runs in exactly the opposite direction from the line Mi-Mz, 
 and the survey is moving forwards in the former line. 
 
 As stated, the side notes are entered in the same book as the main-line 
 notes, but usually in the back. It is well to head a certain page, say, Sta. 1, 
 and then to follow with all the side notes taken at that station, and similarly 
 for the succeeding stations. The condition of all property corners should be 
 carefully described, as their present state is often very different from what 
 it was at the time the original deeds were made. Thus, a corner described as a 
 hemlock sapling in a deed dated 1790, may now be a tree 2 or 3 ft. in diameter, 
 may be a stump, may have entirely rotted away so that only an expert can tell 
 from the decayed remains that a hemlock once marked the corner, or a good- 
 sized oak, sugar maple, or hickory may have replaced it, the hemlock having 
 been destroyed but a few years after the deed was made and a tree of another 
 species grown in its place. 
 
 Frequently there are reservations around farm houses from under which 
 the coal may not be mined. Sometimes the corners of these reserves (as they 
 are often called) can be reached in a single sight; if not, a branch line must be 
 run to them from the line of the main survey. 
 
 When locating houses by stadia sights, two men are necessary. One can 
 hold the stadia rod at the opposite corners of the house, but a second is required 
 to hold the tape by which the dimensions of the buildings are secured. Roads 
 are located by the fences on either side, the road legally occupying all the space 
 between the fences, even if part of it is grown up in weeds and the wagons 
 
72 SURVEYING 
 
 have maderbut a single line of ruts. Roads are commonly either 1 or 2 rd., 
 that is, 16.5 or 33 ft. in width, and should be so mapped. 
 
 Small brooks are located by taking a stadia sight to their center at each 
 . important bend. Larger creeks should have one bank located with the stadia, 
 the stadia rodman estimating the width of the stream, which should be entered 
 in the notes. Large rivers should have a regular traverse run along the bank, 
 the opposite side being located by stadia sights. In the case of very large 
 rivers, a transit line must be run along each bank and the shore line located by 
 stadia sights. Stadia sights should be taken to points along the bpttoms of all 
 dry gulleys, to the summits of all ridges, and to any marked change in the degree 
 of slope of a hill. 
 
 If the vertical angles have been taken when the distances between the sta- 
 tions were measured and the stadia sights taken as just explained, there will be 
 gathered in the course of the survey enough data to make a very complete 
 topographic, or contour, map of the property. This will particularly be true, 
 if, as is customary, the boundaries of the individual farms making up the entire 
 property are surveyed. The reason for surveying the single farms is that very 
 frequently the operating coal company has not the same rights in all of them, 
 so that the method of mining is affected by what the company can and cannot do. 
 
 The kind, dip, and strike of all outcropping ledges or other exposures of 
 rock should be noted and mapped. The information thus obtained, combined 
 with the elevations obtained with the stadia, etc., furnishes the data from which 
 geological cross-sections may be made. 
 
 The first page of the notebook should give the name of the company for 
 whom the work is done, the location of the property, name of the engineer in 
 charge of the work, the names of the helpers, and each day's work should be 
 dated; and if the members of the corps have changed, this, too, should be a 
 matter of record. 
 
 If more than one property is being surveyed from the same office, a separate 
 set of field books should be devoted to each. It is an excellent plan at night 
 to copy at least the main-line notes in a permanent notebook, which is left at 
 the office, or at the farmhouse if the corps is in the field. Sometimes the side 
 notes are also copied. These copies are made so that all the records may not be 
 destroyed, necessitating an entirely new survey, should anything serious happen 
 to the field book. When not in use, all field books, both originals and copies, 
 should be kept in a fireproof vault. 
 
 Closing Surveys. To diminish the chance of error, even if double angles 
 have been read, the survey must be closed upon itself or some part of a former 
 closed survey. That is, the transit must a second time occupy the initial 
 station, so that the first azimuth read may be referred back to the last line of 
 the survey. If the azimuth (or bearing) as read the second time agrees with 
 that obtained at the first reading, the angular readings are proved to have been 
 correctly made. If the error in closure is not more than 1' to 3' in a line 4 or 
 5 mi. in length, most surveyors will balance the survey, but in important work 
 the error must (or should) be located so that the survey will close exactly 
 in angle. Usually one or more stations will be selected as the most probable 
 ones at which the error (all or in part) was made. These stations will be those 
 at which good sights were not to be had owing, say, to smoke obscuring the 
 point of the plumb-bob underground or, in the case of surface surveys, to the 
 station stake on either backsight or foresight being beyond a roll in the ground 
 so that the tack or the point of the rod was not visible. These doubtful sta- 
 tions may be reoccupied and the angles remeasured with special care. If not 
 located at the probable places of error, the survey, so far as the angle measure- 
 ments are concerned, may be rerun in its entirety; but this is rarely necessary. 
 If the angles cannot be made to close upon resurvey, the failure to do so is prob- 
 ably caused by cumulative errors, a few seconds at each station. These errors 
 are, singly, too small to measure, but in a survey of 40 or 50 stations may 
 amount to 1' or more. Errors in linear measurement are far more common 
 than errors in angular measurement, as there is no field check upon the work 
 with the tape unless the distances are read twice, on the foresight from the one 
 station and on the backsight from the next. A wrong reading of the vertical 
 angle will, of course, affect the horizontal distance. Errors in measurement 
 are often of 5 or 10 ft. due to incorrectly reading the graduations on the tape. 
 Perfect linear measurements are far more difficult to make than perfect angular 
 measurements. This is because the correct length of a line is very materially 
 affected by variations in the length of the tape due to the effects of sag, ten- 
 sion, changes in temperature, etc. In highly accurate work, corrections should 
 be made for all of these. 
 
SURVEYING 73 
 
 The allowable error in closure depends on many things, the chief of which 
 is financial. If it will C9st more to locate and correct the error than the value 
 of the land saved, it will not pay to do so. In other words, far more time 
 (consequently, money) may be spent upon a survey of coal land worth $2,500 
 an A. than upon land costing but $5 an A. In ordinary rolling country, such 
 as prevails in the coal fields of the eastern states, with instruments in good 
 adjustment and using ordinary precautions, the error in closure should not be 
 greater than 1 ft. in 3,000 ft. to 1 ft. in 5,000 ft., and trained corps will do better. 
 In bituminous mines, which are commonly in flat coal, underground surveys 
 may easily be closed within 1 ft. in 10,000 ft. to 1 ft. in 20,000 ft. The higher 
 accuracy obtainable underground is due chiefly to the fact that mine temper- 
 atures are extremely uniform so that corrections for expansion or contraction 
 of the tape are unnecessary. Likewise, the tape is stretched on the ground 
 and errors due to sag are thus eliminated. 
 
 LEVELING 
 
 DESCRIPTION OF INSTRUMENTS 
 
 In leveling, but two instruments are used, the level and a leveling rod. 
 
 The level consists of a telescope to which is fitted, on the under side, a long 
 level tube. The telescope rests in a Y at each end of a revolving bar, which is 
 attached to a tripod head very similar to that used for a transit. The tele- 
 scope is similar to the telescope of a transit. 
 
 The leveling rod is merely a straight bar of wood, 6 ft. or more in length, 
 divided into feet and tenths of a foot. A target divided into four equal parts 
 by two lines, one parallel with the staff, and the other at right angles to it, 
 and painted red and white, so as to make it prominent at a distance, slides on 
 the rod and is provided with a clamp screw. The center of the target is cut 
 out and a vernier, graduated decimally, is set in, which enables the rodman to 
 read as close as ^^7 ft- If a long rod is required, it is made of two sliding bars, 
 which, when closed, are similar to a single rod, as described above. When used 
 at points where it is necessary to shove the target to a greater height than 6 or 
 65 ft., the target is clamped at the highest graduation on the front of the rod, 
 and the rod is extended by pushing up the back part, which carries the target 
 with it. The readings, in this case, are made either from the vernier on a 
 graduated side, or a vernier on the back. The rodman must always hold his 
 rod perfectly plumb or perpendicular. 
 
 LEVEL ADJUSTMENTS 
 
 The proper care and adjustment of the level is of great importance. A very 
 slight error in adjustment will completely destroy the utility of any work done. 
 
 1. To Adjust the Line of Collimation. Set the tripod firmly, remove the 
 Y pins from the clips, so as to allow the telescope to turn freely, clamp the instru- 
 ment to the tripod head, and, by the leveling and tangent screws, bring either 
 of the wires upon a clearly marked edge of some object, distant from 100 ft. 
 to 500 ft. Then with the hand, carefully turn the telescope half way around, 
 so that the same wire is compared with the object assumed. Should it be 
 found above or below, bring it half way back by moving the capstan-headed 
 screws at right 'angles to it, remembering, always, the inverting property of the 
 eyepiece; now bring the wire again upon the object, and repeat the first oper- 
 ation until it will reverse correctly. Proceed in the same manner with the 
 other wire until the adjustment is completed. Should b9th wires be much 
 out, it will be well to bring them nearly correct before either is entirely adjusted. 
 
 2. To Adjust the Level Bubble. Clamp the instrument over either pair of 
 leveling screws, and bring the bubble into the center of the tube. Now turn 
 the telescope in the wyes, so as to bring the level tube on either side of the cen- 
 ter of the bar. Should the bubble run to the end, it shows that the vertical 
 plane, passing through the center of the bubble, is not parallel to that drawn 
 through the axis of the telescope rings. To rectify the error, bring it by esti- 
 mation half way back, with the capstan-headed screws, which are set in either 
 side of the level holder, placed usually at the object end of the tube. Again 
 bring the level tube over the center of the bar, and adjust the bubble in the 
 center, turn the level to either side, and, if necessary, repeat the correction 
 until the bubble will keep its position, when the tube is turned in. or more 
 to either side of the center of the bar. The necessity for this operation arises 
 from the fact that when the telescope is reversed, end for end, in the wyes in 
 the other and principal adjustment of the bubble, it is not easy to place the 
 
74 SURVEYING 
 
 level tube in the same vertical plane, and, therefore, it is almost impossible 
 to effect the adjustment without a lateral correction. 
 
 Haying now, in a great measure, removed the preparatory difficulties, it 
 is possible to proceed to make the level tube parallel with the bearings of the 
 Y rings. To do this, bring the bubble into the center with the leveling screws, 
 and then, without jarring the instrument, take the telescope out of the wyes 
 and reverse it end for end. Should the bubble run to either end, lower that 
 end, or, what is equivalent, raise the other by turning the small adjusting nuts, 
 on one end of the level, until, by estimation, half the correction is made; again 
 bring the bubble into the center and repeat the whole operation, until the 
 reversion can be made without causing any change in the bubble. It is well 
 to test the lateral adjustment, and make such correction as may be necessary 
 in that, before the horizontal adjustment is entirely completed. 
 
 3.' To Adjust the Wyes. To adjust the wyes, or, more precisely, to bring 
 the level into a position at right angles to the vertical axis, so that the bubble 
 will remain in the center during an entire revolution of the instrument, bring 
 the level tube directly over the center of the bar, and clamp the telescope 
 firmly in the wyes. Place it, as before, over two of the leveling screws, unclamp 
 the socket, level the bubble, and turn the instrument half way around, so that 
 the level bar may occupy the same position with respect to the leveling screws 
 beneath. Should the bubble run to either end, bring it half way back by the 
 Y nuts on either end of the bar; now move the telescope over the other set of 
 leveling screws, bring the bubble again into the center, and proceed precisely 
 as just described, changing to each pair of screws, successively, until the adjust- 
 ment is very nearly perfected, when it may be completed over a single pair. 
 
 The object of this approximate adjustment is to bring the upper parallel 
 plate of the tripod head into a position as nearly horizontal as possible, in 
 order that no essential error may arise, in case the level, when reversed, is not 
 brought precisely to its former situation. When the level has been thus 
 completely adjusted, if the instrument is properly made and the sockets are 
 well fitted to one another and the tripod head, the bubble will reverse over 
 each pair of screws in any position. Should the engineer be unable to make it 
 perform correctly, he should examine the outside socket carefully, to see that 
 it sets securely in the main socket, and also notice that the clamp does not 
 bear upon the ring that it encircles. When these are correct, and the error 
 is still manifested, it will probably be in the imperfection of the interior spindle. 
 
 After the adjustments of the level have been effected and the bubble remains 
 in the center in any position of the socket, the engineer should carefully turn 
 the telescope in the wyes, and sighting upon the end of the level, which has 
 the horizontal adjustment along each side of the wye, make the tube as nearly 
 vertical as possible. When this has been secured, he may observe, through the 
 telescope, the vertical edge of a building, noticing if the vertical hair is parallel 
 to it; if not, he should loosen two of the cross- wire screws at right angles to 
 each other, and with the hand on these, turn the ring inside, until the hair is 
 made vertical; the line of collimation must then be corrected again, and the 
 adjustments of the level will be complete. 
 
 USING THE LEVEL 
 
 When the instrument is being used, its legs must be set .firmly into the 
 ground, and neither the hands nor person of the operator be allowed to touch 
 them. The bubble should then be brought over each pair of leveling screws 
 successively, and the instrument leveled in each position, any correction being 
 made in the adjustments that may appear necessary. Care should be taken 
 to bring the wires precisely in focus, and the object distinctly in view, so that 
 all errors of parallax may be avoided. 
 
 An error of parallax is seen when the eye of an observer is moved to either 
 side of the center of the eyepiece of a telescope, in which the foci of the object 
 and eyeglasses are not brought precisely upon the cross-wires and object; in 
 such a case, the wires will appear to move over the surface and the observation 
 will be liable to inaccuracy. In all instances, the wires and object should be 
 brought into view so perfectly that the spider lines will appear to be fastened 
 to the surface, and will remain in that position however the eye is moved. 
 
 If the socket of the instrument becomes so firmly set in the tripod head as 
 to be difficult of removal in the ordinary way, the engineer should place the 
 palm of the hand under the Y nuts at each end of the bar, and give a sudden 
 upward shock to the bar, taking care, also, to hold his hands so as to grasp it 
 the moment it is free. 
 
SURVEYING 
 
 75 
 
 FIELD WORK 
 
 If the survey has been carefully made and vertical angles taken at every 
 sight, leveling will be necessary only in cases where extreme accuracy in regard 
 to vertical heights is necessary. In most cases of practical work at collieries, 
 particularly in determining thickness of strata, general rise or fall of an inside 
 road, etc., the elevations calculated by the use of the vertical angle will be close 
 enough, but there are frequently instances when leveling must be done, to 
 insure success in certain work. In this connection, it is well to state that if the 
 transit telescope is supplied with a long level tube, and it is, as a whole, in 
 first-class adjustment, levels can be successfully run with it if the transitman 
 uses due care. Having his instrument in proper adjustment and his notebook 
 ruled, the levelman is ready to proceed with the work. 
 
 The rodman holds the rod on the starting point, the elevation of which is 
 either known or assumed. The levelman sets up his instrument somewhere 
 in the direction in which he is going, but not necessarily, or usually, in the 
 precise line. He then sights to the rod and notes the reading as a backsight 
 or + (plus) sight, entering it in the proper column of his notebook, and adding 
 it to the elevation of the starting point as the "height of instrument." The 
 rodman then goes ahead about the same distance, sets his rod on some well- 
 defined and solid point, and the levelman sights again to the target, which 
 the rodman moves up or down the rod until it is exactly bisected by the hori- 
 zontal cross-hair in the telescope, as he did when giving the backsight. This 
 reading is noted as a foresight or (minus) sight. The foresight subtracted 
 from the height of instrument gives the elevation of the second station. The 
 rodman holds this latter point, and the levelman goes ahead any convenient 
 distance, backsights to the rod, and proceeds as before. In this case, it is 
 assumed that levels are only being taken between regular stations or two 
 extreme points. 
 
 If a number of points in close proximity to each other are to be taken, the 
 rodman, after giving the backsight, holds his rod at each point desired. The 
 readings of any number in convenient sighting distance are taken and recorded 
 as foresights, and any descriptive notes are made in the column of remarks. 
 These are each subtracted from the height of instrument, and the elevation 
 found is noted in column headed Elevation. After all the intermediate points 
 are taken, the rodman goes ahead to some well-defined point, which is called 
 a turning point (T. P.) in the notes. The elevation of this is found and recorded . 
 The rodman remains at this point until the levelman goes ahead, sets up and 
 takes a backsight. This backsight reading, added to the elevation of the 
 turning point, gives a new height of instrument from which to subtract new 
 foresights, and thus obtain the elevation of the next set of points sighted to. 
 
 When running levels over a long line, the levelman should set frequent 
 bench marks (B. M.). These are any permanent well-defined marks that can 
 be readily found and identified at any future time. By leveling to them he 
 has secured the elevation of points from which to start any subsequent levels 
 that may be necessary. A good bench mark can always be made on the side 
 or root of a large tree or stump by chopping it away so as to leave a wedge- 
 shaped projection with the point up. A nail should be driven in the highest 
 point of this, to mark where the rod was held, and the tree or stump blazed 
 
 LEVEL NOTES 
 
 Station 
 
 B. S. 
 
 P. S. 
 
 H. Inst. 
 
 Elev. 
 
 Remarks 
 
 1 
 
 
 
 
 100. 
 
 Assumed elevation of Sta. 1. 
 
 
 3.412 
 
 
 103.412 
 
 
 
 2 
 
 
 4.082 
 
 
 99.33 
 
 Sta. 2 of survey. See page 
 
 
 
 
 
 
 Vol. - 
 
 
 
 6.791 
 
 
 96.621 
 
 Sight taken to ground at N. E. 
 cor. John Smith's house. 
 
 3 = T. P. 
 
 
 4.862 
 
 
 98.55 
 
 Sta. 3 of survey noted above. 
 
 
 11.698 
 
 
 110.248 
 
 
 
 4 
 
 
 9.817 
 
 
 100.431 
 
 Sta. 4 of survey noted above. 
 
 B. M. 1 
 
 
 6.311 
 
 
 103.937 
 
 B. M. 1 is on north side of large 
 
 
 
 
 
 
 white oak. 
 
 5 
 
 
 6.427 
 
 
 103.821 
 
 Sta. 5 of survey noted above. 
 
70 
 
 SURVEYING 
 
 above the bench mark. In this blaze, the number of the bench mark, which 
 should, of course, correspond with the number in the notebook, should be cut 
 or painted. In the mines, prominent frogs or castings in the main roads, if 
 permanent, make good bench marks. 
 
 In underground leveling, extreme care must be observed to record the 
 algebraic signs of .the readings, which show whether the level rod was held 
 in its usual position, indicated by a -f- sign or the absence of any sign, or upside 
 down, indicated by the -sign. 
 
 Proof of Calculations. The calculations are proved by adding together 
 the backsights and also the foresights taken to turning points and last station. 
 Their difference equals the difference of level between the starting point and 
 last station. Thus: 
 
 Foresights Backsights 
 
 4.S62 3.412 
 
 6.427 11.698 
 
 11.289 15.110 
 
 11.289 
 
 3.821 = 103.821 - 100.0 or 3.821 
 TRIGONOMETRIC LEVELING 
 
 Trigonometric leveling determines the difference in elevation between two 
 points from the measurement of the distance between the points, and from the 
 vertical angle between them. Although generally less accurate than level- 
 ing with a Y level, it is much more rapid and is especially adapted for pre- 
 liminary work in a hilly country, or 
 for the leveling of mine slopes and 
 pitching rooms where the Y level can- 
 not be used with any advantage or 
 accuracy. By reading the angles and 
 by checking the measurements, a very 
 high degree of accuracy can be ob- 
 tained in trigonometric leveling. 
 
 Case 1. Assume the elevation of 
 A, Fig. 1, to be 100 ft. above tide. 
 With the transit set up over A and prop- 
 erly leveled, sight to a point C on a rod 
 so that BC equals AD. Measure the 
 vertical angle Z and the inclined distance DC, then the difference in the eleva- 
 tion between A and B equals BC = CDXsin Z, and the elevation of B equals 
 100 +BC. 
 
 Case 2. Assume the elevation of 
 station A, Pig. 2, in the roof of a mine 
 to be 100 ft. above tide. Then, with the 
 transit set up directly under A and 
 properly leveled sight to a point C upon 
 the plumb-line suspended from the sta- 
 tion B, measure the vertical angle X, 
 inclined distance DC, and roof distance 
 BC. From this, the distance CY = DC 
 X sin X. The elevation of B is then 
 found as follows: The elevation of 
 B = elevation of A-AD+(DCXsin X) 
 + BC. 
 
 There are many modifications of this 
 simple method, but from these dia- 
 grams the most complex modifications can be worked out. 
 TRIGONOMETRIC LEVEL NOTES 
 
 FIG. 1 
 
 FIG. 2 
 
 Station 
 
 Vertical 
 Angle 
 Degrees 
 
 Inclined 
 Distance 
 
 100 
 100 
 100 
 100 
 
 Vertical 
 Distance 
 
 Height of 
 Instrument 
 Feet 
 
 Roof 
 Distance 
 Feet 
 
 Elevation 
 Feet 
 
 A 
 A-B 
 B-C 
 C-D 
 D-E 
 
 + 5 
 +2 
 -3 
 -4 
 
 +8.72 
 + 3.49 
 -5.23 
 -6.98 
 
 2 
 3 
 4 
 2 
 
 3 
 2 
 3 
 1 
 
 + 100.00 
 109.72 
 112.21 
 105.98 
 98.00 
 
SURVEYING 77 
 
 CONNECTING OUTSIDE AND INSIDE WORK THROUGH 
 SHAFTS AND SLOPES 
 
 SURVEYING SHAFTS 
 
 As the dip of the bed increases, it becomes more difficult to make a connec- 
 tion and the chances of accuracy diminish. In the survey of a pitching plane, 
 one station is located, with respect to the adjacent ones, by multiplying the 
 distance by the cosine of the vertical angle. The greatest angular accuracy 
 for a given distance is where the vertical angle is 0. As the pitch or vertical 
 angle of sight increases the cosine diminishes until, at a vertical sight, distance 
 Xcos. vertical angle = 0. 
 
 In the case of an adit level, or a slope of less than 45, there is no difficulty 
 beyond the want of absolute rigidity in setting up the transit, and the danger 
 of moving it in going about it. The difficulty increases more rapidly than does 
 the pitch, and as the distance X cos. vertical angle diminishes, though the dis- 
 tance is fixed, the chances of error increase. When the slope reaches 60, there 
 is an impracticability in running a line down a slope, as the line of collimation 
 of the telescope strikes the graduated limb of the instrument. A person can 
 use a prismatic eyepiece and see up the slope; but cannot look down. As it 
 is assumed that it is unnecessary to use an additional telescope, the line must 
 be run by intermediates. To do this, the transit should be set up at the bot- 
 tom of the slope where the longest sight up the same can be secured and a back- 
 sight taken on a station of the underground work; or a backsight should be set 
 for the occasion (both stations will afterwards be connected with the work 
 below). With the prismatic eyepiece, a sight should be taken up the slope on 
 a line that will give the longest sight and, at the same time, afford a good 
 intermediate place to set up the transit, as, on a pitch of 60 or more, it is 
 absolutely necessary that the legs of the transit should be set solidly (in holes 
 in the floor, or between the sills of the track) so that they will not be moved by 
 subsequent walking about it. By this method, all the sights will be taken from 
 one side alone, and the tripod legs can be shortened to make the sight possible 
 without building a standing place if the man is short. 
 
 Call this station A ; at the foot of the slope locate B, where the transit can 
 be readily set up, and as far up the slope as possible (this distance must be 
 at least 100 ft.), and in a continuation of A B, locate C. Set up at B and take 
 foresight to C; locate D under the same conditions that governed the placing 
 of B, and, in a continuation of the line BD, place E. Set up at D with fore- 
 sight at E, and locate F and G as before. The survey is carried by the inter- 
 mediates B, D, F, etc., to the top, by a series of foresights to C, E, G, etc. 
 
 The term shaft in American coal-mining practice is applied only to ver- 
 tical openings, though in metal mining, both in the United States and abroad, 
 it is also applied to highly inclined slopes. For such shafts, most of the methods 
 given in the textbooks are worthless, as they are for transit work and the dis- 
 tance Xcos. vertical angle in rare cases may be as great as 20 ft., while the 
 distance varies from 100 to 1,500 ft. Again, to sight down a shaft neces- 
 sitates the erection of a temporary (and therefore more or less unsteady) sup- 
 port for the tripod of the transit, and the chances of variation in its position 
 as the different sights are made are so great that it is difficult to say when a 
 movement has not taken place that will vitiate the work. 
 
 In sighting up a shaft of greater depth than 100 ft., there is annoyance if 
 not danger from dripping water or the fall of more solid substances. _ In a 
 wet shaft the object glass is instantly covered with water, and a sight is impos- 
 sible. Also, it is necessary to stand upon a platform, and it is hard to tell when 
 this is perfectly rigid. From all these considerations the methods with a transit 
 are never used by engineers in the anthracite regions, and the connections are 
 made as follows: 
 
 When the bottom of the shaft can be reached by an adit or a slope in a 
 roundabout route of such length as to render errors in measurement of dis- 
 tance of great importance, the angles are carried by a transit with as long 
 sights as possible, and no distances are measured, from a point on the surface 
 in the shaft to a point vertically below it in the mine. Sometimes the guide 
 of the cage is taken when it has been recently set, as the guides are plumbed 
 into position; but the better way is to suspend an iron plummet by a copper 
 wire: sink the former in a barrel of water or bucket of oil so as to lessen the 
 tendency to swing on account of the pull upon the bob and wires from the 
 air-currents, or falling drops in a wet shaft. The top of the barrel should be 
 
78 SURVEYING 
 
 covered with two pieces of plank with a semicircular groove of 3 in. radius cut 
 out of the middle for the passage of the wire, to catch the substances whose fall 
 upon the water would cause waves. The heavier the plummet and the lighter 
 the wire, the less the tendency to swing. This wire can be sighted at by 
 parties above and below at the same time, and the swing can be bisected 
 to get the position of the wire. A number of sights that agree can be taken 
 as accurate. 
 
 When the shaft is the only way to get below from above, it must be plumbed 
 with two or more wires suspended as just described. When two wires are used, 
 the wires should be so hung that an instrument can be set up below in a line 
 passing through them produced, and at a sufficient distance from them to 
 insure an accurate sight. When more than two wires are used, the under- 
 ground station can be located at any point at which all the wires can be seen 
 from the instrument. 
 
 Case 1. Two wires are used, which are located as far apart as possible. 
 Two pieces of scantling cd and ef, Fig. 1, are spiked across the opposite cor- 
 ners of two compartments of a shaft to allow the cages to pass up and down 
 without interference. The station X is (roughly) located in a line through 
 the corners x, and is connected with the outside survey. From this station 
 locate in the line Xxx two spads for holding the wires of the plumb-bobs. 
 These are driven up to the head in the scantlings in such a way that the line 
 of sight passes through the center of the holes in their heads. When the 
 distances Xa and ab are measured, the work of the survey above ground is com- 
 pleted. The light copper wire is rolled 
 upon a reel, and one end is fastened to a 
 light plumb-bob to keep it free from 
 coils or kinks in descending. It can 
 thus be readily lowered without acci- 
 dent. When at the bottom, the upper 
 end is fastened in the spad and the 
 Jieavy bob applied to the bottom and 
 
 FIG. 1 placed in the empty barrel. The cages 
 
 are then run slowly up and down, 
 with an observer on each, to see that the wires hang free from top to bot- 
 tom. By this time the wire will have stretched so that it will be straight, 
 all slack is taken up, the barrel filled with water, and the top boards put in 
 place. As a last check, the distance between the wires below is measured, to 
 see if it agrees with the distance above. 
 
 Lining in below a point Y on the line ab, make a hole in the roof 2 in. in 
 diameter, and drive in a broad plug. Setting up the transit under Y, sight" 
 at the wires a and b alternately. A number of methods for illuminating the 
 wires have been used. But the most satisfactory method is to place a large 
 white target behind both wires and illuminate them by a large lamp with a 
 reflector behind it. The wire stands out black against the target, and can be 
 followed across it. As there is considerable distance between the wires, and 
 as the transit is comparatively near them, there is little chance of getting a 
 sight of one, when the telescope is focused upon the other, and so the focus 
 has to be set between them. This gives a hazy sight at each; but both are 
 shown against the white background in strong relief. After the transit head 
 is shifted so that the line of sight coincides approximately with both, they should 
 be focused upon alternately so as to see if the line bisects the swing of 
 each. If so, the work is done; if not, the shifting of the transit head must fol- 
 low until the end is attained. It frequently requires 2 hr. or more of steady 
 observation to complete the work, and, when it seems as if the proper point 
 were secured, one of the wires will show by its swaying that it has been deflected 
 from the vertical by a peculiar slant of wind, and the result obtained must be 
 checked again. When through, there is no absolute certainty that the point 
 marked is in the accurate extension of the line ab at the surface. Having de- 
 cided on the proper place, a spad must be driven into the plug overhead and 
 a plumb-bob hung to it to see if it is over the axis of the transit, as shown by 
 the screw on the telescope. If not, the spad must be driyen so that the point 
 of the bob does so hang, and the station Y is said to be in the line ab. The 
 distance Ya and the angles to any station of the underground survey must then 
 be measured and when the line ab is connected with the surveys at daylight 
 and below, the plumb-bobs may be removed. 
 
 The disadvantages of this method are that there is no absolute certainty 
 that the point Y is in the line ab prolonged, and this want of certainty should 
 not exist in so important a measurement. 
 
SURVEYING 
 
 79 
 
 
 The work must be performed by daylight, and the length of time neces- 
 sary to complete it makes it impossible to work the shaft for at least 5 da., 
 and may cause annoyance to the operators, or, if you are working for a lessee, 
 lead them to refuse to let you have the use of the shaft at the time most suit- 
 able for your purpose. 
 
 Underground it may be hard to obtain a long sight on any line running 
 through the larger axis of the shaft. Any shorter line will give too short a 
 base line and will increase the chances of error. 
 
 Case 2. Fig. 2 shows the top set of timbers in a shaft of two hoisting com- 
 partments, down which it is desired to carry a known course or meridian on the 
 surface to the entry below. It is necessary first, to find out which side of the 
 shaft is best adapted for setting up the transit, as the point to be marked in 
 the mines will be vertically under the point on the surface; consequently, 
 the side with the widest opening leading from the foot of the shaft should be 
 selected. 
 
 Having carried the meridian to a convenient point near the top of the 
 shaft, and having found that the south side of the shaft is the most accessi- 
 ble, determine, with an ordinary string, the location of the point A, from 
 which the hangers for the plumb-lines will be exactly located, by means of 
 the transit. Now mark with chalk on 
 the timbers where the strings cross. 
 These marks, though not accurate, 
 serve as guides in setting the hangers. 
 Make a permanent station at the point 
 A and carry the meridian to it. 
 
 The hangers can be made of strap 
 iron, 5 in. thick by 2 in. wide, and at 
 least 16 in. long. In one end of the 
 iron, have a jaw with a fine cut at the 
 apex, or a drill hole just large enough 
 to contain the wire to be used for 
 plumbing. There should be two or 
 three countersunk holes in the hanger, 
 through which to fasten it to the tim- 
 bers by means of heavy wire nails. A 
 top view of the hanger is shown in 
 Fig. 2. In most shafts there is a space 
 from 2 to 4 in. wide between the ends 
 of the cage and the sides of the tim- 
 bers. In order to hoist and lower the 
 cage to see that the wires are hanging freely, it is best to set the hangers in 
 such a position on the timbers that the wires will hang in the middle of the 
 space. The hangers should be permanently fastened over the chalk marks 
 previously made on the north side of the shaft, with the jaws pointing toward 
 A , and on the south side of the shaft the outer end of the hanger may be fastened 
 temporarily. 
 
 Now, set the transit over the station at A, take the backsight, foresight on 
 the wire hole of the hanger C and set the wire hole of the hanger B on the 
 same line. Record this course and foresight on the wire hole of the hanger 
 E, fixing as before the wire hole of the hanger D in the same line. Record 
 this course, and then the meridian to be carried into the workings below is 
 established. Measure carefully and record the distances A to B, A to C, 
 B to C, A to D, AtoE,D to E, B to D, and C to E, in order to establish a point 
 at the bottom of the shaft vertically below A, and check the work in the 
 office. 
 
 The transit party can now descend to the bottom of the shaft, taking with 
 it four buckets of oil, the weights or plumb-bobs to be attached to the wire, 
 and all the surveying instruments, leaving a responsible person on the surface 
 to handle the wires. Having arrived at the bottom of the shaft, the transit- 
 man should have the cage hoisted 3 ft. above the landing, throw several planks 
 across the timbers on which to set the buckets of oil, signal to the man on top 
 to lower a wire and fasten it securely, passing it through the wire hole of the 
 hanger, attach the plumb-bob and adjust the wire to such length that, when 
 sustaining the full weight of the plumb-bob, the latter will' not touch the bot- 
 tom of the bucket. He should then place the weight in the oil, using care 
 not to let the full weight come upon the wire with a jerk, but should let the 
 weight down slowly, so that the wire will receive the full strain gradually. 
 The three remaining wires should be set in a similar way. 
 
 FIG. 2 
 
80 
 
 SURVEYING 
 
 After the wires have been hanging a few minutes with the weights attached, 
 the latter may move from one side to the other of the buckets. They should 
 be watched carefully and the buckets moved until all the weights hang per- 
 fectly free, then everything should be let alone until the wires become steady. 
 The cages can now be hoisted and lowered for the purpose of examining the 
 wires to see that they hang free and plumb, care being taken that the cages 
 are not brought so close to the landings as to disturb the hangers at the top, 
 or the buckets at the bottom. 
 
 To find a point vertically below A, a string may be stretched along the 
 wires B and C, care being taken not to touch them; another may be stretched 
 along the wires D and ; then, with a plumb-line, a point on the bottom ver- 
 tically below the intersection of the strings may be determined. The dis- 
 tances AB, AD, BD, and CE should then be measured and compared with the 
 corresponding distances at the top of the shaft. If these distances compare 
 favorably, the wires are, in all probability, steady, and the work of determin- 
 ing the desired course with the transit may be begun. 
 
 Set the transit up over the point of intersection just found; backsight on 
 the wires B and C; foresight on the wires D and E, and compare the included 
 angle and the distances with the corresponding angle and distances at the 
 surface. If these do not correspond, move the transit in the direction 
 necessary to increase or decrease the angle 
 or distances, as the case may be. Repeat 
 this operation until the exact point vertically 
 below A is determined. 
 
 A simple device that is of great advantage 
 _jj is to have three links from an ordinary 
 trace chain placed in the wires on the side 
 toward the transit, and a few feet above 
 the buckets. This not only enables the 
 wires to turn freely, but also enables the 
 transitman to sight through one of the links 
 
 I to the wire beyond, whereby he can place 
 
 Q the transit in exact line with the wires more 
 
 A easily than if the links were not there, 
 
 /h Case 3. Two, three, or four wires 
 
 ;|\\ may be used, being secured and hung as 
 
 / l\\ ^B before. They are located in the angles of the 
 
 / l\\ I compartments x. Pig. 3. These are con- 
 
 / \ \ IBM nected with four stations A, B, C, and D, 
 
 ve \u x \ I the lines AB and CD being at right angles to 
 
 \ Ml A| each other for convenience in the subse- 
 
 \ ||/ / quent calculation, and are connected with 
 
 \ I / I the outside survey. From A and B, taking 
 
 \ i / AB as a base line, the points x are located. 
 
 W/ The same is repeated from C and D, taking 
 
 CD as a base line. Thus are obtained four 
 locations of each wire; these are tabulated, 
 and any variations in a reading must be 
 followed by a repetition of the same. The 
 mean of the readings gives the location. 
 (Subsequently, the subject of calculating 
 work will be taken up.) It can be briefly 
 stated that the bearings of each wire to each 
 of the others, as referred to the base line 
 of the survey, are then calculated and the 
 distance between the wires accurately meas- 
 ured. This finishes the work at daylight. 
 
 There may be two general types of ar- 
 rangements of the bottom of the shaft, and 
 both arrangements have been sketched and 
 lettered similarly. The first is a case when 
 the shaft is arranged across the dip of the 
 bed, and the second is parallel to the same. 
 In both cases and 7 are taken as far apart as 
 possible, and all the wires x are located from 
 each station with reference to the other. The 
 distances between the wires above and below are also accurately measured 
 as a check. There will be four locations of and 7 from the four wires, 
 
 FIG. 3 
 
SURVEYING 
 
 81 
 
 and the mean of these is taken as the correct one. In every case of 
 angle measurement, a series of readings of each angle is taken on different 
 parts of the graduated limb, to avoid instrumental errors, and the 
 mean of these is taken as the true reading. From the locations of and 7, 
 the course between them, as referred to the mean base line, is calculated, and 
 07 is the base line for the underground work. The angle readings above and 
 below can be made at the same time with different instruments, and, in taking 
 the readings below, it is not necessary to wait for absolute quiet in the wires, 
 as that is seldom found. A small swing can be bisected by the cross-hair, 
 and the readings are duplicated until a constant result is secured. By this 
 method a greater accuracy and speed is obtained, and the angles below can be 
 accurately measured, no matter how the shaft may be arranged. 
 
 The T-Square Method. 'The T-square method of taking the line under- 
 ground is especially valuable in shafts with several small compartments or 
 in cramped places where one cannot line in 
 with the wires. The wires are placed in sep- 
 arate compartments and as far apart as pos- 
 sible. The apparatus is made by the car- 
 penter, and consists of a straightedge and 
 T squares. The former is merely a planed 
 pine board about 8 in. X I in. and 1 ft. longer 
 than the distance between the wires. It rests 
 approximately horizontally on slats tacked 
 across the shaft for supports. It is brought 
 to about \ or fg in. from each wire and 
 then nailed to the slats sufficiently to pre- 
 vent slipping. One man should be at each 
 wire. The I squares are most serviceable if 
 made with a movable head clamped by a 
 thumbscrew, and of planed pine, about 2 5 in. 
 XI in. Except in cramped quarters, the 
 T squares will be set at right angles, and 
 should be placed together in clamping, to 
 insure that each set is at precisely the same angle. 
 
 Fig. 4 shows a cramped position, similar to what sometimes arises, in which 
 the movable head gives more latitude in working. After clamping, the 
 T squares are slid along the straightedge until close to the wire, but not touch- 
 ing it, and are there clamped by a G clamp, both men working at one T square. 
 The ends of the T squares C and D must be supported on blocks so that the 
 T squares lie approximately in the same horizontal plane. Everything up 
 to the next step need be only approximately and quickly placed, but the great- 
 est care must be exercised in measuring out equal distances AC and BD from 
 the wires. If the wire vibrates, the middle of its swing must be determined 
 by a pencil or pin. When holding a foot-mark (not the end of the tape) oppo- 
 site the wire on the T square, an even number of feet should be measured, the 
 point marked with a sharp pencil, and a pin inserted. When this has been 
 done for both wires the parallelogram ABDC is obtained, in which the only 
 essential is that CD shall be exactly parallel to AB, the line of the wires. The 
 transit should now be set over the most convenient of the two points, as D. 
 To get the azimuth of DC, and, consequently, the line of the wires, sight must 
 
 be taken on a known 
 
 FIG. 4 
 
 A 
 
 d 
 
 I 
 1 
 1 
 
 I /] 
 ayw !/ ! 
 
 point E for a backsight, 
 and the angle EDC 
 measured. Another 
 point F must be estab- 
 lished on the line of the 
 
 
 
 L j L ?*. 
 
 '"~~:Y~~7/~] r~~ 
 
 backsight, in order that 
 its course may be pre- 
 
 
 
 
 served after the instru- 
 
 
 
 ---1 r~~ 
 i i 
 
 ment and T square are 
 removed. 
 
 . 
 
 FIG. 5 By this means the 
 
 closing angle at E may be read after the wires are removed from the shaft. Un- 
 derground, the method is the same, except that DC is the known course, and 
 is used as the backsight. To give the coordinates of the instrument at D with 
 the greatest precision, the angle ADC and the distance AD should be measured. 
 Check Methods. The results obtained by the use of the methods just 
 described should be checked as soon as an underground connection between 
 
82 SURVEYING 
 
 the hoisting shaft and air-shaft has been driven. Single wires are hung, one 
 in each shaft, and the distance between them on the surface is measured. The 
 latitude and departure of both A and B, Fig. 5, are known as they are tied 
 in to the outside survey. In the mine, the stations a and b are occupied by the 
 transit and the angles Aab and abB repeatedly measured. The underground 
 distances Aa, ab. and bB are carefully measured. With these data, it is easily 
 possible to calculate the latitude and departure of the mine stations a and b, 
 and consequently the azimuth of the line ab, which serves as a base for all future 
 extensions of the mine suryey. It should be noted that Fig. 5 shows the sim- 
 plest arrangement of the sights that is possible, but two; ordinarily there will 
 be anywhere from four to ten or more stations required to carry the line from 
 one shaft to another. As the surface and mine temperatures may be very dif- 
 ferent, particularly during the winter and summer months, a correction should 
 be made for the expansion or contraction of the tape. 
 
 SURVEYING SLOPES OR INCLINED SHAFTS 
 
 Where a single sight reaches from top to bottom of the slope, the problem 
 is simple enough. A station can be established on the inside of the foot-wall 
 plate at the collar and others in similar positions at each level. The instru- 
 ment set up over any station can command the whole 
 slope and the level opposite. 
 
 Where the slope is sunk on several dips, the survey 
 is a much more difficult matter. Fig. 1 illustrates 
 cases of common occurrence. The slope may be 
 divided into sections like A DEB, which are convex 
 downwards, and others such as EBC, which are con- 
 cave downwards. As a rule a set-up can be avoided 
 at the convex knuckles if desired, and need only be 
 made at those that are concave. 
 
 Bent Plumb-Line Method. Point A may be invisi- 
 ble from point B, but the survey may be carried from 
 FIG 1 ~ one P9 int to the other by the bent plumb-line method. 
 
 In this case, establish a station at A, the foot-wall 
 side of the collar, the center point being a small nail head projecting hori- 
 zontally. Attach a long plumb-line to this and carry the other end to B. 
 Here it will probably be necessary to use a small screw-eye, with its head turned 
 into the vertical plane of the slope for the center point. Pass the plumb-line 
 through this and draw it fairly tight. Now attach a plumb-bob at an inter- 
 mediate point and regulate the tautness so that the line is clear at all points. 
 The curves in the slope may be such that two plumb-bobs may have to be 
 hung, as at D and E, and even a third may become necessary. 
 
 As the plumb-line, perhaps 100 ft. long, is apt to be disturbed by the air- 
 currents, it is often better to mark a point on a convenient timber near D, 
 and another near E, so close to the string that there is no doubt of the points 
 lying in exactly the same vertical plane as the plumb-line. If these points 
 are once established, the string and weights can be taken out of the slope, 
 leaving four points in the same vertical plane, and whose horizontal projections 
 lie in the same course. 
 
 Now set up the transit at A and measure the azimuth angle from the back- 
 sight to D, thereby giving the bearing from A to B. If D should be invisible 
 from B, depress the telescope after sighting on D and locate the point N in 
 the same vertical plane, and so situated that it is visible from both A and B. 
 Measure the vertical angle and distance to N. Now set up the transit at B, 
 use the course BE for a backsight, and foresight to C. Measure the vertical 
 angle and distance BN. The line BN might have been used as a backsight, 
 and E serve as an additional check. The point N is really an intermediate 
 station, but as it lies in the course AB, a set-up there is unnecessary. In 
 simple cases, the bent plumb-line method is a very convenient one for carrying 
 a survey from the surface to the first level, and a longer horizontal projection 
 of the sight AD can be secured than if a set-up were made in the shaft at D; 
 but in complicated cases, such as the one shown, it may often be quicker to 
 make the extra set-up than to use the plumb-line. In all sights for determin- 
 ing azimuth, the vertical angles must be kept as low as possible, and the hori- 
 zontal projection of the course long. 
 
 Method by a Single Wire in the Slope. When surveying a slope by using a 
 single wire, stretch a rather fine wire, free from^kinks, down the slope, as shown 
 in Fig. 2, being careful that it touches nowhere in the slope. Take two plumb- 
 bobs provided with fine round strings and suspend one from A and the other 
 
SURVEYING 83 
 
 from B so that they nearly touch the same side ,of the wire MN. In order to 
 have the plumb-lines as far apart as possible, the line at B must be quite long 
 and a can of water provided to keep the bob from swinging. The plumb-line 
 is fastened to a nail B nearly in the proper position. A bar of wood, with a 
 block fastened to it, should be placed to one side and a little 
 below B. The block must have a hole through which a small 
 screw bolt can easily screw. On this bolt is placed a spool in 
 which a groove is turned and which is sandpapered and greased 
 so that the string will slip easily as the bolt is turned. Now, 
 place the transit in line with the two plumb-bobs, as in an ordi- 
 nary case of shaft plumbing. Repeat this operation below. 
 The plumb-bobs in both cases hang in the same vertical plane 
 and thus the true bearings are found underground. Even the 
 plumb-lines may be dispensed with, but the method will not 
 then be so accurate. The instrument will be set nearly in the 
 vertical plane passing through the wire, leveled and sighted at M. 
 The telescope should be dipped until the lowest point on the 
 wire is visible and the amount by which the cross-hair and wire FIG. 2 
 fail to coincide noted and the instrument shifted accordingly. 
 But if this method is tried, the two points sighted at will not be nearly so 
 far apart horizontally as the plumb-lines, and any error in leveling will also 
 vitiate the result. This method of the single wire, however, provides no way 
 of obtaining the coordinates. 
 
 UNDERGROUND, OR MINE, SURVEYING 
 
 INTRODUCTION 
 
 The same instruments and the same methods of measuring and recording 
 angles and distances are used on the surface and in the mine. The chief dif- 
 ference between surface and underground work is one of detail 9nly. In the 
 mine, lamps are needed to give light, sights are taken to a string or to the 
 point of a plumb-bob, and stations are placed in the roof and not in the ground. 
 The main-line notes are kept in the same way above and below ground, but 
 the method of taking and recording side notes is materially different. 
 
 Mine surveying in flat coal seams differs in minor details from that used in 
 pitching seams, and this difference in detail has been greatly exaggerated until 
 it has become a prevailing belief that anthracite (pitching) and bituminous 
 (flat, usually) mine surveying methods are absolutely distinct. There is, in 
 all underground work, a difference in the organization of the corps and con- 
 sequently in some minor details in carrying on the work, depending on whether 
 the survey of an entire and extensive mine is to be undertaken or whether, 
 as is commonly the case, the survey is made merely to connect recent develop- 
 ments with those previously surveyed. 
 
 FLAT WORK 
 
 Because it is necessary for the gangways, or entries, in pitching work to 
 follow the foldings and twistings of the seam, the physical difficulties in the 
 way of the surveyor are greater in that kind of work than in flat seams. In 
 pitching seams, short sights and many of them are the rule; in flat work, long 
 sights and few are general. In fact, in flat seams the headings or entries are 
 commonly driven on points; that is, they are driven upon some predetermined 
 course for long distances, even 2 or 3 mi. in the case of large properties. At 
 regular intervals, pairs of cross-, or butt, entries are driven at right angles to 
 the main entries; from these, in turn, the rooms are driven. Hence, the sur- 
 veyor in the average bituminous mine (bituminous mines are commonly flat) 
 is chiefly concerned with prolonging straight lines for several thousand feet 
 in the case of butt entries, and up to 2, 3, or 4 mi. and more in the case ot 
 long main entries. The angles measured are chiefly right angles at the points 
 where a butt entry intersects the main entry, or at the mouths of rooms 
 driven from a butt entry. 
 
 The bituminous-mine surveyor is very rarely called on to make a com- 
 plete survey of underground workings. He usjually moves up the points (sights) 
 at more or less regular intervals of time or of distance driven, measures the 
 distance from the old set of points to the new, takes the necessary side notes, 
 and at once plots them; the mine map, so far as the main headings and cross- 
 entries are concerned, is thus up to date within a month or so at the most. 
 
84 SURVEYING 
 
 In fact, whether the sights are moved up with regularity or not, the mine fore- 
 man is always able to determine the position of the working face by measur- 
 ing back from it to the last survey station appearing on the tracing or blue- 
 print furnished him, and adding this distance thereto, laying it off in the direc- 
 tion the heading is being driven. 
 
 Stations. An essential part of the equipment of the mine surveyor is a 
 carpenter's brace and from three to six bits, or drills, which can be made from 
 files thrown away by the miner. With these, a hole from f to 1 in. in diameter 
 and from 1 to 1? in. deep may be drilled in the roof where a station is neces- 
 sary. From ten to fifty plugs should also be carried by the corps. These 
 plugs are pieces of poplar or other softwood about *| to f in. longer than the 
 drill hole. They are square in section, the side being a little longer than the 
 diameter of the hole in which they are to be used; the lower end may.be roughly 
 rounded. After the hole is drilled, one of these plugs is fitted in and driven 
 home by blows from the hatchet until from to f in. projects below the roof. 
 A spad, spud, or as sometimes called a nail, is then driven into the plug. The 
 spads or nails are made from mule-shoe nails, through the flattened heads of 
 which |-in. holes have been drilled or punched. These spads may also be pur- 
 chased from dealers in surveyors' supplies, but are commonly made by the 
 'blacksmith's helper at odd times. 
 
 Sometimes stations are made by driving a tack or nail in a tie, which has 
 been notched or flattened with a hatchet to receive it, or by driving a spad in 
 the collar or cap-piece of a set of timbers. Neither of these methods is to be 
 recommended, as the position of a tie, and with it that of the station tack, 
 is practically sure to be changed in a few months from the pounding it receives 
 from passing cars, mules, and men, or from alining the track. Stations in 
 collars are less liable to be shifted than those in the track, but as the pressure 
 due to mining operations comes upon the timbers they, too, are apt to be shifted 
 out of line. Sometimes stations that must be set at an exact distance from a 
 previous station (as when a butt entry is to be started, say, 225.25 ft. from the 
 main entry station) are of necessity made in a tie if the roof at the exact spot 
 is not in condition to hold a plug (or has been shot down for an overcast) . In 
 such a case the station is placed in the tie and as soon as the butt entry or other 
 place has advanced sufficiently to have sight plugs set in, these are placed, 
 and the use of the tack abandoned. 
 
 In longwall work, much difficulty is experienced at times through the sta- 
 tions being shifted out of line through the settling of the overlying rocks. This 
 settling may extend over a period of years or may stop after a few months. 
 While the setth'ng is in progress, the timbers must frequently be renewed, so 
 that they and the constantly disturbed roof and floor afford a poor place for 
 permanent stations. Hence, during the period of settlement at least, stations 
 m longwall mines must be placed in the floor. For the foregoing reasons, 
 combined with heavings of the floor as the weight comes unevenly upon the 
 pillars, these stations are almost certain to be disturbed, and should not be 
 used to extend a previous survey until one or more older stations have been 
 reoccupied by the transit and the angles and distances remeasured to be abso- 
 lutely certain that no such disturbance has taken place. If displacement has 
 occurred, it will be necessary to go back along the line until three stations 
 have been found in their original position. From these a new set of lines 
 must be run, using the old stations if solid enough, remeasuring the angles and 
 distances, but not necessarily retaking the side notes. 
 
 Stations are commonly marked by enclosing them in a circle, square, or 
 triangle, or by a + mark of white paint. > White lead, or Dutch white, thinned 
 with linseed oil is ordinarily used, and is applied with an ordinary sash tool. 
 If the paint has to be kept a number of days, it should be covered with water, 
 which should be poured off before the paint is used. 
 
 In addition to marking the station itself so that it may readily be found, 
 some system of lettering or numbering must be devised so that the stations 
 may be distinguished one from the other. Stations on the main entry fre- 
 quently have the letter M prefixed and are numbered in regular order from the 
 drift mouth, thus, M-l, M-2, etc. Or the stations on the main entry may use 
 the letter A, those on its air-course the letter B, those on the manway the let- 
 ter C, and similarly for other parallel entries. As butt entries are usually 
 known by a number corresponding to the order in which they were turned off 
 from the main entry, the stations on such entries, while numbered consecu- 
 tively, have prefixed to them the letter R or L to indicate whether the entry 
 is turned to the right or the left of the main entry, as well as the serial num- 
 ber proper to the entry. Thus, Ll-12 or 1L-12 indicates the twelfth station 
 
SURVEYING 85 
 
 on the first left-hand cross-entry, or, as commonly said, on the first left. Sim- 
 ilarly R5-6, R-56, or 5R-6, is the sixth station on the fifth cross-entry to the 
 right. If entries are driven from one side only of the main entry, the pre- 
 fixed letters R and L may be omitted. In this case, the foregoing stations 
 will be numbered 1-12 and 5-6, respectively. Air-courses are not usually 
 run on sights. If they are, the stations in them may be numbered in the same 
 way as those on the heading proper with a letter, such as A, to denote the fact 
 that they are on the air-course. Stations coming between regular stations on 
 an entry commonly receive the number of the preceding station with some 
 letter added. Thus 56 D is a station on the fifth cross-entry at a point 
 between regular stations 6 and 7. 
 
 Some corps number the stations in a heading as are stakes in a railroad 
 survey. The station at the mouth of the heading on the main entry is called 0, 
 and the first station in the heading will be, say, 2+56.29, the second 4+81.96, 
 etc. This means that these stations are 256.29 and 481.96 ft., respectively, 
 from the mouth of the entry. The distance between the stations is of course 
 481.96 - 256.29 = 225.67 ft. While this system of numbering shows at a glance 
 the exact distance an entry has been driven, such large numbers may be a 
 source of trouble and of possible error when used to describe the backsight, 
 instrument, and foresight stations as entered in the field notes. 
 
 Rarely are stations numbered in the order in which they chance to be 
 placed. It may happen that station 56 will be on the main entry, 57 on the 
 fifth right, and 58 on the tenth left and follow, say, stations numbered 36, 48, 
 and 51. This system, or want of system, is not commended, as it leads to 
 confusion. 
 
 While the numbers of stations are frequently painted on the roof along- 
 side the station mark, it is better practice to paint them on the rib a short 
 distance before the station is reached. In this way the foresight man can 
 see them without having to walk in a stooping posture. 
 
 Sighting. Sights in underground work are commonly taken either to the 
 point of a plumb-bob suspended by a cord passed through the hole in the head 
 of the spad marking the station, or to the cord itself. In the first case, a lamp 
 is held a short distance back of the point of the bob to render it visible against 
 a background of flame. In the latter case, the cord is best illuminated by 
 placing a white paper or cardboard behind it and holding the lamp in front 
 and to one side. The string shows as a dark line against a white ground, but 
 care must be taken not to confuse the string with the shadow it casts upon the 
 paper. 
 
 What are known as plumb-lamps, or plummet lamps, are a great convenience. 
 These are very heavy plumb-bobs, suspended in gimbals to ensure verticality, 
 which are hollowed to form an oil chamber, and are provided with a wick. 
 The bisection of the lamp flame, if the wick is turned low, affords a sufficiently 
 accurate setting of the transit when placing room sights, surveying rooms, and 
 even in moving up sights in a butt entry, provided the backsight is not too 
 close to the instrument and the flame is not greatly disturbed by the ventilat- 
 ing current. It is obvious that the use of the plummet lamp, which will burn 
 for several hours and is always ready for backsighting on, saves the labor of 
 one man. In accurate sighting, the point or the cord of the plumb-lamp may 
 be used as just explained. Where the velocity of the air is great enough to 
 cause the plumb-bob to oscillate, long narrow bobs must be used, and these 
 must be shielded from the direct current by the backsight man. In drafty 
 places, a hole may be dug out_ in the ballast between the ties and the bob let 
 into this shelter, the sight being taken to the string. Cords for suspending 
 plumb-bobs should be braided to avoid twisting under the weight of the bob, 
 should be well-oiled, and should be hung with a slip knot so that the point 
 may be raised or lowered. 
 
 Various means are employed to illuminate the cross-hairs in the telescope. 
 Commonly this is done by holding a lamp a little beyond, above, and to one 
 side of the object glass. Sometimes a reflector is provided. This con- 
 sists of a piece of silvered metal, inclined at an angle of about 30, that is 
 soldered on one edge to a metal ring that fits around the object end of the 
 telescope. The reflector has an oval hole through it t9 permit the passage 
 of the line of sight. The reflection of the light carried in the surveyor's 
 cap sufficiently illuminates the hairs to permit their being centered upon 
 an object. In some rare cases, transits have the horizontal axis pierced (the 
 opening being closed by a piece of glass), through which hole a lamp held 
 at the end of the telescope axis will throw enough light to render the 
 cross-hairs visible. 
 
86 SURVEYING 
 
 Centers. If stations are made in the ties, the transit may be set up over 
 them exactly as in outside work. However, stations are commonly made in 
 the roof. The transit may be set under a station if a center mark is punched 
 in the collar surrounding the telescope and to which the transverse axis is 
 attached. When the telescope is level, this mark is immediately above the 
 point of a plumb-bob suspended from beneath the instrument. By slightly 
 loosening the leveling screws, the plate may be shifted until the center of the 
 instrument is exactly below the P9int of a bob suspended from the station spad. 
 However, care must be taken in tightening the leveling screws, that the instru- 
 ment is not thrown out of line. Commonly, the station in the roof is trans- 
 ferred to what is called a center placed on the floor, and over this center the 
 instrument is set in the ordinary way. 
 
 The center may be made from a large square or hexagonal nut some 2 in. 
 across. A wire nail or spad is set in the center of the hole in the nut, which 
 is filled with melted lead or Babbitt metal. The point of the nail is cut off 
 about $ in. above the top of the nut and sharpened with a file. Or a very 
 satisfactory center may be made by boring a hole 11 in. in diameter and 1 in. 
 deep in a thick plank, setting a brad in the center with its head down, and 
 filling in with melted lead, at the same time holding the brad in a vertical posi- 
 tion with its end projecting slightly above the top of the plank. After cooling, 
 the brad may be sharpened as before. 
 
 A plumb-bob is hung from the station and the string adjusted until the 
 point of the bob just clears the point of the center. By sighting across the 
 two points at an angle of 90, the point in the center may be shifted into coin- 
 cidence with the point of the bob. If the center has been lost or forgotten, 
 a plank may be laid across the rails under the station and the position of the 
 point of the plumb-bob marked upon it with a pencil. After removing the 
 plumb-bob and its cord, the transit may be set over the center or pencil mark 
 in the usual way. 
 
 Placing Stations on Line. Two cases of placing stations on line may arise: 
 (1) The station may be on the prolongation of the heading line and at any 
 indefinite distance from the instrument. (2) The station may (or may not) 
 be on the line of the heading, but is at a fixed, definite distance from the instru- 
 ment. 
 
 The first is the common case when the last station on a straight heading 
 is, say, 200 to 250 ft. back from the face, and a new station must be set ahead 
 and on line so that sight plugs may be placed from it. The transit should be 
 set up at the station nearest the face, a backsight taken on an outer station 
 on the line, and the telescope plunged. Where the roof is solid and from 25 to 
 50 ft. back from the face, the foresight man should hold his lamp against the 
 roof so that its flame may be lined in by the surveyor, a smear with the lamp- 
 wick or an X with a piece of chalk should then be made on the roof when the 
 line is secured.. The point of the drill may be placed on this mark and the 
 lamp held behind it. If not in line, the drill may be shifted to the right or left 
 until it is. The hole should then be started by pressing upwards and turning 
 the brace. As the point of the drill is apt to slip on smooth rock, as soon as 
 the hole has a grip, another sight should be taken to make sure that the drill 
 is still in line. If it is not in line, a new sight should be taken and a new hole 
 started a few inches away. The hole should be drilled to the required depth 
 and the plug driven firmly home. The point of a spad should then be stuck 
 in the plug near its center with the head hanging vertically and the eye facing 
 the transit.. Holding the flame 9f the lamp behind the spad, it must be moved 
 to the right or left until its point is exactly in line. Still holding the lamp 
 behind it, the spad should be driven firmly home, the blows of the hatchet being 
 inclined so that the head of the spad may be driven to the right or the left as 
 the transitman, who is following the work, may direct. When the spad is 
 driven home, the lamp should be held behind its eye and, with gentle taps of 
 the hatchet, it should be knocked to the right or left until the vertical hair 
 exactly bisects the hole. For many purposes, the alinement is now sufficiently 
 accurate. For important work, however, the plumb-bob should be hung from 
 the spad and the final and exact alinement made by sighting to its point or 
 to the cord. The distance between the old and new stations should be measured 
 and if, in addition, the side notes are taken the work may be placed upon the 
 mine map at once. 
 
 The second case arises when a branch or cross-entry is driven from the 
 main entry, either to meet a similar place being driven toward it or to inter- 
 sect another place at a fixed point. The instrument is set up on the main 
 entry at .the point nearest to that from which the branch road is to be driven, 
 
SURVEYING 87 
 
 a backsight is taken upon an outer station, and the telescope plunged. The 
 foresight must now be placed not only on the entry line, but at an exact dis- 
 tance, say, 186.27 ft., from the transit. The tape must be stretched in line, 
 and at the exact distance from the station, a pencil mark 3 or 4 in. long made 
 at right angles to the line of sight. This mark may be made on the face of 
 a tie that has been cleaned off, if one is at the right distance; or on a piece of 
 plank made to span the space between two ties. The point of a tack or a 
 brad should be placed in this line and a lamp held behind it. The tack must 
 then be shifted until it is in line and driven home. If the distance the branch 
 road is to be driven is short and the station at its mouth will not be needed 
 again, the instrument may be set over the tack, and after setting the vernier 
 at or at the back azimuth or bearing of the entry line, the deflection angle, 
 azimuth, or bearing on which the new place is to be driven may be set off on 
 the upper plate and upon this line the sight plugs may be placed. The sur- 
 veyor is recommended to always use the system of reading and recording 
 angles with which he is most familiar, except, of course, when the system is 
 inaccurate. 
 
 If the station must be preserved (which is commonly the case) , the position 
 of the tack just placed in the tie must be transferred to a permanent station 
 in the roof. To do this, leave the transit as it was after setting the tack. 
 Suspend a plumb-bob from the roof, holding the string in such a way between 
 the thumb and forefinger that when the helper says the point is directly over 
 the tack, a smear of chalk (previously applied to the thumb) may easily be 
 made on the roof. Hold the drill on the mark and have it lined^in from the 
 transit. After the bit grips the rock, again line in from the transit and check 
 the distance measurement by again dropping a plumb-line upon the tack. 
 Drill the hole and drive home a plug, which may be of somewhat larger sur- 
 face area than the prdinary station plug. Draw a pencil line across the face 
 of the plug by joining the holes left by the points of two brads set near the 
 inner and outer edges thereof and which have been lined in from the transit. 
 (These brads need not be driven up, as they are used only for giving the ends 
 . of the line.) Next suspend the plumb-bob over the edge of a knife blade (the 
 thumb is too blunt), so that the cord is on the pencil line, and when the helper, 
 by sighting across the point and the tack, announces that they are directly 
 over one another (that is, the distance is exact) make a mark, with a pencil, 
 on the plug. A spad may now be placed in this mark and should be on the 
 entry line and at the proper distance from the instrument. However, before 
 driving it home, check the alinement. After driving home, perfect the aline- 
 ment by sighting to the point of the bob or to its cord. Some prefer, after 
 the plug is driven up, to suspend the plumb-bob from a spad, which is shifted 
 by the transitman to the right or left until in the line of the heading, and by 
 the foresight man's helper inbye and outbye along the heading line until at 
 the exact distance, after which it is slpwly driven up, being checked during the 
 process. By the first method, there is no trouble in placing spads within less 
 than T&T ft. of the exact spot and any desired degree of accuracy may be 
 obtained by taking time. 
 
 Placing Sights. The entries always and the rooms usually, in flat seams, 
 are driven on sights. These sights are a pair of plugs set on the pre- 
 determined line about 2 ft. apart in which are driven spads that are set exactly 
 on line. Pieces of coal, iron nuts, or other weights are hung from the spads 
 and before an undercut is made the foreman, miner, or machine runner sights 
 across the strings and marks the center line on the face with a piece of chalk. 
 Under ordinary conditions, sights should be moved up about every 200 ft. 
 of advance in the working face; although this distance may be increased where 
 the ventilation is good and lessened where it is poor. While a pair of sights 
 may be placed near the face from an instrument _station 200 ft. or more back 
 therefrom, the better practice is to place a station ahead as just explained. 
 The transit is then moved to this station, a backsight taken as before, the 
 telescope plunged and the two sight plugs placed some 10 to 15 ft. ahead of the 
 instrument, the final alinement being effected by bisecting the two eyes._ This 
 makes the survey station independent of the sight plugs and the spad in it is 
 not apt to be pulled out of line, as will be the case if the station is one of the 
 sight plugs. The practical certainty of finding the station in good condition 
 more than repays for the labor of setting the extra plug and making the extra 
 
 While entry sights are commonly and naturally placed in the center of the 
 opening, many consider it better to place them to one side and over, say, the 
 right-hand rail. By so doing, a conscientious track foreman can use them to 
 
88 SURVEYING 
 
 keep his own work in line and, being proud of a fine piece of work, will urge 
 the miners to drive the headings straight. With heavy trains and motors 
 and the high speed required for large outputs, the importance of a straight 
 track is apparent. 
 
 When rooms are driven on sights, usually each room is given a pair of sight 
 plugs, but in some cases only every other room is so provided, the intermediate 
 room being kept in line, as well as possible, by leaving a pillar of constant 
 thickness on each side, which thickness is determined by measuring through 
 the cross-cuts. As the direction of rooms is rarely of prime importance, sights 
 in them are not moved up, unless it is absolutely impossible to see the face 
 from them by reason of smoke, roof falls, etc. Room sights are commonly 
 placed in the necks anywhere from 8 to 20 ft. from the entry line. Surveyors 
 prefer to wait until the necks have been turned for a number of rooms before 
 placing the sights in any of them. The instrument is then set up at any con- 
 venient station and the line of sight made to coincide with that of the entry. 
 A series of tacks is placed in line the proper distance apart (when rooms are 
 turned at 90, distance = width of room + width of pillar) and are driven down 
 into the tie or into a plank laid across the rails, one tack for each room. The 
 instrument is set up over each tack in succession and a right angle to the head- 
 ing line is turned and two sight plugs are placed in the room neck as far from 
 the entry as possible. The distance of each tack from the entry station is 
 noted and the distance from the line of the entry to the outbye room sight plug 
 is also measured and recorded. Room sights may be set by bisecting the eye 
 of the spad and are commonly placed 18 in. to 2 ft. from the rib. Where rooms 
 are inclined to the entry, the distance between their centers measured along 
 the line of the entry is found from the formula: 
 
 _.. , width of room + thickness of pillar 
 
 Distance = V^ r = 
 
 sin angle of inclination 
 
 Surveying and Note Keeping. The laws of most states require that the 
 mine workings be surveyed and mapped at least once every 6 mo. If the neces- 
 sary measurements and side notes have been taken at the times the entry 
 sights have been moved up and have been mapped, the mine, so far as the main 
 roads are concerned, is always within a few weeks of being up to date. If 
 this has not been done, the procedure will depend on whether lines of sight 
 are carried up one or both entries of a pair. If each entry has its sights, the 
 end of the tape should be held at the last station appearing on the map and 
 the tape stretched out to the next station. The surveyor may then walk 
 along the tape and, when opposite a break-through, note the distance to both 
 sides of the opening as say +256 to +267 (the opening being 11 ft. wide). 
 The assistant should carry the end of a tape (usually a 50-ft. metallic tape) 
 to the rib at each side of the cross-cut, and the surveyor should measure the 
 distance to the nearest J-ft. mark to these points from the entry line and note 
 whether the break-through has been driven to the right or left from the entry. 
 Room necks may be located in the same way. 
 
 It is advisable, where the entry is crooked, to note the places where the tape 
 comes nearest and farthest from the rib. Many surveyors do not take offsets 
 to the corners of the pillars made by the various openings, merely noting the 
 plusses, or distance measured along the tape opposite which these openings 
 come. When so mapped, the entries appear perfectly straight, which makes an 
 attractive but inaccurate map. When the exact distance between stations 
 as well as the necessary vertical angles have been taken at the time the stations 
 were moved up, the use of a transit is unnecessary when making the entry sur- 
 veys, but it is highly advisable to remeasure these distances as a valuable, 
 in fact as the only possible, check on the original distance measurements until 
 a close is made and the survey calculated. 
 
 After taking the notes between the first pair of stations, those between the 
 next pair should be taken, and similarly until the foresight man with the tape 
 reel is at the last station. This may be anywhere from 25 to 200 ft. from the 
 face. To get the entry line, the foresight man, carrying the reel, should be sent 
 ahead; and when he is at the face, the tape may be brought in line by sighting 
 over the entry sight plugs to a lamp held on the reel. After completing the 
 side notes on one entry, those on the parallel entry or entries are taken. These 
 notes are entered in tabular form as taken, beginning at the bottom of the 
 page and working toward the top. The plusses, or distances from the instru- 
 ment, are in one column and in other columns are the offsets to the corners 
 of the openings, each placed in the horizontal line of the proper plus. 
 
SURVEYING 
 
 89 
 
 Each surveyor will have his own set of abbreviations: Common ones are 
 Bt for break-through (or cc for cross-cut) , Rm for room, r or rb for rib Thus 
 -f-256, 5.5 Btr, means that at 256 ft. from the station and 5.5 from the line 
 is the corner of a break-through, which is driven to the right. Sometimes 
 
 these notes are amplified and illustrated by sketches x 
 
 as shown in Figs. 1 and 2. In most mines, particu- 
 larly in the case of butt entries, only the room 
 entry is driven on points, the air-course being kept 
 as nearly on a parallel line as possible by main- 
 taining a constant thickness of pillar between it 
 and the room entry. In this case, the distance 
 from the tape or the offset is measured not only to 
 the edge of the cross-cut, but also to the correspon- 
 ding edge of it on the air-course and to the far side 
 of the air-course as well. These three measure- 
 ments might be recorded as follows: + 254 
 5-26-37 and +263, 6-26-36. The plusses are at 
 254 and 263 ft. from the station and show that the 
 break through is 9 ft. wide. At the first plus, the 
 distance to the corner of the break-through is 5 ft., 
 the distance to the corresponding corner on the air- 
 course is 26 ft. (the pillar being 26 5 = 21 ft. thick) , 
 and 37 ft. to the rib of the air-course, which is 37 
 26 = 11 ft. wide. At the inner side of the cross- 
 
 in 
 
 ..i. 5 AC- r 
 
 ];;:.. LJ 
 
 16*61 
 5 - 135 -S 
 * 
 
 3 -1106 
 4- -9f -6 
 
 5 -n -r 
 
 
 FIG. 1 
 
 + */ J 
 
 cut the pillar is 26- 6 = 20 ft. thick, and the air-course 36-26=10 ft. wide. 
 The advantage in measuring continuously out from the tape is twofold: The 
 surveyor does not have to leave the entry, and consequently has time to enter 
 his notes in a concise and cleanly way as the foresight man does the running 
 around and, above all, by standing on the entry he is able to keep the small 
 tape with which the side notes are taken, exactly at right angles to the large 
 tape; further, notes thus kept are easier to map, requiring but one setting of 
 the scale, regardless of the number of offsets taken from any plus. 
 
 It is usual to make sketches as the side notes are taken, in order to illustrate 
 and make plain any points that might be obscure to the office man that plots 
 the notes. Two forms of such notes are shown in Figs. 1 and 2; both are of the 
 same entry, the air-course parallel to which is located by measurements through 
 the break-throughs. Such notes are begun at the bottom of a page and 
 sketched upwards in the order in which they are taken. The form shown in 
 Fig. 2 is preferable as being the clearer. It will be noticed that in both cases 
 the air-course is located not by continuous offsets, but 
 by single measurements through the pillar, the disad- 
 vantages of which method have been explained. The 
 ends of pillars are so rarely square that it is commonly 
 difficult to decide at just what point a break-through 
 begins. This is illustrated at a and b, Fig. 2. The 
 proper way to locate such a rounded pillar is to take a 
 plus and offset at the point where the pillar begins to 
 round (+155, a) and a second plus and offset where a 
 sight tangent to the end of the pillar may be had 
 ( + 157, b). The distance between the stations is al- 
 ways noted on the sketch. In the case illustrated, the 
 distance from the last station to the face is shown (8 ft.) 
 beyond the figures for the length of the line. 
 
 The survey of a series of rooms in which sights have 
 been placed is a comparatively simple matter. The 
 sight strings are lowered (the miner generally keeps 
 them hung up against the rib), and the helper goes to 
 the face, unwinding the 400-ft. tape as he goes. The 
 end of the tape is held at the first or outer sight plug, 
 the distance of which from the line of the entry was 
 measured when the sights were placed. The transit- 
 man, by means of the room sights, places the man at 
 the face in line and takes the side notes in the manner 
 explained. If the rooms have not been driven on sights, 
 it is customary to place a tack in a tie at the mouth of each room, the tacks 
 all being on the entry line, but at irregular distances apart as they are placed 
 so that the instrumentman may see the face. After the tacks are lined in, 
 their respective distances from the instrument are measured and recorded. 
 
 
 
 J. 
 
 :n" 
 
 FIG. 2 
 
90 SURVEYING 
 
 The instrument is set over the tack at the first 1-09111, the vernier is set at the 
 azimuth or bearing of the entry, and a backsight is taken upon some station. 
 The foresight man unwinds the tape on his way to the face, where.he holds the 
 reel on an X he has marked on the coal in chalk, and to which the transitman 
 takes a sight. The of the tape being at the instrument, a line is established 
 to the face, and the side notes may be taken as before explained. In many in- 
 stances a line is run up every other room only (thus, up rooms 1, 3, 5, 7, etc.) 
 the intermediate rooms being located with sufficient accuracy by offsets through 
 the cross-cuts. 
 
 It sometimes happens that practically all the rooms on an entry are so 
 blocked with falls of slate that it is impossible to see to the face and thus sur- 
 vey each room separately. In such a case, a line is run from the entry up 
 some room not blocked by falls and a survey made of the faces of the rooms by 
 running a line along them through the break-throughs. If desired, stations 
 may be established in ties in each room near the face, and sights taken down 
 the room until stopped by the falls; or a line may be run down every other room. 
 Usually, offsets from the line along the face will locate the pillars and face line 
 with sufficient accuracy for all practical purposes, particularly if a good por- 
 tion of the rooms have been mapped from surveys made before the fall of roof 
 took place. 
 
 Level Notes. All level notes are kept as in outside work, with the exception 
 that, as the rod is reversed in getting the elevation of a station in the roof, 
 the record of the reading is prefixed with a minus sign. A record of such a 
 reversed rod, when the target is 3.78 ft. below the station, is recorded 3.78. 
 
 A shaft is measured (if deep) by a fine steel wire running about an accu- 
 rately graduated wheel (a sufficient number of turns being laid to prevent 
 slipping) and noting the number of turns before the bottom is reached. The 
 wire may be measured before and after the operation, to insure against stretch- 
 ing. An aneroid mining barometer, if in good condition, will give quite accurate 
 results if a number of trips are made between top and bottom, to give an aver- 
 age. In this case the barometer must be left quiet 10 or 15 min., to be sure 
 that it has expanded or contracted to the proper degree. For rough measure- 
 ments, the length of the winding rope between top and bottom is taken. 
 
 By one of these methods a bench mark should be located below, connected 
 with the outside work, and referred to tide water. The rod must be reversed 
 to get the elevation of all stations in the roof, and all such readings are noted 
 with the minus sign, as 4.32' (read 4.32 ft. below station). Roof stations 
 are almost certain to settle, from the pressure of the superincumbent rocks. 
 To check such settling, the distance from roof to floor must be accurately meas- 
 ured. Some measure from floor to rail of track; this i,s inaccurate, as the track 
 may be shifted or the grade changed in making repairs, or to take out a sag. 
 
 Whenever a level survey is begun the distance between roof and floor should 
 be measured to see if it agrees with the notes. If it differs, the fact should be 
 stated under the original notes, as a check for future work. 
 
 PITCHING WORK 
 
 The survey of workings in highly inclined coal seams does not differ in 
 methods from those employed in surveying mines in flat seams, but there are 
 sundry minor modifications in detail varying from mine to mine, as peculiar 
 or local difficulties have to be overcome. 
 
 Stations. The seams are usually folded along the line of strike so that the 
 entnes, or gangways, that are driven approximately upon a water-level, are 
 curved and crooked to the same extent as the seam. For this reason, gang- 
 ways cannot be driven upon sights, and stations are established as needed as 
 the survey proceeds. As these stations are placed solely with a view to obtain- 
 ing as long or as many sights from one point as possible and as the spads used 
 do not have to be set exactly on line, much smaller drills and plugs may be used 
 in pitching than in flat work. In some cases, the holes are only $ to \ in. in 
 diameter and but \ in. to 1 in. long as a maximum. Various devices for quickly 
 establishing these more or less temporary stations have been adopted in the 
 anthracite regions of Pennsylvania, some of which are here given. 
 
 1. The simplest top station is a shallow conical hole, made with the point 
 of the foresight man's hatchet, which is dug into the top rock and rotated, 
 and is called by some a jigger station. Corps using these entirely have a 
 jigger consisting of a steel-pointed extension rod, with an offset holding a 
 paint brush. The rod is long enough to allow the point to , be driven 
 into the roof at any height, and its rotation marks a circle with the brush, 
 which is also used to mark the number beside it. Centers are set under such 
 
SURVEYING 91 
 
 stations and sights are given by another tool also called a jigger. This is an 
 extension rod, beyond the upper end of which projects a piece of sheet iron 
 shaped like an isoceles triangle, with the upper and smaller angle cut off so as 
 to form an end i in. broad, and in this end is cut a U-shaped groove. 
 
 The sights are given and the centers set by putting the plummet cord in 
 this groove, and placing the end in the jigger hole in the roof. The cord 
 must be more than twice the length of the section of the place, as it must 
 be held in the hand, run over the jigger notch, and hung vertically to the plum- 
 met, which must come to the floor when the stations are set. The rod and 
 cord are held in the left hand, and the right is free to steady the bob, give sight, 
 or set the center. ; The advantages are the quickness with which the centers 
 are set and the sights given, and the ease with which the highest stations 
 are reached. The disadvantages are the impossibility of making the jigger 
 hole perfectly conical, so that the jigger can be set in the same place on two 
 successive sights, and the plummet cord will hang exactly in the same place. 
 
 2. A twist drill ^ in. in diameter is used to make a hole in the roof; a 
 piece of cord <>T, better, a copper wire is placed across this, and a hardwood 
 shoe peg is driven into the hole and binds the cord tight. The plummet is 
 tied to the lower end. A cord will soon rot, and, if in the gangway, is pulled 
 out by the drivers for whip lashes, while the wire is more permanent; but 
 even this will be pulled out by catching in the topping of a car in a low place. 
 
 3. The use of spads is dispensed with, and all the stations put in rock 
 roof where possible. A i-in. twist drill makes a vertical hole 1 in. deep. Into 
 this, when a sight is to be taken, the foresight man puts a steel clip with ser- 
 rated edges. This is made by bending upon itself a thin piece of steel ^ in. 
 wide. When the ends are pressed together it will go into the hole, and the 
 spring of the sides and the serrated edges hold the clip in the hole so that it 
 is hard to pull out. The cord passes through a hole in the center of the bend 
 and is, therefore, in the center of the hole no matter how the clip is inserted. 
 It is removed by pressing together the ends of the clip. This is the easiest 
 and quickest way of working, as there is no eyehole to be freed from dirt and 
 no knot to be tied and untied. The hanging of the plummet takes a fraction 
 of a second, and the station will remain as long as the roof keeps up. The 
 disadvantages are the putting of the holes inclined to the vertical by a care- 
 less man, and the many roofs that are unfit for piercing with a twist drill. 
 
 Stations are generally marked upon some regular system, as in flat work, 
 although in some mines the objectionable practice of numbering stations at 
 random as they happen to be placed still prevails. In the case of leased prop- 
 erties two surveys will commonly be made, one by the operator and another 
 by the land owner. When this happens, each corps will have its distinctive 
 mark as, for example, the one a circle and the other a cross (+), with possibly 
 a distinguishing letter selected from the name of the corps as a further means 
 of identification. If both corps use the same station each will place about 
 it its distinguishing sign and number, and the notes will state " Sta. 617 = Sta. 432 
 of ( ) Corps." 
 
 Surveying Methods. The method of surveying gangways and keeping 
 notes does not differ from that employed in flat seams, except from the fact 
 that three consecutive stations not being in line, a deflection angle and bear- 
 ing or azimuth must be read at each set up. As the grade between stations 
 may be, in fact commonly is, pronounced, particular attention must be paid 
 to reading the vertical angle. Parallel entries (room entry and its air-course) 
 are commonly at such a distance above or below one another that it is not 
 usually possible to locate the one by measurements made through the cross- 
 cuts from the other and a separate line must be run in each. In case it is 
 possible to locate the air-course by means of offsets from the main gangway, 
 a clinometer, frequently a brass protractor with a plummet attached, must be 
 hung from the stretched tape to give its angle of inclination. All such inclined 
 offset sights must be reduced to the horizontal before being mapped. 
 
 If the seam pitches more than 30, the rooms are worked with batteries; 
 the heavy timbers forming these usually preclude the possibility of sighting 
 from the 'gangway to the face. Work of this kind is surveyed by lines out the 
 gangway and back through the faces of the rooms, which are generally clear 
 of timber. The line along the face should be tied into the gangway line as 
 soon as opportunity offers. 
 
 If the seam makes much gas, sights must be taken to safety lamps unless 
 the portable battery hat lamps are used. The latter afford a very satisfactory 
 light and, being absolutely clean, are preferable not only to the ordinary safety 
 lamp in gaseous mines, but to the oil lamp in any mine. 
 
92 SURVEYING 
 
 The angle of dip of the seam should be taken at each station and at inter- 
 mediate points if it changes radically. The thickness and quality of the coal 
 should be observed frequently and changes of importance noted on the map. 
 
 Locating Pillars for Surface Support. It is customary to leave unmined 
 pillars of coal to support important buildings, reservoirs, etc., on the surface. 
 The usual method of locating these pillars is to extend vertical planes through 
 the boundary lines of such objects, and leave untouched all parts of the super- 
 incumbent beds embraced by those planes. This is accurate only when the 
 strata are horizontal or vertical, as beds settle normally to the planes of the 
 strata and not in a vertical line in case the open spaces are stowed. If the 
 spaces are left open, they are first filled by falls, and then the settling goes on 
 according to the above rule. No cut is necessary to show the method of set- 
 tling, and the place where the bed is to be left untouched may be found as 
 follows: Draw a vertical section through the point to be supported, and also the 
 underlying bed on the line of the dip of the bed the section being accurately drawn 
 to any scale. Draw through the extremities of the object to be supported, lines to 
 the bed, which will make right angles with it. The space included will give the 
 dimension of the pillar measured along the dip of the bed, and the dimensions 
 of the object taken at right angles to the first plane will give the other dimension of 
 the pillar. 
 
 MINE CORPS 
 
 The number of men required in making a mine survey and the nature of 
 their duties depend on the nature of the work to be performed. If sights 
 are to be moved up two men, the transitman and foresight man, can do the 
 work; but if distances are to be measured, a third man is advisable to assist 
 with the tape if time is an object. The third man is essential if stations are 
 to be set at exact distances from the instrument. In all ordinary survey work 
 where offsets are to be taken, four men are essential and five are advisable. 
 There must be two men to hold the long tape between stations on the entry, 
 and two to hold the tape with which the offsets are taken, one of whom may 
 be the transitman, but it is better to have a special crew for taking offsets, 
 leaving the surveyor free to record the notes, determine the position of the 
 stations, etc. Much time will be saved if one of the four men can set up the 
 transit and read the angles. 
 
 When making a complete survey of an extensive property, particularly 
 in pitching work where short sights are the rule and branch gangways on 
 divers grades are common, it is a material help to place the survey stations 
 before an attempt is made to measure the angles or distances. To do this, 
 the transitman will require two assistants and the services of 
 a mine foreman or other official familiar with the workings and 
 I who will, in emergencies, hold a lamp where needed. The 
 
 backsight man remains at the station from which the survey 
 >. I . is to start and the party goes ahead to the most distant point 
 > v ' 7 therefrom that the lamp is visible. At this point, a station is 
 established in the roof with the drill, plug, and spad, and its 
 proper number painted on the rib or roof. The backsight man 
 comes up to the new station and the party g9es ahead loca- 
 ting a second and succeeding station or stations as may be 
 needed. Very frequently several sights must be taken from 
 one station, a common case being that shown in the accom- 
 panying figure, where the road forks. Here a helper is sent up 
 each branch, the mine foreman holding his lamp at the back- 
 sight, and the transitman shifts his position until he finds a point from which 
 the three lamps are visible and there establishes a station. For this work the 
 transit is not necessary, only a bucket holding the brace, and drills, plugs 
 spads, and a hatchet, and possibly a 100-ft. tape, being taken into the mine. 
 
 CARE OF INSTRUMENTS 
 
 The transit should be removed from the tripod and placed in the instru- 
 ment box with its plates undamped when not in use. When going to and 
 from work, the transit should not be carried on the transit head, or the spindle 
 will become sprung. Nor should it be carried with the arm crooked under 
 the telescope as the weight comes on the axis, and that soon gets sprung so 
 that all the adjusting in the world will not make it work right. When carried 
 
 the hand, it should be reversed and the hand slipped under the compass 
 plate and brought over so as to clamp both plates. In this way there will be 
 no strain on any part. The person carrying the transit should be the first to 
 
SURVEYING 93 
 
 ascend a slope or any pitching place and the last to descend, so that loose stones 
 or dirt that may be dislodged may not affect or endanger the instrument or 
 trip the carrier. He must be sure that the tripod head is screwed firmly on 
 the tripod. The possible slip of the instrument through not observing this 
 caution may be a source of trouble in the failure to agree of the duplicate angles 
 read at each station. As soon as the corps comes back from the mine, the tape 
 must be stretched, tested, wiped, and piled. It can be inspected to see if 
 marks are too much worn, or it stands in need of mending, the marking pot 
 is cleared of muck, and fresh white paint is mixed, if the corps is going out in 
 24 hr.; the plummets will have their strings overhauled and freed from knots; 
 hatchets will be sharpened, and axes ground, pouches overhauled, and a supply 
 of tacks or spads taken. The transit is set up and wiped with a cloth wet with 
 alcohol, so as to remove dirt, oil, and paint. If water has gotten between the 
 graduated limb and compass box, the verniers must be uncovered and the whole 
 wiped dry. If sulphureted hydrogen from the powder smoke has tarnished 
 the silver surfaces of any of the graduated circles, it must be removed with 
 whiting. Alcohol should be always used instead of water, as it will quickly 
 evaporate and leave the parts dry. The telescope glasses are then wiped with 
 soft chamois leather, and the instrument is tested for want of adjustment before 
 it is put away in its box. 
 
 How often the transit will require adjusting depends on the quality of 
 the instrument and the care it receives when in use. When moving up sights 
 by backsighting and plunging the telescope, the adjustment of the vertical 
 hair must be perfect or the fpresight will be to the right or to the left of the 
 prolongation of the line joining the backsight and instrument stations; this 
 adjustment is, thence, of prime importance to the surveyor in flat work, who 
 is chiefly occupied in moving up sights as the workings advance. This adjust- 
 ment is also of importance when reading deflection angles by the methods 
 explained. Sights may be set without regarding the adjustment of the ver- 
 tical hair, by setting the vernier at 0, backsighting, and turning off an angle 
 of 180, but this involves two accurate readings and settings of the yernier. 
 Deflection angles may be determined in the same way, by subtracting the 
 included angle from 180, and with the same objections to the method. A 
 method sometimes employed to move up sights, which is independent of the 
 cross-hair adjustment and does not require the reading of an angle is as fol- 
 lows: Assume that stations numbered, say, 200 and 201 are those nearest 
 the face and that Sta. 202 is to be placed on the line 200-201 prolonged. Set 
 up at Sta. 200, and foresight upon Sta. 201, remove the plumb-bob and cord 
 from Sta. 201 and set Sta. 202 at the proper distance ahead on the line thus 
 prolonged. 
 
 For plumbing wet shafts, kerosene resists the extinguishing power of water 
 better than fish oil, and is less readily blown out by a strong ventilating cur- 
 rent. It makes more smoke, and, in tight headings, or mines with poor ven- 
 tilation, with a large party, fouls the air much more readily than fish oil. Some- 
 times a mixture of the two is burnt in very drafty places, where it is hard to 
 maintain a light. Kerosene is burned in the plummet lamp unless it is used 
 with the safety attachment. Sweet oil, or any oil burning without smoke, 
 must then be used. Smoke clogs the openings in the gauze, restricts the 
 entry and escape of gases, and, especially if the gauze is damp with oil, may 
 ignite and communicate the flame from within to the outside body of gas. 
 
 TRAVERSING AND MAPPING 
 
 TRAVERSING 
 
 The latitude of a point is its distance north or south of some parallel of 
 latitude, or line running east and west. The departure of a point is its distance 
 east or west of some meridian, or line running north and south; it is the same 
 as the longitude of the point. Latitudes are measured in a direction at right 
 angles to the departures. The distance that one end of a line is due north 
 or south of the other end is the difference of latitude of the two ends of the 
 line, and is called the northing or southing, or simply the latitude of the end 
 considered. The distance that one end of a line is due east or west of the other 
 end is the difference in longitude of the two ends of the line, and is called the 
 easting or westing, or simply the departure. 
 
 The process of calculating and tabulating the latitudes and departures of the 
 courses of a survey is known as traversing the survey. To do this, all distances 
 
94 
 
 SURVEYING 
 
 must either be measured horizontally or be reduced to horizontal distances 
 by means of the vertical angle. The horizontal angles must either be read as 
 auadrant courses, or must be reduced from azimuth to quadrant courses. 
 
 Latitude-= distance X cos of bearing 
 Departure = distance X sin of bearing 
 
 Below is given, in tabular form, the calculated notes of a closed com- 
 nass survev All the work shown should be kept in ink m the permanent, 
 office record books. The notes in the first three columns, headed Station 
 Bearing Distance, are the same as the corresponding columns of the held 
 notes. If the field notes show that the distances were measured along the 
 
 TRAVERSED SURVEY NOTES 
 
 
 
 
 Latitude 
 
 Departure 
 
 Total 
 Latitude 
 
 Total 
 Departure 
 
 tion 
 
 Bearing 
 
 tance 
 
 A 
 
 .g 
 
 ^ 
 
 tn 
 
 
 
 
 
 
 | 
 
 
 
 
 % 
 
 3 
 
 a 
 W 
 
 
 
 S 
 
 & 
 
 
 
 
 1-2 
 
 N35E 
 
 270.00 
 
 221 
 
 
 155 
 
 
 221 
 
 
 155 
 
 
 2-3 
 
 N 83 30' E 
 
 129.00 
 
 15 
 
 
 128 
 
 
 236 
 
 
 283 
 
 
 3-4 
 
 S57E 
 
 222.00 
 
 
 121 
 
 186 
 
 
 115 
 
 
 469 
 
 
 4-5 
 
 S 34 15' W 
 
 355.00 
 
 
 293 
 
 
 200 
 
 
 178 
 
 269 
 
 
 5-1 
 
 N 56 30' W 
 
 322.56 
 
 178 
 
 
 
 269 
 
 
 
 
 
 
 
 
 
 
 
 
 414 
 
 414 
 
 469 
 
 469 
 
 
 
 
 
 slope, as would be the case in an ordinary transit survey, two extra columns 
 should be provided, one for the measured distances and another for the ver- 
 tical angles. If the elevations are to be deduced from the vertical angles, 
 something that is necessary if a topographic map of the property is to be made, 
 two additional columns will be needed, in one of which should be placed the 
 differences in elevation of consecutive stations, and in the other, the total ele- 
 vation of each station above sea level. 
 
 From the latitudes and departures of the individual stations, it is customary 
 to determine the latitude and departure of each station with reference to the 
 first station of the survey. These are commonly called the total latitudes and 
 total departures, or total northings, southings, eastings, or westings, as may be. 
 
 The latitudes and departures of the individual stations are calculated by 
 the formulas given. The total latitudes and departures are obtained by adding 
 continuously and algebraically to the assumed latitude and departure of the 
 first station, the latitudes and departures of the individual stations. The first 
 station is frequently called the origin of coordinates, and its northing, southing, 
 easting, and westing are commonly taken as zero (0). As a check on entering 
 the latitudes and departures in the right columns, it should be noted that 
 when the bearing is less than 45, the departure is less than the latitude; 
 and when the bearing is greater than 45, the departure is greater than the 
 latitude. 
 
 Errors in Closure. If the survey is a continuous one around a tract, and 
 ending at the place of beginning, the sum of the northings should equal the 
 sum of the southings, and the sum of the eastings should equal the sum of the 
 westings. Or, in other words, the sum of all the latitudes north, should equal 
 the sum of all the latitudes south; and the sum of all the departures east, 
 should equal the sum of all the departures west. It is evident that by 
 coming back to the place of beginning the surveyor has traveled the same 
 distance north as he has south, and the same distance east as he has west. 
 However, in practice, as has been intimated under the heading Closing Sur- 
 veys, no such agreement is possible. In fact, should a survey actually bal- 
 ance or close, it should be assumed that the closure is apparent and not real; 
 the sum of the errors in one direction being exactly offset by the sum of the 
 errors in the opposite direction. 
 
 . The error in closure of a survey is the ratio that the length of the line join- 
 ing the initial and final stations (as determined by the survey) bears to the 
 
SURVEYING 95 
 
 entire distance run. The length of this line is that of the hypotenuse of a 
 right-angled triangle of which the errors in latitude and departure are the two 
 sides. Thus, if the coordinates of the starting point are 0, and after running 
 around a tract of land a distance, by survey of, say, 25,000 ft., it is found that 
 the total eastings exceed the total westings by 4.25 ft., and that the total 
 northings exceed the total southings by 1.5 ft., the survey will have failed to 
 close by V4.25 2 +1.502=4.51 ft. The error in closure will be 25,000-^-4.51 
 = 1 ft. in 5,543ft. (about). The bearing of the line of error (as it may be called) 
 may be found from the formula: 
 
 Tan bearing err r in 
 
 error in latitude l.o 
 from which the bearing is N 70 34' E. That is to say, owing to errors in 
 measurement, the final point instead of coinciding with the initial point, is 
 found to be N 70 34' E, 4.51 ft. from it. 
 
 Balancing Surveys. In surveys made with the compass and chain, it may 
 be safely assumed that the failure to close is as much due to errors in angular 
 measurement as in chaining. In this case, the latitudes and departures may 
 each be corrected by certain amounts, some being increased and other being 
 decreased, until a perfect balance is secured between the northings and south- 
 ings on the one hand and between the eastings and the westings on the other 
 by means of the following rule: 
 
 Rule I. The correction to be applied to any particular latitude or departure 
 is to the total error in latitude or departure as the corresponding distance is to the 
 entire distance covered by the survey. 
 
 Each correction is to be applied in such a way as to diminish the whole 
 error at the particular station. 
 
 In the case of surveys made with the transit, the angular measurements 
 are highly accurate and it is very probable that errors in closing are due almost 
 entirely to incorrect chaining. This is particularly so if the sum of the deflec- 
 tion angles is 360 (in which case the survey closes exactly in angle) or is not 
 more than 1' different for each mile or two (averaging, say, fourteen stations 
 per mile) surveyed. In this case the rule for determining the corrections to 
 be applied to each individual latitude or departure is: 
 
 Rule II. The correction to be applied to any particular latitude or departure 
 is to the whole error in latitude or departure as the corresponding latitude or depar- 
 ture is to the arithmetical sum of all the latitudes or departures. 
 
 As before, each correction should be so applied as to diminish the whole 
 error at each station. 
 
 Locating Special Work. The rules given for finding the error in closure of 
 a survey, as well as its bearing, are applied to determine the length and bearing 
 of a line (as that of a tunnel or entry) required to connect two points whose 
 latitudes and departures are known. Thus, suppose that it is required to connect 
 Sta. 57, whose latitude is 2,046,25 N and departure 18.76 E, with Sta. 49 whose 
 latitude is 1,625.75 N and departure 159.26 E. It is apparent that Sta. 49 is 
 2,046.25-1,625.75 = 420.50 ft. south, and 159.26-18.76=140.50 ft. east of 
 Sta. 57. The distance between the two stations is V420.50 2 -f- 140.50 2 = 443.35 ft. 
 Again, 
 
 _ , . difference in departures 140.5 00 . 10 
 Tan bearing = ,. = 77^-5. = .33413 
 
 difference in latitudes 420.5 
 
 whence the angle is 18 29'. As Sta. 49 is south and east of Sta. 57, the bear- 
 
 ing and length of the line joining Sta. 57 and Sta. 49 is S 18 29' E, 443.35 ft. 
 
 It must be noted that the exact tangent of 18 29' is .33427, or .00014 more 
 
 than the calculated one. In the distance between the stations, 443.35 ft., 
 
 a line run on a bearing of S 18 29' E will miss Sta. 49 by .06 ft. Hence, an 
 
 exact closure cannot generally be obtained with an instrument graduated to 
 
 minutes only. The distance between the stations may be found without having 
 
 to extract the square root, the bearing having been obtained, by the formula 
 
 _. difference in latitudes 420.5 - - 
 
 Distance = = -^ -r^ = 443.36 ft. 
 
 cos of bearing .94842 
 
 MAPPING 
 
 Laying Off a Map. It is very commonly the case that a mining property has 
 its greatest linear dimension in any other direction than an east-and-west 
 line. Thus a property containing, say, 2,000 A., might have approximate 
 dimensions of 2$ mi. in a general northeast and southwest direction, and of 
 
96 SURVEYING 
 
 H mi. at right angles thereto. Mine maps are required by the .laws of most 
 states to be on a scale of 100 ft. to 1 in., although 200 ft. to 1 in. is permissible 
 in some cases. On the larger scale, the property just described would have a 
 northeast and southwest length of 128 in. (10 ft. 8 in.) and a length at right 
 angles thereto of 79.2 in. (6 ft. 7.2 in.). It is apparent that if such a property 
 is mapped with its meridian at right angles to the length of the paper (that 
 is like ordinary maps in an atlas with the north toward the top) a goodly 
 portion of the survey will extend both above and below the top and bottom 
 edges of any paper now made for draftsmen's use. Such a property must be 
 laid down with its longest dimension parallel to the longest dimension ot the 
 paper, regardless of the direction of the meridian. 
 
 To determine the best way to lay off the map on the paper, it is customary 
 to make a skeleton map of the property on a small scale, say, on one of 1,000 ft. 
 to 1 in. (in the foregoing case the dimensions would be 12.8 in. X 7.92 in.) and lay 
 this upon a sheet of paper that represents, on the same scale, the paper to 
 be used for the finished map. By shifting one upon another, a position will 
 eventually be found where the property may be drawn upon the sheet. By 
 pricking through with a needle point, the stations may be transferred from the 
 skeleton map to the sheet representing the drawing paper, and the connecting 
 lines drawn. A border should be drawn around this minature map at one-tenth 
 the distance from the edge that the border will be from the edge of the large map. 
 There will now be available for laying off the paper, a minature reproduction of 
 the outlines of the finished map. To draw the coordinate lines, lay off upon the 
 large sheet, using their location on the small map as a guide, the most easterly 
 and most westerly corners of the property. Any other two corners will do, pro- 
 vided they are separated by as long a distance as is conveniently possible. 
 Connect the selected corners by a line and calculate the bearing there9f. If 
 it is assumed that this line has a bearing of N 58 30' E, all lines making an 
 angle of 58 30' to the left of this base will be north-and-south lines, or 
 meridians. 
 
 When mapping extensive surveys, it is a slow and usually an inaccurate 
 process to measure from the initial station the total latitude and departure by 
 which every other station is located, as many of the distances will be very long, 
 from 5,000 to 10,000 ft. or more (from 50 to 100 in. on the scale of the map) ; 
 therefore, mine maps are laid off in a series of squares 1,000 ft. (10 in.) on 
 edge with their sides in the meridian. To locate a station whose coordinates 
 are, say, latitude 8,250 N and departure 6,500 E, measure along the meridian 
 marked 6,000 a distance 250 ft. north of its intersection with the parallel 
 marked 8,000. At this point erect a perpendicular to the meridian (or draw 
 a line parallel to the latitude) and lay off along it a distance of 500 ft. to the 
 east. The point thus plotted will have the coordinates in question. 
 
 To draw these squares, place a meridian, determined by the method ex- 
 plained, upon the map somewhere near the middle. Upon this, mark a series 
 of points exactly 10 in. apart. Through the extreme points draw perpendiculars 
 to the meridian by any of the methods of geometry. Upon these parallels 
 lay off spaces of 10 in. both east and west from the meridian and through these 
 points draw the remaining meridians. On the most eastern and western mer- 
 idian thus established, lay off further spaces of 10 in., the points marking which 
 may be connected with those on the first meridian laid down upon the map, 
 thus completing the work. These squares should be laid off in pencil and 
 lightly inked in with the utmost accuracy. The work should be done during 
 a single day when conditions of temperature and humidity are as nearly con- 
 stant as possible, as atmospheric changes will cause paper to expand or con- 
 tract and thus change the size of the squares. In the case of large properties, 
 the proper placing of the meridians and parallels so that all the corners, etc. 
 will come on one sheet of paper is a matter of painstaking work. Often the 
 shifting of the meridians or parallels 1 or 2 in. either way will accomplish this 
 much to be desired result; and this can only be done by cut-and-try methods 
 combined with more or less calculation and recalculation of the coordinates 
 of the extreme points as the meridians and parallels are shifted. If the map 
 will extend over upon a second sheet, this should be laid off in squares in a sim- 
 ilar manner to the first, and should have laid down upon it enough of the work- 
 ings, etc., appearing last upon the first sheet, that it may be used independently 
 of it. In other words, the second sheet of the map should overlap for 2 or 3 in. 
 on that of the first sheet. 
 
 The question of numbering the meridians and parallels or, what is in 
 effect the same thing, determining the location of the zero of coordinates, is a 
 matter of importance. In most maps, some one meridian will be marked 0, 
 
SURVEYING 97 
 
 those to the right of it will be designated as 1 E, 2 E, 3 E, etc., and those to 
 the left, 1 W, 2 W, 3 W, etc. Similarly, some one parallel will be marked 0, 
 and those above and below it will be respectively 1 N, 2 N, 3 N, etc., and 1 S, 
 2 S, 3 S, etc. A better plan is to call the most westerly meridian and most 
 southerly parallel 0. In this way all the latitudes will be north and all the 
 departures will be east, all additions made to determine the total latitudes and 
 departures will be algebraic without shifting from one column to another and 
 there will be but two columns for the total latitudes and departures instead of 
 four. Under this plan, there is much less liability to error when making cal- 
 culations involving differences in latitudes and departures, for these differences 
 will always be obtained by subtraction and never by addition, as is fre- 
 quently the case when the first system of numbering the meridians and 
 parallels is used. For example, under the first system two points having 
 latitudes of 200 N and 300 S, respectively, will differ in latitude by 200 + 300 
 = 500 ft.; under the second system, these same points will have latitudes of, 
 say, 800 N and 300 N, the difference being 800-300 = 500, as before. 
 
 Mapping the Field Notes. The stations made to determine the bounda- 
 ries of the property are first placed upon the map, using the total latitude 
 and departure of each for this purpose; the method having been described. 
 After two consecutive stations have been plotted, as a check on the work, 
 the distance between them should be measured. This should agree with the 
 horizontal distance reduced from the field measurements. After the survey 
 stations are plotted, the property corners should be mapped in the same way, 
 checking up the plotted distance between them and the survey station from 
 which they were determined. By joining these corners, the outer boundaries 
 of the property will now appear upon the map. Preferably by means of a pro- 
 tractor reading to minutes and using any convenient meridian as a base, the 
 side shots to buildings, runs, etc., as determined from each station, should 
 be laid off. These directions should be transferred to the proper station and 
 the distance measurements laid off thereupon; this gives all the points taken 
 from that station. After all the side shots are taken, the map may be inked 
 in, provided all possible checks prove that the penciled work is correct. If a 
 topographic map is desired, the stadia sights taken to determine the topography 
 may be located and contours, 10, 20, 25, or 50 ft. apart drawn in. The flatter 
 the country, the smaller should be the contour interval. In ordinary rolling 
 country, where the contours merely serve as a guide to determine the width 
 of pillar in the mine, a contour interval of 25 ft. suffices; in mountainous coun- 
 try, 50 ft. is close enough. 
 
 The mine workings are mapped in exactly the same way as the surface 
 features so far as survey lines are concerned, but there is a difference in mapping, 
 as there is in taking, the side shots. On the surface, points are determined by 
 noting their bearing and distance from some station; underground, points are 
 located by offsets at right angles to the line of sight and must be so mapped. 
 
 Property corners are marked by a small circle in black and property lines 
 are reasonably heavy ones joining adjacent circles, but not passing within the 
 circumference, the exact corner being a pin point at the center of the circle. 
 On the map should appear the bearing and length of all property lines. A 
 description of the corner should be given as W. O. (for white oak), stone, etc. 
 If the original corner is gone and something else is in place the description 
 should say "W. O., now stone," or "Stone, orig. W. O.," or "Stone (W. O.)," 
 the original corner being placed in parentheses. 
 
 The boundaries of all the individual properties making up the entire tract 
 should appear on the map, as well as the name of the owner of each and the 
 acreage. All reservations from under which the coal cannot be mined or to 
 which the company's rights are unusual or peculiar, must be carefully mapped. 
 The names of the owners of adjacent properties should appear. The outcrop 
 of all workable seams should be given in brown, as well as the location of all 
 test openings thereon and the thickness and character of the coal. The posi- 
 ti9n of all oil and gas wells should be accurately determined and mapped, 
 with memoranda as to their opera'tion, production (if any) etc. Abandoned 
 and improperly plugged wells are a constant source of danger in some parts 
 of the country and too much time cannot be spent in accurately locating them. 
 The base-line monuments, together with the azimuth or bearing of the line 
 joining them should be given, as well as all meridian reference lines connected 
 therewith. 
 
 Mine workings should be shown in black, the stations being denoted by 
 small circles in the same color. The numbers of all stations and their eleva- 
 tion above sea level should appear. If more than one seam is worked, the 
 
98 SURVEYING 
 
 operations in the separate seams should be given a distinctive color, none of 
 which (except the principal workings which may be shown in black) should 
 be used in mapping any surface feature. 
 
 When mapping the operations in a single seam, it is not unusual to outline 
 the work done by different colors to represent the extraction during each semi- 
 annual period. Thus, the workings advanced between January 1 and June 30, 
 1914, would be shown, say, in blue; those from July 1 to December 31, 1914, 
 in red; those from January 1 to June 30, 1915, in green; and similarly for each 
 succeeding period 9f 6 mo. While this serves to show the extent of the oper- 
 ations for any semiannual peripd, and this is desirable, it makes an ugly map, 
 and many prefer to plat the mine workings in one single color, drawing a dash 
 across the face of the working places after each semiannual posting has been 
 made. The date, as 6-30-1914, placed by a dash indicates the date at which 
 the posting was made. If many seams are worked under the one property 
 and all are platted on the same sheet, it leads to confusion and it is a better 
 plan not to map them this way, but to make a series of property maps, one 
 for the workings of each seam, or at the most, for the workings of two adjacent 
 seams. Then, if it is desired to note the relationship between the workings 
 of all the seams, a tracing may be made upon which the workings in all the 
 seams are given. 
 
 Coloring a Map. 'The survey line by which the corners were determined 
 is frequently placed on the map in red ink. It is not necessary to give the bear- 
 ings and distances of the lines, but the stations should be numbered and their 
 elevation above sea level given if this has been determined. Contour lines 
 appear in brown, those marking even hundreds of feet aboye sea level being 
 heavier than intermediate ones. Small brooks appear as a single line of Prus- 
 sian blue; larger ones are shown by two parallel lines; and creeks and rivers 
 have their banks shown as they actually exist. If a creek is named, this name 
 should appear on the map. Roads are denoted in brown and should appear 
 in their legal width. Houses are commonly outlined in black, as are tipples, 
 coke ovens, etc. Railroads are denoted by fine parallel lines, marked with black 
 dashes about fg in. in length; black-and-white dashes of the same length alter- 
 nating. 
 
 It is a question whether it is advisable to tint a map with water colors or 
 not. If the map is a final or finished one upon which no further operations 
 will appear it is advisable to tint it properly; but in the case of a working map, 
 there will be so many erasures as the workings advance, as pillars are drawn, 
 as new lines of railroad are constructed, etc., that the effect of the tinting is soon 
 spoiled. When tinting is used, the inner edge of the property lines should 
 receive a wash in India ink (which will appear in dark gray-black) about i in. 
 wide. Crop lines should receive a similar but narrower band in brown. Roads 
 should have a light wash in yellow ocher, and narrow streams, those appear- 
 ing less than 1 in. in width (100 ft. wide in nature) a light wash in Prussian 
 blue. Large ponds and wide streams if tinted for their full width should be 
 colored with indigo, as the Prussian blue is rather too vivid. Frequently, 
 streams and lakes are not colored for their full width with a flat tint; instead 
 the color is applied with the maximum intensity at the shore line, being grad- 
 ually drawn out to nothing 1 in. or less therefrom. The projections of houses, 
 barns, tipples, etc., should receive a light wash of crimson lake. Theoretically, 
 unworked areas of coal should be given a flat tint of India ink, the tint being 
 removed to correspond to the mining operations. This is, of course, not 
 practicable, so it is customary to leave the unworked coal, white, and to color 
 the excavations made in mining. As stated, this makes an attractive map when 
 first completed, but as the workings advance and pillars are drawn, the scratch- 
 ing out of previously applied tints, produces an unpleasant effect. 
 
 I he paper upon which a mine map is made should be the very best eggshell, 
 linen mounted, obtainable. When not in use it, with all other permanent 
 records, should be kept in a fireproof vault. 
 
SURVEYING 
 
 99 
 
 DETERMINATION OF MERIDIAN 
 
 LATITUDE AND LONGITUDE 
 
 If a meridian, that is, a circle passing through the axis of the earth, is passed 
 through a given point of the earth's surface, the angular distance of the point 
 from the equator, measured on the meridian, is the latitude of that point. A 
 plane parallel to the equator cuts the earth's surface in a circle called a par- 
 allel of latitude. All the points on a parallel of latitude have the same latitude. 
 The longitude of a place is the angle that the plane of the meridian of the 
 
 S'ace makes with the plane of a reference meridian (usually the meridian of 
 reenwich). This angle may be measured on the equatorial circle or on the 
 parallel of latitude of the given place. Longitude is counted from the reference 
 meridian toward the west. 
 
 CELESTIAL SPHERE 
 
 The celestial sphere is an imaginary sphere enclosing all the heavenly bodies. 
 It is of such enormous dimensions that, in comparison with it, the earth may 
 be considered as a mere dot. The earth's axis produced indefinitely is called 
 the axis of the celestial sphere. This axis intersects the celestial sphere in two 
 points, called the north pole and the south pole of the heavens. All the great 
 circles of the celestial sphere passing through this axis are called hour circles. 
 The circle in which the plane of the equator intersects the celestial sphere is 
 called the celestial equator. The point on the equator that the sun in its 
 apparent motion over the celestial sphere crosses on March 21, as it passes 
 from the southern to the northern hemisphere, is called the vernal equinox. 
 
 REFERENCE CIRCLES 
 
 The accompanying illustration, which represents the celestial hemisphere, 
 shows all the reference circles that are used for determining the position of a 
 heavenly body. O is the position of the earth; OP, one-half of the axis of the 
 celestial sphere, P being the north pole; VQV ' L, part of the celestial equator; 
 X, the vernal equinox; and YXC, part of the sun's path. PX is the hour 
 circle passing through X, called the equinoctial colure. S is any star, and PSA 
 is the hour circle passing through it. XA is the right ascension of the star. 
 
 which is the arc on the equator measured eastwards from the vernal equinox 
 to the hour circle passing through the star. A S is the declination of the star; 
 that is, its angular distance from the equator. The declination is considered 
 positive when the star is north and negative when south of the equator. The 
 complement angle of the declination, SP, is called the polar distance of the star. 
 
 The zenith of a point on the earth's surface is the point Z in which the line 
 passing through the center of the earth and the given point intersects the celes- 
 tial sphere above the given point. The horizon is the plane NYM passing 
 through the given point and perpendicular to this line. 
 
 The celestial meridian of a given point is a great circle passing through the 
 zenith of the point and the poles. The celestial meridian cuts the horizon in 
 two points 2V and M, called, respectively, the north point and the south point. 
 
100 SURVEYING 
 
 A vertical circle is one that passes through the zenith and is perpendicular 
 to the horizon. 
 
 The prime vertical is the vertical circle at right angles to the meridian; it 
 intersects the horizon in two points V and V, called the west and the east point, 
 
 The altitude of a heavenly body is its angular distance DS from the horizon, 
 measured along the vertical circle passing through the body. The zenith 
 distance, is the angular distance SZ of the star from the zenith, measured along 
 the same circle. The zenith distance is the complement of the altitude. 
 
 The azimuth of a star is the angle in the plane of the horizon intercepted 
 by the planes of the meridian and the vertical circle passing through the star. 
 It is measured from the north point toward the east or from the south point 
 toward the west. NMD is the azimuth of S, measured from the north toward 
 the east, and MD is the azimuth of 5 when measured from the south toward the 
 west. 
 
 The hour angle of a star is the arc QA intercepted on the equator between 
 the meridian and the foot of the hour circle passing through the star; it is 
 measured from the meridian toward the west. 
 
 TIME 
 
 The passing of a heavenly body across the meridian of a place is called its 
 culmination, or transit. It is upper or lower culmination, according as it is then 
 occupying the highest or the lowest position with regard to the horizon. 
 
 The interval of time that elapses between two successive upper or lower 
 transits of a star over the same meridian is called a sidereal day. This day 
 begins, for any place, when the vernal equinox crosses the meridian above the 
 pole; this instant is called sidereal noon. Sidereal hours, minutes, and sec- 
 onds are reckoned from to 24 hr., starting from sidereal noon. Time 
 expressed in sidereal days and fractions (hours, minutes, seconds) is called 
 sidereal time. 
 
 Prom this, it follows that sidereal time is the hour angle of the vernal 
 equinox; also, that the right ascension of a star is equal to the sidereal time of 
 its transit, or culmination. For any other position of the star, the sidereal 
 time equals the algebraic sum of the right ascension and the hour angle of the 
 star. 
 
 The interval between two successive upper transits of the sun is called a true 
 solar day, or an apparent day. Owing to the fact that the motion of the sun is 
 not uniform and that the solar days are not of equal duration, apparent time 
 is not used for the ordinary affairs of life. 
 
 The mean sun is an imaginary body supposed to start from the vernal 
 equinox at the same time as the true sun, and to move uniformly on the equator, 
 returning to the vernal equinox with the true sun. The time between two suc- 
 cessive upper transits of the mean sun is called a mean solar day, and time 
 expressed in mean solar days is called mean solar time, or simply mean time. 
 This is the time shown by ordinary clocks and watches. 
 
 A mean solar day is the mean of the duration of all the true solar days in a 
 year (a year being the time in which either the true or the mean sun makes 
 a complete circuit of the heavens). As there are 365.2422 true solar days and 
 366.2422 sidereal days in a year. 1 mean solar da. = 366.2422-:- 365.2422 
 = 1.0027379 sidereal day =24h 3 m 56.55 s , sidereal time. 
 
 Likewise, 1 sidereal day = 365.2422 -J- 366.2422 = .99726957 mean solar day 
 = 23h 56 m 4.09 s , mean solar time. 
 
 The equation of time is a certain quantity that must be added algebraically 
 to the apparent solar time to obtain the corresponding mean time. The value 
 of this quantity for each day of the year is given in the American Ephemeris.* 
 
 Civil Time and Astronomical Time. By civil time is meant the time that 
 is usually reckoned in ordinary life. For astronomical purposes, the day is 
 considered to begin at noon, and hours counted from to 24. When time is 
 reckoned in this manner it is called astronomical time. The civil day begins 
 at 12 o'clock at night, and the astronomical day begins 12 hr. later. For 
 instance, the date October 17, 7h 14 m 3 s , astronomical time, means 7h 14 m 3 s 
 after noon of the civil date October 17, and is in civil time, 7h 14 3 s P. M. 
 The astronomical date February 20, 18h 6 m 12<* means 18^ 6 12" after noon 
 
 *The American Ephemeris and Nautical Almanac may be obtained from 
 the Director of the Nautical Almanac, Naval Observatory, Washington, D. C. 
 Remittance must be made in cash or a post-office money order for $1.25. 
 Stamps and checks are not taken. 
 
SURVEVlftG' J 101 
 
 of the civil date February 20, or 6h^6 m ISP-after Tr^iduiJht-'o* Jfelor'uArV 2i/' that 
 is, February 21, 6h 6 12* A. M. '-,-'',' , - < ' * 
 
 Longitude and Time. The mean sun describes a complete circle in 24 mean 
 solar hours. In 1 hr. it moves over 360 ^24= 15 of arc; in 1 min. of time, 
 over 15' of arc; and in 1 sec. of time, 15" of arc. 
 
 Relation Between Time and Longitude. Let A and B be two places on the 
 earth's surface, B being west of A. Let their respective longitudes be h a and 
 hf,, and let the difference between h a and hi,, expressed in measure of time, be d g , 
 Let, also, T a be the time at A when the time at B is Tb. Then, 
 
 T a = T b +d p (1) 
 
 and T b = T a -d ? (2) 
 
 EXAMPLE 1. The longitude of Washington, west of Greenwich, is 5h 8 m 1 s ; 
 that of San Francisco, 8b 9 m 47 3 . What is the time at: (a) Washington when 
 it is 9h 3 m at San Francisco? (b) San Francisco when it is 19h 54 m 30 s at 
 Washington? 
 
 SOLUTION. (a) Here A, the eastern locality, is Washington and B is 
 San Francisco; also, <fc=8l 9 m 47*-5b 8 m l" = 3h l m 46 s . Therefore, applying 
 formula 1, Ta = 9h 3 m +3h l m 46 3 = 12h 4 m 46 s 
 
 (b) Applying formula 2, 
 
 ra = 19h 54 1 * 1 30s _3h lm 46s = 16h 52 44 s . 
 
 Standard Time. Time referred to the meridian of a given place is called the 
 local time of that place. To obviate complications in comparing local times 
 of different localities, for use in ordinary affairs of life standard times have 
 been adapted for regions between certain longitudes. The United States is 
 divided into four zones, or sections of standard time. The time in each zone 
 is referred to the meridian passing through its center. These central meridians 
 are 15 or lh distant from one another and are, respectively, 75, 90, 105, 
 and 120 west of Greenwich; or, in hours, 5h, 6h, 7h, and 8h west of Greenwich. 
 Each of these meridians controls the watch time of all places within 7 on 
 
 S* 3 m 8* 7h 3 m 7 " 6*30" 6" 5^30 6* 4*30 
 
 f ThnI S refer- [ Pac \f ic \Mountain\ Central | Jgqtern[ 
 
 70 12730' I20 P irfdrf 105 97 3O 9O 82 3O 75 6730 
 
 _ 
 
 called eastern time; to the 90 meridian, central time; to the 105 meridian, 
 mountain time; and to the 120 meridian, Pacific time. 
 
 To Change Standard Time Into Local Time and Vice Versa. Standard 
 time can be changed into local time or local time can be changed into standard 
 time by applying formula 1 or formula 2, according as the given place is east 
 or west of the reference meridian of the zone in which the place is located. 
 
 EXAMPLE. The standard time, by a watch, at a place whose longitude is 
 81 37', is 9h 37 m 45 s A. M.; what is the local time? 
 
 SOLUTION. As the longitude is 81 37', the place lies within the zone of the 
 75 meridian; and being west of the latter, formula 2 must be applied. In this 
 case, r = 9h 37 45" and dp- = 81 37' -75 = 6 37' = 26 m 28 s . Therefore, 
 r* = 9h 37 m 45 s -26 m 28 s = 9& ll m 17" A. M. 
 
 DETERMINATION BY OBSERVING POLARIS AT CULMINATION 
 
 The position of Polaris, or the north star, can easily be ascertained by means 
 of the group of stars called the Dipper, or the Great Bear. As shown in the 
 accompanying illustration, a straight line joining the stars, a and /3, called 
 the -pointers, nearly intersects Polaris. There are two times during the day 
 when the star crosses the meridian. It is then said to be at its upper or 
 lower culmination, as the star is then occupying either the highest or the lowest 
 position with reference to the horizon. When the star is in either of these 
 positions, the vertical plane passing through it and the observer's station is the 
 meridian of the place, and its intersection with the horizon is therefore a true 
 north-and-south line. 
 
 Field Work. Select a date on which Polaris is at either lower or upper 
 culmination during the night (preferably during the early part of the evening) . 
 Determine, by means of the accompanying table, the exact time of culmination, 
 being careful to reduce the tabular values to standard civil time. It is safer, 
 in order to avoid confusion, for the observer to set his watch to show local time. 
 About 15 m before the time of culmination, set the transit in such a position that 
 an unobstructed view toward the north may be obtained for a distance of 
 between 300 and 500 ft. Drive a stake, and mark by a tack the exact point 
 
102 
 
 Q-<S_ 
 
 S 
 
 rfj 
 
 a 4 
 
 .d 
 
 e ili!;;ils5g33as8S83asg3asg3^ 
 
 . | CO C Tt< CO <N i-< ( 
 
 OS 6 
 
 _d 
 
 2 8 
 
 OS _ 
 
 J3 
 
 ^ S 
 
 ^ COiO-^cOCNi-^OCON^O! 
 
 i-J 00 t-; * (N OS CO CO IO CO 00 O * l> rH CO CD b- OS OS rH O 00 CO 
 
 co g ooc ' 
 
 r^lOTjtiQkCiOTjtiOT^iO-^iOTjflOrJtiCT^iCT^iC-^iC^iO 
 ^ I CO 1C * CO W H O CO <N T-I O TO 00 b- CO C * CO (N I O OS 00 b- 
 
 1 i> TJ< co q oo cq oo oo q rH co ic os c<i cp op i-i CM T< TJ< CD 10 co i-< 
 
 I ^ 1C * Tj( O 1C 1C iO >O C * 1C C C Tj< iC TJ< C C 5 Tjt 1C C iC 
 CO C Tf CO M rH O CO M ^H O OS 00 b- CO C ^ CO (N <-H O OS 00 b- 
 
 (NOSOqiCiCrHCOCOOt^OSrHlCOOC 
 
 CDiCTjtcOCNrHOCO(NrHOOSOOb-COC-*CO<NrHOOSOOb. 
 NC<IC^C<|rHrHi-(rHrHrHrHi-(rHi-l 
 
 oo^T^rHos^ososNcoci> : rHTjHoqqcorjjcqcDooi> : cco 
 
 COlC-<i*CO(NrHOCO(NrHOOSOOb-CDlCTHCO<NrHOOSOOb- 
 <N(N<NC<JrHrHrHrHrHrHrHrHrHrH 
 
SURVEYING 103 
 
 occupied by the instrument. About && before tlie tifna of jCirlnaination, direct 
 the telescope to the star, holding a.' lamp ia front irid a littlest o\/ftrd jOiie side 
 of the objective glass to illuminate tha cross-hairs. Set both clamps, and with 
 either tangent screw set the vertical cross-hair exactly on the star. The star 
 will appear to be moving toward the left or toward the right according as it is 
 approaching upper or lower culmination. Follow it in its motion by turning 
 the tangent screw until the exact time of culmination (which, preferably, 
 should be called out by an assistant). This completes the observation of the 
 star. Now depress the telescope, direct it to a point on the ground about 
 400 or 500 ft. from the instrument, and have an assist- j> , ,, . . 
 ant drive a tack in the top of a stake in line with the * Ofe [\ ' 
 line of sight; this completes the operation. The line j V 
 between t the two stakes is a true north-and-south | \. 
 line, or true meridian. [ y 
 
 Time of Culmination of Polaris. -The accom- \ 
 
 panying table contains the times of upper culmina- \ 
 
 tion of Polaris for the dates given. The lower culmi- \ 
 
 nation occurs nearly lib 58 m before and after the \ 
 
 upper culmination, and can be determined from the \ 
 
 latter. In the table the extreme right-hand column \ 
 
 contains the difference between the times of culmi- \ 
 
 nation for any two succeeding days. Each difference \ 
 
 applies to any day between the date horizontally \ 
 
 opposite that difference in the left-hand column, \ 
 
 and the following date. Thus, the difference 3.95 m , \ 
 
 which is horizontally opposite January 1, indicates V 
 
 that, between January 1 and January 15, the time of \ 
 
 culmination decreases by 3.95 m per da. For instance, \ a 
 
 the time of culmination on January 8 is obtained x 
 
 by subtracting from the time of culmination for Jan- I _. a 
 
 uary 1 the product 3.95 X 7 =27.65, the number ^i " \ ,' 
 
 of days elapsed from January 1 to January 8 being ^/ 
 
 seven. 
 
 It should be borne in mind that the times given #9#per or Great Meat* 
 in the table are mean local times counted in the astronomical way; that is, 
 from 0^ to 24h, beginning at noon. 
 
 EXAMPLE. Find the time of upper culmination of Polaris on September 
 6, 1913. 
 
 SOLUTION. Referring to the table, 
 
 Upper culmination, Sept. 1, 1913 = 14^45.3 
 
 Difference for 1 da =3.92m 
 
 Correction for 5 da =3.92mX5= 19.6m 
 
 Time of culmination on Sept. 6 = 14t25.7m 
 
 This means that upper culmination will occur when 14h 25.7 m have elapsed 
 since local noon Sept. 6; that is, at 2b 25.7 m A. M., Sept. 7. 
 
 DETERMINATION BY OBSERVING POLARIS AT ELONGATION 
 
 When a star is at its extreme westerly or easterly position, it is said to be 
 at western or eastern elongation. This position with reference to the meridian 
 of the place is determined by the angle that a vertical plane passing through 
 the star and the point of observation is making with the meridian. This 
 angle is called the azimuth of the star, and its values for Polaris, for the years 
 1913 to 1922 and latitudes 5 to 74, are given in the accompanying table. 
 
 Polaris is at eastern elongation about 5h 55 m before it reaches its upper cul- 
 mination; and at western elongation, 5& 55 m after upper culmination. The 
 times of elongation can, therefore, be readily determined from those of culmi- 
 nation taken from the table. 
 
 EXAMPLE. Find the time of western elongation of Polaris on March 1, 
 1914. 
 
 SOLUTION. On referring to the table, it is found that the upper culmination 
 is at 2h 52.5 m , local astronomical time, or 2h 52.5 m , P. M., local civil time. Polaris 
 is at western elongation 5h 55 m later or at 8h 47.5, p. M., local civil time. 
 
 Making the Observation and Marking the Meridian. Determine the 
 approximate time of elongation as just explained. About 20 m before that 
 time, set the transit over a point properly marked, and level it carefully. Set 
 the vernier at 0. Direct the telescope to the star, and, with both clamps set, 
 follow the star by means of the lower tangent screw. If the star is approaching 
 
.. 
 
 SURVEYING 
 
 104 
 
 eastern- eitmgati&m tt \nlL* Be movmg to -the right; if western, to the left. 
 About't'ho tlmo t,t .efor-gattort, it-wfll be, noticed that the star ceases to move 
 horizontally, and that its image appears to follow the vertical cross-hair of the 
 instrument. The star has then reached its elongation and the observation is 
 completed. Take the azimuth from the table. Depress the telescope, and 
 turn it through an angle equal to the azimuth, to the west or to the east, accord- 
 ing as the star was at eastern or western elongation. The line of sight will then 
 
 AZIMUTHS OF POLARIS AT ELONGATION 
 
 i 
 
 Year 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Q 
 
 li 
 
 313 
 
 1 
 
 914 
 
 1 
 
 915 
 
 1 
 
 916 
 
 1 
 
 317 
 
 1 
 
 918 
 
 1 
 
 )19 
 
 1 
 
 920 
 
 1 
 
 321 
 
 1 
 
 922 
 
 ri 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i-J 
 
 K 
 
 g 
 
 S 
 
 c 
 
 b 
 
 .s 
 
 bo 
 
 
 
 b 
 
 G 
 
 a 
 
 G 
 
 M 
 
 .H 
 
 M 
 
 
 B) 
 
 c 
 
 u 
 
 _c 
 
 
 Q 
 
 2 
 
 Q 
 
 
 Q 
 
 
 Q 
 
 3 
 
 G 
 
 2 
 
 Qj 
 
 Q 
 
 2 
 
 o 
 
 c 
 
 3 
 
 C 
 
 2 
 
 Q 
 
 2 
 
 O 
 
 G 
 
 
 5 
 
 1 
 
 9.8 
 
 1 
 
 9.5 
 
 j 
 
 9.2 
 
 1 
 
 8.8 
 
 1 
 
 8.5 
 
 1 
 
 8.2 
 
 1 
 
 7.9 
 
 1 
 
 7.6 
 
 1 
 
 7.3 
 
 1 
 
 7.0 
 
 6 
 
 
 9.9 
 
 
 9.6 
 
 
 9.3 
 
 
 9.0 
 
 
 8.6 
 
 
 8.3 
 
 
 8.0 
 
 
 7.7 
 
 
 7.4 
 
 
 7.1 
 
 8 
 
 
 10.2 
 
 
 9.8 
 
 
 9.5 
 
 
 9.2 
 
 
 8.9 
 
 
 8.6 
 
 
 8.3 
 
 
 7.9 
 
 
 7.7 
 
 
 7.4 
 
 10 
 
 1 
 
 10.6 
 
 1 
 
 10.3 
 
 1 
 
 10.0 
 
 1 
 
 9.7 
 
 1 
 
 9.3 
 
 1 
 
 9.0 
 
 1 
 
 8.7 
 
 1 
 
 8.4 
 
 1 
 
 8.1 
 
 1 
 
 7.8 
 
 12 
 
 
 11.0 
 
 
 10.7 
 
 
 10.4 
 
 
 10.1 
 
 
 9.7 
 
 
 9.4 
 
 
 9.1 
 
 
 8.8 
 
 
 8.5 
 
 
 8.2 
 
 14 
 
 
 11.6 
 
 
 11.3 
 
 
 11.0 
 
 
 10.6 
 
 
 10.3 
 
 
 10.0 
 
 
 9.7 
 
 
 9.4 
 
 
 9.0 
 
 
 8.7 
 
 16 
 
 
 12.3 
 
 
 12.0 
 
 
 11.7 
 
 
 11.3 
 
 
 11.0 
 
 
 10.7 
 
 
 10.4 
 
 
 10.1 
 
 
 9.7 
 
 
 9.4 
 
 18 
 
 
 13.1 
 
 
 12.8 
 
 
 12.4 
 
 
 12.1 
 
 
 11.8 
 
 
 11.5 
 
 
 11.1 
 
 
 10.8 
 
 
 10.5 
 
 
 10.2 
 
 20 
 
 1 
 
 14.0 
 
 1 
 
 13.7 
 
 L 
 
 13.4 
 
 1 
 
 13.0 
 
 1 
 
 12.6 
 
 1 
 
 12.3 
 
 1 
 
 11.9 
 
 1 
 
 11.6 
 
 1 
 
 11.3 
 
 1 
 
 10.9 
 
 22 
 
 
 15.0 
 
 
 14.7 
 
 
 14.4 
 
 
 14.1 
 
 
 13.8 
 
 
 13.4 
 
 
 13.1 
 
 
 12.7 
 
 
 12.4 
 
 
 12.1 
 
 24 
 
 
 16.0 
 
 
 15.7 
 
 
 15.4 
 
 
 15.1 
 
 
 14.8 
 
 
 14.5 
 
 
 14.1 
 
 
 13.8 
 
 
 13.5 
 
 
 13.2 
 
 26 
 
 
 17.4 
 
 
 17.0 
 
 
 16.7 
 
 
 16.3 
 
 
 16.0 
 
 
 15.7 
 
 
 15.3 
 
 
 14.9 
 
 
 14.6 
 
 
 14.3 
 
 28 
 
 
 18.8 
 
 
 18.5 
 
 
 18.1 
 
 
 17.8 
 
 
 17.4 
 
 
 17.0 
 
 
 16.7 
 
 
 16.3 
 
 
 16.0 
 
 
 15.7 
 
 30 
 
 1 
 
 20.3 
 
 1 
 
 19.9 
 
 1 
 
 19.6 
 
 1 
 
 19.2 
 
 1 
 
 18.9 
 
 1 
 
 18.5 
 
 1 
 
 18.2 
 
 1 
 
 17.9 
 
 1 
 
 17.5 
 
 1 
 
 17.1 
 
 32 
 
 
 22.0 
 
 
 21.6 
 
 
 21.2 
 
 
 20.9 
 
 
 20.5 
 
 
 20.1 
 
 
 19.8 
 
 
 19.4 
 
 
 19.0 
 
 
 18.7 
 
 34 
 
 
 23.8 
 
 
 23.5 
 
 
 23.1 
 
 
 22.8 
 
 
 22.4 
 
 
 22.1 
 
 
 21.7 
 
 
 21.3 
 
 
 21.0 
 
 
 20.6 
 
 36 
 
 
 26.0 
 
 
 25.6 
 
 
 25.2 
 
 
 24.9 
 
 
 24.5 
 
 
 24.1 
 
 
 23.8 
 
 
 23.4 
 
 
 23.0 
 
 
 22.6 
 
 38 
 
 
 28.2 
 
 
 27.8 
 
 
 27.5 
 
 
 27.1 
 
 
 26.8 
 
 
 26.4 
 
 
 26.0 
 
 
 25.6 
 
 
 25.2 
 
 
 24.8 
 
 40 
 
 1 
 
 30.7 
 
 1 
 
 30.3 
 
 1 
 
 30.0 
 
 1 
 
 29.6 
 
 1 
 
 29.2 
 
 1 
 
 28.8 
 
 1 
 
 28.4 
 
 1 
 
 28.0 
 
 1 
 
 27.6 
 
 1 
 
 27.2 
 
 42 
 
 
 33.6 
 
 
 33.2 
 
 
 32.8 
 
 
 32.4 
 
 
 32.0 
 
 
 31.6 
 
 
 31.1 
 
 
 30.7 
 
 
 30.3 
 
 
 29.9 
 
 44 
 
 
 36.7 
 
 
 36.3 
 
 
 35.8 
 
 
 35.4 
 
 
 35.0 
 
 
 34.6 
 
 
 34.1 
 
 
 33.6 
 
 
 33.2 
 
 
 32.8 
 
 46 
 
 
 40.1 
 
 
 39.7 
 
 
 39.2 
 
 
 38.8 
 
 
 38.4 
 
 
 37.9 
 
 
 37.5 
 
 
 37.1 
 
 
 36.6 
 
 
 36.2 
 
 48 
 
 
 43.9 
 
 
 43.4 
 
 
 43.0 
 
 
 42.5 
 
 
 42.2 
 
 
 41.8 
 
 
 41.3 
 
 
 40.8 
 
 
 40.3 
 
 
 39.9 
 
 50 
 
 1 
 
 48.1 
 
 1 
 
 47.7 
 
 1 
 
 47.2 
 
 1 
 
 46.8 
 
 1 
 
 46.3 
 
 1 
 
 45.9 
 
 1 
 
 45.4 
 
 1 
 
 44.9 
 
 1 
 
 44.4 
 
 1 
 
 43.9 
 
 52 
 
 
 52.9 
 
 
 52.4 
 
 
 52.0 
 
 
 51.5 
 
 
 51.0 
 
 
 50.5 
 
 
 50.0 
 
 
 49.5 
 
 
 49.0 
 
 
 48.5 
 
 54 
 
 
 58.3 
 
 
 57.8 
 
 
 57.3 
 
 
 56.8 
 
 
 56.3 
 
 
 55.8 
 
 
 55.2 
 
 
 54.7 
 
 
 54.2 
 
 
 53.7 
 
 56 
 
 
 4.4 
 
 
 3.8 
 
 
 3.3 
 
 2 
 
 2.7 
 
 2 
 
 2.2 
 
 2 
 
 1.7 
 
 2 
 
 1.1 
 
 2 
 
 0.5 
 
 2 
 
 0.0 
 
 1 
 
 59.4 
 
 58 
 
 
 11.3 
 
 
 10.7 
 
 
 10.1 
 
 
 9.6 
 
 
 9.0 
 
 
 8.4 
 
 
 7.8 
 
 
 7.2 
 
 
 6.6 
 
 
 6.0 
 
 60 
 
 2 
 
 19.0 
 
 2 
 
 18.4 
 
 2 
 
 17.8 
 
 2 
 
 17.2 
 
 2 
 
 16.6 
 
 2 
 
 16.0 
 
 2 
 
 15.3 
 
 2 
 
 14.7 
 
 2 
 
 14.0 
 
 2 
 
 J3.4 
 
 62 
 
 
 28.1 
 
 
 27.4 
 
 
 26.7 
 
 
 26.0 
 
 
 25.4 
 
 
 24.7 
 
 
 24.0 
 
 
 23.4 
 
 
 22.7 
 
 
 22.0 
 
 64 
 
 
 38.7 
 
 
 38.0 
 
 
 37.3 
 
 
 36.5 
 
 
 35.9 
 
 
 35.2 
 
 
 34.5 
 
 
 33.8 
 
 
 33.0 
 
 
 32.3 
 
 66 
 
 
 50.9 
 
 
 50.1 
 
 
 49.4 
 
 
 48.6 
 
 
 47.8 
 
 
 47.0 
 
 
 46.2 
 
 
 45.5 
 
 
 44.7 
 
 
 43.9 
 
 68 
 
 3 
 
 5.7 
 
 3 
 
 4.8 
 
 :? 
 
 4.0 
 
 3 
 
 3.1 
 
 3 
 
 2.2 
 
 3 
 
 1.3 
 
 3 
 
 0.4 
 
 
 59.6 
 
 
 58.7 
 
 
 57.7 
 
 70 
 
 3 
 
 22.8 
 
 3 
 
 21.8 
 
 3 
 
 20.8 
 
 3 
 
 19.9 
 
 3 
 
 18.9 
 
 3 
 
 17.9 
 
 3 
 
 16.9 
 
 3 
 
 15.9 
 
 3 
 
 15.0 
 
 3 
 
 14.0 
 
 72 
 
 
 45.2 
 
 
 44.2 
 
 
 43.1 
 
 
 42.0 
 
 
 41.0 
 
 
 40.0 
 
 
 38.9 
 
 
 37.8 
 
 
 36.8 
 
 
 35.7 
 
 74 
 
 4 
 
 12.1 
 
 4 
 
 11.0 
 
 1 
 
 9.8 
 
 4 
 
 8.7 
 
 4 
 
 7.5 
 
 4 
 
 6.4 
 
 4 
 
 5.2 
 
 4 
 
 4.1 
 
 4 
 
 3.0 
 
 4 
 
 1.8 
 
 be directed along the true meridian, and by marking another point 400 or 500 ft 
 from that occupied by the instrument, the direction of the true meridian will 
 be established. 
 
 This is the most accurate method of determining the true meridian, and, 
 where possible, should be used in preference to others. 
 
 u** u m ?- rk L lng m numents are not commonly set in the meridian, some 
 
 change in the method of making the observations from that described is 
 
 necessary. Having the cross-hair on Polaris at the point of greatest elongation, 
 
SURVEYING 105 
 
 the telescope is brought down and the angle between the star and the 
 monument is read. The telescope is inverted and again set on Polaris and the 
 angle to the monument read. This angle may be read four or six times, even 
 more, as the change in position of the pole star for 15 m before and after elonga- 
 tion is not measurable by an ordinary transit. The mean of the two, four, or 
 six readings of the angle is taken as the true angle. By making a sketch of 
 the position of Polaris with reference to the meridian and of the position of 
 the monuments with reference to Polaris, it will be apparent whether the azi- 
 muth of the star is to be added to or subtracted from the angle between it 
 and the monuments to give the azimuth of the line joining said reference points. 
 As the determination of the meridian is of great importance it is well, unless 
 the engineer has had experience in the work, to repeat the observations on a 
 second night. 
 
 DETERMINATION BY SOLAR OBSERVATION 
 
 Formula for Azimuth of the Sun. One of the most convenient methods of 
 determining the meridian is to measure the altitude of the sun at any hour 
 angle with a transit. At the same time that the altitude is measured, deter- 
 mine, also, the horizontal angle between the sun and a fixed object, or refer- 
 ence mark. Then, the azimuth of the sun is calculated "by the formula that 
 follows. The azimuth of the reference mark is then equal to the algebraic 
 sum of the azimuth of the sun and the measured angle between the sun and 
 the mark. Finally, the true north-and-south line may be located from the 
 azimuth of the reference mark. 
 
 Let a = required azimuth counted from north toward east; 
 
 2 = zenith distance of sun, which is equal to 90 minus altitude; 
 8 = declination of sun; and 
 <J> = latitude of observer; then 
 
 2 \ sin z cos </> 
 
 Two values of will correspond to the computed sin -; one angle will be 
 
 acute and the other obtuse. The acute angle should be used for morning 
 observations and the obtuse for afternoon observations. 
 
 Values of 8 and <J>. The method just described requires that the declina- 
 tion of the sun at the time of observation, and the latitude of the place be known. 
 The declination of the sun for every day of the year at the instant of Wash- 
 ington noon, together with the hourly change, is given in the Ephemeris, and 
 has to be reduced to the time of observation as follows: 
 
 Rule. Change the local time to Washington time by adding algebraically to the 
 former the longitude of the place counted from Washington. Take from the Ephem- 
 eris the declination corresponding to the preceding Washington noon and add 
 algebraically the product of the hourly change by the time elapsed since Washing- 
 ton noon. 
 
 EXAMPLE. Find the true declination of the sun for 9 A. M. January 5, 1903, 
 at Philadelphia. 
 
 SOLUTION. Jan. 5, 9 A. M., civil time = Jan. 4, 21h, astronomical time. 
 The longitude of Philadelphia is 7 m 37 8 = .127^. The Washington time 
 corresponding to 9 A. M. is 21t-.127h = 20.873h. From the Ephemeris, the 
 declination at Washington at noon Jan. 4 is 22 47' 43", and the hourly 
 change is 15.06". The algebraic increase is, therefore. 15.06X20.873 = 5' 14"; 
 thus, the declination at 9 A. M. is -22 47' 43"+5' 14"= -22 42' 29". 
 
 DETERMINATION OF LATITUDE, AND CORRECTIONS FOR 
 ALTITUDE 
 
 Approximate Determination of Latitude From Polaris. In nearly all 
 methods of determining the true meridian, the latitude of the place of obser- 
 vation must be known, at least approximately. In the majority of cases 
 the latitude can be taken from a map or book of reference. In case this can- 
 not be done, a sufficiently close value may be obtained by measuring, with a 
 transit, the altitude of Polaris, which is very nearly (within about 1) equal 
 to the latitude of the place. 
 
 This method of determining latitude is founded on the following very sim- 
 ple and useful principle: 
 
 Principle. The latitude of any place on the earth's surface is equal to the alti- 
 tude of the pole with respect to the horizon of that place. 
 
106 
 
 SURVEYING 
 
 For more accurate work, the tables given in the Ephemeris, entitled, For 
 Finding the Latitude by Polaris, may be used. The simple directions for using 
 them are there given in full. 
 
 Latitude by Solar Observation. Latitude may be determined by measur- 
 ing the sun's altitude, with the sextant or transit, at the instant of its passage 
 across the meridian; that is, at apparent noon. The time of apparent noon 
 may be determined by adding algebraically the equation of time to the noon 
 of local mean time, as previously explained. Then begin the observations 
 about 15 m before apparent noon and repeat them every minute or two. At 
 first the altitude will be increasing; then, it will be decreasing. The maximum 
 altitude obtained will be the apparent meridian altitude. To this the correc- 
 tions that follow must be applied, giving the true altitude. _ The true altitude 
 is then subtracted from 90, and the remainder is the zenith distance. The 
 latitude is then equal to the algebraic sum of the zenith distance and the declina- 
 tion of the sun at the instant of apparent noon. 
 
 Corrections for Altitude. The observed altitude of a heavenly body must 
 be corrected for: (1) refraction, (2) parallax, and (3) semi-diameter. 
 
 1. Refraction is the change of direction of the rays of light when they pass 
 from one medium into another of different density. Its amount for different 
 altitudes is given in the table on page 107. It is subtractive. When the 
 altitude is less than about 8 to 10, the refraction becomes so uncertain that 
 the measurement is of no value for accurate work. 
 
 2. Parallax is the difference in direction of a heavenly body as actually 
 observed and the direction it would have if seen from the earth's center. This 
 correction is necessary when the sun is observed; its values for different alti- 
 tudes are given in the accompanying table. It is additive. 
 
 SUN'S PARALLAX IN ALTITUDE TO BE APPLIED. TO ALL MEASURED 
 
 (Additive to observed altitude) 
 
 Altitude 
 Degrees 
 
 Parallax 
 Seconds 
 
 Altitude 
 Degrees 
 
 Parallax 
 Seconds 
 
 Altitude 
 Degrees 
 
 Parallax 
 Seconds 
 
 
 
 9 
 
 40 
 
 7 
 
 69 
 
 3 
 
 6 
 
 9 
 
 45 
 
 6 
 
 72 
 
 3 
 
 12 
 
 9 
 
 48 
 
 6 
 
 75 
 
 2 
 
 16 
 
 8 
 
 51 
 
 5 
 
 78 
 
 2 
 
 20 
 
 8 
 
 54 
 
 5 
 
 81 
 
 1 
 
 25 
 
 8 
 
 57 
 
 5 
 
 84 
 
 1 
 
 30 
 
 8 
 
 60 
 
 4 
 
 87 
 
 o 
 
 34 
 
 7 
 
 63 
 
 4 
 
 90 
 
 
 
 36 
 
 7 
 
 66 
 
 3 
 
 
 
 3. The correction for semi-diameter is also necessary when the sun is 
 
 1 nftT g t0 t the - aC V that *$*&* u PP er or the low er ed g e of thfdisk! 
 Fnvf, n t he + center, is observed. This correction may be taken from the 
 fcphemeris in the same manner as the sun's declination. For the purpose of 
 ordinary calculations, however, this may be taken from the following table: 
 fime of year (approx.)... Jan. 1, Apr. 1, July 1 Get 1 
 
 Sun's semi-diameter 16' 18" 16' 2" 15' 45" 16' 2" 
 
 upper oneisobTerved. 11 ** * m ""* * bserved ' and Attractive when the 
 nh Corr , ec f tions . for Observation of the Sun for Azimuth. When the sun is 
 ?hfr7^;n r f aZ A mi i th '- a COI T ec . tion for semi-diameter must also be applied to 
 the reading of the horizontal circle; this may be found by dividing the correc- 
 
 add J ftn tli S y the * ( Sf m f of - the sun>s altitud e- This correction is to be 
 added to the reading of the horizontal circle if the hair is placed tangent to 
 
 ch-cll if t e he ge h a f ' e ! SUn A and subtract u ed ' rom the reading P of the horizontal 
 
 Wh v ? 1S Pj aced + ta n g ent to the right edge of the sun. 
 ment t r 3 g observatlon s of the sun for azimuth, the errors of adjust- 
 b^ the Wlowfrfc, 6 "" ^ a ,? d tj.e correction for semi-diameter may be eliminated 
 complete" ' h aSSUmes that the vertical circle of the tran sit 
 
 at theVztauTmLt Se V UP f With the hori ? ontal P la *e reading when sighting 
 uth mark. For forenoon work, the sun should be so sighted that 
 
SURVEYING 
 
 MEAN REFRACTION TO BE APPLIED TO ALL MEASURED 
 ALTITUDES 
 
 (Subtractive from apparent altitude) 
 
 107 
 
 App. 
 Alti- 
 tude 
 
 Re- 
 frac- 
 tion 
 
 App. 
 Alti- 
 tude 
 
 Re- 
 frac- 
 tion 
 
 te 
 
 tude 
 
 Re- 
 frac- 
 tion 
 
 App. 
 Alti- 
 tude 
 
 Re- 
 frac- 
 tion 
 
 App. 
 Alti- 
 tude 
 
 Re- 
 frac- 
 tion 
 
 
 
 33 
 
 5 
 
 9 54 
 
 10 
 
 5 15 
 
 20 
 
 2 35 
 
 34 
 
 24 
 
 
 
 
 
 10 10 
 
 5 10 
 
 20 10 
 
 2 34 
 
 34 30 
 
 23 
 
 
 
 
 
 10 20 
 
 5 5 
 
 20 20 
 
 2 32 
 
 35 
 
 21 
 
 
 
 
 
 10 30 
 
 5 
 
 20 30 
 
 2 31 
 
 35 30 
 
 20 
 
 
 
 5 20 
 
 9 23 
 
 10 40 
 
 4 56 
 
 20 40 
 
 2 29 
 
 36 
 
 18 
 
 
 
 
 
 10 50 
 
 4 51 
 
 20 50 
 
 2 28 
 
 36 30 
 
 17 
 
 
 
 
 
 11 
 
 4 47 
 
 21 
 
 2 27 
 
 37 
 
 16 
 
 
 
 
 
 11 10 
 
 4 43 
 
 21 10 
 
 2 26 
 
 37 30 
 
 14 
 
 
 
 5 40 
 
 8 54 
 
 11 20 
 
 4 39 
 
 21 20 
 
 2 25 
 
 38 
 
 13 
 
 
 
 
 
 11 30 
 
 4 34 
 
 21 30 
 
 2 24 
 
 38 30 
 
 11 
 
 
 
 
 
 11 40 
 
 4 31 
 
 21 40 
 
 2 23 
 
 39 
 
 10 
 
 
 
 
 
 11 50 
 
 4 27 
 
 21 50 
 
 2 21 
 
 39 30 
 
 9 
 
 1 
 
 24 29 
 
 6 
 
 8 28 
 
 12 
 
 4 23 
 
 22 
 
 2 20 
 
 40 
 
 8 
 
 
 
 
 
 12 10 
 
 4 20 
 
 22 10 
 
 2 19 
 
 41 
 
 5 
 
 
 
 
 
 12 20 
 
 4 16 
 
 22 20 
 
 2 18 
 
 42 
 
 3 
 
 
 
 
 
 12 30 
 
 4 13 
 
 22 30 
 
 2 17 
 
 43 
 
 1 
 
 
 
 6 20 
 
 8 3 
 
 12 40 
 
 4 9 
 
 22 40 
 
 2 16 
 
 44 
 
 59 
 
 
 
 
 
 12 50 
 
 4 6 
 
 22 50 
 
 2 15 
 
 45 
 
 57 
 
 
 
 
 
 13 
 
 4 3 
 
 23 
 
 2 14 
 
 46 
 
 55 
 
 
 
 
 
 13 10 
 
 4 
 
 23 10 
 
 2 13 
 
 47 
 
 53 
 
 
 
 6 40 
 
 7 40 
 
 13 20 
 
 3 57 
 
 23 20 
 
 2 12 
 
 48 
 
 51 
 
 
 
 
 
 13 30 
 
 3 54 
 
 23 30 
 
 2 11 
 
 49 
 
 49 
 
 
 
 
 
 13 40 
 
 3 51 
 
 23 40 
 
 2 10 
 
 50 
 
 48 
 
 
 
 
 
 13 50 
 
 3 48 
 
 23 50 
 
 2 9 
 
 51 
 
 46 
 
 2 
 
 18 35 
 
 7 
 
 7 20 
 
 14 
 
 3 45 
 
 24 
 
 2 8 
 
 52 
 
 44 
 
 
 
 
 
 14 10 
 
 3 43 
 
 24 10 
 
 2 7 
 
 53 
 
 43 
 
 
 
 
 
 14 20 
 
 3 40 
 
 24 20 
 
 2 6 
 
 54 
 
 41 
 
 
 
 
 
 14 30 
 
 3 38 
 
 24 30 
 
 2 5 
 
 55 
 
 40 
 
 
 
 7 20 
 
 7 2 
 
 14 40 
 
 3 35 
 
 24 40 
 
 2 4 
 
 56 
 
 38 
 
 
 
 
 
 14 50 
 
 3 33 
 
 24 50 
 
 2 3 
 
 57 
 
 37 
 
 
 
 
 
 15 
 
 3 30 
 
 25 
 
 2 2 
 
 58 
 
 35 
 
 
 
 
 
 15 10 
 
 3 28 
 
 25 10 
 
 2 1 
 
 59 
 
 34 
 
 
 
 7 40 
 
 6 45 
 
 15 20 
 
 3 26 
 
 25 20 
 
 2 
 
 60 
 
 33 
 
 
 
 
 
 15 30 
 
 3 24 
 
 25 30 
 
 1 59 
 
 61 
 
 32 
 
 
 
 
 
 15 40 
 
 3 21 
 
 25 40 
 
 1 58 
 
 62 
 
 30 
 
 
 
 
 
 15 50 
 
 3 19 
 
 25 50 
 
 1 57 
 
 63 
 
 29 
 
 3 
 
 14 36 
 
 8 
 
 6 29 
 
 16 
 
 3 17 
 
 26 
 
 1 56 
 
 64 
 
 28 
 
 
 
 
 
 16 10 
 
 3 15 
 
 26 10 
 
 1 55 
 
 65 
 
 26 
 
 
 
 8 10 
 
 6 22 
 
 16 20 
 
 3 12 
 
 26 20 
 
 1 55 
 
 66 
 
 25 
 
 
 
 
 
 16 30 
 
 3 10 
 
 26 30 
 
 1 54 
 
 67 
 
 24 
 
 
 
 8 20 
 
 6 15 
 
 16 40 
 
 3 8 
 
 26 40 
 
 1 53 
 
 68 
 
 23 
 
 
 
 
 
 16 50 
 
 3 6 
 
 26 50 
 
 1 52 
 
 69 
 
 22 
 
 3 30 
 
 13 6 
 
 8 30 
 
 6 8 
 
 17 
 
 3 4 
 
 27 
 
 1 51 
 
 70 
 
 21 
 
 
 
 
 
 17 10 
 
 3 3 
 
 27 15 
 
 1 50 
 
 71 
 
 19 
 
 
 
 8 40 
 
 6 1 
 
 17 20 
 
 3 1 
 
 27 30 
 
 1 49 
 
 72 
 
 18 
 
 
 
 
 
 17 30 
 
 2 59 
 
 27 45 
 
 1 48 
 
 73 
 
 17 
 
 
 
 8 50 
 
 5 55 
 
 17 40 
 
 2 57 
 
 28 
 
 1 47 
 
 74 
 
 16 
 
 
 
 
 
 17 50 
 
 2 55 
 
 28 15 
 
 1 46 
 
 75 
 
 15 
 
 4 
 
 11 51 
 
 9 
 
 5 48 
 
 18 
 
 2 54 
 
 28 30 
 
 1 45 
 
 76 
 
 14 
 
 
 
 
 
 18 10 
 
 2 52 
 
 28 45 
 
 1 44 
 
 77 
 
 13 
 
 
 
 9 10 
 
 5 42 
 
 18 20 
 
 2 51 
 
 29 
 
 1 42 
 
 78 
 
 12 
 
 
 
 
 
 18 30 
 
 2 49 
 
 29 30 
 
 1 40 
 
 79 
 
 11 
 
 
 
 9 20 
 
 5 36 
 
 18 40 
 
 2 47 
 
 30 
 
 1 38 
 
 80 
 
 10 
 
 
 
 
 
 18 50 
 
 2 46 
 
 30 30 
 
 1 37 
 
 81 
 
 9 
 
 4 30 
 
 10 48 
 
 9 30 
 
 5 31 
 
 19 
 
 2 44 
 
 31 
 
 1 35 
 
 82 
 
 8 
 
 
 
 
 
 19 10 
 
 2 43 
 
 31 30 
 
 1 33 
 
 83 
 
 7 
 
 
 
 9 40 
 
 5 25 
 
 19 20 
 
 2 41 
 
 32 
 
 1 31 
 
 84 
 
 6 
 
 
 
 
 
 19 30 
 
 2 40 
 
 32 30 
 
 1 30 
 
 86 
 
 4 
 
 
 
 9 50 
 
 5 20 
 
 19 40 
 
 2 38 
 
 33 
 
 1 29 
 
 88 
 
 2 
 
 
 
 
 
 19 50 
 
 2 37 
 
 33 30 
 
 1 26 
 
 90 
 
 
 
108 
 
 SURVEYING 
 
 it occupies position 1, Fig. 1, with reference to the cross-hairs; the time, ver- 
 tical angle, and horizontal angle are noted. Then the upper plate is loosened, 
 the instrument turned 180 in azimuth, the telescope inverted, and the sun 
 . sighted again, as in position 2. In position 1 , the sun is moving toward both 
 hairs; in position 2, the telescope should be set approximately as shown by 
 the dotted circle, so that the sun will clear both hairs at the same instant. For 
 
 rfffernoon 
 
 FIG. 1 
 
 FIG. 2 
 
 afternoon work, the positions shown in Fig. 2 should be used. The observa- 
 tions are taken in pairs; if the second observation of a pair cannot be obtained 
 promptly after the first one (owing to a passing cloud, or some other cause), 
 the first must be ignored and considered as useless. 
 
 It should be noted that the reversal of the transit between the observations 
 eliminates the index error of the vertical circle, the error of level in the horizon- 
 tal axis of the telescope, and the error of collimation of the telescope. By 
 sighting in diagonal corners of the field of view and taking the mean of the obser- 
 vations, the corrections (both horizontal and vertical) due to the semi-diameter 
 of the sun are eliminated. To simplify the notes, 180 should be added to 
 (or subtracted from) the horizontal plate reading when the instrument is 
 inverted. 
 
 EXAMPLE. The following measurements were taken in the manner just 
 described. The four means of the circle readings were formed in the field. 
 The declination of the sun was 9 30' 5", and the approximate latitude 
 +39 57'. Find the azimuth of the reference mark. 
 
 Telescope 
 
 Time 
 
 P. M. 
 
 Vertical 
 Circle 
 
 Horizontal 
 Circle 
 
 Direct 
 
 3:27 
 
 19 39' 00" 
 
 99 52' 00" 
 
 Inverted 
 
 3-29 
 
 19 52 00 
 
 99 49 00 
 
 Mean 
 
 3:28 
 
 19 45 30 
 
 99 50 30 
 
 Direct 
 
 3:32 
 
 18 46 00 
 
 100 55 30 
 
 Inverted . . . 
 
 3:34 
 
 19 3 00 
 
 100 49 00 
 
 Mean 
 
 3-33 
 
 18 54 30 
 
 100 52 15 
 
 Direct . . 
 
 3-36 
 
 18 4 30 
 
 101 46 00 
 
 Inverted . . . 
 
 3:38 
 
 18 23 30 
 
 101 35 00 
 
 Mean 
 
 3-37 
 
 18 14 00 
 
 101 40 30 
 
 Direct 
 
 3-40 
 
 17 26 30 
 
 102 29 30 
 
 Inverted . 
 
 3-42 
 
 17 43 00 
 
 102 21 00 
 
 Mean 
 
 3-41 
 
 17 34- 45 
 
 102 25 15 
 
 
 
 
 
 SOLUTION. 
 
 Mean of the four vertical circle readings . 18 37' 11 
 
 Refraction _2 48 
 
 Parallax 
 
 True altitude of center 18 34' 31" 
 
 Zenith distance = 90- true altitude .' . .' 71 25' 29" 
 
 To find the azimuth of the sun: 3 = 71 25' 29"; 4> = 39 57' 0"; 
 5= T 9 30' 5"; J( 8 +$+) = 50 56' 12"; iOH-0-8) = 60 26' 17". Sub- 
 stituting these values in the formula for the azimuth of the sun. 
 
 50 56' 12" sin 60 26' 17" 
 
 sin 71 25' 29" cos 39 57' 
 
SURVEYING 
 
 109 
 
 The two values of fa are 60 17' 15" and 119 42' 45" ( = 180- 60 17' 15"). 
 As the observations were made in the afternoon, the obtuse angle should be 
 used. This gives = 2X119 42' 45" = 239 25' 30". The mean of the four 
 horizontal readings is 101 12' 8". Subtracting this from the azimuth of the 
 sun, the azimuth of the reference mark is found to be 239 25' 30" 101 12' 8' 
 = 138 13' 22". 
 
 RAILROAD SURVEYING 
 
 DEFINITIONS OF CIRCULAR CURVES 
 
 The line of a railroad consists of a series of straight lines connected by 
 curves. Each two adjacent lines are united by a curve having the radius 
 
 FIG. 3 
 
 best adapted to the conditions of the surface. The straight lines are called 
 tangents, because they are tangent to the curves that unite them. 
 
 Railroad curves are usually circular and are divided into three general 
 classes, namely, simple, compound, and reverse curves. 
 
 A simple curve is a curve having but one radius, as the curve AB, Fig. 1, 
 whose radius is AC. 
 
 A compound curve is a continuous curve composed of two or more arcs 
 of different radii, as the curve CDEF, Fig. 2, which is composed of the arcs CD, 
 DE, and EF, whose respective radii are GC, HD, and KE. In the general 
 class of compound curves may be included what are known as easement curves, 
 transition curves, and spiral curves, now used very generally on the more impor- 
 tant railroads. 
 
 A reverse curve is a continuous curve composed of the arcs of two circles 
 of the same or different radii, the centers of which lie on opposite sides of the 
 curve, as in Fig. 3. The two arcs composing the curve meet at a common 
 point or point of reversal M, at which point they are tangent to a common line 
 perpendicular to the line joining their centers. Reverse curves are becoming 
 less common On railroads of standard 
 gauge. 
 GEOMETRY OF CIRCULAR CURVES 
 
 The following principles of geometry 
 are of special importance as relating to 
 curves: 
 
 1. A tangent to a circle is perpen- 
 dicular to the radius at its tangent 
 point. Thus, in Fig. 4, AF is perpen- 
 dicular to BO at its tangent point B, 
 and ED is perpendicular to CO at C. 
 
 2. Two tangents to a circle from 
 any point without the circle are equal 
 in length, and make equal angles with 
 the chord joining their points of tan- 
 gency. Thus, BE and CE are equal, 
 and the angles EEC and ECB are 
 equal. 
 
 3. An angle not exceeding 90 
 formed by a chord and the tangent at 
 
 one of its extremities, is equal to one-half the central angle subtended by the 
 chord. Thus, the angle EBC = ECB = * BOC. 
 
 4. An angle not exceeding 90 having its vertex in the circumference of a 
 circle and subtended by a chord of the circle, is equal to one-half the central 
 angle subtended by the chord. Thus, the angle GBH, whose vertex B is in the 
 
110 SURVEYING 
 
 circumference, is subtended by the chord GH and is equal to one-half the cen- 
 tral angle GOH, subtended by the same chord GH. 
 
 5 Equal chords of a circle subtend equal angles at its center and also in 
 its circumference, if the angles lie in corresponding segments of the circle. 
 Thus if BG, GH, HK, and KC are equal, BOG = GOH, GBH = HBK, etc. 
 
 6 ' The angle of intersection FEC of two tangents of a circle is equal to 
 the central angle subtended by the chord joining the two points of tangency. 
 Thus, the angle CEF = BOC. 
 
 7 A radius that bisects any chord of a circle is perpendicular to the chord. 
 8. A chord subtending an arc of 1 in a circle having a. radius = 100 ft. is 
 
 very closely equal to 1.745 ft. 
 
 ELEMENTS AND METHODS OF LAYING OUT A CIRCULAR CURVE 
 
 The degree of curvature of a curve is the central angle subtending a chord 
 of 100 ft. Thus, if, in Fig. 4, the chord BG is 100 ft. long and the angle BOG 
 is 1 the curve is called a one-degree curve; but if, with the same length of chord, 
 the angle BOG is 4, the curve is called a four-degree curve. 
 
 The deflection angle of a chord is the angle formed between any chord of 
 a curve and a tangent to the curve at one extremity of the chord. It is equal 
 to one-half the central angle subtended by the chord. The deflection angle for 
 a chord of 100 ft. is called the regular deflection angle, and is equal to one-half the 
 degree of curvature. The deflection angle for a subchord that is, for a chord 
 less than 100 ft. is equal to one-half the degree of curvature multiplied by the 
 length of the subchord expressed in chords of 100 ft. The length c of a sub- 
 chord or of any chord is given by the formula 
 in which c = 2R sin D 
 
 R = radius; 
 D = deflection angle of that chord. 
 
 Relation Between Radius and Deflection Angle. From the formula just 
 given, _ c 
 
 2smD 
 
 If Dioo is the deflection angle for a chord of 100 ft., then 
 g_ 50 
 
 /V ~: - ^r 
 
 sin Dim 
 For a 1 curve, Dioo = 30' and R = 5,730, nearly. For curves less than 10, 
 
 the radius may be taken as ' , in which DC is the degree of curvature. The 
 
 DC 
 
 accompanying table gives the length of the radius, in feet, for degrees of curva- 
 ture ranging by intervals of 5' and 10' from 0' to 20. 
 
 Tangent Distance. The point where a curve begins is called the point of 
 curve, and is designated by the letters P. C.; and the point where the curve 
 terminates is called the point of tangency, and is designated by the letters P. T. 
 The point of intersection of the tangents is called the point of intersection; it 
 is designated by the letters P. I. 
 
 The distance of the P. C. or P. T. from the P. I. is called the tangent dis- 
 tance, and the chord connecting the P. C. and P. T. of a curve is commonly 
 called its long chord. This term is also applied to chords more than one sta- 
 tion long. 
 
 If / denotes the angle of intersection and R the radius of the curve, then the 
 tangent distance 
 
 Laying Out a Curve With a Transit. When the angle of intersection / has 
 been measured and the degree of curve decided upon, the radius of the curve 
 can be taken from the Tablebf Radii and Deflections or it can be figured by the 
 formula 5,730 
 
 *"~nT 
 
 The tangent distance is then computed and measured back on each tangent 
 from the P. I., thus determining the P. C. and P. T. Subtracting the tangent 
 distance from the station number of the P. I. will give the station number 
 of the P. C. Ordinarily, this will not be an even or full station. The length 
 of the curve is then computed by dividing the angle / by the degree of curve, 
 the quotient giving the length of the curve in stations of 100 ft. and decimals 
 thereof. After having found the length of the curve, compute the deflection 
 angles for the chords joining the P. C. with all the station points; set the transit 
 at the P. C.; set the vernier at 0, sight to the intersection point, and turn off 
 
SURVEYING 
 
 111 
 
 1U93UBX 
 
 OOCOt > -OlCOOi'oO''^OOC<lt > -rHCOO'^OiCOOOC s }SOrHiOO^t ( OOCOt N -rHCOO 1 ^ 
 
 )cocococococococococococococococococococococococoiM(N<N 
 
 99.139(1 
 
 .i-HOO^OSCOOOCOOOCOGOCO- 
 
 1U3SUBX 
 
 33JS3Q 
 
 'OO l OOOO l OO l OO l OO | OOiOO 
 M * TJ< 10 O rH rHC^Ol CO CO ^ ^ 
 
 )COiO(NC5t^T}<rHCOCOCOOOO'O(NCT>^-^rHOOCD 
 
 ;i>coo3C5qrH(N(NeO't>ciocot^t>;aoo5qqrH 
 
 O>OO'OOiOOiCOiOO>OOiCOiOO 
 i-l r-4 <N (N CO CO ^ -tf 10 10 rH r-( (N <N CO 
 
 rH rH (N <N CO CO 
 
 COIOOO rH Tf < 
 t^T)< rH C5CO ( 
 
 O-H(N<NCO' 
 
 t^OCOiOOOrHTtiC 
 t>.OOQCO5OO'-i( 
 
 -J rH rH rH rH rH rH (N (N (N IM' <N (N M (N 
 
 I * IO t~- OO O rH ( 
 
 " OrH OiCX3t>ODiO iO*TjTTir^"^Co"co"co"co"co"c<fc^C^<N*C<fc<rC<f C^fc^iN't 
 
 33J33Q 
 
112 
 
 SURVEYING 
 
 successively the deflection angles, at the same time measuring the chords and 
 marking the stations. The station of the P. T. is found by adding the length 
 of curve in chords of 100 ft. to the station of the P. C. 
 
 If the entire curve cannot 
 
 X be run from the P. C. on ac- 
 
 count of obstructions to the 
 view, run the curve as far as 
 the stations are visible from the 
 P. C. and run the remainder of 
 the curve from the last station 
 that can be seen. Suppose that ' 
 in the 10 curve shown in Fig. 1 
 the station at H, 200 ft. from 
 the P. C., which is at B, is the 
 last point on the curve that can 
 be set from the P. C. A plug 
 is driven at H and centered 
 carefully by a tack driven at 
 the point. The transit is now 
 moved forward and set up at H. 
 As the deflection angle EBH is 
 10 to the right, an angle of 10 
 is turned to the left from and 
 the vernier clamped. The in- 
 strument is then sighted to a flag at B, the lower clamp set, and by 
 means of the lower tangent screw the cross-hairs are made to bisect the 
 flag exactly. The vernier clamp is then loosened, the vernier set at 0, and 
 the telescope plunged. The line of sight will then be on the tangent IP, and 
 the deflection angles to K and C can be turned off from this tangent, and 
 the stations at K and C located in the same manner that the stations at G and 
 H were located from B, because the angle at IHB between the tangent IH and 
 the chord BH is equal to the angle EBH between the tangent EB and the 
 same chord. 
 
 This method of setting the vernier for the backsight when the instrument 
 is moved forwards to a new instrument point on the curve is sometimes called 
 the method by zero tangent. The essential principle of the method is that the 
 vernier always reads zero when the instrument is sighted on the tangent to 
 the curve at the point where the instrument is set, and the deflection angles are 
 made to read from the tangent to the curve at this point in the same manner 
 as if this point were the P. C. of the curve. 
 
 Tangent and Chord Deflections. Let A B, Fig. 2, be a tangent joining the 
 curve BCEH at B. If the tangent AB is prolonged to D, the perpendicular 
 distance DC from the tangent to the curve is called a tangent deflection. If the 
 chord BC is prolonged to the point G, so that CG = CE, the distance GE is called 
 a chord deflection. If the 
 radius R of the curve and 
 the length of the chord c are 
 known, the tangent deflection / 
 can be determined by the 
 formula 
 
 fc*. 
 
 J 2R 
 
 This formula can be used A. 
 for any length of chord or ra- 
 dius. If CE = BC, the chord 
 
 deflection 
 
 = -. For this 
 
 condition the Table of Radii 
 and Deflections gives the ch9rd 
 deflection and tangent deflection 
 for 100-ft. chords and for de- 
 grees of curvature varying by 
 intervals of 5' and 10' from 5' 
 to 20. 
 
 When the two chords preceding the station considered are of unequal 
 lengths, the chord deflection = Cl(ci + c * ) , where ci is the length of the first chord 
 
SURVEYING 113 
 
 and cz the length of the second chord preceding the station considered. When 
 the tangent deflection / is known, the chord deflection 
 
 *-/('+;) 
 
 Special Values of Chord and Tangent Deflection. For a chord of 100 ft. 
 preceded by one of the same length the chord deflection for a 1 curve is 1.745; 
 for a 2 curve, it is twice that amount, or 3.49; and so on. The tangent 
 deflection, being half the chord deflection, will be .873 ft. for a 1 curve, 1.745 
 for a 2 curve, etc. The tangent deflection for a chord of any length equals 
 the tangent deflection for a chord of 100 ft. multiplied by the square of the 
 given chord expressed as the decimal part of a chord of 100 ft. 
 
 Application of Chord and Tangent Deflection. Let it be required to restore 
 center stakes on the 4 curve, Fig. 3, at each full station. The points A and B 
 determine the direction of the tangent, the point B being the P. C., which is at 
 Sta. 8+25. For a 4 curve the regular chord deflection for 100 ft. is 4 X 1.745 
 = 6.98 ft., and the tangent deflection is 3.49 ft. The distance from P. C. to the 
 next full station is 75 ft.; hence, the tangent deflection CF = .75 2 X3.49 = 1.96 ft. 
 The point F is found by first measuring 75 ft. from B, thus locating the point C 
 in the line AB prolonged, then from C measuring CF = 1.96 ft., at right angles to 
 BC; the point F thus determined will be Sta. 9. Next, the chord BF is pro- 
 longed 100 ft. to D; BF is only 75 ft., DG is computed from the preceding 
 formula; thus, do = 3.49 
 (1 + flW = 6.11. This A & _ i __C 
 
 distance is measured at 8+25] jf<X y"**^r -r 
 
 right angles to BD; the - p 
 
 point G thus deter- 
 mined will be Sta. 10. [ 
 The point H, which is 
 Sta. 11, and the P. T. of 
 the curve, is determined 
 in the same manner, ex- 
 cept that, as the chords p ir 
 FG and GH are each 
 100 ft. long, the regular 
 chord deflection of 6.98 ft. is used for EH. A stake is driven at each station 
 thus located. Although a chord deflection is not at right angles to the chord 
 theoretically, yet the deflection is so small, as compared with the length of the 
 chord, that for curves of ordinary degree it is usually measured at right angles. 
 
 Middle Ordinate. The middle ordinate of a chord is the ordinate to the 
 curve at the middle point of the chord. The following formulas give 
 the relation between the length of the chord c, the radius of the curve R, and 
 the middle ordinate m. 
 
 To Determine Degree of Curve From Middle Ordinate. It is sometimes 
 necessary to determine the radius or the degree of a curve in an existing track 
 when no transit' is available. By measuring the middle ordinate of any con- 
 venient chord, the degree of the curve can be calculated from the relative values 
 of the ordinate and chord. As the track is likely not to be in perfect aline- 
 ment, it is well to measure the middle ordinate of different chords in different 
 parts of the curve; also, as the middle ordinate of a chord measured to the 
 inner rail will somewhat exceed the middle ordinate of the same chord measured 
 to the outer rail, the ordinate of each chord should be measured to both rails 
 and the average of the two taken as the value of the ordinate. Having meas- 
 ured the middle ordinate of one or more chords, the degree of curve D e can be 
 found by the formula 
 
 _ _ 45,840w 
 
 De ~ ~&~ 
 
 The following rule is sometimes applied in determining the degree of curve: 
 
 Rule. Measure the middle ordinate to a chord of 67.71 ft.; express it in feet 
 
 and decimals of a foot, and multiply by 10; the result will be the degree of the curve. 
 
114 
 
 SURVEYING 
 
 Rules for Measuring the Radius of a Curve. Stretch a string, say 20 ft. 
 long, or longer if the curve is not a sharp one, across the curve corresponding 
 to the line from A to C, in Fig. 4. Then measure 
 from B the center of the line AC, and at right angles 
 with it, to the rail at D. Multiply the distance A to 
 B, or one-half the length of the string, in inches, by 
 B itself; measure the distance D to B in inches, and multi- 
 
 ply it by itself . Add these two products, and divide the 
 
 sum by twice the distance from B to D, measured 
 
 exactly in inches and fractional parts of inches. This will give the radius of 
 the curve in inches. 
 
 It may be more convenient to use a straightedge instead of a string. Care 
 must be taken to have the ends of the string or straightedge touch the same 
 part of the rail as is taken in measuring the distance from the center. If the 
 string touches the bottom of the rail flange at each end, and the center measure- 
 ment is made to the rail head, the result will not be correct. 
 
 In practice, it will be found best to make trials on different parts of the 
 curve, to allow for irregularities. 
 
 ILLUSTRATION. Let AC be a 20-ft. string; half the distance, or AB, is then 
 10 ft., or 120 in. Suppose BD is found on measurement to be 3 in. Then 120 
 X 120 =14,400, and 3X3 = 9; 14,400+9 = 14,409, which, divided by 2X3 = 6, 
 equals 2,401$ in., or 200 ft. 1J in., which is the radius of the curve. The 
 
 formula ^ = R, applied to the example is 
 
 2BD 
 
 12Q2+9 
 2X3 
 
 = 2,40Uin. = 
 
 1J in. 
 
 Other Ordinates. Any ordinate y to the curve at a distance a from the 
 middle point of a chord may be determined by means of the formula: 
 
 By using long chords, a curve may be laid out or obstacles passed by means 
 of ordinates. Suppose that it is required to run out the curve A EH, Fig. 5, 
 with several obstacles in the direct line of the curve, as shown, Sta. 3 being the 
 P. C., and the regular stations on the curve being in the positions indicated by 
 the numbers 4, 7, 8, etc. The positions of Stas. 5 and 6 are indicated by the 
 letters C and D. The stations are to be located in their proper positions on the 
 curve, between the obstructions, 
 wherever it is possible to do so. 
 In addition to this, it is customary 
 to mark with a tack or otherwise 
 the point where the line of the 
 curve intersects each obstruction. 
 
 Beginning at the point of / 
 
 curve A , which is at Sta. 3, the 
 curve can be run in as far as the 
 first obstruction, which is the 
 building P, setting the stakes on 
 the curve at Stas. 4 and 5, and 
 a tack in the side of the building 
 P at the point where the line of 
 curve intersects it, according to 
 the deflection angle as deter- 
 mined by its distance from Sta. 5. 
 It is not possible to proceed fur- 
 ther in the regular manner, how- 
 ever, because Sta. 6 cannot be 
 seen from the P. C. Therefore, 
 it is necessary to locate Sta. 7 by 
 deflection angle V'BE, from B or 
 Sta. 4, to determine the chord 
 4-7, which, in this case, is a long 
 chord of three stations, and to calculate the ordinates D'D and C'C by sub- 
 stituting for a in the preceding formula the value of MC = MD' = half a station 
 or 50 ft. ' 
 
 Fig. 5 shows also another method of passing a building S, namely by 
 running an equilateral triangle FLG. In this method, the instrument is set 
 3P *i a ;- 8 and S , lghte i back - to the P " C - Then ' the telescope is reversed and 
 the deflection angle for Sta. 9 is turned off the same as if no obstruction existed 
 
 FIG. 5 
 
SURVEYING 
 
 115 
 
 The telescope will then be sighted on the line FG, although the point G will not 
 be visible. The angle GFL, equal to 60, is then turned, and the point L is 
 located so that FL = FG = 100 ft. The instrument is next moved to L, and the 
 line LG is run, making 60 with FL. On this line the distance LG = 100 ft. is 
 measured, giving the point G, which is Sta. 9. The transit is then set up at this 
 point and sighted to L, and an angle of 60 is turned off to the right, giving the 
 direction of the line 9-8, the intersection of which with 5 is marked. The 
 remainder of the curve may be run in the following manner: Set the vernier 
 at an angle equal to the deflection angle of the chord 9-8 to the left from the 0; 
 clamp the upper plate, sight at the point set in the line 9-8; then clamp the 
 lower plate and set vernier at 0. The line of sight will then be in the tangent 
 at point 9, and by plunging the telescope the remainder of the curve can be 
 run as if the point 9 were the P. C. 
 
 FIELD NOTES FOR CURVES 
 
 Various styles of field notebooks are published, in which the pages are 
 ruled to suit the different kinds and methods of field work. The accompany- 
 ing, which are the field notes of a portion of a line containing a curve, represent 
 a good form for recording the field notes of a curve that is run in by the method 
 of zero tangent. 
 
 In the first column are recorded the station numbers; in the second column, 
 the deflections with the abbreviations P. C. and P. T., together with the degree 
 of curve and the abbreviation R or L, according as the line curves to the right 
 or left. At each transit point on the curve, the total or central angle from the 
 P. C. to that point is calculated and recorded in the third column. This total 
 angle is double the deflection angle between the P. C. and the transit point. In 
 
 these notes, there is but one intermediate transit point between the P. C. and 
 the P. T. The deflection from the P. C. at Sta. 3+20 to the intermediate 
 transit point at Sta. 4+50 is 2 36'. The total angle is double this deflection, 
 or 5 12', which is recorded on the same line in the third C9lumn. The record 
 of total angles at once indicates the stations at which transit points are placed. 
 The total angle at the P. T. will be the same as the angle of intersection, pro- 
 vided the work is correct. When the curve is finished, the transit is set up at 
 the P. T., and the bearing of the forward tangent taken, which affords an 
 additional check upon the previous calculations. The magnetic bearing is 
 recorded in the fourth column, and the deduced, or calculated, bearing is re- 
 corded in the fifth column. 
 
 EARTHWORK 
 
 Cuts and Fills. When building a railroad, cuts and fills are introduced 
 to equalize the irregularities of the natural soil. Figs. 1 and 2 show a typical 
 fill and cut in ordinary firm earth or gravel. 
 
 Slope Ratio. In cuts in the hardest rock, the average slope is made usually 
 1:1; that is, \ horizontal to 1 vertical. As the soil becomes less firm, the slope 
 must be flattened until, for a soil of firm earth or gravel, a slope of 1 to 1 may be 
 permissible, although a slope of \\:\ is commonly adopted. In very soft soil, 
 the slope ratio is sometimes cut down even as far as 4 horizontal to 1 vertical. 
 
116 
 
 SURVEYING 
 
 The standard practice in a fill is 1J horizontal to 1 vertical. When a fill is 
 made of the material from a rock cut, it is possible to make a stable embank- 
 ment with a slope ratio of 1:1. On side-hill work, where a slope ratio of 1^:1 
 or even 1:1 might require a very long slope, it is often advisable to make a rough 
 dry wall of the stones from a rock cut that will have a slope ratio of f :1, or it 
 may even be steeper. 
 
 FIG. 1 
 
 Width of Excavations and Embankments. The width required for a 
 standard-gauge single-track roadbed may be estimated as follows (see Figs. 1 
 and 2) : The tie will be between 8 and 9 ft. long, usually 8 ft. 6 in., and at the 
 ends the ballast will slope down to subgrade. The extra width required for 
 this will be about 1 or 2 ft. at each end of the tie. Usually, the embankment 
 is widened for about 2 ft. beyond the ballast on each side. The absolute 
 minimum for the width of subgrade for a fill is, therefore, 8|ft.+2X(l+2) ft. 
 = 14j ft. This width would be used only for light-traffic, cheaply constructed 
 roads; 16 to 18 ft. is far more common, while 20 ft. and even more is frequently 
 used, as the danger of accident due to a washing out of the embankment is 
 materially reduced by widening the roadbed. 
 
 In cuts, the proper width for two ditches should be added. Unless the 
 soil is especially firm, the ditches should have a side slope of 1 J:l. If the ditch 
 is 12 in. wide at the base and 12 in. deep, with side slopes of 1?:1, each ditch 
 will require a total width of 4 ft. This will add 8 ft. to the width of the cut at 
 the elevation of subgrade. The usual distance between track centers for 
 double track is 13 ft. Therefore, whatever rate of side slopes and width of 
 ditches is required for single-track work,, the width for double-track work must 
 be 13 ft. greater. When excavation is made through rock, the side slopes of 
 the ditches may properly be made much steeper; the danger of scouring during 
 heavy rain storms being eliminated, the total required width may be very 
 materially reduced from the figures just given. The heavy expense of excavat- 
 ing through solid rock requires that such economy shall be used if possible. 
 
 Grade Profile. For the purpose of constructing a road as well as for cal- 
 culating the earthwork, a grade profile is prepared by setting stakes on the 
 center line at every full station and also at all intermediate points at which the 
 inclination of the natural surface of the ground changes abruptly; then, by 
 leveling, the elevation of the natural surface at each stake is determined and 
 plotted, as explained under Leveling. The established grade is then drawn in. 
 
 FIG. 2 
 
 It consists of a series of straight lines, the elevations of the ends of which are 
 clearly indicated. These elevatipns are those of the subgrade ac. Figs. 1 and 2. 
 A short portion of a profile is shown in Fig. 3. The horizontal line XX' 
 represents a reference plane, and the broken line AGH shows the position of 
 the established grade. The station numbers are written along the line XX', 
 and the elevations of the corresponding points of the established grade are 
 
SURVEYING 
 
 117 
 
 written along the grade line. Thus, in Fig. 3, the elevation of subgrade at 
 Sta. 90, or A, is 100 ft.; at Sta. 93, or G, it is 102.28 ft.; and at Sta. 94, or H, 
 it is 101.78 ft. . 
 
 The gradient of the established grade is the per cent, of rise or fall of grade; 
 that is, the number of feet by which the elevation increases or decreases in 
 100 ft. It is usually marked on the grade line in the manner shown in Fig. 3. 
 
 The depth of center stake is the difference between the elevation of the 
 
 natural surface at any stake and the elevation of the subgrade. The eleva- 
 tion of the natural surface is found in the level notes, while the elevations of 
 the subgrade are computed from the gradients and also entered in the level 
 notes. The difference for each stake is then figured and entered in a column 
 headed Depth of Center Stake, being preceded by the letter C or F to indi- 
 cate cut or fill. 
 
 EXAMPLE. Stakes are set at the stations indicated in the first column of the 
 accompanying field notes. The gradient is +.76% from Sta. 90 to Sta. 93, 
 and -.50% beyond Sta. 93. The elevation of the established grade at Sta. 90 
 is 100 ft.; the elevation of the natural surface at each stake is given in the third 
 column. Find the center depth at each stake. (See Fig. 3.) 
 
 Station 
 
 Subgrade 
 
 Elevation 
 
 Depth of 
 Center Stake 
 
 94 
 
 101.8 
 
 102.6 
 
 C .8 
 
 93 
 
 102.3 
 
 103.3 
 
 C 1.0 
 
 92+51 
 
 101.9 
 
 97.3 
 
 F4.6 
 
 92 
 
 101.5 
 
 99.6 
 
 F 1.9 
 
 91+32 
 
 101.0 
 
 104.1 
 
 C3.1 
 
 91 
 
 100.8 
 
 103.2 
 
 C 2.4 
 
 90 
 
 100.0 
 
 100.0 
 
 
 
 SOLUTION. The elevations of the subgrade at the station stakes are deter- 
 mined as follows: 
 
 Station Elevation 
 
 91 
 91+32 
 
 92 
 92+51 
 
 93 
 
 94 
 
 100.00+1. 00 X 
 100.00+1. 32 X 
 100.00+2.00X 
 100.00+2.51 X 
 100.00+ 3.00 X 
 
 .76=100.8 
 .76 = 101.0 
 .76 = 101.5 
 .76=101.9 
 .76 = 102.3 
 
 102.28+ 1.00 X - .50 = 101.8 
 
 The center depth is the difference between the corresponding numbers in 
 the second and third columns. This is a fill if the subgrade is higher than 
 the natural surface; otherwise, it is a cut. 
 
 Slope Stakes. In addition to center stakes, slope stakes are used to mark 
 the points where the side slopes of a cut or a fill intersect the natural surface 
 of the ground. In Fig. 4, c is the center stake and m and m' are the slope 
 stakes. The method of locating slope stakes is as follows, all letters referring 
 to Fig. 4: 
 
 Let b be the width IV of the roadbed; d, the depth ceof the center stake; 
 and 5 the slope ratio = lk + mk = l'k' + m'k'. For the upper stake at m, let x 
 be the distance mq from the slope stake to the center line; y+d, the elevation 
 of m above the subgrade = qc+ce = mk. Similarly for the lower stake at m'. 
 
118 
 
 SURVEYING 
 
 let x f be the horizontal distance m'q' from m' to the center line, and let d-y' 
 -m'k', the elevation of m' above the subgrade. 
 
 Then, 
 
 and 
 
 (1) 
 (2) 
 
 If the natural surface mem' is a level line, so that q, c, and q' are at the 
 same elevation, then y = o, y' = o, and . 
 
 x = x' = ca = ca' = 2+sXd (3) 
 
 Formulas 1 and 2 are called slope-stake equations and formula 3 is called the 
 level-section equation. The last formula is available when the ground is nearly 
 level. When the ground is sloping or irregular formula 1 is employed, but 
 not directly as the value of y is not known until after the stake has been located. 
 The distance x or x' is determined by successive trials. Suppose, for example, 
 that in Fig 4 d = 6.3, and let the rod reading on the point c be 5.9. Suppose, 
 also,' that 5= 1.5 : 1 andfe = 20. Then, if the ground is level, by formula 3, 
 
 ac = 20 + 1.5X6.3 = 19.5 ft. 
 
 To find the location of m, the rodman will hold the rod at some point more 
 than 19.5 ft. from cr. Suppose that he holds it at , 20 ft from cr, and that the 
 
 reading on the 
 rod in this po- 
 sition is 2.8. 
 Then, the height 
 of this point 
 above c equals 
 the reading on c 
 
 /~n minus the read- 
 
 ing' on n, or 5.9 
 - 2.8 = 3.1 ft. 
 The computed 
 distance from 
 the rod to cr is, 
 by formula 1, 
 + 1.5 X 6.3 
 + 1.5 X 3.1 
 = 24.2 ft. As 
 the measured 
 distance (20 ft.) 
 is much smaller 
 than this, the 
 rod must be 
 moved much 
 farther out. 
 
 Suppose that 
 the rod is car- 
 ried out 7 ft. so that the measured distance to cr is 27 ft., and suppose that 
 the reading on the rod in this position is .8 ft. The elevation of this trial point 
 above c will be 5.9 .8 = 5.1 ft., and by formula 1, the computed distance x 
 is +1-5X6.3+1.5X5.1 = 27.2 ft. This agrees so closely with the measured 
 distance that the slope stake may be driven at this point. 
 
 The lower slope stake at m' is set in the same manner as the upper, except 
 that the distance of each trial point below c is measured, and formula 2 is used 
 in computing the corresponding value of *'. The distance of the trial point 
 from cr will in this case be taken less than the distance ca' computed by for- 
 mula 3. As in the preceding case, if the measured distance from cr to the trial 
 point is less than the computed distance, the point should be moved out; if 
 greater, it should be moved in. 
 
 Form of Notes in Cross-Section Work. When each slope stake has been 
 set as just explained, its distance from the center line and the elevation of the 
 stake above or below subgrade are entered in the field book in the form of a 
 fraction. The numerator of this fraction is the distance of the stake above 
 or below subgrade, and the denominator is the distance of the stake from the 
 center line. Thus, if the slope stakes in the preceding example are set at 
 Sta. 131, the complete entry in the notebook will be as follows: 
 
SURVEYING 
 
 119 
 
 Station 
 
 Subgrade 
 
 Elevation 
 
 Center 
 Depth 
 
 Left 
 
 Right 
 
 132 
 131 
 130 
 
 149.80 
 148.80 
 147.80 
 
 159.7 
 155.1 
 147.2 
 
 C9.9 
 C6.3 
 F .6 
 
 C11.4 
 
 C2.3 
 
 27.2 
 
 13.5 
 
 The fraction y' indicates that the left slope stake at m. Fig. 4, is 27.2 ft. 
 
 from the center line of the roadbed and 11.4 ft. above subgrade. Similarly, the 
 
 (~*2 ^ 
 fraction -r~ indicates that the right slope stake m' is 13.5 ft. to the right of the 
 
 center line and 2.3 ft. above subgrade. These expressions are called slope- 
 stake fractions. 
 
 When the ground between the slope stakes and the center stake is irregular, 
 the elevations and distances from the center of the intermediate points where 
 the ground changes abruptly are determined and also entered in the notebook 
 in the form of fractions. 
 
 RAILROAD LOCATION 
 
 The preliminary survey is made by the methods given, a random line being 
 run along the proposed route and a map of the region made covering several 
 hundred feet on each side of the traverse. The map should show both banks of 
 any streams and enough levels should be taken to show the contours within 
 the width covered by the map. This width will depend on the nature of the 
 ground, being less in hilly than in flat country. In general, the map should 
 cover the ground from the toe of one side hill to the toe of the other and should 
 extend a distance up each hill to an elevation beyond which it would not be 
 practicable to make a cut. After this preliminary line has been mapped, a 
 preliminary estimate of the cost of the proposed work may be made. 
 
 Preliminary Estimate. When making a preliminary estimate, great accu- 
 racy is not necessary, and no time should be wasted in useless refinements of 
 calculation. The estimate should be high enough to cover all probable cost, 
 and a liberal allowance should be made to cover unforeseen contingencies that 
 may develop during construction. Most experienced engineers make it a rule 
 to add 10% to a preliminary estimate in order to provide for contingencies. 
 
 When estimating for earthwork, the cross-sections may be considered as 
 level cuttings; that is, the cross-section surface may be considered as level, 
 unless its slope angle exceeds 10, in which case a suitable allowance must be 
 made for the slope. The preliminary estimate, which also includes approxi- 
 mate figures for material and labor required for culverts, bridges, trestles, 
 piers, and abutments is then classified and summarized. A sample of a good 
 form of a preliminary estimate of the cost of a proposed railroad follows: 
 
 ESTIMATE OF COST A & B RAILROAD 
 
 Clearing 625 A. at $20 per A $ 12,500 
 
 Earth excavation: 900,000 cu. yd. at 17c 153,000 
 
 Loose-rock excavation: 300,000 cu. yd. at 40c 120,000 
 
 Solid-rock excavation: 200,000 cu. yd. at 80c 160,000 
 
 Overhaul exceeding 600 ft.: 300,000 cu. yd. at lc.. . 
 
 Borrowed embankment: 80,000 cu. yd. at 17c 
 
 Piling: 12,000 lin. ft. at 25c 
 
 Framed trestles: 300,000 ft. B. M. at $35 per M.. 
 
 First-class masonry: 2,800 cu. yd. at $12 
 
 Second-class masonry: 4,200 cu. yd. at $8 
 
 Box culvert masonry: 2,300 cu. yd. at $5 
 
 Dry-rubble masonry: 2,600 cu. yd. at $4 
 
 Concrete masonry: 3,000 cu. yd. at $6 
 
 Riprap: 2,000 sq. yd. at $1.50 
 
 Cast-iron pipe culverts: 40,000 Ib. at 3c 
 
 Vitrified pipe culverts: 1,800 lin. ft. at $1.50 
 
 Total, exclusive of bridges and track 
 
 Add 10 per cent 
 
 3,000 
 13,600 
 3,000 
 10,500 
 33,600 
 33.600 
 11,500 
 10,400 
 18,000 
 3,000 
 1,200 
 2,700 
 $589,600 
 58,960 
 Total cost for grading and trestles $648,560 
 
120 
 
 SURVEYING 
 
 Location. The location is the operation of fitting the line to the ground 
 in such a manner as to secure the best adjustment of the almement and grade, 
 
 consistent with an economical 
 cost of construction. It is then 
 best projected on the map, and 
 it is called a paper location. 
 
 An example of such location 
 is illustrated in Fig. 1. Here, 
 the line follows the valley of 
 Bear River, and the gradient 
 is determined by the slope of 
 the stream. The gradient 
 adopted is .5%, or .5 ft. per 
 station. The preliminary line 
 is shown dotted, and the located 
 line is drawn full. 
 
 Let the grade elevation for 
 Sta. 16 be 155 ft.; the grade ele- 
 vation for Sta. 17 will, there 
 fore, be 155 ft. + .5 ft. = 155.5 ft. 
 The grade elevation for Sta. 18 
 will be 155.5+.5 = 156 ft. By 
 the same process, the grade 
 elevation is found for each sta- 
 tion shown in the plat; and by 
 means of interpolation between 
 two contour curves, points 
 having the required elevation 
 are located opposite the corre- 
 sponding stations of the pre- 
 liminary survey. Each point 
 is marked by a small dot en- 
 closed in a circle. A line join- 
 
 ing the points thus designated 
 will be the grade contour, or the 
 
 FIG. 1 
 
 line where the required gradient 
 meets the surface of the ground. 
 The tangents AB and CD are 
 then projected so as to conform 
 as closely as practicable to the grade contour, and a suitable curve is inserted 
 for the intersection angle EFD. This is most conveniently done by means of 
 a curved protractor, an illustration of which is shown in Fig. 2. This instru- 
 ment, which is made of transparent material, is shifted until there is found a 
 curve that will fit the topography and will close the angle between the tangents, 
 as required. 
 
 Curvature. There is no fixed rule for limiting curvature, but for a per- 
 manent track it is desirable to have the curvature as easy as possible. For 
 all ordinary 
 traffic condi- 
 tions, it is good 
 practice to use 
 such curves as 
 will best C9n- 
 form to existing 
 topographical 
 conditions. Any 
 curve up to 10 
 will be no ob- 
 stacle to a speed 
 of 35 mi. per hr. f 
 the average 
 speed of passen- 
 ger trains. This 
 practice will af- 
 ford a range in FIG. 2 
 curvature that will meet the requirements of almost any locality. 
 . Compensation for Curvature. The effect of curvature on a railroad line 
 18 to cause a resistance to the movement of trains. When a curve occurs on a 
 
SURVEYING 
 
 121 
 
 gradient, the effect of the curve resistance on ascending trains is practically 
 the same as increasing the gradient. It is customary, when fixing the final 
 grades, to lighten the grade on a curve by an amount sufficient to offset the resis- 
 tance due to the curvature. This operation is called compensating for curvature. 
 The usual rate of compensation for curvature is .03 to .05 ft. per 100 ft. per 
 degree of curvature. For example, where the maximum gradient on tangents 
 is 1%, the maximum gradient on a 6 curve, allowing a compensation of .03 ft. 
 
 r degree, would be 1- (.03X6) = .82%. 
 a compensation of .05 ft. per degree 
 were made, the grade on a 6 curve would 
 be 1- (.05X6) = .70%. 
 
 Final Grade Lines. The establishing 
 of final grade lines is illustrated in Fig. 3, 
 where the uncompensated grade is 1.3%, 
 and the compensation for curvature, as 
 shown on the final grade line, is .03 ft. per 
 degree. The location notes for this line are 
 as given on page 122. 
 
 The elevation of the grade at Sta. 27 is 
 fixed at 120 ft., and at Sta. 52, at 152.5 ft., 
 giving between these stations an actual rise 
 of 32.5 ft. and an uncompensated grade of 
 1.3%. These grade points are marked on 
 the profile with small circles. The total 
 curvature between Sta. 27 and Sta. 52 is 
 108|. The resistance due to each degree 
 of curvature being taken as equivalent to 
 an increase of .03 ft. in grade, the total 
 resistance due to 108.5 is equivalent to 
 .03X108.5 = 3.255 ft. additional rise be- 
 tween Sta. 27 and Sta. 52. Hence, the 
 total theoretical grade between these sta- 
 tions is the sum of 32.5 ft., the actual 
 rise, and 3.255 ft. due to curvature, or 40 
 35.755 ft. Dividing 35.755 by 25, the num- 
 ber of stations in the given distance, there 
 results 35.755 -r- 25 =+1.4302 ft., as the 
 grade for tangents on this line. The 
 starting point of this grade is at Sta. 27. 
 The P. C. of the first curve is at Sta. 29, 
 giving a tangent of 200 ft. which is equal to 
 two stations. As the grade for tangents is 
 + 1.4302 ft. per station, the rise in grade 
 between Sta. 27 and Sta. 29 is 1.4302X2 
 = 2.8604 ft. The elevation of grade at 
 Sta. 27 is 120 ft., and the elevation of grade 
 at Sta. 29 is 120+2.8604 = 122.8604 ft. 
 which is recorded on the profile as shown in 
 the diagram, with the rate of grade, namely, 
 + 1.4302, written above the grade line. 
 The first curve is 8, and, as the compen- 
 sation per degree is .03 ft., then, for 8, and 
 a full station, the compensation is .03X8 
 = .24 ft. The grade on the curve will 
 therefore be the tangent grade minus the 
 compensation, or 1.4302 - .24 = +1.1902 ft. 
 per station. The P. C. of this curve is 
 at Sta. 29, the P. T. at Sta. 33, making 
 the total length of the curve 400 ft. or 
 four stations. The grade on this curve is 
 
 FIG. 3 
 
 + 1.1902 ft. per station and the total rise on the curve is 1.1902X4 = 4.7608 ft. 
 The elevation of the grade at the P. C. at Sta. 29 is 122.8604; hence, the 
 elevation of grade at the P. T. at Sta. 33 is 122.8604+4.7608 = 127.6212 ft., 
 which is recorded on the profile together with the grade, namely, +1.1902, 
 written above the grade line. The P. C. of the next curve is at Sta. 37+50, 
 giving an intermediate tangent of 450 ft., or four and one-half stations. The 
 grade for tangents is +1.4302 ft. per station; hence, the total rise on the tan- 
 gent is 1.4302X4.5 = 6.4359 ft. Adding 6.4359 ft., to 127.6212 ft., the elevation 
 
122 SURVEYING 
 
 of grade at Sta. 37+50 is found to be 134.0571 ft., which is recorded on the 
 profile, together with the rate of grade for tangents. 
 LOCATION NOTES 
 
 
 
 52+00 
 
 End of Grade 
 
 49 + 75 P. T. 
 
 
 44+25 P. C. 9 R. 
 
 49 30' 
 
 42+00 P. T. 
 
 
 37+50 P. C. 6 L. 
 
 27 00' 
 
 33+00 P. T. 
 
 
 29+00 P. C. 8 R. 
 
 32 00' 
 
 27+00 
 
 Beginning of grade 
 
 The next curve is 6, and the compensation in grade per station is .03 ft. 
 X6 = .18 ft. The grade on this curve will therefore be 1.4302 .18= 1.2502 ft. 
 per station. The length of the curve is 450 ft., or four and one-half stations, 
 and the total rise in grade on this curve is +1.2502 ft. X 4.5 = 5.6259 ft. The 
 elevation of the grade at Sta. 37+50, the P. C. of the curve, is 134.0571. The 
 elevation of the grade at Sta. 42, the P. T., is therefore 134.0571 + 5.6259 
 = 139.683 ft., which is recorded on the profile, together with the rate of grade 
 on the 6 curve, namely, +1.2502. The P. C. of the next curve is at Sta. 44 
 +25, giving an intermediate tangent of 225 ft., or two and one-fourth stations, 
 The total rise on the tangent is, therefore, 1.4302X2.25 = 3.21795 ft. The 
 elevation of grade at the P. T. at Sta. 42 is 139.683; therefore, the elevation of 
 grade at Sta. 44+25 is 139.683+3.21795= 142.90095 ft., which is recorded on 
 the profile, together with the grade +1.4302. 
 
 The last curve is 9, and the compensation in grade per station is .03X9 
 = .27 ft. The grade on this curve is therefore, 1.4302 -.27 = 1.1602 ft. per 
 station. The length of the curve is 550 ft., or five and one-half stations, and 
 the total rise on the curve is 1.1602X5.5 = 6.3811 ft. The elevation of grade 
 at Sta. 44+25, the P. C. of the 9 curve, is 142.90095; hence, the elevation of 
 grade at the P. T., at Sta. 49 + 75, is 142.90095+6.3811 = 149.28205 ft., which is 
 recorded on the profile, together with the grade, +1.1602. The end of the 
 line is at Sta. 52, giving a tangent of 225 ft., or two and one-fourth stations. 
 The rise on this tangent is 1.4302X2.25 = 3.21795 ft., which is added to 
 149.28205, the elevation of the P. T. at Sta. 49 + 75. The sum, 152.5 ft., is 
 the elevation of grade at Sta. 52. 
 
 The sum of the partial grades should equal the total rise between the 
 extremities of the grade line. The points where the changes of grade occur 
 are marked on the profile with small circles, which are connected by fine lines 
 representing the grade line. These points of change are projected on a hori- 
 zontal line at the bottom of the profile. The portions of this line that represent 
 curves are dotted, and the portions that represent tangents are drawn full. 
 The P. C. and P. T. of each curve are marked with small circles on this 
 horizontal line, and are lettered as shown in the diagram. 
 
 Where the grades are light and the curves have large radii, there will be no 
 need of compensation for curvature. Where the grades exceed .5% and the 
 curves 5, compensation should be made. 
 
 VERTICAL CURVES 
 
 If the grade of the center line of track changes at any point, the two 
 grade lines that intersect at this point form with each other an angle more or 
 less abrupt. If this angle points upwards, it is called a spur; if it points down- 
 wards, it is called a sag. The angles CVD in Fig. 1 (a) and (b) are spurs; the 
 angles CVD in Fig. 2 (a) and (b) are sags. 
 
 Vertical Curve at a Spur. If AV and BV, Fig. 3, are two grade lines 
 meeting at V, a vertical curve CM D must be introduced to join these lines. 
 
SURVEYING 
 
 123 
 
 Between C and D, the actual grade is established along the vertical curve CM D, 
 instead of along CV and VD. The projections RT and TS of the distances VC 
 and VD from the vertex to the points at which the vertical curve begins and 
 
 fb) 
 
 FIG. 2 
 
 ends are always chosen equal. If K is the middle point of the straight line CD, 
 the vertical curve is always so chosen that it will bisect VK\ that is, so that 
 VM^MK. 
 
 Let E be the elevation of C, Fig. 3, E' that of D, and H that of V, so that E 
 - RC, E' = SD, and ff = VT. Then, 
 
 The distance FM is called the correction in grade at the point V. 
 Vertical curves are always made parabolic. It is a property of the parabola 
 that the correction in grade am at any point a is given by the equation. 
 
 The distance CV= VD is always made a whole number of stations; and, to 
 simplify the work, the grade stakes a, b, c, etc., are so set that they divide the 
 distance CV into a 
 number of equal 
 parts. The correc- 
 tions in grade at 
 points a', b', and c' 
 along DV are equal 
 to those for the cor- 
 responding points 
 along CV. That is, 
 if Ca = Da', then 
 am a'm' ; if Cb 
 *=Db r , then bm 
 = b'm',etc. 
 
 EXAMPLE. A 
 + .4% grade meets 
 
 FIG. 3 
 
 .5% grade at Sta. 190, the elevation of which is 161.3 ft. If a vertical 
 curve 400 ft. long is inserted, what is the correction in grade and the corrected 
 grade elevation at each station and half station? 
 
 SOLUTION. In this example, VC = VD = 200 ft. The elevation of C is 161.3 
 -2X. 4 = 160.5 ft., = E; that of D is 161.3 -2X. 5 = 160.3 ft., = E'; that of K 
 is * (E'+E) = *X (160.5 + 160.3) = 160.4 ft.; and that of V is H = 161.3 ft. 
 Substituting these values in the formula for VM, 
 
 = $X (161.3 - 160.4) = .45 ft. 
 Since, for the first stake, Ca = 50 ft. and CF 
 
 . 200 ft., the formula for am 
 
 gives am = (? a )*X VM = T ^X .45 = .03 ft. = a'm' 
 
 Similarly, bm= (M8) 2 XFM = iX.45 = .ll = 6'm' 
 
 cm = (ifcjj)* X VM = ft X .45 = .25 = c'm' 
 The original and corrected grade elevations are as follows: 
 
 Station 
 
 188 
 + 50 
 
 189 
 + 50 
 
 190 
 +50 
 
 191 
 +0 
 
 192 
 
 Original 
 Elevation 
 160.50 
 160.70 
 160.90 
 161.10 
 161.30 
 161.05 
 160.80 
 160.55 
 160.30 
 
 Correction 
 
 .00 
 .03 
 .11 
 .25 
 .45 
 .25 
 .11 
 .03 
 .00 
 
 Corrected 
 Elevation 
 160.50 
 160.67 
 160.79 
 160.85 
 160.85 
 160.80 
 160.69 
 160.52 
 160.30 
 
12 4 SURVEYING 
 
 Vertical Curve at a Sag. If two grade lines, AV and VB Fig. 4, meet so 
 as to form a sag, the vertical curve will evidently be wholly above both 
 grade lines. Using the same notation as before, the correction m grade at the 
 
 B point V will be 
 
 The correction 
 in the grade at any 
 point a will be given 
 by the preceding 
 formula for am, as 
 
 Datum Plane ^ before. This cor- 
 
 . rection, however, is 
 
 FlG - 4 now to be added 
 
 to the old elevation of the grade at a to obtain the corrected elevation. 
 EXAMPLE. The grade of CV, Fig. 4, is- 1.2%, that of VD is +.6%, and 
 the elevation of V is'+49.2 ft. Find the corrections in grade and the corrected 
 elevations at stakes 100 ft. apart, if the length of the vertical curve is 600 ft. 
 SOLUTION. The unconnected grade elevations are as follows: 
 Along CV Along VD 
 
 At first stake. 52.8 At fifth stake 49.8 
 
 At second stake 51.6 At sixth stake 50.4 
 
 At third stake 50.4 At seventh stake, D 51.0 
 
 At fourth stake, V 49.2 
 
 Therefore. i(E+E') = *X (52.8+51.0) = 51.9; 
 
 and, by the preceding formula, 
 
 VM = |X (51.9-49.2) = 1.35 ft. 
 
 The formula for am may now be applied. Correction in grade at second 
 stake, 100 ft. from C, is (i) 2 X 1.35 = 4X1.35=-. 15, correction at sixth stake. 
 Correction at third stake, (gg) 2 X 1.35 = |X 1.35 = .60, correction at fifth stake. 
 The corrected elevations will be 
 
 At C 52.80+ .00 = 52.80 
 
 At second stake 51.60+ .15 = 51.75 
 
 At third stake 50.40+ .60 = 51.00 
 
 At fourth stake 49.20+1.35 = 50.55 
 
 At fifth stake 49.80+ .60 = 50.40 
 
 At sixth stake 50.40+ .15 = 50.55 
 
 At D 51.00+ .00 = 51.00 
 
 CURVED TRACK 
 
 The difference in length between the inner and the outer rail of a standard- 
 gauge curve may be found by either of the following rules: 
 
 Rule I. Multiply the Degree of the curve by the length, in stations of 100 //., 
 and this product by l&; the result will be the difference in length between the 
 inner and the outer rail, in inches. 
 
 Rule II. Multiply the distance between the center lines of the rails by the 
 length of the curve, in feet, and divide the product by the radius of the track curve; 
 the quotient will be the required difference in length, expressed in feet. 
 
 For light curves laid to exact gauge, the first rule is the simpler one, but for 
 short curves where the gauge is widened, the second rule should be used. 
 
 Curving Rails. When laying track on curves, in order to have a smooth 
 line, the rails themselves must conform to the curve of the center line. To 
 accomplish this, the rails must be curved. The curving should be done with 
 a rail bender or with a lever, preferably with the former. To guide those in 
 charge of this work, a table of middle and quarter ordinates for a 30-ft. rail for all 
 degrees of curve should be prepared. The middle ordinates in the following 
 table are calculated by the formula 
 
 in which m = middle ordinate; 
 
 c = length of chord, assumed to be of same length as rail; 
 R = radius of curve. 
 
 This formula is not theoretically correct; yet the error is so small that it 
 may be ignored in practical work. 
 
SURVEYING 
 
 125 
 
 In curving rails, the ordinate is measured by stretching a cord from end to 
 end of the rail against the gauge side, as shown in the accompanying illustra- 
 tion. Suppose the rail AB is 30 ft. in 
 length, and the curve 8, then the mid- 
 dle ordinate at a should be 
 
 To insure a uniform curve to the rails, the ordinates at the quarter points b 
 and b' should be tested. In all cases the quarter ordinates should be three- 
 quarters of the middle ordinate. In the illustration, if the rail has been properly 
 curved, the quarter ordinates at b' and b will be f X If in. = IJf, say If. 
 
 MIDDLE ORDINATES FOR CURVING RAILS 
 
 Degree of 
 Curve 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 30 
 
 Length of Rail, in Feet 
 
 28 
 
 26 
 
 24 
 
 22 
 
 Middle Ordinates, in Inches 
 
 j. 6 
 
 I! 
 
 20 
 
 TURNOUTS 
 
 A turnout is a contrivance for passing from one track to another. The 
 principal parts are the switch, the frog, and two guard-rails. The switch, 
 which is the movable part of the turnout, consists of two switch rails BA and 
 CD, Fig. 1. The fixed ends B and C of the switch rails are called the heels of 
 the switch, and the movable ends A and D, the toes of the switch. The cross- 
 tie that supports the toes of the switch is called the head-block, and the tie- 
 rod at the toes, the head-rod. The distance A A' or DD' through which the 
 toes move is called the throw of the switch. A frog is shown at K and two 
 guard-rails at R and R'. 
 
 Switches. There are two kinds of switches, which differ in the arrange- 
 ment and form of switch rails, namely, the stub switch and the point switch. 
 In the stub switch, Fig. 1, a part of each main-track rail is bent over to connect 
 with the side track. In the point switch, Fig. 2, the outer rail DV of the main 
 track is spiked rigidly to the ties; the opposite rail EA'U, lying partly in the 
 main track and partly in the side track, is also firmly spiked. These two rails 
 are immovable. The two switch rails BA and CD are planed to thin edges at A 
 and D. The ends B and C of these rails are the fixed ends or heels; the thin 
 edges at A and D are the toes. The head-block is at H, and the head-rod at g. 
 
126 
 
 SURVEYING 
 
 The point of the center line at which the turnout begins is called the point 
 of switch In Figs. 1 and 2, W is the point of switch. In stub switches, the 
 point of switch is midway between the heels; in point switches, 
 it is midway between the toes and 
 above the head-block. 
 
 Frogs and Guard-Rails. A frog is 
 a combination of rails so arranged that 
 the broad tread of the wheel will 
 always have a surface on which to 
 roll, and that the flange of the wheel 
 will have a channel through which to 
 pass. A frog is shown in position on 
 the track at K, Fig. 1, and a larger plan 
 of the part at ab, Figs. 1 and 2, is shown 
 in Fig. 3. 
 
 The wedge-shaped part akb of the 
 frog is called the tongue of the frog, 
 and its point k is called the actual 
 point of frog. The actual point of frog 
 is somewhat shortened and rounded. 
 The intersection c of the outside edges 
 ac and be of the tongue is called the 
 theoretical point of frog. When the 
 point of frog is referred to, the theo- 
 retical point is usually meant. The 
 bent rails wr are called wing rails; the 
 narrowest part mp of the frog is called 
 the throat. The throat of the frog 
 must be wide enough to allow the 
 flanges of the wheels to pass through; 
 it is usually made about 2 in. wide. 
 
 Frog Angle and Frog Number. The 
 angle acb, Fig. 3, between the outside 
 
 E 
 
 FIG. 1 
 edges of the tongue of theTrog is called the frog angle. 
 
 If 
 
 FIG. 2 
 This is also equal to the 
 
 angle dee between the outside edges of the tongue produced beyond c.' The frog 
 angle which is represented by F is also equal to the angle between the two 
 tracks. 
 
 The distance ab between the gauge lines at the end of the tongue is called 
 the heel width; the distance de, the mouth width. If sch is the bisector of the 
 angle F, the distance ch is called the length of frog. 
 
 The ratio of the length to the heel width is called the frog number, and is 
 usually denoted by n; that is, 
 
 n = ch -r- ab 
 
 The relation between n and F is expressed by the formulas 
 
 and 
 
 cotF = 
 
 FIG. 3 
 
 Frogs are usually designated by their numbers; thus, a No. 8 frog is one 
 in which n = 8. 
 
 If the distance sh and the widths ab and de, Fig. 3, are measured on a frog, 
 the frog number n can be determined by the formula 
 
 sh 
 n ~ab+de 
 
SURVEYING 
 
 127 
 
 Guard-Rails. Guard-rails, which are usually from 10 to 15 ft. long, are 
 placed opposite the frog on the main track and the switch track, as at R 
 and R' in Figs. 1 and 2. The clear 
 space between the head of the guard-rail 
 and the head of the main or the switch 
 rail should be about 2 in. 
 
 Radius and Lead of a Turnout for 
 Stub Switches. Let RN, Fig. 4, be the 
 main track and QP the turnout. Let 
 Q be the point of switch and K the point 
 of frog. If a stub switch is employed, 
 the main-track rails will be securely 
 spiked along YB and LD\ the parts BG 
 and DV of these rails will be movable, 
 so that they may be bent outwards to 
 meet the turnout rails W and Z. Here, 
 then, the ends B and D are the heels 
 of the switch, and G and V are the toes. 
 The head-block is underneath G and V. 
 
 In order to lay out a turnout when 
 the frog angle is given, it is necessary 
 to find the radius r, in terms of the frog 
 angle, and the distance KB from the 
 point of frog to the heel of switch, which distance is called the lead and is desig- 
 nated by L. 
 
 The formulas for r and L are: 
 
 r=i g cot 2 JF = 2gn s 
 and L= g cot \F 
 
 In these formulas g denotes the gauge. 
 8| in. = 4.708 ft. 
 
 The accompanying table, some parts of which are calculated from the fore- 
 going formulas, can be used in laying out a turnout with a stub switch. The 
 
 FIG. 4 
 
 R L 
 
 The standard gauge of track is 4 ft. 
 
 DIMENSIONS OF STUB-SWITCH TURNOUTS 
 
 Track Circular From Heel of Switch to Point of Frog. Throw = 5f In. 
 
 Frog 
 Num- 
 ber 
 n 
 
 Frog Angle F 
 
 LeadL 
 
 Chord 
 (QT) 
 
 Radius 
 
 Degree 
 of 
 Curve 
 d 
 
 Length 
 of 
 Switch 
 Rails 
 
 Dis- 
 tance 
 Ka, 
 Fig.l 
 
 4.0 
 
 14 15' 00" 
 
 37.67 
 
 37.38 
 
 150.67 
 
 38 46' 
 
 11.73 
 
 1.50 
 
 4.5 
 
 12 40 59 
 
 42.37 
 
 42.12 
 
 190.69 
 
 30 24 
 
 13.19 
 
 1.69 
 
 5.0 
 
 11 25 16 
 
 47.08 
 
 46.85 
 
 235.42 
 
 24 32 
 
 14.65 
 
 1.87 
 
 5.5 
 
 10 23 20 
 
 51.79 
 
 51.58 
 
 284.85 
 
 20 13 
 
 16.15 
 
 2.06 
 
 6.0 
 
 9 31 38 
 
 56.50 
 
 56.30 
 
 339.00 
 
 16 58 
 
 17.64 
 
 2.25 
 
 6.5 
 
 8 47 51 
 
 61.21 
 
 61.03 
 
 397.85 
 
 14 26 
 
 19.09 
 
 2.44 
 
 7.0 
 
 8 10 16 
 
 65.92 
 
 65.75 
 
 461.42 
 
 12 26 
 
 20.53 
 
 2.62 
 
 7.5 
 
 7 37 41 
 
 70.62 
 
 70.47 
 
 529.69 
 
 10 50 
 
 22.03 
 
 2.81 
 
 8.0 
 
 7 9 10 
 
 75.33 
 
 75.19 
 
 602.67 
 
 9 31 
 
 23.48 
 
 3.00 
 
 8.5 
 
 6 43 59 
 
 80.04 
 
 79.90 
 
 680.36 
 
 8 26 
 
 24.93 
 
 3.19 
 
 9.0 
 
 6 21 35 
 
 84.75 
 
 84.62 
 
 762.75 
 
 7 31 
 
 26.43 
 
 3.37 
 
 9.5 
 
 6 1 32 
 
 89.46 
 
 89.33 
 
 849.85 
 
 6 45 
 
 27.97 
 
 3.56 
 
 10.0 
 
 5 43 29 
 
 94.17 
 
 94.05 
 
 941.67 
 
 6 05 
 
 29.37 
 
 3.75 
 
 10.5 
 
 5 27 9 
 
 98.87 
 
 98.76 
 
 1,038.19 
 
 5 32 
 
 30.85 
 
 3.94 
 
 11.0 
 
 5 12 18 
 
 103.58 
 
 103.47 
 
 1,139.42 
 
 5 02 
 
 32.31 
 
 4.12 
 
 11.5 
 
 4 58 45 
 
 108.29 
 
 108.19 
 
 1,245.36 
 
 4 36 
 
 33.78 
 
 4.31 
 
 12.0 
 
 4 46 19 
 
 113.00 
 
 112.90 
 
 1.356.00 
 
 4 14 
 
 35.17 
 
 4.50 
 
 frog number, which is usually given, is stated in the first column; the corre- 
 sponding frog angle in the second column; and the lead, or BK, Fig. 4, in the 
 third column. Then follow columns containing the chord QT, Fig. 4, which is 
 
128 
 
 SURVEYING 
 
 equal to 2r sin F; the radius of the turnout; the corresponding degree of curve 
 which is equal to 5iZi9 ; the length I of switch rails A B, Fig. 1, obtained by the 
 
 formula 1= V*(2r <); and the distance Ka, Fig. 1, or cw, Fig. 3, With dif- 
 ferent forms of frogs, this distance varies; the engineer should therefore measure 
 
 it for the different frogs he uses, as it 
 is necessary in determining the length 
 of spiked rail Aa, Fig. 1. 
 
 Turnout Dimensions for Point 
 Switches. Let MN, Fig. 5, be the 
 center line of the main track and MJ 
 that of the turnout. Let BA and CD 
 be the two switch rails whose fixed 
 ends, or heels, are at B and C, and 
 whose toes are at A and D. These 
 rails are usually of a uniform length 
 of 15 ft., except for the sharpest 
 curves. 
 
 The center line MIJ will, when a 
 point switch is used, have a some- 
 what different position from that 
 which it has when a stub switch is 
 employed. In the stub-switch turn- 
 out, the rails A'TU and DCK are 
 bent to a uniform curve between M 
 and J; in a point switch, the outer rail is made up of a straight part DC, 
 which is the switch rail, and a curved part CE, which is tangent to DC 
 at C. On this account, the lead A'K is less with a point switch than with a 
 
 DIMENSIONS OF POINT-SWITCH TURNOUTS 
 
 Turnouts With Straight Point Rails and Straight Frog Rails; 
 Gauge 4 Ft. 8^. In. 
 
 FIG. 5 
 
 
 
 to 
 
 
 
 
 
 
 
 g 
 
 t_. 
 
 ^ 
 
 fc 
 
 K) 
 
 ^ 
 
 "o-a 
 
 CJ" 
 
 -t-i ^ 
 
 O ctf 
 
 ^.S^ 
 
 q 
 
 to 
 
 fee 
 
 & 
 
 1 
 
 ]! 
 
 a 
 
 3 
 
 rt 
 M 
 
 11 
 
 1 
 
 o 
 
 |J3 
 
 O5 
 
 !i| 
 
 4.0 
 
 14 15' 00" 
 
 3 40' 
 
 32.20 
 
 125.21 
 
 47 05' 
 
 23.09 
 
 7.5 
 
 1.50 
 
 4.5 
 
 12 40 49 
 
 3 40 
 
 34.29 
 
 159.25 
 
 36 36 
 
 25.03 
 
 7.5 
 
 1.69 
 
 5.0 
 
 11 25 16 
 
 2 45 
 
 41.85 
 
 197.65 
 
 29 22 
 
 29.88 
 
 10.0 
 
 1.87 
 
 5.5 
 
 10 23 20 
 
 2 45 
 
 44.16 
 
 240.44 
 
 24 00 
 
 32.03 
 
 10.0 
 
 2.06 
 
 6.0 
 
 9 31 39 
 
 1 50 
 
 56.00 
 
 288.09 
 
 19 59 
 
 38.66 
 
 15.0 
 
 2.25 
 
 6.5 
 
 8 47 51 
 
 1 50 
 
 58.84 
 
 340.19 
 
 16 54 
 
 41.34 
 
 15.0 
 
 2.44 
 
 7.0 
 
 8 10 16 
 
 1 50 
 
 61.65 
 
 397.65 
 
 14 27 
 
 43.98 
 
 15.0 
 
 2.62 
 
 7.5 
 
 7 37 41 
 
 1 50 
 
 64.36 
 
 460.00 
 
 12 29 
 
 46.50 
 
 15.0 
 
 2.81 
 
 8.0 
 
 7 9 10 
 
 50 
 
 67.04 
 
 527.91 
 
 10 52 
 
 48.99 
 
 15.0 
 
 3.00 
 
 8.5 
 
 6 43 59 
 
 50 
 
 69.60 
 
 600.94 
 
 9 33 
 
 51.38 
 
 15.0 
 
 3.19 
 
 9.0 
 
 6 21 35 
 
 50 
 
 72.20 
 
 681.16 
 
 8 25 
 
 53.80 
 
 15.0 
 
 3.37 
 
 9.5 
 
 6 1 32 
 
 50 
 
 74.70 
 
 767.11 
 
 7 28 
 
 56.11 
 
 15.0 
 
 3.56 
 
 10.0 
 
 5 43 29 
 
 50 
 
 77.04 
 
 858.14 
 
 6 41 
 
 58.28 
 
 15.0 
 
 3.75 
 
 10.5 
 
 5 27 9 
 
 50 
 
 79.51 
 
 959.00 
 
 5 59 
 
 60.57 
 
 15.0 
 
 3.94 
 
 11.0 
 
 5 12 18 
 
 50 
 
 81.82 
 
 1,065.52 
 
 5 23 
 
 62.69 
 
 15.0 
 
 4.12 
 
 11.5 
 
 4 58 45 
 
 1 50 
 
 84.09 
 
 1,180.16 
 
 4 51 
 
 64.78 
 
 15.0 
 
 4.31 
 
 12.0 
 
 4 46 19 
 
 1 50 
 
 86.16 
 
 1,299.93 
 
 4 24 
 
 66.67 
 
 15.0 
 
 4.50 
 
 stub switch. As point switches are used on the main line where very accurate 
 work is required, it is necessary to take account of the fact that the short frog 
 rails are not curved, the part EE' of the rail being straight. 
 
SURVEYING 
 
 129 
 
 In computing the dimensions of a point-switch turnout, the usual data are 
 the length AB = DC of the switch rail, the angle CDP between the outer switch 
 rail and the main rail. This angle is called the switch angle, and will be rep- 
 resented by 5. The frog number or the frog angle must also be known, as well 
 
 FlG. 6 
 
 as the length of the straight part EE'. It is then required to determine the 
 radius OI of the center line of a turnout whose outer rail shall be tangent to 
 the switch rail DC at C and to the frog rail EE' at E, and to find the lead A'K of 
 this turnout. 
 
 The formulas for computing these quantities are so complicated that, in 
 practice, tables giving the various dimensions of point switches are always 
 employed. 
 
 The accompanying table contains all the dimensions necessary for laying 
 
 __! = CD of the switch rails, and the length KE = Ka of the straight frog rail. 
 Turnouts From the Outer Side of a Curved Track. A turnout from the 
 outer side of a curved track is shown in Fig. 6. The radius DE = Rof the main 
 track, the frog angle F, or frog number n, and the gauge g are usually known; 
 from these the lead BK = L, and the radius Oe = roi the center line of the turnout 
 must be computed. The angle M , must first be found by the formula 
 
 a < gn 
 
 tan \M cot jr = -^ 
 
 Then, the lead must be determined 
 by the formula 
 
 Finally, r is given by the formula 
 
 When r has been found, the degree 
 of curve is given by the formula 
 5/730 
 
 If the main-track curve is not very 
 sharp, this value of d may be obtained 
 by subtracting the degree of curve of 
 the main track from that obtained from the sixth column of the table for stub 
 switches. The lead L may also be taken from the table. 
 
 If the curvature of the main track is very sharp, or if the frog angle is very 
 small, the turnout may curve in the same direction as the main track; in which 
 case, the degree of curve taken from the stub-switch table will be less than the 
 degree of curve of the main track. The difference between the two degrees 
 of curve will still be equal to the degree of curve of the turnout. If the 
 degrees of curve are equal, the turnout rails will be straight. 
 
 FIG. 7 
 
130 
 
 SURVEYING 
 
 Turnout from the Inner Side of a Curved Track. A turnout from the inner 
 side of a curved track is shown in Fig. 7. The radius OR of the turnout is 
 always less than the radius DH of the main track. The degree of curve of the 
 center line of the turnout and the lead BK are found as follows: 
 
 Rule I. Take from the table for a stub or for a 
 point switch, the value of the degree of curve corre- 
 sponding to the given frog number. Add this to the 
 degree of curve of the main track. The sum is the 
 degree of curve of the turnout. 
 
 Rule II. Take the value of the lead from the table 
 for a stub or for a point switch, corresponding to 
 Y the given frog number. This will be the value of the 
 1 desired lead BK, Fig. 7. 
 
 CONNECTING CURVES 
 
 A connecting curve is a curve introduced to con- 
 nect a turnout with a side track. Thus, in Fig. 8, 
 the two parallel straight tracks are connected by 
 the turnout ME and the curved track ED. The 
 values of n and g, and the distance a, usually 
 taken as 13 ft., must be known; then the radius r' 
 O\D = OiE, and distance KT may be computed 
 by the formulas 
 
 r' = 2(a-g) 
 
 and 
 
 KT-- 
 
 'XL 
 
 L is the lead PK of the turnout, and, in such 
 cases as this, is always to be taken from the table for a stub switch, even when 
 the point switch is inserted, because in deriving the formula for KT, QK and 
 ME are assumed to be circular arcs. 
 
 CROSS-OVERS 
 
 A cross-over is a stretch of track that connects two parallel tracks, and 
 enables a train to pass from one track to the other. Thus, in Fig. 9, if UV 
 and U'V are two parallel tracks, the track RZR' is a cross-over. This cross-over 
 consists of two equal turnouts Rm 
 and R'm', whose frog angles at K y 
 
 and K' are equal, and a reversed 
 curve mZm f connecting the ends of 
 these turnouts, Z being the point of 
 reversal. 
 
 Cross-Over Between Two Paral- 
 lel Straight Tracks. To lay out the 
 cross-over, it is necessary to know 
 the radius r, the central angle M, 
 and the distance BE*=B'E'. The 
 radius r may be taken from the 
 table for stub switches. Then, 
 
 and 
 
 When the tracks are less than 30 ft. 
 
 apart, the value of ~ may be 
 
 dropped. The formulas for sin M 
 and BE then become, respectively. 
 
 sin M 
 
 and 
 
 $ 
 
 FIG. 
 
 The preceding formulas apply only to stub switches; to apply them to point 
 switches, proceed as follows: Having located one frog point K of the point- 
 switch turnout, measure back from K the lead KB for a stub-switch turnout 
 taken from the table, and from the point R of the center line opposite B run 
 
SURVEYING 
 
 131 
 
 in the curve RmZ to the point of reversal. Then measure off the distance 
 BE = 2 ^laT, and from the point B' opposite to E lay off the stub-switch lead 
 B'K' to locate the second point of frog K'. Then run in the center-line curve 
 R'Z. The two frog points and the reversed curve mZm' are thus located. 
 Finally, measure back from K and K' the distances Kb = K'b' equal to the lead 
 for point switches, to locate the toes of the point switches at 6 and b r , and com- 
 plete the location of these switches as explained under Laying Out Turnouts. 
 
 It is evident that the whole length of the cross-over when point switches are 
 employed is be = b'e'j=BE 2XBb = 2'*Iar 2XBb. Therefore, 
 
 be = b'e' = 2'*Jar 2X (lead of stub switch lead of point switch) 
 
 A stake is usually driven at Z, midway between the inner rails and mid- 
 way between the points 2V and N f , and the turnout curves are continued to this 
 
 point. This is more accurate than to attempt to deterrr 
 by the use of the central angle M . 
 Another Form of Cross-Over Between 
 Two Parallel Straight Tracks. A second 
 form of cross-over is shown in Fig. 10. 
 In this form, the ends of the two equal ^ 
 
 line 
 
 V 
 
 i 
 
 i 
 k- 
 
 i 
 
 thep 
 
 a 
 EB' 
 
 oin 
 
 V 
 
 1 
 
 *1 
 
 R f 
 
 t of reversal 
 H' 
 
 KTK'T'. The cross-over with a reversed ^^xj^ 
 curve, Fig. 9, is much shorter than this ^v 
 straight-track cross-over, and thus requires 
 less length of track and occupies less 
 room. The straight-track form is, how- 
 ever, to be preferred; it is less wearing on 
 the rolling stock because it gives the wheel 
 trucks a better opportunity to adjust them- 
 selves to the reversion of curvature. 
 In order to lay out a straight-track 
 cross-over, it is only necessary to compute 
 the distance BE = B'E', Fig. 10, in addi- 
 tion to the usual dimensions of the two If 
 turnouts, which may be done by taking 
 the lead L from the stubswitch table and 
 applying the formula: 
 
 BE=2L--+(a-2g)n 
 
 i 
 
 
 1 
 
 i 
 i 
 
 * 
 
 1 
 i 
 
 
 
 ' T / 
 e' 
 
 t 
 
 A 
 
 *' 
 *"fc, 
 
 
 [ 
 
 I 
 
 F 
 
 IG. 10 
 
 i 
 V' 
 
 
 The turnout Rm having been put in place, the distance BE is laid off and the 
 heels B' and H' of the second turnout are located opposite the point E. This 
 turnout is then laid out as far as m f , and finally the straight rails KT' and K'T 
 are laid adjoining the ends of the two turnouts. 
 
 The only modification of the work for a point switch arises from the fact 
 that the lead Kb = K'b' of the point switch is less than that of the stub switch. 
 The whole length of cross-over is, for a point switch, 
 
 be = 2L' -r~ -f- (a 2g)n 
 Here L' is the lead taken from the table for point switches. 
 
 LAYING OUT TURNOUTS 
 
 To Lay Out a Stub Switch. Having decided on the position of the end b, 
 Fig. 11, of the frog rail, measure the total length of the frog and deduct it from 
 the length of the rail to be cut, marking with red chalk on the flange of the rail 
 the point at which the rail is to be cut. From Fig. 3, 
 
 n = 
 ab 
 and ch = nX ab 
 
 To calculate the distance from the heel to the theoretical point of frog, 
 the width of the frog at the heel is measured and multiplied by the frog num- 
 ber. For example, if the width of the frog at the heel is 85 in., and a No. 8 frog 
 is to be used, the theoretical distance from the heel to the point of frog is 8.5X8 
 = 68 in. = 5 ft. 8 in. Measure off this distance from the point marking the heel 
 of the frog; this will locate the point of frog, which should be distinctly marked 
 with red chalk on the flange of the rail. It is a common practice to make a 
 distinct mark on the web of the main-track rail, directly opposite to the point 
 
13 2 SURVEYING 
 
 of froe This point, being under the head of the rail, is protected from wear 
 and the weather. The heel of the turnout is then located by measuring back 
 the lead from the point of frog. Next, make a chalk-mark on both main-track 
 rails on a line marking the center of the head-block; a more permanent mark 
 is made with a center punch. Stretch a cord touching these marks, and drive 
 a stake on each side of the track, with a tack in each; this line should be at 
 right angles to the center line of the track, and the stakes should be sufficiently 
 far from the tracks not to be disturbed when putting in switch ties. Next, 
 cut the switch ties to proper length; draw the spikes from the track ties, three 
 or four at a time, and remove the ties from the track, replacing them with switch 
 ties and tamping the latter securely in place. When all the long ties are 
 tamped cut the main-track rail for the frog, being careful that the amount cut 
 off is just equal to the length pf the frog. If, by increasing or decreasing the 
 length of the lead 5%, the cutting of a rail can be avoided, this should be done, 
 especially for frogs above No. 8. 
 
 Full-length rails (30 ft.) should be used for moving or switch rails, and 
 care should be taken to leave a joint of proper width at the head chair. The 
 head-chairs should be spiked to the head-block so that the main-track rails 
 will be in perfect line. From 8 to 10 ft. of the switch rails should be spiked 
 to the ties. The tie-rods are placed between the switch ties, which should not 
 be more than 15 in. from center to center of tie. The connection-rod should 
 be attached to the head-rod and switch stand. With these connections made 
 the switch stand is easily placed to give the proper throw of the switch. 
 
 It is common practice to fasten the switch 
 stand to the head-block with track spikes, but a 
 
 better fastening is made with 
 
 bolts. The stand is first property 
 
 placed, the holes are marked and 
 
 bored, and the bolts passed 
 
 through from the under side ,of 
 
 the head-block. This obviates all 
 
 danger of movement of the switch 
 
 stand in fastening, which is liable 
 
 to occur when spikes are used, ' 
 
 and insures a perfect throw. 
 
 The use of track spikes is ad- 
 missible when holes are bored to 
 
 receive them, in which case a - 
 
 i-in. auger should be used for 
 
 standard track spikes. The 
 
 switch stand should, when pos- 
 sible, be placed facing the switch; 
 
 so as to be seen from the engineer's 
 
 , ., side of the engine the right- .,, i n 
 
 11 hand side. riG- ** 
 
 To find the position of the chord of the arc of the outer rail of the turnout 
 curve, stretch a cord from the heel a, Fig. 11, to the point b, of the frog. Mark 
 the middle point c and the quarter points d and e, and at these points lay off the 
 offsets dd', cc f , and ee f . Add to these offsets the distance from the gauge line 
 to the outside of the rail flange, and mark the points on the switch ties. Spike 
 the rail to these marks and place the other at easy track gauge from it. Spike 
 the rails of the turnout, as far as the point of frog, to exact gauge, unless the 
 gauge has been widened owing to the sharpness of the curve. Beyond the 
 point of frog, the curve may be allowed to vary a little in gauge to prevent a 
 kink from showing opposite the frog. In case the gauge is widened at the frog, 
 increase the guard-rail distance an equal amount. For a gauge 4 ft. 8^ in., 
 place the side of the guard-rail that comes in contact with the car wheels at 
 4 ft. 6f in. from the gauge line of the frog. This gives a space of 1 J in. between 
 the mam rail and the guard-rail. In case the gauge is widened J or ^ in. , increase 
 the guard-rail distance an equal amount. 
 
 When the turnout curve is very sharp, it will be necessary to curve the 
 switch rails, to avoid an angle at the head-block. The rails should be carefully 
 nirved before being laid, and great pains should be taken to secure a perfect 
 
 To Lay Out a Point Switch. The frog point K, Fig. 12, having been 
 located exactly as for a stub switch, the lead KB is next laid off from K to the 
 toe of switch B, and the positions of B and D are marked on the main-track 
 rails. *rom D, the length DN of the switch rail, which is usually 15 ft., is then 
 
SURVEYING 
 
 133 
 
 measured forwards to 2V, and the position of 2V is marked on the web or flange 
 of the rail. The heel M is usually 5| in. from the point 2V. The point / is 
 located on a line perpendicular to MD and at a distance %g from M. The point / 
 is similarly located from the point H. As a check on the work, the length of 
 the clwrd 77 should have the value given in the table for point switches. 
 
 Switch ties of the requisite number and length should be prepared and 
 placed in the track in proper order. As in the case of stub switches, all long 
 switch ties should be in place before the rail is cut for placing the frog; also, the 
 ends M and L of the rails, with which the switch points connect, should be 
 exactly even; otherwise the tie-rods will be skewed, and the switch will not 
 work or fit well. The tie-rods should next be fastened in position, care being 
 taken to place them in their proper order, the head-rod being numbered 1. 
 Each rod is marked with a center punch, the number of punch marks corre- 
 sponding to the number of the rod. 
 
 The switch rails are now coupled with the rails LK and MK, and the sliding 
 plates are then placed in position and securely spiked to the ties. The head- 
 rod is then connected with the switch stand, and the switch is closed, giving a 
 clear main track. The stand is then adjusted for this position of the switch, and 
 bolted fast to the head-block. Next, rail BR is crowded against the switch 
 point so as to insure a close fit, and secured in place with a rail brace at each 
 tie. The laying of the rails of the turnout is then continued. 
 
 The rail MH is to be bent and spiked in place by laying off offsets from the 
 chord MH exactly as explained for stub switches. The rail between M and H 
 usually consists of two pieces of 
 plain rail bent to the proper 
 curve. The outer rail of the 
 main track is not disturbed. 
 
 Switch Timbers. Every 
 first-class railroad has its own 
 standards for switches, which 
 include the necessary switch 
 timbers. The number of ties 
 and their lengths may be deter- 
 mined by the following rules: 
 
 Rule I. To find the number 
 of ties required for any switch 
 lead, reduce to inches the distance 
 from the head-block to the last long 
 tie behind the frog, and divide 
 this distance by the number of ^~. ^_ 
 inches from center to center of ties; _'e A 
 the quotient will be the number of 
 ties required. 
 
 Rule II. Measure the length 
 of the tie next the head-block and the length of the last long tie behind the frog. Find 
 the difference, in inches, between them. Divide this difference by the number of ties 
 in the switch lead; the quotient will be the increase in length per tie from the head-block 
 toward the frog to have the ends of the tie in proper line on both sides of the track. 
 
 Practical Method of Laying Out Sharp Curves in a Mine. Curves in a 
 mine are usually so sharp that they are designated as curves of so many feet 
 radius, instead of as curves of so many degrees. For example, suppose that it 
 is required to connect the two headings A and B, Fig. 13 (a) , which are perpen- 
 dicular to each other, with a curve of 60 ft. radius. Prepare the device shown 
 in (b), by taking three small wires or inelastic strings fg, gh, and gk, each 10 ft. 
 long, and connecting one end of each to a small ring, and the other end of two to 
 the ends of a piece of wood If ft. long. Form a neat loop at end /of string g/. 
 
 To use this device, lay off on the center line of the heading B, cd ancf de 
 equal to 60 ft. and 10 ft., respectively. Place the loop / of the device described 
 over a small wire peg driven in at e, and the ring g over a similar peg at d. 
 Take hold of the stick hk, pull the strings gh and gk taut, and place the center 
 mark on hk on the center line of the heading B. Drive a small peg in at m, 
 located by the point k, which is on the curve. Move the device forwards, 
 place the loop / over the peg at d, the ring g over the peg at m, and take hold 
 of the stick hk and pull until the strings gh and gk are taut, and the strings fg 
 and gh are in a straight line. The point k will fall on the curve at n, which 
 mark by driving in a peg. To locate other points, proceed exactly as in the 
 last step. The distance cd in any case is found by the forniula 
 
134 
 
 in which 
 
 SURVEYING 
 
 "T 
 
 jf 
 
 radius of curve; 
 
 intersection angle of center lines of headings. 
 Fig. 14 shows a graphic method of laying out curves, when it is desired to 
 connect a main entry a with a cross-entry b by a curve of a given radius. Here, c 
 is the point of curve on the main-entry center line and d is the point of tan- 
 gency on the center line of the cross-entry, which is assumed to be turned off 
 at right angles from the main entry. From c and d, arcs with a radius equal to 
 
 the desired radius of 
 curvature are des- 
 cribed, thus locating 
 the center e of the 
 curve. From this 
 point, with the same 
 radius, the curve cd, 
 which is the center of 
 the proposed passage- 
 way, is described. The 
 curves fg and hi are 
 then drawn, making 
 the curved entry any 
 desired width. Linejk, 
 so located that it 
 will not cut either rib 
 of the curved roadway, 
 should then be drawn 
 and on it points 5 feet 
 apart should be laid off 
 to the given scale and 
 the right and left dis- 
 tances to the rib scaled, 
 as shown in the figure. 
 If a plat of this kind is 
 
 Cress Cnfiy 
 
 FIG. 14 
 
 ill 
 
 drawn on a large enough scale, the angles and distances may be scaled suffici 
 ently accurate for the practical work of the mine foreman. A blueprint or trac- 
 ing of the plat is furnished to the mine foreman, and from it he lays off the right 
 and left distances from the center line of the main entry and from the line jk. 
 The line jk is located by means of two stations placed with the transit at ft and a 
 point either to the right or left of b, as may be most convenient, and along the 
 line bl. For the distances given in the illustration and the radius of curvature 
 of 70 ft., the angle cjk as taken from the drawing is about 120 15'; the angle 
 atjld, about 149 45'; the distance cj, 35 ft. 9 in; jl, 58 ft.; and Id, 11 ft. 6 in. 
 These distances are given as about so much, to show that they are scaled from 
 a drawing and are not calculated by trigonometry. 
 
 STADIA SURVEYING 
 
 Stadia surveying is the process of measuring distances and elevations by 
 observing through a telescope the distance intercepted on a rod between two 
 horizontal cross-hairs. These hairs are carried on the same ring as the regular 
 horizontal cross-hair, and are equidistant from it. The rod used may be an 
 ordinary level rod, but, if much stadia work is to be done, it is advisable to 
 select some one of the special rods designed for the work; a description of 
 these may be found in any instrument maker's catalog. 
 
 The distance intercepted on the rod between the cross-hairs of the telescope 
 bears a certain relation to the distance of the rod from the instrument. As the 
 transit is provided with a vertical circle or arc, the angle of inclination between 
 the line of sight and the horizon may be determined in case of inclined sights. 
 The space intercepted between the cross-hairs on the rod, taken in connection 
 with the vertical angle, enable the distance and elevation of the rod to be cal- 
 culated. When the line of sight is horizontal, the distance d of the rod from the 
 instrument can be determined from the formula 
 
 in which R = stadia reading or distance intercepted between the stadia wires ; 
 s = stadia "constant; 
 * = instrument constant. 
 
SURVEYING 135 
 
 The values of the stadia and instrument constants are usually determined 
 by the instrument maker. The instrument constant varies from about .75 ft. 
 to 1.33 ft. in different transits, according to the size and power of their tele- 
 scopes. Its value is usually marked on a card attached to the inside of the 
 instrument box. It is a general rule that unless definitely stated to the con- 
 trary, the stadia constant is made equal to 100; that is, in a horizontal line 
 of sight, the stadia wires will intercept a distance of 1 ft. on a rod whose distance 
 from the instrument is 100 ft. plus the instrument constant. Thus, if the 
 stadia constant is 100 and the instrument constant is 1.33 ft., if the stadia wires 
 intercept a distance of 8.37 ft. on the rod, the distance from the rod to the 
 transit is 8.37X 100 + 1.33 = 838.33 ft.; the line of sight being horizontal. 
 
 Stadia wires are either fixed or adjustable. The former are firmly placed 
 by the instrument maker so that the stadia constant is 100. They cannot get 
 out of adjustment and are much to be preferred to the other and older method 
 of mounting, in which the distance between the wires may be varied to intercept 
 any distance on the rod. In the event of the constants not being known, they 
 may be determined as follows: Select a piece of level ground and set tacks in 
 stakes at exactly 50 ft. apart for a distance of 400 to 800 ft. Let Rz and Ri be 
 two stadia readings taken at the respective distances dz and di\ then, 
 
 dt-di 
 S R 2 -Ri 
 
 . diRz-dzRi 
 
 and t = = p 
 
 KZ KI 
 
 Several pairs of readings and their corresponding distances are substituted in 
 these formulas, and the mean of all the resulting values of 5 and * calculated. 
 
 EXAMPLE. 'Determine the stadia and the instrument constant from the 
 following data: 
 
 Distance Measured Rod Reading 
 
 Feet Feet 
 
 50 .488 
 
 100 .988 
 
 200 1.988 
 
 300 2.991 
 
 400 3.986 
 
 SOLUTION. Take 50 ft. for the value of di and 100 ft., 200 ft., etc. suc- 
 cessively for the values of di, and apply the preceding formulas for s and i. 
 For the first pair of observations: 
 
 100-50 
 
 ""m=j&- m 
 
 . 50 X. 988 -.488X100 , 
 
 and * = i988^488 = L2 ft< 
 
 The other values are figured in a similar manner and the whole is tabulated 
 as follows: 
 
 s i 
 
 100.000 1.200 
 
 1 0.0 1.2 
 
 9 9.8 8 1.2 5 8 
 
 1 0.0 5 7 1.172 
 
 4 ) 3 9 9.9 3 7 4 )_4.8jJ_0 
 
 means 99.984 = 5 1.208 = * 
 
 Reduction of Inclined Sights. For the purpose of determining distances 
 and differences in elevation when the rod is above or below the level of the 
 instrument what are known as stadia reduction tables have been prepared. 
 Their use is best explained by an illustration. 
 
 EXAMPLE. Using a transit with fixed cross-hairs, the stadia constant being 
 100 and the instrumental constant being 1, the distance intercepted on the rod 
 was 4.25 ft. and the vertical angle was 18 23'. What was the horizontal and the 
 vertical distance from the rod to the instrument? 
 
 SOLUTION. Referring to the table in the column headed 18 and oppo- 
 site 22' in the column headed M, for 18 22' a horizontal distance of 90.07 is 
 found; and opposite 24', for 18 24', a horizontal distance of 90.04 is found. 
 For 18 23', therefore, the horizontal distance will be the mean, or 90.055. The 
 first column of the three lowest lines of the table contains the symbols c = .75, 
 
136 SURVEYING 
 
 e= 1.00, and e = 1.25. In this c is the instrument constant, the value of which 
 is riven by the maker. In the case in question c=1.00. Following hori- 
 zontally along the line of c = 1.00, the figures .95 are found in the column headed 
 " 18 Hor. Dist." This .95 is the proportion of the instrument constant to be 
 added to the reduced distance when the vertical angle is between 18 and 19. 
 The horizontal distance is then, 
 
 Distance = rod reading X tabular horizontal distance+c; 
 
 From this 
 
 distance = 4.25X90.055 + .95 = 382.73 + .95 = 383.68 ft. 
 
 Referring again to the table but using the second of the two columns 
 under 18 that headed Diff. Elev. and by interpolating between the values 
 of 22' and 24', the Diff. Elev. for 18 23' is f9und to be 29.925. The pro- 
 portion of the instrumental constant is found, in the line beginning c=1.00 
 in the column headed 18 but under the subcolumn, Diff. Elev., to be .32 for all 
 values of the vertical angle between 18 and 19. The difference in elevation 
 
 Diff. Elev. = rod reading X tabular Diff. Elev. + c 
 
 From this 
 
 Diff. Elev. = 4.25X29.925 +.32 =127. 18 +.32 = 127.50 ft. 
 
 Use of Stadia. The stadia is not used as much as it should be by the 
 mining engineer, particularly in securing data for making a contour map of 
 the property of which he is in charge. In rolling and hilly country, some 
 . points upon the surface may be from 500 to 1,500 ft. higher than others and 
 this difference in the thickness of the rocks, and consequent pressure upon the 
 coal, will have a great bearing on the thickness of pillars, method of drawing 
 stumps, etc., underground. If the traverse made to determine the boundaries 
 of the property has been made with a 400-ft. tape, the elevations of the stations 
 are known from the distances and vertical angles. By setting up at the various 
 stations, stadia sights may be taken to points at any distances within which 
 the rod may be read. This will be 1,200 or 1,400 ft. for a 12-ft. or 14-ft. rod. 
 Sights of double this distance may be taken if the upper hair and the regular 
 horizontal hair are used instead of the two stadia hairs; that is, if the two upper 
 hairs are used in place of the first and third. Distances so determined must 
 be multiplied by 2, as they are half distances. In this case the engineer must 
 be certain that the horizontal hair is exactly midway between the stadia hairs. 
 This may be ascertained by reading a distance with the upper and middle hairs 
 and then with the middle and lower hairs. If these distances are the same, 
 the hairs are evenly spaced; if the distances do not agree, their mean must 
 be taken. x 
 
 Cloudy days when the air is free from vibrations are best for stadia work. 
 An ordinary erecting transit will give excellent results up to 1,200 and 1,800 ft., 
 depending on its power, and a high class inverting telescope with large objec- 
 tive may be used for distances up to 3,000 ft. A good rodman is essential, 
 and if long sights are being taken and the slopes are regular, one observer can 
 keep two rodmen busy. The rod should be held at all points where there is 
 any marked change in the degree of slope. Small inequalities in the surface 
 may be neglected, it being apparent that an error of 20 to 30 ft. in determining 
 the thickness of the rocks overlying the seam is of no importance. 
 
 When the sights are too long to permit of the rod being plainly read, the 
 rodman should drive a stake and place a tack in it to mark the station. The 
 edge of the rod should then be held on the tack, the rodman running his hand 
 up and down the side of the rod that is to be sighted to. The transitman 
 should then move up and take further stadia sights from the station just 
 established. In traversing valleys or swales cutting across a property or in 
 determining the line of a ridge all the work may be done with the stadia with 
 a degree of accuracy well within reasonable requirements and far more easily, 
 rapidly, and cheaply, than with a transit, 400 ft. tape, and leveling instrument. 
 In locating isolated and distant houses, the opposite side of a wide river from 
 that on which the traverse is being run, in fact in all work where an error 
 of 1 : 500 or 1 : 1,000 is allowable, the stadia is to be preferred to the tape. 
 
SURVEYING 
 
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 SURVEYING 
 
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SURVEYING 
 
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 SURVEYING 
 
 BAROMETRIC LEVELING 
 
 Of the two types of barometer in general use, the mercurial barometer is 
 better adapted for work at permanent stations, and the aneroid barometer, 
 shown in the accompanying figure, by reason of its portability, is better suited 
 for use in the field. In the barometer, the difference in the pressure of the 
 air at two different stations not in the same horizontal plane, is made the basis 
 for measuring the difference in their elevation. The aneroid barometer con- 
 sists of a circular metallic air-tight box, either of brass or aluminum (because 
 of its lightness). One side is covered with a thin corrugated plate and only 
 enough air is left within the box to compensate for the diminished stiffness 
 of the cover at higher temperatures. This cover rises or falls as the outer 
 pressure changes, and this motion is greatly magnified by a series of levers 
 and is transmitted to a pointer moving over a scale on the circumference of 
 the outer face. This scale is commonly doubly graduated. The inner scale is 
 graduated by inches, tenths, and hundredths, to correspond with the gradu- 
 ations of a standard mercurial barometer. The outer scale is graduated in 
 thousands, hundreds, and tens of feet, indicating elevations above sea level 
 corresponding to the atmospheric pressures recorded by the inner scale. The 
 
 fineness of these outer graduations 
 varies, the ordinary aneroid reading 
 direct to 10 ft. and by estimation to, 
 say, 2 ft., while very large forms of the 
 instrument are provided with a vernier, 
 magnifying glass, etc., by which they 
 may be read to single feet. Such refine- 
 ment in reading is unnecessary, as in- 
 strument and weather irregularities 
 introduce much greater uncertainties 
 than those caused by too coarse gradu- 
 ating. 
 
 In some aneroids the two sets of 
 graduations are fixed, the zero of the 
 altitude scale being opposite the 31-in. 
 mark of the mercurial scale, and this 
 relation cannot be changed, but in most 
 instruments of this kind the zero may 
 be shifted either by turning an arrange- 
 ment like the stem of a watch or by 
 turning the milled edge of the aneroid 
 itself. The zero of the altitude scale 
 may be made to coincide with either 
 the 30- or 31-in. mark of the mercurial 
 scale, but whichever mark is decided on 
 by the instrument maker must always 
 be used. That this is the case will be 
 obvious from the table of Barometric 
 Elevations, which shows that a difference of 1 in. in the length of the mercurial 
 column between 29 and 30 inches corresponds to a difference of 924 ft. in 
 elevation, whereas a difference of 1 in. of mercury between 13 and 14 in. corre- 
 sponds to a difference of 2,020 ft. in elevation. Hence, as the length of the 
 altitude scale corresponding to a difference in elevation of 1,000 ft. is not 
 uniform, any shifting of the zeros of the two scales will bring inharmonious 
 graduations opposite one another. 
 
 Aneroids vary in size from 1| to 2 to 3 in. in diameter for the standard 
 forms up to 5 in. in diameter for the larger ones provided with a vernier, etc. 
 They are commonly graduated from 31 in. down to 27, 25, 21, 19, 17, and 
 14 in. of mercury, corresponding to approximate elevations of from 1,000 ft. 
 below sea level to 3,000, 5,000, 10,000, 12,000, 16,000, and 20,000 ft. above the 
 same. The larger barometers are no more accurate than the smaller ones and 
 nothing is gained by having them graduated to record smaller pressures 
 (greater elevations) than those prevailing where the instrument is to be used. 
 Ihus, east of the Mississippi River, a 2-in. or 2$-in. aneroid graduated from 27 
 to 32 in. (corresponding to elevations of 3,000 ft. above to 2,000 ft. below sea 
 level), will answer for all purposes of the coal-mining engineer, except for 
 exploratory work in the highest mountains of the Carolinas, etc. A barometer 
 reading to 17 in. (about 16,000 ft.) will answer for all parts of the continental 
 
SURVEYING 141 
 
 United States, as the highest peaks of the Rocky Mountains are but little over 
 14,000 ft. high. It must be remembered that the less the pressure (the greater 
 the altitude) the barometer will record, the finer are the graduations on both 
 scales and, consequently, the more difficult is precise reading. 
 
 A small screw in the center of the back permits the index pointer to be 
 accurately adjusted to correspond with the reading of a standard mercurial 
 barometer. This adjustment is originally made by the instrument maker, 
 but the aneroid should be compared from time to time with a standard barom- 
 eter at some station of the United States Weather Bureau, 9r elsewhere. 
 
 The word compensated stamped on the face of an aneroid barometer does 
 not mean that in determining elevations differences in temperature are not to 
 be considered, but only that the instrument reads correctly at all temperatures 
 and that no allowance need be made for the effect of changes in temperature 
 upon the instrument itself. 
 
 Too much reliance must not be placed on the accuracy of elevations as 
 determined by the aneroid. All this instrument does is to measure the pressure 
 of the air at a given place at a certain time. As this pressure must and does 
 vary at the same place as the weather changes, it must be apparent that the 
 difference in elevation between two distant points can be determined with even 
 approximate accuracy only when two barometers are used and which are read 
 simultaneously at the two points in question. At sea level, 1 in. of the mer- 
 curial column corresponds to a difference in elevation of about 900 ft. Changes 
 of -fa i n - frequently take place in 1 hr., & in. in 1 da., and in event of storms, 
 ranges of 1 in. are not unusual. Thus, as fa in. represents about 90 ft. of 
 elevation, a single reading of the barometer may give an elevation for a place 
 900 ft. greater or less than the true one under unfavorable atmospheric condi- 
 tions, and one of as much as 100 ft. under the best. On the other hand, if the 
 barometer is read two or three times daily for a period of 1 yr. or more, the 
 temperature being noted at the same time and the proper corrections made, 
 a very fair idea may be obtained as to the difference in elevation between the 
 station in question and that of any other station at which simultaneous obser- 
 vations have been made. Thus, the daily readings may be made by the 
 engineer at some isolated station and their mean for a period of time compared 
 with those made at any station of the United States Weather Bureau any 
 number of miles distant. 
 
 Barometric Formulas.* The general formula for obtaining the difference 
 of elevation between two points is, 
 
 z = 60,520[l + .001017(/-r-r-64)] log ^ 
 
 n 
 in which z = difference of elevation of the two points; 
 
 h and * = reading of barometer and thermometer at upper station; 
 H and T = reading of barometer and thermometer at lower station. 
 This equation may be referred to an approximate sea level (height of mer- 
 curial barometer 30 in. instead of 29.92 in.) and to a mean station temperature 
 of 50 F., that is t + T is made equal to 100 F., in which t and T may have any 
 values as long as their sum equals 100 F. Making the substitutions 
 
 on on 
 
 2 = 62,737 log ^-62,737 log ^ 
 n a. 
 
 The accompanying table of Barometric Elevations, from the United States 
 
 30 
 Coast and Geodetic Survey, contains values for 62,737 log -p for all readings 
 
 n 
 
 of the aneroid from 13 to 31 in. for use in connection with the foregoing formula, 
 no allowance being made for the amount of aqueous vapor in the air. At 
 other temperatures and for an assumed average humidity a correction obtained 
 from the table of Corrections for Temperature and Humidity must be applied 
 to the difference in eleyation as obtained from the first table. Thus, if A is 
 the difference in elevation obtained from the table of Barometric Elevations, 
 and C the correction for temperature and humidity from the second table, 
 z = A (1+Q 
 
 EXAMPLE. The means of the readings of the barometer and the thermom- 
 eter at the summit and base of a mountain were: Summit, barometer 17.92 in., 
 thermometer 26 F.; base, barometer 24.15, thermometer 64 F. If the 
 
 * Adapted from The Theory and Practice of Surveying, by J. B. Johnson, 
 published by John Wiley & Sons, New York City. 
 
142 
 
 SURVEYING 
 BAROMETRIC ELEVATIONS* 
 
 h 
 
 Inches 
 
 A 
 Feet 
 
 Differ- 
 ence 
 for .01 
 
 Feet 
 
 h 
 Inches 
 
 A 
 Feet 
 
 Differ- 
 ence 
 for .01 
 Feet 
 
 h 
 Inches 
 
 A 
 Feet 
 
 Differ- 
 ence 
 for .01 
 Feet 
 
 13.0 
 13.1 
 13.2 
 13.3 
 13.4 
 13.5 
 13.6 
 13.7 
 13.8 
 13.9 
 14.0 
 14.1 
 14.2 
 14.3 
 14.4 
 14.5 
 14.6 
 14.7 
 14.8 
 14.9 
 15.0 
 15.1 
 15.2 
 15.3 
 15.4 
 15.5 
 15.6 
 15.7 
 15.8 
 15.9 
 16.0 
 16.1 
 16.2 
 16.3 
 16.4 
 16.5 
 16.6 
 16.7 
 16.8 
 16.9 
 17.0 
 17.1 
 17.2 
 17.3 
 17.4 
 17.5 
 17.6 
 17.7 
 17.8 
 17.9 
 18.0 
 18.1 
 18.2 
 18.3 
 18.4 
 
 22,785 
 22,576 
 22,368 
 22,162 
 21,958 
 21,757 
 21,557 
 21,358 
 21,160 
 20,962 
 20,765 
 20,570 
 20,377 
 20,186 
 19,997 
 19,809 
 19,623 
 19,437 
 19,252 
 19,068 
 18,886 
 18,705 
 18,525 
 18,346 
 18,168 
 17,992 
 17,817 
 17,643 
 17,470 
 17,298 
 17,127 
 16,958 
 16,789 
 16,621 
 16,454 
 16,288 
 16,124 
 15,961 
 15,798 
 15,636 
 15,746 
 15,316 
 15,157 
 14,999 
 14,842 
 14,686 
 14,531 
 14,377 
 14,223 
 14,070 
 13,918 
 13,767 
 13,617 
 13,468 
 13,319 
 
 -20.9 
 20.8 
 20.6 
 20.4 
 20.1 
 20.0 
 19.9 
 19.8 
 19.8 
 19.7 
 19.5 
 19.3 
 19.1 
 18.9 
 18.8 
 18.6 
 18.6 
 18.5 
 18.4 
 18.2 
 18.1 
 18.0 
 17.9 
 17.8 
 17.6 
 17.5 
 17.4 
 17.3 
 17.2 
 17.1 
 16.9 
 16.9 
 16.8 
 16.7 
 16.6 
 16.4 
 16.3 
 16.3 
 16.2 
 16.0 
 16.0 
 15.9 
 15.8 
 15.7 
 15.6 
 15.5 
 15.4 
 15.4 
 15.3 
 15.2 
 15.1 
 15.0 
 14.9 
 14.9 
 
 19.0 
 19.1 
 19.2 
 19.3 
 19.4 
 19.5 
 19.6 
 19.7 
 19.8 
 19.9 
 20.0 
 20.1 
 20.2 
 20.3 
 20.4 
 20.5 
 20.6 
 20.7 
 20.8 
 20.9 
 21.0 
 21.1 
 21.2 
 21.3 
 21.4 
 21.5 
 21.6 
 21.7 
 21.8 
 21.9 
 22.0 
 22.1 
 22.2 
 22.3 
 22.4 
 22.5 
 22.6 
 22.7 
 22.8 
 22.9 
 23.0 
 23.1 
 23.2 
 23.3 
 23.4 
 23.5 
 23.6 
 23.7 
 23.8 
 23.9 
 24.0 
 24.1 
 24.2 
 24.3 
 24.4 
 
 12,445 
 12,302 
 12,160 
 12,018 
 11,877 
 11,737 
 11,598 
 11,459 
 11,321 
 11,184 
 11,047 
 10,911 
 10,776 
 10,642 
 10,508 
 10,375 
 10,242 
 10,110 
 9,979 
 9,848 
 9,718 
 9,859 
 9,460 
 9,332 
 9,204 
 9,077 
 8,951 
 8,825 
 8,700 
 8,575 
 8,451 
 8,327 
 8,204 
 8,082 
 7,960 
 7,838 
 7,717 
 7,597 
 7,477 
 7,358 
 7,239 
 7,121 
 7,004 
 6,887 
 6,770 
 6,654 
 6,538 
 6,423 
 6,308 
 6,194 
 6,080 
 5,967 
 5,854 
 5,741 
 5,629 
 
 -14.3 
 14.2 
 14.2 
 14.1 
 14.0 
 13.9 
 13.9 
 13.8 
 13.8 
 13.7 
 13.6 
 13.5 
 13.4 
 13.4 
 13.3 
 13.3 
 13.2 
 13.1 
 13.1 
 13.0 
 12.9 
 12.9 
 12.8 
 12.8 
 12.7 
 12.6 
 12.6 
 12.5 
 12.5 
 12.4 
 12.4 
 12.3 
 12.2 
 12.2 
 12.2 
 12.1 
 12.0 
 12.0- 
 11.9 
 11.9 
 11.8 
 11.7 
 11.7 
 11.7 
 11.6 
 11.6 
 11.5 
 11.5 
 11.4 
 11.4 
 11.3 
 11.3 
 11.3 
 11.2 
 
 25.0 
 25.1 
 25.2 
 25.3 
 25.4 
 25.5 
 25.6 
 25.7 
 25.8 
 25.9 
 26.0 
 26.1 
 26.2 
 26.3 
 26.4 
 26.5 
 26.6 
 26.7 
 26.8 
 26.9 
 27.0 
 27.1 
 27.2 
 27.3 
 27.4 
 27.5 
 27.6 
 27.7 
 27.8 
 27.9 
 28.0 
 28.1 
 28.2 
 28.3 
 28.4 
 28.5 
 28.6 
 28.7 
 28.8 
 28.9 
 29.0 
 29.1 
 29.2 
 29.3 
 29.4 
 29.5 
 29.6 
 29.7 
 29.8 
 29.9 
 30.0 
 30.1 
 30.2 
 30.3 
 30.4 
 
 4,968 
 4,859 
 4,751 
 4,643 
 4,535 
 4,428 
 4,321 
 4.215 
 4,109 
 4,004 
 3,899 
 3,794 
 3,690 
 3,586 
 3,483 
 3,380 
 3,277 
 3,175 
 3,073 
 2,972 
 2,871 
 2,770 
 2,670 
 2,570 
 2,470 
 2,371 
 2,272 
 2,173 
 2,075 
 1,977 
 1,880 
 1,783 
 1,686 
 1,589 
 1,493 
 1,397 
 1,302 
 1,207 
 1,112 
 1,018 
 924 
 830 
 736 
 643 
 550 
 458 
 366 
 274 
 182 
 91 
 00 
 - 91 
 181 
 271 
 361 
 
 -10.9 
 10.8 
 10.8 
 10.8 
 10.7 
 10.7 
 10.6 
 10.6 
 10.5 
 10.5 
 10.5 
 1.04 
 10.4 
 10.3 
 10.3 
 10.3 
 10.2 
 10.2 
 10.1 
 10.1 
 10.1 
 10.0 
 10.0 
 10.0 
 9.9 
 9.9 
 9.9 
 9.8 
 9.8 
 9.7 
 9.7 
 9.7 
 9.7 
 9.6 
 9.6 
 9.5 
 9.5 
 9.5 
 9.4 
 9.4 
 9.4 
 9.4 
 9.3 
 9.3 
 9.2 
 9.2 
 9.2 
 9.2 
 9.1 
 9.1 
 9.1 
 9.0 
 9.0 
 9.0 
 Q 
 
 18.5 
 
 13,172 
 
 
 24.5 
 
 5,518 
 
 
 30.5 
 
 451 
 
 c q 
 
 18.6 
 
 13,025 
 
 
 24.6 
 
 5,407 
 
 
 30.6 
 
 540 
 
 
 18.7 
 18.8 
 18.9 
 
 12,879 
 12,733 
 12,589 
 
 14.6 
 14.4 
 -14.4 
 
 24.7 
 24.8 
 24.9 
 
 5,296 
 5,186 
 5,077 
 
 11.0 
 10.9 
 -10.9 
 
 30.7 
 30.8 
 30.9 
 
 629 
 717 
 805 
 
 8.8 
 8.8 
 - 8.8 
 
 "Calculated for barometer at sea level = 30 in. and a mean temperature of 50 F. 
 
SURVEYING 
 CORRECTIONS FOR TEMPERATURE AND HUMIDITY 
 
 143 
 
 T+t 
 F. 
 
 C 
 
 T + t 
 F. 
 
 C 
 
 T+t 
 
 F. 
 
 C 
 
 
 
 -.1025 
 
 60 
 
 -.0380 
 
 120 
 
 + .0262 
 
 5 
 
 .0970 
 
 65 
 
 .0326 
 
 125 
 
 .0315 
 
 10 
 
 .0915 
 
 70 
 
 .0273 
 
 130 
 
 .0368 
 
 15 
 
 .0860 
 
 75 
 
 .0220 
 
 135 
 
 .0420 
 
 20 
 
 .0860 
 
 80 
 
 .0166 
 
 140 
 
 .0472 
 
 25 
 
 .0752 
 
 85 
 
 .0112 
 
 145 
 
 .0524 
 
 30 
 
 .0698 
 
 90 
 
 .0058 
 
 150 
 
 .0575 
 
 35 
 
 .0645 
 
 95 
 
 - .0004 
 
 155 
 
 .0626 
 
 40 
 
 .0592 
 
 100 
 
 + .0049 
 
 160 
 
 .0677 
 
 45 
 
 .0539 
 
 105 
 
 .0102 
 
 165 
 
 .0728 
 
 50 
 
 .0486 
 
 110 
 
 .0156 
 
 170 
 
 .0779 
 
 55 
 
 .0433 
 
 115 
 
 .0209 
 
 175 
 
 .0829 
 
 60 
 
 - .0380 
 
 120 
 
 + .0262 
 
 180 
 
 +.0879 
 
 elevation of the base was 6,025 ft. above sea level, what was the elevation of 
 the summit? 
 
 SOLUTION. From the first table, 
 
 Height for 17.92 in. = 14,039.6 ft. 
 Height for 24. 15 in. = 5,910.5ft. 
 
 Approx. difference in elevation = 8,129.1 ft. 
 As r+* = 90, from the second table, C= -.0058, and 
 
 2 = 8,129.1 X(l-. 0058)= 8,082ft. 
 Elevation of base = 6,025ft. 
 
 Elevation, top of mountain = 14,010 ft. 
 
 Use of Barometer. The mining engineer ordinarily has but one aneroid 
 and this is not commonly provided with a thermometer. With a single instru- 
 ment reliable results are difficult to obtain, and depend as much on good and 
 uniform weather conditions as on the skill and carefulness of the engineer. 
 In fact, the results obtained during storms, whether of wind or rain, are not to 
 be relied on at all. The single aneroid, then, should be used only when weather 
 conditions are of the best. In the morning, before starting out, its reading 
 should be noted and recorded. If a thermometer is available, it, too, should 
 be read. As the aneroid is usually employed in exploratory work in which 
 more or less time is required to examine various coal openings, it should be read 
 a few minutes after reaching an opening and again on leaving, the times and 
 temperatures being noted as well. After the examination of one opening is 
 completed, the engineer should hasten as rapidly as possible to the next; that 
 is, he should move rapidly Trom place to place but should remain a sufficient 
 time at each to estimate the changes in pressure (and consequently in apparent 
 elevation) that are taking place. By taking two observations at each opening 
 at intervals of, say, 5 hr., a correction curve showing the changes in pressure 
 may be worked out by means of which an allowance may be made for these 
 changes while the barometer is being carried from place to place. Thus, a 
 reading at Sta. A at 9.15 A. M., showed an elevation of 810 ft., and a reading 
 at Sta. B at 9.30 A. M. showed one of 860 ft., and a second at B at 10 A. M. 
 indicated 875 ft. This last reading shows a change in apparent elevation of 
 15 ft. in 30 min., or at the rate of .5 ft. per min. The apparent difference in 
 elevation between A and B (first readings) is 50 ft., but a part of this difference 
 is due to a change in the atmospheric pressure. The two readings at Sta. B 
 show that the elevations are apparently increasing at the rate of .5 ft. per min. ; 
 therefore, as it took 15 min. to go from A to B, the elevation of B over A 
 apparently increased 7.5 ft. Hence, the actual difference in elevation between A 
 and B is not 50 ft. but 50 7.5 = 42.5 ft. Very satisfactory results may be 
 obtained in this way; and if the time between stations is short, corrections for 
 changes in temperature, etc., need not be made, provided the difference in 
 
144 
 
 SURVEYING 
 
 elevation is not great. By taking double readings at each station, a con- 
 tinuous curve can be worked out and applied to correcting the day's observa- 
 tions. If possible, the aneroid should be reread at the various openings on the 
 way home, and the mean of the afternoon and morning readings taken as the 
 true reading. The instrument should be read upon reaching the starting point 
 at night and again when leaving the next morning. 
 
 When two barometers are available, their readings are compared at start- 
 ing, one being carried into the field and the other retained at headquarters 
 where it is read by an assistant throughout the day at intervals of 10 or 
 15 min., a record being kept of the time, temperature, and pressure. The 
 field man, then, need take but one reading at a station, preferably just before 
 leaving, and should likewise note the temperature and time. These double 
 readings, unless the field-man is so far from the base that weather conditions 
 are markedly different, afford a complete check on fluctuations in pressure 
 due to changed atmospheric conditions. 
 
 Care of the Barometer. The aneroid should not be removed from its case; 
 should not be subjected to violent jars; nor exposed to or read while affected 
 by artificial heat. It should be read in a horizontal position and on sunny 
 days should be allowed to remain in the shade for, say, 5 min. before being read, 
 that all its parts may have time to assume the temperature of the air at the 
 station. 
 
 PRACTICAL PROBLEMS IN SURVEYING 
 
 1. To Prolong a Straight Line. Let AB, Fig. 1, be a straight line whose 
 position on the ground is fixed by stakes set at A and B, and let it be required 
 A n f, to prolong the line to C. This 
 
 _ J. can ke done in two ways; 
 
 namely, by foresight only, or 
 by backsight and foresight, the 
 
 FIG. 1 
 latter method being commonly called backsight. 
 
 By Foresight. The transit is set over the point at A , and the line of sight 
 directed to a flag held at B; if the point C is to be set at a given distance from B, 
 the chainmen measure the required distance, the head chainman being kept in 
 line by the transitman. When the required distance has been measured, the 
 point C, which evidently lies in the prolongation of A B, is marked by a stake 
 or otherwise. 
 
 By Backsight. The transit is set over the point at B and a sight taken on 
 a flag held at A. The telescope is then plunged so that it is directed along 
 the prolongation of A B. Any re- 
 quired distance BC may then be 
 measured from B in the direction indi- 
 cated by the line of sight. 
 
 2. To Run a Line Over a Hill 
 When the Ends of the Line Are Invis- 
 ible From Each Other. The points A 
 and B, Fig. 2, are supposed to be on 
 the opposite sides of a hill, and to be 
 
 invisible from each other. It is desired to run a line between them, or to 
 locate S9me intermediate points. 
 
 Having set two poles at A and B, two flagmen with poles station them- 
 selves at C and D, approximately in line with A and B, and in such positions 
 that the poles at B and D are visible from C, and those 
 at C and A are visible from D. The flagman at C lines 
 in the pole at D between C and B, and then the flag- 
 man at D lines in that at C between D and A. Then 
 the flagman at C again lines in that at D, and so on 
 until C is in the line between D and A at the same time 
 that D is in line between C and B. The points C and 
 D will then be in line with A and B. 
 
 3. To Erect a Perpendicular to a Line at a Given 
 5^J'"~"*i*J lt be required to erect a perpendicular to 
 th , e lme AB at the P int B > Fi e- 3. A triangle whose 
 are in the proportion of 3, 4, and 5 is a right 
 ; for 5' = 4*+3'. The following 
 
 3O - J8 
 
 FIG 3 
 
 .. ' 
 
 mptl'; H = . e oowng 
 
 method is based on this principle: Lay off on BA a distance BC of 30 ft. (or 
 thl'n-n t-Ttf r 1 ^ !^ 6 Cham at one of the extremities as C, and the end of 
 link at the other extremity B. Hold the end of the fiftieth link 
 
 th 
 the 
 
SURVEYING 
 
 145 
 
 and draw the chain until both parts are taut. The point D where the end of 
 the fiftieth link is held will then be a point in the perpendicular, and the direc- 
 tion of the latter will therefore be BD. 
 
 The distance BC may be any other convenient multiple of 3. In general, 
 if BC is denoted by 3a, BD must be 4a, and CD must be 5a. Thus, BC may be 
 made equal to 21 ( = 3X7) li.; in which 
 case BD must be 4X7 = 28, and CD 
 must be 5 X 7 = 35 li. As 35 + 28 = 63, 
 one end of the chain must be fixed at 
 one of the extremities of BC, the end 
 of the sixty-third link at the other 
 extremity, and the chain pulled from 
 the end of the thirty-fifth link until 
 both parts are taut. 
 
 4. To Determine the Angle Be- 
 tween Two Lines. Let AD and AE, 
 Fig. 4, be two lines on the ground. 
 
 C 
 
 FIG. 4 
 
 To determine the angle DAE, measure off 
 
 from A on AD and AE equal distances AB and AC. Measure the distance BC. 
 Then the angle DAE is calculated from the relation 
 
 EXAMPLE. If AB and AC are each 100 ft. and BC is 57.6 ft., what is the 
 value of the angle DAE? 
 
 SOLUTION. Substituting the values of BC and A B in the formula, 
 
 44'X2 = 33 28'. 
 
 ~- = . 28800; 
 
 whence, %DAE = 16 44'. nearly; and, therefore, DAE 
 
 5. To Find the Distance of an Inaccessible Point. Case I. Let it be 
 required to determine the distance from the point B to an inaccessible point P, 
 Fig. 5. Measure BC in any convenient direc- 
 tion and run a line A'D' parallel to BC. 
 Measure AD, the distance between the points 
 where the lines PB and PC intersect A'D'. 
 Measure also AB. Then, 
 
 ABXBC 
 BP= AD-BC 
 
 EXAMPLE. If, in Fig. 5, C=100 ft., AB 
 = 52.4 ft., and AD = 124.2 ft., what is the dis- 
 tance BPJ 
 
 SOLUTION. Substituting these values in 
 the formula, 
 52.4X100 
 
 Case II. Measure a horizontal base line AB, Fig. 6, and take the angles 
 formed by the lines BAC and ABC, which gives 
 two angles and the included side. Assuming 
 the angle A to be 60, the angle B 50, and the 
 side AB = 50Q ft., angle C= 180-(60+50) 
 = 70. 
 
 Then, sin 70 : AB = sin A : BC, and sin 
 70 : AB = sin B : AC: or, .939693 : 500 
 = .866025 : BC.or 460.8+ , and .939693 : 500 
 = .766044 : AC, or 407.6 + . 
 By logarithms: 
 
 Log 500= 2.698970 
 
 Log sin 60= 9.937531 
 
 12.636501 
 
 Log sin 70= 9.972986 
 
 2.663515 = log of 460.8 + . 
 
 FIG. 6 
 
 Log 500= 2.698970 
 
 Log sin 50= 9.884254 
 
 12.583224 
 
 Log sin 70= 9.972986 
 
 2.610238 = log of 407.6 +. 
 
146 
 
 SURVEYING 
 
 6. To Determine the Distance Between Two Points Invisible From Each 
 Other or Separated by an Impassable Barrier. Case I. Let it be required 
 
 to find the distance 
 between two points A 
 and B, Fig. 7, that are 
 invisible from each 
 other. First run a ran- 
 dom line AD' in such a 
 manner that it will pass 
 TJ^~ ^_ . as near B as can be es- 
 FlG. 7 ^- timated. From B drop 
 
 a perpendicular BD on A D' t and compute the required distance A B by the formula 
 
 EXAMPLE. If, in Fig. 7, the distance AD is 206.1 ft. and the distance BD 
 is 35.1 ft., what is the distance from A to Bl 
 
 SOLUTION. Here A D = 206.1 and BD = 35.l; therefore, substituting in 
 the formula, AB= V 206.12+35.12 = 209.1 ft. 
 
 Case II. Select any convenient station, as C, 
 Fig. 8, measure the lines CA and CB, and the angle 
 included between these sides, so as to obtain two 
 sides and the included angle. Assuming the angle 
 C to be 60, the side CA, 600 ft., and the side CB, 
 500 ft., the following formula is obtained: 
 
 CA+CB : CA-CB = tan 4 : tan ^. 
 180 -60 
 
 Then, 
 
 A+B 
 
 -, or 60. 
 
 -; or, 1,100 : 100 = 1.732050 : .157459, 
 
 Then, 1,100 : 100 = tan 60 : tan 
 
 a 
 
 or tangent of = , or 8 57'. 
 
 Then, 60+8 57' = 68 57', or angle B, 
 
 and 60 - 8 57' = 51 03', or angle A , 
 
 Having found the angles, find the third side by the same method as case II, 
 of problem 5. 
 
 The foregoing formula, worked out by logarithms, is as follows: 
 
 Log 100= 2.000000 
 Log tan 60 = 10.238561 
 
 Log 1.100 
 
 12.238561 
 3.041393 
 9.197168 = log tan of 
 
 -, or 8 57'. 
 
 Then, 
 
 60+8 57' = 68 57', or angle B, 
 and 60 -8 57' = 51 03', or angle A 
 
 NOTE. The greater angle is always opposite 
 the greater side. 
 
 7. To Find the Distance Between Two Inac- 
 cessible Objects When Points Can Be Found From 
 Which Both Objects May Be Seen. Let A B, Fig. 
 9, be the line, the ends A and B of which are inac- 
 cessible. Select two points P and Q from which 
 both ends of the line can be seen, and at a distance 
 from each other of about 300 or 400 ft. Measure 
 the line PQ, and the angles K, L, M, and 2V. 
 Then, from triangle APQ, 
 
 FIG. 9 
 
 in which R = 180 -(K+L)-M. 
 From triangle BPQ, 
 
 BP = 
 
 in which 5 = 180-L-(M+ZV). 
 
 ; - 
 
 PQsin (M+N) 
 sin 5 
 
SURVEYING 
 
 147 
 
 Then, from triangle ABP, 
 
 and 
 
 A R 
 
 (BP-AP)cos 
 
 EXAMPLE. If, in Fig. 9, the distance PQ is 400 ft., and the angles, as meas- 
 ured, are K = 37 10', L = 36 30', M = 52 15', 2V = 32 55', what is the dis- 
 
 ' an SoLUTiON. In the triangle APQ, R = 180- (37 10' + 36 30'+52 15') 
 = 54 05', and 400 sin 52 15' 
 
 AP ~iin~54^05'~ 
 
 180- (36 30'+52 15' +-32 55') =58 20', M+N 
 
 In the triangle BPQ, S= 180 
 = 52 15'+32 55' = 80 10', and 
 
 
 sin 58 20' 
 Also, A>37 10', $ K=18 35', and 
 
 i fv v\ (468.30-390.53) , ., 
 tan 1 (X- F) = -- cot 18 35 
 
 whence, I (X F) = 15 04', and therefore 
 
 (468.30-390.53) cos 
 
 sm 15 04' 
 
 8. To Determine the Angle Between Two Lines AB and CD, Whose 
 Point of Intersection P is Inaccessible, Also, the Distances BP and DP. This 
 problem is of frequent occurrence in 
 railroad work, the two given lines being 
 the center lines of two straight tracks 
 that are to be connected by a curve 
 Measure the distance BD, Fig. 10, and 
 the [angles K and L. Then, M = 180 
 
 A 
 
 and 
 
 BD sin K 
 
 9. Survey of a Closed Field. If 
 
 a closed field is to be surveyed without 
 
 the aid of an angle-measuring instru- 
 
 ment, the area may be divided into "P r m 
 
 triangles by means of diagonals, which 
 
 are measured on the ground. The area of each triangle may then be deter- 
 
 mined by the formula A = V 5 ( 5 - fl )"o-6)( 5 -c) 
 
 in which a, b, and c represent the three sides and 5 represents one-half of their 
 
 a+b+c 
 sum, or . 
 
 When obstacles make it impossible to 
 measure directly the diagonals of a field, 
 as, for instance, the diagonal BE, Fig. 11, 
 a tie line FG parallel to BE is run and 
 measured. Then, _GFXAB 
 BE ~ AF~~ 
 
 To run the line FG, produce BA and 
 select any convenient point F and measure 
 AF. Then produce EA and locate G from 
 the relation 
 AFXAE 
 
 FIG. 11 
 
 EXAMPLE. In Fig. 11, let the lengths of the sides be as follows: AB 
 = 320 ft., BC = 217 ft., CD=196 ft., DE = 285 ft., and A=304 ft. It is 
 required to calculate the length of the diagonal BE by means of a tie-line. 
 
 SOLUTION. Let the line BA be prolonged 100 ft. beyond A ; that is, make 
 
 AF=100 ft. Then AG must be equal to A F . X g A E = 10 21 304 = 95 ft. Let 
 
 . g 
 AD 
 
 the length of GF, as found by measurement, be 125 ft. 
 
 GFXAB 125X320 
 BE - 400 ft 
 
 Then, 
 
148 
 
 SURVEYING 
 
 FIG. 12 
 
 n 
 
 10. To Determine the Height of a Vertical Object Standing on a Hori- 
 zontal Plane. Measure from the foot of the object any convenient horizon- 
 
 tal distance AB, Fig. 12; at the point A, take the angle 
 of elevation BAC. Then, as B is known to be a right 
 angle, two angles and the included side of a triangle are 
 obtained. Assuming that the line AB is 300 ft. and the 
 angle BAC = 4Q, the angle C=180-(90+40) = 50. 
 Then, sin C : AB = sin A : BC, or .766044 : 300 = .642788 
 : BC, or C = 251.73 + ft. Or, by logarithms: 
 
 Log 300= 2.477121 
 Log sin 40= 9.808067 
 12.285188 
 Log sin 50= 9.884254 
 
 2.400934 or log of 251.73+ ft. 
 
 11. To Find the Distance of a Vertical Object Whose Height is Known. 
 At a point A, Fig. 13, take the angle of elevation to the top of the object. 
 Knowing that the angle B is a right angle, the angles B and A and the side 
 BC are known. Assuming that the side BC = 200 ft. and 
 
 the angle A =30, a triangle is formed as follows: Angle 
 A = 30, B = 90, C = 60, and the side BC = 200 ft. Then 
 sin A : BC = s'm C : AB, or .5 : 200 = .866025 : AB, 
 AB = 346.41 ft. By logarithms: 
 
 Log 200= 2.301030 
 
 Log sin 60= 9.937531 
 
 12.238561 
 
 Log sin 30= 9.698970 
 
 2.539591 or log of 346.41 ft. 
 
 12. To Find the Height of a Vertical Object Standing Upon an Inclined 
 Plane. Measure any convenient distance DC, Fig. 14, on a line from the foot 
 of the object, and, at the point D, measure the angles of elevation EDA and 
 
 EDB, and the angle CDB; also at C measure 
 
 the angle BCD. In the triangle BDC, the side 
 
 BD may be calculated for the angles at D and 
 
 C and the side CD are known. Then, in the 
 
 right-angled triangle BED the sides BE and ED 
 
 may be calculated, 
 
 as the side BD and 
 
 the angle at D are 
 
 known. Next, in 
 
 the right-angled 
 
 triangle A ED, the 
 
 side AE may be / /STVii 
 
 calculated, for the / /. T\- 
 
 Final- / /fe;.,| \ 
 
 FlG 13 
 
 FIG. 14 
 
 side ED and the angle at D are known. 
 
 ly, the height of the object may be found by sub- 
 stracting the length AE from the length BE. 
 
 13. To Find the ^ 
 
 Height of an Inac- F IG. 15 
 
 cessible Object Above a Horizontal Plane. First 
 Method. Measure any convenient horizontal 
 line AB, Fig. 15, directly toward the object, 
 and take the angles of elevation at A and B. 
 In the triangle ABC, the side AC may be calcu- 
 lated as the angles at A and B and the side 
 AB are known. Then, in the right-angled tri- 
 angle CD A, the side CD, which is the height of 
 the object, may be calculated as the angle at 
 A and the side AC are known. 
 
 Second Method. If it is not convenient to 
 measure a horizontal base line toward the object, 
 measure any line AB, Fig. 16, and also measure 
 the horizontal angles BAD, ABD, and the angle of elevation DEC. Then, by 
 means of the two triangles ABD and CBD, the height CD can be found. Then, 
 with the line A B and the angles BAD and ABD known, the third angle is readily 
 found, and the side BD can be found. Then, in the triangle BDC, the angle B 
 is known, by measurement, D = 90, and the side BD is known. Then, the 
 side CD, or the vertical height, can be found by preceding methods. 
 
 FIG. 16 
 
MECHANICS 149 
 
 MECHANICS 
 
 ELEMENTS OF MECHANICS 
 
 GENERAL LAW 
 
 All machinery, however complicated, is merely a combination of six ele- 
 mentary forms, viz.: the lever, the wheel and axle, the pulley, the inclined plane 
 the wedge, and the screw; and these six can be still further reduced to the lever 
 and the inclined plane. They are termed mechanical powers, but they do not 
 produce force; they are only methods of applying and directing it. The law 
 of all mechanics is: 
 
 Law. The power multiplied by the distance through which it moves is equal 
 to the weight multiplied by the distance through which it moves. 
 
 Thus, 20 Ib. of power moving through 5 ft. = 100 Ib. of weight moving 
 through 1 ft. In the following discussion friction is not considered. 
 
 LEVERS 
 
 There are three classes of levers: (1) power at one end, weight at the other, 
 and fulcrum between, as shown in Fig. 1; (2) power at one end, fulcrum at 
 
 FIG. 1 FIG. 2 FIG. 3 
 
 the other, and weight between, as shown in Fig. 2; (3) weight at one end, 
 fulcrum at the other, and power between, as shown in Fig. 3. 
 
 The handle of a blacksmith's bellows is a lever of the first class; the hand 
 is the power and the bellpws the weight, with the pivot between as the fulcrum. 
 A crowbar used for prying down top rock is a lever of the second class; the 
 hand is the power, the rock to be barred down the weight, and the point in the 
 roof against which the bar presses is the fulcrum . The treadle of a grindstone 
 is a lever of the third class; the foot is the power, the hinge at the back of the 
 foot is the fulcrum, and the moving of the machinery is the weight. A lever 
 is in equilibrium when the arms balance each other. The distances through 
 which the power and the weight move depend on the comparative length of 
 the arms. 
 
 Let P = power; 
 
 W = weight 
 
 L = power's distance from fulcrum C\ 
 1 = weight's distance from fulcrum C; 
 c = distance between power and weight; 
 Arranging these terms according to the law of mechanics, 
 PL = Wl, orP: W=l : L 
 
 p = W =*T 
 
 In levers of the first class, a = L-\-l\ 
 
 T Wa 
 
 whence L = W+P 
 
 In levers of the second class, a 
 
 T W<1 
 
 whence L= w _ p 
 
 In levers of the third class, a = l L; 
 
 , Wa . Pa 
 
 whence 
 
150 
 
 MECHANICS 
 
 In first- and second-class levers, as ordinarily used, power is gained and 
 time is lost; in the third class, power is lost and time is gained. 
 
 EXAMPLE. Having a weight of 2,000 Ib. to lift with a lever, the short end 
 of which is 2 ft. from the fulcrum and the long end 10 ft., how much power will 
 be required? 
 
 SOLUTION. Applying the formula L : 1 = W : P, 10 : 2 = 2,000 : P : whence 
 P= (2,000X2) -f- 10 = 400 Ib. 
 
 The compound lever, Fig. 4, consists of several levers so constructed that 
 the short arm of the first acts on the long arm of the second, and so on to the 
 last. If the distance from A to the fulcrum is four times the distance from the 
 
 fulcrum to B, then a power of 5 Ib. 
 at A will lift 20 Ib. at B. If the 
 arms of the second lever are of the 
 same comparative length, the 20-lb. 
 power obtained at B will exert a 
 pressure of 80 Ib. on E; and if the 
 
 third lever has the same compara- 
 
 MG - 4 tive lengths, this 80 Ib. at E will 
 
 lift 320 Ib. at G. Thus, a power of 5 Ib. at A will balance a weight of 320 Ib. 
 at G. But, in order to raise the weight 1 ft., the power must pass through 
 320 -T- 5 = 64 ft. WHEEL AND AXLE 
 
 The wheel and axle, Fig. 5, is a modification of the lever. The ordinary 
 windlass is a common form. The power is applied to the handle, the bucket is 
 the weight, and the axis of the windlass is the fulcrum. 
 The long arm of the' lever is the handle, and the short arm 
 is the radius of the axle. Thus, F is the fulcrum, Fc the 
 long arm, and Fb the short arm. The wheel and axle has 
 the advantage that it is a kind of perpetual lever. It is not 
 necessary to prop up the weight and readjust the lever, but 
 both arms work continuously. 
 
 By turning the handle or wheel around once, the rope 
 will be wound once around the axle, and the weight will 
 be lifted that distance. Applying the law of mechanics, 
 power X circumference of wheel = weight X circumference of 
 axle; 9r, as the circumferences of circles are proportional 
 to their radii, P : W = r : R; whence PR= Wr. Therefore, FIG. 5 
 
 A train, Fig. 6, consists of a series of wheels and axles that act on one another 
 on the principle of a compound lever. The driver is the wheel to which power 
 is applied. The driven wheel or follower, is the one that receives motion from 
 the driver. The pinion is the small gear-wheel on the axle. 
 
 If the diameter of the wheel A is 16 in., 
 and of the pinion B 4 in., a pull of 1 Ib. 
 applied at P will exert a force of 4 Ib. on 
 the wheel C; if the diameter of C is 6 in., 
 and of D 3 in., a force of 4 Ib. on C will 
 exert a force of 8 Ib. on 
 E. If E is 16 in. in 
 diameter, and F 4 in., a 
 force of 8 Ib. on E will 
 raise a weight of 32 Ib. 
 on F. In order, how- 
 ever, to lift this amount, 
 
 , according to the prin- 
 
 /<====>> ciple already named, 
 
 I w I the weight will only pass 
 
 | _ \ FIG. 6 through one thirty-sec- p IG 7 
 
 ond of the distance of 
 
 the power. Thus, power is gained and speed lost. To reverse this, power 
 may be applied to the axle, and, with a correspondingly heavy power, speed 
 gained. Referring to Fig. 7, applying the law of mechanics, 
 Wrr\" PRR'R" 
 
 RR'R" = rr'r" 
 
MECHANICS 151 
 
 n : n" = r'r" : RR' 
 v.v' = rr'r" iRR'R" 
 
 in which , ', n" = number of revolutions; 
 
 v, v' velocity or speed of rotation; 
 r, r', r", etc.=radii of pinions; 
 R, R', R", etc. = radii of wheels. 
 
 INCLINED PLANE 
 
 In Fig. 8, the power must descend a distance equal to AC in order to 
 elevate the weight to the height BC; hence, PX length of inclined plane 
 = WX height of inclined plane, or P : W = height of 
 inclined plane : length of inclined plane; or, 
 
 ~~ / h sin a 
 
 To Find Weight Required to Balance Any Weight 
 on Any Inclined Plane. Multiply the given weight by 
 the sine of the angle of inclination. Thus, to find the ^ 
 weight required to balance a loaded car weighing 2,000 
 Ib. on a plane pitching 18, multiply 2,000 by the sine FIG. 8 
 
 of 18, or 2,000 X. 309017 = 618.034 Ib. 
 
 Or, if the length of the plane and the vertical height are given, multiply 
 the load by the quotient of the vertical height divided by the length. Thus, 
 if a plane between two levels is 300 ft. long and rises 92.7 ft., and the load is 
 
 92 7 
 2,000 Ib., the balancing weight 'is found as follows: 2.000X -^ = 618 Ib. 
 
 Case /. To find the horsepower required to hoist a given load up an inclined 
 plane in a given time, use the formula 
 
 (Load, in lb.+ weight of hoisting rope, in Ib.) X vertical height load is raised, in ft. 
 33, 000 X time of hoisting, in minutes 
 
 EXAMPLE. Find the horsepower required to raise, in 3 min., a car weigh- 
 ing 1 T. and containing 1 T. of material up an inclined plane 1,000 ft. long 
 and pitching 30, if the rope weighs 1,500 Ib. 
 
 SOLUTION. The total load equals car + contents + rope = 2,000+2,000 
 + 1,500 = 5,500 Ib. The vertical height through which the load is hoisted 
 
 equals 1, 000 X sin 30 = 1 ,000 X .5 = 500 ft.; therefore, H. p - = "33 000 x 3 =2 ?.7. 
 
 Case II. When the power acts parallel to the base, use the formula 
 
 WX height of inclined plane = P X length of base. 
 
 These rules are theoretically correct, but in practice an allowance of about 
 30% must be made for friction and contingencies. 
 
 SCREW 
 
 The screw consists of an inclined plane wound around a cylinder. The 
 inclined plane forms the thread, and the cylinder, the body. It works in a 
 nut that is fitted with reverse threads to move on the thread of the screw. 
 The nut may run on the screw, or the screw in the nut. The power may be 
 applied to either, as desired, by means of a wrench or a lever. 
 
 When the power is applied at the end of a lever, it describes a circle of 
 which the lever is the radius r. The distance through which the power passes 
 is the circumference of the circle; and the height to which the weight is lifted 
 at each revolution of the screw is the distance between two of the threads, 
 called the pitch, p. Therefore, P X circumference of circle = WX pitch; or 
 P : W = p : 2*r; whence, Wp ^_2-nrP 
 
 P = 2^ "~T~ 
 
 The power of the screw may be increased by lengthening the lever or by 
 diminishing the distance between the threads. 
 
 EXAMPLE. How great a weight can be raised by a force of 40 Ib. applied 
 at the end of a wrench 14 in. long, using a screw with 5 threads per in.? 
 
 SOLUTION. Substituting in the formula WX i = 40X28X3.1416; whence 
 
 The wedge usually consists of two inclined planes placed back to back, as 
 shown in Fig. 9. In theory, the same formula applies to the wedge as to the 
 inclined plane, Case II. 
 
 P : W = thickness of wedge : length of wedge. 
 
152 
 
 MECHANICS 
 
 Friction, in the other mechanical powers, materially diminishes their efficiency; 
 
 in this it is essential, since, without it, after each blow the wedge would fly 
 back and the whole effect be lost. Again, in the 
 others the power is applied as a steady force; in this 
 it is a sudden blow, and is equal to the momentum 
 of the hammer. 
 
 FIG. 9 
 
 The pulley is simply another form of the lever 
 that turns about a fixed axis or fulcrum. With a 
 single fixed pulley, shown in Fig. 10, there can be no 
 gain of power or speed, as 
 the force P must pull 
 
 down as much as the weight W, and both move 
 with the same velocity. It is simply a lever of 
 the first class with equal arms, and is used to change 
 the direction of the force. If v = velocity of W ; v 
 = velocity of P; then P= W and v = v'. 
 
 A form of the single pulley, where it moves 
 with the weight, is shown in Fig. 11. In this, one- 
 half of the weight is sustained by the hook, and the 
 other half by the power. As the power is only 
 one-half the weight, it must move through twice 
 the space; in other words, by taking twice the * IG - 1U FIG. 11 
 
 time, twice as much can be raised. Here power is gained and time lost; there- 
 fore, P = $W andv' = 2. 
 
 Combinations of Pulleys. (1) In Fig. 12, the weight W is sustained by 
 three cords, each of which is stretched by a tension equal to the P; hence, 
 
 8421 
 
 FIG. 12 
 
 FIG. 13 
 
 FIG. 14 
 
 FIG. 15 
 
 FIG. 16 
 
 1 lb. of power will balance 3 Ib. of weight. (2) In Fig. 13, a power of 1 lb. 
 will in the same manner sustain a weight of 4 lb., and must descend 4 in. to raise 
 the weight 1 in. (3) Fig. 14 represents the ordinary tackle block used by 
 mechanics, which can be calculated by the following general rule: 
 
 Rule. In any combination of pulleys where one continuous rope is used, a 
 load on the free end will balance a weight on the movable block as many times as 
 great as the load on the free end as there are parts of the rope supporting the load, 
 not counting the free end. 
 
 (4) In the cord marked 1, Fig. 15, each part has a tension equal to the 
 power P; and in the cord marked 2, each part has a tension equal to 2 P, and so 
 on with the other cords. The sum of the tensions acting on the weight W is 
 16; hence, W= 16 P. If n = number of pulleys, 
 
 P = ~ W=2 n P 
 
 2 np K 
 
 Differential Pulley. In the differential pulley, shown in Fig. 16, W-^^ 
 
 In all pulley combinations, nearly one-half the effective force is lost by friction. 
 
MECHANICS 153 
 
 FALLING BODIES 
 
 When the center of gravity of a moving body passes over equal distances 
 in equal intervals of time, the body has a uniform motion; otherwise, the motion 
 is variable. The velocity in a uniform motion is constant and is equal to the 
 distance traversed by the center of gravity of the body in a unit of time, as 
 feet per second, miles per hour, etc. When, in a variable motion, the velocity 
 increases or decreases uniformly with the time, the motion is designated, respec- 
 tively, as uniformly accelerated or uniformly retarded, and the rate of increase 
 or decrease is called acceleration or retardation, being equal to the amount that 
 the velocity increases or decreases in a unit of time. A body falling under 
 the action of gravity is a case of uniformly accelerated motion, the accelera- 
 tion being equal to 32.16 ft. per sec. and being usually denoted by g. 
 
 Let t = number of seconds that body falls; 
 
 v = velocity, in feet per second, at end of time t; 
 h = distance that body falls during time t. 
 
 Then, = gt = = V2gA = 8.02 V h 
 
 WORK 
 
 Work is the overcoming of resistance through a distance. The unit of work 
 is the foot-pound; that is, it equals 1 Ib. raised vertically 1 ft. The amount 
 of work done is equal to the resistance, in pounds, multiplied by the distance, 
 in feet, through which it is overcome. If a body is lifted, the resistance is the 
 weight, or the overcoming of the attraction of gravity, the work done being the 
 weight W, in pounds, multiplied by the height h of the lift, in feet, or Wh ft.-lb. 
 
 Power is the amount of work performed in a unit of time. One horsepower 
 is 550 ft.-lb. of work in 1 sec., 33,000 ft.-lb. in 1 min. or 1,980,000 ft.-lb. in 1 hr. 
 In the metric system, 1 H. P. is 75 meter-kilograms per second, usually written 
 75 m. Kg.-sec. 
 
 Kinetic energy is the capacity of a moving body to perform work. If the 
 moving body has a weight W and a velocity v, the work that it is capable of 
 
 doing in being brought to rest is --. A body falling through a height of h ft. 
 acquires during its fall a" velocity of v= -\l2gh; its kinetic energy is therefore, 
 
 2g 
 
 EXAMPLE 1. What is the horsepower of a stream of water discharging 
 12 cu. ft. per sec. through a height of 125 ft.? 
 
 SOLUTION. The kinetic energy per second, is 62.5X12X125 ft.-lb., 62.5 
 being the weight of 1 cu. ft. of water. The horsepower is, therefore, 
 
 EXAMPLE 2. What is the kinetic energy per second of a jet of water whose 
 area of cross-section is .1 sq. ft. and whose velocity is 10 ft. per sec.? 
 
 SOLUTION. In this case, W=62.5X. 1X10'= 62.5 Ib. The kinetic energy 
 is therefore, 62.5X10^6^50 
 
 2g 
 
 COMPOSITION AND RESOLUTION OF FORCES 
 
 The resultant of two or several forces acting on a body is the single force 
 that, if acting alone, would produce the same effect as the several forces com- 
 bined. The latter forces are called components with respect to the resultant. 
 
 Composition of forces is the process of finding the resultant when the com- 
 ponents are known, and the converse process of finding the components when 
 the resultant is given, is called resolution offerees. 
 
15 4 MECHANICS 
 
 Parallelogram of Forces. If two forces, as Fi and Ft, Fig. 1, are repre- 
 sented in magnitude and direction by two lines, as OA and OB, their resultant R 
 will be represented in magnitude and direction 
 -? by the diagonal OC of the parallelogram OACB 
 which is constructed by drawing BC and AC 
 parallel to OA and OB, respectively, and join- 
 ing the intersection C with O. 
 
 The resultant R can also be determined an- 
 alytically: its magnitude by the formula 
 R = VFi 2 +F2 2 2FiF 2 cos L, and the angles 
 Mi and M 2 that R makes with Fi and Ft, re- 
 FiG. 1 spectively, may be found by the formulas, 
 
 F 2 sin L 
 sin Mi = 
 
 and sin M 2 = 
 
 R 
 
 Fi sin L 
 
 R 
 
 For rectangular components, L = 90. The formulas then become: 
 
 Resolution of Forces. A given force 
 may have an innumerable number of 
 combinations of components. The prob- / 
 lem is, however, determinate when the &/. 
 directions of the components are given, a. wo 
 
 Let OC, Fig. 2, represent in magnitude ' r G< 
 
 and direction the force R acting at O, and let it be required to find its 
 components in the directions OX 2 and OX\. Draw from C, lines parallel to 
 these directions meeting OXi at A and OXz at 5. Then, OA and OB are the 
 required components Fi and F 2 . They may also be determined analytically 
 by the formulas, = R sin Ms 
 
 1- 
 
 and F 
 
 sin (Mi+M 2 ) 
 
 When Fi and F 2 are perpendicular to each other, 
 and F 
 
 MOMENTS OF FORCES 
 
 The moment of a force about a point is the product 
 obtained by multiplying the magnitude of the force by the 
 perpendicular distance from the point to the line of action 
 / of the force. In the accompanying figure, the moment of 
 
 I . F about the point C is Fp; and about the point Ci it is Fpi. 
 
 The point to which a moment is referred, or about which 
 a moment is taken is called the center of moments, or origin 
 of moments. The perpendicular p or p\ from the origin of 
 moments on the line of action of the force is called the lever 
 arm or simply the arm, of the force with respect to the origin. 
 A moment is expressed in foot-pounds, inch-tons, etc., 
 according to the units to which the force and its arm are 
 referred. 
 
 The moment is either positive or negative, depending 
 on the direction in which the force tends to cause rota- 
 tion. It is positive for clockwise motion, and negative 
 for counter-clockwise motion. Thus, the moment of F 
 ^ about C is positive and the moment about Ci is negative, 
 because, if the arms p and pi were bars, the force would tend to rotate p in a 
 clockwise direction, and pi in a counter-clockwise direction. 
 
MECHANICS 155 
 
 CENTER OF GRAVITY 
 
 The center of gravity of a figure or a body is that point upon which the 
 figure or the body will balance no matter in what position it may be placed, 
 provided it is acted upon by no other force than gravity. 
 
 If a plane figure is alike, or symmetrical, on both sides of a center line, 
 the latter line is termed an axis of symmetry, and the center of gravity lies in 
 this line. If the figure is symmetrical about any other axis, the intersection 
 of the two axes will be 'the center of gravity of the section; thus, the center of 
 gravity of a parallelogram is at the intersection of the diagonals and that of a 
 circle or an ellipse is at the geome- 
 trical center of the figure. The cen- 
 ter of gravity of a triangle lies on a 
 line drawn from a vertex to the mid- 
 dle point of the opposite side, and at 
 a distance from that side equal to 
 one-third the length of the line; or it 
 is at the intersection of lines drawn 
 from the vertexes to the middle 
 points of the opposite sides. 
 
 To find the center of gravity of a 
 
 trapezoid, Fig. 1, lay off BF = DC and 
 
 DE = AB; the center of gravity is at the intersection of EF with Mi Mi, the line 
 joining the middle points of the parallel sides. GMi can also be determined 
 by the formula ,, _m(bi+2bz) 
 
 \J lyL 1 rt/t i T \ 
 
 3(61+62) 
 
 The center of gravity of any quadrilateral may be determined as follows: 
 First divide it, with a diagonal, into two triangles, and join with a straight 
 line the centers of gravity of the two triangles; then, with the second diagonal, 
 divide the figure into two other triangles and join the centers of gravity of these 
 triangles with a straight line. The center of gravity of the quadrilateral is at 
 the intersection of the lines joining the centers of gravity of the two sets of 
 triangles. 
 
 For an arc of a circle, the center of gravity lies on the radius drawn to the 
 middle point of the arc (an axis of symmetry) and at a distance from the 
 center equal to the length of the chord multiplied by the radius and divided 
 by the length of the arc. 2r 
 
 For a semicircle, the distance from the center = = .6366 r, when r = radius. 
 
 For the area included in a half circle, the distance of the center of gravity 
 from the center is 4r 
 
 3ir 
 
 For a circular sector, the distance of the center of gravity from the center 
 equals two-thirds of the length of the chord multiplied by the radius and 
 divided by the length of the arc. 
 
 For a circular segment, let A be its area and C the length of its chord; then 
 
 C 3 
 the distance of the center of gravity from the center of the circle is equal to j^-- 
 
 The center of gravity of any irregular plane figure can be determined by 
 applying the following principle: The static moment of any plane figure with 
 regard to a line in its plane that is, the product of its area A by the distance 
 D of its center of gravity from that line is equal to the algebraic sum of the 
 static moments of the separate parts into which the figure may be divided, with 
 regard to the same axis, or 
 
 AD = aidi -\-azdz, etc., 
 
 in which, fli, 02, etc., denote the areas of the subdivided parts of the figure, and 
 d\, di, etc. are the distances of their respective centers of gravity from the 
 reference line. Solving this equation for the value of D, 
 = aidi + azdz + etc. 
 
 A 
 
 The figure whose center of gravity is required is divided into separate parts 
 whose centers of gravity are easily ascertained, usually into rectangles or 
 triangles. A suitable axis is then assumed with reference to which the expres- 
 sions a\di, a-id<i, etc. are found, and their sum is divided by A =ai+a2+etc., the 
 quotient giving D. The center of gravity of the whole figure lies, therefore, on 
 a line parallel to the assumed axis and distant D from it. In a similar manner, 
 
156 
 
 MECHANICS 
 
 another line containing the center of gravity is obtained, the intersection of the 
 two lines giving its exact position. *.-*..._ 
 
 EXAMPLE 1. Find the center of gravity of the cross-section of the dam 
 
 shown in Fig. 2. 
 
 A\~~2o'-^-n SOLUTION. Divide the section into 
 
 ^^ the rectangles ABC'l and HEFG and 
 
 the triangle CDC', and assume the lines 
 X-X and Y-Y as reference lines. 
 Then, 
 
 and 
 
 01*1 +02*2 +03*3 
 
 %r* 
 
 01 + 02 + 03 
 
 From the illustration, 01 
 = 2,000, yi = 70, 
 
 = 1,587, y 2 = 43, * 2 = 45.33; 
 = 1,720, ys = 10, and xa = ' 
 ting these values, 
 
 _ 2,000X70+1.587X43 + 1.720X10 
 2.000+1.587 + 1,720 
 
 = 42.48 
 
 _ 2,000X20 +1.587X45.33 + 1.720X43 
 
 F.c.2 "135.03 
 
 EXAMPLE 2. Find the center of gravity of the bridge chord section shown 
 
 SOLUTION. The center of gravity is on the line YY, which is an axis of 
 symmetry. To find the distance y, divide the section into angles and plates 
 and take moments about XX. The areas and centers of gravity of the angles 
 might be located by the preceding principles or taken from a manufacturer's 
 handbook. They are: For the 4""X4"X*" angle, area = 3.75 sq. in. and 
 distance from center of gravity to back of angle = 1 . 18 in. ; for the 3 \" X 3 \" X \" 
 angle, area = 3.25 sq. in. and distance from center of gravity to back of angle 
 = 1.06 in. Hence, the moment of the bottom angles is 2X3.75X1.18 = 8.85 
 and that of the top angles is 2X3.25X (151.06) =90.61. The moment of the 
 two web-plates is 2X15X^X7.5= 112.5, and that 
 of the cover-plate, 24 X I X 15.25 = 183.00. The 
 sum of the moments is, 8.85+90.61 + 112.5+183.00 
 = 394.96. The sum of the areas is 2X3.25+2X3.75 
 +24X^+2X15X^ = 41 sq. in. Then, y = 394 .96 -f- 41 
 = 9.63 in. 
 
 Center of Gravity of Solids. For a solid having 
 three axes of symmetry, all perpendicular to each 
 other, like a sphere, cube, right parallelepiped, etc., 
 the point of intersection of these axes is the center 
 of gravity. 
 
 For a cone or pyramid, draw a line from the 
 apex to the center of gravity of the base; the 
 required center of gravity is one-fourth the length of this line from the base, 
 measured on the line. 
 
 For two bodies, the larger weighing W lb., and the smaller P lb., the center 
 of gravity will lie on the line joining the centers of gravity of the two bodies and 
 
 at a distance from the larger body equal to Mr , where o is the distance 
 
 between the centers of gravity of the two bodies. 
 
 For any number of bodies, first find the center of gravity of two of them, 
 and consider them as one weight whose center of gravity is at the point just 
 found. Find the center of gravity of this combined weight and a third body. 
 So continue for the rest of the bodies, and the last center of gravity will be the 
 center of gravity of the whole system of bodies. 
 
 To find the center of gravity mechanically, suspend the object from a point 
 near its edge and mark on it the direction of a plumb-line from that point; then 
 suspend it from another point and again mark the direction of a plumb-line. 
 The intersection of these two lines will be directly over the center of gravity. 
 
MECHANICS 
 
 157 
 
 MOMENT OF INERTIA 
 
 The moment of inertia of a plane surface about a given axis is the sum of the 
 products obtained by multiplying each of the elementary areas, into which 
 the surface may be conceived to be divided, by the square of its distance from 
 the axis. 
 
 MOMENTS OF INERTIA, ETC. 
 
 Name of Section 
 
 / 
 
 7 
 
 c 
 
 r* 
 
 Solid circular 
 Hollow circular | 
 Solid square 
 Hollow square 
 
 
 
 e 
 
 ird* 
 64 
 
 ir(d-di) 
 
 *d3 
 32 
 
 *(<*-<*,) 
 
 d 
 16 
 
 d2 + dl 
 
 64 
 
 d 
 12 
 
 d*-di* 
 
 32d 
 
 d3 
 
 6 
 d*-dS 
 
 16 
 
 rf2 
 
 12 
 
 dz+di* 
 
 B 
 
 
 
 
 12 
 
 
 12 
 
 6d3 
 
 12 
 
 bd*-bidi* 
 
 64 
 
 bd* 
 6 
 
 6rf"-6idi 
 
 12 
 
 62 
 
 12 
 
 W-fcl'dl 
 
 
 
 i 
 
 L 
 
 I- 
 
 U 
 
 i 
 
 3 
 
 Solid rectangular ' 
 
 *. 
 
 
 
 Hollow 
 rectangular 
 
 
 12 
 
 bd* 
 36 
 
 rid* 
 64 
 
 M 
 
 6d 
 24 
 
 TT&d2 . 
 
 32 
 
 ir(b&-bidi*) 
 
 12(W-Mi) 
 
 rfz 
 18 
 
 6 
 16 
 
 &3d-6i'di 
 
 A 
 
 Solid triangular 
 Solid elliptic * 
 
 Hollow elliptic * iS 
 
 r ~ 
 
 pl|pi 
 
 I " bCam 
 t -> 
 Cross with equal |T g 
 arms (approxi- ^^^M 
 mate) OF 
 
 Angle with equal | 
 arms (approxi- * || 
 mate) U 
 
 (.oo* 1 Oiai ; 
 bffi-bidS 
 
 32d 
 bdz-bidf 
 
 16(6d-6irfi) 
 b*d-fa*di 
 
 12 
 
 6d 
 
 12(bd-bidi) 
 
 d* 
 22.5 
 
 d2 
 25 
 
 The moment of inertia is usually designated by the letter /. The value of 
 the moment of inertia used in calculating the strength of beams and columns is 
 usually taken about the neutral axis of the figure, which, with the exception of 
 reinforced-concrete sections, passes through the center of gravity of the figure. 
 
 Formulas for the values of / about an axis passing through the center 
 of gravity of the section are given for various forms of sections in the 
 
158 
 
 MECHANICS 
 
 accompanying table. For any other section, it can be computed by means 
 of the following principles: 
 
 Principle I. The moment of inertia of a section about any axis is equal to the 
 algebraic sum of the moments of inertia about the same axis, of the separate parts of 
 which the figure may be conceived to consist. 
 
 Principle II. The moment of _ 
 
 inertia of any figure about an axis 
 not passing through the center of 
 gravity, is equal to the moment of 
 inertia about a parallel axis through 
 n f ,. , the center of gravity, plus the product 
 ^ | of the entire area of the section by 
 f 1 c | the square of the distance between 
 
 the two axes. 
 
 EXAMPLE 1. Find the moment 
 of inertia about the neutral axis 
 
 --I-- -4JC 
 
 FIG. 2 
 
 XX of the Bethlehem I column section having dimensions as shown in Fig. 1. 
 SOLUTION. Conceive the section to consist of the square A BCD minus 
 twice the rectangle abed. Then, by applying principle I and the formulas of 
 the table for moments of inertia. 
 
 12* 2X5.75X10.5 3 
 
 -* 
 
 - r 
 
 : 618.6 
 
 12 12 
 
 NOTE. This result can be obtained directly by the I-beam formula, given 
 in the same table. 
 
 EXAMPLE 2. Find the moment of inertia of the section shown in Fig. 2 
 about the neutral axis parallel to the cover-plate. 
 
 SOLUTION. The neutral axis passes through the center of gravity, which has 
 been found to be. 9. 63 in. from the back of the bottom angles. The distances 
 of the centers of gravity of the subdivisions of this section from the axis XX, 
 Fig. 2, are: 
 
 For the cover-plate 15.25-9.63 = 5.62 
 
 For the web-plates 9.63 7.50 =2.13 
 
 For the 3"X3"X J" L's, 15.00-1.06- 9.63 =4.31 
 
 For the 4"X4"xr L's, 9.63-1.18 =8.45 
 
 The moments of inertia of the respective parts about their own neutral axes 
 parallel to XX are: 04. y i i\s 
 
 For the cover-plate 12 = ' 25 
 
 For the web-plates 2X ** -281.25 
 
 From a steel manufacturer's handbook, the value of / for a 3|"X35"X \" L 
 is found to be 3.64; and for a 4"X4"X*" L it is 5.56. Applying principle 
 II, the moment of inertia of the entire section is, / = .25+24 X | X 5.62 2 +281.25 
 
 +2X15X|X2.13 2 +2X3.64 + 2X3.25X4.31 2 +2X5.56+2X3.75X8.45 2 
 = 1,403.22. 
 
 RADIUS OF GYRATION 
 
 Let /denote the moment of inertia of any section and a its area; then, the 
 relation between / and a is expressed in the formula, / = ar 2 , in which r is a con- 
 y stant depending on the shape of the section and is 
 
 -" H called the radius of gyration of the section referred to 
 the same axis as /. Then, 
 
 EXAMPLE 1. What is the radius of gyration of the 
 "* section shown in Fig. 1 about the axis XX? 
 
 SOLUTION. The moment of inertia of this section 
 has been found to be 618.6 and its area is 2X12X1 
 + 10.5X 5 = 23.25 sq. in. Substituting in the formula, 
 
 18^6 . 
 
 EXAMPLE 2. Determine the distance b in the strut 
 made up of two latticed channels, as shown in Fig. 3, 
 so that the radii of gyration about the axes XX and YY will be equal. 
 
 FIG. 3 
 
MECHANICS 159 
 
 SOLUTION. Let I x , r x , I y , r y be, respectively, the moments of inertia and 
 radii of gyration of a single C about the axes XX and YY; a its area and CG, its 
 center of gravity, then, from the figure, b = d c, and I x = ar x ' i \ also, I y = ary* 
 -{-ad 2 . Hence, by the condition of the problem, ar x ^ = ar y 2-}- ad"*, or r x t = r y z 
 + d*. Whence, d - ^r x 2 - r y *. The values of r x , r" y and c for any C may be taken 
 from a steel manufacturer's handbook. For instance, for a 15-in. E of 33 Ib. 
 
 r x = 5.62, r~ = 12, and c = .794; hence, d= \5.622-.9122 = 5.546, and b = d-c 
 = 5.546 -.794 = 4.752. 
 
 A practical rule giving good approximate results for a channel column or 
 strut is to subtract r y from r x ; the result is 6. Applying this rule to the 15-in. 
 C of 33 Ib. column or strut, b = 5.62 - .912 = 4.708. 
 
 SECTION MODULUS AND MOMENT OF RESISTANCE 
 
 The expression -, in which / is the moment of inertia and c the distance of 
 
 the outermost fiber of the section from the neutral axis, is called the section 
 modulus. For a given material, this quantity is a measure of the capacity of 
 the section to resist bending. Multiplied by the unit stress to which the outer- 
 most fibers are subjected under given loads, the product gives the amount of 
 bending moment the section is resisting, and is called moment of resistance. 
 If / is the unit stress that certain loads develop in the outermost fibers of the 
 section, the moment of resistance is T 
 
 K,-\f 
 
 EXAMPLE 1. What is the section modulus of a 20-in. I beam of 75 Ib. whose 
 moment of inertia is 1,268.9? 
 
 SOLUTION. As the neutral axis passes through the center of the section, the 
 distance c is in this case equal to one-half the depth; that is 20 -j- 2 = 10. The 
 section modulus is therefore I _ 1,268.9 _ 
 
 ---^--126.9 
 
 EXAMPLE 2. When subjected to loads perpendicular to the cover-plates the 
 outermost fibers of the section shown in Fig. 2, are stressed to 16,000 Ib. per 
 sq. in. What is the resisting moment of the section? 
 
 SOLUTION. The moment of inertia of the section has been found to be 
 1,403.22, and the outermost fibers are 9.63 in. from the neutral axis; hence, the 
 section modulus is equal to 1,403.22 -=-9.63 = 145.7; this multiplied by 16,000 
 gives 2,331,200 in.-lb. 
 
 Formulas for obtaining directly the section moduli of sections frequently 
 used are given in the table of Moments of Inertia, etc. 
 
 FRICTION 
 
 Friction is the resistance that a body meets from the surface on which it 
 moves. It depends on the degree of roughness of the surfaces in contact, and 
 is directly proportional to the perpendicular pressure between the surfaces. It 
 is independent of the extent of the surfaces in contact as long as the normal 
 pressure remains the same. It is generally greater between surfaces of the same 
 material than between those of different materials, and greater between soft 
 bodies than hard ones. 
 
 Coefficient of Friction. The ratio between the resistance to the motion 
 of a body due to friction and the perpendicular pressure between the surfaces is 
 called the coefficient of friction. When the coefficient of friction between two 
 surfaces is known, the frictional resistance is obtained by multiplying the 
 normal pressure by the coefficient. 
 
 EXAMPLE 1. What is the resistance per linear foot of a retaining wall against 
 sliding when the normal pressure on the foundation is 10,000 Ib. per lin. ft. of 
 wall and the coefficient of friction of the masonry on the foundation is .65? 
 
 SOLUTION. The frictional resistance is 10,000 X .65 = 6,500 Ib. 
 
 The coefficient of friction of the wheels of suddenly stopping engines and 
 cars on the rails is usually assumed at .20. The rails on bridges or trestles will 
 transfer to the bridge or trestle tower the frictional forces produced by the brakes 
 in order to stop the cars, causing stresses that must be provided for. 
 
160 
 
 MECHANICS 
 
 EXAMPLE 2. What is the longitudinal force on a bridge caused by the 
 sudden stopping of a car weighing 60,000 Ib? 
 
 SOLUTION. The longitudinal force will be 60,000 X. 20= 12,000 Ib. 
 
 Angle of Friction. When a body, as B in the accompanying illustration, 
 
 weighing W Ib. is placed on an inclined plane making an angle a with the 
 
 horizontal, the normal pressure is N = W cos a; and, if the coefficient of friction 
 
 is denoted by /, the frictional resistance against sliding down of the body is 
 
 F =fN=fW cos a. This force acts in 
 a direction opposite to that of the force 
 P=Wsina. When the angle a is such 
 that F just balances, or is equal to P, so 
 that the slightest force will cause the 
 body to slide, the angle is then called 
 the angle of friction. The tangent of 
 that angle is equal to the coefficient of 
 friction, or/=tan a. 
 
 Angle of Repose. On a sloping 
 bank of loose material, such as sand, 
 earth, etc., when the angle of slope is 
 such that the particles are on the point 
 of moving, the angle is called the angle of repose. It is the same as the angle 
 of friction of the material on itself. The slope is then called the slope of 
 repose, or the natural slope of the material, for it is the slope that the material 
 will assume when subject to gravity only. 
 
 EXAMPLE. The coefficient of friction of dry sand on itself is .65; what is 
 its angle of repose? 
 
 SOLUTION. The angle of repose is the same as the angle of friction, whose 
 tangent equals the coefficient of friction; consequently, .65 = tan a, and from a 
 table of natural tangents a = 33. 
 
 The accompanying tables give coefficients of friction and angles of repose of a 
 number of materials. 
 
 COEFFICIENTS OF FRICTION AND ANGLES OF REPOSE FOR 
 MASONRY MATERIALS 
 
 Material 
 
 Coefficient 
 of 
 Friction 
 
 Angle of 
 Repose 
 Degrees 
 
 Fine-cut granite, on same, dry 
 
 .60 
 .65 
 .70 
 .75 
 .65 
 .60 
 .65 
 .65 
 .60 
 .75 
 .70 
 .65 
 .50 
 .50 
 .50 to .60 
 .35 to .45 
 .50 
 .35 
 
 31 
 33 
 35 
 37 
 33 
 31 
 33 
 33 
 31 
 37 
 35 
 33 
 27 
 27 
 27 to 31 
 19 to 24 
 27 
 19 
 
 Fine-cut granite, on rough-pointed granite, dry 
 Rough-pointed granite, on same, dry 
 
 Well-dressed soft limestone, on same, dry 
 
 Concrete blocks, on same, dry 
 
 Concrete blocks, on fine-cut granite dry 
 
 Common brick, on same, dry 
 
 Common brick, on well-dressed soft limestone, dry . . 
 Common brick, on well-dressed hard limestone, dry 
 Common brick, on same, with slightly damp mortar 
 Hard brick, on same, with slightly damp mortar .... 
 Hard limestone, on same, with slightly damp mortar 
 Common brick, on same, with fresh mortar 
 
 Well-dressed granite, on same, with fresh mortar. . . . 
 Granite, roughly worked, on dry sand and gravel 
 Granite, roughly worked, on wet sand. . . . 
 
 Granite, roughly worked, on dry clay 
 
 Granite, roughly worked, on moist clay . 
 
 
 Rolling Friction. The friction between the circumference of a rolling body 
 and the surface upon which it rolls is known as rolling friction. It is due to the 
 compressibility of substances, the weight of the rolling body causing a small 
 depression in the supporting surface and a flattening of the roller. Its magni- 
 tude depends on the materials of the roller and the supporting surface, and is 
 proportional to the normal pressure exercised by the roller on the rolling sur- 
 face. It depends also on the diameter of the roller, being less for large rollers 
 
MECHANICS 
 
 161 
 
 than for small ones. On highways with soft compressible surfaces, the resis- 
 tance is also affected by the width of the wheel tires, being greater for narrow 
 tires than for wide ones. 
 
 COEFFICIENTS OF FRICTION, ANGLES OF REPOSE, AND WEIGHTS 
 OF EARTHS 
 
 Material 
 
 Coefficient 
 of Friction 
 
 Angle of 
 Repose 
 Degrees 
 
 Weight 
 Pounds per 
 Cubic Foot 
 
 Mixed earth, dry. . . . 
 Mixed earth, damp. . 
 Mixed earth, wet. . . . 
 
 Sand, dry 
 
 Sand, wet 
 
 Loam, dry 
 
 Loam, wet 
 
 Clay, dry 
 
 Clay, wet 
 
 .70 
 .80 
 .40 
 .65 
 .05 
 .70 
 .50. 
 1.00 
 .30 
 
 35 
 39 
 22 
 33 
 3 
 
 35 
 27 
 45 
 17 
 
 95 
 
 115 
 
 115 
 
 110 
 
 125 
 
 75 to 100 
 90 to 120 
 
 100 
 
 125 
 
 COEFFICIENTS AND ANGLES OF FRICTION FOR MISCEL- 
 LANEOUS MATERIALS 
 
 Materials 
 
 Coefficient 
 of Friction 
 
 Angle 
 of Friction 
 
 Cast iron on cast iron .15 
 
 Cast iron on brass .15 
 
 Cast iron on oak .49 
 
 Wrought iron on wrought iron .14 
 
 Wrought iron on cast iron . .19 
 
 Wrought iron on brass .17 
 
 Wrought iron on mahogany .18 
 
 Wrought iron on oak .62 
 
 Steel on cast iron .20 
 
 Steel on brass .15 
 
 Steel on ice .014 
 
 Yellow copper on cast iron .19 
 
 Yellow copper on oak .62 
 
 Brass on cast iron .22 
 
 Brass on brass .20 
 
 Brass on wrought iron .16 
 
 Bronze on cast iron .21 
 
 Bronze on wrought iron .16 
 
 Bronze on bronze .20 
 
 Oak on oak .48 
 
 Oak on elm .25 
 
 Oak on cast iron .37 
 
 Leather on oak .33 
 
 Leather belt on oak drum .27 
 
 Leather belt on cast iron .56 
 
 Leather packing .56 
 
 Deg. Min. 
 
 8 32 
 
 8 32 
 26 6 
 
 7 58 
 10 46 
 
 9 39 
 
 10 12 
 31 47 
 
 11 19 
 
 8 32 
 48 
 
 10 46 
 31 48 
 
 12 25 
 
 11 19 
 
 9 6 
 11 52 
 
 9 5 
 
 11 19 
 
 25 38 
 
 14 3 
 20 19 
 18 16 
 
 15 7 
 
 The first table on page 162 gives the maximum, minimum, and mean values 
 of the coefficient of rolling friction for different roadway surfaces. They are 
 expressed in pounds required to overcome the resistance on a level road of a 
 gross ton (2,240 lb.). The mean value is also expressed as a ratio between 
 the frictionaj resistance and the load. 
 
 The friction of liquids moving in contact with solid bodies is independent 
 of the pressure, because the forcing of the particles of the fluid over the 
 
IQ2 MECHANICS 
 
 oroiections on the surface of the solid body is aided by the pressure of the sur- 
 rounding particles of the liquid, which tend to occupy the places of those 
 
 ROLLING FRICTION FOR DIFFERENT ROADWAY SURFACES 
 
 Character of Roadway 
 Surface 
 
 Rolling Friction 
 
 In Pounds per Gross Ton 
 
 Mean 
 In Terms 
 of Load 
 
 Maximum 
 
 Minimum 
 
 Mean 
 
 Earth, ordinary 
 Earth, dry and hard 
 Gravel, common 
 Gravel, hard rolled 
 Macadam ordinary 
 
 300 
 125 
 147 
 
 140 
 80 
 64 
 
 80 
 40 
 
 50 
 56 
 
 40 
 39 
 
 125 
 75 
 140 
 
 60 
 41 
 30 
 
 45 
 25 
 
 26 
 32 
 
 20 
 15 
 
 200 
 100 
 143 
 75 
 90 
 60 
 50 
 140 
 75 
 90 
 56 
 34 
 56 
 38 
 44 
 
 30 
 22 
 
 | 
 
 ' t 
 *% 
 
 * 
 
 lizr 
 
 Macadam, good 
 Macadam, best 
 
 Cobblestone, ordinary .... 
 Cobblestone, good. .'. 
 
 Granite block, good 
 
 Granite block, best 
 Belgian block, ordinary 
 Belgian block, good 
 
 Plank 
 
 Wooden block, in good condi- 
 
 Asphalt 
 
 
 forced over. Therefore, the coefficients of friction of liquids over solids do 
 not correspond with those of solids over solids. The resistance is directly as 
 the area of surface or contact. 
 
 COEFFICIENTS OF FRICTION IN AXLES 
 
 Axle 
 
 Bearing 
 
 Ordinary 
 Lubrication 
 
 Lubricated 
 Continuously 
 
 Bell metal 
 
 Bell metal . . 
 
 .097 
 
 
 Cast iron 
 
 Bell metal 
 
 .07 
 
 .049 
 
 Wrought iron 
 Wrought iron 
 
 Bell metal 
 Cast iron 
 
 .07 
 .07 
 
 .05 
 .05 
 
 Cast iron 
 Cast iron 
 Wrought iron 
 
 Cast iron 
 Lignum vitae 
 Lignum vitae 
 
 .07 
 .10 
 .12 
 
 .05 
 
 Friction naturally varies with the character of the surfaces, lubrication, 
 and the nature of the lubricant. The best lubricants for the purposes should 
 always be used, and the supply should be regular. When machinery is well 
 lubricated, the lubricant keeps the surfaces apart, and the frictional resistance 
 becomes very small, or about the same as the friction of liquids. 
 Frictional Resistance of Shafting. 
 Let K coefficient of friction; 
 
 PF=work absorbed, in foot-pounds; 
 
 P = weight of shafting and pulleys -{-resultant stress of belts; 
 
 H = horsepower absorbed; 
 
 D diameter of journal, in inches; 
 
 R = number of revolutions per minute. 
 
MECHANICS 163 
 
 Then, ORDINARY OILING CONTINUOUS OILING 
 
 W=.0182PD .0112PD 
 
 H = .000000556PDK .000000339PDK 
 
 K = .066 .044 
 
 As a rough approximation, 100 ft. of shafting, 3 in. diameter, making 120 
 rev. per min., requires 1 H.P. 
 
 For friction of air in mines, see Coefficient of Friction, under Ventilation. 
 
 Friction of Mine Cars. The friction of mine cars varies so much that it is 
 impossible to give a formula for calculating it in every case. No two mine 
 cars will show the same frictional resistance, when tested with a dynamome- 
 ter, and, therefore, nothing but an average friction can be dealt with. The 
 construction of the car, the condition of the track, and the lubrication are 
 important factors in determining the amount of friction. 
 
 Some of the requisites of good oil box and journal bearings may be stated. 
 Tightness is a prerequisite, and, in dry mines where the dust is very penetrating, 
 this is especially important; the bearings should be sufficiently broad; the oil 
 box large enough to hold sufficient oil to run 1 mo. without renewal, and so 
 constructed that, while it may be quickly and easily opened, it will not open 
 by jarring or by being accidentally struck by a sprag or a lump of coal. 
 
 There are a number of patented self-oiling wheels that are improvements 
 on the old-style plain wheels, and each of these has undoubtedly some point of 
 superiority over the old style. 
 
 Among the most extensively used of these patented wheels are those with 
 annular oil chambers, and those with patent bushings. Their superiority con- 
 sists in the fact that, if properly attended to, a well-lubricated bearing is secured 
 with greater regularity and less work than when the old-style wheel is used. 
 
 With a view of adopting a standard wheel, the Susquehanna Coal Co., of 
 Wilkes-Barre, Pa., experimented for a number of years with different styles 
 of self -lubricating wheels. 
 
 Mr. R. Van A. Norris, E. M., assistant engineer, made a series of 989 tests 
 with old-style wheels, some of which had patent removable bushings, and 
 others annular oil chambers, and the self- oiling wheel. The old wheels were 
 found to be practically alike in regard to friction. All the wheels were of 
 the loose outside type, 16 in in diameter, mounted on 2| in. steel axles, with 
 journals 5J in. long. The axles passed loosely through solid cast boxes, bolted 
 to the bottom sills of the cars, and were not expected to revolve. 
 
 The table of friction tests shows the results obtained with both old- and 
 new-style wheels, and is of interest to all colliery managers, inasmuch as 
 the figures given for the old-style wheels alone are the most complete in existence 
 and, as stated before, they are good averages. 
 
 Tests were made on the starting and running riction of each style of 
 wheel, under the conditions of empty and loaded cars level and grade track, 
 curves, and tangents. The instruments used were a Pennsylvania Railroad 
 spring dynamometer, graduated to 3,000 lb., with a sliding recorder, a hydraulic 
 gauge (not recprding) reading to 10,000 lb., graduated to 25 lb , and a spring 
 balance, capacity 300 lb., graduated to 3 lb. All these were tested and found 
 correct previous to the experiments. 
 
 Most of the observations on single cars were made with the 300-lb. balance. 
 The two types of old-style wheels have been classed together in the table. Each 
 car was carefully oiled before testing, and several of each type were used, the 
 results being averages from the number of trials shown in the table. 
 
 In the experiments on the slow start and motion, the cars were started 
 very slowly by a block and tackle, and the reading was taken at the moment 
 of starting. They were then kept just moving along the track for a considerable 
 distance, and the average tractive force was noted, the whole constituting one 
 experiment. 
 
 The track selected for these experiments was a perfectly straight and 
 level piece of 42 in. gauge, about 200 ft. long, in rather better condition than 
 the average mine track. The cars were 41| in. gauge, 31 ft. wheel base, 10 ft. 
 long, capacity about 85 cu. ft., with 6-in. topping. 
 
 To ascertain the tractive force required at higher speeds, trips of one, four 
 and twenty cars, both empty and loaded, were attached to a mine locomotive 
 and run about 1 mi. for each test, the resistance at various points on the 
 track, where its curve and grade were known, being noted, care also being 
 taken to run at a constant speed. Unfortunately, only four of the new-style 
 cars were available on the tracks where these trials were made. 
 
 The remarkably low results for the twenty-car trips are attributed to 
 variations in the condition of the track, and the fact that the whole train 
 
164 
 
 MECHANICS 
 
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MECHANICS 
 
 165 
 
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166 
 
 MECHANICS 
 
 was seldom pulling directly on the locomotive, the cars moving by jerks, so 
 that correct observations were impracticable. The hydraulic gauge was used 
 for these twenty-car tests, and the needle showed vibrations from 1 to 4 1 . and 
 back The mean was taken as nearly as possible. The gauge was rather too 
 quickly sensitive for the work, and the Pennsylvania Railroad dynamometer 
 was not strong enough to stand the starting jerks and the strain of accelerating 
 
 >P6< The tests jerked R O p e Haul were made on an empty-car haulage system, 
 about 500 ft. long, with overhead endless rope running continuously at a speed 
 of 180 ft per min., the cars being attached to the moving rope by a chain, 
 a ring at the end of which was slipped over a pin on the side of the car. The 
 increase of friction on the heavier grades was due to the rope pulling at a 
 greater angle across the car. Correction was not made for this angularity at 
 the time, and the rope has since been rearranged, so that the correction cannot 
 now be made. There were not enough curve experiments to permit the 
 deduction of any general formula for the resistance of these cars on curves. 
 
 The experiments on grade agree fairly well with those on a level, the rather 
 higher values obtained being probably due more to the greater effort required 
 in moving them, and the consequent jerkiness of the motion, than to any real 
 increase in resistance. As the experiments on all styles of wheels were made in 
 an exactly similar manner, the comparative value of the results is believed to 
 be nearly correct, the probable error in each set of experiments, as computed by 
 the method of least squares, varying from about 4% for slow start and motion to 
 12% for the rapid motion and twenty-car trips. 
 
 Ball and Roller Bearings. Some of the leading manufacturers now provide 
 mine-car wheels with either ball or roller bearings. In the former type, a series 
 of steel balls placed within the hub bear upon the axle; and in the latter type, 
 a series of steel rollers. In other features, however, such as the method of 
 lubrication, etc., the improved wheels are essentially the same as the old. Only 
 a limited number of tests have thus far been published upon the savings effected 
 by the use of these improved bearings in power-transmission shafting, mine- 
 car wheels, etc., but these indicate a diminution of from 15 to 75% in the fric- 
 tion over the old type of bearings. In the case of mine cars, those equipped 
 with the new type of bearing require about one-half the drawbar pull formerly 
 demanded either to start them from rest or to continue them in motion. 
 
 Quoting from one of the leading manufacturers of spiral roller bearings: 
 "The saving in power varies to a certain extent with conditions. In some cases 
 it has run as high as 60%; in others, it has been as low as 30%; a safe average 
 saving is 40% to 50%. The following series of tests was made in November, 
 1912. The twenty-five cars used in the test had been in constant use for about 
 6 mo.; the wheels were 16 in. and the axles 21 in. in diameter. 
 
 
 
 Average 
 Starting 
 Pull 
 Pounds 
 
 Average 
 Constant 
 Pull 
 Pounds 
 
 Gross 
 Weight 
 Pounds 
 
 Up-Grade 
 Per Cent. 
 
 Constant 
 Tractive 
 Effort 
 Per Ton 
 Pounds 
 
 Tractive 
 Effort 
 Per Ton, 
 Corrected 
 For Level 
 
 
 
 
 
 
 
 Pounds 
 
 Plain 
 
 297 
 
 120 
 
 5,800 
 
 .25 
 
 41.3 
 
 26.8 
 
 Spiral \ 
 Roller/ 
 
 104 
 
 80 
 
 5,800 
 
 .25 
 
 27.5 
 
 13.0 
 
 Lubrication. There is probably no factor that has a more direct bearing 
 on the cost of production per ton of coal and ores than the lubrication of mine 
 machinery, and yet it is doubtful if there is another item connected with the 
 operation of a mine less understood by owners, their managers, and engineers in 
 charge. 
 
 Steam plants are equipped with boilers of the highest known efficiency; 
 heaters are used that, by utilizing waste steam, will heat the feedwater for 
 boilers to the highest point. Modern engines that will develop a horsepower 
 with the least amount of steam are installed; bends, instead of elbows, are 
 placed in steam and exhaust pipes, so that the friction and back pressure 
 may be reduced to a minimum. In a word, everything is done in the equip- 
 ment of a plant to secure economy in its operation. After all this is done, 
 
MECHANICS 167 
 
 frequently a long step is taken in the opposite direction by the use of an oil 
 unsuited to the existing conditions, and those in charge of the plant are led 
 to believe that the lubrication is all that could be desired, simply because 
 the engines and machinery run quietly and the temperature of the bearings 
 does not become alarmingly high. The office of a lubricant is not merely to 
 secure this result, but, primarily, to reduce friction and wear to a minimum; 
 and an oil that will do this is the best oil to use, no matter what the price per 
 gallon may be. 
 
 Few realize the great loss in power due to the friction of wearing parts. 
 One of the greatest living authorities on lubrication writes: 
 
 "It may probably be fairly estimated that one-half the power expended 
 in the average case, whether in mill, mine, or workshop, is wasted on lost work, 
 being consumed in overcoming the friction of poorly lubricated surfaces." 
 
 He adds that a reduction of 50% in the work lost by friction has often been 
 secured by a change of lubricants. 
 
 As one of many instances showing the loss that will occur by the use of 
 inferior lubricants, attention is called to two flour mills located in one of the 
 Middle States. One of the plants was equipped with a condensing engine 
 capable of developing 1 H. P. on 24 Ib. of water per hr.; the other plant had 
 a simple engine, taking 30 Ib. of water per hr. The plant containing the con- 
 densing engine was purchased by the owner of the plant containing the simple 
 engine. The new owner of the plant was surprised to learn that the cost of 
 operation per barrel of flour manufactured was equally as great in the new plant 
 as in the old one. The engines were indicated, and valves found to be properly 
 adjusted and the engine working within the economical range, so far as load was 
 concerned. The loss was then attributed to the boilers, but an evaporative test 
 proved that there was no practical difference here, as the boilers, in both instan- 
 ces, were evaporating a fraction over 8 Ib. of water per Ib. of coal. At this point, 
 the question of lubrication was taken up, and, on the advice of an expert sent 
 by a prominent manufacturer of lubricants to look over the plant, an entire 
 change was made in the lubricants used, and, as a result, a money saving of 
 over $2.25 per da. (practically $700 per annum this in a plant of less than 
 250 H. P.) was effected, notwithstanding the fact that the new lubricants 
 used cost considerably more per gallon than those formerly \|sed. This sim- 
 ply indicates that the price of an oil is of little importance in comparison with 
 its friction-reducing power. Friction costs money, because it means greater 
 cost of operation per unit of output. 
 
 Among the expenses chargeable to waste power, due to inferior lubrica- 
 tion, may be included: (1) The cost of power produced in excess of that 
 really required to operate the mine per ton of output. In this calculation 
 should be included the proper proportion of salaries of engineers, and all other 
 items that contribute to the cost of the motive department, as well as the cost 
 of mining the fuel consumed in producing this excess power. (2) Wear and 
 tear of machinery, which is constantly doing more work per ton of coal mined 
 than should be required of it. 
 
 There is also an element of danger that ought to receive serious consid- 
 eration, as, while it is true that cylinder and bearing lubricants of indifferent 
 merit will, under ordinary conditions, keep the cylinders from groaning and 
 the bearings from becoming hot, experiments have proved that, in accom- 
 plishing such results, the oils in use were being taxed to their utmost; and 
 there is record of many instances where, as a result of using oils of such lim- 
 ited endurance, accidents of a serious nature have occurred, necessarily 
 causing shut-downs just at the time when the operation of the plant to its 
 fullest capacity was imperative. It is most difficult to do much more than 
 point out the danger due to the use of inferior lubricants, leaving it to the 
 purchaser himself to determine as to the intrinsic worth of the lubricants 
 offered to him. In making his selection he would do well to consult with 
 and heed the advice of some highly responsible manufacturer of lubricants 
 who has given to the question, in all its phases, the most careful study, and 
 who would most probably have the benefit of a wide experience in the applica- 
 tion as well as the manufacture of lubricants. Some buyers have, to their 
 ultimate regret, adopted, as a method of determining the merits of lubri- 
 cants, a schedule of laboratory tests. Such a method is not only useless, but 
 it is misleading to any one other than a manufacturer of lubricants, who makes 
 use of it merely as a means of insuring uniformity in his manufactured products, 
 and not as a measure whereby to judge their practical value. Indeed, many 
 oils can be very properly described by practically the same schedule of tests, 
 and yet are widely apart when their utility for a given service is considered. 
 
168 MECHANICS 
 
 As a general guide in purchasing cylinder oil for mine lubrication, it might 
 be said that a dark-colored oil is of greater value, as a rule, than one that has 
 been filtered to a red or light amber color, as the process of filtration neces- 
 sarily takes from the oil a considerable percentage of its lubricating value, 
 and at the same time the process is an expensive one. In short, if a light- 
 colored oil is insisted upon, a high price must be paid for an inferior lubricant. 
 As a word of caution, however, it would be well to add right here that irre- 
 sponsible manufacturers frequently take advantage of the fact that the most 
 efficient and best known cylinder oils are dark-colored, and endeavor, with 
 more or less success, to market as "cylinder oil" products absolutely unsuited 
 to the lubrication of steam cylinders, and that would consequently be expen- 
 sive could they be procured without cost. 
 
 For the lubrication of engine bearings, where modern appliances for 
 feeding are used, an engine oil of a free running nature is best, as it more quickly 
 reaches the parts requiring lubrication than an oil of a more sluggish nature. 
 It, of course, must not be an oil susceptible to temperature changes, but must 
 be capable of performing the service required of it under the most severe con- 
 ditions, where an oil of less backbone would fail. Such an oil would also be 
 suitable for the lubrication of dynamos, and should also give satisfaction where 
 used in lubricating the cylinders of air compressors. Where the machinery is 
 of an old type and loose-jointed, or when the bearings are open and the oil is 
 applied directly to them by means of an oiler, an engine oil of a more sluggish, 
 or viscid, nature is best. 
 
 Perhaps of equal importance to the lubrication of power machinery must 
 be considered the lubrication of the axles of mine cars. This is important, 
 first, because of the fact that perhaps three-fourths of the oil used about a coal 
 mine is used for this purpose, and, secondly, because there is really a marked 
 difference in the quality and, therefore, in the efficiency of lubricants used for 
 this purpose. Fully nine-tenths of the prominent railroads of this country are 
 today using car-axle oil, costing perhaps as much per gallon as much of the so- 
 calledi cylinder oil that is used in coal mines, they having discovered, by exhaust- 
 ive experiments, that the increased efficiency gained by using an oil of such 
 quality many times offsets the difference in the cost per gallon and enables 
 them to secure A greater mileage without any increase in their power or other 
 fixed charges. This will apply just as forcibly to the lubrication of coal cars, 
 no matter whether the power is derived from mules or electric motors; there- 
 fore, this feature of lubrication of mine equipment should receive more careful 
 attention than it does receive, as a rule. 
 
 There is considerable waste in the lubrication of mine cars. This waste is 
 hard to avoid, and, naturally, makes the buyer hesitate before adopting the use 
 of a car oil that costs very much per gallon; but even in the face of this waste 
 the increased efficiency secured by the use of a high-grade car oil will warrant 
 its use. Such waste is pretty hard to correct in mines where the old-fashioned 
 style of car axle is still in use, and where the oil is applied through an ordinary 
 spout oil can into the axle box, and allowed to drip off the axles and on to the 
 ground. When axles are equipped in the same manner as those of freight cars, 
 or where cars are equipped with one of the several different styles of patent 
 car wheels and axles that are coming into use quite extensively, it is possible 
 to regulate the feeding of the oil to the axles, so as to reduce the waste to a 
 minimum. One of these patent car wheels, which is perhaps better known than 
 any other, is constructed with a hollow hub that acts as a reservoir for the oil, 
 the oil passing from this reservoir through small holes on to a felt washer, 
 which it must saturate, and by which it is applied to the axles. Such wheels 
 require a limpid oil, as a heavy, sluggish oil will not so readily saturate the felt 
 washer referred to. A tight cap is adjusted to the end of the axle, to prevent 
 waste of oil. These wheels will run quite a length of time without reoiling 
 after the reservoir is once filled. While it costs something to equip mine cars 
 with these patent axles, such an outlay will result in more economical oper- 
 ation, particularly if at the same time the very best quality of car oil obtainable 
 is used. 
 
 Lubricant Tests. There are certain simple tests that may readily be made 
 to determine the suitability of certain oils for certain grades of work. When 
 testing oils for use in connection with engines running under constant load 
 and speed, Mr. W. W. Davis, of Boston, recommends that a thermometer be 
 placed in the bearing so that the bulb rests on the shaft, a constant feed of oil 
 being maintained. Another thermometer is hung in the engine room near 
 the bearing and away from drafts of air, so as to show the temperature of 
 the room. Commence the test when the engine is started, note the rise of 
 
STRENGTH OF MATERIALS 169 
 
 temperature at frequent intervals, also that of the room; continue the test 
 until the temperature of the bearing ceases to rise. Every hearing will in the 
 course of a few hours reach a point where heat is radiated as fast as generated. 
 Deducting the temperature of the room from that of the bearing will give the 
 rise in temperature due to friction. If the engine runs during the day only, 
 the bearing will cool off over night and after cleaning thoroughly with gasoline, 
 will be in condition to test another oil the next day. 
 
 While it is true that the coefficient of friction often decreases with the rise 
 in temperature, in everyday practice it is safe to assume that of two oils the one 
 that will keep the bearing the cooler is the best lubricant, so in tests of this kind 
 the oil showing the least rise in temperature will be the better lubricant. Such 
 tests can also be made in ring-oiled bearings of motors, dynamos, or shafting. 
 
 When testing the value of two or more cylinder oils, Mr. Ward recommends 
 that one oil be fed in at a given rate for a few days, the cylinder head then 
 removed, and the inner surface wiped over with a piece of soft white paper. 
 If there is no stain of oil and a liberal amount has been used, either the steam 
 is very wet or not enough fatty oil has been used in compounding the lubricant. 
 A separator will remove the excess moisture from the steam, when further 
 tests will indicate if there is enough fatty 91! present. 
 
 The same tests can be used to determine the least amount necessary to 
 maintain good lubrication. By gradually reducing the amount of oil fed 
 and examining the surfaces from time to time the proper amount necessary 
 to maintain good lubrication can be determined. Where tests of this kind are 
 to be made some means must be provided for the easy removal of the cylin- 
 der heads. 
 
 BEST LUBRICANTS FOR DIFFERENT PURPOSES (THURSTON) 
 
 LO b y te cXp?eS'a1? inrOCkdriUSdriVen } Light mineral lubricatin e oils - 
 VeJgreYpressures and slow speed . '. '. '. '. . { ^g^** 00 *- and ther S Ud 
 
 Heavy pressures and slow speed {^^SSlS 
 
 Heavy pressures and high speed { ^raL^ ^ **' 
 
 Light pressures and high speed {** ^^rol^m. liv6 ' 
 
 | Lard oil, tallow oil, heavy mineral 
 Ordinary machinery < oils, and the heavier vegetable 
 
 I oils. 
 Steam cylinders Heavy mineral oils, lard, tallow. 
 
 ( Clarified sperm, neat's foot, por- 
 Watches and other delicate mechanism. < poise, olive, and light mineral 
 
 L lubricating oils. 
 
 For mixture with mineral oils, sperm is best; lard is much used; olive and 
 cottonseed are good. 
 
 STRENGTH OF MATERIALS 
 
 DEFINITIONS 
 
 Stress is the cohesive force by which the particles of a body resist the exter- 
 nal load that tends to produce an alteration in the form of the body. It is 
 always equal to the effective external force acting upon the body; thus, a bar 
 subjected to a direct pulling force of 1,000 Ib. endures a stress of 1,000 Ib. 
 
 Unit stress is the stress or load per unit of area, usually taken per square inch 
 of section. For instance, if the bar just mentioned is 1 in. X 2 in. in section, the 
 unit stress of the bar will be 1,000^-2 (sectional area) = 500 Ib. 
 
 Tensile stress is produced when the external forces tend to stretch a body, 
 or pull the particles away from one another. A rope by which a weight is 
 suspended is an example of a body subjected to tensile stress. 
 
 Compressive stress is produced when the forces tend to compress the body, 
 9r push the particles closer together. A post or column of a building is sub- 
 jected to compresive stress. 
 
170 STRENGTH OF MATERIALS 
 
 AVERAGE ULTIMATE STRENGTHS OF METALS, IN POUNDS PER 
 SQUARE INCH 
 
 Kind of Metal 
 
 Com- 
 pression 
 
 Ten- 
 sion 
 
 Elastic 
 Limit 
 
 Shear- 
 ing 
 
 Modu- 
 lus of 
 Rup- 
 ture 
 
 Modulus 
 of 
 Elasticity 
 
 Aluminum: 
 Aluminum, commercia 
 Aluminum, nickel 
 Brass, Bronze, and Cop 
 per: 
 
 12,000 
 30,000) 
 
 15,000 
 40,000 
 
 24000 
 
 6,500 
 22,000 
 
 6,000 
 
 12,000 
 36,000 
 
 20,000 
 
 11,000,000 
 9 000 000 
 
 Brass wire, annealed 
 (softened by reheat- 
 ing) 
 Brass wire, unannealed 
 Bronze, aluminum 
 Bronze, gun metal 
 Bronze, manganese. . . . 
 Bronze, phosphor 
 
 120,000 
 (20,000) 
 120,000 
 
 50,000 
 80,000 
 75.000 
 32,000 
 60,000 
 50,000 
 66000 
 
 16,000 
 
 10,000 
 30,000 
 24,000 
 40000 
 
 
 53,000 
 
 14,000,000 
 10,000,000 
 
 14,000,000 
 4 500 000 
 
 Copper, bolts 
 
 30,000 
 
 30,000 
 
 
 
 
 
 Copper, cast 
 Copper wire, annealed 
 (softened by reheat- 
 ing) 
 
 (40,000) 
 
 24,000 
 36000 
 
 6.000 
 
 30,000 
 
 22,000 
 
 10,000,000 
 15 000 000 
 
 Copper wire, unan- 
 nealed 
 Cast and Wrought Iron: 
 Iron, cast 
 
 80,000 
 
 60,000 
 15000 
 
 10,000 
 6000 
 
 18000 
 
 30000 
 
 18,000,000 
 12 000 000 
 
 Iron chains 
 Iron, corrugated 
 Iron wire, annealed 
 (softened by reheat- 
 ing) 
 
 
 35,000 
 60000 
 
 
 
 40,000 
 
 15 000 000 
 
 Iron wire, unannealed. 
 Iron, wrought, shapes. . 
 Iron, wrought, rerolled 
 bars .... 
 
 46,000 
 48000 
 
 80,000 
 48,000 
 
 50 000 
 
 27,000 
 26,000 
 
 27 000 
 
 40,000 
 40 000 
 
 44,000 
 48 000 
 
 25,000,000 
 27,000,000 
 
 26 000 000 
 
 Lead: 
 Lead, cast 
 
 
 2 000 
 
 1 000 
 
 
 
 1 000 000 
 
 Lead pipe. 
 
 
 1 600 
 
 
 
 
 
 Cast and Structural Steel: 
 Steel, castings 
 Steel, structural, soft . . 
 Steel, structural, me- 
 dium 
 
 70,000 
 56,000 
 
 64 000 
 
 70,000 
 56,000 
 
 64 000 
 
 40.000 
 30,000 
 
 3 000 
 
 60,000 
 48,000 
 
 50 000 
 
 70.000 
 54.000 
 
 60 000 
 
 30,000,000 
 29,000,000 
 
 20 000 OOO 
 
 Steel wire, annealed 
 (softened by reheat- 
 ing) 
 
 
 80 000 
 
 000 
 
 
 
 on nnn nnn 
 
 Steel wire, unannealed 
 Steel wire, crucible 
 Steel wire, for suspen- 
 sion bridges 
 Steel wire, special tem- 
 pered 
 Tin and Zinc: 
 Tin, cast . 
 
 (6 000) 
 
 20,000 
 80,000 
 
 200,000 
 300,000 
 
 q zfto 
 
 60,000 
 0,000 
 
 0,000 
 
 
 
 30,000,000 
 30,000,000 
 
 30,000,000 
 
 Zinc, cast 
 
 (20*000) 
 
 5 000 
 
 4 000 
 
 
 7 OOfi 
 
 
 
 
 
 
 
 
 
 ino7 --Compression values enclosed in parentheses indicate loads producing 
 10% reduction in original lengths. 
 
STRENGTH OF MATERIALS 
 
 171 
 
 Shearing stress is produced when the forces tend to cause the particles in 
 one section of a body to slide over those of the adjacent section. A steel plate 
 acted on by the knives of a shear, and a beam carrying a load, are subjected 
 to shearing stress. 
 
 Tension, compression, and shear are called simple or direct stresses, to dis- 
 tinguish them from bending and torsion. 
 
 The amount of alteration in form of a body produced by a stress is called 
 deformation, or strain. It may be tensile deformation, compressiye deforma- 
 tion, or shearing deformation, according as the stress producing it is tensile, 
 compressive, or shearing. The rate of deformation, also called unit deformation, 
 is the deformation of a body, subjected to tension or compression, per unit of 
 AVERAGE ULTIMATE STRENGTHS OF WOODS, IN POUNDS 
 PER SQUARE INCH 
 
 
 Tension 
 
 Compression 
 
 Transverse 
 
 Shearing 
 
 
 
 
 With Grain 
 
 
 
 
 
 
 Kind 
 
 d 
 
 .s 
 
 
 G 
 
 
 en >> 
 
 .s 
 
 .3 
 
 of 
 Timber 
 
 1 
 
 G 
 
 G 
 
 c 
 
 *2g 
 
 1 
 
 iji 
 
 3 -. 
 
 G 
 
 2 
 G 
 
 
 
 1 
 
 1 
 
 ||| 
 
 1 
 
 |s| 
 
 H 
 
 I 
 
 I 
 
 
 
 
 1 
 
 "o !uQ 
 
 
 
 
 
 
 
 
 
 W 
 
 O-o 
 
 
 
 
 
 
 White oak 
 
 12,000 
 
 2,000 
 
 7,000 
 
 5.000 
 
 2,000 
 
 7.000 
 
 1,500,000 
 
 800 
 
 4.000 
 
 White pine 
 
 7.000 
 
 500 
 
 5,500 
 
 3,500 
 
 700 
 
 4,000 
 
 1,000,000 
 
 400 
 
 2,000 
 
 Southern long- 
 
 
 
 
 
 
 
 
 
 
 leaf or Georgia 
 
 
 
 
 
 
 
 
 
 
 pine 
 Douglas fir 
 
 12,000 
 8,000 
 
 600 
 
 7,000 
 5,700 
 
 5,000 
 4,500 
 
 1,400 
 800 
 
 7,000 
 5,000 
 
 1,500,000 
 1,400,000 
 
 600 
 500 
 
 5,000 
 
 Short-leaf yel- 
 
 
 
 
 
 
 
 
 
 
 low pine 
 
 9,000 
 
 500 
 
 6,000 
 
 4,500 
 
 1,000 
 
 6,000 
 
 1,200,000 
 
 400 
 
 4,000 
 
 Red pine (Nor- 
 
 
 
 
 
 
 
 
 
 
 way pine) 
 
 8,000 
 
 500 
 
 5,000 
 
 4,000 
 
 800 
 
 5,000 
 
 1,130,000 
 
 
 
 Spruce and 
 
 
 
 
 
 
 
 
 
 
 Eastern fir 
 
 8,000 
 
 500 
 
 6,000 
 
 4,000 
 
 700 
 
 4,000 
 
 1,200.000 
 
 400 
 
 3,000 
 
 Hemlock 
 
 6,000 
 
 
 
 4,000 
 
 600 
 
 3,500 
 
 900,000 
 
 350 
 
 2,500 
 
 Cypress 
 
 6,000 
 
 
 5,000 
 
 4,000 
 
 700 
 
 5,000 
 
 900,000 
 
 
 
 Cedar 
 
 7,000 
 
 
 5,500 
 
 3,500 
 
 700 
 
 4,000 
 
 700,000 
 
 400 
 
 1,500 
 
 Chestnut 
 
 8,500 
 
 
 
 4,000 
 
 900 
 
 5,000 
 
 1,000,000 
 
 600 
 
 2,000 
 
 California red- 
 
 
 
 
 
 
 
 
 
 
 wood 
 
 7,000 
 
 
 
 4,000 
 
 600 
 
 4,500 
 
 700,000 
 
 400 
 
 
 California 
 
 
 
 
 
 
 
 
 
 
 spruce 
 
 
 
 
 4,000 
 
 
 5,000 
 
 1,200,000 
 
 
 
 Factor of safety 
 
 10 
 
 10 
 
 5 
 
 5 
 
 4 
 
 6 
 
 2 
 
 4 
 
 4 
 
 length. If an iron bar 6 ft. long is subjected to a force that elongates it 1 in., 
 the rate of deformation will be 1 in. -5- 72 (length of the bar, in inches) = .0139 in. 
 The modulus or coefficient of elasticity is the ratio between the stresses and 
 corresponding deformations for a given material, which may have a somewhat 
 different modulus of elasticity for tension, compression, and shear. If / is the 
 increase per unit 9f length of a material subjected to tensile stress, and p the 
 unit stress producing this elongation, the modulus of elasticity 
 
 For example, a wrought-iron bar, 80 in. long, subjected to a unit tensile stress 
 p of 10,000 lb., stretched .029 in. The unit strain I, or stretch per inch of 
 length, is .029 in.T-80 in. = .0003625 in. Then, 
 
172 
 
 STRENGTH OF MATERIALS 
 
 The relation E = p -5- Us true only when equal additions of stress cause equal 
 increases of strain. Previous to rupture, this condition ceases to exist, and the 
 material is said to be strained beyond the elastic limit, which, therefore, is that 
 degree of stress within which the modulus of elasticity is nearly constant and 
 equal to the unit stress divided by the unit strain. 
 
 The ultimate strength of a given material in tension, compression, or shear 
 is that unit stress which is just sufficient to break it, and is equal to the maxi- 
 mum stress causing rupture divided by the original area of the cross-section. 
 The accompanying tables show the average ultimate strengths, in pounds per 
 square inch, of both metals and woods. 
 
 Working stress is the maximum unit stress to which the parts of a structure 
 are to be subjected. 
 
 Factor of safety is the ratio of ultimate strength to working stress. The 
 factor of safety required for a structure depends on the material and on the 
 character of the loads applied that is, whether the loads are quiescent or such 
 that cause impact and vibrations. For stone and brick, a factor of safety of 
 from 10 to 30 is used; for timber, from 8 to 15; for cast iron, from 6 to 20; for 
 reinforced concrete, from 4 to 6; and for structural steel, from 3 to 6. 
 
 It is obvious that structures subjected to loads causing impact should be 
 designed for a higher factor of safety than those having to carry static loads. 
 When a structure, as a bridge, carries both dead load and live loads, the modern 
 practice favors the specifying of one working unit stress for both kinds of loads, 
 and providing for the effect of vibration by increasing the live-load stress or 
 bending moment by an amount / determined from a so-called impact formula. 
 The formula most in use for railroad bridges is 
 
 300 
 ' 
 
 in which 5 = maximum live-load stress or bending moment in member, 
 
 L = length, in feet, of single track that must be loaded in order to 
 obtain value 5. 
 
 SIMPLE, OR DIRECT, STRESS 
 
 Formula for Simple Stress. If P is an external force producing tension, 
 compression, or shear uniformly distributed over an area A, and s is the unit 
 working stress, the fundamental formula for designing parts of structures 
 subjected to a simple, or direct, stress is 
 P = sA 
 
 When designing members that are in tension, A must be taken as the net 
 area of the section. This is determined by deducting from the gross section 
 the greatest number of pin, bolt, or rivet holes that can be cut by a plane at 
 right angles to the section. Rivet holes are usually taken f in. larger than 
 the diameter of the rivet. 
 
 Important Applications of Formulas for Direct Stress. 1. ^Tension mem- 
 bers aiid short compression members of roof or bridge trusses are examples of 
 simple stress, and their sections are determined by the preceding formula. 
 
 EXAMPLE. A tension member of a roof truss is made of two 3|"X3"X \" 
 angles connected by one line of rivets J in. in diameter. What stress will it 
 carry at 16,000 Ib. per sq. in.? 
 
 FIG. 
 
 FIG. 2 
 
 SOLUTION. The gross sectional area of a 3i"X3"X J" angle is 3.25 sq. in. 
 The deduction for one rivet hole is (| + i)X| = .5. The net area is 3.25 -.5 
 = 2 J 5 - A he carrying capacity of the angle is therefore 2.75X 16,000 = 44,000 Ib. 
 TJ?-' i I? J"} ts als ? are examples of simple stress. In the joint shown 
 
 Fig. 1, the rivet is in single shear, because there is only one section e of the 
 rivet subjected to a shearing stress. The amount R that one rivet will carry 
 being equal to the area of the cross-section of the rivet multiplied by the unit 
 
STRENGTH OF MATERIALS 
 
 3 
 
 173 
 
 11 
 
 OS C 
 
 IO b 
 
 00" O3 
 
 8 
 
 O O O O 
 q 00 CO O3 
 
 iff <N" co" co" 
 
 o o ojo o 
 
 CO 00 ,' <N b- 
 
 !O O 
 
 :o co 
 o oo :<N CD 
 
 rH tH IN (N CO 
 
 2 
 
 o" 
 
 OO" O3* 
 
 (N CO 
 
 00" 03 
 
 *gSl 
 
 O O O O ;C 
 iH & 5 (N 't 
 
 00 10 <N 03 |c 
 
 i!8 
 
 0:0 
 3^ 
 
 i IN ;<N co co 
 
 b- b- 
 
 co" 
 
 
 82 
 
 rH 00 
 
 o* -* 
 
 1 
 
 g2 
 
 <l 00 
 
 O C 
 
 00 C 
 CO* 03 
 
 00 O 
 
 o 
 
 * 
 O b- 
 
 2 
 
 <N 00 CO 
 
 "O 
 00* OS rH 
 
 I 
 
 5 0s" 
 
 o o b-:oo 
 
 *1 
 
 !r-i 00 
 
 
 S8^ x 
 
 CO b- OS 
 
 o o o o 
 
 CD O b- 
 
 CD* 03~ rH 
 
 TjH CO CO IO 00 
 
 -88 
 
 _5 
 
 8000 
 GO rH b* 
 b- b- O3 ^ O 
 
 OS CO b- 
 
 000 
 
 ^H CO Tt* CO 
 
 111 
 
 2 " 
 
 CO GO 00 CO 
 
 5< CD b- 
 
 O CO i-l TH 
 
 CO CO TjH 
 
 i-H O 
 
 o oo 
 
 CO b. 
 
174 STRENGTH OF MATERIALS 
 
 shearing stress, or R = sA, the number n of rivets required to transfer a stress 
 T by single shear is ,_^_JL 
 
 . n ~R~As 
 
 In Fig. 2, the rivet is subjected to shear on two sections, d and e, and it is 
 said to be in double shear. The amount of stress that one rivet can carry in 
 double shear is twice that of one in single shear, and, using the preceding nota- 
 tion, _ T 
 
 H ~2R 
 
 The bearing value of a rivet is the compressive stress induced by the rivet 
 in bearing on the plate, and is also calculated by the simple-stress formula 
 
 P = sA 
 in which P = value of rivet in bearing; 
 
 5 = unit working stress in bearing; 
 A = bearing area. 
 
 It is customary to assume that the bearing area A is the thickness of the 
 plate multiplied by the diameter of the rivet. In calculating the required 
 number of rivets, both the shearing and the bearing value of one rivet are 
 determined and the critical value (the smaller) used. 
 
 The accompanying table gives the shearing and bearing values of rivets, in 
 pounds, for different values of the working stress. 
 
 3. Strength of Cylindrical Shells and Pipes With Thin Walls. When a 
 cylinder is subjected t9 internal pressure, the tensile stress developed in the 
 walls or shell of the cylinder is called circumferential stress, or hoop tension. 
 Let s = intensity of this stress; 
 
 d = internal diameter of cylinder; 
 
 p = intensity of pressure on inner surface of the cylinder; 
 
 t = thickness of shell. 
 
 pd pd 
 
 l ~2s 2t 
 
 The first formula serves to compute the thickness when p, d, and s (working 
 stress) are given; and the second one is used to compute the intensity of stress 
 when the intensity of pressure p and the dimensions of the cylinder are given. 
 
 EXAMPLE. What should be the thickness of walls of a cast-iron water pipe, 
 inside diameter 24 in., to resist a water pressure of 200 Ib. per sq. in., using a 
 unit working stress of 2,000 Ib.? 
 
 SOLUTION. Here, d = 24, p = 200, and s = 2,000. Substituting in the formula 
 for*, M 200X24 
 
 4. Temperature Stresses. If a bar subjected to change of temperature is 
 constrained so that it can neither expand nor contract, the constraint exerts on 
 it a force sufficient to prevent the deformation. This causes in the bar a 
 corresponding stress called temperature stress. It is compressive when the 
 change of temperature is a rise, and tensile when a fall. 
 
 Let T be the stress induced in a bar, whose area is a, by a rise or fall of <; 
 also let c be the coefficient of expansion and E the modulus of elasticity of the 
 material. Then, T = ctaE 
 
 The coefficient of expansion for a number of substances is given in the 
 section on Heat, Fuels, Etc. 
 
 EXAMPLE. A wrought-iron bar 1.5 in. square has its ends fastened to firm 
 supports. What is the stress produced in it by a change of 50 in its tempera- 
 ture? 
 
 SOLUTION. Here, = 25,000,000; = 1.5X1.5 = 2.25 sq. in., and < = 50; 
 and, c = . 00000686. Substituting in the formula, T=, 00000686X50X2.25 
 X 25,000,000 = 19,294 Ib. 
 
 BEAMS 
 
 A beam is a body resting upon supports and liable to transverse stress. 
 Beams are designated by the number and location of the supports, and may 
 be simple, cantilever, fixed, or continuous, 
 
 A simple beam is one that is supported at each end, the distance between its 
 supports being the span. 
 
 A cantilever is a beam that has one or both ends overhanging the support; 
 or a beam that has one end firmly fixed and the other end free. 
 
 A fixed beam is one that has both ends firmly secured. 
 
 A continuous beam is one which rests upon more than two supports. 
 
STRENGTH OF MATERIALS 
 
 175 
 
 Reactions. The loads acting on a beam are balanced by the reactions or 
 supporting forces; their sum must therefore be equal to the sum of the loads. 
 To find any reaction, as #2, at B, Fig. 1, take moments of all the external forces 
 about the other support A and divide their sum by the span. With reference to 
 Fig. 1, 
 
 The reaction R\ can be found in a similar manner by taking moments about 
 the support B. Their sum Ri+Ri must be equal to the sum of loads 
 
 EXAMPLE. Find the reactions of a cantilever bridge loaded as shown in 
 Fig. 2. 
 
 SOLUTION. Substituting given values in the formula and noting that the 
 moment of Pi about B is of opposite sign to the moments of the other loads, 
 
 10.000X120+8.000X90 + 15.000X40-20.000X30 
 Ri = - jgQ - = 12,800 Ib. 
 
 and 
 
 _ 
 
 loO 
 
 The sum of the loads is 10,000 + 8,000+15,000+20,000 = 53,000. The sum of 
 the reactions is 40.200+12,800 = 53,000. 
 
 External Shear and Bending Moment. The forces acting on a beam tend, 
 on the one hand, to shear its fibers vertically and, on the other hand, to bend 
 it, producing compressional stresses in the fibers on one side of the neutral axis 
 and tensional on the other side. The tendency to shear the fibers vertically is 
 determined by the external shear, and that of bending by the bending moment. 
 For brevity, external shear is often called simply shear, but it must not be con- 
 fused with shearing stress at the section. 
 
 Forces acting upwards are considered positive, and those acting downwards, 
 negative. The external shear at any section of a beam is the algebraic sum of 
 all the external forces (loads and reactions) on one side of the section. It 
 is equal to either reaction minus the sum of the loads between that reaction 
 and the section considered. The maximum shear is always equal to the 
 greater reaction. For a simple beam with a uniformly distributed load, the 
 maximum shear is at the supports, and is equal to one-half the load, or to the 
 reaction; the shear changes at every point of the loaded length, the minimum 
 shear being zero at the center of the span. The maximum shear in a simple 
 beam having a single load concentrated at the center is equal to one-half the 
 load, and is uniform throughout the beam. Where a beam supports several 
 concentrated loads, changes in the amount of shear occur only at the points 
 where the loads are applied. 
 
 The external shear is resisted by the internal shear, or shearing stress, of the 
 beam, which is numerically equal to the external shear. If the external shear is 
 denoted by V, and the area of the cross-section by A , the average intensity of 
 
 Y 
 shearing stress in the section is . This shearing stress is not uniformly 
 
 A 
 distributed, and in beams of rectangular cross-section, the maximum intensity 
 
 of shearing stress is . Hence, a rectangular beam must be so designed that 
 
 this value will not exceed the working shearing strength of the material. 
 
 In metallic beams with thin webs (plate girders), the shearing stress may be 
 considered as uniformly distributed over the cross-section of the web. There 
 is, also, at every horizontal or longitudinal section of the beam, a horizontal 
 shearing stress the intensity of which at any point is equal to the intensity of the 
 vertical shearing stress at that point. 
 
176 STRENGTH OF MATERIALS 
 
 Although the maximum intensity of shearing stress, both horizontal and 
 vertical, in wooden beams is usually small, the shearing strength of wood along 
 the grain is also small. As the horizontal external shear usually acts along the 
 grain, the safe load for a wooden beam may depend on its shearing strength and 
 not on its bending strength. For instance, the safe load for a beam 4 in. X 12 in. 
 and 4 ft. long is 16,000 lb., uniformly distributed, when based on a fiber strength 
 of 1,000 lb. per sq. in. Such a load will produce a shearing stress per unit 
 
 of area equal to ^ ' =250 lb. per sq. in., which exceeds the working 
 
 2, /x 4o 
 shearing stress for the wood along the grain by about 100 lb. per sq. in. 
 
 The bending moment at any section of a loaded beam is equal to the algebraic 
 sum of the moments of all the external forces (loads and reactions) to the right or 
 left of the section about that section. For example, 
 the bending moments at several points on the 
 beam shown in Fig. 3 are as follows: At Wi 
 = /?io; at W2 Ri(a+b) Wib; at W3 = Ri(a-\-b-\-c) 
 [Wzc+Wi(b + c)], or Rid. 
 
 The bending moment varies, depending on the 
 shear, and attains a maximum value at the point 
 Fir ^ 8* wnere the shear changes sign. If the loads are con- 
 
 centrated at several points, the maximum bending 
 moment will be under the load at which the sum of all the loads between one 
 support up to and including the load in question first becomes equal to, or 
 greater than, the reaction at the support. Hence, to find the maximum bend- 
 ing moment in any simple beam: 
 
 Rule. Compute the reactions and determine the point where the shear changes 
 sign. Calculate the moment about this point of either reaction, and of each load 
 between the reaction and the point, and 
 subtract the sum of the latter moments 
 from the former. 
 
 EXAMPLE. What is the maximum 
 bending moment of the beam loaded as 
 shown in Fig. 4? 
 
 SOLUTION. The reactions due to 
 the uniform load are equal to one-half 
 of the load; those due to the concen- 
 trated loads are computed by the prin- 
 ciple given under Reactions. Both 
 
 added give /?i = 18,170 lb. and R 2 ^ R. & ' 
 
 = 14,330 lb. Beginning at Ri and sub- FlG ' 4 
 
 tracting the loads in succession, it is found that the shear just to the left of 
 the load d is 18,170 16,500; and just to right of the load d it becomes nega- 
 tive. Hence, the shear changes sign under the load d and the bending moment 
 is maximum at that point. It is equal to 
 
 18,170 X 13 - 10,000 X 7 - = 123,960 ft.-lb. 
 
 Formulas for the maximum bending moments and shears for beams loaded 
 and supported in different ways are given in the following table. 
 
 For a beam supporting moving loads, the maximum bending moment occurs: 
 
 1. For a single load, when the load is at the middle of the span. 
 
 2. For two equal loads, under either load, when the two loads are on 
 opposite sides of the center, and one of the loads is at a distance from the center 
 equal to one-fourth the distance between the loads. 
 
 3. For two unequal loads, under the heavier load, when that load and the 
 center of gravity of the two loads are equidistant from the center of gravity 
 of the beam. 
 
 EXAMPLE. A beam 24 ft. long supports two moving loads 6 ft. apart. The 
 left-hand load is 8,000 lb., and the right-hand load is 4,000 lb. Find the maxi- 
 mum bending moment. 
 
 SOLUTION. The center of gravity of the loads is 2 ft. from the left-hand 
 load. The maximum bending moment occurs under the heavy load, and 
 obtains when the latter is 1 ft. to the left of the center of the beam. The left 
 
 reaction is, then, =5,500 lb., and the maximum bending moment is 
 
 5,500X11 = 60,500 ft.-lb. 
 
 Designing of Beams. In every section of a carrying beam there is induced 
 an internal moment called the moment of resistance, which is equal to the bending 
 
STRENGTH OF MATERIALS 
 
 177 
 
 S 
 
 H 
 
 |a^ 
 
 Is 
 
 r 
 
 5 K 
 
 l 
 
 Sl w ' 
 
 1=1 
 
 h 
 
178 STRENGTH OF MATERIALS 
 
 moment at that section. As previously explained, the resisting moment is 
 equal to -/; and, if the maximum bending moment is denoted by M, M = -f; 
 
 whence, 
 
 M = 7 
 
 / c 
 
 which is the fundamental formula for the designing of beams; / is the working 
 stress in flexure, which is the modulus of rupture divided by a suitable factor 
 of safety. 
 
 The modulus of rupture, also called the ultimate strength of flexure, is the 
 extreme fiber stress that a material subjected to bending can withstand. Its 
 value is intermediate between the ultimate strength in compression and tension. 
 The accompanying tables give the average values of the modulus of rupture for 
 a number of materials. 
 
 When a beam is to be designed to carry certain loads, the maximum bending 
 moment is determined and divided by /. The latter is usually given or is found 
 by dividing the modulus of rupture of the material by a suitable factor of safety. 
 The problem then reduces itself to the finding of a section that has a value of 
 
 -, the section modulus, equal to -7. For rolled- steel sections, the value of - can 
 
 j c 
 
 be taken from a manufacturer's handbook. For a rectangular section, 
 
 7 = M2 
 
 c 6 
 
 b being the breadth and d the depth of the secti9n. As the expression contains 
 two unknown quantities b and d, a value for either one may be assumed and 
 substituted, and the formula solved for the other. If a built-up beam is used 
 the section has to be found by trial; a suitable section is first assumed and its 
 section modulus is computed by the principles given under the heading Moment 
 
 of Inertia; if necessary, it is modified until it is equal to -7. 
 
 EXAMPLE. Design both a rolled-steel I beam and a solid wooden beam TO ft 
 long, each to carry a uniform load of 250 Ib. per ft. in addition to a central load 
 of 2,000 Ib., assuming for wood a working stress of 1,000 Ib. per sq. in. and for 
 steel 15,000 Ib. per sq. in. 
 
 SOLUTION. The maximum bending moment occurs at the middle of the 
 beam and is equal to the sum of the moments due to the uniform load and the 
 central load; therefore, 
 
 For a steel beam, = J^QQQ = 6.5. From a manufacturer's handbook, a 
 6-in. I beam of 12.25 lb. has a section modulus of 7.3 and can therefore be used. 
 
 For a wooden beam, = y = 97.5 = p assuming that b = 6 in., d = V97T5 
 = 10 in. nearly. 
 
 Stiffness. When designing a beam, it is sometimes necessary to ascer- 
 tain the amount that it will deflect under given loads. This, for instance, is the 
 case when designing supports for machinery parts or joists for plastered ceilings, 
 in which latter case the deflections should not exceed 3^ of the span. The 
 following table gives deflection formulas for the most usual cases. In these 
 formulas I is the span, in inches; W, the total load acting on the beam; /, 
 the moment of inertia of the cross-section of the beam; and E, the modulus of 
 elasticity of the material. 
 
 EXAMPLE 1. A simple timber beam 10 ft. long, and having a width of 4 in. 
 and a depth of 12 in., carries a uniform load of 400 lb. per ft. What is the 
 deflection? 
 
 SOLUTiON.yAccording to the table, the deflection for a uniformly distributed 
 
 In this case> * =1 X12 = 120; W= 400X10 = 4,000; E 
 
 = 1,500,000; and I = ~~~ = 576. Substituting in the formula, 
 
STRENGTH OF MATERIALS 
 
 179 
 
 ^ 
 
 S co 
 
 &ftj 
 
 tS 10 
 
 LL 
 
 Hg) 
 
180 
 
 STRENGTH OF MATERIALS 
 
 COLUMNS 
 
 The strength of a compression member depends on the ratio of its length 
 to its least lateral dimension, or, what is the same thing, on the ratio of slender- 
 ness; that is, the ratio of its length to its radius of gyration. 
 
 For compression members whose ratio of slenderness does not exceed 30, 
 
 r> 
 
 the formula S = ~T. f r simple stress, may be used. 
 
 When this ratio exceeds 30, but is not more than 150, s should be deduced 
 from Rankine's formula, s u 
 
 in which 
 
 *? 
 
 ultimate strength in compression; 
 
 1 = length; 
 r = radius 
 
 ius of gyration. 
 coefficient from table. 
 The ultimate strength in compression s, t should be divided by a suitable 
 factor of safety. Both / and r are expressed in the same unit. The values of ki, 
 which depend on the material of the column and the condition of its ends 
 that is whether fixed or round are given in the following table: 
 
 VALUES OF fei (RANKINE'S FORMULA) 
 
 Material 
 
 Both Ends 
 Flat or Fixed 
 
 One End 
 Round 
 
 Both Ends 
 Round 
 
 Cast iron 
 Wrought iron. 
 Steel 
 Wood 
 
 1 
 
 1.78 
 
 4 
 
 5,000 
 1 
 
 5,000 
 1.78 
 
 5,000 
 4 
 
 36,000 
 1 
 25,000 
 1 
 
 36,000 
 1.78 
 
 36,000 
 4 
 
 25,000 
 
 1.78 
 
 25,000 
 4 
 
 
 3,000 
 
 3,000 
 
 3,000 
 
 When the value of - exceeds 150, Euler's formula, which is given later, 
 
 should be used. 
 
 The straight line formula is more convenient for determining the value of s, 
 and is now in extensive use. It is only approximate, giving values of s that 
 differ somewhat from those obtained by Rankine's formula; but the difference 
 is on the side of safety. For the same notation as before, the straight-line 
 
 formula is s = s u k - 
 
 CONSTANTS FOR THE STRAIGHT-LINE AND EULER'S FORMULAS 
 
 1 . - 
 
 Medium Steel 
 
 Wrought Iron 
 
 Cast 
 Iron 
 
 Flat 
 Ends 
 
 Pin 
 Ends 
 
 Flat 
 Ends 
 
 Pin 
 
 Ends 
 
 Flat 
 Ends 
 
 Su 
 
 52,500 
 179 
 
 lt>5 
 666m 
 
 52,500 
 220 
 
 159 
 
 444 m 
 
 42,000 
 128 
 
 218 
 666m 
 
 42,000 
 157 
 
 178 
 444 m 
 
 80,000 
 438 
 
 122 
 395 m 
 
 k. :::::\ 
 
 limit of - 
 nE*t 
 
STRENGTH OF MATERIALS 
 
 181 
 
 The values of s u and k are given in the accompanying table, in which will 
 also be found the limit of - within which the formula may be used. When - 
 
 exceeds this limit, Euler's formula, which follows, should be used. 
 
 EXAMPLE. What is the ultimate strength per square inch of a medium- 
 steel column 25 ft. long both ends of which are fixed and the radius of gyration 
 of which is 2.5? 
 
 SAFE LOADS FOR HOLLOW, CYLINDRICAL, CAST-IRON COLUMNS 
 
 (The Carnegie Steel Co., Limited) 
 
 1 
 
 1 
 
 o> 
 
 Length of Columns in Feet 
 
 ^ 
 
 c 5 
 
 side Diai 
 Inches 
 
 Jl 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 -4 
 
 C 
 
 tP 
 
 US! 
 
 i * 
 
 
 s 
 
 JE: 
 
 Safe Load, in Tons of 2,000 Lb. 
 
 & 
 
 11' 
 
 6 
 
 
 26.2 
 
 23.0 
 
 20.1 
 
 17.5 
 
 15.2 
 
 13.2 
 
 11.5 
 
 
 
 8.6 
 
 26.95 
 
 6 
 
 
 37.5 
 
 33.0 
 
 28.8 
 
 25.0 
 
 21.7 
 
 18.9 
 
 16.5 
 
 
 
 12.4 
 
 38.59 
 
 6 
 
 
 42.7 
 
 37.6 
 
 32.8 
 
 28.5 
 
 24.7 
 
 21.5 
 
 18.8 
 
 
 
 14.1 
 
 43.96 
 
 6 
 
 1 
 
 47.6 
 
 41.9 
 
 36.5 
 
 31.8 
 
 27.6 
 
 24.0 
 
 21.0 
 
 
 
 15.7 
 
 49.01 
 
 6 
 
 H 
 
 52.2 
 
 46.0 
 
 40.1 
 
 34.8 
 
 30.2 
 
 26.3 
 
 23.0 
 
 
 
 17.2 
 
 53.76 
 
 7 
 
 1 
 
 47.7 
 
 43.1 
 
 38.5 
 
 34.3 
 
 30.4 
 
 26.9 
 
 23.9 
 
 21.2 
 
 18.9 
 
 14.7 
 
 45.96 
 
 7 
 
 1* 
 
 61.1 
 
 55.2 
 
 49.3 
 
 43.8 
 
 38.9 
 
 34.4 
 
 30.6 
 
 27.1 
 
 24.2 
 
 18.9 
 
 58.90 
 
 7 
 
 H 
 
 67.2 
 
 60.8 
 
 54.3 
 
 48.3 
 
 42.8 
 
 37.9 
 
 33.7 
 
 29.9 
 
 26.7 
 
 20.8 
 
 64.77 
 
 8 
 
 f 
 
 57.9 
 
 53.3 
 
 48.6 
 
 44.1 
 
 39.7 
 
 35.8 
 
 32.2 
 
 28.9 
 
 26.1 
 
 17.1 
 
 53.29 
 
 8 
 
 1* 
 
 74.6 
 
 68.7 
 
 62.5 
 
 56.7 
 
 51.1 
 
 46.0 
 
 41.4 
 
 37.3 
 
 33.6 
 
 22.0 
 
 68.64 
 
 8 
 
 u 
 
 89.9 
 
 82.8 
 
 75.5 
 
 68.4 
 
 61.7 
 
 55.5 
 
 49.9 
 
 44.9 
 
 40.5 
 
 26.5 
 
 82.71 
 
 9 
 
 1 
 
 68.1 
 
 63.6 
 
 58.9 
 
 54.2 
 
 49.6 
 
 45.2 
 
 41.2 
 
 37.5 
 
 34.1 
 
 19.4 
 
 60.65 
 
 9 
 
 1 
 
 88.0 
 
 82.3 
 
 76.2 
 
 70.0 
 
 64.1 
 
 58.4 
 
 53.2 
 
 48.4 
 
 44.1 
 
 25.1 
 
 78.40 
 
 9 
 
 11 
 
 106.6 
 
 99.6 
 
 92.2 
 
 84.8 
 
 77.6 
 
 70.8 
 
 64.4 
 
 58.7 
 
 53.4 
 
 30.4 
 
 94.94 
 
 9 
 
 
 123.8 
 
 115.7 
 
 107.1 
 
 98.5 
 
 90.1 
 
 82.2 
 
 74.8 
 
 68.1 
 
 62.0 
 
 35.3 
 
 110.26 
 
 9 
 
 ll 
 
 139.6 
 
 130.5 
 
 120.8 
 
 111.1 
 
 101.6 
 
 92.7 
 
 84.4 
 
 76.8 
 
 69.9 
 
 39.9 
 
 124.36 
 
 10 
 
 1 
 
 101.4 
 
 95.9 
 
 89.8 
 
 83.6 
 
 77.4 
 
 71.5 
 
 65.8 
 
 60.5 
 
 55.5 
 
 28.3 
 
 88.23 
 
 10 
 
 li 
 
 123.3 
 
 116.5 
 
 109.1 
 
 101.6 
 
 94.1 
 
 86.8 
 
 79.9 
 
 73.4 
 
 67.5 
 
 34.4 
 
 107.23 
 
 10 
 
 if 
 
 143.7 
 
 135.8 
 
 127.3 
 
 118.5 
 
 109.7 
 
 101.2 
 
 93.2 
 
 85.6 
 
 78.7 
 
 40.1 
 
 124.99 
 
 10 
 
 ll 
 
 162.7 
 
 153.8 
 
 144.1 
 
 134.1 
 
 124.2 
 
 114.6 
 
 105.5 
 
 97.0 
 
 89.1 
 
 45.4 
 
 141.65 
 
 11 
 
 1 
 
 114.8 
 
 109.4 
 
 103.5 
 
 97.3 
 
 91.0 
 
 84.8 
 
 80.2 
 
 73.1 
 
 67.7 
 
 31.4 
 
 98.03 
 
 11 
 
 
 139.9 
 
 133.3 
 
 126.1 
 
 118.6 
 
 110.9 
 
 103.3 
 
 97.8 
 
 89.4 
 
 82.5 
 
 38.3 
 
 119.46 
 
 11 
 
 if 
 
 163.5 
 
 155.9 
 
 147.5 
 
 138.6 
 
 128.7 
 
 120.8 
 
 114.3 
 
 104.1 
 
 96.4 
 
 44.8 
 
 139.68 
 
 11 
 
 If 
 
 185.7 
 
 177.1 
 
 167.5 
 
 157.5 
 
 147.3 
 
 137.2 
 
 129.8 
 
 118.3 
 
 109.5 
 
 50.9 
 
 158.68 
 
 11 
 
 2 
 
 206.6 
 
 196.9 
 
 186.3 
 
 175.1 
 
 163.8 
 
 152.6 
 
 144.4 
 
 131.5 
 
 121.8 
 
 56.6 
 
 176.44 
 
 12 
 
 1 
 
 128.0 
 
 122.9 
 
 117.2 
 
 111.0 
 
 104.7 
 
 98.4 
 
 92.2 
 
 86.1 
 
 80.4 
 
 34.6 
 
 107.51 
 
 12 
 
 
 156.4 
 
 150.1 
 
 143.1 
 
 135.7 
 
 127.9 
 
 120.2 
 
 112.6 
 
 105.2 
 
 98.2 
 
 42.2 
 
 131.41 
 
 12 
 
 ji 
 
 183.3 
 
 175.9 
 
 167.7 
 
 159.0 
 
 149.9 
 
 140.9 
 
 132.0 
 
 123.3 
 
 115.1 
 
 49.5 
 
 154.10 
 
 12 
 
 If 
 
 208.7 
 
 200.4 
 
 191.0 
 
 181.1 
 
 170.7 
 
 160.4 
 
 150.3 
 
 140.5 
 
 131.1 
 
 56.4 
 
 175.53 
 
 12 
 
 2 
 
 232.7 
 
 223.4 
 
 213.0 
 
 201.9 
 
 190.4 
 
 178.9 
 
 167.6 
 
 156.6 
 
 146.1 
 
 62.8 
 
 195.75 
 
 13 
 
 1 
 
 141.2 
 
 136.3 
 
 130.7 
 
 124.7 
 
 118.5 
 
 112.1 
 
 105.8 
 
 99.5 
 
 93.5 
 
 37.7 
 
 117.53 
 
 13 
 
 11 
 
 172.8 
 
 166.8 
 
 160.0 
 
 152.7 
 
 145.0 
 
 137.2 
 
 129.4 
 
 121.8 
 
 114.4 
 
 46.1 
 
 143.86 
 
 13 
 
 H 
 
 203.0 
 
 195.9 
 
 187.9 
 
 179.3 
 
 170.3 
 
 161.1 
 
 152.0 
 
 143.1 
 
 134.3 
 
 54.2 
 
 168.98 
 
 13 
 
 If 
 
 231.6 
 
 223.6 
 
 214.5 
 
 204.7 
 
 194.4 
 
 183.9 
 
 173.5 
 
 163.3 
 
 153.3 
 
 61.9 
 
 192.88 
 
 13 
 
 2 
 
 258.9 
 
 249.9 
 
 239.7 
 
 228.7 
 
 217.3 
 
 205.5 
 
 193.9 
 
 182.5 
 
 171.3 
 
 69.1 
 
 215.56 
 
 14 
 
 1 
 
 154.3 
 
 149.6 
 
 144.3 
 
 138.5 
 
 132.3 
 
 125.9 
 
 119.5 
 
 113.1 
 
 106.8 
 
 40.8 
 
 127.60 
 
 14 
 
 u 
 
 189.2 
 
 183.4 
 
 176.9 
 
 169.7 
 
 162.2 
 
 154.4 
 
 146.5 
 
 138.6 
 
 131.0 
 
 50.1 
 
 156.31 
 
 14 
 
 H 
 
 222.6 
 
 215.8 
 
 208.1 
 
 199.7 
 
 190.8 
 
 181.7 
 
 172.3 
 
 163.1 
 
 154.1 
 
 58.9 
 
 183.67 
 
 14 
 
 If 
 
 254.4 
 
 246.7 
 
 237.9 
 
 228.3 
 
 218.1 
 
 207.6 
 
 197.0 
 
 186.5 
 
 176.2 
 
 67.4 
 
 210.00 
 
 14 
 
 2 
 
 284.8 
 
 276.2 
 
 266.4 
 
 255.6 
 
 244.2 
 
 232.4 
 
 220.6 
 
 208.8 
 
 197.2 
 
 75.4 
 
 235.12 
 
 15 
 
 1 
 
 167.4 
 
 162.9 
 
 157.8 
 
 152.1 
 
 146.0 
 
 139.7 
 
 133.3 
 
 126.8 
 
 120.4 
 
 44.0 
 
 137.28 
 
 15 
 
 
 205.5 
 
 200.0 
 
 193.7 
 
 186.7 
 
 179.3 
 
 171.5 
 
 163.6 
 
 155.7 
 
 147.9 
 
 54.0 
 
 168.48 
 
 15 
 
 U 
 
 242.1 
 
 235.7 
 
 228.2 
 
 220.0 
 
 211.2 
 
 202.1 
 
 192.8 
 
 183.5 
 
 174.2 
 
 63.6 
 
 198.74 
 
 15 
 
 If 
 
 277.2 
 
 269.8 
 
 261.3 
 
 251.9 
 
 241.9 
 
 231.4 
 
 220.7 
 
 210.1 
 
 199.5 
 
 72.9 
 
 227.45 
 
 15 
 
 2 
 
 310.8 
 
 302.5 
 
 293.0 
 
 282.5 
 
 271.2 
 
 259.5 
 
 247.5 
 
 235.5 
 
 223.6 
 
 81.7 
 
 254.90 
 
182 STRENGTH OF MATERIALS 
 
 SOLUTION. By the straight-line formula, 
 
 QC vv 1 O 
 
 5 = 60,000- 179 X f ^~ = 38,520 Ib. per sq. in. 
 
 Using Rankine's formula, 
 
 38.070tb.pers,. in. 
 
 + 25,OOOX2.52 
 
 Euler's Formula. Structural members in compression whose ratio of 
 slenderness exceeds 150 should preferably not be used. Sometimes, however, 
 
 long columns cannot be avoided, and when - exceeds the limits for which the 
 
 preceding formulas may be applied, Euler's formula should be used. This 
 formula is as follows: 
 
 in which E = modulus of elasticity of material; 
 
 = constant. 
 
 The value of the constant n depends on the end condition; it has the 
 value of 1 for columns with both ends pivoted and 4 for columns with both ends 
 fixed. The table of constants on page 180 gives the values of nv 2 E, expressed 
 in millions of pounds. 
 
 Formula for Wooden Columns. The formula for determining the strength 
 of wooden columns having flat or square ends was deduced from exhaustive 
 tests of full-size specimens, made at the Watertown Arsenal, Mass., and may be 
 expressed as follows: 
 
 in which 5 = ultimate strength of column, per square inch of section; 
 
 U = ultimate compressive strength of material, per square inch; 
 / = length of column, in inches; 
 d = dimension of least side of column, in inches. 
 
 This formula may be applied to all wooden columns, the length or height 
 of which is not under 10 times nor over 45 times the dimension of the least side. 
 
 In other words, -y should not be less than 10 nor more than 45. If the length 
 
 a 
 
 is less than 10 times the least side, the direct compressive strength of the 
 material per square inch, multiplied by the sectional area of the column in 
 square inches, will give the strength of the column. If the length is over 45 
 times the least side, Rankine's formula should be used. 
 
 COMBINED STRESSES 
 
 Bending Combined With Compression or Tension. Assume that P is the 
 axial force acting on the beam; M , the maximum bending moment to which the 
 beam is subjected; A, the cross-sectional area of the beam; 7, its moment of 
 inertia; and c, the distance from the neutral axis of the most distant fiber, 
 having the same kind of stress (tension or compression) as that caused by P. 
 Then, the working stress should not exceed 
 
 P , Me 
 
 5= A+-F 
 
 In case of compression, 5 should, in addition, be deduced from one of the 
 compression formulas previously given. 
 
 The preceding formula for 5 is the one commonly used in practice, but it is 
 only approximate. When more accurate results are required, the following 
 formula should be used, 
 
 P , Me 
 
 Here, I is the span; E, the modulus of elasticity, and k', a constant having 
 the following values: 
 
STRENGTH OF MATERIALS 
 
 183 
 
 Value of k 
 For a cantilever loaded at end ............................. % 
 
 For a cantilever loaded uniformly .......................... \ 
 
 For a beam supported at both ends and loaded at center ..... ^ 
 
 For a beam supported at both ends and loaded uniformly ...... ^ 
 
 For a beam fixed at both ends and loaded at center .......... ^ 
 
 For a fixed beam uniformly loaded ......................... -fa 
 
 The minus sign before k is for the case when the direct stress is compressive, 
 and the plus sign, when it is tensile. 
 
 STRENGTH OF HEMP AND MANILA ROPES AND OF CHAINS 
 
 Ropes. If C is the circumference of a rope, in inches, and P the working load, 
 in pounds, then, for hemp and manila rope, 
 P = 10C2 
 
 This formula gives a factor of safety of from 7^ for manila or tarred hemp 
 rope to about 11 for the best three-strand hemp rope. 
 
 For iron-wire rope of seven strands, nineteen wires to a strand, 
 
 and for the best steel-wire rope of seven strands, nineteen wires to the strand, 
 P = 1,OOOC 2 
 
 The last two formulas are based on a factor of safety of 6. 
 
 Chains. If P is the safe load, in pounds, and d the diameter of link, in 
 inches, then, for open-link chains made from a good quality of wrought iron, 
 
 and for stud->link chains, P = IS.'oOOd* 
 
 Chain Cables. The strength of a chain link is less than twice that of a 
 straight bar of a sectional area equal to that of one side of the link. A weld 
 exists at one end and a bend at the other, each requiring at least one heat, 
 which produces a decrease in the strength. The report of the committee of 
 the U. S. Testing Board, on tests of wrought-iron and chain cables, contains 
 the following conclusions: 
 
 "That, beyond doubt, when made of American bar iron, with cast-iron studs, 
 the studded link is inferior in strength to the unstudded one. 
 
 "That when proper care is exercised in the selection of material, the strength 
 of chain cables will vary by about 5% to 17% of the resistance of the strongest. 
 Without this care the variation may rise to 25%. 
 
 "That with proper material and construction the ultimate resistance of the 
 chain may be expected to vary from 155% to 170% of that of the bar used in 
 making the links, and show an average of about 163%. 
 
 "That the proof test of a chain cable should be about 50% of the ultimate 
 resistance of the weakest link." 
 
 From a great number of tests of bars and unfinished cables, the com- 
 mittee considered that the average ultimate resistance and proof tests of chain 
 cables made of the bars, whose diameters are given, should be such as are shown 
 in the accompanying table. 
 
 ULTIMATE RESISTANCE AND PROOF TESTS OF CHAIN 
 CABLES 
 
 Diam- 
 eter of 
 Bar 
 
 Average 
 Resistance 
 = 163% of 
 
 Proof 
 Test 
 
 Diam- 
 eter of 
 Bar 
 
 Average 
 Resistance 
 = 163% o/ 
 
 Proof 
 Test 
 
 Inches 
 
 Bar 
 
 Pounds 
 
 Pounds 
 
 Inches 
 
 Bar 
 
 Pounds 
 
 Pounds 
 
 1 
 
 71,172 
 
 33,840 
 
 1* 
 
 162,283 
 
 77,159 
 
 1A 
 
 79,544 
 
 37,820 
 
 ir 
 
 174,475 
 
 82,956 
 
 |I 
 
 88,445 
 97,731 
 
 42,053 
 46,468 
 
 it 
 
 187.075 
 200,074 
 
 88,947 
 95,128 
 
 
 107,440 
 
 51,084 
 
 I'M 
 
 213,475 
 
 101,499 
 
 1& 
 
 117,577 
 
 55,903 
 
 if 
 
 227,271 
 
 108,058 
 
 If 
 
 128,129 
 
 60,920 
 
 Jii 
 
 241,463 
 
 114,806 
 
 
 139,103 
 
 66,138 
 
 2 
 
 256,040 
 
 121,737 
 
 H 
 
 150,485 
 
 71,550 
 
 
 
 
184 
 
 STRENGTH OF MATERIALS 
 
 PRACTICAL PROBLEMS IN THE STRENGTH OF 
 BEAMS AND PROPS 
 
 To Find the Quiescent Breaking Load of a Horizontal Square or Rectangular 
 Beam Supported at Both Ends and Loaded at the Middle. Multiply the 
 breadth, in inches, by the square of depth, in inches; divide the product by 
 distance in feet, between supports, and multiply the quotient by the con- 
 stant given in the Table of Constants for Seasoned Timber. Take as the safe 
 working load one-third of the breaking load. 
 
 To Find the Quiescent Breaking Load of a Horizontal Cylindrical Beam. 
 Divide the cube of the diameter, in inches, by the distance between the sup- 
 ports in feet, and multiply the quotient by the constant. 
 
 When the load is uniformly distributed on the beam, the results obtained 
 by the foregoing rules should be doubled. 
 
 EXAMPLE 1. Find the quiescent breaking load and safe working load of 
 a yellow-pine collar 8 in. square, 12 ft. between legs. 
 
 SOLUTION. Breaking load = 
 10,666 Ib. for green timber. 
 
 8X82 
 12 
 
 X 500 = 21,333 Ib. for seasoned, and 
 
 Safe working load = 7,111 Ib. for seasoned, and 3,556 Ib. for green timber. 
 EXAMPLE 2. Find the quiescent breaking load, and the safe working 
 load of a hemlock collar 10 in. diameter, 7 ft, between legs. 
 
 1 f)3 
 
 SOLUTION. Breaking load = X 236 = 33, 7 14 Ib. for seasoned, timber, and 
 
 33 714-^2 = 16,857 Ib. for green timber. 
 
 Safe working load = 33, 7 14 -r-3 = 11,238 Ib. for seasoned, and 33,714-1-6 or 
 11 238-4-2 = 5,619 Ib. for green timber. 
 
 To Find the Load a Rectangular Collar Will Support When Its Depth Is 
 Increased. When the length and width remain constant, the load varies as 
 the square of the depth. 
 
 EXAMPLE. A rectangular collar 10 in. deep supports 15,000 Ib. What will 
 it support if its depth is increased to 12 in.? 
 
 SOLUTION. Applying the rule just given 10 2 : 12* = 15,000 : 21,600. 
 
 Having the Length and Diameter of a Collar, to Find the Diameter of a 
 Longer Collar to Support the Same Weight. For the same load, the strength 
 of collars varies as the cubes of their diameters, and inversely as their lengths. 
 
 EXAMPLE. If a collar 6 ft, long and 8 in. diameter supports a certain 
 weight, what must be the diameter of a collar 12 ft. long to support the same 
 weight? 
 
 TABLE OF CONSTANTS FOR SEASONED TIMBER 
 
 Woods 
 
 Constant 
 
 Woods 
 
 Constant 
 
 Square or 
 Rectan- 
 gular 
 
 Round 
 
 Square or 
 Rectan- 
 gular 
 
 Round 
 
 Ash, white 
 Ash, swamp 
 Ash, black 
 Balsam, Canada . . . 
 Beech white . 
 
 650 
 400 
 300 
 350 
 450 
 550 
 450 
 450 
 250 
 450 
 350 
 600 
 400 
 650 
 600 
 
 383 
 236 
 177 
 206 
 265 
 324 
 265 
 266 
 147 
 265 
 206 
 353 
 236 
 383 
 353 
 
 Locust 
 Lignum vitae. . . . 
 Larch 
 Maple 
 Oak, red or b ack 
 Oak, white 
 Oak, live..... ... 
 Pine, white/ 
 Pine, yellow 
 
 600 
 650 
 400 
 550 
 550 
 600 
 600 
 450 
 500 
 550 
 550 
 450 
 500 
 350 
 
 353 . 
 
 383 
 236 
 324 
 324 
 353 
 353 
 265 
 295 
 324 
 324 
 265 
 295 
 206 
 
 Beech, red 
 
 Birch, black 
 Birch, yellow 
 Cedar, white 
 Chestnut 
 
 Elm 
 
 Poplar 
 
 Elm, rock 
 Hemlock 
 
 Spruce 
 
 
 Hickory 
 
 Willow 
 
 Ironwood ....;... 
 
 
 
STRENGTH OF MATERIALS 
 
 185 
 
 SOLUTION. Applying the rule just given \12:>/6 
 Having the Loads 
 
 8 in. : 6.35 in. 
 
 s of Two Beams of Equal Length and the Diameter of One. 
 to Find the Diameter of the Other. When the lengths are equal, the diameters 
 vary as the cube roots of the loads, or the cubes of the diameters vary as the 
 loads. 
 
 EXAMPLE 1. A beam 11 in. in diameter supports a load of 32,160 Ib. What 
 will be the diameter of another beam the same length, to support a load of 
 19,440 Ib.? 
 
 SOLUTION. Applying the rule just given 
 
 -^32,160 : ^19,440 = 11 : 9.3. 
 
 EXAMPLE 2. A beam 8 in. in diameter will support a load of 10,240 Ib. 
 What load will a beam the same length and 7 in. in diameter support? 
 
 SOLUTION. Applying the rule just given 8 3 : 7 s = 10,240 : 6,860. 
 
 The preceding Table of Constants has been calculated for seasoned timber; 
 for green timber, take one-half of these constants. The safe working load is 
 one-third of the breaking load. 
 
 To Find the Diameter of a Collar When the Weight Increases in Proportion 
 to the Length. Find the required diameter to support the same weight as the 
 short collar. Then the length of the short collar is to the length of the long 
 one as the diameter found to support the original weight is to the required 
 diameter. 
 
 EXAMPLE. If a collar 6 ft. long, 8 in. in diameter, supports a certain weight, 
 what must be the diameter of a collar 12 ft. long to support twice the weight? 
 
 03 ( )3 
 
 SOLUTION. From the rule just given, 1:2 = -: ~- , or 1 : 2 = 2X 8 3 : ( ) 3 , 
 
 
 12.7. 
 
 To Find the Breaking Load of Either Square or Rectangular Wooden Pil- 
 lars or Props. Call one side of the square or the least side of the rectangle the 
 breadth. Divide the square of the length, in inches, by the square of the 
 breadth, in inches, multiply the quotient by .004, add 1 to the product and 
 divide the crushing load by the result. Then multiply this quotient by the 
 number of square inches in the end of the prop 
 
 Or, breaking load in Ib. ; 
 
 Crushing load , 
 
 in which 
 
 1 = length, in inches; 
 b = breadth, in inches, 
 d = depth, in inches 
 
 CRUSHING LOADS OF WELL-SEASONED AMERICAN WOODS 
 
 Wood 
 
 Crushing 
 Load 
 Pounds 
 per Square 
 Inch 
 
 Wood 
 
 Crushing 
 Load 
 Pounds 
 per Square 
 Inch 
 
 Ash 
 
 6,800 
 
 Maple, sugar, black . . . 
 
 8,000 
 
 Beech 
 Birch .... 
 
 7,000 
 8,000 
 
 Maple, white, red 
 Oak, white, red, bla k. . 
 
 6,800 
 7,000 
 
 Cedar red 
 
 6,000 
 
 Oak, scrub, basket. . . . 
 
 6,000 
 
 Cedar, white 
 
 4,400 
 5 300 
 
 Oak, chestnut, live. . . . 
 Oak pin 
 
 7,500 
 6,500 
 
 Hemlock 
 
 5 300 
 
 Pine, white 
 
 5,400 
 
 
 8 000 
 
 
 5000 
 
 Linden 
 
 5,000 
 9 800 
 
 Pine, Georgia 
 
 8,500 
 5,000 
 
 
 7 000 
 
 Spruce, black 
 
 5,700 
 
 Maple, broad-leafed, 
 
 5 300 
 
 Spruce, white 
 Willow 
 
 4,500 
 4,400 
 
 g 
 
 
 
 
 For green timber, take one-half of the crushing strength given in the 
 foregoing table. The safe working load equals one-third of crushing load. 
 
186 
 
 STRENGTH OF MATERIALS 
 
 3uno'<j 
 
 aoj ppy 
 
 COCOrHOO500t~t~ 
 rHrHi-HrHOOOO 
 
 CD O 00 00 O CO 00 CO i 
 CSjrHO50000J>CDCOl 
 
 rH rH O O O O O OOOOOOOO 
 
 rH 00 >O CO (M rH 
 
 FOR ST 
 
 Pounds.) 
 
 . 
 punod A\iag; JQJ ppv 
 
 00 t^ 05 I> 05 CO IN T>< CD 05 T}< 00 rj( O CD 
 rH CO IN|O5 t>. O rJH CO (N rH O O5 O5 00 GO 00 l> 
 
 CO (N IN'|rH rH rH rH rH rH rHrHCOOCSdOCJ 
 
 ^q3ia^ 
 puno'd Aa 
 
 CO<NC5COTj<COCSlrHO 
 
 od Aaag joj ppv 
 
 CO O O5 Colt* 00 O iO 00 -<f<NrH(NCOCOO5CO 
 rH CO CD C^JOO IO CO rH O5 OOI>CDiOTj<COlNCN 
 
 1C Tj5 CO CO|(N <N (N (N rH rHrHrHrHrHrHr-;^ 
 
 1U.3I9.AY UI 9SB9JOUJ 
 
 ' A-iaAg joj ppy 
 
 05 t^ CO * CO C? rHOO05050000t^ 
 JH ,_( ,-J rH rH i-H rH rH i-H O O O O O 
 
 M >O . 
 
 (N.Q 
 CNl-5 
 
 IO CO rf< Tti rH 00|(N CO 00 t>- 00 (N 00 O Tj< rt< O 
 t>I CO 10 * Tj5 COJCO CO (N <N (N (N (N <N <N rH rH 
 
 Ul 9SB9JOUJ 
 
 junoj AaaAg; J 
 
 CDOCDCOOOOCDiO^COC^IrHrHOt 
 
 COCO(NCNCNrHrHrHrH rH rH i-H rH rH < 
 
 ^OC5OCO<N<NO 
 
 O<N0005rH^)OCD 
 
 rH O5 t- CD CO >6 IO 
 
 CO CO CO CO CO (N <N CN 
 
 Dunoj Aaag aoj ppy 
 
 00 CO O5 O CN CO 
 ^ Tl< 10 O5 CO 00 
 O5 00 t- CO CO >O 
 
 (N CO Tjl CO rH O5 O5 rH 
 j; O t>; rjj (N 05 t-; CO 
 
 Al ui asBaaouj 
 AaaA jo 
 
 ?unO(j Aaag joj ppy 
 
 CO W (N rH rH< 
 
 05Tj<O5rH05IN05OCO 
 
 cot^rH^hMojiocoq 
 oot>i>cc>|cdio>ofjiOT)5 
 
 puno<j Ajag joj ppy 
 
 CO IN(NrHrHOOOC 
 
 O CN O 00 Tfi 
 
 oo q co co rH 
 d d os 06 06 
 
 CO Tt CO rH 
 
 CO <N 00 *O 
 
 AV U T 3SB3JOUJ 
 
 Aj9A jo 
 
 punoj Aj9Ag joj ppy 
 
 
 lO^COINi-HrHOO 
 
 osoot^ifJ-^TticoiM'r-! 
 
 CO^O5COCOO5'OTf<T}(t--. 
 COOOCOO5OrHOOlOCNO5 
 
 (NCO^iOCDr^OOOiO rH O3 CO <* >O CD t^ 00 O5 O 
 !-HrHrHrHrHrHrHrH(N (N CN <N (N (N (N IN IN (N CO 
 
CONCRETE ' 187 
 
 EXAMPLE. What is the breaking load of a well-seasoned hemlock post 
 10 in.XS in. and 12 ft. long? 
 
 SOLUTION. Applying the rule just given, 5,300 -^ [l+ (^~X.004)] 
 
 = 2,308.4 Ib. per sq. in. of area. 2,308.4X80= 184,672 Ib. Ans. 
 
 To Find the Breaking Load of a Cylindrical Wooden Prop. Find the break- 
 ing load of a square prop whose ends are equal in area to those of the cylin- 
 drical one, and proceed according to foregoing rule. 
 
 EXAMPLE. What is the safe working load for a hemlock mine prop 10 in. 
 diameter, 10 ft. long? 
 
 SOLUTION. The area of the end of the prop = 78.54 sq. in. A square of equal 
 area will have sides equal to V78.54 = 8.86+in. Then, 
 
 5,300 -f- [l+ (jff^X. 004)] =3,058.3 Ib. per each sq. in. of area. 
 
 And 3,058.3 X 78.54 = 240, 198 Ib. This is the crushing strength of a similar 
 prop of seasoned timber, but, as mine timber is used in its green state, take 
 one-half of 240,198 Ib., or 120,099 Ib., as the crushing load of the prop in ques- 
 tion. Then, the safe working load is one-third of this, or 40,033 Ib. 
 
 The strength of similar props varies as the cubes of their diameters, and 
 inversely as their lengths. 
 
 IRON AND STEEL BEAMS 
 
 Constants for use in calculating the strength of iron and steel beams are: 
 Cast iron, 2,000; wrought iron, 2,200; steel, 5,000. Hard steel will break the 
 same as cast iron; soft steel will bend like wrought iron. The elastic limit 
 of wrought iron is reached at about 2,200 Ib. As it does not break, the limit of 
 elasticity should be used. 
 
 To Find the Quiescent Breaking Load of a Horizontal Square or Rectangular 
 Iron or Steel Beam Supported at Both Ends and Loaded at the Middle. Mul- 
 tiply the square of its depth, in inches, by its breadth, in inches; multiply this 
 result by the constant for the material used, and divide by the length, in feet, 
 between the supports. For the net load, subtract one-half the weight of the 
 beam. 
 
 To Find the Quiescent Breaking Load of a Cylindrical Iron or Steel Beam. 
 Find the breaking load of a square beam the sides of which are equal to the 
 diameter of the round one, and multiply by .6. 
 
 The safe working load in each of the preceding cases is one-third of the 
 breaking load. If the load is equally distributed over the beam, it will be twice 
 as great. 
 
 CONCRETE 
 
 CEMENTING MATERIALS 
 
 DEFINITIONS 
 
 Any substance that becomes plastic under certain treatment and subse- 
 quently reverts to a tenacious and inelastic condition may, in a broad sense, be 
 termed a cement. However, nearly all the cementing materials employed in 
 building construction are obtained by the heating, or calcination, as it is called, 
 of minerals composed wholly or in part of lime. The different composition of 
 these minerals, as well as the properties of the calcined products, enables the 
 various resulting substances to be classified as limes, hydraulic cements, plasters, 
 and miscellaneous cements. Although all these materials have cementing 
 properties, the term cement is commonly used to apply only to the group made 
 up of hydraulic cements, hydraulic meaning that these substances possess the 
 ability to set, or become hard, under water. 
 
 Limes and hydraulic cements (commonly called simply cements) are com- 
 posed essentially of oxide of calcium, or lime, generally called quicklime, with 
 which may be combined certain argillaceous, or clayey, elements, notably 
 silica and alumina, it being to these elements that the hydraulic properties of 
 certain of these materials are due. The quantity of silica and alumina present 
 in these substances enables them to be classified as common limes, hydraulic 
 limes, and cements. 
 
188 CONCRETE 
 
 The ratio of the quantity of silica and alumina present in these materials 
 to the quantity of lime is called the hydraulic index. In common limes, this 
 index is less than ,>&; in hydraulic limes, it lies between ^ and /<&; and in 
 cements, it exceeds i$y. These limes merge into 9ne another so gradually, 
 however, that it is often difficult to distinguish the dividing line between them. 
 
 LIMES 
 
 The commercial varieties of lime may be classified as common, hydrated, 
 and hydraulic. The common limes, also called quicklimes, may be subdivided 
 into rich, or fat, lime, and meager, or poor, lime. 
 
 Common Limes. The grade of common lime known as fat, or rich, lime 
 is almost pure oxide of calcium, CaO, and contains only about 5% of impurities. 
 It has a specific gravity of about 2.3 and a great affinity for water, of which it 
 absorbs about one-quarter of its weight. This absorption is accompanied by 
 a great rise in temperature, by the lime bursting, and by the giving off of vapor. 
 The lime finally crumbles into a powder. This powder occupies from two and 
 one-half to three and one-half times as much volume as the original lime, the 
 exact amount depending on its initial purity. When the lime is in this plastic 
 state, it is said to be slaked. It is then unctuous and soft to the touch, and 
 from this peculiarity it derives the name of fat or rich. 
 
 Meager, or poor, lime consists of from 60 to 90% of pure lime, the remainder 
 being impurities, such as sand or other foreign matter. These impurities have 
 no chemical action on the lime, but simply act as adulterants. Compared with 
 fat lime, poor lime slakes more slowly and evolves less heat. The resulting 
 paste is also thinner and not so smooth, greatly resembling fat slaked lime 
 mixed with sand. Poor lime is not so good for building purposes as fat lime, 
 nor has it such extensive use. 
 
 Hydrated Lime. The class of lime called hydrated lime (calcium hydrate) 
 is merely thoroughly slaked fat lime dried in the form of a fine powder, Ca(OH)t. 
 It is used extensively in conjunction with cement for making mortar, and also 
 in the sand-lime brick industry. 
 
 Hydraulic Limes. Limes that contain enough quicklime to slake when 
 water is added, and enough clay or sand to form a chemical combination 
 when wet, thus giving them the property of setting under water, are called 
 hydraulic limes. The slaking qualities vary, the time of setting under water 
 also varies, but these limes usually become as hard as stone in 3 or 4 da. The 
 use of hydraulic lime has rapidly decreased in this country. Large quantities 
 were formerly imported from Europe. 
 
 CEMENTS 
 
 Cement may be divided into four general classes: Portland, natural, 
 puzzolan (also called pozzuolana), and mixed. The relative importance of 
 each cement is indicated by the order in which it is named. 
 
 Portland cement may be defined as the product resulting from the process 
 of grinding an intimate mixture of calcareous (containing lime) and argillaceous 
 (containing clay) materials, calcining (heating) the mixture until it starts to 
 fuse, or melt, and grinding the resulting clinker to a fine powder. It must 
 contain not less than 1.7 times as much lime by weight as it does of those 
 materials that give the lime its hydraulic properties, and must contain no 
 materials added after calcination, except small quantities of certain substances 
 used to regulate the activity or the time of setting. 
 
 Natural cement is the product resulting from the burning and subsequent 
 pulverization of an argillaceous limestone or other suitable rock in its natural 
 condition, the heat of burning being insufficient to cause the material to start 
 to melt. 
 
 Puzzolan cement is a material resulting from grinding together, without 
 subsequent calcination, an intimate mixture of slaked lime and a puzzolanic 
 substance, such as blast-furnace slag or volcanic scoria. That made from slag is 
 know as slag cement. 
 
 Mixed cements cover a wide range of products obtained by mixing, or 
 blending, the foregoing cements with one another or with other inert sub- 
 stances. Sand cements, improved cements, and many second-grade cements 
 belong to this class. Mixed cements, however, are of comparatively little 
 importance. 
 
 Properties of Cements. The hydraulic cements differ from the limes in 
 that they do not slake after calcination and that they set, or harden, under 
 water. They can be formed into a paste with water without any sensible 
 increase in volume and with little, if any, disengagement of heat. They do 
 
CONCRETE 
 
 189 
 
 not shrink appreciably in hardening, so that the sand and broken stone with 
 which they are mixed are employed merely through motives of economy and 
 not, as with limes, of necessity. 
 
 The color of the different grades of cement is variable, but in certain cases 
 it is distinctive. Portland cement is a dark bluish or greenish gray; if it is a 
 light yellow, it may indicate underburning. Natural cement ranges in color 
 from a light straw, through the grays, to a chocolate brown. Slag cement is 
 gray with usually a tinge of lilac. In general, however, the color of cement is 
 no criterion of its quality. 
 
 Cement is packed either in wooden barrels or in cloth or paper bags, the 
 latter being the form of package most commonly employed. A barrel of 
 Portland or of slag cement contains the equivalent of 4 bags, while but 3 bags 
 of natural cement equal a barrel. The average weights of the various cements 
 are given in the accompanying table. 
 
 In proportioning mortar or concrete by volume, a common assumption is 
 that a bag of Portland cement occupies .9 cu. ft. This practice, however, is, 
 not entirely uniform. 
 
 AVERAGE WEIGHTS OF HYDRAULIC CEMENTS 
 
 Kind of Cement 
 
 Net Weight 
 of Bag 
 Pounds 
 
 Net Weight 
 of Barrel 
 Pounds 
 
 Weight per Cubic Foot 
 Pounds 
 
 Packed 
 
 Loose 
 
 Portland 
 
 94 
 94 
 
 82 
 
 376 
 
 282 
 330 
 
 100 to 120 
 75 to 95 
 80 to 100 
 
 70 to 90 
 45 to 65 
 55 to 75 
 
 Natural 
 
 Slag 
 
 
 Portland cement may be distinguished by its dark color, heavy weight, 
 slow rate of setting, and greater strength. Natural cement is characterized by 
 lighter color, lighter weight, quicker set, and lower strength. Slag cement is 
 somewhat similar to Portland, but may be distinguished from it by its lilac- 
 bluish color, by its lighter weight, and by the greater fineness to which it is 
 ground. 
 
 Portland cement is adaptable to any class of mortar or concrete construc- 
 tion, and is unquestionably the best material for all such purposes. Natural 
 and slag cements, however, are cheaper, and, under certain conditions, may be 
 substituted for the more expensive Portland cement. All heavy construction, 
 especially if exposed, all reinforced-concrete work, sidewalks, concrete blocks, 
 foundations of buildings, piers, walls, abutments, etc. should be made with 
 Portland cement. In second-class work, as in rubble masonry, brick sewers, 
 unimportant work in damp or wet situations, or in heavy work in which the 
 working loads will not be applied until long after completion, natural cement 
 may be employed to advantage. Slag cement is best adapted to heavy founda- 
 tion work that is immersed in water or is at least continually damp. This kind 
 of cement should never be exposed directly to dry air, nor should it be subjected 
 either to attrition or impact. 
 
 SAND AND ITS MIXTURES 
 
 Sand is an aggregation of loose gr&ins of crystalline structure, derived from 
 the disintegration of rocks. It is called silicious, argillaceous, or calcareous, 
 according to the character of the rock from which it is derived. Sand is 
 obtained from the seashore, from the banks and beds of rivers, and from land 
 deposits. 
 
 The first class, called sea sand, contains alkaline salts that attract and 
 retain moisture and cause efflorescence in brick masonry. This efflorescence 
 is not at first apparent but becomes more marked as time goes on. It can be 
 removed temporarily, at least, by washing the stonework in very dilute hydro- 
 chloric acid. 
 
 The second, termed river sand, is generally composed of rounded particles, 
 and may or may not contain clay or other impurities. 
 
 The third, called pit sand, is usually composed of grains that are more 
 angular; it often contains clay and organic matter. When washed and screened 
 it is a good sand for general purposes. 
 
19 o CONCRETE 
 
 Sand is used in making mortar because it prevents excessive shrinkage and 
 reduces the quantity of lime or cement required. Lime adheres better to the 
 particles of sand than it does to its own particles; hence, it is considered that 
 sand adds strength to lime mortar. On cement mortar, on the contrary, sand 
 has a weakening effect. 
 
 Properties of Sand. The weight of sand is determined by merely filling 
 a cubic-foot measure with dried sand and obtaining its weight. Dry sand 
 weighs from 80 to 120 Ib. per cu. ft.; moist sand, however, occupies more space 
 and weighs less per cubic foot. The weight of sand is more or less dependent 
 on its specific gravity and on the size and shape of the sand grains, but, other 
 things being equal, the heaviest sand makes the best mortar. 
 
 The specific gravity of sand ranges from 2.55 to 2.80. For all practical 
 purposes the specific gravity may be assumed to be 2.65 with little danger of 
 
 By percentage of voids is meant the amount of air space in the sand. Struc- 
 turally, it is one of the most important properties of sand. The greater these 
 voids, the more cement paste will be required to fill them in order to give a 
 dense mortar. The percentage of voids may be determined by observing the 
 quantity of water that can be introduced into a vessel filled with sand, but 
 it is best computed as follows: 
 
 r -j , 100 X weight per cubic foot 
 percentage of voids = 100 -- 62 . 5X specific gravity 
 
 EXAMPLE. What is the percentage of voids in a sand having a specific 
 gravity of 2.65 and weighing 105 Ib. per cu. ft.? 
 
 SOLUTION. Substituting in the formula, the percentage of voids is 
 
 The percentage of voids depends principally on the size and shape of the 
 sand grains and the gradation of its fineness, and hence will vary from 25 
 to 50%. Sand containing over 45% of voids should not be used to make 
 mortars. 
 
 The shape of the grains of sand is of chief importance in the influence that the 
 sand exerts on the percentage of voids. Obviously, a sand with rounded grains 
 will compact into a more dense mass than one whose grains are angular or flat 
 like particles of mica. Therefore, the more nearly the grains approach the 
 spherical in shape, the more dense and strong will be the mortar for the same 
 amount of cement. This fact is contrary to the common opinion on the 
 subject. 
 
 The fineness of sand is determined by passing a dried sample through a 
 series of sieves having 10, 20, 30, 40, 50, 74, 100, and 200 meshes, respectively, 
 to the linear inch. The result of this test, expressed in the amount of sand 
 passing each sieve, is known as the granulometric composition of the sand. 
 Material that does not pass a J-in. screen is not considered to be sand, and 
 should be separated by screening. Sand that is practically all retained on a 
 No. 30 sieye is called coarse, while 80 or 90% of sand known as fine will pass 
 through this sieve. Fine sand produces a weaker mortar than coarse sand, but a 
 mixture of fine and coarse sand will surpass either one in those cases, at least, 
 where there is not enough cement to fill voids using either sand. 
 
 The purity, or cleanness, of -sand may be roughly ascertained by rubbing 
 it between the fingers and observing how much dirt remains. To determine 
 the percentage of the impurities more accurately, a small dried and weighed 
 sample is placed in a vessel and stirred up with water. The sand is allowed to 
 settle, the dirty water poured off, and the process repeated until the water pours 
 off clear. The sand is then dried and weighed. The loss in weight gives the 
 quantity of impurities contained in the sand. The presence of dirt, organic 
 loam, mica, etc. is decidedly injurious and tends to weaken the resulting 
 mortar. Clay or fine mineral matter in small proportions may actually result 
 in increased strength, but excessive quantities of these materials may be a 
 possible source of weakness. The best modern practice limits the quantity of 
 impurities found by this washing test to 5%. 
 
 Attention is called to the fact that the sand found and used around many 
 collieries is inferior. It is apt to be dirty and to consist of fine uniform grains. 
 Such sand is sometimes suitable for building brattices or small foundations 
 where a certain amount of air-tightness or weight, but not strength, is required. 
 In all important work or in reinforced concrete, however, good, carefully selected 
 sand should be used. The sand should always be tested to see whether it will 
 make a mortar or a concrete of the desired qualities. 
 
CONCRETE 191 
 
 Preparation of Sand. Sand is prepared for use by (1) screening to remove 
 the pebbles and coarser grains, the fineness of the meshes of the screen depend- 
 ing on the kind of work in which the sand is to be used; (2) washing, to remove 
 salt, clay, and other foreign matter; and (3) drying if necessary. When dry 
 sand is required, it is obtained by evaporating the moisture either in a machine, 
 called a sand dryer, or in large, shallow, iron pans supported on stones, with a 
 wood fire placed underneath. 
 
 LIME AND CEMENT MORTARS 
 
 Mortars are composed of lime or cement and sand mixed to the proper 
 consistency with water. The proportions of the ingredients depend on the 
 character of the work in which the mortar is to be used. 
 
 In proportioning mortar, the quantities of the separate ingredients are 
 usually designated by a ratio, such as 1-1, 1-2, 1-3, etc. Thus, 1-2 signifies 
 that 1 part of lime or cement is used to 2 parts of sand, etc. For great accuracy 
 these measurements should be made by weight, but they are usually specified 
 to be measured by volume. 
 
 Lime Mortars. In lime mortar, besides effecting an economy, the presence 
 of sand is necessary to prevent the shrinkage that would otherwise occur during 
 the hardening of the paste. 
 
 When a mortar is made of lime and sand, enough lime should be present 
 to just cover completely each grain of sand. An excess of lime over this 
 quantity will cause the mortar to shrink excessively on drying, while a deficiency 
 of lime will produce a weak and crumbly mortar. The correct quantity of 
 lime depends on the character of the ingredients, the method of treatment 
 and, to some extent on the judgment of the builder. The mixtures employed 
 vary from 1-2^ to 1-5. Building laws in many municipalities require the use of 
 a 1-3 mixture, and for most materials this proportion will be found satisfactory, 
 although for rich, fat limes a l-3 or a 1-4 mixture is sometimes preferable. 
 
 In mixing lime mortar, a bed of sand is made in a mortar box, and the 
 lime distributed as evenly as possible over it, first measuring both the lime and 
 the sand in order that the proportions specified may be obtained. The lime is 
 then slaked by pouring on water, after which it should be covered with a layer 
 of sand, or, preferably, a tarpaulin, to retain the vapor given off while the lime 
 is undergoing the chemical reaction of slaking. Additional sand is then used, 
 if necessary, until the mortar attains the proper proportions. 
 
 Care should be taken to add just the proper quantity of water to slake the 
 lime completely to a paste. If too much water is used, the mortar will never 
 attain its proper strength, while if too little is used at first, and more is added 
 during the process of slaking, the lime will have a tendency to chill, thereby 
 injuring its setting and hardening properties. Rather than make up small 
 batches, it is considered better practice to make lime mortar in large quantities 
 and to keep it standing in bulk so that it can be used as needed. 
 
 Lime mortar is employed chiefly for brickwork of the second class, and its 
 use is continually decreasing as that of cement increases. It is absolutely 
 unsuitable for any important construction, because it possesses neither strength 
 nor the property of resisting water. It cannot be used in damp or wet situ- 
 ations, nor should it ever be laid in cold weather, as it is very susceptible to 
 the action of frost, being much injured thereby. Moreover, since it hardens 
 by the action of dry air, only the exterior of lime mortar ever becomes fully 
 hardened, so that anything like a concrete with lime as a matrix is impossible. 
 However, for second-class brickwork, such as is commonly used in the walls of 
 smaller buildings, lime mortars are economical and sufficiently good. 
 
 The strength of lime mortars is extremely variable, depending on the 
 ingredients themselves and on their treatment, environment, etc. It is unsafe 
 to figure a lime-mortar joint as possessing much strength, since only a part 
 of the joint is hardened and capable of developing any strength at all. The 
 tensile strength of thoroughly hardened 1-3 lime mortars averages from 40 to 
 70 Ib. per sq. in., and the compressive strength from 150 to 300 Ib. 
 
 Cement Mortars. The sand for all mortars should be clean, of suitable 
 size and granulometric composition. For structures designed to withstand 
 heavy unit stresses, or for those intended to resist either the penetration of 
 moisture or the actual pressure of water, the selection of the sand should 
 be most carefully made. A simple method of determining the best sand for 
 cement mortar is to prepare mixtures of the cement, sand, and water, using 
 the same quantities in each case, and then to place each mixture in a measure; 
 that mixture giving the least volume of mortar may be considered to contain 
 the most desirable sand for use. 
 
192 
 
 CONCRETE 
 
 Limestone screenings, brick dust, crushed cinders, etc., are sometimes 
 substituted for sand in making mortars, and, if care is taken in their selection, 
 they may prove economical and entirely suitable for certain purposes. 
 
 The theory of the composition of a correctly proportioned mortar is that the 
 cement paste will just a little more than fill all the voids between the particles 
 of sand, thus giving an absolutely dense mortar at the least expense. The 
 correct proportion of cement to sand, therefore, is more or less variable, depend- 
 ing on the granulometric composition of the sand. Since, however, Portland- 
 cement paste that has set weighs nearly as much as sand, and since the average 
 sand contains about 30 to 40% of voids, it is evident that 1-3 mixtures most 
 nearly approach the best and most economical proportion. 
 
 Mortars, however, are made in proportions varying from 1-1 to 1-8. The 
 richer mixtures are used for facing, pointing, waterproofing, granolithic mix- 
 tures, etc., the 1-2 mixture being usually made for such purposes. The 
 leaner mixtures are used for.rough work, filling, backing, etc., but should never 
 be employed where either much strength or much density is desired. Natural- 
 cement mortars are commonly made 1 part of sand less than Portland-cement 
 mortars intended for the same purpose; that is, where a 1-3 Portland-cement 
 mortar would be used, a 1-2 natural mortar would be required, although 
 natural-cement mortars should be decreased by about 2 parts of sand to equal 
 the strength of Portland. In other words, a 1-4 Portland mortar closely equals 
 the strength of a 1-2 natural mortar. Puzzolan cements are usually propor- 
 tioned the same as Portlands. 
 
 Cements are commonly proportioned by volume, the unit volume of the 
 cement barrel being assumed. If a 1-3 mortar is desired, a box having a 
 capacity of 10.8 cu. ft. is filled with sand and mixed with 4 bags or 1 bbl. of 
 cement. A box 3 ft. 3^ in. square and 1 ft. deep will have a capacity of very 
 nearly 10.8 cu. ft. and, besides, makes a convenient size of box for actual work. 
 
 For general purposes, the mortar should be of a plastic consistency firm 
 enough to stand at a considerable angle yet soft enough to work easily. Wet 
 mortars are easiest to work and are the strongest. However, they are subject 
 to greater shrinkage, are slower setting, and are more easily attacked by frost. 
 Dry mortars, on the other hand, are often friable and porous. 
 
 In the accompanying table are given the quantities of materials required 
 to produce 1 cu. yd. of compacted mortar. The proportions are by volume, 
 a cement barrel being assumed to contain 3.6 cu. ft. Of course, the exact values 
 vary with the variety of sand, etc., but the table will serve as an approximation. 
 
 MATERIALS REQUIRED PER CUBIC YARD OF MORTAR 
 
 Kind of Mixture 
 
 Portland Cement 
 Barrels 
 
 Loose Sand 
 Cubic Yards 
 
 1-1 
 
 4 95 
 
 65 
 
 1-2 
 
 3 28 
 
 88 
 
 1-3. 
 
 2 42 
 
 1 01 
 
 1-1 
 
 1 99 
 
 1 06 
 
 1-5 
 
 1 62 
 
 1 11 
 
 1-6... 
 
 1 34 
 
 1 15 
 
 1-7 
 
 1 18 
 
 1 17 
 
 1-8 
 
 1 05 
 
 1 18 
 
 
 
 
 EXAMPLE. How much cement and sand will be required to obtain 8.5 cu. 
 yd. or l-i Portland-cement mortar? 
 
 SOLUTION. According to the table, 1 cu. yd, of a 1-3 Portland-cement 
 mortar requires 2.42 bbl. of cement; therefore, 8.5 cu. yd. will require 8.5 
 X 2.42 = 20.57 bbl. of cement. Also, since 1 cu. yd. of a mixture of this kind 
 requires 1.01 cu. yd. of sand, the quantity of sand required will be 8.5X1.01 
 = 8.59 cu. yd. 
 
 Mortar that is to be mixed by hand is prepared on a platform or in a mortar 
 box. The sand is first measured by means of a bottomless box with handles 
 on the sides. After filling the box, the sand is struck off level, the box lifted 
 up, and the sand spread in a low, flat pile. The required number of bags of 
 cement are then emptied on the sand and spread evenly over it. The pile is 
 then mixed with shovels, working through it not less than four times. After 
 
CONCRETE 
 
 193 
 
 this operation, the dry mixture is formed into a ring, or crater, and the water 
 intended to be used is poured into the center. The material from the sides of 
 the basin is then shoveled into the center until the water is entirely absorbed, 
 after which the pile is worked again with shovels and hoes until the mixture is 
 uniform and in a plastic condition. 
 
 Another method of mixing, where a mortar box is used, is to gather the 
 mixed dry materials at one end of the box and pour in the water at the other 
 end, drawing the mixture into the water with a hoe, a little at a time, and 
 hoeing until a plastic consistency is obtained. 
 
 Properties and Uses of Ceirent Mortars. The strength of a mortar is 
 measured by its resistance to tensile, compressive, cross-breaking, and shearing 
 stresses, and also by determinations of its adhesion to inert surfaces, its resist- 
 ance to impact, abrasion, etc. There is no definitely fixed ratio between the 
 strength of mortar subjected to these different stresses, but there is nevertheless, 
 a close relation between them, so that, practically, it may be assumed that if a 
 mortar shows either abnormally high or low values in any one test, the same 
 relation will develop when tested under other stresses. In practice, therefore, 
 the strength of mortar is commonly determined through its resistance to tensile 
 stresses, and its resistance to other forms of stress is computed from these 
 results. 
 
 TENSILE STRENGTH OF CEMENT MORTARS 
 
 Proportions 
 
 Age of Mortar 
 
 7 da. 
 
 28 da. 
 
 3 mo. 
 
 7 da. 
 
 28 da. 
 
 3 mo. 
 
 Cement 
 Parts 
 
 Sand 
 Parts 
 
 Tensile Strength, in Pounds per Square Inch 
 
 Portland Cement 
 
 Natural Cement 
 
 1 
 1 
 
 1 
 1 
 1 
 1 
 1 
 1 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 
 450 
 280 
 170 
 125 
 80 
 50 
 30 
 20 
 
 600 
 380 
 245 
 180 
 140 
 115 
 95 
 70 
 
 610 
 395 
 280 
 220 
 175 
 145 
 120 
 100 
 
 160 
 115 
 85 
 60 
 40 
 25 
 15 
 10 
 
 245 
 175 
 130 
 100 
 75 
 60 
 50 
 45 
 
 280 
 215 
 165 
 '135 
 110 
 90 
 75 
 65 
 
 The tensile strength of mortar has been shown to vary with the character 
 of its ingredients, with its consistency, its age, and with many other factors. 
 In the above table is given a fair average of the tensile strength that may be 
 expected from mortars of Portland and natural cements that are made in the 
 field and with a sand of fair quality but not especially prepared. 
 
 The strength of Portland-cement mortar increases up to about 3 mo.; 
 after that period, it remains practically constant for an indefinite time. 
 Natural-cement mortar, on the other hand, continues to increase in strength 
 for 2 or 3 yr., its ultimate strength being about 25% in excess of that attained 
 in 3 mo. The strength of slag-cement mortar averages about three-quarters 
 of that of Portland-cement mortar. 
 
 The compressive strength of cement mortars is usually given in textbooks 
 as being from eight to ten times the tensile strength. This value is rather 
 high for the average mortar, a ratio of from 6 to 8 being one more nearly 
 realized in practice. The ratio increases with the age and richness of the 
 mortar, and varies considerably with the quality of the sand. Portland- 
 cement mortars of 1-3 mixture that are 3 mo. old develop, on an average, a 
 compressive strength of about 1,800 Ib. per sq, in., while 1-2 natural-cement 
 mortars average about 1,600 Ib. 
 
 The strength of mortars in cross-breaking and shear may be taken at about 
 'one and one-half to two times the tensile strength, with a fair amount of accu- 
 racy. 
 
194 CONCRETE 
 
 The adhesion of mortars to inert materials varies both with the character 
 of the mortar and with the roughness and porosity of the surfaces with which 
 they are in contact. The adhesion of 1-2 Portland-cement mortar, 28 da. old, 
 to sandstone averages about 100 Ib. per sq. in. ; to limestone, 75 Ib. ; to brick, 
 60 Ib.; to glass, 50 Ib.; and to iron or steel, 75 to 125 Ib. Natural-cement mor- 
 tars have nearly the same adhesive strength as those made of Portland cement. 
 
 In bricklaying and in other places in which mortar is employed it is fre- 
 quently desired to use a material that is more plastic or smooth than pure 
 cement mortar. This quality is usually obtained by adding from 10 to 25% 
 of lime to the mortar. This addition of lime not only renders the mortar more 
 plastic, and hence easier to work, but also increases both its adhesive strength 
 and its density, which assists in making the mortar waterproof. Hydrated 
 lime is to be preferred for use in cement mortar, because its complete slaking is 
 assured. Hydrated lime may also be readily handled and measured on the 
 work. 
 
 Occasionally, small quantities of cement are added to lime mortars so as 
 to make them set quicker and to increase their strength. Such mixtures, how- 
 ever, are not especially economical nor are they convenient in practice. 
 
 Retempering of Mortar. Mortar composed of cement, sand, and water 
 soon begins to set and finally becomes hard. When it is desired to use this 
 material, more water has to be added and the mixture worked until it again 
 becomes plastic. This process is called retempering. Laboratory tests gen- 
 erally show that retempering slightly increases the strength of mortar, but the 
 reworking is more thorough as a rule in the laboratory than would be the case 
 in actual work. Any part of the hardened mortar that is not retempered is a 
 source of weakness when incorporated in the building. The adhesive strength 
 of cement, moreover, is greatly diminished by this process. For these reasons, 
 it is generally inadvisable to permit the use of retempered mortars; but if they 
 are allowed, great care should be taken to see that the second working is thor- 
 ough and complete. 
 
 Laying Mortar in Freezing Weather. Frost, or even cold, has a tendency 
 to retard greatly the set of cement mortars. When the temperature, moreover, 
 is so low that the water with which the mortar is mixed freezes before it com- 
 bines with the cement, it may, if care is not exercised, result in complete destruc- 
 tion of the work. A single freezing is not particularly harmful, because when 
 thawing occurs, the arrested chemical action continues. A succession of alter- 
 nate freezings and thawings, however, is extremely injurious. Nevertheless, 
 Portland-cement mortars may be laid even under the worst conditions if cer- 
 tain precautions are observed, but mortars of natural cement should never be 
 used in extremely cold weather, as they are generally completely ruined by 
 freezing. 
 
 The bad results that arise during mild frosts may be successfully guarded 
 against by heating the sand and water and by using a quick-setting cement 
 mixed rich and as dry as possible. In extremely cold weather, salt must be 
 added to the water, so as to convert it into a brine that requires a temperature 
 lower than 32 F. to freeze it. The common rule for adding salt is to use a 
 quantity equal to 1% of the weight of the water for each degree of temperature 
 that is expected below 33 F. Thus, at 32 F., a 1% solution would be used, 
 while at 25, an 8% solution would be required. Solutions greater than 12% 
 should not be employed, and if a temperature below 20 F. is expected, heat 
 must be used in addition to the salt. The finished work should also be pro- 
 tected with canvas or straw. Manure should not be used for this purpose, 
 because the acids it contains tend to rot the cement. Unless the conditions are 
 such as to make it imperative, it is not advisable to lay mortars during freezing 
 weather. 
 
 Shrinkage of Mortars. Cement mixtures exposed to the air shrink during 
 the process of hardening, while those immersed in water tend to expand. The 
 shrinkage of ordinary cement mortars is slight, and when they are used as a 
 bonding material it need not be considered. When used as a monolith, as in 
 sidewalks, shrinkage is guarded against by keeping the mortar wet during set- 
 ting. This can be done by covering with moist straw or by sprinkling the 
 mixture with water. 
 
 - By grouting is meant the process of filling spaces in masonry 
 
 with a thin, semifluid mixture known as grout. This mixture consists of cement, 
 1 or 2 parts of sand, and an excess of water. Grout can be used for filling the 
 voids in walls of rubble masonry for backing arches and tunnels, for filling the 
 joints between paving brick, and in all places where mortar cannot be laid in 
 the ordinary manner. When hardened, grout is weak, friable, and porous. 
 
CONCRETE 195 
 
 CEMENT TESTING 
 
 FIELD INSPECTION AND SAMPLING 
 
 When cement is mentioned anywhere in the following pages, Portland cement, 
 is meant, as this is by far the most important cement. 
 
 In order to determine correctly the structural value of a shipment of cement, 
 an examination in the field is very necessary. A number of packages of cement 
 should be weighed at intervals, and the average weight should never be per- 
 mitted to fall below 94 Ib. per bag, as mortar and concrete are usually propor- 
 tioned on the assumption of this weight. Each package should also be plainly 
 marked with the brand and name of the manufacturer; those not branded 
 should be discarded, and, if possible, a mixture of different brands should be 
 avoided. 
 
 A possible indication of inferiority is the presence of lumps throughout the 
 bulk of the material. On standing, cement gradually absorbs moisture from the 
 air. At first this moisture is present in merely a minute and harmless state, 
 but eventually it combines chemically with the cement; that is, in the same 
 manner as when cement and water are actually mixed together in practice. 
 In the first condition, lumps usually appear, but they are so soft that they may 
 be readily crushed with the fingers, and of course would be entirely broken up 
 when mixed into mortar. When, however, the cement contains lumps that are 
 hard and pebble-like and that can be crushed only with considerable effort, it 
 indicates that chemical action has begun. Cement containing any appreciable 
 amount of these hardened lumps is generally of decidedly inferior quality, and 
 it should never be permitted to enter any important part of a structure. 
 
 Storing cement too long will tend to weaken it. Cement from 2 to 6 mo. old 
 is usually the safest and will produce the best results. 
 
 The color of Portland cement, ranging from bluish to yellowish gray, affords 
 no indication of quality except in cases where different shipments or different 
 parts of the same shipment show a variation in color, thus pointing to a lack of 
 uniformity. 
 
 Sampling. When securing a sample for testing, the essential point is to get 
 one that will fairly represent the entire shipment whose qualities are to be 
 determined. The common practice is to take a small portion of material from 
 every tenth barrel or, what is the same thing, from every fortieth bag. When 
 tests are to be made, however, on a shipment of only a few barrels, more 
 packages than one in ten should be opened; and when the shipment is large, 
 say over 150 bbl., it should be subdivided and each portion tested separately. 
 The bags selected should be taken at random and from different layers and not 
 all from one part of the pile. 
 
 The cement, moreover, should be taken not only from the top of the pack- 
 ages, but from the center and sides as well. When the cement is contained in 
 barrels, a sampling auger is used to extract the sample, a hole being bored in the 
 staves midway between the heads. After the samples of cement have been 
 taken from the packages they are thoroughly mixed in a can or basin, and this 
 mixed sample is used for the various tests. To make a complete series of tests, 
 the sample should contain from 6 to 8 Ib. The cement, after sampling and 
 before testing, must be well protected, as exposure to heat, cold, dampness, 
 or any other abnormal condition may seriously affect the results. 
 
 Purpose and Classification of Tests. In order that a mortar or a con- 
 crete made with cement shall give good results in actual construction, it must 
 possess two important properties, namely, strength and durability. The primary 
 purpose of cement testing, therefore, is to determine whether any particular 
 shipment of cement possesses sufficient strength and durability to admit of its 
 use in construction. 
 
 A determination of the quality of cement necessitates the employment of 
 several tests, which may be classified as primary tests and secondary tests. The 
 former tests, which include tests for soundness and tensile strength, are made to 
 give directly a measure of the essential qualities of strength and durability. 
 Unfortunately, neither of these tests is capable of being made with precision. 
 Therefore, the secondary tests, which include tests to determine the time of 
 setting, the fineness, the specific gravity, and the chemical analysis, are made 
 to obtain additional information in regard to the character of the material. 
 However, with the possible exception of the test of time of setting, the secondary 
 tests have but little importance and only indicate by their results indirectly the 
 properties of the material. 
 
196 
 
 CONCRETE 
 
 PRIMARY TESTS 
 
 Tests for Soundness. The property of cement that tends to withstand 
 any forces that may operate to destroy or disintegrate it is known as soundness. 
 This property, which is sometimes called constancy of volume, is the most impor- 
 tant requisite of a good cement. 
 
 The most common cause of unsoundness in Portland cement is an excess 
 of free or uncombined lime, which crystallizes with great increase of volume, 
 
 and thus breaks and destroys the bond of the cement. This excess of lime 
 may be due to incorrect proportioning or to insufficient grinding of the raw 
 materials, to underburning, or to lack of sufficient storing before use, called 
 seasoning. A certain amount of seasoning is usually necessary, because almost 
 every cement, no matter how well proportioned or burned it may be, will con- 
 tain a small amount of this excess of lime, which, on standing, will absorb mois- 
 ture from the air, slake, and become inert. 
 
 Excess of magnesia or the alkalies may also cause unsoundness, but the 
 ordinary cement rarely contains a sufficient amount of these ingredients to be 
 harmful. Sulphate of lime is occasionally responsi- 
 ble for unsoundness, but this ingredient usually acts 
 in the opposite direction, tending to make sound 
 a cement that otherwise might disintegrate. 
 
 The property of soundness is determined in one 
 or more of three ways: by measurements of expan- 
 sion, by normal tests, and by accelerated tests. 
 
 Measurements of expansion are made by form- 
 ing specimens of cement, usually in the shape of 
 prisms, and measuring the change in volume by 
 means of a micrometer screw. At the present time, 
 however, it is believed that expansion is not a sure 
 index of unsoundness, so that this test is seldom 
 / employed. 
 
 Normal tests consist in making specimens of 
 
 ^ IG- * cement mixed with water, preserving them in air 
 
 or in water under normal conditions, and observing their behavior. The com- 
 mon practice is to make on glass plates about 4 in. square, from a paste of neat 
 or pure cement, two circular pats about 3 in. in diameter, | in. thick at the 
 center, and tapering to a thin edge. These pats are kept in moist air for 24 hr. ; 
 then one of them is placed in fresh water of ordinary temperature and the other 
 
CONCRETE 
 
 197 
 
 is preserved in air. The condition of the pats is observed 7 da. and 28 da. 
 from the date of making, and thereafter at such times as may be desired. 
 
 The most characteristic forms of failure are illustrated in Figs. 1 and 2. 
 Fig. 1 (a) shows a pat in good condition. View (b) illustrates shrinkage cracks 
 that are due, not to inferior cement, but to the fact that the pat has been 
 allowed to dry out too quickly after being made. Pats must be kept in a moist 
 atmosphere while hardening, or these cracks, indicative merely of careless 
 manipulation, will develop. View (c) shows cracks that are due to the expan- 
 sion of the cement; this condition is common in the air pats, and is not indi- 
 cative of injurious properties. Pats kept in water, however, should not show 
 these cracks. View (d) shows cracking of the glass plate to which the pat is 
 attached; this cracking is caused by expansion or contraction of the cement, 
 combined with strong adhesion to the glass; it rarely indicates injurious prop- 
 erties. View (e) illustrates blotching of the its, the cause of which should 
 always be investigated by chemical analysis or otherwise, which may or may not 
 warrant the rejection of the material. Slag cements or cements adulterated 
 with slag invariably show this blotching. View (/) shows the radial cracks 
 that mark the first stages of disintegration; such cracks should never occur 
 with good material. They are signs of real failure, and cement showing them 
 should never be used. 
 
 Fig. 2 shows three pats that, for different reasons, have left the glass plate 
 on which they were made. The disk shown in (a) left the plate because of lack 
 of adhesion; the one in (6), through contraction; and the one 
 in (c), through expansion. The condition illustrated in (a) is 
 never dangerous in either air or water; that in (c) is only dan- 
 gerous when existing in a marked degree; and that in (b) hardly 
 ever occurs in water, but in air it often indicates dangerous 
 properties. Air pats that develop the curvature shown in (b) 
 generally disintegrate later. A curvature of about f in. in a 
 3-in. pat can be considered to be about the limit of safety. 
 
 The normal pat tests are the only absolutely fair and ac- 
 curate methods of testing cements for soundness, but the 
 serious objection to them lies in the fact that frequently several 
 months or even years elapse before failure in the cement so 
 tested becomes apparent. To overcome this difficulty the 
 accelerated tests have been de- 
 vised. These tests are intended 
 to produce in a few hours results 
 that require months in the nor- 
 mal tests. 
 
 Many forms of accelerated 
 tests have been devised. At 
 present, however, the only tests 
 employed commercially are the 
 boiling test and the steam test. 
 The boiling test is made by 
 forming specimens of neat- 
 cement paste into pats, such as are employed for the normal tests, or prefer- 
 ably into balls about 1? in. in diameter. The specimens are allowed to remain 
 in moist air for 24 hr. and are then tested. 
 
 The form of the apparatus used for the boiling test is shown in Fig. 3. It 
 consists of a copper tank that is heated by a Bunsen burner and is filled with 
 water. The water in the tank is kept at a uniform height by means of a con- 
 stant-level bottle. A wire screen placed an inch from the bottom of the tank 
 prevents the specimens from coming into contact with the heated bottom. The 
 test pieces, which are 24 hr. old, are placed in the apparatus, which is filled with 
 water of a normal temperature, and heat is applied at a rate such that the water 
 will come to boiling in about i hr. Quiet boiling is continued for 3 hr., after 
 which the specimens are removed and examined. Care must be taken that the 
 water employed is clean and fresh, because impure water may seriously affect 
 the results. The same water, also, should never be used for more than one test. 
 A good cement will not be affected by this treatment, and the ball will remain 
 firm and hard. Inferior cement will fail by checking, cracking, or entirely 
 disintegrating. 
 
 The steam test is made in the same way as the boiling test, except that 
 instead of immersing the specimens in water, they are kept in the steam above 
 the water. The apparatus employed is the same as that used for the boiling 
 
198 CONCRETE 
 
 test. The wire screen, however, is raised so that it is an inch above the sur- 
 face of the water; also, there must be provided a cover that is close enough to 
 retain the steam without creating pressure. The steam test is less severe than 
 the boiling test and is somewhat less accurate. 
 
 The result of the normal tests, if properly made and interpreted, may be 
 considered reliable guides to the soundness of the material, and cement failing 
 in these tests should always be rejected. The accelerated tests, on the other 
 hand, merely furnish indications, and are by no means infallible. A cement 
 passing the boiling test can generally be assumed sound and safe for use, but, 
 if failure occurs, it simply means that other tests should be performed with 
 greater care and watchfulness. It often is advisable to hold for a few weeks 
 cement that fails in boiling, so that the expansive elements may have an oppor- 
 tunity to hydrate and become inert; but if the material fulfils all the conditions 
 except the boiling test, and is sound in the normal tests up to 28 da., it is gen- 
 erally safe f9r use. All things being equal, however, a cement that will pass the 
 boiling test is to be preferred. 
 
 Tests for Tensile Strength. The tensile-strength test is for the purpose 
 of ascertaining a measure of the ability of the material to withstand the loads 
 that the structure must carry. This test is made by forming specimens, called 
 briquets, of cement and cement mortar, and determining the force necessary to 
 rupture them in tension at the expiration of fixed intervals of time. Cement 
 constructions are rarely called on to withstand tensile stresses, but if the tensile 
 strength is known, the resistance to other forms of stress may be computed with 
 a fair degree of accuracy. The tensile-strength test is the most convenient for 
 laboratory determinations, on account of the small size of the specimens and the 
 comparatively low stress required to cause rupture. 
 
 Cement is tested both neat or pure and in a mortar commonly composed of 
 1 part of cement and 3 parts of sand. The periods at which the briquets are 
 broken have been fixed by usage at 7 da. and 28 da. after making, although 
 tests covering much longer periods of time are necessary in research or in inves- 
 tigative work. 
 
 The strength of cement and cement mortars varies considerably with the 
 amount of water employed in making the briquets. Dry mixtures ordinarily 
 give the higher results for short-time tests, and wet mixtures show stronger with 
 a greater lapse of time. For testing purposes, therefore, it is essential that 
 all cements be mixed, not with the same amount of water, but with the 
 amount that will bring all the cements to the same physical condition, or to 
 what is called normal consistency. Different cements require different per- 
 centages of water because of their varying chemical composition, degree of 
 burning, age, fineness, etc, 
 
 The normal consistency of neat-cement pastes may be determined by either 
 of the methods that follow. In these tests, the quantities are given in grams. 
 
 The first method is taken from that part of the final report of the Special 
 Committee on Uniform Tests of Cement of the American Society of Civil 
 Engineers which may be found on pp. 679 to 684, inclusive, of Vol. LXXV, Dec., 
 1912, of the Transactions of that Society. In this method that quantity of 
 cement that it is proposed to use subsequently in each batch for making test 
 pieces should be weighed, but in no case should less than 500 grams be taken. 
 The amount is placed on a non-absorbent mixing slab in the form of a crater, 
 and a definite amount of water poured into the center. The cement is turned 
 over from the sides into the center with a trowel until the water is absorbed. 
 It is then kneaded vigorously for 1 min. and quickly formed into a ball and 
 tossed six times from one hand to the other maintained 6 in. apart. During the 
 operation of kneading and making the ball the hands should be protected by 
 rubber gloves. The ball of cement on the palm of the hand is then pressed into 
 the large end of the hard-rubber ring of the Vicat apparatus in such a way that 
 the ring is completely filled with paste. A Vicat apparatus working on the 
 same principle as the one illustrated in the Society's report and with the same 
 weight of movable rod and the same principal dimensions is described in connec- 
 tion with Tests for Times of Setting. The excess paste at the large end of the 
 ring is removed with one movement of the palm of the hand, the ring is placed 
 large end down on the plate under the movable rod, and the excess paste on the 
 top is sliced off with a trowel held at an angle. The paste must not be com- 
 pressed. The plunger is brought into contact with the surface of the material, 
 quickly released, and its penetration noted. The penetration should be 
 exactly 10 millimeters in $ min.; if the test shows a greater or less amount, 
 other trials must be made, using more or less water, until the correct consist- 
 ency is obtained. 
 
CONCRETE 
 
 199 
 
 The other method is to form of the paste a ball about 2 in. in diameter and 
 to drop this ball on a table from a height of about 2 ft. If the cement is of the 
 correct consistency, the ball will not crack nor will it flatten to less than one- 
 half its original thickness. The percentage of water required will vary from 
 16 to 25, depending on the characteristics of the material, the average cement 
 taking about 20%. 
 
 The consistency of sand mortars, however, cannot be obtained by either of 
 the foregoing methods, because the sand grains do not permit of the measure- 
 ment of the consistency by penetration, and the mixture is too incoherent for 
 use of the ball method. 
 
 The accompanying table gives the amount of water required to make mor- 
 tar of normal consistency and is given in the report of the committee just 
 referred to above. It is for a mortar consisting of 1 part of cement and 
 3 parts of Standard Ottawa Sand. The amount of water is given as a percent- 
 age of the combined weight of the cement and sand. Each percentage corre- 
 sponds with the water required for a normal consistency with the neat cement 
 formed by the method recommended by the Committee. 
 
 PERCENTAGE OF WATER FOR STANDARD SAND MORTAR 
 
 Water in 
 
 Water in 
 
 Water in 
 
 Water in 
 
 Water in 
 
 Water in 
 
 Neat 
 
 Standard 
 
 Neat 
 
 Standard 
 
 Neat 
 
 Standard 
 
 Cement 
 
 Mortar 
 
 Cement 
 
 Mortar 
 
 Cement 
 
 Mortar 
 
 Per Cent. 
 
 Per Cent. 
 
 Per Cent. 
 
 Per Cent. 
 
 Per Cent. 
 
 Per Cent. 
 
 15 
 
 8.0 
 
 23 
 
 9.3 
 
 31 
 
 10.7 
 
 16 
 
 8.2 
 
 24 
 
 9.5 
 
 32 
 
 10.8 
 
 17 
 
 8.3 
 
 25 
 
 9.7 
 
 33 
 
 11.0 
 
 18 
 
 8.5 
 
 26 
 
 9.8 
 
 34 
 
 11.2 
 
 19 
 
 8.7 
 
 27 
 
 10.0 
 
 35 
 
 11.3 
 
 20 
 
 8.8 
 
 28 
 
 10.2 
 
 36 
 
 11.5 
 
 21 
 
 9.0 
 
 29 
 
 10.3 
 
 37 
 
 11.7 
 
 22 
 
 9.2 
 
 30 
 
 10.5 
 
 38 
 
 11.8 
 
 The following formula has been devised to give the normal consistency to 
 any mortar with any sand. It will be noted that the values derived by the 
 formula differ somewhat from those given in the table. 
 
 Let x = per cent, of water required for sand mixture; 
 
 2V = per cent, of water required to bring neat cement to normal con- 
 sistency; 
 
 n = parts of sand to one of cement; 
 S = constant depending on character of sand. 
 
 _. 3JV+5n+l 
 
 Then ' * = ^(^+Tr 
 
 For crushed-quartz sand, the constant 5 is 30; for Ottawa sand, it becomes 
 25; and for the bar and bank sands used in construction, it varies from 25 to 35, 
 and must be determined for each particular sand. 
 
 EXAMPLE. How much water is required in a mixture of 1 part of cement 
 and 3 parts of crushed-quartz sand? The neat cement requires 19% of water 
 to give normal consistency. 
 
 SOLUTION. Here, N = 19, 5 = 30, and = 3. Substituting these values in 
 the formula, _ 3X19+30X3 + 1 _ ~~ 
 
 4XC3 + 1) 
 
 Sand for Mortar Tests. The size, gradation, and shape of the particles of 
 sand with which cement mortars are made have great influence on the resulting 
 strength. There are two varieties of standard sand for cement testing, one an 
 artificial sand of crushed quartz, the particles of which are angular in shape, 
 and the other a natural sand from Ottawa, Illinois, the particles of which are 
 almost spherical. Both sands are sifted to a size that will pass a sieve of 20 
 meshes to the inch and be retained on a sieve of 30 meshes, the diameters of 
 the sieve wires being .0165 and .0112 in., respectively. The Ottawa sand will 
 develop strengths in 1-3 mortars about 20 to 30% greater than those obtained 
 with crushed quartz, and it is theoretically the better sand for testing. On 
 most important works, tests for purposes of comparison are also made of the 
 actual sand entering the construction. 
 
200 
 
 CONCRETE 
 
 Briquets. The form of tensile briquet, adopted as standard in the United 
 States, is shown in the accompanying figure; its cross-section is exactly 1 sq. in. 
 These briquets are made in molds that come either single or in gangs of three, 
 four, or five. The gang molds are preferable, as they tend to produce greater 
 uniformity in the results. Molds should be made of brass or of some other 
 non-corrodible material; those made of cast iron soon rust and become unfit 
 for use. 
 
 When making the briquets, 1,000 g. of cement is carefully weighed and 
 placed on the mixing table in the form of a crater, and into the center of this 
 is poured the amount of water that is necessary 
 to give the correct normal consistency. Cement 
 from the sides of the crater is then turned into 
 the center, by means of a trowel, until all the 
 water is absorbed, after which the mass is vigor- 
 ously worked with the hands, as dough is kneaded, 
 for 1$ min. When sand mixtures are being 
 tested, 250 g. of cement and 750 g. of sand are 
 first weighed and thoroughly mixed dry until the 
 color of the pile is uniform; then the water is 
 
 r~i 1 i ; added and the operation is completed by vigorous 
 / V * kneading. 
 / \ After kneading, the material is immediately 
 
 placed into the molds, which should have been 
 wiped with oil to prevent the cement from stick- 
 ing to them. The entire mold is filled with ma- 
 terial at once not compacted in layers and 
 pressed in firmly with the fingers without any 
 ramming or pounding. An excess of material is 
 then placed on the mold and a trowel drawn over 
 it under moderate pressure, at each stroke cut- 
 ting off more and more of the excess material, until the surface of the briquets 
 is smooth and even. The mold is then turned over, and more material placed 
 in it and smoothed, as before. The mixing and molding should be performed 
 on a surface of slate, glass, or some other smooth, non-absorbent material. 
 During the mixing the operator should wear rubber gloves, so as to protect 
 his hands from the action of the lime in the cement. 
 
 For 24 hr. after making, the briquets are stored in a damp closet so that 
 the cement can harden in a moist atmosphere. The damp closet is simply a 
 tight box of soapstone with doors of wood lined with zinc, or some similar 
 arrangement, with a receptacle for water at the bottom and racks for holding 
 the briquets. The briquets remain in the molds while in the damp closet, 
 but at the expiration of 24 h, they are removed, marked, and placed in clean 
 water near 70 F. until broken. 
 
 Testing Machines. There are many styles of testing machines on the 
 market; that shown is called a shot machine and is made by the Fairbanks 
 Company. It is constructed on the cast-iron frame a, and is operated as 
 follows: The cup / is hung on the end of the beam d, the poise r placed at 
 the zero mark, and the beam balanced by turning the weight /. The hopper b 
 is then filled with fine shot, and the briquet to be tested is placed in the 
 clips h. The hand-wheel p is now tightened sufficiently to cause the gradu- 
 ated beam d to rise until the indicators at k are in line. In the case is a ten- 
 sion arrangement containing a worm and worm-gear that is connected to an 
 axis that is threaded and passes up through the hand wheel p and into a block 
 connected to the lower clip. A knob in the case engages this gear when it is 
 required. After the hand-wheel p has been tightened until the indicators are 
 in line, the worm is engaged and the automatic valve j is opened so as to 
 allow the shot to run into the cup /. The flow of the shot can be regulated by 
 means of a small valve located where the spout joins the reservoir. As the 
 briquet stretches, the beam is kept stationary by applying tension to the 
 briquet by means of the hand wheel 5. When the briquet breaks, the beam d 
 drops and by means of the lever i automatically closes the valve j. After 
 the specimen has broken, the cup with its contents is removed, and the 
 counterpoise g is hung in its place. The cup / is then hung on the hook 
 under the large ball e, and the shot weighed. The weighing is done by using 
 the poise r on the graduated beam d and the weights n on the counterpoise g. 
 The result will show the number of pounds required to break the specimen. 
 A mold for a single briquet is shown at c. 
 
CONCRETE 
 
 201 
 
 The load should be applied in all tests at the uniform rate of 600 Ib. per 
 min. The briquets should be broken as soon as they are removed from the 
 storage tanks and while 
 they are still wet, because 
 drying out tends to lower 
 their strength. The aver- 
 age of from three to five 
 briquets should be taken 
 as the result of a test. 
 
 Results of Tensile- 
 Strength Tests. The ten- 
 sile strength of briquets 
 tested in the preceding man- 
 ner should increase with age 
 up to about 3 mo., and 
 should then remain practi- 
 cally stationary for longer 
 periods. The average re- 
 sults of tests of Portland 
 cement made in the Phila- 
 delphia laboratories, cover- 
 ing aperiod of several 
 years and based on over 
 200,000 briquets, are given 
 in the accompanying table. 
 Specifications for strength 
 commonly stipulate mini- 
 mum values for the 7- and 
 28-da. tests, the customary 
 requirements for Portland 
 cement being 500 Ib. at 7 
 da. and 600 Ib. at 28 da., 
 when tested neat, and 170 
 Ib. at 7 da. and 240 Ib. at 
 28 da., when tested in a 
 mortar consisting of 1 part 
 of cement and 3 parts of 
 crushed-quartz sand. When 
 Ottawa sand is used, the 
 requirements for mortar 
 should be raised to 200 and 
 280 Ib., respectively. Re- 
 trogression in strength in 
 the periods specified is not often allowed. Although this retrogression in neat 
 briquets between 7 and 28 da. is not necessarily indicative of undesirable 
 
 TENSILE STRENGTH OF CEMENT BRIQUETS 
 
 
 
 J 
 
 1 
 
 | 
 
 | 
 
 
 
 ntS 8 
 
 fcjS S 
 
 w, u 
 
 .jj+j 8 
 
 
 
 <fe 3 
 
 *^> 3 
 
 <J> 3 
 
 <> 3 
 
 
 Mixture 
 
 S.Sw 
 
 s^ 
 
 SficH* 
 
 Scc^ 
 
 
 
 E Q, 
 
 Q as a 
 
 P M 
 
 Qg P. 
 
 
 
 "*1 
 
 "1 
 o 
 
 " S l 
 
 " s l 
 
 
 
 
 
 
 
 
 Neat 
 
 
 420 
 
 710 
 
 770 
 
 775 
 
 1 cement, 
 1 cement, 
 
 1 crushed-quartz sand 
 2 crushed-quartz sand 
 
 360 
 210 
 105 
 
 590 
 370 
 210 
 
 695 
 455 
 300 
 
 700 
 465 
 310 
 
 1 cement, 
 
 4 crushed-quartz sand 
 
 60 
 35 
 
 130 
 80 
 
 210 
 155 
 
 230 
 195 
 
 
 
 
 
 
 
202 
 
 CONCRETE 
 
 properties according to some authorities, yet if the mortar briquets show 
 retrogression, the cement should be condemned. Abnormally high strength 
 in the 7-da. test of neat cement, say over 900 lb., may generally be taken as an 
 indication of weakness rather than of superiority, because such a condition 
 is usually created by an excess of lime or of sulphates, either of which may be 
 injurious. Neat cement testing from 600 to 800 lb., at 7 da. is generally the 
 most desirable. 
 
 SECONDARY TESTS 
 
 Tests for Time of Setting. The time-of-setting test is made to determine 
 whether or not the cement will become hard at the time most desirable in actual 
 construction. If it begins to set too soon, the crystallization of the particles 
 will have begun before the mortar or concrete is thoroughly tamped into place. 
 If, on the other hand, the cement sets too slowly the material is more likely to 
 suffer from exposure to heat, cold, dampness, and frost; also, the progress of 
 the work will be much delayed on account of the greater interval required 
 between different sections, and the longer time the forms must be left up. 
 
 In the setting of cements, two stages are recognized: When the paste begins 
 to harden or to offer resistance to change of form, called initial set; and when 
 the setting is complete, or when the mass cannot be appreciably distorted 
 without rupture, called hard set. The time-of-setting test consists, therefore, 
 in determining the time required for the cement to reach these two critical 
 points. 
 
 The test is made by mixing cement with the amount of water required to 
 produce normal consistency, in the same manner as for neat tensile briquets, 
 forming specimens, placing them under one of 
 the forms of apparatus, and observing the time 
 that elapses between the moment the mixing 
 water is added and the moments when the paste 
 acquires initial set and hard set. 
 
 The Vicat needle, shown in Fig. 1, consists 
 of a frame k, holding a movable rod /, which 
 carries a cap d at the upper end and a needle h 
 at the lower. A screw / holds the rod in any 
 desired place. The position of the needle is 
 shown by a pointer moving over a graduated 
 scale. The rod with needle and cap weighs 
 exactly 300 g. and the needle is 1 mm. in 
 diameter with the end cut off square. When 
 making tests of normal consistency, the plunger 
 b, which is 1 cm, in diameter, is substituted for 
 the needle h, and the cap a for the cap d, the 
 difference in weight between the needle and 
 plunger being compensated by the difference in 
 the weight of the caps. The mold i for hold- 
 ing the cement paste is in the form of a trun- 
 cated cone. It has an upper diameter of 6 cm., 
 a lower diameter of 7 cm., and a height of 4 cm., 
 and rests on a 4"X4"X i" glass plate j. 
 
 After the cement paste is mixed, the mold 
 is filled by forcing the cement through the 
 large end; then, after turning it over and smoothing the top, it is placed 
 on the glass plate under the needle. The needle is lowered until it is 
 exactly in contact with the surface of the paste, then quickly released and the 
 depth to which it penetrates is read from the graduated scale. Initial set is 
 said to have taken place when the needle ceases to penetrate to within 5 mm. of 
 the bottom of the specimen; and hard set takes place when the same needle 
 ceases to make an impression on the surface. Trials of penetration are made 
 every 5 or 10 min. until these points are reached. 
 
 Time of setting varies considerably with the amount of mixing water 
 employed, so that it is essential that every sample tested be brought exactly to 
 normal consistency; otherwise, the results may be in decided error. Variations 
 in temperature in both environment and in the mixing water, also influence the 
 results. Standard practice requires that both the materials and the room in 
 which the tests are made be at a temperature of as nearly 70 P. as practicable. 
 When specifying results to be obtained in testing the time of setting, it is 
 obvious that a minimum value should be stipulated for initial set and a 
 maximum, as well as a minimum, for hard set. It must also be remembered 
 that a cement mixed with an aggregate and with an excess of water in the 
 
CONCRETE 203 
 
 field, will require from two to four times as long to set as the neat-cement 
 paste mixed with little water in the laboratory. Cement, therefore, showing 
 an initial set at the expiration of 20 min. with the Vicat needle, will rarely 
 begin to set on the actual work in less than f hr., which gives ample time for 
 mixing and placing the materials, and cement setting in less than 10 hr./will 
 usually have hardened completely in the work in 24 or at least in 36 hr. 
 Specifications usually stipulate that Portland cement shall show initial set in 
 not less than 20 minutes and shall develop hard set in not less than 1 hr. nor 
 more than 10 hr. Cement reaching initial set in less than 12 or 15 min. should 
 never be used for any work. 
 
 Tests for Fineness. The fineness of cement is important, because it affects 
 both the strength and the soundness of the product. The fineness of cement 
 is determined by passing it through a series of sieves of different mesh and then 
 measuring the amount retained on each. Three sieves are commonly employed, 
 namely, those having 50, 100, and 200 wires to the linear inch. Sieves for 
 cement testing should never be used until they have been carefully examined 
 and found to conform to the following standard specifications: 
 
 1. Cloth for cement sieves shall be of woven brass wire of the following 
 diameters: No. 50, .0090 in.; No. 100, .0045 in.; and No. 200, .00235 in. 
 
 2. Mesh to count on any part of the sieve as follows: No. 50, not less than 
 48 nor more than 50 per lin. in. ; No. 100, not less than 96 nor more than 100 
 per lin. in.; and No. 200, not less than 188 nor more than 200 per lin. in. 
 
 3. Cloth to be mounted squarely and to show no irregularities of spacing. 
 The method of using the sieves in the fineness test is to weigh out 50 g. of 
 
 cement on a scale sensible at least to fa g. and to place it on the No. 200 sieve, on 
 which it is shaken until not more than ^j g. passes the sieve at the end of 1 min. 
 of shaking. The arrival of this stage of completion can be watched either by 
 using a pan under the sieve or by shaking over a piece of paper. The residue 
 remaining on the sieve is weighed, placed on the No. 100 sieve and the operation 
 repeated, again weighing the residue. The amount remaining on the No. 50 
 sieve is then determined similarly. The process of sifting can be accelerated 
 by placing a small quantity of coarse shot or pebbles on the sieves with the 
 cement during the shaking. These may be separated from the cement by 
 passing the residue with the shot through a coarse sieve, such as the No. 20. 
 
 Portland cement should be ground to such a fineness that it will leave a 
 residue of not more than 25%, by weight, on the No. 200 sieve, and not 
 more than 8% on the No. 100 sieve. Of these two requirements, the first 
 is the more important, because it is only that part of the cement passing the 
 finest sieve that is active in the setting and hardening of the material. The 
 amount remaining on the No. 100 sieve is also important, because this part is 
 most liable to cause unsoundness in the cement, and although specifications 
 do not call for tests with the No. 50 sieve, it is usually employed for the same 
 reason as the No. 100 sieve. Any appreciable residue on this sieve indicates 
 that the material is much more liable to unsoundness. Any cement failing to 
 pass the fineness! test should be watched more carefully in the soundness and 
 strength tests, but if these tests show good results up to 28 da., the cement 
 can, as a rule, be used safely. It must be remembered, however, that only 
 that part passing the No. 200 sieve is really cement, so that a coarsely ground 
 shipment is practically equivalent to one adulterated with weak and unsound 
 material. 
 
 Tests for Specific Gravity. The object of the specific gravity test is to 
 furnish indications of the degree of burning, the presence or absence of adultera- 
 tion, and the amount of seasoning that the cement has received. When Port- 
 land cement is burned, the separate ingredients are in close contact and grad- 
 ually combine by a process of diffusion. The greater the amount of this 
 burning the more thoroughly are the elements combined. Thus, by their 
 contraction they give, in volume, a higher density or specific gravity. Since, 
 to secure good cement the burning must have been made within definite limits, 
 it follows that the specific gravity must also lie within fixed limits if the cement 
 has been properly manufactured. 
 
 The common adulterants of Portland cement, namely, limestone, natural 
 cement, sand, slag, cinder, etc., all have specific gravities ranging from 2.6 to 
 2.75, while the specific gravity of Portland cement averages about 3.15. An 
 appreciable amount of adulteration, therefore, is at once indicated in the 
 results of the test. 
 
 Seasoning is indicated because the cement on standing gradually absorbs 
 water and carbonic acid from the air. These ultimately combine with it and 
 thus lower the specific gravity. 
 
204 CONCRETE 
 
 Of the many forms of apparatus employed for the specific-gravity test, the 
 Le Chatelier flask, shown in Fig. 2, is the one most commonly used. It is also 
 the one adopted by the technical societies as standard. It consists of a glass 
 flask about 30 cm. high. The lower part up to mark a contains 120 cc., and 
 the bulb between the marks a and b contains exactly 20 cc. The neck of the 
 flask above the mark b is graduated into j* ff cc. The funnel c inserted in the 
 neck is to facilitate the introduction of the cement. 
 
 The method of conducting the specific-gravity test is as 
 follows: 64 g. of cement is carefully weighed on scales that 
 should have a sensibility of at least .005 g. The flask is 
 filled to the lower mark a with benzine or kerosene, which 
 has no action on the cement, and is carefully adjusted 
 
 Precisely to the mark by adding the liquid a drop at a time, 
 he funnel is then placed in the neck of the flask and the 
 weighed cement introduced slowly through it, the last traces 
 of the cement being brushed through with a camel's-hair 
 brush. The funnel is then renwved and the height of the 
 benzine read from the graduations, estimating to .01 cc. 
 The displaced volume is then 20 plus the reading, in cubic 
 centimeters, and the specific gravity of the cement is 64 
 divided by that quantity. For example, suppose that the 
 reading on the flask is .54, then the displaced volume will 
 be 20 +.54 = 20.54 and the specific gravity will be 64 
 -7-20.54 = 3.116. 
 
 The apparatus must be protected from changes in tem- 
 perature while in use; even touching the flask with the 
 fingers will change the volume of the liquid noticeably. 
 The flask is sometimes immersed in water during the tests 
 to prevent these changes of temperature, but this precau- 
 tion is unncessary if proper care is exercised. 
 
 The specific gravity of well-burned Portland cement 
 averages about 3.15 and should not fall below 3.1. If it 
 falls below 3.1, tests should also be made on dried and on 
 ignited samples to ascertain whether or not this condition 
 has been produced by reason of excessive seasoning. As a 
 rule, low specific gravity merely indicates well-seasoned 
 cement, and if sound and sufficiently strong, such cement 
 is the best sort of material for use, as its durability is 
 scarcely open to question. 
 
 Tests of Natural and Slag Cements. The methods of 
 conducting tests of natural and slag cements are, in all important particulars, 
 identical with those employed for Portland cement, although the results ob- 
 tained and the interpretation to be put on them are often radically different. 
 In the testing, the only essential difference is in the amount of water required 
 by these cements to produce normal consistency; natural cement requires from 
 23 to 35% and slag cement takes about 18%, or an average of 2 or 3% less 
 than Portland. Tests of natural cement for tensile strength are also fre- 
 quently made on 1-1 and 1-2 mortars, but recent practice is to test mortars 
 of all kinds of cement in 1-3 mixtures. For these cements, moreover, the 
 specific-gravity test has practically no significance, except in determining the 
 uniformity with which the different brands are made. 
 
 FIG. 2 
 
 CEMENT SPECIFICATIONS 
 
 A good example of a complete modern specification for Portland cement is 
 here given. 
 
 SPECIFICATIONS FOR PORTLAND CEMENT 
 
 Kind. All cement shall be Portland of the best quality, dry and free from 
 lumps. By Portland cement is meant the finely pulverized product resulting 
 from the calcination to incipient fusion of an intimate mixture of properly pro- 
 portioned argillaceous and calcareous materials to which no addition greater 
 than 3% has been made subsequent to calcination. 
 
 Packages. Cement shall be packed in strong cloth or canvas bags, or in 
 sound barrels lined with paper, which shall be plainly marked with the brand 
 
CONCRETE 
 
 205 
 
 and the name of the manufacturer. Bags shall contain 94 Ib. net and barrels 
 shall contain 376 Ib. net. 
 
 Inspection. All cement must be inspected, and may be reinspected at any 
 time. The contractor must submit the cement, and afford every facility for 
 inspection and testing, at least 12 da. before desiring to use it. The chief 
 engineer shall be notified at once on receipt of each shipment at the work. No 
 cement will be inspected or allowed to be used unless delivered in suitable 
 packages properly branded. Rejected cement must be immediately removed 
 from the work. 
 
 Protection. The cement must be protected in a suitable building having 
 a wooden floor raised from the ground, or on a wooden platform properly pro- 
 tected with canvas. It shall be stored so that each shipment will be separate, 
 and each lot shall be tagged with identifying number and date of receipt. 
 
 Quality. The acceptance or rejection of a cement to be used will be based 
 on the following requirements: 
 
 Specific gravity: Not less than 3.1. 
 
 Ultimate tensile strength per square inch: POUNDS 
 
 7 da. (1 da. in air, 6 da. in water) 500 
 
 28 da. (1 da. in air, 27 da. in water) 600 
 
 7 da. (1 da. in air, 6 da. in water), 1 part cement to 3 parts of 
 
 standard quartz sand 170 
 
 28 da. (1 da. in air, 27 da. in water), 1 part of cement to 3 parts of 
 
 standard quartz sand 240 
 
 Fineness: Residue on No. 100 sieve not over 8%, by weight; residue on No. 
 200 sieve not over 25%, by weight. 
 
 Set: It shall require at least 20 min. to develop initial set, and shall develop 
 hard set in not less than 1 hr. nor more than 10 hr. These requirements may 
 be modified where the conditions of use make it desirable. 
 
 Constancy of Volume: Pats of cement 3 in. in diameter, | in. thick at center, 
 tapering to thin edge, immersed in water after 24 hr. in moist air, shall show 
 no signs of cracking, distortion, or disintegration. Similar pats in air shall also 
 remain sound and hard. The cement shall pass such accelerated tests as the 
 chief engineer may determine. 
 
 Analysis: Sulphuric anhydride, SOz, not more than 1.75%; magnesia, 
 MgO, not more than 4%. 
 
 The common requirements for high-grade Portland, natural, and slag 
 cements are given in the following table. 
 
 REQUIREMENTS FOR HIGH-GRADE CEMENTS 
 
 Requirements 
 
 Portland 
 Cement 
 
 Natural 
 Cement 
 
 Slag 
 Cement 
 
 Specific gravity: 
 Not less than 
 
 3.1 
 
 2.8 
 
 2.7 
 
 Fineness: 
 Residue on No. 100 sieve, not over 
 Residue on No. 200 sieve, not over 
 Time of Setting: 
 Initial not less than 
 
 8% 
 25% 
 
 20 min. 
 
 10% 
 30% 
 
 10 min. 
 
 3% 
 10% 
 
 20 min. 
 
 
 Ihr. 
 
 30 min. 
 
 1 hr. 
 
 Hard, not more than 
 Tensile strength per sq. in. 
 7 da., neat, not less than 
 28 da. neat not less than 
 
 10 hr. 
 
 500 Ib. 
 600 Ib. 
 
 3 hr. 
 
 125 Ib. 
 225 Ib. 
 
 10 hr. 
 
 350 Ib. 
 450 Ib. 
 
 7 da., 13 quartz, not less than 
 
 170 Ib. 
 
 50 Ib. 
 
 125 Ib. 
 
 28 da., 1-3 quartz, not less than 
 Soundness: 
 Normal pats in air and water for 28 da. / 
 to be I 
 
 240 Ib. 
 
 sound and 
 hard 
 
 110-lb. 
 
 sound and 
 hard 
 
 200 Ib. 
 
 sound and 
 hard 
 
 Boiling test to be { 
 
 sound and 
 
 
 sound and 
 
 Analysis: 
 
 4% 
 
 
 4% 
 
 Anhydrous sulphuric acid, SOa, not over 
 Sulphur 5 not over 
 
 1.75% 
 
 
 1 3% 
 
 
 
 
 
206 CONCRETE 
 
 PLAIN CONCRETE 
 
 DEFINITIONS AND TERMS 
 
 Concrete is usually made of cement, sand, and broken stone. The cement 
 in a plastic state, either by itself or with the sand that is generally mixed with 
 it, is called the matrix, and the broken stone, gravel, or other material used as a 
 filler is called the aggregate. The sand is correctly classed as a part of the aggre- 
 gate, although some engineers include it with the matrix. The aggregate is used 
 to cheapen concrete. Pure, or neat, cement, when wet with water, would in 
 a way fulfil all the physical requirements of concrete, but it would be too 
 expensive. 
 
 In the concrete of today, hydraulic cement is used almost exclusively. For 
 this reason, the term concrete, as commonly used, refers only to that variety. 
 In specifying any other kind of concrete, the usual custom is to mention it 
 by its full name, as bituminous concrete, lime concrete, etc. Such varieties, how- 
 ever, are of comparatively little importance. . 
 
 The term concrete, besides being restricted to hydraulic-cement concrete, 
 has another restriction: the aggregate must not be sand alone, although it may 
 be partly sand. A mixture of hydraulic cement, sand, and water is called by the 
 special name of mortar. 
 
 Concrete is usually named from the kind of aggregate used. For example, 
 stone concrete embodies the use of broken stone or coarse pebbles, while in cinder 
 concrete, the aggregate consists of cinders or broken slag. 
 
 The proportion of cement and sand to the broken stone depends on the 
 spaces between the stones, which are known as voids. In all instances, there 
 must be sufficient mortar to fill the voids entirely and to cover all surfaces of the 
 separate stones. 
 
 AGGREGATES OTHER THAN SAND 
 
 The aggregates or broken stone used in concrete work should possess three 
 qualities: (1) They should be hard and strong, so as to resist crushing and 
 shearing or transverse stresses; (2) they should have surface texture that will 
 permit the cement mortar to adhere to their surfaces; and (3) where the con- 
 crete is to be used for building construction, such as in reinforced-concrete work, 
 and for fireproofing, they should possess refractory, or fire-resisting, qualities. 
 Usually, aggregates that break in such a way as to allow the smallest spaces, or 
 interstices, between the particles, will make the strongest concrete for con- 
 struction purposes because the voids can be most economically filled with 
 cement mortar. 
 
 Size of Aggregates. When measuring broken stone, the size of the stone 
 is determined by the size of the ring through which it will pass. For instance, a 
 2-in. stone is one that will pass through a ring, or hole, that is 2 in. in diameter. 
 
 The broken stone used in concrete work varies in size with the nature of the 
 work. For foundation and mass construction, it is the custom to use broken 
 stone of a size that will pass through a 2- or 2^-in. ring. For filling the 
 spandrels of bridges or the spaces between walls, where mere bulk is desired, 
 broken stone of a much larger size is used. 
 
 In reinforced-concrete work, the broken stone must be small, owing to the 
 narrow spaces in the forms. For columns and wall work, stone that will pass 
 through a 1- or f-in. ring is suitable, while for filling beam and girder forms, 
 where numerous reinforcing rods occur, the broken stone is sometimes so small 
 as to pass through a ^-in. ring. 
 
 The latest practice in making concrete is to use stone as it comes from the 
 crusher, without screening it. While such stone, termed the run of crusher, 
 contains broken stone of a size specified, it also has smaller particles of stone 
 and such stone dust as is carried along with the broken stone from the crusher. 
 Where the run of crusher is used, the proportion of the cement and sand must 
 be changed, because the stone dust takes the place of some of the sand. In 
 using run of crusher the very finest dust should be washed or screened out as it 
 tends to coat the large pieces and to prevent the cement from adhering to them. 
 
 The size of the aggregates has much to do with the quality and strength of 
 the concrete. It can, however, be stated as a general proposition, that the 
 larger the stones the stronger will be the concrete. This fact was well proved 
 in a series of tests made at the Watertown Arsenal in 1898. These tests also 
 showed that the concrete becomes heavier per cubic foot, or, in other words, 
 
CONCRETE 207 
 
 more dense, the larger the stone used. All these tests were made with con- 
 crete manufactured in the proportion of 1 part of cement, 1 part of sand, 
 and 3 parts of broken stones, or a 1-1-3 (1 to 1 to 3) mixture, as it is usually 
 expressed. The figures on cinder concrete in the table are added simply to 
 give a comparison of weights, for it will be noted that the cinder concrete is 
 older than the other concretes, and therefore stronger in proportion. 
 
 Aggregates that consist of stone of varying sizes are best for making con- 
 crete, owing to the fact that they pack closer. It is well, however, to screen 
 all the fine particles, such as i-in. sizes, and use them with the sand, as other- 
 wise they will not mix properly with the cement. 
 
 Selection of Aggregates. Usually the character of the aggregates used in 
 mixing concrete depends on the availability of the supply. Where there is 
 much choice in the selection of the aggregates those that are hardest and break 
 with a cubical fracture will make the best concrete, although rounded pebbles 
 are considered by some engineers to P9ssess great advantages. 
 
 Some years ago the American Society of Civil Engineers, American Society 
 for Testing Materials, American Railway Engineering and Maintenance of Way 
 Association, and the Association of American Portland Cement Manufacturers 
 appointed committees to obtain information concerning the practice in and 
 properties of concrete and reinforced concrete and recommend formulas for 
 design, etc. This general committee is commonly known as the Joint Com- 
 mittee and references will be made to its report in the following pages. These 
 references are taken from the Proceedings of the American Society of Civil 
 Engineers, Vol. XXXIX, No. 2, pp. 117 to 168, where the Progress Report of 
 the Special Committee of that Society on concrete and reinforced concrete will 
 be found. It was presented to that society by its committee on Jan. 15, 1913. 
 
 The relative merit of various aggregates for concrete cannot of course be 
 defined accurately, because in any one aggregate the quality may vary con- 
 siderably. The working stresses for concrete have been discussed by the 
 Joint Committee. This committee recommends in its report certain tests for 
 the ultimate strength of concrete. In the absence of such tests there are given 
 certain values for the strength of concrete that should be obtained under 
 certain conditions. The values given vary among other things with the kind 
 of aggregate used. The aggregates are arranged into four groups in so far as 
 they govern the strength of the concrete. These groups are as follows: 
 
 First group, granite, trap rock. 
 
 Second group, gravel, hard limestone, and hard sandstone. 
 
 Third group, soft limestone and sandstone. 
 
 Fourth group, cinders. 
 
 The difference in quality between any two adjacent groups is not constant. 
 
 Elsewhere in the report it is stated: "Cinder concrete should not be used 
 for reinforced-concrete structures. It may be allowable in mass for very 
 light loads or for fire-protection purposes. The cinders should be composed 
 of hard, clean, vitreous clinker, free from sulphides, unburned coal, or ashes." 
 
 PROPORTIONING OF INGREDIENTS 
 
 Effect on Strength and Imperviousness. The strength of concrete depends 
 on the strength of the cement and the thoroughness with which the cement 
 binds together the various pieces of aggregate. The more completely the 
 voids are filled, the more completely will the aggregate be held together. 
 Therefore, the more solid and condensed the concrete is, the less voids it will 
 have, and the stronger it will be. The same is true with regard to making con- 
 crete water-proof; the more dense the concrete is, the more nearly water-proof 
 it is. 
 
 A mixture of 1 part of cement, \\ parts of sand, and 3 parts of stone, which 
 would be considered extravagantly rich for a dry place, is probably as dense 
 a concrete, and as good for waterproofing qualities, as can be made. 
 
 When a concrete is made of cement, sand, and stone, and the stone is of such 
 a size that it will pass through a 3-in. ring, but will not pass through a 22-in. 
 ring, the concrete is weaker and requires more cement than one made with 
 graded stone from 3-in. down. . When the stone is graded in size, the stones 
 of smaller size fill the voids between the larger stones and thus reduce the 
 quantity of cement and sand required. 
 
 Proportioning by Weights. The ingredients for a sample batch of concrete 
 are weighed out in known proportions and mixed to the desired consistency on a 
 sheet of steel. They are then tamped in a piece of 10-in. pipe capped at one 
 end. The pipe thus partly filled is weighed, and subtracting the weight of the 
 receptacle a check is obtained. The height of the concrete in the pipe is then 
 
208 
 
 CONCRETE 
 
 g 3"g cT COMPRESSIVE STRENGTH OF CONCRETE MADE OF DIFFERENT-SIZED STONES 
 
 0, 
 
 (2 
 
 J3d spunoj 
 
 rH (N COOOO 
 
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 q <N .0.000 
 
 10 10 rJ<COTH 
 
 measured and the 
 mixture dumped out 
 before it hardens. 
 After all the appar- 
 atus is cleaned another 
 batch of concrete is 
 mixed, using the same 
 weight of water, ce- 
 ment , and total weight 
 of sand and stone as 
 before, but a different 
 ratio of weight of 
 sand to weight of 
 stone. The height of 
 this concrete in the 
 pipe is measured. 
 This operation is re- 
 peated. The concrete 
 occupying the least 
 volume is the densest 
 and strongest that can 
 be made with that 
 particular sand and 
 stone as they are and 
 with the given pro- 
 portion of cement. 
 The volumes corre- 
 sponding to the 
 weights can be found 
 by trial measure- 
 ments. 
 Usual Proportions 
 of Materials. It is 
 not always necessary 
 to use the strongest 
 concrete, as the con- 
 crete may be required 
 to withstand only 
 slight stresses and be 
 simply used for its 
 weight. The strong- 
 est concrete would 
 then be unnecessarily 
 expensive. Often the 
 foregoing method 
 of proportioning con- 
 crete is not employed 
 and the engineer 
 specifies a mixture 
 from his own experi- 
 ence without testing 
 the aggregates in any 
 way, except to see 
 that the stone is un- 
 der the specified maxi- 
 mum size and properly 
 graded, and that the 
 sand is in large grains, 
 graded down, and free 
 from dirt and loam. 
 A common proportion 
 for unimportant work 
 is 1-3-6. This pro- 
 portion may be used 
 oundations for asphalt 
 e 1-2-4 is used in piers, 
 in other places where 
 
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 foundations below groun 
 Cements, and for similar i 
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 222 2 S* * * ^ 
 
 d, in engine bases, in the : 
 >urposes. A richer mixtui 
 'orced-concrete work, anc 
 
CONCRETE 209 
 
 In regard to the proportioning of ingredients the Joint Committee states 
 as follows: 
 
 " Quality and Proportions. The materials to be used in concrete should be 
 carefully selected, of uniform quality, and proportioned with a view to secur- 
 ing as nearly as possible a maximum density. 
 
 " Unit of Measure. The unit of measure should be the cubic foot. A bag 
 of cement, containing 94 Ib. net should be considered the equivalent of 1 cu. ft. 
 
 "The measurement of the fine and coarse aggregates should be by loose 
 volume. 
 
 "Relation of Fine and Coarse Aggregates. The fine and coarse aggregates 
 should be used in such relative proportions as will insure maximum density. 
 In unimportant work, it is sufficient to do this by individual judgment, using 
 correspondingly higher proportions of cement; for important work these 
 proportions should be carefully determined by density experiments, and the 
 sizing of the fine and coarse aggregates should be uniformly maintained or the 
 proportions changed to meet the varying sizes. 
 
 "Relation of Cement and Aggregates. For reinforced-concrete construction, 
 1 part of cement to a total of 6 parts of fine and coarse aggregates measured 
 separately should generally be used. For columns, richer mixtures are gen- 
 erally preferable; and in massive masonry or rubble concrete, a mixture of 1-9 
 or even 1-12 may be used. 
 
 "These proportions should be determined by the strength or the wearing 
 qualities required in the construction at the critical period of its use. Experi- 
 enced judgment based on individual observation and tests of similar conditions 
 in similar localities is an excellent guide as to the proper proportions for any 
 particular case. 
 
 "For all important construction, advance tests should be made of concrete 
 composed of the materials in the proportions, and of the consistency to be 
 used in the work. These tests should be made under laboratory conditions 
 to obtain uniformity in mixing, proportioning, and storage, and in case the 
 results do not conform to the requirements of the work, aggregates of a better 
 quality should be chosen or richer proportions used to obtain the desired 
 results." 
 
 Water for Concrete. The wetter the concrete is, the easier it will be put 
 in place, but mixtures that are too wet are not so strong as medium mixtures. 
 The amount of water that will make the best mixture is such that after the 
 concrete has been put in place and rammed it will quake like jelly when struck 
 with a spade, and water will come to the surface. If the concrete is wetter than 
 this, the water will have a slight chemical effect on the cement, and, moreover, 
 the sand and cement will tend to separate from the broken stone. 
 
 In cinder concrete, owing to the porosity of the cinders, it is necessary to 
 use a little more water, so that the cement will be liquid enough to fill the little 
 cavities in each cinder. This precaution is indispensable when the concrete is 
 to be used with steel, as otherwise the steel will be rapidly corroded by the 
 action of air reaching it through the pores in the cinders. 
 
 DESTRUCTIVE AGENCIES 
 
 Various causes may affect the strength and durability of concrete. The 
 principal causes have been discussed by the Joint Committee already referred 
 to, and as the various effects are often more or less complex it is probably best 
 to quote directly from the Joint Committee. 
 
 "Corrosion of Metal Reinforcement. Tests and experience indicate that 
 steel sufficiently embedded in good concrete is well protected against corrosion, 
 no matter whether located above or below water level. It is recommended 
 that such protection be not less than 1 in. in thickness. If the concrete is 
 porous, so as to be readily permeable by water, as when the concrete is laid 
 with a very dry consistency, the metal may corrode on account of the presence 
 of moisture and air. 
 
 "Electrolysis. The most recent experimental data available on this subject 
 seem to show that while reinforced-concrete structures may, under certain con- 
 ditions, be injured by the flow of electric current in either direction between 
 the reinforcing material and the concrete, such injury is generally to be expected 
 only where voltages are considerably higher than those that usually occur in 
 concrete structures in practice. If the iron is positive, trouble may manifest 
 itself by corrosion of the iron accompanied by cracking of the concrete; if the 
 iron is negative, there may be softening of the concrete near the surface of the 
 iron, resulting in a destruction of the bond. The former, or anode effect, 
 decreases much more rapidly than the voltage, and almost, if not quite, 
 
210 CONCRETE 
 
 disappears at voltages that are most likely to be encountered in practice. The 
 cathode effect, on the other hand, takes place even at very low voltages, and 
 is, therefore, more important from a practical standpoint than that of the anode. 
 
 "Structures containing salt or calcium chloride, even in very small quanti- 
 ties, are very much more susceptible to the effects of electric currents than 
 normal concrete, both the anode and cathode effects progressing much more 
 rapidly in the presence of chlorine. 
 
 "There is great weight of evidence to show that normal reinforced-concrete 
 structures free from salt are in very little danger under most practical condi- 
 tions, while non-reinforced-concrete structures are practically immune from 
 electrolysis troubles. The results of experiments now in progress may yield 
 more conclusive information on this subject. 
 
 "Sea- Water. The data available concerning the effect of sea-water on 
 concrete or reinforced concrete are limited and inconclusive. Sea walls out 
 of the range of frost action have been standing for many years without apparent 
 injury; in many harbors where the water is brakish, through rivers discharging 
 into them, serious disintegration has taken place. This has occurred chiefly 
 between low- and high-tide levels, and is due, evidently, in part to frost. 
 Chemical action also appears to be indicated by the softening of the mortar. 
 T9 effect the best resistance to sea- water, the concrete must be proportioned, 
 mixed, and placed so as to prevent the penetration of sea-water into the mass 
 or through the joints. The cement should be of such chemical composition 
 as will best resist the action of sea-water; the aggregates should be carefully 
 selected, graded, and proportioned with the cement so as to secure the maxi- 
 mum possible density; the concrete should be thoroughly mixed; the joints 
 between old and new work should be made water-tight; and the concrete should 
 be kept from exposure to sea-water until it is thoroughly hard and impervious. 
 
 "Acids. Concrete of first-class quality, thoroughly hardened, is affected 
 appreciably only by strong acids that seriously injure other materials. A 
 substance like manure is injurious to green concrete, but after the concrete has 
 hardened thoroughly it satisfactorily resists the action of such acid. 
 
 "Oils. When concrete is properly made and the surface is carefully finished 
 and hardened, it resists the action of such mineral oils as petroleum and ordinary 
 engine oils. Oils that contain fatty acids produce injurious effects, forming 
 compounds with the lime that result in a disintegration of the concrete in 
 contact with them. 
 
 "Alkalies. The action of alkalies on concrete is problematic. In the 
 reclamation of arid land, where the soil is heavily charged with alkaline salts, 
 it has been found that concrete, stone, brick, iron, and other materials are 
 injured under certain conditions. It would seem that at the level of the 
 ground water, in an extremely dry atmosphere, such structures are disin- 
 tegrated through the rapid crystallization of the alkaline salts, resulting from 
 the alternate wetting and drying of the surface. Such destructive action can 
 be prevented by the use of a protective coating, and is minimized by securing 
 a dense concrete." 
 
 Effect of Fire on Concrete. Concrete is essentially a fire-proof material. 
 All the ingredients of which it is composed are of a highly refractory nature, 
 the aggregates being the elements of the mixture that are most quickly affected 
 by intense heat. This is especially true of granite and limestone aggregates, 
 the former being likely to crack or burst when heated, and the latter to calcine. 
 After cement has set, the chemical union of its particles is liable to destruction 
 by fire, because intense heat robs the cement of the water of crystallization, 
 or dehydrates the cement, thus softening the material and making it crumbly. 
 If concrete in a mass is subjected to intense heat, this action of dehydration 
 extends into the concrete for a depth of only | to 5 in., and is not likely to 
 penetrate farther. 
 
 Effect of Mine Water on Concrete. The water from coal mines contains 
 sulphuric acid, ammonium compounds, and other chemicals decidedly injurious 
 to concrete. The use of concrete about the mines has assumed large propor- 
 tions only in the last few years, and as yet no cheap method that is always 
 effective has been uniformly adopted to protect the concrete from this water. 
 Since the mine water will not attack silica, sand containing at least 92% silica 
 should be used. The stone employed should also be acid-resisting and at least 
 90% insoluble in dilute hydrochloric acid. The cement should be properly 
 burned and should be the best obtainable for such work. Some of the coal 
 companies have special specifications for cement. Although the foregoing 
 precautions will not make concrete entirely permanent in some conditions, 
 they will increase its life. 
 
CONCRETE 211 
 
 Expansion and Contraction. Considere, a French concrete expert, has 
 found by experiment that a 1-3 mortar will shrink from about .05 to .15% 
 when setting in air, and that the shrinkage will be two to three times as 
 great with neat cement. The shrinkage in concrete will be much less than 
 with neat cement or cement mortar. 
 
 The shrinkage of concrete is lessened by embedding in it steel rods or bars, 
 as these, by their tensile resistance, prevent the shrinkage of the material when 
 setting. By the experiments of Considere, it is found that with 1-3 mortar 
 reinforced with steel the shrinkage when setting is about one-fifth that of the 
 same mortar without the steel reinforcement. 
 
 Effect of Thermal Changes on Concrete. Nearly all materials expand 
 slightly as they become heated. Concrete and steel also follow this law. The 
 contraction or the expansion of concrete due to changes in temperature is 
 about the same as that of steel. The average coefficient of expansion of a 
 1-2-4 concrete for each Fahrenheit degree in change of temperature is .0000055. 
 Experiments made on 1-3-6 concrete give a coefficient of expansion of .0000065, 
 which is practically the same as the coefficient of steel. 
 
 Effect of Vibration on Concrete. The effect of constant vibration on 
 concrete structures has not been definitely determined. Many buildings and 
 bridges constructed of concrete reinforced with steel rods and bars have with- 
 stood heavy and constant vibration, both continuous and intermittent, for an 
 extended period of years with no apparent deterioration in strength. Fresh 
 concrete is always, however, subject to deterioration by vibration, and the 
 strength of concrete subjected to jar or shock when setting is materially re- 
 duced, because the process of crystallization between the particles, and the 
 consequent cohesion of the mass, seems to be partly destroyed. 
 
 WORKING STRESSES AND STRENGTH VALUES OF CONCRETE 
 
 The ultimate strength of concrete varies so with the proportion of the 
 mixture, manner of working, character of ingredients, and age of material, 
 that it is necessary to assume low unit working stresses for it. 
 
 There can be no unit stresses recommended for use for all conditions. It 
 takes experience to make good concrete. Moreover, complete and detailed 
 instructions and directions must be followed; more complete and detailed than 
 there is room for here. The Joint Committee's report recommends for allow- 
 able stresses for concrete, certain percentages of the crushing strength of 
 cylinders of the concrete, of certain size, and tested under certain conditions. 
 In the absence of tests to learn this crushing strength, this report states that 
 for cylinders of certain size, age, and method of manufacture, if made of 1-2-4, 
 according to the directions laid down, of gravel, hard limestone, or hard sand- 
 stone, the crushing strength should be 2,000 pounds per square inch. The 
 allowable stresses for such a concrete, when made of Portland cement, with 
 static loads are: 
 
 Axial compression, columns under 12 diameters ........... 450 
 
 Compression in extreme fiber of beam, due to bending ..... 650 
 
 Shear in beams, without web reinforcement .............. 40 
 
 Shear, pounding shear ................................. 120 
 
 Bond, plain bars ...................................... 80 
 
 Bond, drawn wire ..................................... 40 
 
 The strength of concrete varies, of course, with the age and richness of the 
 mixture. To show this variation, the ultimate compressive strength of con- 
 crete of various ages and mixtures made from Portland cement, sand, and 
 crushed stone, is given in the accompanying table. These results represent 
 the product of some six hundred tests made by W. Purves Taylor, engineer- 
 in-charge of the municipal testing laboratory of Philadelphia. Of course, to 
 obtain similar figures, the concrete must be made and tested as it was in this 
 experiment. The table, however, shows the increase of strength with age 
 and richness of mixture. 
 
 CONCRETE MIXTURES 
 
 Methods of Measuring Ingredients. After deciding what proportions of 
 ingredients will be used for the concrete, the engineer must be able to calculate 
 the quantity of each material that he must order. An ordinary box car holds 
 from 400 to 600 bags of cement. The purchaser is charged for the bags by the 
 manufacturer, unless they are of paper, but he gets a rebate for those that 
 are returned. 
 
212 CONCRETE 
 
 AVERAGE ULTIMATE CRUSHING STRENGTH OF CONCRETE 
 
 Proportion of 
 
 Ultimate Crushing Strength 
 
 Ingredients 
 
 Pounds per Square Inch 
 
 Cement 
 
 Sand 
 
 Stone 
 
 7 da. 
 
 1 mo. 
 
 3 mo. 
 
 6 mo. 
 
 1 
 
 20 
 
 4 
 
 1,600 
 
 2,150 
 
 2,400 
 
 2,500 
 
 1 
 
 2.5 
 
 5 
 
 1,430 
 
 1,950 
 
 2,250 
 
 2,350 
 
 
 3.0 
 
 6 
 
 1,250 
 
 1,800 
 
 2,100 
 
 2,200 
 
 
 3.5 
 
 7 
 
 1,100 
 
 1,660 
 
 1,960 
 
 2,080 
 
 
 4.0 
 
 8 
 
 980 
 
 1,520 
 
 1,820 
 
 1,950 
 
 
 4.5 
 
 9 
 
 850 
 
 1,400 
 
 1,690 
 
 1,840 
 
 
 5.0 
 
 10 
 
 750 
 
 1,260 
 
 1,550 
 
 1,720 
 
 1 
 
 5.5 
 
 11 
 
 650 
 
 1,120 
 
 1,420 
 
 1,600 
 
 1 
 
 6.0 
 
 12 
 
 600 
 
 1,000 
 
 1,300 
 
 1,500 
 
 Cement is usually measured by the barrel just as it comes from the manu- 
 facturer, or as 4 bags to the barrel, while broken stone and sand are measured 
 loose in a barrel. Portland cement, after it is taken out of its original package 
 and stirred up, fills a larger volume than when packed. It is therefore necessary 
 to state just how the cement is to be measured; and, as said before, the custom 
 is to measure it by the barrel, compact. A cement barrel contains about 
 3.8 cu. ft. 
 
 Fuller's Rule for Quantities. A practical rule has been devised by W. B. 
 Fuller whereby, after the proportions of ingredients have been fixed, the 
 quantity of material for a certain work may be obtained with reasonable 
 closeness. It is called Fuller's rule for quantities, and may be expressed in 
 mathematical symbols as follows: 
 Let c = number of parts of cement; 
 5 = number of parts of sand ; 
 g = number of parts of gravel or broken stone; 
 C = number of barrels of Portland cement required for 1 cu. yd. of 
 
 concrete; 
 
 5 = number of cubic yards of sand required for 1 cu. yd. of concrete; 
 G = number o cubic yards of stone or gravel required for 1 cu. yd. of 
 concrete. 
 
 Then 
 
 3 - 8 r Ar 
 
 Cs ' and G = 
 
 in the second formula, S = -^=- 
 
 If the broken stone is. of uniformly large size, with no smaller stone in it, 
 the voids will be greater than if the stone were graded. Therefore, 5% must 
 be added to each value found by the preceding formulas. 
 
 EXAMPLE. If a 1-2-4 mixture is considered, what will be: (a) the number 
 of barrels of cement? (&) the number of cubic yards of sand? and (c) the number 
 of cubic yards of stone required for 1 cu. yd. of concrete? 
 
 SOLUTION. (a) Here c = l, s = 2, and g = 4. Substituting these values in 
 
 the first formula, C = ^ = 1.57. 
 1+2+4 
 
 (b) Substituting the values of C and 
 X 1.57X2 = .44. 
 
 (c) Substituting the values of C and g in the third formula, C = |f X 1.57 
 X4 = .88. 
 
 WORKING OF CONCRETE 
 
 Mixing of Concrete. Concrete may be mixed either by hand or by machine- 
 or small work, the concrete is mixed by hand in small batches, such as would 
 be made up from 1 or 2 bags of cement. When mixing, hand work should be 
 performed on a flat, water-tight platform. The sand, after it has been meas- 
 ured, is spread over the platform in an even layer. Upon the sand is placed 
 the cement, and these two materials are turned over with shovels at least three 
 
CONCRETE 213 
 
 times, or until the uniform color of the mixture indicates that they are thor- 
 oughly incorporated. The stones, or aggregates, having previously been well 
 wetted, are then placed on the top of the mixture of sand and cement, and 
 these materials are also turned at least three times, water being added after 
 the first turning. The water should always be added in small quantities. If 
 a hose is used for this purpose, it should be fitted with a sprinkling nozzle, as 
 otherwise much of the cement is liable to be washed out of the mixture. The 
 concrete, when ready for placing, should be of uniform consistency, either 
 mealy for a dry mix or mushy for a wet mix. In large work, the mixing should 
 be done by machine. 
 
 Retempering of Concrete. If the cement of the concrete has attained its 
 initial set before being placed that is, if the concrete has commenced to 
 harden remixing with water, or retempering the concrete, as it is called, should 
 not be allowed; and if concrete treated in this manner has been deposited in 
 the forms, it should be taken out and removed from the site of the operation, 
 because concrete cannot be retempered properly, except in small quantities 
 for laboratory tests. 
 
 Concreting at High Temperatures. If the weather is extremely warm, the 
 stone and sand are liable to become heated to a high temperature. In such 
 cases, when the materials are being mixed, the water necessary for the crystal- 
 lization of the cement is rapidly absorbed by the stone and the sand, or else 
 is rapidly evaporated by contact with them. Besides, the extreme heat will 
 hasten the setting of the cement, which gives it a tendency to cake in the mixing 
 machine, producing lumpy and inferior concrete. In order to overcome such 
 difficulties, the stone should be thoroughly wetted with a hose, and the sand and 
 stone should be kept under cover, away from the direct rays of the sun. Like- 
 wise, the mixing platform or machine should be roofed over. It is well, also, 
 to wet down the finished concrete work with a hose several times a day in 
 extremely hot weather, and less frequently in moderate temperatures. 
 
 and placed even at this temperature, if there is a possibility that the temper- 
 ature will fall. If concrete is frozen, its setting is retarded and it is liable 
 to become worthless, never properly setting and obtaining the requisite hard- 
 ness and strength. There is, however, no certainty of the action of frost on 
 concrete, as frozen concrete will frequently thaw out and set, with apparently 
 little loss of strength. 
 
 To prevent the freezing of concrete when the temperature has fallen below 
 32 F., salt is sometimes used in the mixture. 
 
 One rule is 1% of salt to the water for each degree below 32 F., as already 
 stated in the case for mortar. More than 12% salt should never be used. The 
 addition of salt, however, is never advisable if a surface finish is required, as 
 the salt is liable to cause efflorescence, or a white deposit, on the surface causing 
 the work to become very unsightly. 
 
 Aggregates that are coated with ice or that have been exposed to severe 
 weather for a long time should be heated or thawed out before being used. 
 Concrete that is exposed to freezing after it is set should always be protected 
 by placing over it a layer of boards and straw, or salt hay, or cement bags; 
 or, where the work is in the nature of a reinforced-concrete floor system, by 
 heating the interior of the structure by means of salamanders or fires. 
 
 Joining of Old Concrete With New. New and old concrete can be joined 
 only with difficulty, and the strength of such a connection is always uncertain. 
 The joining of old and new concrete work is best done by thoroughly chipping, 
 or cutting away, the old surface, saturating it with water, and working into it 
 thin coats of a 1-1 Portland-cement mortar, and, then, while the coating is 
 still fresh, placing against it the new concrete. 
 
 There are some high-grade, imported cements that, in the form of cement 
 mortar, more readily adhere to old concrete work than the usual Portland 
 cements. These cements are frequently used for patching arid piecing out work 
 already in place. 
 
214 CONCRETE 
 
 ELEMENTS OF STEEL REINFORCEMENT 
 
 PRINCIPLES OF CONSTRUCTION 
 
 When a beam is subjected to tranverse stress, due to loads, the portion 
 of the beam section above the neutral axis, or axis along which there is no 
 stress, is in compression, while in that portipn below the neutral axis, tensile 
 stresses are created. Ordinarily, concrete is about ten times as strong in 
 compression as it is in tension. Thus, it can readily be seen that a beam of 
 plain concrete without steel reinforcement will fail primarily from lack of 
 
 tensile resistance, without realizing its full compressive strength. In order, 
 therefore, to make concrete an economical material to use in construction, its 
 deficiency in tensile resistance must be made up by embedding steel rods, 
 bars, or some other form of metallic reinforcement in that portion of the beam 
 section subjected to tensile stress. 
 
 In order to explain more fully this primary principle of reinforced, concrete, 
 reference is made to the reinforced, rectangular concrete beam here shown. 
 The neutral line of the section is shown at y\ y\ in the side view (a) , while the 
 neutral axis is represented by y y in the end view (b). When the concrete beam 
 is under tranverse stress, there is neither tensile nor compressive stress at the 
 neutral axis. Therefore, the point a in the beam which is on the neutral axis, is 
 subjected to zero stress. 
 
 Should the concrete be cut away below the neutral plane, leaving the steel 
 reinforcing rods, or bars, exposed as at b, the strength of the beam will not be 
 greatly affected, as the necessary tension below the neutral axis is supplied by 
 the reinforcing rods of steel, while the necessary compression above it is fur- 
 nished by the concrete, as at c. The amount of compression in each square 
 inch of concrete above the neutral axis varies from zero at the axis to a maxi- 
 mum at the extreme upper surface of the beam. The concrete below the 
 neutral axis yy is usually so filled with very fine cracks that all the tension 
 must be carried by the steel alone. 
 
 In ordinary reinforced-concrete column construction, merely vertical rods 
 are employed. They are tied together, however, at intervals with wire or 
 other ties. 
 
 The principle ot hooped columns is best explained as follows: It is well 
 known that a column of sand will not resist compression, because it will spread, 
 while a cylinder of very thin metal will sustain only a small load. However, 
 if the cylinder is filled with sand, the tensile strength of the cylinder combined 
 with the compressive resistance of the sand, will produce a column capable of 
 resisting considerable compression. This principle is applied to the reinforce- 
 ment of concrete columns by binding, or tying, together the concrete with 
 cylindrical hoops, or helical, or spiral, windings of steel a few inches below 
 the surface. 
 
 PARTS OF STEEL REINFORCEMENT 
 
 In the accompanying illustration is shown a perspective view (a) of a 
 complete bay of a reinforced-concrete floor system, and a diagrammatic repre- 
 sentation (b) of a typical system of reinforcement for a concrete girder and 
 column. In (a), the heavy members A running between columns are com- 
 monly known as girders, and the lighter members B running between girders, 
 as beams. In both (a) and (&), the rods, or bars, a are the main reinforcing 
 bars, or rods, of the girders. The beams, of course, have similar main rein- 
 forcing bars. Of these main reinforcing bars, several are bent up, as at b, to 
 form trussed bars. The web reinforcement of the girders is shown at c, and 
 consists of U-shaped pieces of iron or steel, called stirrups. The rods that 
 
CONCRETE 
 
 215 
 
 reinforce the slab of the reinforced-concrete floor system, called slab rods, are 
 shown at d. This slab reinforcement may consist of straight rods, expanded 
 
 metal, woven-wire lath, or any other metallic reinforcement. The stirrups 
 are bent over at the upper ends or fastened to the slab rods so that they will 
 not pull put. The rods of the columns e are called longitudinal column rods, 
 and the ties /, column ties. 
 
 Any rod, or bar, used to resist shearing stresses is designated as a shear bar. 
 A rod, or bar, used to resist the shrinkage of the concrete in setting, or to 
 provide against cracks due to thermal changes, is called a shrinkage rod. Shrink- 
 age rods are shown at g in view (a). Sometimes all the slab rods run one way 
 and an occasional shrinkage bar is used at right angles to them as shown, to pre- 
 vent shrinkage cracks. A rod used to connect abutting beams or girders is 
 called a tension bar or a tie bar. The short rods used at the splice when longi- 
 tudinal column rods are butted are called splice rods, or bars. 
 
 Members to Resist Lines of Failure. In the accompanying figure are 
 illustrated a typical beam having the usual type of steel reinforcement and 
 
 the several methods of failure that might occur. At a are shown cracks, or 
 lines of failure, that would be caused by lack of tensile resistance in the main 
 reinforcing rods b. These cracks, are usually invisible, and generally extend 
 
216 
 
 CONCRETE 
 
 from the bottom surface to the neutral axis. They are nearly always present 
 in concrete, but, of course, so long as the steel holds, the beam will not fail. 
 
 If the main reinforcing rods do not extend to the bearings, failure by vertical 
 shear may occur near the abutments, along the line x x. Failures of this kind 
 seldom happen, because the main rods usually extend across all such lines 
 of vertical shear, and add greatly to the shearing resistance of the beam. 
 
 If the slab concrete is not placed at the same time that the concrete of the 
 beam section is poured, failure by shearing usually occurs at the junction of the 
 beam with the slab, as shown at c. The shearing resistance at this junction 
 should be increased, however, by extending stirrups d into the slab. If the 
 crack c opens, it usually joins with a crack, like e, at each end of the beam, as 
 suggested in the preceding paragraph. 
 
 The lines of failure indicated at e are those that usually occur from diagonal 
 tension stresses that cross these lines of failure at right angles. A beam is 
 held against failure in this manner by placing stirrups in the concrete either 
 vertically or obliquely. The bending up of the main reinforcing rods to form 
 the trussed bar, as shown at ff, will also assist in resisting such stresses, and, 
 besides, will provide against negative bending moment where tension instead 
 of compression is created at gg. The line of fracture shown at ee is typical of 
 nearly all reinforced-concrete failures. 
 
 AREAS AND WEIGHTS OF SQUARE AND ROUND BARS 
 
 c: rp 
 
 Square 
 
 
 
 Round 
 
 
 
 olZG 
 
 Inches 
 
 Area 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 Area 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 T6 
 
 .0039 
 
 .013 
 
 .0031 
 
 .010 
 
 i 
 
 .0156 
 
 .053 
 
 .0123 
 
 .042 
 
 A 
 
 .0352 
 
 .120 
 
 .0276 
 
 .094 
 
 i 
 
 .0625 
 
 .213 
 
 .0491 
 
 .167 
 
 JL 
 
 .0977 
 
 .332 
 
 .0767 
 
 .261 
 
 1 
 
 .1406 
 
 .478 
 
 .1104 
 
 .376 
 
 iV 
 
 .1914 
 
 .651 
 
 .1503 
 
 .511 
 
 I 
 
 .2500 
 
 .850 
 
 .1963 
 
 .668 
 
 & 
 
 .3164 
 
 1.076 
 
 .2485 
 
 .845 
 
 | 
 
 .3906 
 
 1.328 
 
 .3068 
 
 1.043 
 
 'fi 
 
 .4727 
 
 1.607 
 
 .3712 
 
 1.262 
 
 A 
 
 .5625 
 
 1.913 
 
 .4418 
 
 1.502 
 
 if 
 
 .6602 
 
 2.245 
 
 .5185 
 
 1.763 
 
 i 
 
 .7656 
 
 2.603 
 
 .6013 
 
 2.044 
 
 16 
 
 .8789 
 
 2.989 
 
 .6903 
 
 2.347 
 
 1 
 
 1.0000 
 
 3.400 
 
 .7854 
 
 2.670 
 
 1ft 
 
 1.1289 
 
 3.838 
 
 .8866 
 
 3.014 
 
 H 
 
 1.2656 
 
 4.303 
 
 .9940 
 
 3.379 
 
 A 
 
 1.4102 
 
 4.795 
 
 1.1075 
 
 3.766 
 
 j 
 
 1.5625 
 
 5.312 
 
 1.2272 
 
 4.173 
 
 1*5 
 
 1.7227 
 
 5.857 
 
 1.3530 
 
 4.600 
 
 8 
 
 1.890G 
 
 6.428 
 
 1.4849 
 
 5.049 
 
 'IS 
 
 2.0664 
 
 7.026 
 
 1.6230 
 
 5.518 
 
 % 
 
 2.2500 
 
 7.650 
 
 1.7671 
 
 6.008 
 
 & 
 
 2.4414 
 
 8.301 
 
 1.9175 
 
 6.520 
 
 f 
 
 2.6406 
 
 8.978 
 
 2.0739 
 
 7.051 
 
 li 
 
 2.8477 
 
 9.682 
 
 2.2365 
 
 7.604 
 
 | 
 
 3.0625 
 
 10.413 
 
 2.4053 
 
 8.178 
 
 it 
 
 3.2852 
 
 11.170 
 
 2.5802 
 
 8.773 
 
 1 
 
 3.5156 
 
 11.953 
 
 2.7612 
 
 9.388 
 
 It 
 
 3.7539 
 
 12.763 
 
 2.9483 
 
 10.024 
 
 2 
 
 4.0000 
 
 13.600 
 
 3.1416 
 
 10.681 
 
CONCRETE 
 
 217 
 
 REINFORCING MATERIALS 
 
 The reinforcement for concrete is almost uniformly steel, but the grade to 
 be used should be determined by one who has made a careful study of this 
 matter. He should both write the specifications and inspect the steel after- 
 wards to make sure that the steel specified has been furnished. Steel used for 
 reinforcement should be 
 free from rust and scale 
 or any coating that will 
 tend to weaken the bond 
 between the metal and 
 the concrete. 
 
 Plain Bar Iron. 
 The cheapest form of 
 metallic reinforcement 
 for concrete is the plain, 
 round, rolled bar. This 
 bar can be obtained in 
 any part of the United 
 States and as its price 
 per pound is lower than 
 that of any other form of rolled steel, it is the cheapest and most available 
 material. For slabs, f- to ^-in. round bars are used, while for beam, girder, 
 and column reinforcement, from f- to H-in. bars are ordinarily employed. 
 
 The principal objection to the use of plain, round bars in reinforced-concrete 
 work is that they are not gripped, or held, well by the concrete. Plain square 
 and flat bars are sometimes used for the reinforcement of concrete, though, 
 generally, both of these sections, when so used, are deformed by twisting. 
 
 FIG. 1 
 
 In the nomenclature of reinforced concrete, round, rolled sections are 
 designated as rods; square sections as bars; and rectangular sections as flats, 
 or flat bars. 
 
 In the preceding table are given the areas and weights of square and round 
 bars from ^- to 2-in. sizes. 
 
 Bars of Special Construction. Some early forms of bars used in reinforce- 
 ment of concrete are shown in Fig. 1. That shown in (a) is known as the 
 Hyatt bar. In 
 (fe) is shown the 
 Staff bar; this 
 consists of a 
 flat bar, through I 
 
 which a coun- , ff \ 
 
 tersunk punch 
 
 has been partly driven, thus forcing the metal out on 
 the opposite side so as to form projections. The De Mann 
 bar is shown in (c). 
 
 There are numerous bars on the market having special 
 mechanical bonds. The complete descriptions of such 
 bars can be obtained from their manufacturers. Only 
 a few will be mentioned here as examples. 
 
 Square-Twisted Bars. The square-twisted bar con- ,. 
 sists of a square bar that is twisted by being given a cer- $xZ%t 
 tain number of turns around its axis, either while it is hot foof-Xreff=o.795f.t. 
 or while it is cold; this bar is often known as the Ran- ^ 
 
 some bar. By twisting the bar to the screw shape, as T? Q 
 
 shown in Fig. 2 (a), a form is obtained that has great re- ^ IG * " 
 
 sistance to pulling from a mass of concrete. If the square bars are twisted 
 cold, their elastic limit and ultimate strength are increased from 8 to 25%. The 
 square-twisted bar can be obtained in various sizes for various purposes. 
 
 Corrugated Bar. In Fig. 2 (fc) is shown a corrugated bar known as the 
 Johnson bar, after its inventor, A. L. Johnson. The corrugations on the 
 sides, of course, increase greatly over smooth bars the grip on the concrete. 
 
218 
 
 CONCRETE 
 
 Kahn Trussed Bar. Fig. 3 (a) shows the Kahn Trussed Bar. The sec- 
 tion of one of these bars is shown in (fe). The fins are partly sheared across 
 
 and also in a direction parallel with 
 the axis of the bar, and are bent 
 up, as shown in (a), so as to form a 
 grip with the concrete and to pro- 
 vide the stirrups, or web members, 
 necessary to resist diagonal stresses. 
 The Kahn bar is made in various 
 sections. 
 
 Expanded Metal. One form of 
 metallic reinforcement for concrete 
 is the distorted steel plate known 
 as expanded metal, a familiar illus- 
 tration of which is shown in Fig. 4 
 (a). This form of reinforcement is 
 manufactured by partly shearing a 
 sheet of steel in parallel rows, as 
 shown in (b), and then pulling the 
 material sidewise, thus forming a 
 diamond mesh. In this way, the 
 area of a sheet is increased about 
 eight times, with a corresponding 
 decrease in weight per unit area and without any waste of material. The 
 material is made in various sizes. Various forms of metal lath are to be had. 
 Woven Wire. Various forms of wire cloth, or woven wire, are also on the 
 market. Among them is Clinton wire cloth. It is a fabric that is secured at the 
 intersections by a perfect, electric weld, and it has at intervals a double wire 
 that twines in and out, as shown at a, Fig. 5. 
 
 Floor Systems. A complete floor system constructed of loose rods is shown 
 in Fig. 6. The beam reinforcement consists of three reinforcing rods. Two of 
 these rods a run straight through the entire length of the beam, while the third b 
 is bent upwards at the ends. This bent member provides tensile resistance 
 at the top of the beams and thus takes care of the negative bending moment, 
 which occurs in all beams fixed at the end. The bend in such rods is usually 
 made at an angle of about 30 with the horizontal. The rods should be straight 
 at the center of the span for at least one- third the distance between the supports. 
 A tie-rod c, that is 4 or 5 ft. in length, and sometimes bent down at the 
 ends, should be placed over the top of the beam juncture. 
 
 The girder reinforcement consists of five rods, two of them c being bent up 
 to provide against negative bending moment. 
 
 In the best work, two short rods / are located transversely through the 
 column. These rods tie the adjoining girders together and provide additional 
 rigidity at the junction of the girders with the column. 
 
 The slab rods h are generally spaced at about 6 in. from center to center. 
 They should bond with the stirrups, or web reinforcement, of the beams, and 
 may be threaded through, interlocked, or 
 wired to them. It is customary to provide ' 
 shrinkage rods that extend at right angles 
 to the regular slab reinforcement, in order ' 
 to prevent shrinkage cracks in the con- 
 crete. For this purpose, J-in. round or ' 
 square rods j are generally spaced about 
 2 ft. from center to center. In order to ' 
 bond the concrete over the main girders 
 securely, it is also good practice to pro- 
 vide over these important members rods 
 d of about the same size as the slab rods. 
 These rods should run through holes 
 punched in the top of the stirrup, as 
 illustrated at g, and should extend at 
 right angles to the axis of the girder. 
 Sometimes, similar rods are used in the 
 slab over beams, as shown at k. 
 
 The longitudinal reinforcement of the 
 concrete columns consists of four round 
 
 FIG. 5 
 
 rods /. It is customary to project them above the concrete of each story 
 about a foot and to splice them by lapping and wiring or by using pipe 
 
CONCRETE 
 
 219 
 
220 
 
 CONCRETE 
 
 sockets m, as illustrated. Frequently, it is not possible to lay out beforehand 
 the electric-light or power wiring, but if this installation is to be adopted 
 IJ-in. pipes to serve as a passageway should be embedded near the center of 
 the span of all beams and girders close to the under side of the slab con- 
 struction, as at n. 
 
 FORM WORK 
 
 CONSTRUCTION AND FINISH OF FORM WORK 
 
 In the erection of reinforced-concrete work, nothing requires more careful 
 consideration than the construction of the form work, or molds, necessary to 
 shape and support the concrete until it has thoroughly set and hardened. 
 Throughout the practice of reinforced-concrete construction various methods 
 of form constructions are in use. 
 
 The greatest economy is gained by constructing the forms so that they can 
 be used over and over again in the structure. Economy in construction can 
 
 FIG. 1 
 
 also be gained by fastening the form work together with a minimum amount of 
 
 nailing. Every nail that is driven gives trouble when the forms are taken down 
 
 to be replaced for the upper floors. In many constructions, wedges and clamps 
 
 are used instead of nails or screws if the forms are to be reused. 
 
 In some instances, both wooden and metal forms are coated on the side next 
 
 to the concrete in order that the forms may be detached more readily. Coating 
 
 the forms also serves to prevent the marking of the grain of the wooden forms 
 
 on the finished concrete work. 
 
 Dead oil, or crude petroleum, has been used with success for this purpose. 
 
 It is not unusual to soap wooden forms, and in some cases tallow and bacon fat 
 
 have been employed. The latter is especially recommended 
 
 for coating metal forms, as it seems to give the best results 
 
 with forms of this material. In some instances, wooden 
 
 forms have been covered on the inside with paper, and even 
 
 canvas has been used, although it is usually found that the 
 paper adheres to the 
 concrete work and is de- 
 tached only with diffi- 
 culty. It is not cus- 
 tomary, however, to oil 
 or coat the forms unless 
 they are to be used for 
 fine exterior work. 
 
 FORMS FOR FLOOR 
 
 SYSTEMS 
 
 ,, Common Types of 
 
 FlG - 2 Form Work. In Fig. 1 
 
 is shown a type of form work extensively used for the construction of rein- 
 forced-concrete floor systems, and in Fig. 2 is shown a perspective of the forms 
 at the intersection of a beam and girder. This form work is designed so that 
 light g-in. dressed tongued-and-grooved material may be used extensively in its 
 
CONCRETE 
 
 221 
 
 construction. It is so arranged that the sides of the beams and girders, to- 
 gether with the slab form boards, may be removed without the necessity of 
 
 PIG. 4 
 
 removing the supports directly underneath the beams and girders. The form 
 for columns in this type of construction is shown in Fig. 3. 
 
 FIG. 5 
 
 FIG. 6 
 
 Forms Constructed of Plank. A superior type of form for a reinforced- 
 concrete floor system is shown in Fig. 4. The wooden forms are supported 
 by 3"X4" studs. As it is important to bring 
 the forms to a true level, a double adjustment 
 wedge is provided at the bottom of the studs. 
 The forms for the columns are made of \%- or 
 2-in. material. In the construction of the beam 
 and girder forms 2-in. planks are generally 
 used for the sides. In order to form a cham- 
 fer on the lower edges of the beams and girders, 
 triangular fillet pieces are nailed in the forms. 
 It is customary in this type of construction to 
 make the forms for the slabs of |-in. plain 
 boards, frequently using tongued-and-grooved material for the purpose. 
 
 Wall Forms With Wire Ties. A type of- wall-form construction that is 
 frequently used is illustrated in Fig. 5. In order to prevent the sides of the 
 
 FIG. 7 
 
222 CONCRETE 
 
 forms from spreading when the concrete is tamped in place, a wire tie c is used. 
 This tie is made taut by twisting with a bar, or stick d. To keep the 
 form boards the proper distance apart for the thickness of the wall, a block 
 or stick e, of wood is sometimes inserted. 
 
 Wall-Form Construction With Clamp Bolts. A wall-form construction 
 similar to that shown in Fig. 5 is illustrated in Fig. 6 (a). In this form, how- 
 
 FIG. 
 
 ever, a clamp bolt a, instead of a wire tie, is used to prevent spreading. If a 
 bolt of this character is used, it must be knocked out before the concrete has 
 finally set and when the form boards are to be raised to form the next course 
 of concrete. The bolt is preferable to the wire tie, because it is removed from 
 the concrete. Wire ties are usually cut off close to the concrete work after the 
 form boards have been removed,, and as the ends frequently project, they rust 
 and thus stain the wall. 
 
CONCRETE 223 
 
 In (b) is shown the construction of a wall f of m in which a pipe separator a 
 is used with the clamp bolt. The pipes may be driven out of the concrete after 
 it has obtained its initial set, or .they may be left in place. 
 
 Clamping Devices and Plank Holders for Wall Forms. Many devices that 
 aid in the construction of concrete walls have been invented. One of the most 
 useful of these devices is the Sullivan pressed-steel plank holder, various forms 
 of which are shown in Fig. 7. These holders are formed from an iron plate by 
 shearing and bending it so as to form clips. The application of this type of 
 plank holder is illustrated in Fig. 8. 
 
 Braces for Wall Forms. If a wall is to be constructed in a place where 
 there is no embankment, a double set of forms braced as shown in Fig. 9 (a) 
 must be used. If the soil of an embankment against which a concrete wall is to 
 be built is unstable, it is necessary to sheath and brace it. This may be accom- 
 plished in the manner shown in (b) or (c). 
 
 CONCRETE MIXERS 
 
 In the construction of a reinforced-concrete structure, the quantity of con- 
 crete to be placed decides the amount of equipment and the character of the 
 machinery that is to be employed. The character of the work also influences 
 these two factors. In all instances, the concrete plant should be equipped 
 with machinery suitable for the size of the work and the number of men that 
 will be available in the construction operation. On small work, the concrete is 
 frequently mixed by hand; it is, however, unusual for the concrete in large 9per- 
 ations to be so mixed. The successful contractor will employ the mixing 
 machine that is found most efficient and will give careful attention to its erec- 
 tion in the field. 
 
 There are many kinds of concrete mixers in commercial use. These mixers 
 are classified according to the principles upon which they operate, and are 
 known as batch mixers and continuous mixers. 
 
 Frequently, the selection of the mixer, especially in work where new equip- 
 ment is to be used, is left to the superintendent. In making the selection, the 
 superintendent should bear in mind the character of the work; that is, whether 
 it is of more importance to turn out great quantities of concrete than it is to 
 have a uniform mixture, or whether, as in a reinforced-concrete building, the 
 most important consideration is to have concrete delivered from the mixer of 
 uniform consistency. Usually, for heavy mass work the continuous mixer is 
 advantageous, but the batch mixer is now more used for work such as that 
 included in ordinary reinforced-concrete buildings. 
 
 The batch mixer often consists of a metal box in the shape of a cube, a 
 cylinder, etc. The materials are put in this box and are mixed by revolving 
 the box on a horizpntal axis. There are often deflectors on the inside of the 
 box to help in mixing. The machines are sometimes discharged by tipping 
 them until the contents slide out of an opening or by other suitable means. 
 
 The continuous mixer often consists of a trough or cylinder or long box 
 square in section. The materials enter continuously at one end and are dis- 
 charged mixed at the other. They are usually mixed, in their passage through 
 the machine, by paddles or deflectors, or by revolving the cylinder or box. 
 The ingredients are often moved from the receiving to the discharging end of the 
 machine either by the trough or cylinder being tilted or by paddles that grad- 
 ually force the mass in one direction. 
 
 CONCRETE STRUCTURES 
 
 It is proposed to mention briefly a few of the uses in engineering to which 
 concrete can be put. Complete examples of work with all details cannot be 
 given in such a short space, but the few words and illustrations may suggest to 
 the designer ideas that may be elaborated and changed to suit various condi- 
 tions. The calculations of stresses and proportioning of parts is beypnd the 
 scope of this work. They should be left to a competent designing engineer. 
 
 Tank Tower of Reinforced Concrete. The tower shown in Fig. 1 was 
 designed to carry a 200,000-gal. steel tank. The tower consists of eight con- 
 crete columns spaced on centers around the circumference of a 26|-ft. circle 
 and surrounding a hollow concrete cylinder with an inside diameter of 8 ft. 
 The columns and cylinders are held together by two intermediate platforms 
 
224 
 
 CONCRETE 
 
 and a heavy platform . or slab, at the top. The footing is spread over the entire 
 base of the tower, and is in the form of a sixteen-sided polygon being 6 ft m 
 thickness and 38 ft. in diameter at the bottom. The central shaft, in addi- 
 tion to carrying some of the load of the tank, acts as a cylinder around which 
 the reinforced-concrete stairs are run and likewise forms a shaft for the pipes 
 leading to and from the tank. The columns of the lower tier are 3 ft. 6 in. 
 square; those of the second tier 3 ft. square; and those of the top tier, 2 ft. 6 m. 
 square. The offset is made at the outside of the column, as shown in Fig. 2. 
 
 The details of construction and the method of reinforcing the columns, 
 cylinder, and balcony floor construction are illustrated m Fig. 3, a halt plan ot 
 
 the structure being shown m (a), and a 
 section through the column construc- 
 tion, balcony, and cylinder, in (b). As 
 will be 9bserved, the thickness of the 
 cylinder is dropped off 3 in. at each tier; 
 thus, the walls of the cylinder at the 
 bottom are 18 in. in thickness, and at 
 the second and the third tier they are 
 15 in. and 12 in., respectively. The 
 reinforcing rods are likewise reduced in 
 size in both the columns and the cylin- 
 der from the first tier upwards. In the 
 lower tiers, the columns have four IJ-in. 
 round rods; in the second tier, four 
 If -in. rods; and in the upper tier, four 
 If-in. rods. The vertical reinforcing rods 
 are placed near the corners of the col- 
 umns and are tied in with J-in. wire ties 
 placed 12 in. from center to center. 
 These rods were figured in estimating 
 the compressive strength of the columns. 
 Their ends are neatly fitted and are 
 surrounded with a pipe sleeve. The 
 bottom rods project into the reinforced- 
 concrete footing and are slipped into pipe 
 
 FIG. 1 
 
 _ y'__ 
 
 J-g- 
 
 r, 
 
 FIG. 2 
 
 sleeves provided with a 12-in. circular cast-iron base. In this way, the bearing 
 strength of the bars was well realized. The cylinder is reinforced with vertical 
 rods placed about 12 in. from center to center, and horizontal reinforcement, 
 consisting of 1-in. hoop rods, is also provided in it. The balcony floors are 
 reinforced with rods that radiate from the cylinder and bear upon the concrete 
 lintels spanning the space between the columns, each of these lintels being rein- 
 forced with four corrugated bars. The floor of the third balcony, which carries 
 the tank, is about 36J ft. in diameter and 16 in. in thickness. It is heavily 
 reinforced with radiating 1-in. rods, and is cantilevered about 4 ft. beyond the 
 
CONCRETE 
 
 225 
 
 column. At each balcony is provided a monolithic railing, or balustrade. This 
 railing is about 3 ft. high and 6 in. in thickness and is reinforced. In the con- 
 struction of this work, a 1-3-5 mixture was used for the foundation and a 
 1-2-4 mixture, placed very wet, was employed for the rest of the construc- 
 tion. The aggregates used throughout the construction were sand and good, 
 
 clean gravel, which, being very coarse, took the place of broken stone. No 
 effort was made to finish the structure after erection, but in placing the con- 
 crete a very wet mixture was used. It was thoroughly spaded along the sides 
 of the forms, so as to force the gravel away from the surface and allow the 
 neat cement to mold smooth against the form boards. The work that resulted 
 was smooth and presentable. 
 
226 
 
 CONCRETE 
 
 Reinforced-Concrete Retaining Walls. Fig. 4 shows a retaining wall of 
 moderate height. The base is spread out at A B so as to make the wall less 
 easily tipped. The earth behind the wall resting on the part B has to be lifted 
 if the wall tips, so this earth also assists in preventing the wall from turning 
 over. The part A, called the toe, extends out in front of the wall, and by 
 increasing the lever arm of the loads also tends to prevent tipping. The load 
 of earth on the part B tends to prevent sliding. If the wall still has a tendency 
 to slide, a projection, as at c, is put on. Weepers d prevent the collection of 
 water, which would endanger its stability. A wall such as shown must be 
 thoroughly and scientifically reinforced. One method of so doing is shown. 
 
 High Retaining Walls. If retaining walls are to be over 12 ft. in height, 
 they are often designed with a buttress every 10 or 12 ft. A design suitable 
 for a high retaining wall is shown in Fig. 5. In order to stiffen the wall and to 
 cause it to act merely as a slab subjected to transverse stress between supports, 
 the buttresses shown at a are provided. As the resultant pressure of the earth 
 is in the direction shown by the arrow b, the buttresses are subjected to trans- 
 
 ! I I I ! ! ! I ' I I I I ' ' 
 
 M M 
 
 j 
 
 MI rr" t ~n"ni 
 
 el i I i M 
 
 "^rUn I n HI 
 
 
 
 verse stress as a cantilever. The tension at the inside edge of the buttress is 
 provided for by Kahn bars c. 
 
 The wall spans from buttress to buttress are reinforced in the same manner 
 as a reinforced floor slab span between beams or girders. The wall is rein- 
 forced with horizontal Kahn bars d and as the thrust of the earth per square 
 foot on the back of the wall increases with the depth, these bars are placed 
 closer together at the bottom, the spacing being increased toward the top. 
 
 To prevent its failure, the footing is reinforced along the inside edge with 
 the beam e. This beam is monolithic with the buttress, so that the footing is 
 logically reinforced with transverse bars /. In order that the entire design may 
 be stiffened and strengthened, gussets or fillets are inserted in the junctions 
 between the buttresses and the footing. To reinforce the footing further, 
 longitudinal bars g are provided. Additional reinforcement h running in a ver- 
 tical direction is provided in the wall. 
 
 Conduits. Reinforced concrete is used for such constructions as water 
 conduits, sewers, aqueducts, etc. A type of conduit for carrying water is 
 
CONCRETE 
 
 227 
 
 shown in Fig. 6. As will be observed, it is reinforced with expanded metal. 
 In nearly all instances, such conduits are constructed with collapsible centering 
 
 1 
 
 
 1 1 . 
 
 
 1 1 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 inside, and with forms and lagging for the outside work. The work is always 
 carried along in sections. 
 
 Coal Breakers in Reinforced Concrete. The Taylor coal breaker was the 
 first all reinforced-concrete breaker constructed in the anthracite fields, 
 although the Pine Hill breaker, at Minersville, Pa., was built in 1906, of rein- 
 forced concrete from the foundations to the 
 main breaker floor, including the coal pockets, 
 slate pockets, and shaker and jig supports. 
 
 Under favorable conditions, the average 
 wooden anthracite breaker has a life of about 
 20 yr., but mostly conditions are unfavorable 
 to such longevity, and this, coupled with the 
 rapidly advancing price of timber suitable 
 for such structures, has caused engineers to 
 consider the more durable iron and rein- 
 forced concrete as building materials. 
 Wherever anthracite is prepared wet, the 
 decay of the timbers is hastened. 
 
 The rear of the breaker in the course of 
 construction is shpwn in Fig. 7. The first 
 two rows of posts in the rear of the breaker 
 are about 2 ft. square and up to the second 
 or pocket floor have a length of 65 ft. Di- 
 
 FiG. 6 
 
 rectly under and between the pockets, where the most weight will come, the 
 2-ft.-square posts are supplemented with 36-in.-square posts. As the posts are 
 
CONCRETE 
 
 FIG. 8 
 
CONCRETE 
 
 229 
 
 carried upwards this size is decreased until at the top floors they are but 12 in. 
 square. 
 
 In Fig. 8 the breaker is shown practically finished with the top forms still 
 in place, and as it looks today from the outside, could be taken for an office 
 building. It will be noted that the architect has furnished windows for day- 
 light; also each post is supplied with tubes for wiring for electric lights, thus 
 making this breaker an exceptional one for light and comfort of the employes. 
 In the construction of the posts and beams, corrugated rods If in. in diameter 
 were placed at each corner,, then bound with hoop bands and wire so as to form 
 a rectangular cage. They were reinforced by smaller corrugated iron rods 
 from f-in. diameter up to l^-in., as the occasion demanded. Inside this cage 
 pipes for the electric wiring were placed and then wooden forms were con- 
 structed around these skeleton post frames. Concrete was poured in a little 
 at a time from the top of the forms and tamped with iron rods about the pipes 
 and rods. In this way the posts were built up to the height of a floor, where 
 the rods for the beams were tied with those of the posts. The beams were 
 made the same as the posts. 
 
 FIG. 9 
 
 It will be noted that the coal pockets are large and provided with two 
 chutes so that two cars can be loaded from the same pocket at the same time. 
 There are fourteen chutes for each track, or twenty-eight for both tracks. To 
 the rear of Fig. 8 is seen the old Taylor breaker, constructed of wood. 
 
 It may be of interest to know that while the Taylor breaker is concrete, 
 500,000 ft. of lumber will be needed inside for machinery bed-plates and other 
 fittings. However, very little if any of this lumber is large sized and there are 
 no sticks such as breaker framing demands. 
 
 Concrete Coal Pockets. The Pennsylyania Coal Co. has erected a new 
 breaker at Throop, Pa. In the construction of this breaker both reinforced 
 concrete and steel are used; reinforced concrete for the coal and rock pockets, 
 and part of the washery, and steel for the main part of the building, which will 
 contain the washery. 
 
 The capacity of the coal pockets is 3,500 T. The coal cars are to be loaded 
 directly beneath the pockets, while box cars are to pass on the outside of the 
 building and are to be loaded from a chute leading from the center of the bottom 
 slab of the pocket. The slope on the bottom of the coal pockets is 9 in 12 and 
 on the rock pockets 6 in 12. The width of these pockets varies from 10 ft. 8 in. 
 to 16 ft. Where the pocket is not over 12 ft. wide, the floor slab is designed so 
 
230 
 
 CONCRETE 
 
 as to carry the load without any beam for support. But for the ppckets 16 ft. 
 wide a beam is placed beneath the floor slab. Fig. 9 shows a view through 
 the coal pockets of this breaker during construction. The forms, it will be 
 
 Concrete Shaft Lining. Concrete is now being used to line shafts in mines. 
 As yet there is no uniform method of doing this work and the designs are 
 changed to suit various conditions to be met. The shaft with concrete lining 
 about to be described is the main shaft of the Filbert mine of the H. C. Fnck 
 Coke Co.; it is located in Fayette County, Pa. 
 
 The shaft, elliptical in plan, measures 13 ft. X 28 ft. in the clear on the center 
 lines of the axes, and has a depth of 550 ft. below the top of the coping to the 
 
 Section A- A. 
 
 FIG. 10 
 
 bottom of the 9-ft. coal bed, and is provided with a sump 15 ft. below the coal. 
 This shaft is divided into four compartments, containing two cageways, a stair- 
 way, and pipe way. 
 
 The plan of the shaft is shown in Fig. 10. At a is shown the concrete lining; 
 at b, the 8"X10" yellow-pine buntons; at c, the 6"X10" buntons; at d, the 
 4"X8" yellow-pine nailing strips; and at e, the yellow-pine cage guides. The 
 compartment reserved for the various pipes that go up the shaft is shown at /. 
 The two hoisting cages are shown at g. At A is a compartment for foot travel- 
 ing fitted with steps and landings. The hoisting part proper is largely lined 
 with 1-in., yellow pine, tongued-and-grooved sheathing. 
 
 The circumference of the inside of the concrete lining is 69 ft., with a clear- 
 opening area of 310 sq. ft., comprising 195 sq. ft. for the two cageways, 80 sq. ft. 
 
CONCRETE 
 
 231 
 
 for the stairway, and 35 sq. ft. for the pipeway. The ends of the shaft conform 
 to a radius of 5 ft. 8 in. and the curvature of the sides to a 45-ft. radius. From 
 the top of the coping to solid rock, a distance of 19 ft., the structure is of heavy 
 concrete construction forming a solid foundation for the structural steel head- 
 frame of 135 ft. superimposed thereon. Fig. 11 shows the irregular-shaped 
 plan and elevation of this portion of the work. This shaft has two water rings 
 constructed therein; one at 78 ft., and the other at 494 ft. below the top of the 
 coping. 
 
 All concrete for lining the shafts is composed of 1 part Portland cement; 
 2 parts clean, sharp, river sand, and 5 parts of stone crushed to pass through 
 H-in. ring. About 50% of the stone used for concrete was obtained from the 
 
 FIG. 11 
 
 materials excavated from the shafts. About 30% was shipped in, crushed 
 ready for use, while about 20% was obtained from a quarry on the grounds. 
 In sinking this shaft, an excavation was first made to a depth of 65 ft. 
 All excavating was done to the full measurements of the outside perimeter of 
 the concrete lining, being kept to a correct line by plumb-bobs suspended from 
 a template placed above the opening. Derricks were used to handle the mate- 
 rial excavated. At the depth mentioned, the concreting was begun. Forms 
 were put in near the bottom to the height of 5 ft. and filled. Then 5 ft. more of 
 forms were put on top of the first forms and again filled. Then another sec- 
 tion was built and filled and so on until the surface was reached. The shaft was 
 then sunk about 50 ft. deeper and concreted up from the bottom in the same 
 way. Then another section of the shaft was sunk, and so on until the job was 
 completed. 
 
232 CONCRETE 
 
 The dividing struts for the compartments of the shafts are 8"X10" bun- 
 tons, spaced vertically 5 ft. center to center. The buntons support the guide 
 rails for the cages these are 8 in.X 10 in., surfaced on four sides and fastened 
 to the dividing struts or buntons as shown in Fig. 12. The buntons are set in 
 the concrete shaft lining to a depth of 6 in. on each end, allowing from 6 in. up 
 of concrete beyond their ends, thus insuring a water-tight wall. The minimum 
 thickness of the concrete lining wall is 12 in. In soft strata, the concrete is as 
 much as 33 in. in thickness, as no voids were left between the rock and lining, 
 all such being carefully filled with concrete. Bolts for the guides have a 1-in. 
 stud nut and two wrought-iron washers $ in. thick. 
 
 Throughout a portion of the shaft, wedge-shaped blocks with a base 
 6 in.X 8 in. and 4 ft. long, tapering to a point, were placed on the buntons just 
 at the face of the concrete lining, making pockets for the removal of the bun- 
 tons, when necessary to replace them. 
 
 To take care of the water during the construction of the shaft above the 
 water rings, two methods were successfully used. During the concreting, 
 when any flow of water was encountered, sheet-iron plates were used to turn 
 the water away from the concrete until it had set sufficiently so as not to be 
 damaged by water flowing over it. Then the sheets were deflected so as to 
 cause the water to run down the face of the rock wall of the shaft, where, at 
 
 intervals around the cir- 
 cumference of the shaft, 
 were placed 3-in. tile 
 
 pipe set in loose broken 
 
 t stone and extending 
 > down behind the, shaft 
 lining to the water ring. 
 The tile pipe, set with 
 open joints, takes care 
 of the water, conducting 
 it to the water ring. 
 To hold the tile pipes 
 to their proper place 
 and to insure their non- 
 stoppage from concrete 
 packing in around them, 
 sheet-iron strips of No. 
 22 gauge were bent into 
 semicircular form and 
 placed around the tile 
 pipe with the open side 
 toward and against the 
 rock face; then broken 
 stone was placed around 
 the pipe within this pro- 
 tection. In this way an 
 
 L 
 
 FIG. 12 
 
 opening was kept between the rock face and the tile pipe, allowing the water 
 to reach the drain and thus flow into the water rings. This also eliminated 
 the danger of water gathering behind the lining wall and exerting undue pres- 
 sure thereon. 
 
 Another method successfully used was to locate the fissure or opening 
 where larger streams entered the excavation, and to enlarge them so as to form 
 a reservoir of several cubic feet capacity; then to tightly close the openings 
 of this reservoir with concrete and sheet iron, having placed a wrought-iron 
 pipe of sufficient capacity to handle the water gathered therein. This pipe 
 conducts the water to a pipe set vertically in the lining-wall concrete and 
 leading to the water rings. This latter method was used only where a large 
 flow of water was encountered. 
 
 The water rings in the shaft were constructed behind the shaft-lining wall, 
 where a niche was blasted out of the rock to form an opening 2 ft. wide and 4 ft. 
 high throughout the entire perimeter of the shaft. The bottom of this niche 
 was concrete in gutter shape, with a drop of 3 in. from its highest to its lowest 
 point, located at the pipe-compartment end of the shaft. At the lowest point 
 a wrought-iron pipe, 2$ in. in diameter, set through the lining wall on an angle 
 of 45 and protected by strainer plates, connected with a line in the pipe com- 
 partment and led the water to a permanent disposal pump. In the shaft-lining 
 wall, on its inner face and throughout the entire perimeter of the wall, and at a 
 point near the top of the water ring, a groove 4$ in. deep and 5 in. from the face 
 
CONCRETE 
 
 233 
 
 of the groove to the edge of the lip extending 1 in. beyond the inner face of 
 the wall was constructed to catch any seepage or water from the surface of the 
 lining. This groove and lip has a fall of 3 in. from its highest to its lowest 
 point, where a 2-in. wrought-iron pipe passes through the lining wall on an 
 angle of 45 leading all water caught in the groove to the water ring. Thus, all 
 the water both behind the lining wall and all water on the inner surface is col- 
 lected in the water rings and thence led to the pumps and expelled from the 
 shaft. 
 
 In the shaft, the approaches leading to the shaft bottom from both the 
 loaded and' empty sides are of concrete. These are of 18-ft. span having a 
 minimum thickness of 24 in. for side walls and crowns. Each arch extends 
 
 Lining 
 
 Section on ( Arch 
 
 Section thipujh Arch 
 
 FIG. 13 
 
 13 ft. from the face, of the shaft lining. Arches of 9-ft. span having a minimum 
 thickness of 18 in. extend a distance of 11 ft. 6 in. from both ends of the face 
 of the shaft lining. These arches connect with the cross-entries and man- 
 way around the shaft bottom. An archway of 4-ft. span was placed in the side 
 walls for entrance to the run-around. At the intersection of all arches with the 
 shaft-lining wall, steel bars were placed for reinforcement. The method of this 
 reinforcement is shown in Pig. 13. All centering was built of 2-in. oak plank, 
 spaced 2? ft. center to center, covered with 2-in. tongued-and-grooved oak 
 lagging. Concreting for the four arches was brought up at one time and also 
 at the same time as the shaft-lining wall was placed. 
 
234 
 
 MASONRY 
 
 MASONRY 
 
 MATERIALS OF CONSTRUCTION 
 
 STONE 
 
 The materials employed in the construction of masonry are stone, brick, 
 terra cotta, and the cementing materials used in the manufacture of mortars; 
 namely, lime, cement, and sand. 
 
 Strength of Stone. In ordinary buildings and engineering structures, 
 stones are generally under compression. Occasionally, they are subjected to 
 cross-stresses, as in lintels over wide openings. They are never subjected to 
 direct tension. As a general rule, a stone should not be subjected to a greater 
 compressive stress than one-tenth of the ultimate crushing strength, as found 
 by experiment. 
 
 The resistance to crushing varies within wide limits, owing to the great 
 variety in the structure of the stones; the method of preparing and finishing 
 the test pieces also affects the results; hence, the great variations found in the 
 values given by different experiments. The accompanying table shows the 
 average resistance of the principal building stones to crushing and to rupture 
 when used as beams. 
 
 CRUSHING STRENGTH AND MODULUS OF RUPTURE OF 
 BUILDING STONE 
 
 Stone 
 
 Crushing Strength 
 Pounds per Square 
 Inch 
 
 Modulus of Rupture 
 Pounds per Square 
 Inch 
 
 Granite 
 Sandstone 
 
 15,000 
 10,000 
 
 1,800 
 1,200 
 
 Limestone 
 Marble 
 
 13,000 
 14 000 
 
 1,500 
 2 160 
 
 
 
 
 MINIMUM SAFE-BEARING VALUES OF MASONRY 
 MATERIALS 
 
 Materials 
 
 Granite, capstone 
 
 Squared masonry 
 
 Sandstone, capstone 
 
 Squared masonry 
 
 Rubble, laid in lime mortar 
 
 Rubble, laid in cement mortar 
 
 Limestone, capstone 
 
 Squared masonry 
 
 Rubble, laid in lime mortar 
 
 Rubble, laid in cement mortar 
 
 Bricks, hard, laid in lime mortar 
 
 Hard, laid in Portland cement mortar 
 
 Hard, laid in Rosendale cement mortar 
 Concrete, 1 Portland, 2 sand, 5 broken stone. 
 
 Safe-Bearing 
 
 Value 
 
 Tons per 
 
 Square Foot 
 
 50 
 25 
 25 
 12 
 
 5 
 10 
 36 
 18 
 
 5 
 10 
 
 7 
 14 
 10 
 10 
 
MASONRY 
 
 235 
 
 ULTIMATE UNIT CRUSHING STRENGTH OF VARIOUS STONES AND 
 STONE MASONRY PIERS 
 
 Material 
 
 Compressive 
 Strength 
 Pounds per 
 Square Inch 
 
 Material 
 
 Compressive 
 Strength 
 Pounds per 
 Square Inch 
 
 Granite, Colo 
 
 15,000 
 14 000 
 
 Limestone, Marquette, 
 Mich. 
 
 8000 
 
 Granite, Mass 
 Granite Me 
 
 16,000 
 15000 
 
 Limestone, Conshohock- 
 en, Pa. 
 
 15,000 
 
 Granite, Minn 
 Granite, N. Y 
 Granite, N. H 
 
 25,000 
 16,000 
 12,000 
 15000 
 
 Marble, Montgomery 
 Co., Pa 
 Marble (dolomite), Lee, 
 Mass 
 
 11,000 
 22,800 
 
 Sandstone, Middletown, 
 Conn 
 
 7,000 
 
 Marble (dolomite), 
 Pleasantville, N. Y. ... 
 
 22,000 
 
 
 
 Marble Italian 
 
 12 000 
 
 Mass 
 
 10000 
 
 Marble, Vt 
 
 10,000 
 
 
 
 Slate 
 
 10,000 
 
 River, N. Y 
 
 12,000 
 
 Piers, ashlar, bluestone. . 
 
 2.100 
 
 Sandstone (brown), Little 
 Falls N Y 
 
 10000 
 
 Piers, ashlar, granite 
 Piers, ashlar, limestone . . 
 
 2,100 
 1,500 
 
 Sandstone, Ohio 
 
 8,000 
 
 Piers, ashlar, common 
 
 1,050 
 
 Hummelstown, Pa. . . 
 
 12,000 
 
 Piers, rubble, cement 
 
 900 
 
 N. Y.... ..! n . gS .. n> . 
 
 12,000 
 
 Piers, rubble, lime mor- 
 
 
 
 
 tar 
 
 480 
 
 Station, N. Y 
 Limestone (oolitic), Bed- 
 ford, Ind 
 
 18,000 
 8,000 
 
 
 
 ULTIMATE CRUSHING STRENGTH OF BRICK MASONRY PIERS 
 
 (Average Age of Brickwork, 6 Mo.) 
 
 Material 
 
 Composition of Mortar 
 
 Compressive 
 Strength 
 Pounds per 
 Square Inch 
 
 Wire-cut brick .... 
 
 1 cement, 5 sand 
 
 3,000 
 
 Dry-pressed brick 
 Dry-pressed brick. 
 
 1 cement, 5 sand 
 1 cement, 1 lime, 3 sand 
 1 cement, 5 sand 
 
 3,400 
 2,300 
 1,700 
 
 Light-hard, sand-struck brick 
 
 1 cement, 5 sand 
 
 1,900 
 
 Light-hard, sand-struck brick 
 Hard, sand-struck brick 
 Hard, sand-struck brick 
 Hard, sand-struck brick 
 Sand-lime brick 
 
 1 cement, 7 sand 
 1 cement, 1 sand 
 1 cement, 1 lime, 3 sand 
 1 cement, 5 sand 
 1 cement, 3 sand 
 
 853 
 2,100 
 1,500 
 1,200 
 1,100 
 
 Sand-lime brick 
 
 1 lime, 3 sand 
 
 450 
 
 Sand-lime brick ' 
 
 Neat cement 
 
 1,400 
 
 
 1 cement, 3 sand 
 
 2,000 
 
 
 
 
236 
 
 MASONRY 
 
 Absorptive Power of Stone. The absorptive power 9! a stone is a very 
 important property, a low absorption generally indicating a good quality. 
 The accompanying table gives the average percentage of water absorbed by 
 stones. 
 
 ABSORPTIVE POWER OF STONE Durability of Stone. The fol- 
 
 lowing rough estimate, based on 
 observations made in the city of 
 New York, indicates the number of 
 years a sound stone may be expected 
 to last without being discolored or 
 disintegrated to such an extent as 
 to require repairs: 
 
 Life of Stone 
 Name of Stone Years 
 
 Coarse brownstone 5 to 15 
 
 Compact brownstone. .100 to 200 
 
 Limestone 20 to 40 
 
 Granite 75 to 200 
 
 Marble 40 to 200 
 
 BRICK 
 
 Size and Weight. The dimensions of bricks vary considerably. The 
 standard adopted by the National Brickmakers' Association is, for common clay 
 brick, 8J in.X4 in.X2J in., and for face or pressed brick (clay) 85 in.X4J in. 
 X2i in. The weight of a common clay brick is about 4 lb.; that of a pressed- 
 clay, enameled brick, about 7 lb. Enameled and glazed bricks are made in two 
 sizes: English size, 9 in.XS in.X4in.; American size, 8 1 in.X2J in.X4| in. 
 The usual dimensions for firebricks are 9 in.X4 in.X2J in.; various sizes and 
 forms are made to suit the required work. The dimensions of the lime-sand 
 bricks are 8| in. X 4| in. X 2jf in. The weight varies between 5 and 6 lb. The 
 accompanying table gives the approximate weight and resistance to crushing 
 of brick. 
 
 WEIGHT AND STRENGTH OF BRICK 
 
 Stone 
 
 Absorptive Capacity 
 Per Cent. 
 
 Granites 
 
 .066 to .155 
 .410 to 5.480 
 
 Limestones 
 
 .200 to 5.000 
 
 Marbles 
 Trap 
 
 .080 to .160 
 .000 to .019 
 
 
 
 --; 
 Kind of Brick 
 
 Weight 
 Pounds per 
 Cubic Foot 
 
 Crushing 
 Strength 
 Pounds per 
 Square Inch 
 
 Best pressed-clay 
 
 150 
 
 5,000 to 15,000 
 
 Common hard-clay 
 
 125 
 
 5,000 to 8 000 
 
 Soft-clay 
 
 100 
 
 450 to 600 
 
 Lime-sand .... 
 
 120 
 
 3,600 to 7,600 
 
 Firebrick . 
 
 120 
 
 1 000 to 1 500 
 
 
 
 
 Requisites for Good Brick. Bricks of good quality should be of regular 
 shape, with parallel surfaces, plane faces, and sharp square edges. They 
 should be of uniform texture; burnt hard; and thoroughly sound, free from 
 cracks and flaws. They should emit a clear ringing sound when struck a sharp 
 blow. A hard well-burned brick should not absorb more than one-tenth of its 
 weight of water; it should have a specific gravity of 2 or more. The crushing 
 strength of a brick laid flat should be at least 6,000 lb. per sq. in. The modulus 
 of rupture should be at least 1,000 lb. per sq. in. 
 
WIRE ROPES 237 
 
 WIRE ROPES* 
 
 GENERAL DESCRIPTION 
 
 WIRE-ROPE MATERIALS 
 
 Wire ropes are used about mines chiefly for hoisting from shafts, for haulage 
 and the transmission of power, for the cables of aerial tramways, for the guy 
 ropes of derricks and smokestacks, etc., and, rarely, for the cables of small, 
 short-span, suspension bridges, as where the town or settlement is situated on 
 the opposite side of a narrow stream from the mine. While wire ropes are now 
 almost universally made of steel, manufacturers still make and list iron ropes, 
 which have a limited field of usefulness. 
 
 Swedish, Swedes, or charcoal-iron ropes are made of a very pure wrought 
 or puddled iron having a tensile strength of from 50,000 to 100,000 Ib. per sq. in. 
 These ropes are soft, tough, and pliable, and are adapted especially for passenger 
 elevators, small hoists, steering gear of vessels, etc., where the loads are inter- 
 mittently applied and are not too great, or where the speed is high and the bend- 
 ing stresses great. It will be noted from tables given later that the ultimate 
 breaking strength of a 6X 19 Swedish iron hoisting rope 1 in. in diameter, is but 
 14.5 T., whereas, the breaking strength of a steel rope of the same kind and 
 size is from 30 to 45 T. For general mine use, iron ropes have been almost 
 entirely superseded by steel ropes because of their greater strength and 
 elasticity. 
 
 Steel ropes are generally made of open-hearth steel having a tensile strength 
 of from 150,000 to 275,000 Ib. per sq. in. and in some cases even more, the 
 tensile strength depending on the composition of the metal and the method of its 
 treatment. Steel ropes are in almost every way superior to iron ropes. The 
 principal advantage is that they have more than double the strength of iron 
 ropes of the same size; consequently, for equal strains, they can be made of 
 much less diameter than iron ropes and can, therefore, be used in connection 
 with much smaller and lighter drums, sheaves, or pulleys. Iron-wire ropes are 
 not so elastic as ropes made of steel wire, hence a larger sheave is required for 
 iron than for steel ropes of the same diameter. Iron ropes, however, are 
 usually more flexible than steel ropes, are less brittle though not so strong, 
 and better resist the acid in mine water. A 1-in. Swedish iron rope has about 
 the same strength as a f-in. ordinary cast-steel rope; weighs 1.58 Ib. per ft. as 
 opposed to .62 Ib.; costs (list price) 26c. per ft. as opposed to 16.5c.; and 
 requires a sheave or drum 6 ft. in diameter as against one 2.5 ft. for a cast-steel 
 rope. 
 
 Cast-steel, crucible-steel, and crucible cast-steel ropes are the trade names 
 given to the ordinary grades of ropes made from wire having an ultimate tensile 
 strength of 160,000 to 210,000 Ib. per sq. in. _ The breaking strength of a 
 6X 19 standard hoisting rope of this grade and 1 in. in diameter is given, in the 
 manufacturers' tables, as 30 T., more than twice the strength of a similar iron 
 rope. Ropes of this material are those commonly used in and around mines 
 for haulage and hoisting purposes. 
 
 Extra strong cast-steel, extra strong crucible-steel, special steel, and patent steel 
 ropes are the trade names for the next stronger grades of ropes, intermediate in 
 strength between cast-steel and plow-steel ropes in strength. The wire from 
 which they are made has an ultimate tensile strength of from 190,000 to 
 230,000 Ib. per sq. in. The breaking strength of a 6X 19 hoisting rope of this 
 grade and 1 in. in diameter is given as 34 T, 11.33% more than that of an 
 ordinary cast-steel rope of the same dimensions. These ropes are also standard 
 and are in general use where it is desirable to increase the factor of safety while 
 retaining the same diameter of rope. 
 
 * Acknowledgement for the use of data and tables in this section is made 
 to the Broderick & Bascom Rope Co., Hazard Manufacturing Co., A. Leschen 
 & Sons Rope Co., John A. Roebling's Sons Co., The Trenton Iron Co., The 
 Waterbury; Co., and the Link Belt Co. As in most instances, the manufacturers 
 have identically the same tables, etc., credit is given generally in this manner, 
 rather than specifically for each item. 
 
238 WIRE ROPES 
 
 Plow-, or plough-steel ropes are made of wires having an ultimate tensile 
 strength of 220,000 to 250,000 Ib. per sq. in. The breaking strength of a 6X 19 
 hoisting rope of this grade and 1 in. in diameter is given as 38 T., or 11.18% 
 more than that of an extra strong cast-steel rope of the same dimensions. Ropes 
 of this grade are not generally recommended, except where it is necessary to 
 have the maximum of tensile strength with the least weight of rope, or where 
 it is necessary to employ a rope of much greater strength but of the same 
 diameter. The first necessity will arise when hoisting through extremely deep 
 shafts; the second, where by reason of increased loads it becomes essential to 
 have a stronger rope, but at the same time the diameter of the rope is fixed by 
 the size of existing drums, sheaves, etc. Plow-steel ropes are extensively 
 employed for logging lines, dredge and wrecking ropes, ballast unloading ropes, 
 quarry ropes, etc. 
 
 Extra, special, or improved plow-steel ropes are made of wires having an 
 ultimate tensile strength of from 240,000 to 300,000 Ib. per sq. in. A rope of 
 this grade of the size cited before has a breaking strength of 45 T., or about 
 11.84% more than an ordinary plow-steel rope of the same dimensions. The 
 comments upon standard plow steel ropes apply as well to ropes of this grade 
 
 CONSTRUCTION OF WIRE ROPES 
 
 Wire ropes consist of a number of strands, each composed of the same 
 number of single wires twisted around a hemp or wire core or center to form a 
 single rope. The hemp core adds practically nothing to the strength of the 
 rope but, being saturated with lubricant, tends to prevent rusting of the wires 
 and, being soft, acts as a cushion for the individual strands, thus reducing 
 internal friction and wear. A wire core adds largely to the internal friction 
 and consequent wear of rope as the strands rub upon the wire center; increases 
 the weight; and, while adding about 10% to the strength, reduces the flexibility 
 in a marked degree, at the same time adding 10% to the cost. Manufacturers, 
 whose judgment should be final, recommend ropes with wire cores only for 
 standing lines, such as the guy ropes of derricks, etc., because they lack the 
 flexibility demanded of running ropes (those used for hoisting, haulage, etc.), 
 and because of their much greater internal wear in bending around drums, 
 
 sheaves, and the like. 
 
 Lay of Ropes. The lay of a rope 
 is the direction of the twist of the 
 strands composing it. Ropes are 
 either right or left lay, the former 
 being the ordinary construction as 
 shown in Fig. 1 where the strands are 
 bent to the right. The left-lay con- 
 struction is shown in Fig. 2. 
 The term lay is also used to describe the direction of twist of the individual 
 wires composing the strands in a rope. Thus, in Fig. 1, while the rope is right 
 lay (strands twisted to the right), the strands are left lay, the single wires being 
 twisted to the left. Similarly, in Fig. 2, while the rope is left lay, the strands 
 are right lay. 
 
 Finally, the term lay is used to designate the pitch of the rope; that is, the 
 rate at which the strands twist or, what is the same thing, the ratio that the 
 length of strand required for one complete turn bears to the diameter of the rope. 
 In ordinary rope making, the lay or 
 (better) pitch of the wires varies from 
 2.5 to 3.5 times the diameter of the 
 rope, and that of the strands from 6.5 
 to 9 times the diameter of the rope. 
 The lay exerts an important influence 
 
 upon the life of a rope. For the same . 
 
 kind and size of rope, the shorter the FlG. 2 
 
 lay or pitch, the greater the flexibility 
 and elasticity, but the less the strength. This falling off in the strength, due to 
 the shortening of the pitch, is brought about by the nicking, or cutting, of one 
 wire by another, which is naturally less when the ropes cross one another at 
 a long angle (long pitch) than when they cross at a sharp angle (short pitch). 
 In practice, ropes are commonly classified as ordinary-lay or regular-lay 
 ropes, and as Lang lay or universal-lay ropes. In the ordinary lay ropes, which 
 are shown in Fig. 1 and Fig. 2, the wires in the strands are twisted in the 
 opposite direction from that of the strands in the rope, while in Lang lay ropes, 
 shown in .big. 3, the single wires and the strands are twisted in the same 
 
WIRE ROPES 
 
 239 
 
 direction. Lang lay ropes may be either right or left twist, and their price is 
 the same as that of ordinary-lay ropes. 
 
 The principal advantages of the Lang lay are that, the wires and strands 
 being twisted in the same direction, the surface of the rope is smoother, the 
 outside wires do not so soon become worries a much longer surface of each wire 
 is exposed to wear, and, the wires being straighter, these ropes are somewhat 
 more flexible. The disadvantages of 
 Lang lay ropes are a tendency to un- 
 twist, rendering them unsuited for 
 hoisting except where guides are used; 
 they can be spliced to ropes of ordin- 
 ary-lay only with difficulty; and when 
 the wires break, the loose ends are 
 very troublesome, because a much 
 greater length of each wire is exposed 
 than in ordinary-lay ropes. Under careful inspection, a regular-lay haulage 
 rope may be used for some time after a few of its wires are (broken here 
 and there throughout its length, except when a dangerous risk would be incurred 
 by so doing. The Lang lay ropes are commonly used tor haulage, particularly 
 where grips are used to attach the cars to the ropes, and are sometimes used for 
 hoisting, but only where the cage works in guides. 
 
 FIG. 3 
 
 HOISTING ROPES 
 
 ROUND ROPES 
 
 6X 19 Ropes. Ropes used for hoisting through shafts are round or flat 
 and in either case may be of uniform or tapering section. Round ropes of 
 uniform section, are practically the only ones used in American mines. The 
 
 standard American 
 hoisting rope, shown in 
 Fig. 1, is composed of 
 6 strands of 19 wires 
 each (114 wires) wrap- 
 ped around a hemp 
 center. It is frequently 
 spoken of as a 6X19 
 FIG. 1 rope. These ropes are 
 
 commonly made of cast- 
 steel or, where greater strength is required, extra strong cast-steel. The 
 diameter of sheave recommended for use with a 1-in. rope of this type is 
 variously given at 4 to 4.5 ft. 
 
 8X19 Ropes. Where extreme flexibility is required, ropes composed of 
 8 strands of 19 wires 
 each (152 wires) may be 
 employed. From the 
 tables given later, it 
 will be noted that the 
 maximum diameter of 
 rope of this section com- 
 monly carried in stock FIG. 2 
 is 1? in. as against 2| 
 
 in. for the 6X19. Fig. 2 shows that the core is much larger in proportion 
 to the area of metal than in a 6X19 rope of the same size and quality. 
 Consequently, this rope is not so strong as a 6X19 rope of the same diameter 
 
 (24 T, as against 30 T. 
 for 1-in. cast-steel rope) 
 and is more liable to 
 flatten out under heavy 
 pressure. The diameter 
 of sheave suggested for 
 use with a 1-in. rope of 
 FIG. 3 this type is variously 
 
 given as 2. 5 to 3.25 ft.; 
 
 materially less than that required for a 6X19 rope. Ropes of this class are 
 recommended for derricks and similar work where small sheaves must be em- 
 ployed, but it should be noted that, so far as the working life of this type is 
 
240 
 
 WIRE ROPES 
 
 concerned, the increased flexibility in a very considerable measure offsets its 
 decreased strength. 
 
 6X37 Ropes. A form of very flexible rope that is not infrequently used 
 in preference to the 8X19, is shown in Fig. 3; in this, the rope is composed 
 of 6 strands of 37 wires each. As ^ere is a much greater area of metal m 
 proportion to the hemp core than in an 8 X 19, the breaking strength of a 1-in. 
 
 cast-steel rope of this 
 type is given as 29 T., 
 only 1 T. less than that 
 of the standard 6X19 
 rope and 3 T. more than 
 the 8X19. The diam- 
 eter of sheave suggested 
 FIG. 4 for this rope is the same 
 
 as that for the 8X19; 
 
 viz., 2.5 to 3.25 ft. As the wires in this rope are, of necessity, smaller than 
 those in a 6X19 rope of the same diameter, it is apparent that this type of 
 rope is not so well adapted to withstand abrasion as those containing larger 
 wires. This rope is employed where the bending strains are very great, as in 
 logging operations, for use with electric cranes, etc. When galvanized, this 
 rope is largely used for hawsers in towing, etc. 
 
 Non-Spinning Ropes. Non-spinning hoisting rope, made by one of the 
 leading manufacturers, is shown in Fig. 4, It is composed of 18 strands of 7 
 wires each (126 wires), 12 of the strands being laid m a reversed direction 
 about 6 which, in turn, are laid about a hemp core. Because of the reversed 
 directions in which the inner and outer sets of strands are laid, there is no 
 tendency to twist and the rope is, thence, adapted to hoisting where the load 
 is not raised between guides but 
 hangs freely as a bucket in shaft- 
 sinking. The rope is slightly more 
 flexible than the standard 6X 19 rope 
 and slightly stronger. However, it 
 cannot be spliced. 
 
 Flattened-Strand Ropes. In 
 order to present a larger and smoother 
 wearing surface, and thus to increase 
 the life of the rope, flattened-strand 
 wire ropes have been devised. In 
 these ropes the strands have an ellip- 
 tic, or triangular, cross-section, de- 
 pending on the shape of the metal 
 center of the strand, and the rope has either a hemp or a wire core. They are 
 made either 5X28 (5 strands of 28 wires each, or 140 wires) as shown in Fig. 5 
 (a), or 6X25 (6 strands of 25 wires each, or 150 wires) as shown in (b). These 
 ropes are made of Swedes iron, and of cast-steel, extra strong cast-steel, and 
 extra plow-steel. The breaking strength of a cast-steel rope of this make, 
 5X28, and 1 in. in diameter is given as 30 T., the same as that of the same 
 size and kind round, 6X19 standard rope. A 6X25 cast-steel rope of this 
 type 1 in. in diameter is given as 33 T., which is greater than that of the 
 corresponding 6X 19 round rope and nearly as great as that of an extra strong 
 cast-steel rope. There is claimed for this rope greater flexibility, less 
 liability of the wires becoming brittle, and freedom from all tendency to spin or 
 kink; also that they maintain their form better than round ropes. 
 
 Scale Ropes. A 
 form of rope made by 
 some manufacturers and 
 used for hoisting, but 
 possibly better adapted 
 to haulage purposes, is 
 shown in Fig. 6, as it is 
 FIG. 6 oi the 6X19 type used 
 
 in standard hoisting 
 
 ropes. This is known as Seale rope or Scale lay rope, and consists of 6 strands 
 of 19 wires each, in which 9 large wires are twisted around 9 small ones, which 
 in turn surround one of the larger size. This rope is intermediate in flexibility 
 and ability to stand abrasion between the standard ropes of 7-wire (haulage) and 
 19-wire (hoisting) strands. This type of rope, on account of the large outside 
 wires, will withstand heavy f rictional wear and is used on slopes, planes, and cable 
 
 FIG. 5 
 
 (ft) 
 
WIRE ROPES 
 
 241 
 
 roads where the rope commonly drags, provided , however, that there are no bends 
 of sharp angle to overstrain the outer wires. While there is more metal in 
 the outer wires than in those of the standard rope, there is correspondingly 
 less in the inner wires, and closer inspection of the outer wires is, therefore, 
 necessary to prevent the rope being used too long. The price of these ropes 
 is the same as the standard 6X 19 hoisting rope of the same grade. 
 
 FLAT ROPES 
 
 Flat ropes, Fig. 7, are composed of a number of loosely twisted ropes of four 
 wires each and without hemp centers. The ropes, of alternately right and 
 left lay, are placed side by side and are then sewed together with soft iron or 
 annealed steel wire to form a single rope. The sewing wires, which vary in 
 number from 8 to 12 pass through the centers of the individual ropes from 
 side to side and often have to be renewed, as they naturally wear faster than 
 the wires composing the rope 
 proper. 
 
 Flat ropes may be made to 
 order of any width to give any 
 desired strength, but the width 
 must, of necessity, be some 
 multiple of the diameter of a 
 single strand. They are made 
 of the same grades of steel as 
 round ropes and, under certain 
 conditions present material ad- 
 vantages over the ordinary FlG. 7 
 type. In very deep shafts 
 
 round ropes have a tendency to twist and untwist, or to spin, something 
 that flat ropes do not do. The width of the reel upon which a flat rope 
 winds is very much less than that of the drum used for round ropes, and 
 as the rope coils upon itself like a ribbon, it tends to equalize the load upon the 
 engine, the effect being approximately the same as that produced by conical 
 drums. Likewise, in hoisting, the rope is always in the same vertical plane, 
 thus avoiding the weaj that round ropes are subject to when wound on a drum. 
 Flat ropes are not used in coal mines in the United States, owing to the com- 
 paratively shallow depths of the shafts, but are quite extensively used in the 
 metal-mining districts, where vertical lifts of 2,000 ft. and over are common. 
 
 TAPER ROPES 
 
 Taper ropes, both round and flat, have been used in deep hoisting. Such 
 a rope has its diameter or width reduced uniformly throughout its length by 
 dropping a single wire at a time, or by decreasing the size of the wire used at 
 regular intervals, so as to reduce the sectional area of the rope in proportion 
 to the weight to be supported. The reason for using taper rope is as follows: 
 When the load is at the bottom of the shaft, the upper part of the rope 
 sustains both the load to be hoisted and the weight of the rope itself. As the 
 rope is wound up, the load on the rope at the drum gradually decreases and, 
 therefore, the size of the rope may be proportionately decreased. Owing to 
 the difficulties of manufacture, taper ropes cannot be made as perfect as straight 
 ropes and their cost is greater; furthermore, they cannot "be used for haulage 
 and other purposes when partly worn, as is the case with straight ropes. 
 
 HAULAGE ROPES 
 
 6X7 Ropes. For underground haulage and for the transmission of power, 
 a rope of the section shown in Fig. 1, and either ordinary or Lang lay, is in 
 
 general use in American 
 mines, to the practical 
 exclusion of any other 
 type. It is composed 
 of 6 strands of 7 wires 
 each (6X7) twisted 
 
 FIG. 
 
 around a hemp center. 
 
 It is decidedly stiffer 
 than a 6X 19 standard hoisting rope and requires larger sheaves, as will appear 
 from the tables. Owing to the small number of wires (there are but 42 as 
 against 114, 152, and 222, in the 6X19, 8X19, and 6X37 hoisting ropes) this 
 
242 
 
 WIRE ROPES 
 
 rope should be used with a higher factor of safety than is employed with hoist- 
 ing ropes, as the breaking of one or two wires materially reduces the strength 
 of the rope. These ropes are made of Swedes iron and of the four grades or 
 strengths of steel previously mentioned. As in the case of hoisting ropes, 
 haulage ropes of iron require the use of deecidedly larger sheaves than do 
 those of steel. Manufacturers recommend a sheave from 10.5 to 11 ft. in 
 diameter for a 1-in. iron rope of this type as against a sheave 7 to 8 ft. in 
 
 diameter for a corresponding steel rope. 
 Flattened-Strand Ropes. Flat- 
 tened-strand rope, similar in general 
 construction to the rope of the same 
 name used for hoisting, is also em- 
 ployed for haulage. Ropes of this type 
 are shown in Fig. 2 (a) and (&). The 
 former shows the 5X9 (45 wires) rope 
 very similar to the 5X28 hoisting rope 
 of the same type. View (b) shows the 
 6X8 haulage rope, which is not un- 
 like the 6X25 hoisting rope. The ulti- 
 mate breaking strength of a 1-in., cast- 
 steel, ordinary, haulage rope is given 
 as 31 T., and those of the 5X9, and 6X8, flattened-strand rope of the same 
 diameter and material are 31 and 34 T., respectively. The diameter of sheave 
 suggested for the standard 6X7 1-in. haulage rope is 7, and 5.75 ft. for either 
 type of the flattened-strand rope. Tne comments made upon hoisting ropes 
 of this type apply here. 
 
 Scale Ropes. Seale lay ropes are used to a certain extent for haulage and 
 those of the Lang lay type are very commonly employed for the same purpose, 
 as explained before. 
 
 FIG. 2 
 
 ROPES FOR MISCELLANEOUS PURPOSES 
 
 Ropes for Cableways. Many of the ropes described, and particularly the 
 6X7 Lang lay, are used for the track or supporting cable of what are variously 
 known as cable-ways, 
 wire-rope tramways, 
 aerial tramways, and the 
 like. In this system of 
 transportation, the ma- 
 terials to be moved are 
 carried in buckets sus- 
 pended from wheeled TJ T _ 
 trucks, which are hauled * IG< 
 by a lighter rope upon a fixed rope known as the cable, or track cable. Such 
 cables are subject to extreme wear and to produce a rope having the maxi- 
 mum of wearing surface, what are known as locked-wire cables and locked-coil 
 cables have been devised. 
 
 The locked-wire construction is shown in Fig. 1. The outside wires are 
 drawn of such a shape as to interlock one with the other, making a smooth 
 cylindrical surface for the carrier wheels to run up9n. Ropes of this type have 
 wire cores and are, consequently, stiffer than ordinary ropes of the same size; 
 
 but as they are proportionally 
 stronger for equal strengths there 
 is probably not much difference in 
 the stiffness of the two forms of 
 construction. The advantages 
 claimed for this rope are lessened 
 wear, both on the part of the rope 
 and on that of the wheels of the 
 traveling carriage; absence of any 
 tendency to twist and turn; and 
 FlG. 2 freedom from unraveling should any 
 
 of the wires break. 
 
 The locked-coil construction is illustrated in Fig. 2. It differs from the 
 preceding only in the smaller number and larger size of the wires, which makes 
 it stiffer. 
 
WIRE ROPES 
 
 243 
 
 Another and cheaper, but very satisfactory, construction for track cables, 
 shown in Fig. 3, is known as the tramway strand, or smooth-coil. It is merely 
 a heavy strand of very large wires resembling a spirally fluted cylinder in appear- 
 ance. The large wires give increased durability over smaller wires, owing to 
 the greater surface exposed to wear. 
 
 A disadvantage of the track 
 cables here illustrated is that they 
 cannot be spliced. In order to 
 connect them the coupling shown 
 in Fig. 4 must be employed. This 
 consists of two, narrow, tapered 
 
 sockets, joined at the middle by a p IG -. 
 
 plug with right- and left-hand screw 
 
 threads. The ends of the wires are spread apart in the funnel-shaped apertures, 
 and the space between them rilled with conical thimbles and narrow wedges 
 made approximately to the shape of the interstices. The sockets are attached 
 to the ends of the cables by a special form of press, after which they are brought 
 nearly together and in line and the proper end of the plug inserted in each. 
 The plug is then turned until the sockets are brought together. 
 
 Ropes for Suspension Bridges. Small suspension bridges at mines are 
 frequently built of old and partly worn hoisting or haulage ropes, but a 
 special form of rope, shown in Fig. 5, is not infrequently used for this pur- 
 pose, particularly if the span is considerable. This is the familiar 6X7 haulage 
 rope, but with a wire instead of a hemp center, which gives increased strength 
 but with lessened flexibility, the latter quality not being of prime importance 
 in bridge construction. 
 
 There are many other purposes for which ropes are used in and around 
 mines, such as in running ropes for derricks, aerial tramways, and steam 
 
 FIG. 4 
 
 shovels, as guy ropes for derricks and smokestacks, as rigging, hawsers, and 
 mooring ropes for vessels engaged in the transportation of coal, etc. The 
 forms of some of these ropes are in Figs. 5, 6, 7, and 8. 
 
 Derrick Ropes. -Guys for derricks and stacks, shrouds and stays aboard 
 ship, etc., are commonly made of ordinary 6X7 rope with a hemp center; 
 though where greater flexibility is required of a 6 strand rope with 12 instead 
 of 7 wires to the strand, that is a 6X 12 rope, is used. The wires are commonly 
 single or double galvanized; that is, they receive a single or double coating 
 of zinc to prevent rusting. 
 
 Hawsers. Steel hawsers, mooring lines, and running rigging for vessels, 
 which must be more flexible than ropes used for guys, standing rigging, etc., 
 are very commonly made of the 6X37 ropes. Special rope for these purposes 
 is made of tne section shown in Fig. 6, in which 6 strands (each with a hemp 
 
 FIG. 5 
 
 FIG. 6 
 
 FIG. 7 
 
 FIG. 
 
 center) of 12 wires each are wrapped around a common hemp core. Such 
 ropes are very much stronger than those of Manila hemp of the same size and 
 are fully as flexible. 
 
 Another form of rope used for the same purposes is shown in Fig. 7. In 
 this case, 6 strands of 24 wires each with a hemp center are wrapped around 
 a common hemp core. This is more flexible than the form shown in Fig. 6 and 
 
244 
 
 WIRE ROPES 
 
 is consequently well adapted for mooring lines, which muse be wound upon 
 capstans, piles, etc. of comparatively small diameter. The strands vary in 
 their make-up ;. with some manufacturers, the 24 wires are all of the same 
 size, while with others, the 12 inner wires are considerably smaller than the 
 outer ones, as in Scale lay ropes. 
 
 Tiller rope is made of six small 6X7 ropes laid around a hemp center as 
 shown in Fig. 8. Containing 252 wires, this is the most flexible wire-rope made. 
 It is used mostly for steering or tiller ropes on steamers, for hand-lines on pas- 
 senger elevators, and in any place where a smooth and very flexible rope is 
 required. The ultimate strengths of tiller ropes are about one-third less than 
 those of standard 6X19 wire ropes of the same size and grade. The minimum 
 diameter of sheaves recommended for usual loads are: for iron, 30 times the 
 rope diameter; for steel, 25 times the rope diameter. Owing to the small size 
 of the wires, tiller rope should be subject to as little abrasion as possible. 
 
 With the exception of tiller rope, and that only when used for passenger 
 elevators, the ropes that have been described are but rarely made of Swedes 
 iron, steel giving much better results. These ropes are almost always gal- 
 vanized, at a cost of about 10% above that of untreated ropes. 
 
 For use in and around oil wells, ropes of 6X 7, 6X 12, and 6X 19 construction 
 are commonly employed. The 6X7 rope is used for sand lines and, when 
 left-lay, for cleaning out or redrilling wet holes. Casing lines and drilling lines 
 for new holes, the latter left-lay, are made of 6 X 19 rope. 
 
 ROPE DRUMS AND FASTENINGS 
 
 Fastening Rope to Drum. A common method of fastening a rope to a 
 drum is shown in Fig. 1 (c), where the rope is passed through a hole in the drum 
 shell and then around the shaft, clamping 
 the end to the rope between the shaft and 
 the shell, as shown. Care should be taken 
 to make the radius of curvature of the hole 
 at a as large as possible, so that the rope 
 will not be bent any sharper than is neces- 
 sary. 
 
 When an iron drum is used, the thick- 
 ness of the rim does not afford enough 
 depth in which to bend the rope, so it is 
 necessary to build in a pocket for the pur- 
 pose, as shown in (b). In no case should 
 the rope be bent sharply at right angles 
 where it passes through the drum shell. 
 
 The securing of the rope to the drum 
 or the drum shaft by several coils around 
 each is unnecessary. With one coil around 
 either the drum or the shaft, a pull of 1 Ib. 
 will resist a weight of 9 Ib.; if two coils, a 
 pull of 1 Ib. will resist 9X9 = 811b.; if three 
 coils, 9X9X9 = 729 Ib.; and so on, multi- 
 plying the former result by 9 'for each ad- 
 ditional coil. 
 
 Rope Sockets. The common method 
 of attaching the socket shown in Fig. 2 to a rope is as follows: The rope is 
 pushed through from the small end and is allowed to project any convenient 
 distance. It is then firmly wrapped with wire at a point a little more than 
 twice the depth of the socket from the end. The end of each strand is un- 
 twisted, a few of the wires cut away, and the others bent back upon themselves. 
 This makes the end of the rope conical, in 
 which condition it is drawn back into the 
 socket, and a conical wedge is rammed 
 into the center of the hemp core to spread 
 the wires against the side of the socket. 
 The socket and a small length of the rope 
 next thereto are covered with a layer of 
 moist fireclay, and melted Babbitt metal is 
 
 FIG. 2 
 
 run into the socket, until it fills the space completely and thus cements the 
 whole into a solid mass. This entire operation must be carefully performed, 
 otherwise all^of the wires will not be engaged, and thus an undue strain will 
 
WIRE ROPES 
 
 245 
 
 be thrown upon other wires or strands, possibly resulting in the failure of the 
 rope at some distance from the socket. 
 
 The following method of attaching the socket is employed by John A. Roeb- 
 ling's Sons Company. As before, the rope is fitted through the socket and 
 allowed to project. Wires are then securely served around the rope, the 
 strands opened for a distance equal to the length of the basket of the socket, and 
 the hemp center cut off the length of the opening. The wires are then well 
 cleaned with kerosene and wiped dry. After the strands are separated into 
 wires, which may be conveniently done with a small piece of pipe, the wires are 
 placed into a solution of equal parts of water and hydrochloric acid or muriatic 
 acid, HCl, for 5 min., and then are cleaned off. They are then redipped into 
 the solution, which has been made weaker by the addition of 1 part of water 
 (now 2 parts of water to 1 part of acid). The wires are then bunched and 
 bound together by wire about 1 in. from the top. When the socket has been 
 pushed over the wires until their ends are even with the top of the basket, 
 fireclay is placed around the rope at the bottom of the socket, to serve as a 
 shield, and melted zinc is poured into the 
 basket of the socket. It will be noted 
 that in this method of fastening none of the 
 wires are cut out and none are bent back 
 upon themselves; the rope is rrerely opened 
 up, untwisted, and the ends of the wires 
 bunched together. 
 
 Instead of using a socket, the end of the 
 rope may be bent around a thimble and the 
 end fastened by clamping the parts of the 
 rope with devices, as shown in Fig. 3 (a) : 
 or with iron bands that are sometimes held 
 in place by nails, inserted between the 
 strands, as in (6) , though this practice is not 
 recommended; or by wrapping the rope with 
 wire, as in (c). In the last method, the end 
 of the rope is frayed, and the loosened 
 wires are arranged evenly around the main 
 portion of the rope before wrapping is 
 commenced. 
 
 WIRE-ROPE TABLES 
 
 The accompanying tables (eleven in number) giving the ultimate strengths 
 of wire ropes, proper size of sheaves to be used therewith, etc. are taken from 
 the latest practice of the leading American manufacturers of wire rope. The 
 strengths given are ultimate strengths, the working strains to which the rope 
 is actually subjected being usually one-fifth of these; that is, a factor of safety 
 of 5 is commonly employed, although one of 6 is not unusual, and even 10 is 
 used, particularly in elevator work where passengers are carried. The use of 
 these tables when selecting a hoisting rope for any particular service is best 
 illustrated by means of an example. 
 
 EXAMPLE. A total load of 8 T. is to be hoisted from a shaft 300 ft. deep. 
 What size rope should be employed, allowing a factor of safety of 5? 
 
 SOLUTION. Since the factor of safety is 5, the rope selected must have 
 an ultimate strength of 5X8 = 40T. Standard hoisting ropes are 6 X 19 and 
 commonly of cast steel. The first table shows that a If-in. rope of this kind 
 has a breaking strength of 38 T., and one \\ in. in diameter, a breaking 
 strength of 56 T. The weight of the smaller rope is 2 Ib. per ft., and of the 
 larger 2.45 Ib. In the one case the weight of the rope will be 300 X 2 = 600 Ib. 
 = .3 T., and in the other 300X2.45 = 735 lb. = .36 T. If a H-in. rope is 
 used, the rope is called upon to sustain a load of 40.3 T.; if a IJ-in. rope is 
 used, the strain is 40.36 T. Therefore, the smaller rope is not quite strong 
 enough and the larger rope is considerably over strength. Probably the 
 ly-in. rope with a factor of safety a little less than 5 would answer, but bet- 
 ter practice demands the selection of the larger rope; the factor of safety being 
 nearly 6. The table also shows that the minimum diameter of sheave or 
 drum for the l|-in. rope is 5 ft., and for the IJ-in. rope, 6 ft. 
 
246 
 
 WIRE ROPES 
 
 
 O^OCOOi 
 t CO W (N y> O 
 
 Minimum Diameter 
 of Sheave or Drum 
 Feet 
 
 * 
 -S 
 
 n 
 
 OSOOt^O 1C iO TTI * CO CO CO C<l IM (N 
 
 i-H T-I rH i-C 
 
 
 11 
 
 11 
 
 Ow 
 
 11 
 
 Ow 
 
 OOOOOOOOO"2 
 
 octDcoiNioiM 
 
 00 O O * CO (N (N >-l i-l 
 
 OOOOOOOOOOC^>O>O 
 OOOOOOO<C1^O>'-<CO(N 
 
 8888 8888888888i2gg 
 
 (N<N "-I iH i-H 
 
 8888 8888888888^S2 
 
 8888 888888888iS 
 8S SgSSgggJSSSS 06 "^ 
 
 8888 88888888SSS8S8 
 
 oooooooooooooooooo^oou, 
 
 goooooooooooggoooo^gg 
 
 OOiCOOt-~C<lTt<C^<N OOt^OOOi CO lOC^IO 00 OCOC<1 
 
 Pq IN i-H i-H .-H i-< 
 
 888888888888888^8883 
 
 OOOOOOOOOOOOOiOiOO'^'OOO'HfN 
 
 jo ' 
 
WIRE ROPES 
 
 247 
 
 saqouj 
 
 te 
 r 
 ron 
 pe 
 
 Appro 
 Weig 
 Foot 
 or Ste 
 Po 
 
 SO'CiOi 
 fOOO-ii 
 
 
 s of 25 Wires 
 Each 
 
 OOOOOOOOOOOOOCO-* 
 
 fOOO-^C^O 
 
 11 
 
 Ow 
 
 OOOOOOOOOOCCOOOCOCO 
 
 CO t^ * 05 O <N <N C^i CO iO 05 CO r-I O5 "5 
 
 l?0(N'-H'-li-l 
 
 OOOOOOOOOO<NO(N<NC<3 
 
248 WIRE ROPES 
 
 SIZES AND STRENGTHS OF FLAT HOISTING ROPES 
 
 Width 
 and 
 Thick- 
 ness 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 Approximate 
 Strength, in Tons 
 of 2.000 Ib. 
 
 Width 
 and 
 Thick- 
 ness 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 Approximate 
 Strength, in Tons 
 of 2,000 Lb. 
 
 Cast 
 Steel 
 
 Plow 
 Steel 
 
 Cast 
 Steel 
 
 Plow 
 Steel 
 
 r*K* HIM 
 
 t~soic>OT}<T}teoco 
 XXXXXXXX 
 
 5.90 
 5.20 
 4.82 
 4.27 
 4.00 
 3.30 
 2.97 
 2.38 
 
 129 
 113 
 105 
 97 
 89 
 81 
 72 
 56 
 
 158 
 138 
 128 
 118 
 108 
 99 
 89 
 69 
 
 1X5* 
 1X5 
 iX4| 
 
 1X4 
 1X3* 
 1X3 
 1 X2i 
 1X2 
 
 3.90 
 3.40 
 3.12 
 2.70 
 2.30 
 2.00 
 1.75 
 1.30 
 
 76 
 72 
 63 
 58 
 49 
 45 
 36 
 27 
 
 99 
 93 
 81 
 76 
 64 
 58 
 46 
 35 
 
 SIZES AND STRENGTHS OF STANDARD 6X? HAULAGE ROPES 
 
 
 
 Minimum 
 
 
 1 
 
 & * 
 
 Approximate Strength, in Tons of 
 of 2,000 Ib. 
 
 Diameter of 
 Sheave or 
 Drum 
 
 I 
 
 *o 
 
 
 Feet 
 
 o. *c 
 
 ll 
 
 
 
 4 
 
 
 
 
 
 
 
 
 5 
 
 Swedish 
 Iron 
 
 Cast 
 Steel 
 
 Extra 
 Cast 
 Steel 
 
 Plow 
 Steel 
 
 Extra 
 Plow 
 Steel 
 
 Iron 
 
 Steel 
 
 1 
 
 u 
 
 32.0 
 
 63.0 
 
 73.00 
 
 82.0 
 
 90.00 
 
 16* 
 
 13* 
 
 3.55 
 
 i 
 
 28.0 
 
 53.0 
 
 63.00 
 
 72.0 
 
 79.00 
 
 15 
 
 III 
 
 3.00 
 
 i 
 
 23.0 
 
 46.0 
 
 54.00 
 
 60.0 
 
 67.00 
 
 13f 
 
 10) 
 
 2.45 
 
 i 
 
 19.0 
 
 37.0 
 
 43.00 
 
 47.0 
 
 52.00 
 
 w 
 
 91 
 
 2.00 
 
 i 
 
 15.0 
 
 31.0 
 
 35.00 
 
 38.0 
 
 42.00 
 
 11 
 
 8 
 
 1.58 
 
 j 
 
 12.0 
 
 24.0 
 
 28.00 
 
 31.0 
 
 33.00 
 
 9f 
 
 
 
 1.20 
 
 i 
 
 8.8 
 
 18.6 
 
 21.00 
 
 23.0 
 
 25.00 
 
 81 
 
 5 
 
 
 .89 
 
 u 
 
 7.3 
 
 15.4 
 
 16.70 
 
 18.0 
 
 20.00 
 
 7* 
 
 5 
 
 
 .75 
 
 I 
 
 6.0 
 
 13.0 
 
 14.50 
 
 16.0 
 
 17.50 
 
 7 
 
 4 
 
 
 .62 
 
 A 
 
 4.8 
 
 10.0 
 
 11.00 
 
 12.0 
 
 13.00 
 
 61 
 
 4 
 
 
 .50 
 
 I 
 
 3.7 
 
 7.7 
 
 8.85 
 
 10.0 
 
 11.00 
 
 5i 
 
 3 
 
 
 .39 
 
 A 
 
 2.6 
 
 5.5 
 
 6.25 
 
 7.0 
 
 7.75 
 
 4| 
 
 3 
 
 
 .30 
 
 1 
 
 2.2 
 
 4.6 
 
 5.25 
 
 5.9 
 
 6.50 
 
 4^ 
 
 2 
 
 
 .22 
 
 JL. 
 
 1.7 
 
 3.5 
 
 3.95 
 
 4.4 
 
 
 
 2 
 
 
 .15 
 
 A 
 
 1.2 
 
 2.5 
 
 2.95 
 
 3.4 
 
 
 3* 
 
 2 
 
 .125 
 
 L 1 
 
 
 
 
 
 
 
 GALVANIZED STEEL CABLES FOR SUSPENSION BRIDGES 
 
 Diameter 
 of Rope 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 Ultimate 
 Strength 
 in Tons of 
 2,000 Lb. 
 
 Diameter 
 of Rope 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 Ultimate 
 Strength 
 in Tons of 
 2,000 Lb. 
 
 2! 
 2f 
 2i 
 2f 
 21 
 
 12.70 
 11.60 
 10.50 
 9.50 
 8.52 
 7.60 
 6.73 
 
 310 
 283 
 256 
 232 
 208 
 185 
 164 
 
 1 
 
 1 
 
 1 
 
 
 5.90 
 5.10 
 4.34 
 3.70 
 3.10 
 2.57 
 
 144 
 124 
 106 
 90 
 75 
 62 
 
WIRE ROPES 
 
 249 
 
 SIZES AND STRENGTHS OF PATENT, FLATTENED-STRAND 
 HAULAGE ROPES 
 
 1 
 
 
 
 8 
 
 oj 
 P 
 
 1 
 
 1 
 1 
 
 1 
 1 
 
 I 
 
 _g 
 
 Approximate Total Strength of 
 Rope, in Tons of 2,000 Lb. 
 
 Minimum 
 Diameter of 
 Sheave or 
 Drum for 
 Either Section 
 of Rope 
 Feet 
 
 Approx- 
 imate 
 Weight 
 per Foot 
 of Iron 
 or Steel 
 Rope 
 Pounds 
 
 o 
 "o 
 
 1 
 
 S 
 
 5 Strands of 
 9 Wires Each 
 
 6 Strands of 
 8 Wires Each 
 
 3 . 
 
 3 
 
 CO 
 
 Oco 
 
 1 
 
 0-3 
 
 co 
 
 H 
 
 M 
 
 & 
 ^o 
 
 M 
 
 w 
 
 31 
 
 4* 
 
 f 
 
 I 1 
 
 fi 
 
 CO 
 
 Jl 
 
 
 
 5X9 
 
 6X8 
 
 ! 
 
 23.0 
 19.0 
 15.0 
 12.0 
 8.8 
 6.0 
 3.7 
 2.2 
 
 63.0 
 53.0 
 46.0 
 37.0 
 31.0 
 24.0 
 18.6 
 13.0 
 7.7 
 4.6 
 
 73.00 
 63.00 
 54.00 
 43.00 
 35.00 
 28.00 
 21.00 
 14.50 
 8.85 
 5.25 
 
 67.0 
 52.0 
 42.0 
 33.0 
 25.0 
 17.5 
 11.0 
 6.5 
 
 68.0 
 57.0 
 50.0 
 40.0 
 34.0 
 26.0 
 20.0 
 14.0 
 8.3 
 5.0 
 
 79.0 
 68.0 
 58.0 
 46.0 
 38.0 
 30.0 
 22.7 
 15.7 
 9.6 
 5.7 
 
 73.0 
 56.0 
 46.0 
 36.0 
 27.0 
 19.0 
 11.9 
 7.0 
 
 sf 
 
 7| 
 
 6 
 4f 
 
 34 
 
 1! 
 
 61 
 
 5 
 
 44 
 34 
 24 
 2 
 
 8 
 
 !' 
 
 3 
 
 2f 
 
 3.65 
 3.10 
 2.55 
 2.05 
 1.65 
 1.24 
 .92 
 .64 
 .40 
 .23 
 
 4.00 
 3.45 
 2.80 
 2.30 
 1.80 
 1.38 
 1.00 
 .72 
 .45 
 .25 
 
 j| 
 
 CAST STEEL LOCKED-WIRE CABLE 
 
 Diameter 
 of Rope 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 Ultimate 
 Strength, 
 in Tons of 
 2,000 Lb. 
 
 Diameter 
 of Rope 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 Ultimate 
 Strength 
 in Tons of 
 2,000 Lb. 
 
 24 - 
 21 
 2 
 1} 
 If 
 
 H 
 
 if 
 U 
 
 15.60 
 12.50 
 10.00 
 7.65 
 6.60 
 5.70 
 4.75 
 3.80 
 
 275 
 220 
 170 
 129 
 114 
 95 
 80 
 67 
 
 H 
 
 I 
 
 3.15 
 2.50 
 1.88 
 1.30 
 .90 
 .72 
 .57 
 
 55.00 
 43.00 
 36.00 
 27.00 
 19.00 
 13.25 
 11.50 
 
 TRAMWAY OR SMOOTH-COIL CABLE 
 
 Diameter 
 of Rope 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 Ultimate 
 Strength, 
 in Tons of 
 2,000 Lb. 
 
 Diameter 
 of Rope 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 Ultimate 
 Strength, 
 in Tons of 
 2,000 Lb. 
 
 Cast 
 Steel 
 
 Plow 
 Steel 
 
 Cast 
 Steel 
 
 Plow 
 Steel 
 
 24 
 
 I 
 
 if 
 if 
 14 
 
 13.10 
 10.36 
 9.35 
 8.40 
 
 7.28 
 6.59 
 5.63 
 
 4.88 
 
 285.0 
 233.0 
 204.0 
 185.0 
 161.0 
 145.8 
 124.0 
 108.4 
 
 335.0 
 266.0 
 240.0 
 218.0 
 189.0 
 171.0 
 146.0 
 127.5 
 
 H 
 
 4.01 
 3.23 
 2.70 
 2.20 
 1.69 
 1.24 
 .86 
 
 88.8 
 71.8 
 60.0 
 49.2 
 37.6 
 27.6 
 19.2 
 
 105.0 
 84.6 
 70.7 
 58.0 
 44.4 
 32.5 
 22.3 
 
250 WIRE ROPES 
 
 GALVANIZED IRON AND STEEL RUNNING ROPE 
 
 
 
 Ultimate 
 
 
 
 Ultimate 
 
 Diameter 
 of 
 Rope 
 
 Weight 
 Foot 
 
 Strength 
 in Tons of 
 2,000 Lb. 
 
 Diame- 
 ter of 
 Rope 
 
 Weight 
 per 
 Foot 
 
 Strength 
 in Tons of 
 2,000 Lb. 
 
 Inches 
 
 Pounds 
 
 
 
 Inches 
 
 Pounds 
 
 
 
 
 
 Iron 
 
 Cast 
 Steel 
 
 
 
 Iron 
 
 Cast 
 Steel 
 
 1& 
 
 1.18 
 
 10.1 
 
 22.5 
 
 & 
 
 .33 
 
 2.80 
 
 6.50 
 
 1 
 
 1.05 
 
 8.7 
 
 19.5 
 
 I 
 
 .26 
 
 2.20 
 
 5.00 
 
 I 
 
 .80 
 
 6.9 
 
 15.5 
 
 iV 
 
 .20 
 
 1.70 
 
 3.90 
 
 f 
 
 .68 
 .59 
 
 6.0 
 5.1 
 
 13.5 
 11.5 
 
 A 
 
 .14 
 .10 
 
 1.30 
 .82 
 
 2.85 
 1.98 
 
 I 
 
 .42 
 
 3.6 
 
 8.0 
 
 
 
 
 
 GALVANIZED STEEL HAWSERS 
 
 
 
 
 
 2L 
 
 
 
 
 
 8. 
 
 Diameter of Rope 
 Inches 
 
 Approximate 
 Circumference 
 Inches 
 
 Weight per Foot 
 Pounds 
 
 Ultimate Strength, 
 in Tons of 
 2,000 Lb. 
 
 of New Manila Ro 
 of Same Strength 
 Inches 
 
 Diameter of Rope 
 Inches 
 
 Approximate 
 Circumference 
 Inches 
 
 Weight per Foot 
 Pounds 
 
 Ultimate Strength, 
 in Tons of 
 2,000 Lb. 
 
 of New Manila Ro 
 of Same Strength 
 Inches 
 
 
 
 
 
 1 
 
 
 
 
 
 1 
 
 w 
 
 2A 
 
 6* 
 
 4.43 
 
 83 
 
 
 11 
 
 41 
 
 2.36 
 
 45 
 
 12.00 
 
 2 
 
 61 
 
 4.20 
 
 77 
 
 
 1& 
 
 4} 
 
 2.16 
 
 41 
 
 11.50 
 
 JL| 
 
 6 
 
 3.89 
 
 71 
 
 
 It 
 
 41 
 
 2.00 
 
 38 
 
 11.00 
 
 H 
 
 5| 
 
 3.42 
 
 66 
 
 
 11 
 
 4 
 
 1.63 
 
 31 
 
 10.00 
 
 ^ 
 
 5* 
 
 3.23 
 
 61 
 
 13.5 
 
 1& 
 
 3} 
 
 1.47 
 
 28 
 
 9.25 
 
 XI 
 
 51 
 
 2.94 
 
 57 
 
 13.0 
 
 H 
 
 3* 
 
 1.33 
 
 26 
 
 8.75 
 
 1 
 
 5 
 
 2.76 
 
 53 
 
 12.5 
 
 
 
 
 
 
 GALVANIZED STEEL MOORING LINES 
 
 Diameter 
 of Rope 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 Ultimate 
 Strength, 
 in Tons of 
 2,000 Lb. 
 
 Diameter 
 of Rope 
 Inches 
 
 Weight 
 per Foot 
 Pounds 
 
 Ultimate 
 Strength, 
 in Tons of 
 2,000 Lb. 
 
 2& 
 
 5.81 
 
 113 
 
 1| 
 
 2.62 
 
 50 
 
 2 
 
 5.51 
 
 106 
 
 
 2.15 
 
 42 
 
 
 5.09 
 
 98 
 
 in 
 
 1.93 
 
 38 
 
 
 4.48 
 
 88 
 
 i-i 6 
 
 1.75 
 
 34 
 
 
 4.24 
 
 82 
 
 1_L 
 
 1.54 
 
 27 
 
 
 3.86 
 
 76 
 
 f? 
 
 1.38 
 
 25 
 
 
 3.63 
 
 74 
 
 
 1.05 
 
 20 
 
 
 3.10 
 
 63 
 
 H 
 
 .90 
 
 17 
 
 
 2.92 
 
 55 
 
 1 
 
 .78 
 
 14 
 
WIRE ROPES 251 
 
 WIRE-ROPE CALCULATIONS 
 
 The working load, also called the proper working load, is the maximum 
 load that a rope should be permitted to support under working conditions. 
 The stress on a rope to which a load is attached, and which bends over a sheave, 
 is made up of the load on the rope, known as the load stress, and the bending 
 of the rope about a sheave or drum, known as the bending stress. That is, if 
 5 = total safe stress; 
 5* = bending stress; 
 5/ = load stress; 
 S = Sd+Si and 5/=5-5*. 
 
 The total stress must not equal the elastic limit of the material composing 
 the rope and is usually taken as from one-third to one-fourth the approx- 
 imate breaking stress. It is only quite recently that account has been taken of 
 this second stress and it is not by any means universal practice to consider it 
 when calculating the size of rope needed for a given purpose. 
 
 If a given weight is to be hoisted with a wire rope, the proper size of rope 
 to use may be taken directly from the tables, but these do not take account of 
 the bending stress, except by allowing for it in the factor of safety assumed. 
 
 A second method calculates the bending stress. The following formulas 
 and the diagram based on them are given by Mr. E. T. Sederholm, former 
 chief engineer for Fraser & Chalmers, and will be found in the hoisting-engine 
 catalog of the Allis-Chalmers Co. The general formula for the bending stress is 
 
 a A 
 St -- p-, 
 
 in which Sf> = bending stress; 
 
 E = modulus of elasticity; 
 a = diameter of each wire; 
 D = diameter of drum or sheave, in inches; 
 A = total area of wire cross-section, in inches. 
 For a rope of 19 wires to the strand the diameter of each wire is about one- 
 
 fifteenth (exactly 2 > of the diameter of the rope. That is, if d= diameter 
 of rope, a = Tr ^; and by substituting 'this in the formula, St= ?-^jL . 
 
 The modulus of elasticity for the different kinds of wire is given different 
 values by different authorities. Mr. Sederholm uses 29,400,000 in his formula 
 and diagram, and Mr. Hewitt 28,500,000, the same modulus being used for 
 the different materials of which ropes are made. 
 
 The cross-section of metal A in a wire rope is approximately Ad 2 , or it may 
 be more accurately calculated by multiplying the cross-section of each wire, 
 as given by a wire table, by the number of wires in the rop.e. 
 
 EXAMPLE. 'Find the bending stress in a 19-wire, cast-steel hoisting rope 
 
 2 in. in diameter, winding on an 8-ft. drum, if A = Ad 2 , and = 29,400,000. 
 
 SOLUTION. Applying the formula just given, the bending moment is 
 
 29 ,400.000 X 23 X. 4 
 **~ 10X 15.52X96X2,000~ dl<51 L ' 
 The approximate breaking stress for such a rope is 106 T., and if a factor of 
 
 3 is assumed 106-^3 = 35+ T. for the safe working stress, and 35-32 = 3 T., 
 for the safe lifting load under the given conditions. 
 
 Mr. Wm. Hewitt, of the Trenton Iron Co., has given a similar but more 
 complicated formula for the bending stress, which is supposed to give some- 
 what more accurate results, as he has introduced terms that allow for the 
 actual radius of the bend at the outside fiber of the rope, while the Sederholm 
 formula assumes the radius of the bend to be the radius of the sheave. 
 
 Mr. Hewitt's formula is as follows: 
 
 2.06 +C 
 
 in which Sb = bending stress, in pounds; 
 
 = modulus of elasticity (28,500,000); 
 
 A = aggregate area of wires, in square inches; 
 
 R = radius of drum or sheave, in inches; 
 
 d = diameter of individual wires, in inches; 
 
 C = a constant depending on number of wires in strands. 
 
252 
 
 WIRE ROPES 
 
 The values of d and C are: 
 
 7 -Wire Rope 19-Wire Rope 
 
 d = % diameter of rope a = A diameter of rope 
 
 C=9.27 . C- 15.45 
 
 For 12-wire and 16-wire ropes the values are intermediate in proportion to 
 the number of wires. In the case of ropes having strands composed of dif- 
 ferent sizes of wires, take the larger of the outer layer for the value of d. 
 
 (By permission of E. T. Sederholm, Chief Engr., Fraser & Chalmers, Chicago.) 
 
 6OOOO 
 
 550OO 
 
 3OOOO 
 
 45000 
 
 ZOOOO 
 
 SOOO 
 
WIRE ROPES 
 
 253 
 
 Mr. Hewitt assumes one-third of the approximate breaking stress as the 
 maximum safe stress and uses 28,500,000 for the modulus of elasticity. 
 
 If the problem given under the Sederholm formula is worked out by the 
 Hewitt formula the safe working load will be 11? T., while the table gives 
 106-^5 = 21.2 T. 
 
 The Sederholm diagram gives for a load of 21.2 T. a sheave between 13 and 
 14 ft. in diameter, the formula gives a sheave of 11 ft. in diameter, while the 
 table gives 9| ft. It is evident that there is a wide difference of opinion 
 among the wire-rope authorities and a good opportunity for experimental 
 work along this line. 
 
 In using the Sederholm or Hewitt formulas, there are two unknown quan- 
 tities, the diameter of the ropa d and the diameter D o'r radius R of the drum. 
 d varies inversely as D, that is, for a given load, the smaller d is taken the 
 larger D must be to give the same conditions of safety. 
 
 If a certain ratio between Sb and Si could be assumed in the formula 
 S = Sb+ Si the problem could be easily solved, but an examination of this 
 ratio in a number of cases where good .results have been obtained from 
 
 hoisting ropes shows it to vary from ^r = 1 to ^ = s . In the transmission of 
 
 jd o O 
 
 power by wire ropes, Mr. Hewitt assumes -^r = kut ^ s relation will scarcely 
 
 o & 
 
 hold in a hoisting problem, and the foregoing problem must be solved by the 
 cut-and-try method. 
 
 Proper Working Load. For steel hoisting ropes, made with 19 wires to 
 the strand, when used on drums of different diameters, the proper working 
 load may be found from the following formula, in which the total strain on 
 the rope, including bending strain and the strain due to load is assumed at' 
 50,000 Ib. per sq. in. of actual steel section. 
 
 Let d = diameter of rope, in inches; 
 
 D = diameter of drum, in inches; 
 S = strain per square inch due to bending; 
 L = proper working load, in pounds. 
 
 S= 1,894,000 X^ 
 
 L = 20,000^ - 757,600 X 
 
 STARTING STRESS ON ROPE 
 
 Dynamometer Tests 
 
 Starting Stress 
 
 Tons 
 
 Cwt. 
 
 First Test 
 Empty cage lifted gently 
 
 1 
 2 
 4 
 5 
 
 2 
 3 
 5 
 5 
 
 7 
 
 5 
 5 
 5 
 8 
 8 
 10 
 11 
 12 
 11 
 
 16 
 10 
 
 10 
 
 17 
 
 
 10 
 
 
 1 
 1 
 3 
 10 
 10 
 10 
 10 
 10 
 10 
 
 Empty cage with 2 5 in slack chain 
 
 Empty cage with 6 in. slack chain 
 
 Empty cage with 12 in. slack chain 
 
 Second Test 
 Cage and four empty cars weighed by machine 
 
 
 
 Cage and four empty cars with 6 in. slack chain 
 
 Cage and four empty cars with 12 in slack chain 
 
 Third Test 
 Cage and full cars weighed by machine 
 
 No 1 lifted gently . ... 
 
 No 2 lifted gently 
 
 No 1 with 3 in. slack chain 
 
 
 No. 1 with 6 in. slack chain / 
 
 No 2 with 6 in slack chain 
 
 
 
 
254 
 
 WIRE ROPES 
 
 Starting Stress on Hoisting Rope. When selecting a hoisting rope, due 
 allowance must be made for the shock and extra stress imposed on the rope 
 when the load is started from rest. Experiments made by placing a dyna- 
 mometer between the rope and the cage have, shown that the starting stress 
 may be from two to three times the actual load. The experiments referred 
 to were made in England and are here given; the tons are those of 2,240 lb., 
 and the hundredweights (.cwt.), 112 lb. 
 
 STRESS OF ROPE ON PLANES 
 
 Rise per 
 100 Ft. 
 Horizontal 
 Feet 
 
 Angle 
 of 
 Inclination 
 
 Stress 
 per Ton of 
 2,000 Lb. 
 Pounds 
 
 Rise per 
 100 Ft. 
 Horizontal 
 Feet 
 
 Angle 
 of 
 Inclination 
 
 Stress 
 per Ton of 
 2,000 Lb. 
 Pounds 
 
 5 
 
 2 52' 
 
 140 
 
 105 
 
 46 24' 
 
 1,484 
 
 10 
 
 5 43' 
 
 240 
 
 110 
 
 47 44' 
 
 1,516 
 
 15 
 
 8 32' 
 
 336 
 
 115 
 
 49 00' 
 
 1^535 
 
 20 
 
 11 10' 
 
 432 
 
 120 
 
 50 12' 
 
 1,573 
 
 25 
 
 14 03' 
 
 527 
 
 125 
 
 51 21' 
 
 1,597 
 
 30 
 
 16 42' 
 
 613 
 
 130 
 
 52 26' 
 
 1,620 
 
 35 
 
 19 18' 
 
 700 
 
 135 
 
 53 29' 
 
 1,642 
 
 40 
 
 21 49' 
 
 782 
 
 140 
 
 54 28'- 
 
 1,663 
 
 45 
 
 24 14' 
 
 860 
 
 145 
 
 55 25' 
 
 1,682 
 
 50 
 
 26 34' 
 
 933 
 
 150 
 
 56 19' 
 
 1,699 
 
 55 
 
 28 49' 
 
 1.003 
 
 155 
 
 57 11' 
 
 1.715 
 
 60 
 
 30 58' 
 
 1,067 
 
 160 
 
 58 00' 
 
 1,730 
 
 65 
 
 33 02' 
 
 1,128 
 
 165 
 
 58 47' 
 
 1,744 
 
 70 
 
 35 00' 
 
 1,185 
 
 170 
 
 59 33' 
 
 1,758 
 
 75 
 
 36 53' 
 
 1,238 
 
 175 
 
 60 16' 
 
 1,771 
 
 80 
 
 38 40' 
 
 1,287 
 
 180 
 
 60 57' 
 
 1,782 
 
 85 
 
 40 22' 
 
 1,332 
 
 185 
 
 61 37' 
 
 1,794 
 
 90 
 
 42 00' . 
 
 1,375 
 
 190 
 
 62 15' 
 
 1,804 
 
 95 
 
 43 32' 
 
 1,415 
 
 195 
 
 62 52' 
 
 1,813 
 
 100 
 
 45 00' 
 
 1,450 
 
 200 
 
 63 27' 
 
 1,822 
 
 Stress in Hoisting Ropes on Inclined Planes of Various Degrees. The 
 
 preceding table is based on an allowance of 40 lb. per T. for rolling fric- 
 tion, but there will be an additional stress due to that portion of the weight 
 of the rope which acts vertically. 
 
 Relative Effect of Various Sized Sheaves or Drums on Life of Wire Ropes. 
 Mine officials and other users of wire ropes have often felt the want of a table 
 or set of tables that would enable them to determine at a glance what effect 
 the use of various sized sheaves would have on various sized ropes. The 
 following tables have been specially prepared for the Coal and Metal Miner's 
 Pocketbook by Mr. Thomas E. Hughes, of Pittsburg, Pennsylvania. The 
 cast-steel ropes for inclines are made of 6 strands of 7 wires each, laid 
 around a hemp core, the cast-steel hoisting ropes are made of 6 strands of 
 19 wires each, laid a hemp core; and the iron hoisting ropes, of 6 strands 
 of 19 wires each, laid around a hemp core. 
 
 CAST-STEEL ROPES FOR INCLINES 
 
 Diameter 
 - of 
 Rope. 
 Inches 
 
 Percentages of Life for Various Diameters 
 
 100 
 
 90 | 80 
 
 75 | 60 | 50 
 
 25 
 
 Diameters of Sheaves or Drums in Feet 
 
 1* 
 If 
 1J 
 l| 
 1 
 
 16.00 
 14.00 
 12.00 
 10.00 
 8.50 
 7.75 
 7.00 
 6.00 
 5.00 
 
 14.00 
 12.00 
 10.00 
 8.50 
 7.75 
 7.00 
 6.25 
 5.25 
 4.50 
 
 12.00 
 10.00 
 8.00 
 7.75 
 6.75 
 6.25 
 5.50 
 4.50 
 4.00 
 
 11.00 
 8.50 
 7.25 
 7.00 
 6.00 
 5.75 
 5.00 
 4.00 
 3.50 
 
 9.00 
 7.00 
 6.00 
 6.00 
 5.00 
 4.50 
 4.25 
 3.25 
 2.75 
 
 7.00 
 6.00 
 5.50 
 5.00 
 4.50 
 3.75 
 3.50 
 3.00 
 2.25 
 
 4.75 
 4.50 
 4.25 
 4.00 
 3.75 
 3.25 
 2.75 
 2.50 
 1.75 
 
WIRE ROPES 
 CAST-STEEL HOISTING ROPES 
 
 255 
 
 Diameter 
 
 Percentages of Life for Various Diameters 
 
 of 
 Rope. 
 
 100 | 90 
 
 80 75 
 
 60 | 50 25 
 
 Inches 
 
 Diameters of Sheaves or Drums in Feet 
 
 14 
 
 14.00 
 
 12.00 
 
 10.00 
 
 8.50 
 
 7.00 6.00 
 
 4.50 
 
 1 
 
 
 12.00 
 
 10.00 
 
 8.00 
 
 7.00 
 
 6.00 
 
 5.25 
 
 4.25 
 
 1 
 
 
 10.00 
 
 8.50 
 
 7.50 
 
 6.75 
 
 5.50 
 
 5.00 
 
 4.00 
 
 1 
 
 
 9.00 
 
 7.50 
 
 6.50 
 
 5.50 
 
 5.00 
 
 4.50 
 
 3.75 
 
 1 
 
 
 8.00 
 
 7.00 
 
 6.00 
 
 5.50 
 
 4.50 
 
 4.00 
 
 3.50 
 
 
 
 7.50 
 
 6.75 
 
 5.75 
 
 5.00 
 
 4.25 
 
 3.50 
 
 3.00 
 
 
 
 5.50 
 
 4.50 
 
 4.00 
 
 3.75 
 
 3.25 
 
 3.00 
 
 2.25 
 
 
 
 4.50 
 
 4.00 
 
 3.75 
 
 3.25 
 
 3.00 
 
 2.50 
 
 2.00 
 
 
 
 4.00 
 
 3.00 
 
 3.00 
 
 2.75 
 
 2.25 
 
 2.00 
 
 1.50 
 
 
 
 3.00 
 
 
 
 2.00 
 
 
 1.50 
 
 
 IRON HOISTING ROPES 
 
 Diameter 
 
 Percentages 01 Lite tor Various JLJiameters 
 
 of 
 Rope. 
 
 100 
 
 90 
 
 80 
 
 75 
 
 60 
 
 5Q 
 
 25 
 
 Inches 
 
 Diameters of Sheaves or Drums in Feet 
 
 li 
 
 12.00 
 
 11.00 
 
 9.00 
 
 7.50 
 
 6.00 
 
 5.00 
 
 4.25 
 
 H 
 
 10.00 
 
 9.00 
 
 7.50 
 
 7.00 
 
 5.25 
 
 4.75 
 
 4.00 
 
 H 
 
 9.00 
 
 7.75 
 
 6.50 
 
 5.75 
 
 4.50 
 
 4.00 
 
 3.50 
 
 if 
 
 8.00 
 
 6.75 
 
 5.50 
 
 5.00 
 
 4.25 
 
 3.50 
 
 3.00 
 
 1 
 
 6.75 
 
 6.00 
 
 5.00 
 
 4.75 
 
 4.00 
 
 3.25 
 
 2.75 
 
 
 
 6.75 
 
 6.00 
 
 5.00 
 
 4.50 
 
 4.00 
 
 3.00 
 
 2.50 
 
 
 
 5.00 
 
 4.75 
 
 4.00 
 
 3.75 
 
 3.00 
 
 2.75 
 
 2.00 
 
 
 
 4.50 
 
 3.75 
 
 3.25 
 
 3.00 
 
 2.75 
 
 2.25 
 
 1.75 
 
 
 
 3.50 
 
 3.25 
 
 3.00 
 
 2.75 
 
 2.00 
 
 1.50 
 
 1.00 
 
 
 
 3.00 
 
 
 2.00 
 
 
 
 1.25 
 
 1.00 
 
 CARE OF WIRE ROPES 
 
 Ordinary Method of Splicing Wire Rope. The tools required for splicing 
 wire ropes by the ordinary method are a pair of iron nippers for cutting off 
 strands; two marline spikes, one round and one 9val, for opening strands; 
 one knife to cut hemp center; two clamps to untwist rope to insert ends of 
 strands or, in place of them, two short hemp-rope slings, with a stick for each 
 as a lever; a wooden mallet and some rope twine. Also, a bench and vise are 
 handy. 
 
 The length of the splice depends on the size of the rope. The larger ropes 
 require the longer splices. The splice of ropes from | in. to f in. in diameter 
 should not be less than 20 ft.; from f in. to 1| in., 30 ft.; and from H in. 
 up, 40 ft. 
 
 To splice a rope, tie each end with a piece of cord at a distance equal to 
 one-half the length of the splice, or 10 ft. back from the end for a f-in. rope, after 
 which unlay each end as far as the cord. Then cut out the hemp center, 
 and bring the two ends together as close as possible, placing the strands of 
 the one end between those of the other, as shown in Fig. 1 (a). Now remove 
 the cord k from the end M of the rope, and unlay any strand, as a, and follow it 
 up with the strand of the other end M' ot the rope that corresponds to it, as 
 a'. About 6 in. of a is left out, and a' is cut off about 6 in. from the rope, 
 thus leaving two short ends, as shown at P in (&), which must be tied for the 
 present by cords as shown. Wind the cord k again around the end M of the 
 rope, to prevent the unraveling of the strands; after which remove the cord k' 
 on the other or M' end of the rope, and unlay the strand &; follow it up, as 
 4>efore, with the strand &', leaving the ends out, and tying them down for the 
 present, as described in the case of strands a and a', see Q\ also, replace the 
 cord k'. Again remove the cord k and unlay the next strand, as c, and follow 
 it up with c', stopping, however, this time within 4 ft. of the first set. Con- 
 
256 
 
 WIRE ROPES 
 
 tinue this operation with the remaining six strands, stopping 4 ft, short of the 
 preceding set each time. The strands are now in their proper places, with the 
 ends passing each other at intervals of 4 ft., as shown in (c). To dispose of 
 the loose ends, clamp the rope in a vise at the left of the strands a and a'. 
 
 6 
 
 FIG. 1 
 
 view (c), and fasten a clamp to the rope at the right of these strands; then 
 remove the cords tied around the rope that hold these two strands down; 
 after which turn the clamp in the opposite direction to which the rope is 
 twisted, thereby untwisting the rope, as shown in (d). The rope should be 
 untwisted enough to allow its hemp core to be pulled out with a pair of 
 nippers. Cut off 24 in. of the hemp cores, 12 in. at each side from the point 
 of intersection of the strands a and a', and push the ends of the strands in 
 their place as shown in (d). Then allow the rope to twist up to its natural 
 shape, and remove the clamps. After the rope has been allowed to twist up, 
 the strands tucked in generally bulge out somewhat. This bulging may be 
 reduced by lightly tapping the bulged part of the strands with a wooden 
 
 rr^> ^T^ ^^=TTv ^^~? 
 k c G . ^~* ^^a 
 
 (C) 
 
 FIG. 2 
 
 mallet, which will force their ends farther into the rope. Proceed in the same 
 manner to tuck in the other ends of the strands. 
 
 Rapid Method of Splicing Wire Rope. The only tools needed in the 
 rapid method of splicing wire ropes are a cold chisel and hammer for cutting 
 
WIRE ROPES 257 
 
 and trimming the strands, and two needles 12 in. long, made of good steel and 
 tapered ovally to a point. Cut off the ends of the ropes to be spliced and 
 unlay three adjacent strands of each back 15 ft.; cut out the hemp center to 
 this point and relay the strands for 7 ft. and cut them off. Pull the ropes by 
 each other until they have the position shown in Fig. 2, (a), cut off a and d', b 
 and c', view (&), making their lengths approximately 10 and 12 ft., respectively, 
 measured from the point where the hemp centers were cut. Place the ropes 
 together, unlay e, d, c, Fig. 2, view (a), keeping the strands together, and follow 
 with e', d', c', (b). Similarly, unlay /', a', b', and follow with /, a, b, until the 
 rope appears as in (c). Next run the strands into the middle of the rope. To 
 do this, cut off the end of the strand e', so that when it is put in place it will 
 just reach to the end x of the hemp core, and then push the needle A, through 
 the rope from the under side, leaving two strands at the front of the needle, 
 as shown. Push the needle B through from the upper side and as close to the 
 needle A as possible, leaving the strands e and e' between them; place the 
 needle A on the knee and turn the needle B around with the coil of the rope, 
 and force the strand e' into the center of the rope. Repeat this operation 
 with the other ends and cut them off so that the ends coming together in the 
 center of the rope will butt against each other as nearly as possible. 
 
 Wear of Wire Ropes. The deterioration of wire ropes may be either 
 external or internal, and may be due (1) to abrasion, due to the rubbing of 
 the outside surface of the rope against other objects, or to the internal chafing 
 of the wires composing the strands against one another; (2) to injury from 
 overloading, to shock due to sudden starting of the load, or to repeated bend- 
 ings about too sharp angles or over sheaves or rollers of too small a diameter 
 for the size of the rope; (3) to rust or corrosion of the wiie from acid waters, or 
 to decay of the hemp cores. 
 
 As a result of abrasion, the wires in a rope are either flattened or torn apart. 
 With properly designed drums and head-frame and properly placed sheaves, 
 a hoisting rope is but slightly abraded, and the wear is due chiefly to bending 
 or to overloading. A haulage rope is subjected to constant abrasion in passing 
 over rollers and sheaves and from dragging along the bottom and sides of the 
 haulage ways and from the grips. It is also often subject to severe shocks and 
 abrasion from the lashing or vibration when the winding engine starts. 
 
 The wear and tear on a rope increases as its velocity is increased; hence, 
 conditions permitting, it is better to increase the output by increasing the 
 load within allowable limits rather than by increasing the velocity of the rope. 
 
 Inspection of Ropes. The life of a hoisting rope depends not only on its 
 quality, but also on the conditions under which it is used and on the care- 
 fulness of the engineer in handling the load. A rope should be inspected often 
 and at regular intervals; at some mines, the hoisting ropes are inspected every 
 morning before lowering the men. The cage is slowly lowered and then raised, 
 each rope being carefully examirTed by an inspector to detect any broken wires. 
 Particular attention should be given to the part of the rope where it is attached 
 to the socket at the cage, as this part is more subject to corrosion and sharp 
 bending than any other. When the core fails at any point the rope should be 
 discarded at once as the wires are likely to kink and break internally as the 
 rope passes over the sheave. At some mines, hoisting ropes are discarded at 
 regular intervals, whether they show wear or not. Haulage ropes do not 
 require as frequent examination and are not discarded as quickly as hoisting 
 ropes, as much less in the way of life and property is dependent on them. If 
 a new piece of loose hemp rope is given one turn around the haulage rope and 
 each end held firmly while the rope is run the presence of loose wire ends will 
 be shown. 
 
 Lubrication of Wire Ropes. Mine water has a very corrosive action on 
 wire ropes, and a rope will soon be destroyed unless the water is prevented 
 from coming in contact with the metal. For this reason, black oil or some 
 lubricating preparation is applied to the rope, but any lubricant used must 
 be free from acids or other substances that will corrode the wire. 
 
 For hoisting ropes, 1 bu. of freshly slaked lime to 1 bbl. of pine or coal 
 tar makes a good lubricant; with pine tar, which contains no acid, tallow may 
 be used instead of lime. Another mixture contains tar, summer oil, axle 
 grease, and a little pulverized mica, mixed to such a consistency that it will 
 penetrate thoroughly between the wires and will not dry or strip off. The 
 lubricant should not be thick enough to render difficult the thorough inspection 
 of the rope, and all lubricants of this nature should be used sparingly after the 
 first application, as the rope should be kept clean and free from grit. Graphite, 
 is also used for the purpose. 
 
258 WIRE ROPES 
 
 Lubricants may be applied by running the engine slowly and allowing the 
 rope to pass through a bunch of waste saturated with lubricant; by rubbing 
 the lubricant into the rope by means of a brush; or by pouring the oil into the 
 groove of the sheave as the rope is run slowly back and forth. A new hoisting 
 rope should be passed through a bath of hot lubricant and thus be thoroughly. 
 
 Haulage ropes are not usually lubricated as thoroughly as hoisting ropes 
 on account of the grease causing slipping of grips and gathering of dirt and 
 dust, but they can be treated with raw linseed oil thickened with lamp-black 
 boiled with an equal portion of pine tar, and the mixture applied while hot. 
 Ordinary black oil, such as is used to oil mine cars and hoisting ropes, can be 
 used on haulage ropes where no friction grips are employed. These mixtures, 
 if fluid, can be poured on the rope as it is run over the sheave, or applied 
 from a leather lined box filled with oil. Patent lubricants known as cable 
 shields or rope fillers, which fill the interstices between the strands, are often 
 used on tail and main ropes. 
 
 General Precautions. Wire rope is as pliable as new hemp rope of the 
 same strength; the former will therefore run on the same sized sheaves and 
 pulleys as the latter. But the greater the diameter of the sheaves, pulleys, 
 and drums, the longer wire rope will last. In the construction of machinery 
 for wire rope, it will be found good economy to make the drums and sheaves 
 as large as possible. 
 
 The tables of wire-rope manufacturers give proper diameters of drum or 
 sheave at from 50 to 65 times the rope diameter; but the expression should 
 more properly be the minimum admissible diameter. For ordinary ser- 
 vice, by using sheaves and drums from 75 to 100 times the diameter of the 
 rope, the average life of hoisting ropes will be materially lengthened. For 
 rapid hoisting, during which abnormal strains are most likely to occur, or 
 where a low factor of safety is employed, a sheave diameter of 150 times that 
 of the rope is to be recommended. 
 
 Experience has demonstrated that the wear increases with the speed; it is 
 therefore better to increase the load than the speed. Wire rope is manufactured 
 either with a wire or a hemp center; the latter is more pliable than the former, 
 and will wear better where there is short bending. 
 
 Wire rope must not be coiled or uncoiled like hemp rope. When mounted on 
 a reel, the reel should be mounted on a spindle or flat turntable to pay off 
 the rope. When shipped in a small coil, without reel, the coil should be rolled 
 over the ground like a wheel, and the rope run off in that way. All untwisting or 
 kinking must be avoided. 
 
 A rope should not be changed from a large drum to a small one, for it 
 will not work so well, neither will it last as long. This is also true, but in a 
 lesser degree, of ropes changed from a small drum to a large one. After having 
 been used for some time on a drum, the rope adapts itself to that diameter and 
 resents a change. Rope sheaves should be made to fit the rope, and should 
 be filled in with well-seasoned blocks of oak or other hardwood, set on end; 
 this will save the rope and increase adhesion. 
 
 CABLEWAYS AND TRAMWAYS 
 
 Cableways. A suspension cableway is a hoisting and conveying device 
 using a suspended cable for a trackway. There are two types: the inclined, or 
 semi-gravity, Fig. 1, and the horizontal, Fig. 2. 
 
 The inclined cableway consists of a cable inclined 20 to 22 to the horizontal, 
 and passing over a cast-iron saddle B on top of a tower or frame A. It is 
 anchored by logs D buried about 5 ft. underground, or from iron plugs secured 
 in the rock, when the rock is near the surface. The trolley carriage G runs down 
 the incline of the cableway by gravity until it reaches a stop. A hoisting rope 
 E operated by a winding drum F leads over a sheave pulley e, thence to a pulley 
 in the carriage G, thence to a fall block M , upwards again to a second pulley in 
 the carriage, and downwards again to the fall block. Winding in the rope 
 hoists the fall block to the carriage, the carriage remaining at the lower stop. 
 When the fall block collides with the carriage, both the carriage and the fall 
 block are pulled up the incline cable, and when the carriage arrives at the 
 head-tower, a gate, or hook, O is lowered to hold it in place. The fall block is 
 then lowered and the load discharged. The engine F has usually a 10" X 12" 
 double cylinder and a single friction drum 37 in. in diameter. 
 
WIRE ROPES 
 
 259 
 
260 
 
 WIRE ROPES 
 
 An endless rope H takes several turns around the sheave J to prevent it from 
 slipping, and both ends are passed over sheaves at the top of the derrick, one 
 end being secured to the front of the carriage, while the other end is taken 
 through the carriage and around the return sheave / and fastened to tne rear 
 end of the carriage G. The endless-rope wheel J is provided with a band brake, 
 which, when applied, holds the carriage securely at any point on the cable. 
 
 All ropes pass through the supporting trolleys K, which are connected by a 
 chain L. These trolleys follow the carriage by gravity, and the chain may or 
 may not be fast to the carriage. 
 
 Instead of chain-connected trolleys, patent button-stop, fall-rope carriers, 
 which are lighter, may be used. These are spaced along an auxiliary rope on 
 which buttons are screwed. The carriers are picked up by a horn on the front 
 of the carriage. These are said to be cheaper for operation than the chain 
 trolleys. 
 
 The length of the span for inclined cableways varies from 200 to 1,200 ft. 
 The main rope is from 1^ to 2 J in. in diameter, the hoisting rope from f to f in., 
 and the endless rope & and in. The rope mostly used is 6 strands, 19 wires to 
 the strand, crucible cast steel. The hoisting rope lasts from 1 to 2 yr., and the 
 main cable from 5 to 10 yr. These cableways are widely used about the slate 
 quarries in Eastern Pennsylvania, where the operating expense for each cable, 
 where two or more are connected with one boiler, is about $5 per da. of 10 hr. ; 
 this includes the engineer, steam, and maintenance of the cableway. 
 
 The horizontal cableway requires a double friction drum and reversible 
 link-motion engine. It may be operated at any inclination of the carrying 
 cable and either from the high or low point of the support, though, if possi- 
 ble, it should be from the higher end. The endless, or traction, rope, is attached 
 to one of the drums of the engine so that the engineer has complete control of 
 the carriage; hence, because of its greater applicability, this system is supplant- 
 ing the inclined, although the inclined costs one-fourth less for installation. 
 The method of operation is similar to the inclined. The amount of rope 
 required is the same in each system. A horizontal cableway of the Hamilton 
 Coal Co., near Tarentum, Pennsylvania, has a span of 2,200 ft. The stationary 
 rope is 2,500 ft. long and 2 J in. in diameter. The hoisting rope is 4,500 ft. long 
 and f in. in diameter. The head-tower is 80 ft. high, the tail-tower is 100 ft. 
 and the rope deflects 80 ft. The skip used holds 3 T. of coal and makes 10 trips 
 per hour. Five men operate the plant and it takes 2 T. of coal for the engine. 
 Based on a capacity of 100 T. per da., the cost of carrying the coal is 13c. per T. 
 For a cableway of average length, 1,000-1,500 ft., the cost of operation should 
 not be one-haft the above cost. A cableway, 2,140 ft. long was used in con- 
 structing the dam at the power plant at Glens Falls, New York. 
 
 One or both towers of a cableway may be mounted on wheels capable of 
 moving on a track at right angles to the cable and the cableway then made 
 to cover a wide territory. 
 
 WIRE-ROPE TRAMWAYS 
 
 Single Tramways. A tramway, in America, is a cableway of the horizontal 
 type consisting of a number of spans. In England, the term cableway includes 
 tramways. 
 
 FIG. 1 
 
 Single wire-rope tramways have a single moving rope, which serves ti 
 support and advance the load at one and the same time, Fig. 1. This rop 
 passes over suitable sheaves at the intermediate supports, and the load i 
 carried in buckets suspended from it by gooseneck or straight hangers. Th 
 hangers are usually attached to the cable by means of a clip, which is eithe 
 
WIRE ROPES 
 
 261 
 
 inserted in the center of the cable or strapped to it. The carriers are often 
 loaded and unloaded while in motion, the loading being accomplished by 
 a traveling mechanical hopper and the unloading by a drop bottom to the 
 bucket. If the line is level, or the grade light, the hangers are provided 
 with box heads filled with wood or leather and rubber, which rest on the 
 rope; the rubber or wood providing sufficient friction to prevent the hangers' 
 slipping. With this system, long spans are evidently out of the question, 
 because with a long span the angle of the rope in the vertical plane, at the 
 supports, becomes so great that the friction will not hold the box head. For all 
 practical purposes, grades exceeding 1 : 4 are to be avoided; and for steeper 
 grades, to prevent slipping, a clamp or a clip inserted in the rope is used to 
 fasten the hanger to the rope. 
 
 The single-moving rope tramways carry loads not exceeding 200 Ib. The 
 speed of the rope for the variety in which the hangers are fastened to the rope 
 may be as high as 450 ft. per min., and for one in which the hanger is loose, 
 200 ft. per min. The single moving-rope tramway has a capacity up to 200 T. 
 per da., and may be built, say, H to 2 mi. long. 
 
 Double Tramways. The more satisfactory and substantial kind of wire- 
 rope tramway has one or more fixed ropes, which constitute the permanent 
 way, and an endless traction rope. The loaded carrier travels outwards on 
 one fixed cable and returns by a parallel one suspended from the opposite 
 side of the same supports. The terminals have suitable appliances for load- 
 ing and unloading the buckets, either by hand or automatically. 
 
 The intermediate supports are built of wood or steel framing, with sad- 
 .dles of cast iron a, Fig. 2 in which the fixed cables b rest. The traction rope c 
 is supported (in the absence of a bucket) by the rollers d, set conveniently on the 
 supports. The load is carried in buckets e, or other contrivances suitable for 
 the purpose, which are suspended from a trolly /, which runs on the fixed 
 cables, the wheels of which are large enough to pass over the rope couplings, and 
 
 also to clear the saddles. Grips g attach the carriers to the traction rope. 
 These grips may be operated by hand or automatically. 
 
 This kind of tramway is capable of carrying individual loads up to 1,400 
 or 1,500 Ib., not including the weights of the bucket and hanger itself. The 
 speed of traction rope may be from 150 to 350 ft. per min. The capacity is 
 from 200 to 1,000 T. per da. of 10 hr. These figures represent good, safe, 
 practice, but they are not, of course, inflexible. 
 
 The maximum length of line that may be built in one section varies largely 
 with conditions of load, spacing of supports, contour of ground, etc. Wire-rope 
 tramways work under great difficulties, and probably 2? to 4 mi. is the econom- 
 ical limit. This has been exceeded, but for a much greater distance the friction 
 becomes too great for economical working of the traction rope. This does not, 
 however, limit the length of tramway which may be built, as the power station 
 may be located at a convenient intermediate point, dividing the line into sec- 
 tions. Several intermediate power stations may be used, and the length of the 
 line greatly increased above the limit given. A tramway at Grand Encamp- 
 ment, Wyoming, is 16 mi. long and carries 40 T. of ore each hour. 
 
262 GLOSSARY OF ROPE TERMS 
 
 GLOSSARY OF ROPE TERMS 
 
 Annealed Wire Rope. -A. wire rope made from wires that have been softened 
 by annealing and the tensile strength thereby lowered. 
 
 Bending Stress The stress produced in the outer fibers of a rope by bend- 
 ing over a sheave or drum. 
 
 Breaking Strain, Breaking Strength, Breaking Stress. The least load that 
 will break a rope. These terms are used indiscriminately to mean the load 
 that will break a rope. The stress on a rope at the moment of breaking is 
 the breaking stress, and the strain or deformation produced in the material by 
 this stress is the breaking strain. 
 
 Bright Rope. 'Rope of any construction, whose wires have not been gal- 
 vanized, tinned, or otherwise coated. 
 
 Cable-Laid Rope. 'Wire cables made of several ropes twisted t9gether, each 
 rope being composed of strands twisted together without limitation as to the 
 number of strands or direction of twist. A fiber cable-laid rope is a rope having 
 three strands of hawser-laid rope, twisted right-handed. 
 
 Cable. Same as cable-laid rope; a fiber cable consists of three hawsers laid 
 up left-handed. 
 
 Cast Steel. Steel that has been melted, cast into ingots, and rolled out into 
 bars. 
 
 Clamp. A device for holding two pieces or parts of rope together by pressure. 
 
 Clip. A device similar to a clamp but smaller and for the same purpose. 
 
 Coir. Cocoanut-husk fiber. 
 
 Compound. A lubricant applied to the inside and outside of ropes pre- 
 venting corrosion and lessening abrasion of the rope when in contact with hard 
 surfaces. 
 
 Core. The central part of a rope forming a cushion for the strands. In 
 wire ropes it is sometimes made of wire, but usually it is of hemp, jute, or some 
 like material. 
 
 Coupling. A device for joining two rope ends without splicing. 
 
 Crucible Steel. A fine quality of steel made by the crucible process. 
 
 Drum. The part of a hoisting engine on which the rope is wound. 
 
 Elastic Limit. That point at which the deformations in the material cease 
 to be proportional to the stresses. 
 
 Elevator Rope. A rope use to operate an elevator. 
 
 Endless Rope. A rope that moves in one direction, one part of which 
 carries loaded cars from a mine at the same time that another part brings the 
 empties into the mine. 
 
 Fiber. A single thread-like filament. 
 
 Flat Rope. A rope in which the strands are woven or sewed together to 
 form a flat, braid-like rope. 
 
 Flattened-Strand Rope. A wire rope whose strands are flattened or oval, 
 and therefore presents an increased wearing surface over that of the ordinary 
 round-strand rope. 
 
 Flattened-Strand Triangular Rope. A wire rope of the flattened-strand con- 
 struction in which the strands are triangular in shape. 
 
 Fleet. Movement of a rope sidewise when winding on a drum. 
 
 Fleet Wheel. A grooved wheel or sheave that serves as a drum and about 
 which one or more coils of a haulage rope pass. 
 
 Galvanized Rope. Rope made of wires that have been galvanized or coated 
 with zinc to protect them from cprrosion. 
 
 Grip Wheel. A wheel, the periphery of which is fitted with a series of toggle- 
 jointed, cast-steel jaws that grip the rope automatically. 
 
 Guy. A strand or rope used to support a pole, structure, derrick, or chim- 
 ney, etc. 
 
 Haulage Rope. A rope used for haulage purposes. 
 
 Hawser. 'Any wire rope used for towing on lake or sea. A fiber hawser 
 consists of three strands laid up right-handed. 
 
 Hawser-Laid Rope has three strands of yarn twisted left-handed, the yarns 
 being laid up right-handed. Synonymous with cable-laid rope as applied to 
 wire ropes. 
 
 Hawser Wire Rope. Galvanized rope of iron or steel, usually composed of 
 6 strands, 12 wires each, principally used in marine work for towing purposes. 
 
 Hemp. A tough, strong fiber obtained from the hemp plant. 
 
GLOSSARY OF ROPE TERMS 263 
 
 Hoisting Rope. A rope composed of a sufficient number of wires and 
 strands to insure flexibility. Such ropes are used in shafts, elevators, quarries, 
 etc. 
 
 Idler. A sheave or pulley running 19086 on a shaft to guide or support a rope. 
 
 Jute. A fiber obtained from the inner bark of two Asiatic herbs: Cor- 
 chorus capsularis and C. olitorius. 
 
 Lang Lay Rope. A rope in which the wires in each strand are twisted in 
 the same direction as the strands in the rope. 
 
 Lay. The direction, or length, of twist of the wires and strands in a rope. 
 
 Live Load. A load that is variable in distinction from a constant load. 
 
 Load Stress. The stress produced by the load. 
 
 Locked-Wire Rope. A rope with a smooth cylindrical surface, the outer 
 wires of which are drawn to such shape that each one interlocks with the 
 other and the wires are disposed in concentric layers about a wire core instead 
 of in strands. Particularly adapted for haulage and rope-transmission purposes. 
 
 Manila. The fiber of Musa textilis; Manila hemp. 
 
 Modulus of Elasticity. The ratio between the amount of extension or 
 compression of a material and the load producing this same extension 
 or compression. 
 
 Plow Steel. A select grade of steel of high tensile strength; first used in 
 rope for plowing fields. 
 
 Proper Working Load. -The maximum load that a rope should be permitted 
 to support under working conditions. (See working load.) 
 
 Regular-Lay Rope. A rope in which the wires in each strand are twisted in 
 opposite direction to the strands in the rope. 
 
 Round-Strand Rope. A rope made of round twisted strands. 
 
 Running Rope. A flexible rope that will pass through blocks and used for 
 hoisting on shipboard. The term is also often used for any moving rope. 
 
 Sheave. A wheel or pulley around or over which a rope passes. 
 
 Shroud Laid, or Four-Strand, Rope has four strands laid around a core. 
 
 Sisal. A nemp; the fiber of the Agave Sisalona. 
 
 Socket. A device fastened to the end of a rope by means of which the rope 
 may be attached to its load; the socket may be opened or closed. 
 
 Splice. 'The joining of two ends of rope by interweaving the strands. 
 
 Step Socket. A special form of socket for use on locked-wire rope. 
 
 Stirrup. An adjustable bale of a socket. 
 
 Stone Wire. -Wire smaller than No. 14 put up in 12-lb. coils, which are 
 about 8 in. inside diameter. 
 
 Strand. A varying number of wires or fibers twisted together; the strands 
 in turn are twisted together, forming a rope. 
 
 Stress. A force or combination of forces tending to change the shape of a 
 body. 
 
 Strain. A change of shape produced in a body. (Stress and strain are 
 often used incorrectly as synonymous terms.) 
 
 Surging. The flapping of a moving rope. 
 
 Swedish Iron. A soft and comparatively pure iron. 
 
 Switch Rope. A short length of rope fitted with a hook on one end and a 
 link on the other, used for the switching of freight cars. 
 
 Tail-Rope. (1) The rope that is used to draw the empties back into a 
 mine in a tail-rope haulage system. (2) A rope attached beneath the cage 
 when the cages are hoisted in balance. 
 
 Taper Rope. A rope that has a gradually diminishing diameter from the 
 upper to the lower end. The diameter of the rope is decreased by dropping 
 one wire at a time at regular intervals. Both round and flat ropes may be 
 made tapered, and such ropes are intended for deep-shaft hoisting with a view 
 to proportioning the diameter of the rope to the load to be sustained at different 
 depths. 
 
 Tensile Strength. The stress required to break a rope by pulling it in two. 
 
 Thimble. An oval iron ring around wnich a rope end is bent and fastened 
 to form an eye. 
 
 Titter Rope. A very flexible wire rope composed of six small ropes, usually 
 of seven-wire strands laid about a hemp core. 
 
 Tinned Rope. Rope made of wires that have been coated with tin to protect 
 them from corrosion. 
 
 Torsion. The process of twisting a wire, thereby showing its ductility. 
 
 Traction Rope. A rope used for transmitting the power in a wire-rope 
 tramway and to which the buckets are attached. 
 
 Transmission Rope. A rope used for transmitting power. 
 
264 POWER TRANSMISSION 
 
 Traveler. A truck rolling along a suspended rope for supporting a load to 
 be transported. 
 
 Turnbuckle. A form of coupling so threaded or swiveled that by turning it 
 the tension of a rope or rod may be regulated. 
 
 Ultimate Tensile Strength. Same as tensile strength. 
 
 Universal Lay. Another term for lang lay. 
 
 Whipping. The flopping of a moving rope. 
 
 Wire Gauge. Standard sizes or diameters for wire. 
 
 Wire Rope. A rope whose strands are made of wires, twisted or woven 
 together. 
 
 Working Load. The maximum load that a rope can carry under the con- 
 ditions of working without danger of straining. (Same as proper working load.) 
 
 Wrought Iron. A comparatively pure and malleable iron. 
 
 Farw. Twisted fiber of which rope strands are made. 
 
 POWER TRANSMISSION 
 
 TRANSMISSION BY WIRE ROPES 
 
 The term transmission, as here used, applies simply to the modification of belt 
 driving, using grooved wheels or sheaves at each end of the line. The power 
 is applied to one sheave and taken off from the other. The friction between 
 rope and sheaves depends directly on the weight and tension of the rope and 
 on the nature of the surfaces in contact. This pressure is better obtained by 
 using a large, heavy rope at a low tension than by using a smaller rope at a high 
 tension. The deflection, or sag, of the rope, between the sheaves, is the same 
 for both upper and lower parts of the rope when the transmission is not run- 
 ning and should be, according to John A. Roebling's Sons Co.-, equal to about 
 3*5 of the span. The deflection may be calculated by the formula from the 
 Trenton Iron Co.: . ws z 
 
 h= ~8T' 
 in which h = deflection, in feet ; 
 
 w = weight of rope per foot, in pounds; 
 s = span, in feet; 
 t tension, in pounds. 
 
 When driving from the under side, this part of the rope will be tightened 
 and its deflection decreased, while the upper part of the rope becomes slackened 
 and its deflection increased. Under proper conditions, the deflection of the 
 lower rope should be about ^, and that of the upper about ^ of the span. 
 The difference in the tensions of the two parts of the rope is the effective pull 
 of the driving sheaves, enabling power to be transmitted. 
 
 Transmission ropes are subject to three stresses: (1) The direct tension, 
 due to the power transmitted, plus the friction and weight of the rope; (2) the 
 bending stress, due to the bending of the rope around the sheaves; (3) the 
 centrifugal tension, due to the centrifugal force in the rapidly running rope. 
 The following data on stresses in transmission ropes are given by Mr. Wm. 
 Hewitt, of the Trenton Iron Co.: When transmitting power by wire rope, 
 working tension should not exceed the difference between the maximum safe 
 stress and the bending stress. It may be greater; therefore, as the bending 
 stress is less, but to avoid slipping, a certain ratio must exist between the 
 tensions in taut and slack portions of the rope when running, which is 
 determined by the formula T = Se^ w ; 
 
 in which T = tension in taut porti9n of rope; 
 5 = tension in slack portion; 
 
 e = base of Naperian systen of logarithms = 2.7182818; 
 n = number of half laps of rope about sheaves or drums at either end 
 
 of line; 
 * = 3.1416; 
 /= coefficient of friction depending on kind of filling in grooves of 
 
 sheaves, or character of material on which rope tracks. 
 The useful effort of transmitting force is the difference between the tension 
 of the taut and slack portions of the rope, T S = Se( f v 1), and to obtain 
 this, the initial tension, or tension when the rope is at rest, must be one-half 
 the sum of the two tensions. 
 
POWER TRANSMISSION 
 
 265 
 
 The following are some of the values. of /: 
 
 Dry rope on a grooved iron drum 120 
 
 Wet rope on a grooved iron drum 085 
 
 Greasy rope on a grooved iron drum 070 
 
 Dry rope on wood-filled sheaves 235 
 
 Wet rope on wood-filled sheaves 170 
 
 Greasy rope on wood-filled sheaves 140 
 
 Dry rope on rubber and leather filling 495 
 
 Wet rope on rubber and leather filling 400 
 
 Greasy rope on rubber and leather filling 205 
 
 The values of the coefficients corresponding to the foregoing values of /, 
 for one up to six half laps of the rope, are given in the accompanying table. 
 
 VALUE OF COEFFICIENTS 
 
 n = Number of Half Laps About Sheaves or Drums at Either 
 End of Line 
 
 /= 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 Values of /' 
 
 .070 
 
 1.246 
 
 1.552 
 
 1.934 
 
 2.410 
 
 3.003 
 
 3.741 
 
 .085 
 
 1.306 
 
 1.706 
 
 2.228 
 
 2.910 
 
 3.801 
 
 4.964 
 
 .100 
 
 1.369 
 
 1.875 
 
 2.566 
 
 3.514 
 
 4.810 
 
 6.586 
 
 .120 
 
 1.458 
 
 2.125 
 
 3.099 
 
 4.518 
 
 6.586 
 
 9.602 
 
 .130 
 
 1.504 
 
 2.263 
 
 3.405 
 
 5.122 
 
 7.706 
 
 11.593 
 
 .140 
 
 1.552 
 
 2.410 
 
 3.741 
 
 5.808 
 
 9.017 
 
 13.998 
 
 .150 
 
 1.602 
 
 2.566 
 
 4.111 
 
 6.586 
 
 10.551 
 
 16.902 
 
 .170 
 
 1.706 
 
 2.910 
 
 4.964 
 
 8.467 
 
 14.445 
 
 24.641 
 
 .200 
 
 1.875 
 
 3.514 
 
 6.586 
 
 12.346 
 
 23.140 
 
 43.376 
 
 .205 
 
 1.904 
 
 3.626 
 
 6.904 
 
 13.146 
 
 25.031 
 
 47.663 
 
 .235 
 
 2.092 
 
 4.378 
 
 9.160 
 
 19.166 
 
 40.100 
 
 83.902 
 
 .250 
 
 2.193 
 
 4.810 
 
 10.551 
 
 23.140 
 
 50.637 
 
 .111.318 
 
 .265 
 
 2.299 
 
 5.286 
 
 12.153 
 
 27.941 
 
 64.239 
 
 147.693 
 
 .300 
 
 2.566 
 
 6.586 
 
 16.902 
 
 43.376 
 
 111.318 
 
 285.680 
 
 .350 
 
 3.001 
 
 9.017 
 
 27.077 
 
 81.307 
 
 244.152 
 
 733.145 
 
 .400 
 
 3.514 
 
 12.346 
 
 43.376 
 
 152.405 
 
 535.488 
 
 1,849.140 
 
 .410 
 
 3.626 
 
 13.146 
 
 47.663 
 
 172.814 
 
 626.577 
 
 2,271.775 
 
 .450 
 
 4.111 
 
 16.902 
 
 69.487 
 
 285.680 
 
 1,174.480 
 
 4,828.510 
 
 .495 
 
 4.716 
 
 22.425 
 
 106.194 
 
 502.881 
 
 2,381.400 
 
 
 .500 
 
 4.810 
 
 23.140 
 
 111.318 
 
 535.488 
 
 2,575.940 
 
 
 . Values of 
 
 .070 
 
 9.130 
 
 4.623 
 
 3.141 
 
 2.418 
 
 1.999 
 
 1.729 
 
 .085 
 
 7.536 
 
 3.833 
 
 2.629 
 
 2.047 
 
 1.714 
 
 1.505 
 
 .100 
 
 6.420 
 
 3.287 
 
 2.280 
 
 1.795 
 
 1.525 
 
 1.358 
 
 .120 
 
 5.345 
 
 2.777 
 
 1.953 
 
 1.570 
 
 1.358 
 
 1.232 
 
 .130 
 
 4.968 
 
 2.584 
 
 1.832 
 
 1.485 
 
 1.298 
 
 1.189 
 
 .140 
 
 4.623 
 
 2.418 
 
 1.729 
 
 1.416 
 
 1.249 
 
 1.154 
 
 .150 
 
 4.322 
 
 2.280 
 
 1.643 
 
 1.358 
 
 1.209 
 
 1.126 
 
 .170 
 
 3.833 
 
 2.047 
 
 1.505 
 
 1.268 
 
 1.149 
 
 1.085 
 
 .200 
 
 3.287 
 
 1.795 
 
 1.358 
 
 1.176 
 
 1.090 
 
 1.047 
 
 .205 
 
 3.212 
 
 1.762 
 
 1.338 
 
 1.165 
 
 1.083 
 
 1.043 
 
 .235 
 
 2.831 
 
 1.592 
 
 1.245 
 
 1.110 
 
 1.051 
 
 1.024 
 
 .250 
 
 2.676 
 
 1.525 
 
 1.209 
 
 1.090 
 
 1.040 
 
 1.018 
 
 .265 
 
 2.539 
 
 1.467 
 
 1.179 
 
 1.072 
 
 1.032 
 
 1.014 
 
 .300 
 
 2.280 
 
 1.358 
 
 1.126 
 
 1.047 
 
 1.018 
 
 1.007 
 
 .350 
 
 2.000 
 
 1.249 
 
 1.077 
 
 1.025 
 
 1.008 
 
 1.003 
 
 .400 
 
 1.795 
 
 1.176 
 
 1.047 
 
 1.013 
 
 1.004 
 
 1.001 
 
 .410 
 
 1.765 
 
 1.164 
 
 1.043 
 
 1.012 
 
 1.003 
 
 1.001 
 
 .450 
 
 1.643 
 
 1.126 
 
 1.029 
 
 1.007 
 
 1.002 
 
 1.000 
 
 .495 
 
 1.538 
 
 1.093 
 
 1.019 
 
 1.004 
 
 1.001 
 
 1.000 
 
 .500 
 
 1.525 
 
 1.090 
 
 1.018 
 
 1.004 
 
 1.001 
 
 1.000 
 
266 
 
 POWER TRANSMISSION 
 
 For a given diameter of sheave, and a variable diameter of wire, a ratio 
 exists between these diameters corresponding to a maximum working tension. 
 This ratio results, approximately, in a working tension of one-third and a 
 bending stress of two-thirds of the maximum safe tension, which is from one- 
 third to two-fifths of the ultimate stress, and practically determines the mini- 
 mum diameter of sheave for any rope. The ratio for any size of wire varies 
 slightly, according to the number of wires composing the rope, and in terms 
 of rope diameter is, Steel Iron 
 
 For 7-wire rope 79.6 160.5 
 
 For 12-wire rope 59.3 120.0 
 
 For 19-wire rope 47.2 95.8 
 
 from which the following table is derived. 
 
 MINIMUM DIAMETERS OF SHEAVES 
 
 
 Steel Rope 
 
 Iron Rope 
 
 Diameter 
 of Rope 
 
 7-Wire 
 
 12-Wire 
 
 19-Wire 
 
 7-Wire 
 
 12-Wire 
 
 19-Wire 
 
 Inch 
 
 
 
 
 
 
 
 
 Diameter of Sheaves, in Inches 
 
 ! 
 
 20 
 
 15 
 
 12 
 
 40 
 
 30 
 
 24 
 
 JL 
 
 25 
 
 19 
 
 15 
 
 50 
 
 38 
 
 30 
 
 I 
 
 30 
 
 22 
 
 18 
 
 60 
 
 45 
 
 36 
 
 A 
 
 35 
 
 26 
 
 21 
 
 70 
 
 53 
 
 42 
 
 i 
 
 40 
 
 30 
 
 24 
 
 80 
 
 60 
 
 48 
 
 
 45 
 
 33 
 
 27 
 
 90 
 
 68 
 
 54 
 
 
 50 
 
 37 
 
 30 
 
 100 
 
 75 
 
 60 
 
 
 55 
 
 41 
 
 32 
 
 110 
 
 83 
 
 66 
 
 
 60 
 
 44 
 
 35 
 
 120 
 
 90 
 
 72 
 
 ; : 
 
 70 
 
 52 
 
 41 
 
 140 
 
 105 
 
 84 
 
 1 
 
 80 
 
 59 
 
 47 
 
 160 
 
 120 
 
 96 
 
 Sheaves. To decrease the bending stresses, the sheaves for wire-rope 
 transmissions are generally of as large diameter as is practicable to give the 
 required speed to the rope. Large sheaves are also advantageous because 
 with them the rope is run at a high velocity allowing of a lower tension, and 
 permitting a rope of smaller diameter to be used than would be possible with 
 smaller sheaves, provided, of course, that the span is of sufficient length to 
 give the necessary weight. 
 
 Sheaves are generally made of cast iron when not exceeding 12 ft. in diam- 
 eter; when larger than this, they are usually built up with wrought-iron arms. 
 Sheaves, upon which the rope is to make but a single half-turn, are made 
 with V-shaped grooves in their circumference. The bottom part of the groove 
 is widened to receive the filling, which consists of some substance to give a 
 bed for the rope to run on and protect it from wear, and to increase the friction 
 so that the rope will not slip. This filling is made of blocks of wood, rubber, 
 leather, or other material. Rubber and leather have been used separately, but 
 blocks of rubber separated by pieces of leather have been found to give the 
 best results. 
 
 Power Transmitted. The horsepower transmitted is equal to the resistance 
 overcome (the effective pull), in pounds, multiplied by the speed of the rope, 
 in feet per minute, and divided by 33,000 that is (formula from John A. Roeb- 
 ling s Sons Co.), TV 
 
 in which H^hprsepower transmitted; 
 
 T = difference in tension between driving and driven sides of rope; 
 
 V = speed of rope, in feet per minute. 
 
 When applying this formula, V is either given or assumed. T is equal to 
 the weight of the rope suspended between the sheaves multiplied by 3 (for the 
 proportion of deflection stated). 
 
POWER TRANSMISSION 
 
 267 
 
 To transmit a given horsepower, the speed of the rope may be increased 
 and the tension (effective pull) correspondingly decreased, and a smaller rope 
 may be used provided other considerations will allow it. 
 
 For determining the horsepower that can be transmitted over a given 
 transmission, the following formula is given by the Trenton Iron Co.: 
 
 H = (cd*-. 000006 (W+g'+g")]s 
 in which H = horsepower that can be transmitted; 
 
 c = constant, depending on material of rope, falling in grooves of 
 sheaves, and number of half laps about sheaves or drums at 
 either end of line; 
 d = diameter of rope, in inches; 
 W = weight of rope, in pounds; 
 g' = weight of terminal sheaves and shafts; 
 g" = weight of intermediate sheaves and shafts. 
 The accompanying table gives the value of c for ropes on different materials. 
 
 TABLE OF CONSTANTS FOR ROPES ON DIFFERENT MATERIALS 
 
 c = for 
 Steel Rope on 
 
 Number of Half Laps About Sheaves or Drums at 
 Either End of Line 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 Value of c 
 
 Iron 
 
 5.61 
 
 6.70 
 9.29 
 
 8.81 
 9.93 
 11.95 
 
 10.62 
 11.51 
 12.70 
 
 11.65 
 12.26 
 12.91 
 
 12.16 
 12.66 
 12.97 
 
 12.56 
 12.83 
 13.00 
 
 Wood 
 
 Rubber and leather 
 
 The values of c for iron rope are one-half of those given. It is evident from 
 these figures that when more than three laps are made it is immaterial what 
 the surface is on which the rope tracks, as far as frictional adhesion is concerned. 
 
 From the foregoing formula, assuming the sheaves to be of equal diameter, 
 and of a size not less than the minimum diameter given in the table, it is pos- 
 sible to find the horsepower that may be transmitted by a steel rope, as is shown 
 in the accompanying table. 
 
 HORSEPOWER THAT MAY BE TRANSMITTED BY A STEEL ROPE 
 MAKING A SINGLE LAP ON WOOD-FILLED SHEAVES 
 
 Velocity of Rope, in Feet per Second 
 
 Diameter 
 
 
 
 
 
 
 
 
 
 
 
 of Rope 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 Inch 
 
 
 
 
 
 
 
 
 
 
 
 
 Horsepower That May Be Transmitted 
 
 1 
 
 4 
 7 
 10 
 
 8 
 13 
 19 
 
 13 
 20 
 
 28 
 
 17 
 26 
 38 
 
 21 
 33 
 
 47 
 
 25 
 
 40 
 56 
 
 28 
 44 
 64 
 
 32 
 51 
 73 
 
 37 
 57 
 80 
 
 40 
 62 
 89 
 
 A 
 
 13 
 
 26 
 
 38 
 
 51 
 
 63 
 
 75 
 
 88 
 
 99 
 
 109 
 
 121 
 
 |- 
 
 17 
 
 34 
 
 51 
 
 67 
 
 83 
 
 99 
 
 115 
 
 130 
 
 144 
 
 159 
 
 
 22 
 
 43 
 
 65 
 
 86 
 
 106 
 
 128 
 
 147 
 
 167 
 
 184 
 
 203 
 
 ? 
 
 27 
 
 53 
 
 79 
 
 104 
 
 130 
 
 155 
 
 179 
 
 203 
 
 225 
 
 247 
 
 If 
 
 32 
 
 63 
 
 95 
 
 126 
 
 157 
 
 186 
 
 217 
 
 245 
 
 
 
 a. 
 
 38 
 
 76 
 
 103 
 
 150 
 
 186 
 
 223 
 
 
 
 
 
 I 
 
 52 
 
 104 
 
 156 
 
 206 
 
 
 
 
 
 
 
 1 
 
 68 
 
 135 
 
 202 
 
 
 
 
 
 
 
 
268 POWER TRANSMISSION 
 
 The horsepower that may be transmitted by iron ropes is one-half of the 
 above. 
 
 The table gives the maximum amount of power capable of being trans- 
 mitted under the conditions stated, so that when using wood-lined sheaves, 
 it is well to make some allowance for the stretching of the rope, and to advocate 
 somewhat heavier equipments than the table would give; that is, if it is 
 desired to transmit 20 H. P., for instance, to put in a plant that would transmit 
 25 to 30 H.P., thus avoiding the necessity of having to take up a comparatively 
 small amount of stretch; On rubber and leather filling, however, the amount 
 of power capable of being transmitted is considerably greater than on wood, so 
 that this filling is generally used; and in this case no allowance need be made 
 for stretch, as such sheaves will likely transmit the power given by the table, 
 under all possible deflections of the rope. 
 
 The transmission of more than 250 H. P. is impracticable with filled sheaves, 
 because the tension is so great that the filling will quickly cut out, and the 
 frictional adhesion on a metallic surface is insufficient where the rope makes but 
 a single lap, or a half lap at either end of the line. 
 
 TRANSMISSION BY HEMP ROPE 
 
 There is a growing tendency toward the substitution of hemp and cotton 
 ropes for belting and line shafting as a means of transmitting power in large 
 factories and shops. The advantages claimed for the rope-driving system are: 
 (1) Economy; for a rope system is cheaper to install than either leather 
 belting or shafting. (2) In the rope system, there is less loss of power by 
 slipping. (3) Flexibility; that is, the ease with which the power is trans- 
 mitted to any distance and in any direction. 
 
 In the United States, a single rope is carried round the pulley as many 
 times as is necessary to produce the required power, and the necessary tension 
 is obtained by passing the rope round a tension pulley weighted to give the 
 desired tension. The ropes used in rope transmission are either of hemp, 
 manila, or cotton; manila ropes are mostly used in the United States. They 
 are of three strands, hawser laid, and may be from \ in. to 2 in. in diameter. 
 
 The weight of ordinary manila or cotton rope is about .3 D z Ib. per ft. of 
 length, where D = diameter of rope, in inches. Letting w = weight per foot of 
 length, w = .3 D 2 . The breaking strength of the rope varies from 7,000 to 
 12,000 Ib. per sq. in. of cross-section. The average value may be taken as 
 7,000 D 2 , when D is the diameter of rope. 
 
 For a continuous transmission, it has been determined by experiment that 
 the best results are obtained when the tension in the driving side of the rope is 
 about & of the breaking strength. That is, 
 
 Ti = tension in tight side = __ = 200 D 
 
 oO 
 
 The ropes run in V-shaped grooves, and the coefficient of friction is, of course, 
 greater than on a smooth surface. The coefficient for grooves with sides at an 
 angle of 45 may be taken at from .25 to .33. 
 
 The horsepower that can be transmitted by a single rope running under 
 favorable conditions is given by the formula 
 
 in which 
 
 H = horsepower transmitted ; 
 D = diameter of rope, in inches ; 
 
 v = velocity of rope, in feet per second. 
 
 The maximum power is obtained at a speed of about 84 ft. per sec. For 
 higher velocities, the centrifugal force becomes so great that the power is 
 decreased, and when the speed reaches 145 ft. per sec. the centrifugal force just 
 balances the tension, so that no power at all is transmitted. Consequently, 
 a rope should not run faster than about 5,000 ft. per min., and it is preferable on 
 the score of durability to limit the velocity to 3,500 ft. per min. 
 
 EXAMPLE. A rope flywheel is 26 ft. in diameter, and makes 55 rev. per min. 
 The wheel is grooved for 35 turns of 1| in. rope. What horsepower may be 
 transmitted? 
 
 SOLUTION. Velocity, in feet per second is 
 
POWER TRANSMISSION 
 
 269 
 
 Applying the formula H = ~~(20Q fnw7) the horsepower transmitted 
 by one rope or turn is 
 
 74.9X(1*)2 S 
 
 825 
 
 Then, 30.16X35 = 1,055.6 H. P. transmitted by the 35 ropes. 
 EXAMPLE. How many times should a 1-in. rope be wrapped around a 
 grooved wheel in order to transmit 200 H. P., the speed being 3,500 ft. per min.? 
 SOLUTION. 3,500 ft. per min. = 3,500 H- 60 = 58i ft. per sec. Applying the 
 formula, the horsepower transmitted with one turn is, 
 
 Hence, 200-^-11.9 = 16.8, say 17 turns. 
 
 Rope pulleys differ from belt pulleys only in their rims. The inclination of 
 the sides of the grooves may vary from 30 to 60. The more acute the angle, 
 the greater the coefficient and, consequently, the wear on the rope. 
 
 The long radius R is determined by drawing a line through the center of the 
 rope at an angle of 22*, with the horizontal, and producing it until it intersects 
 a line drawn through the tops of the ribs dividing the grooves, then, with this 
 point of intersection as a center, drawing the curve forming the side of the 
 groove tangent to the circumference of the rope. The advantage claimed for 
 this groove is that the rope will turn more freely in it, thus presenting new 
 sets of fibers to the sides of the grooves and increasing the life of the rope. 
 
 The diameter of a rope pulley should be at least 30 times the diameter of the 
 rope. Good results are obtained when the diameters of pulleys and idlers on the 
 driving side are 40 times, and those on the driven side 30 times, the rope 
 diameter. Idlers used simply to support a long span may have diameters 
 as small as 18 rope diameters, without injuring the rope. 
 
 When possible, the lower side of the rope should be the driving side, for in 
 that case the rope embraces a greater portion of the circumference of the pulley, 
 and increases the arc of contact. 
 
 When the continuous system of rope transmission is used, the tension 
 pulley should act on as large an amount of rope as possible. It is good practice 
 to use a tension pulley and carriage for every 1 ,200 ft. of rope, and have at least 
 10% of the rope subjected directly to the tension. 
 
 Aside from the grooved rim, rope pulleys are constructed the same as other 
 pulleys. They may be cast solid, in halves, or in sections. The pulley grooves 
 must be turned to exactly the same diameter; otherwise, the rope will 
 be severely strained. 
 
 HORSEPOWER OF MANILA ROPES 
 
 (Link-Belt Engineering Co.) 
 
 am. of Rope 
 Inches 
 
 ill 
 
 * 
 
 Breaking 
 Strain 
 Pounds 
 
 Working 
 Strain 
 Pounds 
 
 1,000 Ft. 
 per Min. 
 
 2,000 Ft. 
 per Min. 
 
 3, 000 Ft. 
 
 per Min. 
 
 4,000 Ft. 
 
 per Min. 
 
 5,000 Ft. 
 per Min. 
 
 CM 
 
 %f 
 
 CM 
 
 %f 
 
 CM 
 
 %f 
 
 ri 
 
 3^ 
 
 CM 
 
 %^ 
 
 & 
 
 
 
 
 a 
 
 > 
 
 8 
 
 > 
 
 a 
 
 &> 
 
 a 
 
 > 
 
 a 
 
 H> 
 
 . 
 
 .15 
 
 4,000 
 
 121 
 
 2* 
 
 90 
 
 4* 
 
 90 
 
 . 
 
 80 
 
 7* 
 
 80 
 
 8* 
 
 70 
 
 1 
 
 .18 
 
 5,000 
 
 151 
 
 al 
 
 110 
 
 5* 
 
 110 
 
 71 
 
 100 
 
 9? 
 
 100 
 
 10? 
 
 90 
 
 1 
 
 .27 
 
 7,500 
 
 227 
 
 4* 
 
 170 
 
 8* 
 
 170 
 
 11? 
 
 160 
 
 14* 
 
 150 
 
 16 
 
 130 
 
 1 
 
 .33 
 
 9,000 
 
 272 
 
 5 
 
 200 
 
 10 
 
 200 
 
 14 
 
 180 
 
 17* 
 
 170 
 
 19 
 
 150 
 
 T 
 
 
 .45 
 
 12,250 
 
 371 
 
 7 
 
 280 
 
 13* 
 
 270 
 
 19 
 
 250 
 
 23* 
 
 230 
 
 26 
 
 210 
 
 1 
 
 
 .50 
 
 14,000 
 
 424 
 
 8 
 
 320 
 
 15* 
 
 310 
 
 22 
 
 290 
 
 27 
 
 270 
 
 29 
 
 240 
 
 1 
 
 
 .65 
 
 18,062 
 
 547 
 
 10* 
 
 410 
 
 20 
 
 400 
 
 28* 
 
 370 
 
 34? 
 
 350 
 
 38 
 
 310 
 
 
 
 .73 
 
 20,250 
 
 613 
 
 11* 
 
 460 
 
 22 
 
 440 
 
 314 
 
 420 
 
 39 
 
 390 
 
 43 
 
 350 
 
 1 
 
 
 .82 
 
 25,000 
 
 760 
 
 
 570 
 
 27? 
 
 550 
 
 39* 
 
 520 
 
 49 
 
 490 
 
 55 
 
 448 
 
 1 
 
 
 1.08 
 
 30,250 
 
 916 
 
 17 
 
 680 
 
 33* 
 
 660 
 
 47* 
 
 630 
 
 58* 
 
 580 
 
 64 
 
 520 
 
 2 
 
 1.27 
 
 36,000 
 
 1,000 
 
 20| 
 
 810 
 
 40 
 
 790 
 
 
 740 
 
 69* 
 
 670 
 
 77 
 
 620 
 
 
 
 1 1 
 
 
 
 I 
 
 
 
 
 
 
270 
 
 POWER TRANSMISSION 
 
 LINE SHAFTING 
 
 Shafting is usually made cylindrically true, either by a special rolling 
 process, when it is known as cold-rolled shafting, or it is turned up in a machine 
 called a lathe. In the latter case, it is called bright shafting. What is known as 
 black shafting is simply bar iron rolled by the ordinary process and turned where 
 it receives the couplings, pulleys, bearings, etc. 
 
 Bright turned shafting varies in diameter by in. up to about 3$ in.; above 
 this the diameter of the shafting varies by in. The actual diameter of 
 a bright shaft is in. 
 
 less than the com- 
 mercial diameter, it 
 being designated from 
 the diameter of the 
 ordinary round bar 
 iron from which it is 
 turned. Thus, a 
 length of what is 
 called 3-in. bright 
 shafting is only 2}f 
 in. in diameter. Cold- 
 rolled shafting is de- 
 signated by its com- 
 mercial diameter; 
 thus, a length of 
 
 CONSTANTS FOR LINE SHAFTING 
 
 Material of Shaft 
 
 No 
 Pulleys 
 Between 
 Bearings 
 
 With 
 Pulleys 
 Between 
 Bearings 
 
 Steel or cold-rolled iron. 
 Wrought iron 
 
 65 
 70 
 90 
 
 85 
 95 
 120 
 
 
 
 
 Cold-rolled iron is considerably stronger than ordinary turned wrought 
 iron, the increased strength being due to the process of rolling, which seems 
 to compress the metal and so make it denser not merely skin deep, but 
 practically throughout the whole diameter. 
 Let D = diameter of shaft ; 
 
 R = revolutions per minute; 
 H = horsepower transmitted; 
 C = constant given in table. 
 
 In the above table the bearings are supposed to be spaced so as to 
 relieve the_shaft of excessive bending; also, in the third vertical column, 
 
 an average number and weight 
 
 MAXIMUM DISTANCE BETWEEN of pulleys and power given off is 
 BEARINGS assumed. 
 
 When determining these con- 
 stants allowance was made to 
 insure the stiffness as well as 
 strength of the shaft. 
 , D3R 
 
 Distance Between Bearings 
 
 Shafts are subject to forces 
 that produce stresses of two 
 kinds transverse and torsiqnal. 
 When the machines to be driven 
 are below the shaft, there is a 
 transverse stress on the shaft, 
 due to the weight of the shaft 
 itself, of the pulley and the ten- 
 sion of the belt. Sometimes, the 
 power is taken off horizontally on 
 one side, in which case the tension 
 of the belt produces a horizontal 
 transverse stress, while the weight 
 of the pulley acts with the weight 
 of the shaft to produce a vertical transverse stress. When the machinery to be 
 driven is placed on the floor above the shaft, the tension of the belt produces 
 a transverse stress in an opposite direction to that due to the weight of the 
 shaft and pulley. 
 
 The torsional strength of shafts, or their resistance to breaking by twisting, 
 is proportional to the cube of their diameter. Their stiffness or resistance to 
 bending is proportional to the fourth power of their diameters, and inversely 
 
 Diameter 
 
 Jbeet 
 
 of Shaft 
 
 
 Inches 
 
 Wrought-Iron 
 Shaft 
 
 Steel Shaft 
 
 2 
 
 11 
 
 11.50 
 
 3 
 
 13 
 
 13.75 
 
 4 
 
 15 
 
 15.75 
 
 5 
 
 17 
 
 18.25 
 
 6 
 
 19 
 
 20.00 
 
 7 
 
 21 
 
 22.25 
 
 8 
 
 23 
 
 24.00 
 
 9 
 
 25 
 
 26.00 
 
POWER TRANSMISSION 
 
 271 
 
 proportional to the cube of the lengths of their spans. No simple general 
 formula can be given that will safely apply to engine and other shafting that 
 is subjected to the bending stresses produced by overhung cranks, the weight 
 of heavy flywheels, the pull of large belts, or to severe shocks produced by the 
 intermittent action of the power or load. The calculations for such shafts 
 should always be based on the special conditions involved. 
 
 In the preceding table are given the maximum distances between the bear- 
 ings of some continuous shafts that are used for the transmission of power. 
 Pulleys from which considerable power is to be taken should always be placed 
 as close to a bearing as possible. 
 
 The diameters of the different lengths of shafts composing a line of shaft- 
 ing may be proportional to the quantity of power delivered by each respective 
 length. In this connection, the positions of the various pulleys depend on 
 the distance between the pulley and the bearing, and on the amount of power 
 given off by the pulleys. Suppose, for example, that a piece of shaft- 
 ing delivers a certain amount of power; then, the shaft will deflect or bend 
 less if the pulley transmitting that power is placed close to a hanger or bear- 
 ing, than if it is placed midway between the two hangers or bearings. It is 
 impossible to give any rule for the proper distance of bearings that could be 
 used universally, as in some cases the requirements demand that the bear- 
 ings be nearer together than in others. If the work done by a line of shafting 
 is distributed quite equally along its entire length, and the power can be 
 applied near the middle, the strength of the shaft need be only one-half as great 
 as when the power is applied at one end of the shaft. 
 
 HORSEPOWER SHAFTING WILL TRANSMIT 
 
 
 Revolutions per Minute 
 
 Diame- 
 
 
 ter 
 
 
 
 
 
 
 
 
 
 
 
 of 
 
 100 
 
 125 
 
 150 
 
 175 
 
 200 
 
 225 
 
 250 
 
 300 
 
 350 
 
 400 
 
 Shaft 
 
 
 
 
 
 
 
 
 
 
 
 Inches 
 
 
 
 Horsepower Transmitted 
 
 
 1.2 
 
 1.4 
 
 1.7 
 
 2.1 
 
 2.4 
 
 2.6 
 
 3.1 
 
 3.6 
 
 4.3 
 
 5.0 
 
 1-? 
 
 2.4 
 
 3.1 
 
 3.7 
 
 4.3 
 
 4.9 
 
 5.5 
 
 6.1 
 
 7.3 
 
 8.5 
 
 9.7 
 
 1 
 
 4.3 
 
 5.3 
 
 6.4 
 
 7.4 
 
 8.5 
 
 9.5 
 
 10.5 
 
 12.7 
 
 14.8 
 
 16.9 
 
 iS 
 
 6.7 
 
 8.4 
 
 10.1 
 
 11.7 
 
 13.4 
 
 15.1 
 
 16.7 
 
 20.1 
 
 23.4 
 
 26.8 
 
 1 
 
 10.0 
 
 12.5 
 
 15.0 
 
 17.5 
 
 20.0 
 
 22.5 
 
 25.0 
 
 30.0 
 
 35.0 
 
 40.0 
 
 2? 
 
 14.3 
 
 17.8 
 
 21.4 
 
 24.9 
 
 28.5 
 
 32.1 
 
 35.6 
 
 42.7 
 
 49.8 
 
 57.0 
 
 2 
 
 19.5 
 
 24.4 
 
 29.3 
 
 34.1 
 
 39.0 
 
 44.1 
 
 48.7 
 
 58.5 
 
 68.2 
 
 78.0 
 
 2^* 
 
 26.0 
 
 32.5 
 
 39.0 
 
 43.5 
 
 52.0 
 
 58.5 
 
 65.0 
 
 78.0 
 
 87.0 
 
 104.0 
 
 015 
 
 33.8 
 
 42.2 
 
 50.6 
 
 59.1 
 
 67.5 
 
 75.9 
 
 84.4 
 
 101.3 
 
 118.2 
 
 135.0 
 
 3-*- 
 
 43.0 
 
 53.6 
 
 64.4 
 
 75.1 
 
 85.8 
 
 95.6 
 
 107.3 
 
 128.7 
 
 150.3 
 
 171.6 
 
 3" 
 
 53.6 
 
 67.0 
 
 79.4 
 
 93.8 
 
 107.2 
 
 120.1 
 
 134.0 
 
 158.8 
 
 187.6 
 
 214.4 
 
 3H 
 
 65.9 
 
 82.4 
 
 97.9 
 
 115.4 
 
 121.8 
 
 148.3 
 
 164.8 
 
 195.7 
 
 230.7 
 
 243.6 
 
 015 
 
 80.0 
 
 100.0 
 
 120.0 
 
 140.0 
 
 160.0 
 
 180.0 
 
 200.0 
 
 240.0 
 
 280.0 
 
 320.0 
 
 4-4 
 
 113.9 
 
 142.4 
 
 170.8 
 
 199.3 
 
 227.8 
 
 256.2 
 
 284.7 
 
 341.7 
 
 398.6 
 
 455.6 
 
 4M 
 
 156.3 
 
 195.3 
 
 234.4 
 
 273.4 
 
 312.5 
 
 351.5 
 
 390.6 
 
 468.7 
 
 546.8 
 
 625.0 
 
 BELT PULLEYS 
 
 Solid and Split Pulleys. Besides being used with ropes or chains for the 
 hoisting of loads, pulleys are extensively employed with belts for transmitting 
 power. Belt pulleys may be divided into two classes, namely, solid pulleys and 
 split pulleys. A solid pulley is one in which the arms, hub, and rim are cast m 
 one solid piece. A split pulley is one that is cast in halves that are afterwards 
 bolted together; the latter style of pulley is more readily placed on or removed 
 from a shaft than is the solid pulley. Pulleys are generally cast in halves or 
 parts when they are more than 6 ft. in diameter. This is done on account of 
 the shrinkage strains in large pulley castings, which render the pulleys liable 
 to crack as a result of unequal cooling of the metal. 
 
272 POWER TRANSMISSION 
 
 Wooden Pulleys. Although most belt pulleys are made of cast iron, 
 wrought iron, and steel, wooden pulleys have come into extensive use. These 
 are built of segments of wood, usually maple, securely glued together. It is 
 possible to procure wooden split pulleys that are fitted with removable bushings, 
 thus allowing the same pulley to be adapted readily to shafting of different 
 diameters. Wooden pulleys are somewhat lighter than cast-iron pulleys for 
 the same service. 
 
 Driving and Driven Pulleys. The pulley that imparts motion to the belt 
 is called the driving pulley, or the driver, and the one that receives motion 
 from the belt is called the driven pulley, or simply the driven. When two 
 pulleys are connected by a belt, the speeds at which the pulleys run are 
 inversely proportional to their diameters. Thus, if two pulleys have diameters 
 of 12 in. and 24 in., the speed of the smaller is to the speed of the larger as 24 to 
 12, or as 2 to 1. The speed of a pulley or of a shaft is usually stated in revo- 
 lutions per minute, abbreviated rev. per min. or R. P. M. 
 
 Diameter and Speed of Driver. It often becomes necessary to calculate 
 the size or the speed of a pulley that drives or is being driven by a machine. 
 
 Let D = diameter of driving pulley, in inches; 
 
 d = diameter of driven pulley, in inches; 
 N = number of rev. per min. of driving pulley; 
 n = number of rev. per min. of driven pulley. 
 
 Then, if the diameter of the driven and the required speeds of both pulleys 
 are given, the diameter of the driver may be found by the formula 
 
 If the speed of the driver is to be found, it is necessary to use the formula 
 
 -5 (2 > 
 
 EXAMPLE. A 12-in. pulley on a certain machine is to run at 160 rev. per 
 min. and is to be driven by belt from a pulley on the shaft of an engine that 
 make 96 rev. per min. What must be the diameter of the pulley on the engine 
 shaft? 
 
 SOLUTION. Substituting in formula 1, 
 
 Diameter and Speed of Driven. If the diameter of the driving pulley 
 and the desired speeds of both pulleys are known, the required diameter of the 
 driven pulley may be found by the formula , 
 
 , I . 
 
 If the speed of the driven pulley is to be found, it is necessary to use the 
 formula 
 
 =T <*> 
 
 EXAMPLE 1. A 30-in. pulley on a line shaft running at 120 rev. per min. 
 is to drive a pulley on a machine at 300 rev. per min. What must be the 
 diameter of the pulley on the machine? 
 
 SOLUTION. Substituting in formula 1, 
 
 EXAMPLE 2. A driving pulley 48 in. in diameter makes 175 rev. per min. 
 andjs connected by belt to a driven pulley 14 in. in diameter. What is the 
 speed of the driven pulley? 
 
 SOLUTION. Substituting in formula 2, 
 n = 48)075 
 
 BELTING 
 
 A belt is a flexible band by which motion is transmitted from one pulley to 
 another. The materials most commonly used for belts are leather, cotton, and 
 rubber, although thin, flat bands of steel are coming into use. Leather belts 
 are usually made either single or double. A single belt is one composed of a 
 single thickness of leather, and a double belt is one composed of two thicknesses 
 
POWER TRANSMISSION 273 
 
 of leather cemented and riveted together throughout the whole length of the 
 belt. Still heavier belts, consisting of three or four thicknesses of leather, and 
 known as triple or quadruple belts, are sometimes made for heavy drives. Cotton 
 belts are made up of a number of layers, or plies, sewed together and treated 
 with a water-proofing substance. They are termed two-ply, three-ply, etc., 
 according to the number of plies they contain. Four-ply cotton belting is 
 usually considered equal to single leather belting. Rubber belts are par- 
 ticularly adapted for use in damp or wet places. They withstand changes of 
 temperature without injury, are durable, and are said to be less liable to slip 
 than are leather belts. 
 
 Sag of Belts. The distance between pulley centers depends on the size of 
 the pulleys and of the belt; it should be great enough so that the belt will run 
 with a slight sag and a gently undulating motion, but not great enough to cause 
 excessive sag and an unsteady flapping motion of the belt. In general, the 
 centers of small pulleys carrying light narrow belts should be about 15 ft. apart 
 and the belt sag 1^ to 2 in.; for large pulleys and heavy belts the distance 
 should be 20 to 30 ft. and the sag 2 to 5 in. Loose-running belts will last 
 much longer than tight ones, and will be less likely to cause heating and wear 
 of bearings. 
 
 Speed of Belts. The higher the speed of a belt, the less may be its width 
 to transmit a given horsepower; consequently, a belt should be run at as high 
 a speed as conditions will permit. The greatest allowable speed for a belt 
 joined by lacing is about 3,500 ft., per min. for ordinary single and double 
 leather belts. For belts joined by cementing, when the joint has about the 
 same strength as the solid belt, the velocity may be as high as 5,000 ft. per 
 min. Higher speeds than these have been used, but there is little to be gained 
 by exceeding about 4,800 ft. per min. In choosing a proper belt speed, due 
 regard must be paid to commercial conditions. Although a high speed of the 
 belt means a narrow and cheaper belt, the increased cost of the larger pulleys 
 that may be required may offset the gain due to the high speed of the belt, 
 at least so far as the first cost is concerned. The speed of a belt, in feet per 
 minute, may be found by multiplying the number of revolutions per minute 
 of the pulley by 3.1416 times the diameter of the pulley, in inches, and 
 dividing the product by 12. 
 
 Horsepower of Belts. The pull on a belt is greatest on the tight, or driving, 
 side, and least on the slack side. The difference between the tensions, or pulls, 
 in these two sides is called the effective pull. The effective pull that may be 
 allowed per inch of width for single leather belts with different arcs of contact 
 is given in the accompanying table. The arc of contact is the portion of the cir- 
 cumference of the smaller pulley that is covered by the belt. The horsepower 
 that can be transmitted by a single leather belt may be found by the formula 
 
 in which H = horsepower of belt; 
 
 C effective pull, taken from table; 
 
 W = width of belt, in inches; 
 
 V = speed of belt, in feet per minute. 
 
 If it is desired to find the width of single belt required to transmit a given 
 horsepower, the formula becomes 
 
 W-SMgS (2) 
 
 EXAMPLE 1. What horsepower can be transmitted by a single leather belt 
 4 in. wide running at a speed of 2,500 ft. per min., if the belt covers one-third of 
 the circumference of the small pulley? 
 
 SOLUTION. The fraction of the circumference covered by the belt is = .333. 
 From the table, the allowable effective pull corresponding to this value is 28.8. 
 Substituting in formula 1, 
 
 28.8X4X2,500 
 
 33.000 --- 8 ' 7H - P - 
 
 EXAMPLE 2. A single leather belt is to run at a speed of 3,000 ft., per min. 
 and is to transmit 18 H. P. Find the width of the belt, if the arc of contact is 
 150. 
 
 SOLUTION. The effective pull corresponding to an arc of contact of 150, 
 from the table, is 33.8. Substituting in formula 2, 
 
 , 33,000X18 
 Ty = 3 
 A 6-in. belt would be used. 
 
274 
 
 POWER TRANSMISSION 
 ALLOWABLE EFFECTIVE PULL 
 
 Arc of Contact 
 
 Allowable 
 Effective Pull 
 Pounds per 
 Inch of Width 
 
 Degrees 
 
 Fraction of 
 Circumference 
 
 90 
 
 112* 
 
 120 
 135 
 150 
 157| 
 180 or over 
 
 .250 
 .312 
 .333 
 .375 
 .417 
 .437 
 .500 or over 
 
 23.0 
 27.4 
 28.8 
 31.3 
 33.8 
 34.9 
 38.1 
 
 The horsepower of a double leather belt may be taken as If times that of a 
 single leather belt of the same width running under the same conditions. 
 Accordingly, the width of a double leather belt required for any service is only 
 & that of a single belt for the same service. 
 
 Lacing of Belts. A very satisfactory way of lacing belts less than 3 in. 
 wide is shown in Fig. 1, in which A is the outside of the belt and B is the side 
 that runs against the face of the pulley. The ends of 
 the belt are first cut square, and then holes are punched 
 in the ends, in corresponding positions opposite one 
 another. The number of holes in each row should 
 always be odd, in the style of lacing shown, using three 
 holes in belts up to 2 in. wide and five holes in belts 
 between 2 and 3 in. wide. The lacing is first drawn 
 through one of the middle holes from the under side, 
 or pulley side, as at 1. Then it is drawn across the 
 upper side and is passed down through 2, across under 
 the belt to 3, up through S, across and down again FIG. 1 
 
 through 2, back under the belt and up through 3 again, 
 
 then across and down through 4 and finally up through 6, where a barb is 
 cut in the edge of the lacing to prevent it from pulling out. This completes the 
 lacing of one half. The other end of the lacing is then carried through the 
 holes in the other half, in the same order. 
 
 For belts wider than 3 in., the lacing shown in Fig. 2 may be used. In 
 this case, there are two rows of holes in each end of the belt to be joined. 
 The row nearer the end of the belt should have one more hole than the row far- 
 ther away. For belts up to 4 4- in. wide use three holes in the first row and two 
 holes in the second row. For belts up to 6 in. wide, use four and three holes, 
 respectively. For wider belts, make the total number of holes in both rows 
 either one or two more than the number of inches of 
 width of the belt, the object being to get an odd total 
 number of holes. For example, a 10-in. belt should 
 have eleven holes, and a 13-in. belt should have fifteen 
 holes. The outside holes of the first row should not 
 be nearer the side edges of the belt than f in. and not 
 nearer the joint edge than | in. The second row should 
 be at least If in. from the joint edge. In Fig. 2, A is 
 the outside face and B the face next the pulley. The 
 lacing is first drawn up through 1 from the pulley side, 
 and then is carried through 2, 3, 4, 5, 6, 7, 6, 7, 4, 5, 2, 
 S, 8, and out at 9 to be fastened. The other end of the 
 lacing is used on the other half of the belt in the same 
 way. 
 
 Care and Use of Belts. It is a much disputed question as to which side of a 
 leather belt should be run next to the pulley. The more common practice, it 
 is believed, is to run the belt with the hair, or grain, side nearest the pulley. 
 This side is harder and more liable to crack than the flesh side; by running it 
 on the inside, the tendency is to cramp or compress it as it passes over the 
 pulley, while, if it ran on the outside, the tendency would be for it to stretch 
 
PROPERTIES OF MATERIALS 275 
 
 and crack. The flesh side is the tougher side, but for the reason just given the 
 life of the belt will be longer if the wear comes on the grain side. The lower 
 side of the belt should be the driving side, the slack side running from the 
 top of the driving pulley. The sag of the belt will then cause it to encompass 
 a greater length of the circumference. Long belts, running in any other direc- 
 tion than vertical, work better than short ones, as their weight holds them more 
 firmly to their work. 
 
 It is bad practice to use rosin to prevent slipping. Rosin gums the belt, 
 causes it to crack, and prevents slipping for only a short time. If a belt in good 
 condition persists in slipping, a wider belt should be used. Sometimes, larger 
 pulleys on the driving and driven shafts are of advantage, as they increase the 
 belt speed and reduce the stress on the belt. Belts may be kept soft and 
 pliable by being oiled once a month with castor oil or neat's-foot oil. 
 
 When rubber belts are used, animal oils or animal grease should never be 
 used on them. If the belt should slip, it may be lightly moistened on the side 
 nearest the pulley with boiled linseed oil. 
 
 Flapping of Belts. One of the most annoying troubles experienced with 
 belting of all kinds is the violent napping of the slack side. Flapping may be 
 due to one or both of the pulleys running out of true, causing the belt to be 
 alternately stretched and released. This will usually cause a belt to flap 
 when running at a high speed. If the belt is rather slack, tightening it may 
 lessen or stop the flapping. Another frequent cause of the flapping of a belt is 
 the want of alinement of the pulleys. To remedy this, the pulleys should be 
 brought in line; should this fail, the belt should be tightened if it is rather 
 loose. If no improvement is noticed and it is not possible to turn the pulleys, 
 the belt speed should be reduced a little, either by the substitution of smaller 
 pulleys or by changing the speed of the driving shaft, according to circum- 
 stances. 
 
 With belts running at speeds above 4,000 ft. per min., flapping may occur 
 when the pulleys are perfectly true and in line with each other, even when the 
 belt has the proper tension. This is believed to be due to air becoming 
 entrapped between the face of the p ulley and the belt; in this case the trouble 
 may be prevented by perforating the belt with a series of small holes. 
 Perforated belts may now be bought in the market. 
 
 Another cause of flapping is that the distance between the pulleys may be 
 too great. In general, the distance between the pulleys should not exceed 
 15 ft. for belts up to 4 in. wide; 20 ft. for belts from 4 to 12 in.; 25 ft., from 
 12 to 18 in.; and 30 ft., f9r wider belts. A belt that is not joined square will 
 flap, especially when running at a rather high speed. 
 
 SPECIFIC GRAVITY, WEIGHT, AND OTHER 
 PROPERTIES OF MATERIALS 
 
 DEFINITIONS 
 
 The specific gravity of a body is the ratio of its weight to the weight of 
 an equal bulk of pure water, at a standard temperature (62 F. = 16.670 C.). 
 Some experimenters have used 60 F. as the standard temperature, others 
 32 and still others, 39.1. To reduce a specific gravity, referred to water 
 at 39.1 F., to the standard of water at 62 F., multiply by 1.00112. 
 
 Rule I. Given the specific gravity referred to water at 62 F., multiply by 
 62.355 to find the weight of 1 cu. ft. of the substance. 
 
 Rule II. Given weight per cubic foot, to find specific gravity, multiply by 
 .016037. 
 
 Rule III. Given specific gravity, to find the weight per cubic inch, multiply by 
 .036085. 
 
 To Find the Specific Gravity of a Solid Heavier Than Water. Weigh the 
 body both in air and in water, and divide the weight in air by the difference of 
 the weights in air and water. 
 
 EXAMPLE. If a piece of coal weighs 480 gr. in air and weighs 82 gr. in 
 water, what is its specific gravity? 
 
 SOLUTION. As 480 82 = 398, or loss of weight in water. Then 480 -i- 
 398 = 1.206, the specific gravity of coal. 
 
276 
 
 PROPERTIES OF MATERIALS 
 
 To Find the Specific Gravity of a Solid Lighter Than Water. Attach to it 
 another body heavy enough to sink it; weigh severally the compound mass 
 and the heavier body in water, divide the weight of the body in air by the 
 weight of the body in air plus the weight of the sinker in water minus the 
 combined weight of the sinker and body in water. 
 
 To Find the Specific Gravity of a Fluid. Weigh both in and out of the fluid 
 a solid (insoluble) of known specific gravity, and divide the product of the 
 weight lost in the fluid and the specific gravity of the solid by the weight of 
 the solid. 
 
 The weight of 1 cu. ft. of water at a temperature of 62 is about 1,000 
 oz. avoir., and the specific gravity of a body, multiplied by 1,000, shows the 
 weight of 1 cu. ft. of that body in ounces avoirdupois. Then, if the magnitude 
 of the body is known, its weight can be computed; or, if its weight is known, 
 its magnitude can be calculated, provided its specific gravity is known; or, of the 
 magnitude, weight, and specific gravity, any two being known, the third may 
 be found. 
 
 To Find the Weight of a Body, in Ounces, From Its Magnitude. Multiply 
 the magnitude of the body in cu. ft., by the specific gravity of the substance 
 multiplied by 1,000. 
 
 To Find the Magnitude of a Body, in Cubic Feet, From Its Weight. Divide 
 the weight of the body in ounces by 1,000 times the specific gravity of the body. 
 
 NOTE. The specific gravity of any substance is equal to its weight in 
 grams per cubic centimeter. 
 
 SPECIFIC GRAVITY OF COMMON SUBSTANCES 
 
 SPECIFIC GRAVITY OF MINERALS AND EARTHS 
 
 Material 
 
 Specific 
 Gravity 
 
 Material 
 
 Specific 
 Gravity 
 
 Alabaster gypseous . 
 
 2.31 
 
 Lime, quick 
 
 1.50 
 
 Alabaster, calcareous . . 
 
 2.76 
 
 Limestone 
 
 2.70 
 
 
 1.72 
 
 Magnetic iron ore . . . 
 
 5.09 
 
 Amethyst 
 
 3.92 
 
 Malachite 
 
 4.01 
 
 Asbestos, starry 
 Asphaltum 
 
 3.07 
 1.40 
 
 Marble, African 
 Marble, common. . . ! ; ,K 
 
 2.71 
 2.67 
 
 Barytes (heavy spar) . . 
 Bluestone 
 
 3.05 to 3.38 
 2.45 to 3.00 
 
 Marble, Egyptian...;.. 7 
 Marble, Parian. ....... . 
 
 . 2.67 
 2.84 
 
 Borax 
 
 1.71 
 
 Marble, Italian, white. 
 
 2.71 
 
 
 3 50 
 
 Marl 
 
 1.60 to 2 34 
 
 Brick . 
 
 2.00 
 
 Mica 
 
 2.80 
 
 Chalk 
 
 2 78 
 
 Niter 
 
 1 90 
 
 Clay 
 
 1.90 
 
 Opal 
 
 2.09 
 
 Coral red 
 
 2 70 
 
 Phosphorus. . . . 
 
 1.77 
 
 Diamond 
 
 3.50 to 3.53 
 
 Plaster of Paris 
 
 1.87 to 2.47 
 
 Earth loose 
 
 1 36 
 
 Potash 
 
 2.10 
 
 Emerald 
 
 3.95 
 
 Quartz 
 
 2.66 
 
 Emerald, aquamarine. . 
 
 2.73 
 4 00 
 
 Rotten stone 
 Ruby 
 
 1.98 
 395 
 
 Feldspar 
 Flint black 
 
 . 2.60 
 2 58 
 
 Salt, common 
 Saltpeter 
 
 2.13 
 209 
 
 Flint, white 
 
 2.59 
 
 Sand 
 
 2.65 
 
 Garnet 
 
 3.60 to 4 20 
 
 
 2.08 to 2 52 
 
 Glass, bottle 
 
 2.73 
 
 Sapphire 
 
 3.98 
 
 Glass, flint 
 
 3 50 
 
 Serpentine 
 
 2.81 
 
 Glass green 
 
 2 64 
 
 Shale 
 
 2 60 
 
 Glass, white 
 
 2.90 
 
 Slate . 
 
 2.80 
 
 Granite, Patapsco 
 
 2.64 
 
 Soil, common 
 
 1.98 
 
 Granite, Quincy 
 Granite, Scotch 
 
 2.65 
 2 62 
 
 Specular iron ore ...... 
 
 5.25 
 248 
 
 Granite, Susquehanna. 
 Graphite 
 
 2.70 
 2 20 
 
 Sulphur, native 
 Talc 
 
 2.03 
 2.90 
 
 Grindstone . . 
 
 2 14 
 
 Topaz 
 
 3 50 
 
 Gypsum, opaque 
 
 2.17 
 
 Tourmaline 
 
 2.07 
 
 Jasper 
 
 2.65 
 
 Turquoise 
 
 2.84 
 
 Lapis lazuli 
 
 2.96 
 
 Zircon 
 
 4.50 
 
 
 
 
 
PROPERTIES OF MATERIALS 
 SPECIFIC GRAVITY OF METALS 
 
 277 
 
 Metal 
 
 Specific 
 Gravity 
 
 Metal 
 
 Specific 
 Gravity 
 
 Aluminum, wrought 
 
 2.660 
 6.712 
 
 Magnesium 
 Manganese 
 
 1.740 
 8 000 
 
 Bismuth 
 Brass, common 
 Brass, wire 
 Bronze, bell-metal 
 
 9.746 
 8.500 
 8.548 
 8.060 
 8.500 
 
 Mercury, solid, at 40 F.. 
 Mercury, liquid, at 32 F. . . 
 Mercury, liquid, at 60 F. . . 
 Mercury, liquid, at 212 F. . 
 Molybdenum 
 
 15.632 
 13.619 
 13.580 
 13.375 
 8.620 
 
 
 1.580 
 
 Nickel, cast 
 
 8 280 
 
 Chromium 
 
 6.000 
 
 Platinum, hammered. ...... 
 
 20.337 
 
 Cobalt 
 
 8.500 
 
 Platinum rolled 
 
 21 042 
 
 Copper, cast 
 
 8.700 
 
 Platinum, wire 
 
 22.009 
 
 
 8.788 
 
 Potassium . . 
 
 .860 
 
 Copper, wire and rolled .... 
 
 8.878 
 19.361 
 
 Silver, pure 
 Sodium ... 
 
 10.474 
 970 
 
 
 19.258 
 
 Steel, cast 
 
 7.919 
 
 Gold' 22 carat fine 
 
 17.486 
 
 Steel, common soft 
 
 7.833 
 
 
 18.680 
 
 Steel, hard and tempered . . 
 
 7.818 
 
 Iron, cast 
 
 7.207 
 
 Tin, Bohemian 
 
 7.312 
 
 
 7.780 
 
 Tin, English 
 
 7.201 
 
 
 7.768 
 
 Titanium . . ... 
 
 5.300 
 
 iron, pure. ... . . 
 
 7 780 
 
 
 17 600 
 
 Lead, hammered 
 
 11.388 
 11 330 
 
 Zinc, cast 
 Zinc rolled 
 
 6.860 
 7 101 
 
 
 
 
 
 SPECIFIC GRAVITY OF LIQUIDS 
 
 Liquid 
 
 Specific 
 Gravity 
 
 Liquid 
 
 Specific 
 Gravity 
 
 Acid, acetic 
 Acid, hydrochloric 
 Acid, nitric 
 Acid, phosphoric 
 Acid, sulphuric. 
 Alcohol, commercial 
 Alcohol, proof -spirit 
 Alcohol, pure 
 Alcohol, wood 
 Beer, lager 
 Bordeaux, wine 
 Bromine 
 
 1.062 
 1.200 
 1.217 
 1.558 
 1.841 
 .833 
 .925 
 .792 
 .800 
 1.034 
 .992 
 2.996 
 .997 
 1.530 
 
 Cider. . . . . 
 
 1.018 
 1.090 
 .739 
 1.450 
 1.054 
 1.032 
 .940 
 .915 
 .870 
 .932 
 .878 
 1.000 
 1.030 
 .992 
 
 Egg 
 
 Ether, sulphuric 
 Honey 
 
 Human blood 
 Milk 
 
 Oil, linseed 
 Oil, olive 
 
 Oil, turpentine 
 Oil whale 
 
 Petroleum 
 Water distilled 
 
 Water, sea 
 Wine 
 
 Chloroform 
 
 SPECIFIC GRAVITY OF GASES AND VAPORS 
 
 Gas or Vapor 
 
 Specific 
 Gravity 
 
 Gas or Vapor 
 
 Specific 
 Gravity 
 
 Air, 32 F. and 1 atmos.. 
 Alcohol, vapor 
 Ammonia 
 Bromine vapor 
 Carbon dioxide 
 
 1.000 
 1.589 
 .589 
 4.540 
 1.520 
 .967 
 2.450 
 5.300 
 .069 
 6.974 
 
 
 .553 
 .917 
 .967 
 1.106 
 .102 
 .900 
 .488 
 1.1912 
 4.700 
 .623 
 
 Nitrogen 
 Olefiant gas 
 Oxygen 
 Smoke, bituminous coal .... 
 Smoke, wood 
 Steam at 212 F 
 Sulphureted hydrogen 
 Turpentine vapor 
 
 Carbon monoxide 
 Chlorine 
 
 Chloroform vapor 
 
 
 Mercury vapor (ideal) 
 
 
 
278 
 
 PROPERTIES OF MATERIALS 
 SPECIFIC GRAVITY OF DRY WOODS 
 
 Wood 
 
 Specific 
 Gravity 
 
 Wood 
 
 Specific 
 Gravity 
 
 Alder 
 
 .80 
 
 Hazel 
 
 .60 
 
 Annie 
 
 .89 
 
 Lemon 
 
 .70 
 
 Ash 
 
 .86 
 
 Lignum vitae 
 
 1.33 
 
 Bay .... 
 
 .82 
 
 Linden 
 
 .60 
 
 Beech 
 
 .85 
 
 Logwood 
 
 .91 
 
 
 .96 
 
 Mahogany, Honduras 
 
 .56 
 
 
 1 33 
 
 Maple 
 
 .79 
 
 Box, Brazilian, red 
 
 PprJar wild 
 
 1.03 
 60 
 
 Mulberry 
 Oak 
 
 .90 
 .95 
 
 Cedar, Palestine 
 
 .61 
 56 
 
 Orange 
 Pear 
 
 .71 
 
 .66 
 
 
 .67 
 
 Pine, southern 
 
 .72 
 
 Cork 
 
 .25 
 
 Pine, white 
 
 .40 
 
 Ebony American 
 
 1.22 
 
 Poplar 
 
 .38 
 
 Elder 
 
 .70 
 
 Poplar, white Spanish 
 
 .53 
 
 Elm 
 
 .56 
 
 Sassafras 
 
 .48 
 
 Filbert 
 
 60 
 
 
 .50 
 
 Fir male 
 
 .55 
 
 Spruce, old 
 
 .46 
 
 
 50 
 
 Walnut 
 
 .61 
 
 
 
 
 
 SPECIFIC GRAVITY OF MISCELLANEOUS SUBSTANCES 
 
 Substance 
 
 Specific 
 Gravity 
 
 Substance 
 
 Specific 
 Gravity 
 
 Amber 
 
 1.085 
 
 India rubber 
 
 .935 
 
 Air 
 
 .0012 
 
 Ivory. 
 
 1.822 
 
 Beeswax . 
 
 .965 
 
 Lard 
 
 .947 
 
 Bone 
 
 1.8 to 2.0 
 
 Pearl, oriental 
 
 2.650 
 
 Butter 
 
 .942 
 
 Spermaceti 
 
 .943 
 
 Cotton 
 
 1.950 
 
 Sugar ... 
 
 1.605 
 
 Fat 
 
 .923 
 
 Tallow sheep and ox 
 
 .923 
 
 Gunpowder, loose 
 Gunpowder, shaken . . . 
 
 .900 
 1.000 
 
 Tallow, calf... 
 Tar. . . 
 
 .934 
 1.000 
 
 Gum Arabic 
 
 1.452 
 
 Wool 
 
 1.610 
 
 AVERAGE WEIGHT OF VARIOUS SUBSTANCES 
 
 WEIGHT OF 1 CU. FT. OF VARIOUS METALS 
 
 Metal 
 
 Weight 
 Pounds 
 
 Metal 
 
 Weight 
 Pounds 
 
 Aluminum 
 
 167 
 
 
 109 
 
 Antimony 
 
 418 
 
 Manganese 
 
 499 
 
 Bismuth 
 Brass, cast 
 
 613 
 504 
 
 Mercury, at 32 F 
 Mercury at 60 F 
 
 849 
 846 
 
 Brass, rolled 
 Bronze 
 
 524 
 546 
 
 Mercury, at 212 F 
 
 836 
 538 
 
 Chromium 
 
 456 
 
 Nickel 
 
 548 
 
 Cobalt 
 
 560 
 
 
 1 270 
 
 Copper, cast 
 
 552 
 
 Platinum rolled . . . 
 
 1,313 
 
 Copper, rolled 
 
 555 
 
 
 1 372 
 
 Gold, cast, 24 carat 
 Gold, pure, hammered 
 
 1,204 
 1 217 
 
 Silver, hammered 
 
 657 
 653 
 
 Gun-metal bronze 
 
 529 
 
 Sulphur 
 
 125 
 
 Indium 
 
 1,400 
 
 Steel 
 
 490 
 
 Iron, cast 
 
 450 
 
 Tin 
 
 458 
 
 Iron, wrought 
 
 480 
 
 Tungsten .... 
 
 1,097 
 
 Lead, commercial, cast 
 
 712 
 
 Zinc 
 
 437 
 
PROPERTIES OF MATERIALS 279 
 
 WEIGHT OF 1 CU. FT. OF VARIOUS WOODS, WHEN DRY* 
 
 Wood 
 
 Weight 
 Pounds 
 
 Wood 
 
 Weight 
 Pounds 
 
 
 
 
 
 Alder 
 
 42 
 
 Cypress, Spanish 
 
 29 
 40 
 
 Apple 
 
 47 
 
 Dagame. . . 
 
 56 
 
 Arbor vitae 
 
 19 
 
 Dogwood 
 
 50 
 
 Ash, black 
 Ash blue 
 
 39 
 34 
 
 Ebony 
 Elder tree 
 
 76 
 43 
 
 Ash, green . . . 
 
 39 
 
 Elm, cork 
 
 45 
 
 Ash Oregon 
 
 35 
 
 Elm, slippery 
 
 43 
 
 Ash, red 
 Ash, white 
 
 38 
 39 
 
 Elm, white 
 Elm, wing. . 
 
 34 
 46 
 
 Aspen 
 
 27 
 
 Filbert tree 
 
 38 
 
 Bamboo 
 
 22 
 
 Fir, balsam 
 
 23 
 
 
 28 
 
 Fir, great silver 
 
 22 
 
 Bay tree ... 
 
 51 
 
 Fir, red, or California 
 
 29 
 
 Beech 
 
 42 
 
 Fir, red, or noble 
 
 28 
 
 Bethabara 
 
 76 
 
 Fir, white 
 
 22 
 
 Birch paper or white 
 
 37 
 
 Greenheart. 
 
 72 
 
 Birch, red 
 
 35 
 
 Gum, cotton 
 
 32 
 
 Birch sweet 
 
 47 
 
 Gum, sour 
 
 39 
 
 
 40 
 
 Gum, sweet 
 
 37 
 
 Blue beech (iron wood) . . 
 
 45 
 43 to 69 
 
 Hackmatack (American 
 larch) 
 
 38 
 
 Box elder 
 
 26 
 
 Hawthorn . . . 
 
 57 
 
 Boxwood Brazilian red 
 
 64 
 
 Hazel . 
 
 38 
 
 Boxwood, Dutch 
 
 83 
 
 Hemlock 
 
 26 
 
 Boxwood French 
 
 57 
 
 Hemlock, western 
 
 28 
 
 Buckeye, Ohio 
 
 28 
 
 Hickory, mocker nut 
 
 53 
 
 Buckeye sweet 
 
 27 
 
 Hickory, pecan . 
 
 49 
 
 Bullet tree 
 
 65 
 
 Hickory, pignut 
 
 56 
 
 Butternut 
 
 25 
 
 Hickory, shagbark, or shell- 
 
 
 
 35 
 
 bark 
 
 51 
 
 Cabacalli . . 
 
 56 
 
 Holly 
 
 36 
 
 
 27 
 
 Hornbeam 
 
 47 
 
 Catalpa, hardy . . . 
 
 25 
 
 Ironwood, or blue beech .... 
 
 45 
 
 Cedar, California, white. . . . 
 Cedar, canoe 
 
 25 
 23 
 
 Ironwood, or hop hornbeam 
 Jasmine, Spanish 
 
 51 
 
 48 
 
 Cedar incense 
 
 25 
 
 Joshua tree. . . 
 
 23 
 
 Cedar, Indian 
 
 82 
 
 Juneberry . . . 
 
 54 
 
 Cedar, juniper 
 
 35 
 
 Karri 
 
 63 
 
 Cedar Palestine 
 
 38 
 
 Kauri 
 
 37 
 
 Cedar, Port Oxford 
 
 28 
 
 Laburnum 
 
 57 
 
 Cedar red 
 
 30 
 
 Lancewood 
 
 53 
 
 Cedar, white, or post . . 
 
 23 
 
 Larch 
 
 38 
 
 Cedar, white (arbor vitae) . . 
 Cedar, wild 
 
 19 
 37 
 
 Larch, tamarack 
 Laurel, California 
 
 46 
 40 
 
 Cedar, yellow 
 
 29 
 
 Laurel, Madrona 
 
 43 
 
 
 36 
 
 Lemon 
 
 45 
 
 Chestnut 
 
 28 
 
 Lignum vitae 
 
 83 
 
 
 36 
 
 Linden 
 
 38 
 
 Citron 
 Cocoa wood. 
 
 45 
 65 
 
 Locust, black, or yellow. . . . 
 Locust, honey 
 
 45 
 
 42 
 
 Cocobolo 
 
 55 
 
 Logwood 
 
 58 
 
 
 24 
 
 Madrona 
 
 43 
 
 Cottonwood black 
 
 23 
 
 Mahoe 
 
 41 
 
 
 29 
 
 Mahogany . . . 
 
 45 
 
 
 
 
 
 * The weight of wood depends largely on the amount of moisture it con- 
 tains. The weights in this and the following tables are for very dry wood and 
 not for green wood. Separate tables are given for Philippine, Indian, 
 and Australian woods. The weight of moisture contained in the wood must 
 be added to the values given in these tables. 
 
280 
 
 PROPERTIES OF MATERIALS 
 
 TABLE (Continued) 
 
 Wood 
 
 Weight 
 Pounds 
 
 Wood 
 
 Weight 
 Pounds 
 
 Mahogany, Mexican 
 Mahogany, Spanish 
 
 32 
 53 
 
 Pine, white, (Pacific States 
 and British Columbia) . . . 
 
 24 
 
 Mahogany, white 
 Maple Oregon 
 
 33 
 30 
 
 Pine, white, (Rocky Moun- 
 tains) 
 
 27 
 
 Maple, red 
 
 38 
 
 Pingow 
 
 47 
 
 Maple silver or soft 
 
 32 
 
 Plum tree 
 
 49 
 
 Maple, sugar, or hard 
 
 43 
 
 Pockwood 
 
 81 
 
 Mastic tree 
 
 53 
 
 Pomegranate tree 
 
 85 
 
 Medlar 
 
 59 
 
 Poon 
 
 36 
 
 Mesquit. . . 
 
 47 
 
 Poplar, or large-tooth aspen 
 
 28 
 
 Missel tree 
 Mora . 
 
 59 
 57 
 
 Poplar, yellow, or tulip tree 
 Quebracho 
 
 26 
 82 
 
 
 36 
 
 
 44 
 
 Oak, black. 
 
 45 
 
 Redwood 
 
 26 
 
 Oak, burr 
 
 46 
 
 Roller wood 
 
 52 
 
 Oak, chestnut . 
 
 46 " 
 
 Rosewood . . 
 
 68 
 
 Oak, cow 
 
 46 
 
 Sal 
 
 60 
 
 Oak, English... 
 
 51 
 
 Sassafras ... . 
 
 31 
 
 Oak, live, California .... 
 
 51 
 
 Shadblow 
 
 54 
 
 Oak, live, Southern United 
 
 
 Shadbush . 
 
 54 
 
 States 
 
 59 
 
 
 28 
 
 Oak, pin 
 
 43 
 
 Spruce Douglas 
 
 32 
 
 Oak, post 
 
 50 
 
 
 29 
 
 Oak, red 
 
 45 
 
 Spruce, single (balsam fir) 
 
 23 
 
 Oak, Spanish 
 
 43 
 
 Spruce Sitka 
 
 26 
 
 Oak, white (North-central 
 and Eastern United 
 
 
 Spruce, white, (Northern 
 United States) 
 
 25 
 
 States) 
 
 50 
 
 Spruce white (RockyMoun- 
 
 
 Oak, white, (Pacific Coast 
 from British Columbia to 
 
 
 tains and British Col- 
 umbia) 
 
 21 
 
 California) 
 
 46 
 
 
 35 
 
 Orange, osage 
 
 48 
 
 Sycamore, California 
 
 30 
 
 Orange tree 
 
 44 
 
 Tamarack 
 
 38 
 
 Paddlewood 
 
 52 
 
 Teak 
 
 50 
 
 Palm, Washington 
 
 32 
 
 Tonka 
 
 64 
 
 Palmetto, cabbage. . . 
 
 27 
 
 Tooart 
 
 67 
 
 Pear 
 
 41 
 
 Tulip tree 
 
 26 
 
 Persimmon . . . 
 
 49 
 
 Tulip wood 
 
 61 
 
 Pine, bull 
 
 29 
 
 
 83 
 
 Pine, Cuban . 
 
 39 
 
 Walnut black 
 
 38 
 
 Pine, Kauri 
 
 60 
 
 
 35 
 
 Pine, loblolly 
 
 33 
 
 Walnut, English 
 
 36 
 
 Pine, long-leaf, or Georgia 
 
 38 
 
 Walnut Italian 
 
 42 
 
 Pine, northern . . 
 
 34 
 
 Walnut Persian 
 
 36 
 
 Pine, Norway 
 
 31 
 
 Walnut white 
 
 25 
 
 Pine, Oregon 
 
 32 
 
 Wasahba 
 
 76 
 
 Pine, pitch 
 
 32 
 
 Whitewood 
 
 26 
 
 Pine, short-leaf, or Carolina 
 
 32 
 
 Willow, black 
 
 27 
 
 Pine, sugar 
 
 22 
 
 
 52 
 
 Pine, white, (North-Central 
 
 
 Yew Dutch 
 
 4P 
 
 and Northeastern States) . 
 
 24 
 
 Yew Spanish 
 
 50 
 
 
 
 Yucca, or Joshua tree 
 
 23 
 
PROPERTIES OF MATERIALS 281 
 
 WEIGHT OF 1 CU. FT. OF PHILIPPINE WOODS, WHEN DRY 
 
 Wood 
 
 Weight 
 Pounds 
 
 Wood 
 
 Weight 
 Pounds 
 
 Acle.. 
 
 Amuguis 
 
 Apitong 
 
 Aranga 
 
 Balacat 
 
 Balacbacan 
 
 Bansalaguin. . . . 
 
 Banuyo 
 
 Batitinan v . 
 
 Betis 
 
 Calantas 
 
 Dungon 
 
 Guijo 
 
 IP" 
 
 Lauan 
 
 Liusin 
 
 Lumbayao 
 
 Macaasin 
 
 Malasantol 
 
 Malugay 
 
 Mayapis 
 
 Molave 
 
 Narra 
 
 Palo Maria 
 
 Sacat 
 
 Sasalit ' 
 
 Supa 
 
 Tanguile 
 
 Tindalo 
 
 Yacal... 
 
 44 
 35 
 44 
 40 
 40 
 25 
 49 
 30 
 39 
 37 
 55 
 45 
 30 
 48 
 52 
 
 WEIGHT OF 1 CU. FT. OF AUSTRALIAN WOODS, WHEN DRY* 
 
 Wood 
 
 Weight 
 Pounds 
 
 Acacia dealbata (silver wattle) 57 
 
 Acacia decurrens (common wattle) 47 
 
 Acacia implexa 44 
 
 Acacia melanoxylon (blackwood; lightwood) 47 
 
 Acacia mollissima (silver wattle) 50 
 
 Acacia pycnantha (golden wattle) 52 
 
 Acacia salicina 48 
 
 Araucaria cunninghamii (pine) 45 
 
 Aster argophyllus (musk tree) 40 
 
 Banksia integrifolia (coast honeysuckle tree) 
 
 Banksia marginata (common honeysuckle tree) 38 
 
 Banksia serrata (heath honeysuckle tree) 50 
 
 Callitris verrucosa (dessert sandarac pine, or cypress) 43 
 
 Castanaspermum australe (black bean) 57 
 
 Casuarina torulusa (forest oak) 66 
 
 Casuarina quadravalvis (drooping she oak) 61 
 
 Cedrela australis (cedar) 28 
 
 Ceratopetalum apetalum (coach wood) 
 
 Dacrydium cupressinum (rimu) 38 
 
 Dissiliaria baloghioides (teak) 60 
 
 Dysoxylon muelleri (red bean) 46 
 
 Eucalyptus amygdalina regnans (mountain ash or peppermint tree) 60 
 Eucalyptus botryoides (blue gum, Gippsland mahogany, or bastard 
 
 mahogany) ' 60 
 
 Eucalyptus corymbosa (bloodwood) 
 
 Eucalyptus corynocalyx (sugar gum) 69 
 
 Eucalyptus diversicolor (karri) 61 
 
 Eucalyptus globulus (blue gum) 57 
 
 Eucalyptus gomphocephala (tuart) 66 
 
 Eucalyptus goniocalyx (bastard box, spotted gum) 
 
 Eucalyptus haewastowa (spotted gum) 69 
 
 Eucalyptus hemiphloia (canary wood, white box, or gray box) 48 
 
 * On account of the unsettled nomenclature of Australian woods, this 
 table gives botanical names, with common names, so far as possible, in paren- 
 thesis after the botanical name. Also see note at foot of table, Weight of 
 Various Woods, page 279. 
 
PROPERTIES OF MATERIALS 
 TABLE (Continued) 
 
 Wood 
 
 Eucalyptus largiflorens (slaty gum) 
 
 Eucalyptus leucoxylon (iron bark, red flowering, or black iron 
 
 bark) 
 
 Eucalyptus longifolia (wollybutt tree) 
 
 Eucalyptus maculata (spotted gum) 
 
 Eucalyptus marginata (jarrah) 
 
 Eucalyptus melliodora (yellow box) 
 
 Eucalyptus microcorys (tallow wood) 
 
 Eucalyptus obliqua (messmate, stringy bark) 
 
 Eucalyptus pilularis (blackbutt, or flintwood) 
 
 Eucalyptus piperita (blackbutt, white stringy bark tree) 
 
 Eucalyptus resinifera (mahogany) 
 
 Eucalyptus robusta (swamp mahogany) 
 
 Eucalyptus rostrata (red gum tree) 
 
 Eucalyptus saligna (gray gum) 
 
 Eucalyptus siderophloia (iron bark) 
 
 Eucalyptus sieberiana (iron bark, gumtop stringy bark, mountain 
 
 ashes) 
 
 Eucalyptus tereticarnis (flooded gum) 
 
 Eucalyptus viminalis (manna gum tree, drooping gum, or white 
 
 gum tree) 
 
 Eugenia smithii (myrtle) 
 
 Exocarpus cupressiformis (native cherry tree) 
 
 Fagus cunninghamii (evergreen beech or native myrtle) 
 
 Hakea leucoptera (water tree) 
 
 Heterodendron oleif olium 
 
 Lomatia f raseri 
 
 Melalenca decussata 
 
 Melalenca parviflora 
 
 Mypqrum insulare 
 
 Myrsine variabilis 
 
 Panax murrayi (palm panax) 
 
 Pimelea microcephala 
 
 Pittosporum bicolor (white wood) 
 
 Pomaderris apetala (hazel) 
 
 Prostanthera lasianthas (mint tree) 
 
 Santalum acuminatum (native peach or quandong) 
 
 Santalum persicarium (native sandalwood) 
 
 Senecio bedf ordii (native dogwood) 
 
 Syncarpia laurifolia (turpentine) 
 
 Tristania conf erta (brush or white box) 
 
 Tristania nerifolia (water gum) 
 
 Viminaria denudata. . . 
 
 WEIGHT OF 1 CU. FT. OF INDIAN WOODS 
 
 (Berkley-Clark) 
 
 Wood 
 
 Weight 
 Pounds 
 
 Wood 
 
 Weight 
 Pounds 
 
 Bibla 
 
 56 
 
 Poon 
 
 39 
 
 Blackwood 
 Erroul 
 Hedoo 
 
 56 
 63 
 39 
 
 Red eyne 
 Teak, Jungle 
 Teak Northern 
 
 68 
 41 
 55 
 
 Khair 
 Kullum . . 
 
 73 
 
 41 
 
 Teak, Southern 
 
 48 
 
 
 
 
 
PROPERTIES OF MATERIALS 
 WEIGHT OF AMERICAN TIMBERS 
 
 Wood 
 
 Specific 
 Gravity 
 
 Weight 
 
 Cubic 
 Foot 
 Pounds 
 
 Weight 
 per Foot 
 Board 
 
 Measure 
 Pounds 
 
 Remarks 
 
 California redwood . 
 California spruce 
 Cedar 
 Chestnut 
 
 .39 
 .40 
 .37 
 .66 
 
 24.16 
 24.97 
 23.10 
 41.20 
 
 2.01 
 2.08 
 1.93 
 3.43 
 
 The weights given 
 are the averages of a 
 large number of de- 
 
 Cypress 
 Douglas fir 
 
 .46 
 .51 
 
 28.72 
 31.84 
 
 2.39 
 2.65 
 
 commercially dry 
 
 Hemlock 
 Red pine (Norway pine)] 
 Short-leaf yellow pine. . . 
 Southern, long-leaf, or 
 Georgia yellow pine.... 
 Spruce and eastern fir . . 
 White oak 
 
 .40 
 .50 
 .51 
 
 .61 
 .40 
 
 .80 
 
 24.97 
 31.31 
 31.84 
 
 38.08 
 24.97 
 49.94 
 
 2.08 
 2.60 
 2.65 
 
 3.17 
 2.08 
 4.16 
 
 less than 15% of 
 moisture. The 
 weights of unsea- 
 soned green lumber 
 will be from 20 to 
 40 % greater. Green 
 
 White pine 
 
 .38 
 
 23.72 
 
 1.98 
 
 taken to weigh 5 
 Ib. per running foot 
 board measure. 
 
 WEIGHT OF 1 SQ. FT. OF BUILDING MATERIALS 
 
 Name of Material 
 
 Average 
 Weight 
 Pounds 
 
 Name of Material 
 
 Average 
 Weight 
 Pounds 
 
 Corrugated (2 
 -in.) galvanized 
 iron 
 
 Corrugated galvar 
 No. 20, average 
 side lap, unboar 
 Copper roofing, 
 standing seam . . 
 Felt and pitch, 
 
 No. 16.. 
 No. 18.. 
 No. 20. . 
 No. 22.. 
 No. 24.. 
 No. 26.. 
 No. 27.. 
 No. 28. . 
 lized iron, 
 amount of 
 ded 
 16-oz., 
 
 without 
 
 2.91 
 2.36 
 1.82 
 1.54 
 1.27 
 .99 
 .93 
 .86 
 
 2.25 
 1.25 
 
 3.00 
 1.75 
 
 2.00 
 6 to 8 
 
 6 to 8 
 10.00 
 
 .50 
 2.00 
 
 2.00 
 4 to 10 
 
 Slate, single , 
 thickness. 
 
 Slag roof, foui 
 Steel roofing, 
 Tiles, Spanish 
 in., 1\ in. tc 
 Tiles, plain, 1 
 Xf in., 5ii 
 White-pine sh 
 thick 
 
 \ in. thick. . . 
 fe in. thick . . 
 Jin. thick. . . 
 | in. thick. . . 
 in. thick. . . 
 fin. thick. . . 
 f in. thick . . . 
 
 -ply 
 standing seam 
 , 14iin.X10 
 weather 
 0s in.X 61 in. 
 n. to weather, 
 eathing, 1 in. 
 
 1.81 
 2.71 
 3.62 
 5.43 
 7.25 
 9.06 
 10.87 
 4.00 
 1.00 
 
 8.50 
 18.00 
 2.00 
 
 3.00 
 5.50 
 6.00 
 
 6 to 10 
 2.00 
 4.00 
 
 5.00 
 3.00 
 6.50 
 
 Glass, | in. thick. 
 Hemlock sheathii 
 thick 
 
 
 Yellow-pine sheathing, 1 in. 
 thick ... . '. 
 
 ig, 1 in. 
 
 Gravel roof and four-ply felt 
 Gravel roof and five-ply felt 
 Roofing, three-ply ready 
 (asphalt, rubberoid, etc.) 
 Purlins, wooden, with 12- to 
 16-ft. span 
 Chestnut or maple sheath- 
 ing, 1 in. thick 
 Ash, hickory, or oak sheath- 
 ing, 1 in. thick 
 Sheet iron, -& in. thick 
 Thatch 
 
 Lead, about | in. thick 
 Lath-and-plaster ceiling 
 
 Mackite, 1 in. thick, with 
 plaster 
 Neponset roofing felt, two 
 layers 
 
 Spruce sheathing, 1 in. thick 
 Shingles, common, 6 in.X 18 
 in., 5 in. to weather 
 Skylight of glass, A to 1 in., 
 including frame 
 
 
 
284 PROPERTIES OF MATERIALS 
 
 WEIGHT OF 1 CU. FT. OF BUILDING MATERIALS 
 
 Material 
 
 Weight 
 Pounds 
 
 Material 
 
 Weight 
 Pounds 
 
 Asphalt-pavement corn- 
 
 130 
 
 Earth, soft, flowing 
 
 108 
 
 
 160 
 
 Earth, dense mud 
 
 125 
 
 
 150 
 
 
 150 
 
 
 
 Granite 
 
 165 to 170 
 
 hard 
 
 125 
 
 Gravel 
 
 117 to 125 
 
 
 150 
 
 Iron, cast* 
 
 450 
 
 Brick! soft, inferior .... 
 
 100 
 
 Iron, wroughtf 
 
 480 
 146 to 168 
 
 Brickwork, in lime m 
 
 120 
 
 Marble 
 
 168 
 
 Brickwork, in cement 
 mortar, average 
 Brickwork, pressed 
 brick, thin joints .... 
 Cement, Portland, 
 packed 
 Cement, Portland, 
 
 130 
 140 
 100 to 120 
 70 to 90 
 
 Masonry, squared gran- 
 ite or limestone 
 Masonry, granite or 
 limestone rubble 
 Masonry, granite or 
 limestone dry rubble 
 Masonry, sandstone. . . 
 Mineral wool 
 
 165 
 150 
 
 138 
 145 
 12 
 
 Cement, natural 
 packed 
 Cement, natural, loose 
 Cement, slag, packed.. 
 Cement, slag, loose 
 
 75 to 95 
 45 to 65 
 80 to 100 
 55 to 75 
 105 
 
 Mortar, hardened 
 Quicklime, ground, 
 loose, or small lumps 
 Quicklime, ground, 
 thoroughly shaken... 
 Sand, pure quartz, dry . 
 
 90 to 100 
 53 
 
 75 
 90 to 106 
 
 
 140 
 
 Sandstone, building, 
 
 
 
 135 
 
 dry 
 
 130 to 151 
 
 
 140 
 
 Slate.. 
 
 160 to 180 
 
 Concrete, reinforced, 
 
 150 
 
 Snow, fresh fallen 
 Steel, structural J 
 
 5 to 12 
 
 489.6 
 
 
 
 Terra cotta 
 
 110 
 
 loose.. 
 
 72 to 80 
 
 Terra - cotta masonry 
 
 
 
 82 to 92 
 
 work 
 
 112 
 
 
 
 Tile 
 
 110 to 120 
 
 ly rammed 
 
 90 to 100 
 
 
 
 
 
 
 
 WEIGHT OF 1 CU. FT. OF MISCELLANEOUS MATERIALS 
 
 Material 
 
 Weight 
 Pounds 
 
 Material 
 
 . Weight 
 Pounds 
 
 Acid, acetic . . 
 
 66 
 
 
 40 
 
 Acid, fluoric 
 Acid, hydrochloric. . . . 
 
 94 
 75 
 
 Asphalt, pure 
 Borax 
 
 80 
 107 
 
 Acid, nitric. 
 
 76 
 
 Bran 
 
 16 
 
 Acid, phosphoric 
 
 97 
 
 Chalk 
 
 156 
 
 Acid, sulphuric 
 Alabaster, white 
 Alabaster, yellow 
 Alcohol, commercial 
 
 115 
 171 
 169 
 52 
 
 Charcoal, birch 
 Charcoal, fir 
 Charcoal, oak 
 
 34 
 
 28 
 21 
 18 
 
 Alcohol, grain 
 Alcohol, wood 
 
 49.6 
 49.9 
 
 Chrome ore dust, well 
 
 160 
 
 Ammonia, 28% 
 
 56 
 
 Clay, ordinary 
 
 120 to 150 
 
 Antimony 
 
 418 
 
 
 119 
 
 Apples . 
 
 38 
 
 Clinker 
 
 85 
 
 Asbestos, starry 
 
 192 
 
 Coal, anthracite, 
 broken 
 
 54 
 
 *Weight per cubic inch, .260 Ib. 
 JWeight per cubic inch, .283 Ib. 
 
 tWeight per cubic inch, .277 Ib. 
 
PROPERTIES OF MATERIALS 
 TA BLE (Continued) 
 
 Material 
 
 Weight 
 Pounds 
 
 Material 
 
 Weight 
 Pounds 
 
 Coal, anthracite, 
 moderately shaken 
 
 58 
 
 Magnesite, calcined... . 
 Mica 
 
 110 
 
 183 
 
 Coal anthracite 
 
 
 
 155 
 
 solid* 
 
 93 
 
 Naphtha 
 
 53 
 
 Coal, bituminous, bro- 
 
 
 Niter 
 
 119 
 
 ken, loose 
 
 50 
 
 Oats . .... 
 
 26 
 
 Coal, bituminous, 
 
 
 Oil, linseed... 
 
 59 
 
 slacked 
 
 52 
 
 Oil olive 
 
 57 
 
 Coal, bituminous, 
 
 
 Oil, turpentine ? . . 
 
 54 
 
 solidt 
 
 84 
 
 Oil whale. 
 
 58 
 
 Coal, cannel, solid 
 Coke, loosej 
 
 79 
 23 to 32 
 
 Ore, iron, magnetite . . . 
 Ore iron hematite 
 
 312 
 306 
 
 Coral, red 
 
 169 
 
 Paper, calendered book 
 
 50 
 
 Cork 
 
 15 
 
 Paper leather-board . . 
 
 59 
 
 
 56 
 
 
 37 
 
 Corn on cob unhusked 
 
 . 58 
 
 Paper, news 
 
 38 
 
 Corn shelled 
 
 45 
 
 
 33 
 
 Corn meal, bolted 
 Corn meal, unbolted. . . 
 
 37 
 38 
 
 Paper, supercalendered 
 book 
 
 69 
 
 Corundum . . ~ 
 
 244 
 
 Paper, wrapping 
 
 10 
 
 Cotton yarn, skeins 
 
 11 
 134 to 157 
 
 Paper, writing 
 
 64 
 150 
 
 
 250 
 
 Pearl oriental 
 
 165 
 
 Ether 
 
 45 
 
 Peat, dry, compressed 
 
 20 to 30 
 
 Feldspar 
 
 166 
 
 
 55 
 
 Flint 
 
 162 
 
 Pitch . 
 
 72 
 
 Glass, common 
 Glass flint 
 
 156 to 172 
 180 to 196 
 
 Plaster of Paris, cast . . 
 Plumbago 
 
 80 
 140 
 
 
 168 
 
 
 41 
 
 Gneiss in loose piles . . . 
 
 96 
 
 Potatoes, white . . 
 
 48 
 
 
 134 
 
 
 57 
 
 Gun-metal 
 
 528 
 56 
 
 Quartz, common, pure. 
 Rosin 
 
 165 
 69 
 
 Gunpowder, shaken. . . . 
 
 63 
 
 Rope, manila 
 
 42 
 
 Gunpowder solid 
 
 105 
 
 Rottenstone 
 
 124 
 
 Gutta percha 
 
 61 
 143 
 
 Salt, coarse 
 Salt West-Indies well- 
 
 45 
 
 Hay, alfalfa, baled . . 
 
 12.5 to 14.3 
 
 dried 
 
 74 
 
 Hay alfalfa double 
 
 
 Saltpeter 
 
 131 
 
 compressed bales. . . . 
 
 25.53 
 
 Shales 
 
 162 
 
 Hay alfalfa cylindri- 
 
 
 Soil common 
 
 124 
 
 cal, double com- 
 
 
 Soapstone 
 
 170 
 
 pressed bales 
 
 36.36 
 
 Spelter (zinc) 
 
 437 
 
 Hay, clover, baled 
 
 14 
 
 Straw 
 
 19 
 
 Hay clover corn- 
 
 
 Sugar 
 
 100 
 
 
 24 ^ 
 
 
 125 
 
 Hay, clover, in mow . . . 
 Hematite iron ore 
 
 4.6 
 306 
 
 Talc, block 
 Tallow, sheep or ox .... 
 
 181 
 58 
 
 Ice 
 
 57 
 
 Tar 
 
 63 
 
 
 58 
 
 Trap rock 
 
 170 
 
 Ivory 
 
 114 
 
 Turf, or peat 
 
 20 to 30 
 
 Land plaster 
 
 80 
 
 Turnips . 
 
 44 
 
 
 17 
 
 
 68 
 
 Macnesia. carbonate. . . 
 
 150 
 
 Wheat.. 
 
 48 
 
 *Anthracite increases about 75% in bulk when broken to any market 
 size: 1 T. loose, averages from 38 to 46 cu. ft. 
 
 |A heaped bushel, loose, weighs about 74 lb., and 1 T. occupies from 43 
 to 48 cu. ft. Bituminous coal, when broken, occupies 75% more space than 
 in the solid. 
 
 JA heaped bushel, loose, weighs from 35 to 42 lb.; 1 T. occupies 
 80 to 97 cu. ft. 
 
286 
 
 PROPERTIES OF MATERIALS 
 
 PROPERTIES OF COAL 
 
 SPECIFIC GRAVITY OF AMERICAN COALS 
 
 (17. 5. Bureau of Mines) 
 
 
 
 
 
 Specific 
 
 
 
 
 
 Gravity 
 
 State 
 
 County 
 
 Locality 
 
 Seam 
 
 "S 59 
 
 
 
 
 . -.. 
 
 
 
 || 
 
 !l 
 
 Alabama 
 
 Walker 
 
 Carbon Hill 
 
 Jagger 
 
 1.32 
 
 1.37 
 
 Alabama 
 
 Bibb 
 
 Garnsey 
 
 Underwood 
 
 1.30 
 
 1.38 
 
 Alabama 
 
 Bibb 
 
 Belle Ellen 
 
 Youngblood 
 
 1.28 
 
 1.32 
 
 Arkansas 
 
 Sebastian 
 
 Midland 
 
 Hartshorne 
 
 1.32 
 
 1.44 
 
 Illinois 
 
 Williamson 
 
 Bush 
 
 No. 6 
 
 1.31 
 
 1.33 
 
 Illinois 
 
 Madison 
 
 Donkville 
 
 No. 6 
 
 1.22 
 
 1.26 
 
 Illinois 
 
 Logan 
 
 Lincoln 
 
 No. 5 
 
 1.22 
 
 1.31 
 
 Illinois 
 
 Sangamon 
 
 Auburn 
 
 No. 6 
 
 1.24 
 
 1.28 
 
 Indiana 
 
 Sullivan 
 
 Hymera 
 
 No. 5 
 
 1.28 
 
 1.42 
 
 Indiana 
 
 Sullivan 
 
 Hymera 
 
 No. 4 
 
 1.25 
 
 1.39 
 
 Indiana 
 
 Pike 
 
 Littles 
 
 No. 5 
 
 1.27 
 
 1.40 
 
 Indiana 
 
 Vigo 
 
 Terre Haute 
 
 No. 7 
 
 1.29 
 
 1.30 
 
 Indiana 
 
 Vigo 
 
 Macksville 
 
 No. 7 
 
 1.25 
 
 1.36 
 
 Indiana 
 
 Park 
 
 Rosedale 
 
 No. 6 
 
 1.24 
 
 1.29 
 
 Indiana 
 
 Sullivan 
 
 Dugger 
 
 No. 4 
 
 1.26 
 
 1.30 
 
 Indiana 
 
 Pike 
 
 Hartwell 
 
 No. 5 
 
 1.26 
 
 1.32 
 
 Kansas 
 Kentucky 
 Kentucky 
 Kentucky 
 
 Linn 
 Bell 
 
 Johnson 
 
 Jewett 
 Straight Creek 
 Big Black Mt. 
 Paintsville 
 
 Weir-Pittsburg 
 Straight Creek 
 High Splint 
 No. 1 
 
 1.23 
 1.27 
 1.29 
 1.27 
 
 1.34 
 1.40 
 1.30 
 1.28 
 
 Kentucky 
 
 Muhlenburg 
 
 Central City 
 
 No. 9 
 
 1.31 
 
 1.44 
 
 Maryland 
 Missouri 
 
 Garrett 
 Randolph 
 
 Westernport 
 Huntsville 
 
 Lw. Kittanning 
 
 1.36 
 1.21 
 
 1.41 
 1.36 
 
 New Mexico 
 
 Colfax 
 
 Van Houten 
 
 Raton 
 
 1.29 
 
 1.37 
 
 New Mexico 
 
 Colfax 
 
 Brilliant 
 
 Raton 
 
 1.30 
 
 1.39 
 
 New Mexico 
 North Dakota 
 
 Colfax 
 Stark 
 
 Blossburg 
 Lehigh 
 
 Raton 
 Lignite 
 
 1.31 
 1.25 
 
 1.35 
 
 1.44 
 
 North Dakota 
 
 McLean 
 
 Wilton 
 
 Lignite 
 
 1.22 
 
 1.23 
 
 Ohio 
 
 Jackson 
 
 . Wellston 
 
 No. 4 
 
 1.29 
 
 1.35 
 
 Ohio 
 
 Jackson 
 
 Wellston 
 
 No. 5 
 
 1.31 
 
 1.36 
 
 Ohio 
 
 Perry 
 
 Shawnee 
 
 No. 6 
 
 1.30 
 
 1.33 
 
 Ohio 
 
 Jefferson 
 
 Bradley 
 
 No. 8 
 
 1.30 
 
 1.39 
 
 Ohio 
 
 Jefferson 
 
 Rush Run 
 
 No. 8 
 
 1.29 
 
 1.33 
 
 Ohio 
 
 Guernsey 
 
 Danford 
 
 No. 7 
 
 1.30 
 
 1.34 
 
 Ohio 
 
 Perry 
 
 Dixie 
 
 No. 6 Hocking 
 
 1.30 
 
 1.42 
 
 Ohio 
 
 Vinton 
 
 Clarion 
 
 No. 4 
 
 1.30 
 
 1.36 
 
 Pennsylvania 
 Pennsylvania 
 Pennsylvania 
 Pennsylvania 
 Pennsylvania 
 Pennsylvania 
 Pennsylvania 
 Pennsylvania 
 Tennessee 
 
 Westmoreland 
 Washington 
 Washington 
 Westmoreland 
 Westmoreland 
 Cambria 
 Somerset 
 Allegheny 
 Campbell 
 
 Greensburg 
 Ellsworth 
 Ellsworth 
 East Millsboro 
 Ligonier 
 Ehrenfeld 
 Kimmelton 
 Bruce 
 Gatliff 
 
 Pittsburg 
 Pittsburg 
 Pittsburg 
 Pittsburg 
 Pittsburg 
 Lw. Kittanning 
 Lw. Kittanning 
 Pittsburg 
 Log Mountain 
 
 1.30 
 1.30 
 1.28 
 1.30 
 1.33 
 1.31 
 1.35 
 1.30 
 1.28 
 
 1.35 
 1.31 
 1.33 
 1.33 
 1.41 
 1.36 
 1.39 
 1.36 
 1.33 
 
 Tennessee 
 Tennessee 
 Tennessee 
 
 Campbell 
 Roane 
 Cumberland 
 
 Gatliff 
 Oliver Springs 
 Waldensia 
 
 Regal Block 
 Wind Rock 
 Lower Sewanee 
 
 1.29 
 1.29 
 1.29 
 
 1.32 
 1.37 
 1.31 
 
 Tennessee 
 
 Fentress 
 
 Wilder 
 
 Wilder 
 
 1.34 
 
 1.39 
 
PROPERTIES OF MATERIALS 
 TABLE (Continued) 
 
 287 
 
 
 
 
 
 Specific 
 
 
 
 
 
 Gravity 
 
 . State 
 
 County 
 
 Locality 
 
 Seam 
 
 Sg 
 
 8>a 
 
 
 
 
 
 It 
 
 s 1* 
 
 
 
 
 
 z| 
 
 JH 
 
 Tennessee 
 
 White 
 
 Clifty 
 
 1st. Abv. Sewanee 
 
 1.34 
 
 1.37 
 
 Tennessee 
 
 Marion 
 
 Orme 
 
 Battle Creek 
 
 1.35 
 
 
 Texas 
 
 Milan 
 
 Olsen 
 
 Lignite 
 
 
 1.25 
 
 Texas 
 
 Wood 
 
 Hoyte 
 
 Lignite 
 
 
 1.26 
 
 Virginia 
 
 Lee 
 
 Crab Orchard 
 
 Wilson 
 
 .27 
 
 1.32 
 
 Virginia 
 
 Lee 
 
 Crab Orchard 
 
 McConnell 
 
 .28 
 
 1.37 
 
 Virginia 
 
 Wise 
 
 Tom's Creek 
 
 Upper Banner 
 
 .27 
 
 1.28 
 
 Virginia 
 
 Lee 
 
 Darby 
 
 Darby 
 
 .28 
 
 1.28 
 
 Washington 
 
 King 
 
 Renton 
 
 Black Lignite 
 
 .28 
 
 .33 
 
 Washington 
 West Virginia 
 West Virginia 
 
 Kittitas 
 Preston 
 Fayette 
 
 Roslyn 
 Bretz 
 Page 
 
 Upper Freeport 
 Ansted 
 
 .32 
 .31 
 
 .27 
 
 .39 
 .35 
 .30 
 
 West Virginia 
 West Virginia 
 
 Fayette 
 Harrison 
 
 Page 
 Clarksburgh 
 
 Eagle 
 Pittsburg 
 
 .27 
 
 1.28 
 
 1.28 
 1.31 
 
 West Virginia 
 West Virginia 
 
 Marion 
 Preston 
 
 Monongah 
 Bretz 
 
 Pittsburg 
 Bakerstown 
 
 1.29 
 1.28 
 
 1.35 
 1.41 
 
 West Virginia 
 West Virginia 
 
 Mingo 
 Fayette 
 
 Glen Alum 
 McDonald 
 
 Glen Alum 
 Sewell 
 
 1.30 
 1.26 
 
 1.34 
 1.38 
 
 West Virginia 
 
 Kanawha 
 
 Acme 
 
 Keystone 
 
 1.27 
 
 1.34 
 
 West Virginia 
 
 Kanawha 
 
 Winifrede 
 
 Winifrede 
 
 1.28 
 
 1.34 
 
 Wyoming 
 
 Weston 
 
 Cambria 
 
 Cambria Fuel Co. 
 
 1.31 
 
 1.37 
 
 Wyoming 
 
 Crook 
 
 Aladdin 
 
 Stillwell Coal Co. 
 
 1.28 
 
 1.40 
 
 Wyoming 
 
 Carbon 
 
 Hanna 
 
 
 1.33 
 
 1.35 
 
 Wyoming 
 
 Sweetwater 
 
 Rock Springs 
 
 
 1.26 
 
 1.30 
 
 Wyoming 
 
 Uinta 
 
 Kemmerer 
 
 
 1.28 
 
 
 Average of 70 American Coals 
 
 1.286 
 
 1.348 
 
 WEIGHTS AND MEASUREMENTS OF COAL 
 
 (Coxe Bros. &= Co., Chicago, III.) 
 
 Coal 
 
 Weight per 
 Cubic Foot 
 Pounds 
 
 He* 
 
 fo OH} 
 yH 
 
 |fe 
 
 6 ft N 
 
 Coal 
 
 Weight per 
 Cubic Foot 
 Pounds 
 
 $3 
 
 fe Of-} 
 
 ja 
 
 Lehigh lump 
 Lehigh cupola 
 Lehigh broken 
 
 55.26 
 55.52 
 56.85 
 
 36.19 
 36.02 
 35.18 
 
 Free-burning egg 
 Free-burning stove. . 
 Free-burning nut . . . 
 
 56.07 
 56.33 
 56.88 
 
 35.67 
 35.50 
 35.16 
 
 Lehigh egg 
 Lehigh stove 
 
 57.74 
 58.15 
 58.26 
 
 34.63 
 34.39 
 34.32 
 
 Pittsburg 
 Illinois 
 Connellsville coke. . . 
 
 46.48 
 47.22 
 26.30 
 
 43.03 
 42.35 
 76.04 
 
 
 53 18 
 
 37 60 
 
 Hocking 
 
 49.30 
 
 40.56 
 
 Lehigh buckwheat 
 
 54.04 
 
 37.01 
 
 Indiana block 
 
 43.85 
 
 45.61 
 
 Lehigh dust 
 
 57.25 
 
 34.93 
 
 Erie 
 Ohio cannel 
 
 48.07 
 49.18 
 
 41.61 
 40.66 
 
 
 
 
 
 
 
288 PROPERTIES OF MATERIALS 
 
 AVERAGE WEIGHT AND BULK OF AMERICAN COALS 
 
 (W. R. Johnson) 
 
 Coal 
 
 Specific 
 Gravity 
 
 Weight of 
 1 Cu. Ft. 
 Solid 
 Pounds 
 
 Weight of 
 1 Cu. Ft. 
 Heaped 
 Pounds 
 
 Bulk of 
 1 T. ( 
 Heaped 
 Cubic Feet 
 
 1. Anthracites 
 2. Bituminous, free-burning. . 
 3. Bituminous, coking 
 Average of 1, 2, and 3 . 
 Foreign and Western 
 Cokes 
 
 .500 
 .358 
 .342 
 .400 
 .318 
 
 93.78 
 84.93 
 83.90 
 87.54 
 82.39 
 
 53.05 
 52.84 
 49.28 
 51.72 
 49.31 
 32.13 
 
 42.35 
 42.42 
 45.71 
 43.49 
 45.51 
 69.76 
 
 
 
 
 
 
 SPECIFIC GRAVITIES OF VARIOUS COALS 
 
 Name of Coal 
 
 Specific 
 Gravity 
 
 Weight of 
 1 Cu. Ft. 
 Pounds 
 
 Weight of 
 1 Cu. Yd. 
 Tons 
 
 Newcastle Hartley, England 
 Wigan 4 ft England 
 
 1.29 
 
 .20 
 
 80.6 
 75.0 
 
 .972 
 .914 
 
 Portland, England 
 Anthracite, Wales : . . . 
 
 .30 
 .39 
 
 81.2 
 86.9 
 
 .978 
 1.047 
 
 Eglington, Scotland ;. . . . 
 
 .25 
 .59 
 
 78.1 
 99.4 
 
 .941 
 1.193 
 
 Anthracite, Pennsylvania 
 Bituminous Pennsylvania 
 
 .55 
 
 .40 
 
 96.9 
 87.5 
 
 1.167 
 1.054 
 
 Block coal, Indiana 
 
 .27 
 
 79.4 
 
 .956 
 
 To Mr. Irving A. Stearns, mining engineer and former general superinten- 
 dent of the Pennsylvania Railroad Co.'s Coal Department, we are indebted 
 for the following summary of tests made by the mining engineers of this com- 
 pany. Although these tests were made 25 yr. ago, they are still of value as 
 
 WEIGHT OF SUSQUEHANNA COAL CO.'S WHITE ASH ANTHRACITE 
 
 Size 
 
 Size of Mesh, 
 in Inches 
 
 Weight per 
 Cubic Foot 
 
 Cubic Feet 
 From 1 
 Cubic Foot 
 
 
 
 
 Pounds 
 
 of Solid 
 
 
 Over 
 
 Through 
 
 
 
 Lump 
 
 4* to 9 
 
 
 57 
 
 1.614 
 
 Broken 
 
 2| to 2J 
 
 3| to 4 
 
 
 53 
 
 1.755 
 
 Egg 
 
 If to2J 
 
 
 2| to 2 
 
 
 52 
 
 1.769 
 
 Large stove 
 Small stove. 
 
 li to 1 
 1 to 1 J 
 
 
 If to 2 
 1 1 to 1 
 
 
 5H 
 51i 
 
 1.787 
 1 795 
 
 Chestnut... 
 
 1 to - 
 
 
 1 to 1 
 
 
 51 
 
 1.804 
 
 Pea 
 
 I to { 
 
 
 f to 
 
 
 50f 
 
 1.813 
 
 No. 1 buckwheat 
 
 & to ], 
 
 
 ito 
 
 
 50| 
 
 1.813 
 
 No. 2 buckwheat. 
 
 
 A to f 
 
 50| 
 
 1.813 
 
 giving the weight of anthracite, but the sizes corresponding to the different 
 grades are not now in use. Sizes of anthracite should be taken from the 
 table Sizes of Prepared Anthracite. These determina^ns showed an average 
 value for the specific gravity of the coal from the various seams upon this 
 
PROPERTIES OF MATERIALS 289 
 
 company's property of 1.4784, together with an average weight per cubic foot 
 of coal in the solid of 92.5 Ib. 
 
 CONTENTS OF HORIZONTAL COAL SEAMS* 
 
 Thickness of Seam 
 
 Lignitef 
 Tons per Acre 
 
 Bituminoust 
 Tons per Acre 
 
 Anthracitef 
 Tons per Acre 
 
 Feet 
 
 Inches 
 
 
 1 
 
 141.32 
 
 152.62 
 
 151.41 
 
 
 2 
 
 282.63 
 
 305.24 
 
 302.82 
 
 
 3 
 
 423.95 
 
 457.87 
 
 454.23 
 
 
 4 
 
 565.27 
 
 610.49 
 
 605.64 
 
 
 5 
 
 706.58 
 
 763.11 
 
 757.06 
 
 
 6 
 
 847.90 
 
 915.73 
 
 908.47 
 
 
 7 
 
 989.22 
 
 1,068.35 
 
 1,059.88 
 
 
 8 
 
 1,130.54 
 
 1,220.98 
 
 1,211.29 
 
 
 9 
 
 1,271.85 
 
 1,373.60 
 
 1,362.70 
 
 
 10 
 
 1,413.17 
 
 1,526.22 
 
 1,514.11 
 
 
 11 
 
 1,554.49 
 
 1,678.84 
 
 1,665.63 
 
 1 
 
 
 
 1.695.80 
 
 1,831.47 
 
 1,816.93 
 
 2 
 
 
 
 3,391.61 
 
 3,662.93 
 
 3,633.86 
 
 3 
 
 
 
 5,087.41 
 
 5,494.40 
 
 5,450.79 
 
 4 
 
 
 
 6,783.21 
 
 7.325.87 
 
 7,267.73 
 
 5 
 
 
 
 8,479.01 
 
 9,157.34 
 
 9.084.66 
 
 6 
 
 
 
 10,174.82 
 
 10,988.80 
 
 10,901.59 
 
 7 
 
 
 
 11,870.62 
 
 12,820.27 
 
 12,718.52 
 
 8 
 
 
 
 13,566.42 
 
 14,651.74 
 
 14,535.45 
 
 9 
 
 
 
 15,262.23 
 
 16,483.20 
 
 16,352.38 
 
 10 
 
 
 
 16,958.03 
 
 18,314.67 
 
 18,169.32- 
 
 Mr. Robert A. Quin, Manager Susquehanna Coal Co., has very kindly 
 furnished the two following tables. The first shows the present (1914) sizes of 
 anthracite, and the second shows the number of cubic feet per ton occupied by 
 each of these sizes, according to the region in which it is mined. 
 
 SIZES OF PREPARED ANTHRACITE 
 
 Size 
 
 Through 
 
 Over 
 
 Square 
 Inches 
 
 Round 
 Inches 
 
 Square 
 Inches 
 
 Roi 
 Inc 
 
 I 
 
 3 J 
 
 2 
 
 1; 
 
 ii 
 
 and 
 
 hes 
 
 
 r 
 
 
 51 
 
 \> 
 
 1| 
 i 
 
 6 
 4 
 3 
 2 
 1 
 
 i 
 
 . 
 
 y 
 
 i 5 
 I 1 
 'i 
 
 Steamboat 
 
 Broken 
 Egg 
 
 Stove 
 
 Chestnut 
 
 Pea 
 
 No. 1 Buckwheat 
 No. 2 Buckwheat 
 No. 3 Buckwheat 
 
 * This table is based on the average specific gravity of American coals. 
 t The contents of the bituminous coal and lignite is given in tons of 2,000 
 Ib.; the contents of anthracite seams, in tons of 2,240 Ib. 
 
290 PROPERTIES OF MATERIALS 
 
 CUBIC FT. IN 1 T. OF ANTHRACITE BROKEN IN TRADE SIZES 
 
 Size 
 
 Wyoming 
 Region 
 Cubic Feet 
 
 Shamokin 
 Region 
 Cubic Feet 
 
 Schuylkill 
 Region 
 Cubic Feet 
 
 Lykens 
 Region 
 Cubic Feet 
 
 
 37.713 
 
 
 
 
 Steamboat 
 
 38.55 
 
 
 38.00 
 
 
 
 39.03 
 
 40.138 
 
 38.60 
 
 43.00 
 
 Egg 
 
 38.66 
 
 42.499 
 
 39.40 
 
 43.41 
 
 Stove 
 
 37.72 
 
 41.559 
 
 40.30 
 
 43.92 
 
 Nut 
 
 40.43 
 
 42.308 
 
 41.00 
 
 44.78 
 
 Pea 
 
 41.63 
 
 42.692 
 
 41.70 
 
 45.16 
 
 No. 1 Buckwheat 
 No. 2 Buckwheat 
 No. 3 Buckwheat 
 
 41.96 
 42.65 
 43.36 
 
 45.373 
 43.282 
 43.686 
 
 42.30 
 43.10 
 43.90 
 
 45.71 
 46.09 
 
 WEIGHTS OF ENGLISH AND FRENCH COALS 
 [Delabeche & Playfair (D. K. Clark) ] 
 
 Name of Coal 
 
 Specific 
 Gravity 
 
 Weight of 
 1 Cu. Ft. 
 
 Cubic 
 Feet 
 in 1 T. 
 Heaped 
 
 Solid 
 
 Heaped 
 
 Wales. Anthracite 
 
 1.370 
 1.390 
 1.280 
 1.315 
 .310 
 .250 
 .256 
 .296 
 .280 
 .270 
 .285 
 .292 
 
 .350 
 .230 
 .273 
 .290 
 .200 
 1.259 
 1.590 
 
 85.4 
 86.7 
 80.3 
 82.3 
 81.8 
 78.0 
 78.3 
 80.8 
 79.8 
 79.8 
 79.6 
 79.6 
 
 84.1 
 76.8 
 79.4 
 80.5 
 74.8 
 78.6 
 99.6 
 
 58.3 
 53.3 
 53.1 
 53.1 
 52.0 
 49.1 
 49.8 
 47.2 
 47.4 
 49.9 
 45.9 
 45.9 
 
 52.6 
 48.3 
 49.7 
 54.3 
 54.6 
 50.0 
 62.8 
 55.0 
 54.3 
 53.7 
 53.1 
 52.5 
 51.8 
 50.0 
 49.3 
 52.5 
 56.2 
 
 38.4 
 42.0 
 42.0 
 42.7 
 43.1 
 45.6 
 45.3 
 47.4 
 47.3 
 44.9 
 48.8 
 47.4 
 
 42.6 
 46.4 
 45.2 
 40.1 
 41.0 
 42.0 
 35.7 
 40.8 
 41.2 
 41.7 
 42.2 
 42.7 
 43.2 
 44.8 
 45.4 
 42.75 
 40.0 
 
 Port Mawr (highest) 
 
 Llynvi (one of the lowest) 
 Average of 37 samples 
 
 Newcastle. Hedley's Hartley (highest) 
 Original Hartley (one of the lowest) . 
 Average of 18 samples 
 Derbyshire and Yorkshire. Elsecar. . . 
 Butterley 
 
 Stavely 
 
 Loscoe soft 
 
 Average of 7 samples 
 Lancashire. Laffack Bushy Park 
 (highest) 
 
 Cannel, Wigan (lowest) 
 Average of 28 samples 
 Scotland. Grangemouth (highest) 
 Wallsend, Elgin 
 
 Average of 8 samples 
 Ireland. Slievardagh, Anthracite 
 France. Labarthe 
 Auvergne and Blanzy . . 
 
 Combelle . . 
 
 Lataupe 
 
 Saint Etienne 
 
 Decise. . 
 
 Mons 
 
 Creusot 
 
 Average of French bituminous coals . 
 Anthracite 
 
 
WIRE AND SHEET-METAL GAUGES 
 
 TABLE OF WIRE AND SHEET-METAL GAUGES 
 
 Number 
 of 
 Gauge 
 
 U.S. 
 Standard 
 Gauge for 
 Sheet and 
 Plate Iron 
 and Steel. 
 Inch* 
 
 British 
 Imperial 
 Standard 
 Wire Gauge. 
 Millim.t 
 
 Bir- 
 ming- 
 ham 
 Gauge 
 Inch 
 
 Ameri- 
 can or 
 Brown 
 & 
 Sharpe 
 Gauge 
 Inch 
 
 Roeb- 
 ling's 
 Gauge 
 Inch 
 
 Tren- 
 ton 
 Iron 
 Co. 'a 
 Wire 
 Gauge 
 Inch 
 
 English 
 Legal 
 Stan- 
 dard 
 
 Inch 
 
 0000000 
 
 .5 
 
 12.7 
 
 
 
 .49 
 
 
 .500 
 
 000000 
 
 .469 
 
 11.78 
 
 
 
 .46 
 
 
 .464 
 
 00000 
 
 .438 
 
 10.97 
 
 
 
 .43 
 
 .45 
 
 .432 
 
 0000 
 
 .406 
 
 10.16 
 
 .454 
 
 .46 
 
 .393 
 
 .40 
 
 .4 
 
 000 
 
 .375 
 
 9.45 
 
 .425 
 
 .40964 
 
 .362 
 
 .36 
 
 .372 
 
 00 
 
 .344 
 
 8.84 
 
 .38 
 
 .3648 
 
 .331 
 
 .33 
 
 .348 
 
 
 
 .313 
 
 8.23 
 
 .34 
 
 .32486 
 
 .307 
 
 .305 
 
 .324 
 
 1 
 
 .281 
 
 7.62 
 
 .3 
 
 .2893 
 
 .283 
 
 .285 
 
 .3 
 
 2 
 
 .266 
 
 7.01 
 
 .284 
 
 .25763 
 
 .263 
 
 .265 
 
 .276 
 
 3 
 
 .25 
 
 6.4 
 
 .259 
 
 .22942 
 
 .244 
 
 .245 
 
 .252 
 
 4 
 
 .234 
 
 5.89 
 
 -.238 
 
 .20431 
 
 .225 
 
 .225 
 
 .232 
 
 5 
 
 .219 
 
 5.38 
 
 .22 
 
 .18194 
 
 .207 
 
 .205 
 
 .212 
 
 6 
 
 .203 
 
 4.88 
 
 .203 
 
 .16202 
 
 .192 
 
 .19 
 
 .192 
 
 7 
 
 .188 
 
 4.47 
 
 .18 
 
 .14428 
 
 .177 
 
 .175 
 
 .176 
 
 8 
 
 .172 
 
 4.06 
 
 .165 
 
 .12849 
 
 .162 
 
 .16 
 
 .16 
 
 9 
 
 .156 
 
 3.66 
 
 .148 
 
 .11443 
 
 .148 
 
 .145 
 
 .144 
 
 10 
 
 .141 
 
 3.26 
 
 .134 
 
 .10189 
 
 .135 
 
 .13 
 
 .128 
 
 11 
 
 .125 
 
 2.95 
 
 .12 
 
 .09074 
 
 .12 
 
 .1175 
 
 .116 
 
 12 
 
 .109 
 
 2.64 
 
 .109 
 
 .08081 
 
 .105 
 
 .105 
 
 .104 
 
 13 
 
 .094 
 
 2.34 
 
 .095 
 
 .07196 
 
 .092 
 
 .0925 
 
 .092 
 
 14 
 
 .078 
 
 2.03 
 
 .083 
 
 .06408 
 
 .08 
 
 .08 
 
 .08 
 
 15 
 
 .07 
 
 1.83 
 
 .072 
 
 .05707 
 
 .072 
 
 .07 
 
 .072 
 
 16 
 
 .0625 
 
 1.63 
 
 .065 
 
 .05082 
 
 .063 
 
 .061 
 
 .064 
 
 17 
 
 .0563 
 
 1.42 
 
 .058 
 
 .04526 
 
 .054 
 
 .0525 
 
 .056 
 
 18 
 
 .05 
 
 1.22 
 
 .049 
 
 .0403 
 
 .047 
 
 .045 
 
 .048 
 
 19 
 
 .0438 
 
 1.01 
 
 .042 
 
 .03589 
 
 .041 
 
 .04 
 
 .04 
 
 20 
 
 .0375 
 
 .91 
 
 .035 
 
 .03196 
 
 .035 
 
 .035 
 
 .036 
 
 - 21 
 
 .0344 
 
 .81 
 
 .032 
 
 .02846 
 
 .032 
 
 .031 
 
 .032 
 
 22 
 
 .0313 
 
 .71 
 
 .028 
 
 .02535 
 
 .028 
 
 .028 
 
 .028 
 
 23 
 
 .0281 
 
 .61 
 
 .025 
 
 .02257 
 
 .025 
 
 .025 
 
 .024 
 
 24 
 
 .025 
 
 .56 
 
 .022 
 
 .0201 
 
 .023 
 
 .0225 
 
 .022 
 
 25 
 
 .0219 
 
 .51 
 
 .02 
 
 .0179 
 
 .02 
 
 .02 
 
 .02 
 
 26 
 
 .0188 
 
 .45 
 
 .018 
 
 .01594 
 
 .018 
 
 .018 
 
 .018 
 
 27 
 
 .0172 
 
 .42 
 
 .016 
 
 .01419 
 
 .017 
 
 .017 
 
 .0164 
 
 28 
 
 .0156 
 
 .38 
 
 .014 
 
 .01264 
 
 .016 
 
 .016 
 
 .0148 
 
 29 
 
 .0141 
 
 .35 
 
 .013 
 
 .01126 
 
 .015 
 
 .015 
 
 .0136 
 
 30 
 
 .0125 
 
 .31 
 
 .012 
 
 .01002 
 
 .014 
 
 .014 
 
 .0124 
 
 31 
 
 .0109 
 
 .29 
 
 .01 
 
 .00893 
 
 .0135 
 
 .013 
 
 .0116 
 
 32 
 
 .0101 
 
 .27 
 
 .009 
 
 .00795 
 
 .013 
 
 .012 
 
 .0108 
 
 33 
 
 .0094 
 
 .25 
 
 .008 
 
 .00708 
 
 .011 
 
 .011 
 
 .01 
 
 34 
 
 .0086 
 
 .23 
 
 .007 
 
 .0063 
 
 .01 
 
 .01 
 
 .0092 
 
 35 
 
 .0078 
 
 .21 
 
 .005 
 
 .00561 
 
 .0095 
 
 .0095 
 
 .0084 
 
 36 
 
 .007 
 
 .19 
 
 .004 
 
 .005 
 
 .009 
 
 .009 
 
 .0076 
 
 37 
 
 .0066 
 
 .17 
 
 
 .00445 
 
 .0085 
 
 .0085 
 
 .0068 
 
 38 
 
 .0063 
 
 .15 
 
 
 .00396 
 
 .008 
 
 .008 
 
 .006 
 
 39 
 
 
 .13 
 
 
 .00353 
 
 .0075 
 
 .0075 
 
 .0052 
 
 40 
 
 
 .12 
 
 
 .00314 
 
 .007 
 
 .007 
 
 .0048 
 
 41 
 
 
 .11 
 
 
 
 
 
 .0044 
 
 42 
 
 
 .10 
 
 
 
 
 
 .004 
 
 43 
 
 
 .09 
 
 
 
 
 
 .0036 
 
 44 
 
 
 .08 
 
 
 
 
 
 .0032 
 
 45 
 
 
 .07 
 
 
 
 
 
 .0028 
 
 46 
 
 
 .06 
 
 
 
 
 
 .0024 
 
 47 
 
 
 .05 
 
 
 
 
 
 .002 
 
 48 
 
 
 .04 
 
 
 
 
 
 .0016 
 
 49 
 
 
 .03 
 
 
 
 
 
 .0012 
 
 50 
 
 
 .025 
 
 
 
 
 
 .001 
 
 291 
 
 * Legal standard 
 
 t Legal standard in Great Britain 
 
292 
 
 PROPERTIES OF MATERIALS 
 STANDARD DECIMAL GAUGE* 
 
 Thickness 
 
 Weight of 
 Square Foot, 
 
 Thickness 
 
 Weight of 
 Square Foot, 
 
 
 in Pounds 
 
 
 in Pounds 
 
 Deci- 
 mal 
 Inch 
 
 Frac- 
 tion 
 Inch 
 
 Milli- 
 meters 
 
 Iron 
 
 Steel 
 
 Deci- 
 mal 
 Inch 
 
 Frac- 
 tion 
 
 Inch 
 
 Milli- 
 meters 
 
 Iron 
 
 Stejel 
 
 .002 
 
 
 .0508 
 
 .08 
 
 .082 
 
 .060 
 
 ft 
 
 1.5240 
 
 2.40 
 
 2.448 
 
 .004 
 .006 
 
 *fe 
 
 .1016 
 .1524 
 
 .16 
 .24 
 
 .163 
 .245 
 
 .065 
 .070 
 
 1 
 
 1.6510 
 1.7780 
 
 2.60 
 2.80 
 
 2.652 
 2.856 
 
 .008 
 
 nv 
 
 .2032 
 
 .32 
 
 .326 
 
 .075 
 
 
 1.9050 
 
 3.00 
 
 3.060 
 
 .010 
 
 TI 
 
 .2540 
 
 .40 
 
 .408 
 
 .080 
 
 5\ 
 
 2.0320 
 
 3.20 
 
 3.264 
 
 012 
 
 Tffff 
 
 .3048 
 
 .48 
 
 .490 
 
 .085 
 
 17 
 
 2.1590 
 
 3.40 
 
 3.468 
 
 !014 
 .016 
 
 yjff 
 
 .3556 
 .4064 
 
 .56 
 .64 
 
 .571 
 .653 
 
 .090 
 .095 
 
 t 
 
 2.2860 
 2.4130 
 
 3.60 
 3.80 
 
 3.672 
 3.876 
 
 .018 
 
 9 
 
 .4572 
 
 .72 
 
 .734 
 
 .100 
 
 
 2.5400 
 
 4.00 
 
 4.080 
 
 .020 
 
 1 
 
 .5080 
 
 .80 
 
 .816 
 
 .110 
 
 
 2.7940 
 
 4.40 
 
 4.488 
 
 .022 
 
 I? 
 
 .5588 
 
 .88 
 
 ,898 
 
 .125 
 
 
 3.1750 
 
 5.00 
 
 5.100 
 
 .025 
 .028 
 
 i 
 
 .6350 
 .7112 
 
 1.00 
 1.12 
 
 1.020 
 1.142 
 
 .135 
 .150 
 
 * 
 
 3.4290 
 3.8100 
 
 5.40 
 6.00 
 
 5.508 
 6.120 
 
 .032 
 
 
 .8128 
 
 1.28 
 
 1.306 
 
 .165 
 
 fijtg 
 
 4.1910 
 
 6.60 
 
 6.732 
 
 .036 
 
 fl.' 
 
 .9144 
 
 1.44 
 
 1.469 
 
 .180 
 
 & 
 
 4.5720 
 
 -7.20 
 
 7.344 
 
 .040 
 
 '.i i 
 
 1.0160 
 
 1.60 
 
 1.632 
 
 .200 
 
 i 
 
 5.0800 
 
 8.00 
 
 8.160 
 
 .045 
 
 a 
 
 1.1430 
 
 1.80 
 
 1.836 
 
 .220 
 
 il 
 
 5.5880 
 
 8.80 
 
 8.976 
 
 .050 
 
 15 
 
 1.2700 
 
 2.00 
 
 2.040 
 
 .240 
 
 
 6.0960 
 
 9.60 
 
 9.792 
 
 .055 
 
 ft 
 
 1.3970 
 
 2.20 
 
 2.244 
 
 .250 
 
 
 6.3500 
 
 10.00 
 
 10.200 
 
 * The weights per square foot of sheet metal given in this table are based on 
 a weight of 480 Ib. per cu. ft., for iron and one of 489.6 Ib. per cu. ft. for steel. 
 
 MISCELLANEOUS TABLES 
 
 WEIGHT OF WROUGHT-IRON BOLTHEADS, NUTS, AND 
 WASHERS 
 
 Diameter of 
 Bolt 
 Inches 
 
 Hexagon Heads 
 and Nuts 
 Per Pair 
 
 Square Heads 
 and Nuts 
 Per Pair 
 
 Round Washers 
 Per Pair 
 
 
 
 20 to 1 Ib. 
 
 16 to lib. 
 
 20 to 1 Ib. 
 
 
 
 10 to 1 Ib. 
 
 81 to 1 Ib. 
 
 10 to 1 Ib. 
 
 
 
 5 to 1 Ib. 
 
 4| to 1 Ib. 
 
 5 to 1 Ib. 
 
 
 
 2f to 1 Ib. 
 
 2i to 1 Ib. 
 
 3 to 1 Ib. 
 
 
 
 2 to 1 Ib. 
 
 .56 Ib. 
 
 .63 Ib. 
 
 
 
 .77 Ib. 
 
 .88 Ib. 
 
 .77 Ib. 
 
 1 
 
 
 1.25 Ib. 
 
 1.31 Ib. 
 
 1.25 Ib. 
 
 1 
 
 \ 
 
 1.75 Ib. 
 
 2.10 Ib. 
 
 1.75 Ib. 
 
 1 
 
 
 2.13 Ib. 
 
 2.56 Ib. 
 
 2.25 Ib. 
 
 1 
 
 
 3.00 Ib. 
 
 3.60 Ib. 
 
 3.25 Ib. 
 
 1 
 
 
 3.75 Ib. 
 
 4.42 Ib. 
 
 4.25 Ib. 
 
 1 
 
 \ 
 
 4.75 Ib. 
 
 5.70 Ib. 
 
 5.25 Ib. 
 
 1 
 
 i 
 
 5.75 Ib. 
 
 7.00 Ib. 
 
 6.50 Ib. 
 
 ll 
 
 7.27 Ib. 
 
 8.72 Ib. 
 
 8.00 Ib. 
 
 2 
 
 
 8.75 Ib. 
 
 10.50 Ib. 
 
 9.60 Ib. 
 
PROPERTIES OF MATERIALS 
 
 293 
 
 WEIGHTS OF SHEETS AND PLATES OF STEEL, WROUGHT IRON, 
 COPPER, AND BRASS 
 
 (Cambria Steel Co) 
 
 American, 
 or Brown 
 & Sharpe, 
 Gauge 
 Number 
 
 Thickness 
 Inch 
 
 Weight Per Square Foot, in Pounds 
 
 Steel 
 
 Iron 
 
 Copper 
 
 Brass 
 
 0000 
 
 .460000 
 
 18.7680 
 
 18.4000 
 
 20.8380 
 
 19,6880 
 
 000 
 
 .409642 
 
 16.7134 
 
 16.3857 
 
 18.5568 
 
 17.5327 
 
 00 
 
 .364796 
 
 14.8837 
 
 14.5918 
 
 16.5253 
 
 15.6133 
 
 
 
 .324861 
 
 13.2543 
 
 12.9944 
 
 14.7162 
 
 13.9041 
 
 1 
 
 .289297 
 
 11.8033 
 
 11.5719 
 
 13.1052 
 
 12.3819 
 
 2 
 
 .257627 
 
 10.5112 
 
 10.3051 
 
 11.6705 
 
 11.0264 
 
 3 
 
 .229423 
 
 9.3605 
 
 9.1769 
 
 10.3929 
 
 9.8193 
 
 4 
 
 .204307 
 
 8.3357 
 
 8.1723 
 
 9.2551 
 
 8.7443 
 
 5 
 
 .181940 
 
 7.4232 
 
 7.2776 
 
 8.2419 
 
 7.7870 
 
 6 
 
 .162023 
 
 6.6105 
 
 6.4809 
 
 7.3396 
 
 6.9346 
 
 7 
 
 .144285 
 
 5.8868 
 
 5.7714 
 
 6.5361 
 
 6.1754 
 
 8 
 
 .128490 
 
 5.2424 
 
 5.1396 
 
 5.8206 
 
 5.4994 
 
 9 
 
 .114423 
 
 4.6685 
 
 4.5769 
 
 5.1834 
 
 4.8973 
 
 10 
 
 .101897 
 
 4.1574 
 
 4.0759 
 
 4.6159 
 
 4.3612 / 
 
 11 
 
 .090742 
 
 3.7023 
 
 3.6297 
 
 4.1106 
 
 3.8838 
 
 12 
 
 .080808 
 
 3.2970 
 
 3.2323 
 
 3.6606 
 
 3.4586 
 
 13 
 
 .071962 
 
 2.9360 
 
 2.8785 
 
 3.2599 
 
 3.0800 
 
 14 
 
 .064084 
 
 2.6146 
 
 2.5634 
 
 2.9030 
 
 2.7428 
 
 15 
 
 .057068 
 
 2.3284 
 
 2.2827 
 
 2.5852 
 
 2.4425 
 
 16 
 
 .050821 
 
 2.0735 
 
 2.0328 - 
 
 2.3022 
 
 2.1751 
 
 17 
 
 .045257 
 
 1.8465 
 
 1.8103 
 
 2.0501 
 
 1.9370 
 
 18 
 
 .040303 
 
 1.6444 
 
 1.6121 
 
 1.8257 
 
 1.7250 
 
 19 
 
 .035890 
 
 1.4643 
 
 1.4356 
 
 1.6258 
 
 1.5361 
 
 20 
 
 .031961 
 
 1.3040 
 
 1.2784 
 
 1.4478 
 
 1.3679 
 
 21 
 
 .028462 
 
 1.1612 
 
 1.1385 
 
 1.2893 
 
 1.2182 
 
 22 
 
 .025346 
 
 1.0341 
 
 1.0138 
 
 1.1482 
 
 1.0848 
 
 23 
 
 .022572 
 
 .92094 
 
 .90288 
 
 1.0225 
 
 .96608 
 
 24 
 
 .020101 
 
 .82012 
 
 .80404 
 
 .91058 
 
 .86032 
 
 25 
 
 .017900 
 
 .73032 
 
 .71600 
 
 .81087 
 
 .76612 
 
 26 
 
 .015941 
 
 .65039 
 
 .63764 
 
 .72213 
 
 .68227 
 
 27 
 
 .014195 
 
 .57916 
 
 .56780 
 
 .64303 
 
 .60755 
 
 28 
 
 .012641 
 
 .51575 
 
 .50564 
 
 .57264 
 
 .54103 
 
 29 
 
 .011257 
 
 .45929 
 
 .45028 
 
 .50994 
 
 .48180 
 
 30 
 
 .010025 
 
 .40902 
 
 .40100 
 
 .45413 
 
 .42907 
 
 31 
 
 .008928 
 
 .36426 
 
 .35712 
 
 .40444 
 
 .38212 
 
 32 
 
 .007950 
 
 .32436 
 
 .31800 
 
 .36014 
 
 .34026 
 
 33 
 
 .007080 
 
 .28886 
 
 .28320 
 
 .32072 
 
 .30302 
 
 34 
 
 .006305 
 
 .25724 
 
 .25220 
 
 .28562 
 
 .26985 
 
 35 
 
 .005615 
 
 .22909 
 
 .22460 
 
 .25436 
 
 .24032 
 
 36 
 
 .005000 
 
 .20400 
 
 .20000 
 
 .22650 
 
 .21400 
 
 37 
 
 .004453 
 
 .18168 
 
 .17812 
 
 .20172 
 
 .19059 
 
 38 
 
 .003965 
 
 .16177 
 
 .15860 
 
 .17961 
 
 .16970 
 
 39 
 
 .003531 
 
 .14406 
 
 .14124 
 
 .15995 
 
 .15113 
 
 40 
 
 .003144 
 
 .12828 
 
 .12576 
 
 .14242 
 
 .13456 
 
204 
 
 PROPERTIES OF MATERIALS 
 
 WEIGHT OF CAST-IRON PIPE PER FT., IN POUNDS* 
 
 DiaTYi 
 
 Thickness of Pipe, in Inches 
 
 -L/icirn- 
 eter of 
 Pipe 
 
 TnrVif><; 
 
 1 
 
 t 
 
 i 
 
 I 
 
 ! 
 
 * 
 
 1 
 
 It 
 
 U 
 
 H 
 
 H H 
 
 2 
 
 incnes 
 
 Weight of Pipe, in Pounds 
 
 1 
 
 3.07 
 
 5.07 
 
 7.38 
 
 
 
 
 
 
 
 
 
 
 
 11 
 
 3.69 
 
 6.00 
 
 8.61 
 
 
 
 
 
 
 
 
 
 
 
 if 
 
 4.30 
 
 6.92 
 
 9.84 
 
 
 
 
 
 
 
 
 
 
 
 if 
 
 4.92 
 
 7.84 
 
 11.10 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 5.53 
 
 8.76 
 
 12.30 
 
 16.2 
 
 
 
 
 
 
 
 
 
 
 2i 
 
 6.15 
 
 9.69 
 
 13.50 
 
 17.7 
 
 
 
 
 
 
 
 
 
 
 2i 
 
 6.76 
 
 10.60 
 
 14.80 
 
 19.2 
 
 24.0 
 
 
 
 
 
 
 
 
 
 2f 
 
 7.37 
 
 11.50 
 
 16.00 
 
 20.8 
 
 25.9 
 
 
 
 
 
 
 
 
 
 3 
 
 7.98 
 
 12.50 
 
 17.20 
 
 22.3 
 
 27.7 
 
 33.4 
 
 
 
 
 
 
 
 
 31 
 
 9.21 
 
 14.30 
 
 19.70 
 
 25.4 
 
 31.4 
 
 37.7 
 
 
 
 
 
 
 
 
 4 
 
 10.30 
 
 16.10 
 
 22.20 
 
 28.5 
 
 35.1 
 
 42.0 
 
 
 
 
 
 
 
 
 41 
 
 11.70 
 
 18.00 
 
 24.60 
 
 31.5 
 
 38.8 
 
 46.3 
 
 
 
 
 
 
 - 
 
 
 5 
 
 12.90 
 
 19.80 
 
 27.10 
 
 34.6 
 
 42.5 
 
 50.6 
 
 
 
 
 
 
 
 
 5* 
 
 14.20 
 
 21.70 
 
 29.50 
 
 37.7 
 
 46.1 
 
 54.9 
 
 
 
 
 
 
 
 
 6 
 
 15.40 
 
 23.50 
 
 32.00 
 
 40.8 
 
 49.8 
 
 59.2 
 
 68.9 
 
 
 
 
 
 
 
 6i 
 
 16.60 
 
 25.40 
 
 34.50 
 
 43.8 
 
 53.5 
 
 63.5 
 
 73.8 
 
 84.4 
 
 
 
 
 
 
 7 
 
 17.80 
 
 27.20 
 
 36.90 
 
 46.9 
 
 57.2 
 
 67.8 
 
 78.7 
 
 89.4 
 
 
 
 
 
 
 7i 
 
 19.10 
 
 29.10 
 
 39.40 
 
 50.0 
 
 60.9 
 
 72.1 
 
 83.7 
 
 95.5 
 
 108 
 
 
 
 
 
 8 
 
 20.30 
 
 30.90 
 
 41.80 
 
 53.1 
 
 64.6 
 
 76.4 
 
 88.6 
 
 101.0 
 
 114 
 
 127 
 
 
 
 
 8| 
 
 21.50 
 
 32.80 
 
 44.30 
 
 56.1 
 
 68.3 
 
 80.7 
 
 93.5 
 
 107.0 
 
 120 
 
 134 
 
 148 
 
 
 
 9 
 
 22.80 
 
 34.60 
 
 46.80 
 
 59.2 
 
 72.0 
 
 85.1 
 
 98.4 
 
 112.0 
 
 126 
 
 140 
 
 155 
 
 
 
 9* 
 
 24.00 
 
 36.40 
 
 49.20 
 
 62.3 
 
 75.7 
 
 89.3 
 
 103.0 
 
 118.0 
 
 132 
 
 147 
 
 163 
 
 
 
 10 
 
 25.10 
 
 38.30 
 
 51.70 
 
 65.3 
 
 79.4 
 
 93.6 
 
 108.0 
 
 123.0 
 
 138 
 
 164 
 
 170 
 
 202 
 
 
 11 
 
 27.60 
 
 42.00 
 
 56.60 
 
 71.5 
 
 86.7 
 
 102.0 
 
 118.0 
 
 134.0 
 
 151 
 
 168 
 
 185 
 
 220 
 
 
 12 
 
 30.00 
 
 45.70 
 
 61.50 
 
 77.7 
 
 94.1 
 
 111.0 
 
 128.0 
 
 145.0 
 
 163 
 
 181 
 
 199 
 
 237 
 
 275 
 
 13 
 
 32.50 
 
 49.40 
 
 66.40 
 
 83.8 
 
 102.0 
 
 120.0 
 
 138.0 
 
 156.0 
 
 175 
 
 195 
 
 214 
 
 254 
 
 294 
 
 14 
 
 35.00 
 
 53.10 
 
 71.40 
 
 89.4 
 
 109.0 
 
 128.0 
 
 148.0 
 
 168.0 
 
 188 
 
 208 
 
 229 
 
 271 
 
 314 
 
 15 
 
 37.40 
 
 56.70 
 
 76.30 
 
 96.1 
 
 116.0 
 
 137.0 
 
 158.0 
 
 179.0 
 
 200 
 
 222 
 
 244 
 
 289 
 
 334 
 
 16 
 
 39.10 
 
 60.40 
 
 81.20 
 
 102.0 
 
 124.0 
 
 145.0 
 
 167.0 
 
 190.0 
 
 212 
 
 235 
 
 258 
 
 306 
 
 353 
 
 17 
 
 42.30 
 
 64.10 
 
 86.10 
 
 108.0 
 
 131.0 
 
 154.0 
 
 177.0 
 
 201.0 
 
 225 
 
 249 
 
 273 
 
 323 
 
 373 
 
 18 
 
 44.80 
 
 67.80 
 
 91.00 
 
 115.0 
 
 139.0 
 
 163.0 
 
 187.0 
 
 212.0 
 
 237 
 
 262 
 
 288 
 
 340 
 
 393 
 
 19 
 
 47.30 
 
 71.50 
 
 96.00 
 
 121.0 
 
 146.0 
 
 171.0 
 
 197.0 
 
 223.0 
 
 249 
 
 276 
 
 303 
 
 357 
 
 412 
 
 20 
 
 49.70 
 
 75.20 
 
 101.00 
 
 127.0 
 
 153.0 
 
 180.0 
 
 207.0 
 
 234.0 
 
 261 
 
 289 
 
 317 
 
 375 
 
 432 
 
 21 
 
 52.20 
 
 78.90 
 
 106.00 
 
 133.0 
 
 161.0 
 
 188.0 
 
 217.0 
 
 245.0 
 
 274 
 
 303 
 
 332 
 
 392 
 
 452 
 
 22 
 
 54.60 
 
 82.60 
 
 111.00 
 
 139.0 
 
 168.0 
 
 196.0 
 
 227.0 
 
 256.0 
 
 286 
 
 316 
 
 347 
 
 409 
 
 471 
 
 23 
 
 57.10 
 
 86.30 
 
 116.00 
 
 145.0 
 
 175.0 
 
 206.0 
 
 236.0 
 
 267.0 
 
 298 
 
 330 
 
 362 
 
 426 
 
 491 
 
 24 
 
 59.60 
 
 89.90 
 
 121.00 
 
 152.0 
 
 183.0 
 
 214.0 
 
 246.0 
 
 278.0 
 
 311 
 
 343 
 
 375 
 
 444 
 
 511 
 
 25 
 
 62.00 
 
 93.60 
 
 126.00 
 
 158.0 
 
 190.0 
 
 223.0 
 
 256.0 
 
 289.0 
 
 323 
 
 357 
 
 391 
 
 461 
 
 531 
 
 26 
 
 64.50 
 
 97.30 
 
 131.00 
 
 164.0 
 
 198.0 
 
 231.0 
 
 266.0 
 
 300.0 
 
 335 
 
 370 
 
 406 
 
 478 
 
 550 
 
 27 
 
 66.90 
 
 101.00 
 
 135.00 
 
 170.0 
 
 205.0 
 
 240.0 
 
 276.0 
 
 311.0 
 
 348 
 
 384 
 
 421 
 
 495 
 
 570 
 
 28 
 
 69.40 
 
 105.00 
 
 140.00 
 
 176.0 
 
 212.0 
 
 249.0 
 
 286.0 
 
 323.0 
 
 360 
 
 397 
 
 436 
 
 512 
 
 590 
 
 29 
 
 71.80 
 
 109.00 
 
 145.00 
 
 182.0 
 
 220.0 
 
 257.0 
 
 295.0 
 
 334.0 
 
 372 
 
 411 
 
 450 
 
 530 
 
 609 
 
 30 
 
 74.20 
 
 112.00 
 
 150.00 
 
 188.0 
 
 227.0 
 
 266.0 
 
 305.0 
 
 345.0 
 
 384 
 
 424 
 
 465 
 
 547 
 
 629 
 
 * These weights are for plain pipe. For hautboy pipe, add 8 in. in length 
 for each joint. For copper, add |; for lead, f; for welded iron, ^. 
 
PROPERTIES OF MATERIALS 295 
 
 CONTENTS OF CYLINDERS OR PIPES FOR 1 FT. IN LENGTH* 
 
 DIAMETERS IN INCHES 
 
 $ 
 
 fj| 
 
 ^ --d 
 
 "o.c.S % 
 
 | 
 
 *1l 
 
 i*i 
 
 8S.sf 
 
 ff -S 
 
 
 Jdw^ 
 
 iUrf'S 
 
 1 1 
 
 g'Sfe 
 
 g.^W'd 
 
 4> > J 
 
 1 G 
 
 Q 5 
 
 wi & 
 
 sfS'S's 
 
 S 
 
 rtQ rt 
 
 |^a5 
 
 cJ C'g 
 
 Q~ 
 
 s .s 
 
 O c3iD 
 
 **!*! 
 
 s w 
 
 p .s 
 
 ^5 
 
 e ^l 
 
 j 
 
 .0208 
 .0417 
 
 .0025 
 .0102 
 
 .02122 
 .08488 
 
 5 
 
 5i 
 
 .4167 
 .4583 
 
 1.020 
 1.234 
 
 8.488 
 10.270 
 
 1 
 
 .0625 
 
 .0230 
 
 .19098 
 
 6 
 
 .5000 
 
 1.469 
 
 12.223 
 
 I* 
 
 .0833 
 
 .0408 
 
 .33952 
 
 6* 
 
 .5417 
 
 1.724 
 
 14.345 
 
 H 
 
 .1042 
 
 .0638 
 
 .53050 
 
 r 
 
 .5833 
 
 1.999 
 
 16.636 
 
 H 
 
 .1250 
 
 .0918 
 
 .76392 
 
 
 .6250 
 
 2.295 
 
 19.098 
 
 11 
 
 .1458 
 
 .1249 
 
 1.0398 
 
 8 2 
 
 .6667 
 
 2.611 
 
 21.729 
 
 2* 
 
 .1667 
 
 .1632 
 
 1.3581 
 
 8i 
 
 .7083 
 
 2.948 
 
 24.530 
 
 
 .1875 
 
 .2066 
 
 1.7188 
 
 9 
 
 .7500 
 
 3.305 
 
 27.501 
 
 2| 
 
 .2083 
 
 .2550 
 
 2.1220 
 
 9i 
 
 .7917 
 
 3.682 
 
 30.641 
 
 21 
 
 .2292 
 
 .3085 
 
 2.5676 
 
 10 
 
 .8333 
 
 4.080 
 
 33.952 
 
 3 
 
 .2500 
 
 .3672 
 
 3.0557 
 
 10 1 
 
 .8750 
 
 4.498 
 
 37.432 
 
 
 .2917 
 
 .4998 
 
 4.1591 
 
 11 
 
 .9167 
 
 4.937 
 
 41.082 
 
 4* 
 
 .3333 
 
 .6528 
 
 5.4323 
 
 1H 
 
 .9583 
 
 5.396 
 
 44.901 
 
 
 .3750 
 
 .8263 
 
 6.8750 
 
 12 
 
 1.0000 
 
 5.875 
 
 48.891 
 
 DIAMETERS IN FEET 
 
 H 
 
 1.25 
 
 9.18 
 
 76.392 
 
 10 
 
 10.00 
 
 587.6 
 
 4,889.12 
 
 li 
 
 1.50 
 
 13.22 
 
 110.00 
 
 10| 
 
 10.50 
 
 647.7 
 
 5,404.24 
 
 li 
 
 1.75 
 
 '17.99 
 
 149.73 
 
 11 
 
 11.00 
 
 710.9 
 
 5,915.84 
 
 2 
 
 2.00 
 
 23.50 
 
 195.56 
 
 HI 
 
 11.50 
 
 777.0 
 
 6,485.72 
 
 2i 
 
 2.25 
 
 29.74 
 
 247.51 
 
 12 
 
 
 846.1 
 
 7,040.00 
 
 2$ 
 
 2.50 
 
 36.72 
 
 305.57 
 
 13 
 
 
 992.8 
 
 8,710.00 
 
 2f 
 
 2.75 
 
 44.43 
 
 369.74 
 
 14 
 
 
 1,152.0 
 
 10,096.00 
 
 3 
 
 3.00 
 
 52.88 
 
 440.00 
 
 15 
 
 
 1,322.0 
 
 11,000.50 
 
 3J 
 
 3.25 
 
 65.28 
 
 544.37 
 
 16 
 
 
 1,504.0 
 
 12,516.00 
 
 3i 
 
 3.50 
 
 71.97 
 
 631.00 
 
 17 
 
 
 1,698.0 
 
 14,166.00 
 
 3| 
 
 3.75 
 
 82.62 
 
 687.53 
 
 18 
 
 
 1,904.0 
 
 15,841.00 
 
 4 
 
 4.00 
 
 94.0 
 
 782.24 
 
 19 
 
 
 2,121.0 
 
 17,691.00 
 
 4i 
 
 4.25 
 
 106.1 
 
 885.40 
 
 20 
 
 
 2,350.0 
 
 19,556.50 
 
 4i 
 
 4.50 
 
 119.0 
 
 990.04 
 
 21 
 
 
 2,591.0 
 
 21,617.00 
 
 4| 
 
 4.75 
 
 132.5 
 
 ,105.71 
 
 22 
 
 
 2,844.0 
 
 23,663.00 
 
 5 
 
 5.00 
 
 146.9 
 
 ,222.28 
 
 23 
 
 
 3,108.0 
 
 25,943.00 
 
 5J 
 
 5.25 
 
 161.9 
 
 ,351.06 
 
 24 
 
 
 3,384.0 
 
 28,160,00 
 
 5| 
 
 5.50 
 
 177.7 
 
 ,478.96 
 
 25 
 
 
 3,672.0 
 
 30,557.00 
 
 5f 
 
 5.75 
 
 194.3 
 
 ,621.43 
 
 26 
 
 
 3,971.0 
 
 34,840.00 
 
 6 
 
 6.00 
 
 211.5 
 
 ,760.00 
 
 27 
 
 
 4,283.0 
 
 35,641.00 
 
 6i 
 
 6.25 
 
 229.5 
 
 1,915.18 
 
 28 
 
 
 4,606.0 
 
 40,384.00 
 
 6i 
 
 6.50 
 
 248.2 
 
 2,177.48 
 
 29 
 
 
 4,941.0 
 
 41,117.00 
 
 6f 
 
 6.75 
 
 267.7 
 
 2,233.96 
 
 30 
 
 
 5,288.0 
 
 44,002.00 
 
 7 
 
 7.00 
 
 287.9 
 
 2,524.00 
 
 31 
 
 
 5,646.0 
 
 46,984.00 
 
 7i 
 
 7.50 
 
 330.5 
 
 2,750.12 
 
 32 
 
 
 6,017.0 
 
 50,064.00 
 
 8 
 
 SAM) 
 
 376.0 
 
 3.128.96 
 
 33 
 
 
 6,398.0 
 
 53,242.00 
 
 8i 
 
 8.50 
 
 424.5 
 
 3,541.60 
 
 34 
 
 
 6,792.0 
 
 56,664.00 
 
 9 
 
 9.00 
 
 475.9 
 
 3,960.16 
 
 35 
 
 
 7,197.0 
 
 59,891.50 
 
 9i 
 
 9.50 
 
 530.2 
 
 4,422.84 
 
 36 
 
 
 7,614.0 
 
 63,364.00 
 
 * The contents of pipes or cylinders in gallons or pounds are to each other 
 as the squares of their diameters. Thus, a pipe 9 ft. in diameter will contain 
 9 times as much as a 3-ft. pipe, or 4 times as much as a 4^-ft. pipe. 
 
296 PROPERTIES OF MATERIALS 
 
 STANDARD DIMENSIONS OF WROUGHT-IRON WELDED PIPES 
 
 
 
 
 
 u 
 
 u 
 
 ll 
 
 ^ 
 
 
 
 M 
 
 
 
 1 
 
 1 
 
 
 1 
 
 1 
 
 1 
 
 !3.g 
 
 .s 
 
 ctf 
 
 S& 
 
 J 
 
 8 
 
 Sg 
 
 g 
 
 a 
 
 w 
 
 P 
 
 
 c 
 
 #8 
 
 w 8 
 
 g 
 
 
 .s 
 
 
 
 & 
 
 2J| 
 
 rt w 
 
 S| 
 
 ll 
 HM 
 
 JZ 
 
 sl 
 
 13 
 a 
 
 ll 
 U 
 
 11 
 
 
 13 
 
 ^2 
 .1*3 
 
 ^ 
 0,3 
 
 <UCO 
 
 <z 
 11 
 
 fi 
 
 
 
 c 
 
 6-3 
 
 a 
 
 f<2 
 
 ! 
 
 li 
 
 1 
 
 w 
 
 
 1 
 
 c 
 
 "x 
 W 
 
 j g 
 
 M 1 - 1 
 
 21 
 
 "c 
 
 "bo'S 
 
 in 
 
 13 
 
 & 
 
 !* 
 
 
 
 
 
 
 
 3 
 
 <u*o 
 
 
 
 
 
 
 
 i 
 
 .40 
 
 .068 
 
 .27 
 
 .85 
 
 1.27 
 
 14.15 
 
 9.440 
 
 .057 
 
 2,513.0 
 
 .002 
 
 .24 
 
 27 
 
 
 .54 
 
 .088 
 
 .36 
 
 1.14 
 
 1.70 
 
 10.50 
 
 7.075 
 
 .104 
 
 1,383.3 
 
 .002 
 
 .42 
 
 18 
 
 1 
 
 .67 
 
 .091 
 
 .49 
 
 1.55 
 
 2.12 
 
 7.67 
 
 5.657 
 
 .192 
 
 751.2 
 
 .005 
 
 .56 
 
 18 
 
 
 
 .84 
 
 .109 
 
 .62 
 
 1.96 
 
 2.65 
 
 6.13 
 
 4.502 
 
 .305 
 
 472.4 
 
 .010 
 
 .84 
 
 14 
 
 3 
 
 1.05 
 
 .113 
 
 .82 
 
 2.59 
 
 3.30 
 
 4.64 
 
 3.637 
 
 .533 
 
 270.0 
 
 .023 
 
 1.13 
 
 14 
 
 1 
 
 1.31 
 
 .134 
 
 1.05 
 
 3.29 
 
 4.13 
 
 3.66 
 
 2.903 
 
 .863 
 
 166.9 
 
 .040 
 
 1.67 
 
 114 
 
 
 1.66 
 
 .140 
 
 1.38 
 
 4.33 
 
 5.21 
 
 2.77 
 
 2.301 
 
 1.496 
 
 96.25 
 
 .063 
 
 2.26 
 
 111 
 
 14 
 
 1.90 
 
 .145 
 
 1.61 
 
 5.06 
 
 5.97 
 
 2.37 
 
 2.010 
 
 2.038 
 
 70.66 
 
 .091 
 
 2.69 
 
 114 
 
 2 
 
 2.37 
 
 .154 
 
 2.07 
 
 6.49 
 
 7.46 
 
 1.85 
 
 1.611 
 
 3.355 
 
 42.91 
 
 .163 
 
 3.67 
 
 114 
 
 24 
 
 2.87 
 
 .204 
 
 2.47 
 
 7.75 
 
 9.03 
 
 1.55 
 
 1.328 
 
 4.783 
 
 30.10 
 
 .255 
 
 5.77 
 
 8 
 
 3 
 
 3.50 
 
 .217 
 
 3.07 
 
 9.64 
 
 11.00 
 
 1.24 
 
 1.091 
 
 7.388 
 
 19.50 
 
 .367 
 
 7.55 
 
 8 
 
 34 
 
 4.00 
 
 .226 
 
 3.55 
 
 11.15 
 
 12.57 
 
 1.08 
 
 0.955 
 
 9.887 
 
 14.57 
 
 .500 
 
 9.05 
 
 8 
 
 4 
 
 4.50 
 
 .237 
 
 4.03 
 
 12.65 
 
 14.14 
 
 .95 
 
 0.849 
 
 12.730 
 
 11.31 
 
 .652 
 
 10.73 
 
 8 
 
 
 5.00 
 
 .247 
 
 4.51 
 
 14.15 
 
 15.71 
 
 .85 
 
 0.765 
 
 15.939 
 
 9.02 
 
 .826 
 
 12.49 
 
 8 
 
 5 3 
 
 5.56 
 
 .259 
 
 5.04 
 
 15.85 
 
 17.47 
 
 .78 
 
 0.629 
 
 19.990 
 
 7.20 
 
 1.02 
 
 14.56 
 
 8 
 
 6 
 
 6.62 
 
 .280 
 
 6.06 
 
 19.05 
 
 20.81 
 
 .63 
 
 0.577 
 
 28.889 
 
 4.98 
 
 1.46 
 
 18.77 
 
 8 
 
 7 
 
 7.62 
 
 .301 
 
 7.02 
 
 22.06 
 
 23.95 
 
 .54 
 
 0.505 
 
 38.737 
 
 3.T2 
 
 2.00 
 
 23.41 
 
 8 
 
 8 
 
 8.62 
 
 .322 
 
 7.98 
 
 25.08 
 
 27.10 
 
 .48 
 
 0.444 
 
 50.039 
 
 2.88 
 
 2.61 
 
 28.35 
 
 8 
 
 9 
 
 9.69 
 
 .344 
 
 9.00 
 
 28.28 
 
 30.43 
 
 .42 
 
 0.394 
 
 63.633 
 
 2.29 
 
 3.30 
 
 34.08 
 
 8 
 
 10 
 
 10.75 
 
 .366 
 
 10.02 
 
 31.47 
 
 33.77 
 
 .38 
 
 0.355 
 
 78.838 
 
 1.82 
 
 4.08 
 
 40.64 
 
 8 
 
 STRENGTH OF METALS PER SQUARE INCH 
 
 Material 
 
 Ulti- 
 mate 
 Tensile 
 Pounds 
 
 Ulti- 
 mate 
 Com- 
 pression 
 Pounds 
 
 Ulti- 
 mate 
 Shear- 
 ing 
 Pounds 
 
 Modu- 
 lus of 
 Rupture 
 Pounds 
 
 Modu- 
 lus of 
 Elas- 
 ticity 
 Millions 
 
 Wrought iron 
 Shape iron . 
 
 50,000 
 48 000 
 
 44,000 
 
 44,000 
 
 48,000 
 
 27 
 2fi 
 
 Structural steel | 
 
 60,000 
 
 
 
 
 
 Cast iron 
 
 65,000 
 18 000 
 
 52,000 
 81 000 
 
 52,000 
 2^ nnn 
 
 60,000 
 A~ f)(\o 
 
 29 
 
 Steel, castings. . . 
 
 70 000 
 
 70 000 
 
 60 000 
 
 70 000 
 
 30 
 
 Brass, cast 
 
 24 000 
 
 *30 000 
 
 on ooo 
 
 on nnn 
 
 
 Bronze, phosphor. . . 
 
 50 000 
 
 
 
 
 14 
 
 Bronze, aluminum 
 Aluminum, commercial 
 
 75,000 
 15,000 
 
 120,000 
 12,000 
 
 12,000 
 
 
 11 
 
 *Unit stress producing 10% reduction in original length. 
 
PROPERTIES OF MATERIALS 
 STANDARD AND EXTRA-GAUGE STEEL BOILER TUBES 
 
 297 
 
 Out- 
 
 Standard 
 Thickness 
 
 Nominal Weight per Foot, in 
 Pounds 
 
 side 
 
 
 
 Diam- 
 
 Nearest 
 
 
 Stand- 
 
 One 
 
 Two 
 
 Three 
 
 Four 
 
 eter 
 
 Birm. 
 
 
 ard 
 
 Extra 
 
 Extra 
 
 Extra 
 
 Extra 
 
 Inches 
 
 Wire 
 
 Inch 
 
 Thick- 
 
 Wire 
 
 Wire 
 
 Wire 
 
 Wire 
 
 
 Gauge 
 
 
 ness 
 
 Gauge 
 
 Gauges 
 
 Gauges 
 
 Gauges 
 
 1 
 
 13 
 
 .095 
 
 .90 
 
 1.04 
 
 1.13 
 
 1.24 
 
 1.35 
 
 H 
 
 13 
 
 .095 
 
 1.15 
 
 1.33 
 
 1.45 
 
 1.60 
 
 1.74 
 
 H 
 
 13 
 
 .095 
 
 1.40 
 
 1.62 
 
 1.77 
 
 1.96 
 
 2.14 
 
 1J 
 
 13 
 
 .095 
 
 1.66 
 
 1.91 
 
 . 2.09 
 
 2.31 
 
 2.53 
 
 ^ 
 
 13 
 
 .095 
 
 1.91 
 
 2.20 
 
 2.41 
 
 2.67 
 
 2.93 
 
 2J 
 
 13 
 
 .095 
 
 2.16 
 
 2.49 
 
 2.73 
 
 3.03 
 
 3.32 
 
 2 
 
 12 
 
 .109 
 
 2.75 
 
 3.05 
 
 3.39 
 
 3.72 
 
 4.12 
 
 2f 
 
 12 
 
 .109 
 
 3.04 
 
 3.37 
 
 3.74 
 
 4.11 
 
 4.56 
 
 3 
 
 12 
 
 .109 
 
 3.33 
 
 3.69 
 
 4.10 
 
 4.51 
 
 5.00 
 
 3i 
 
 11 
 
 .120 
 
 3.96 
 
 4.46 
 
 4.90 
 
 5.44 
 
 5.90 
 
 3J 
 
 11 
 
 .120 
 
 4.28 
 
 4.82 
 
 5.30 
 
 5.88 
 
 6.38 
 
 31 
 
 11 
 
 .120 
 
 4.60 
 
 5.18 
 
 5.69 
 
 ' 6.32 
 
 6.86 
 
 4 
 
 10 
 
 .134 
 
 5.47 
 
 6.09 
 
 6.76 
 
 7.34 
 
 8.23 
 
 4| 
 
 10 
 
 .134 
 
 6.17 
 
 6.88 
 
 7.64 
 
 8.31 
 
 9.32 
 
 5 
 
 9 
 
 .148 
 
 7.58 
 
 8.52 
 
 9.27 
 
 10.40 
 
 11.23 
 
 6 
 
 8 
 
 .165 
 
 10.16 
 
 11.19 
 
 12.57 
 
 13.58 
 
 14.65 
 
 7 
 
 8 
 
 .165 
 
 11.90 
 
 13.11 
 
 14.74 
 
 15.93 
 
 17.19 
 
 8 
 
 8 
 
 .165 
 
 13.65 
 
 15.04 
 
 16.91 
 
 18.28 
 
 19.73 
 
 9 
 
 7 
 
 .180 
 
 16.76 
 
 19.07 
 
 20.63 
 
 22.27 
 
 24.18 
 
 10 
 
 6 
 
 .203 
 
 21.00 
 
 22.98 
 
 24.82 
 
 26.95 
 
 29.47 
 
 11 
 
 5 
 
 .220 
 
 25.00 
 
 27.36 
 
 29.71 
 
 32.51 
 
 34.29 
 
 12 
 
 4 
 
 .229 
 
 28.50 
 
 31.19 
 
 34.01 
 
 36.52 
 
 39.92 
 
 13 
 
 4 
 
 .238 
 
 32.06 
 
 35.25 
 
 38.57 
 
 40.70 
 
 45.98 
 
 STANDARD LAP-WELDED CHARCOAL-IRON BOILER TUBES 
 
 
 
 
 
 Length of 
 
 
 Diameter 
 Inches 
 
 Thick- 
 
 Circumference 
 Inches 
 
 Transverse Area 
 Square Inches 
 
 Tube in Feet 
 per Square 
 Foot of 
 
 Weight 
 per 
 
 
 ness 
 
 
 
 Surface 
 
 Foot 
 
 
 Inch 
 
 
 
 
 P H 
 
 Out- 
 
 In- 
 
 
 Out- 
 
 In- 
 
 Out- 
 
 In- 
 
 Out- 
 
 In- 
 
 oun s 
 
 side 
 
 side 
 
 
 side 
 
 side 
 
 side 
 
 side 
 
 side 
 
 side 
 
 
 1 
 
 .810 
 
 .095 
 
 3.142 
 
 2.545 
 
 .785 
 
 .515 
 
 3.820 
 
 4.479 
 
 .90 
 
 u 
 
 1.060 
 
 .095 
 
 3.927 
 
 3.330 
 
 1.227 
 
 .882 
 
 3.056 
 
 3.604 
 
 1.15 
 
 H 
 
 1.310 
 
 .095 
 
 4.712 
 
 4.115 
 
 1.767 
 
 1.348 
 
 2.547 
 
 2.916 
 
 1.40 
 
 if 
 
 1.560 
 
 .095 
 
 5.498 
 
 4.901 
 
 2.405 
 
 1.911 
 
 2.183 
 
 2.448 
 
 1.65 
 
 2 
 
 1.810 
 
 .095 
 
 6.283 
 
 5.686 
 
 3.142 
 
 2.573 
 
 1.910 
 
 2.110 
 
 1.91 
 
 2i 
 
 2.060 
 
 .095 
 
 7.069 
 
 6.472 
 
 3.976 
 
 3.333 
 
 1.698 
 
 1.854 
 
 2.16 
 
 2h 
 
 2.282 
 
 .109 
 
 7.854 
 
 7.169 
 
 4.909 
 
 4.090 
 
 1.528 
 
 1.674 
 
 2.75 
 
 2| 
 
 2.532 
 
 .109 
 
 8.639 
 
 7.955 
 
 5.940 
 
 5.035 
 
 1.389 
 
 1.508 
 
 3.04 
 
 3 
 
 2.782 
 
 .109 
 
 9.425 
 
 8.740 
 
 7.069 
 
 6.079 
 
 1.273 
 
 1.373 
 
 3.33 
 
 3i 
 
 3.010 
 
 .120 
 
 10.210 
 
 9.456 
 
 8.296 
 
 7.116 
 
 1.175 
 
 1.269 
 
 3.96 
 
 3* 
 
 3.260 
 
 .120 
 
 10.996 
 
 10.242 
 
 9.621 
 
 8.347 
 
 1.091 
 
 1.172 
 
 4.28 
 
 3f 
 
 3.510 
 
 .120 
 
 11.781 
 
 11.027 
 
 11.045 
 
 9.676 
 
 1.019 
 
 1.088 
 
 4.60 
 
 4 
 
 3.732 
 
 .134 
 
 12.566 
 
 11.724 
 
 12.566 
 
 10.939 
 
 .955 
 
 1.024 
 
 5.47 
 
 4* 
 
 4.232 
 
 .134 
 
 14.137 
 
 13.295 
 
 15.904 
 
 14.066 
 
 .849 
 
 .903 
 
 6.17 
 
 5 
 
 4.704 
 
 .148 
 
 15.708 
 
 14.778 
 
 19.635 
 
 17.379 
 
 .764 
 
 .812 
 
 7.58 
 
 6 
 
 5.670 
 
 .165 
 
 18.850 
 
 17.813 
 
 28.274 
 
 25.250 
 
 .637 
 
 .674 
 
 10.16 
 
 7 
 
 6.670 
 
 .165 
 
 21.991 
 
 20.954 
 
 38.485 
 
 34.942 
 
 .546 
 
 .573 
 
 11.90 
 
 8 
 
 7.670 
 
 .165 
 
 25.133 
 
 24.096 
 
 50.266 
 
 46.204 
 
 .477 
 
 .498 
 
 13.65 
 
 9 
 
 8.640 
 
 .180 
 
 28.274 
 
 27.143 
 
 63.617 
 
 58.630 
 
 .424 
 
 .442 
 
 16.76 
 
 10 
 
 9.594 
 
 .205 
 
 31.416 
 
 30.141 
 
 78.540 
 
 72.292 
 
 .382 
 
 .398 
 
 21.00 
 
298 
 
 PROPERTIES OF MATERIALS 
 WEIGHT OF WROUGHT IRON* 
 
 Thick- 
 ness or 
 Diam- 
 eter 
 Inches 
 
 Weight 
 of 
 1 Sq. Ft. 
 Pounds 
 
 Weight 
 of 
 Square 
 Bar 1 Ft. 
 Long 
 Pounds 
 
 Weight 
 of 
 Round 
 Bar 1 Ft. 
 Long 
 Pounds 
 
 Thick- 
 ness or 
 Diam- 
 eter 
 Inches 
 
 Weight 
 of 
 1 Sq. Ft. 
 Pounds 
 
 Weight 
 of 
 Square 
 Bar 1 Ft. 
 Long 
 Pounds 
 
 Weight 
 of 
 Round 
 Bar 1 Ft. 
 Long 
 Pounds 
 
 
 
 5.052 
 
 .0526 
 
 .0414 
 
 4 
 
 
 176.8 
 
 64.47 
 
 50.63 
 
 
 
 10.10 
 
 .2105 
 
 .1653 
 
 4 
 
 
 181.9 
 
 68.20 
 
 53.57 
 
 
 
 15.16 
 
 .4736 
 
 .3720 
 
 4 
 
 
 186.9 
 
 72.05 
 
 56.59 
 
 
 
 20.21 
 
 .8420 
 
 .6613 
 
 4 
 
 
 192.0 
 
 75.99 
 
 59.69 
 
 
 
 25.26 
 
 1.316 
 
 1.033 
 
 4 
 
 
 197.0 
 
 80.05 
 
 62.87 
 
 
 
 30.31 
 
 1.895 
 
 1.488 
 
 5 
 
 
 202.1 
 
 84.20 
 
 66.13 
 
 
 
 35.37 
 
 2.579 
 
 2.025 
 
 5 
 
 
 212.2 
 
 92.83 
 
 72.91 
 
 1 
 
 
 40.42 
 
 3.368 
 
 2.645 
 
 5 
 
 
 222.3 
 
 101.9 
 
 80.02 
 
 1 
 
 
 45.47 
 
 4.263 
 
 3.348 
 
 5 
 
 
 232.4 
 
 111.4 
 
 87.46 
 
 
 
 50.52 
 
 5.263 
 
 4.133 
 
 6 
 
 
 242.5 
 
 121.3 
 
 95.23 
 
 
 
 55.57 
 
 6.368 
 
 5.001 
 
 6 
 
 
 252.6 
 
 131.6 
 
 103.3 
 
 
 
 60.63 
 
 7.578 
 
 5.952 
 
 6 
 
 
 262.7 
 
 142.3 
 
 111.8 
 
 
 
 65.68 
 
 8.893 
 
 6.985 
 
 6 
 
 
 272.8 
 
 153.5 
 
 120.5 
 
 
 
 70.73 
 
 10.31 
 
 8.101 
 
 7 
 
 282.9 
 
 165.0 
 
 129.6 
 
 
 
 75.78 
 
 11.84 
 
 9.300 
 
 71 
 
 293.0 
 
 177.0 
 
 139.0 
 
 2 
 
 
 80.83 
 
 13.47 
 
 10.58 
 
 7* 
 
 303.1 
 
 189.5 
 
 148.8 
 
 2i 
 
 
 85.89 
 
 15.21 
 
 11.95 
 
 7i 
 
 313.2 
 
 202.3 
 
 158.9 
 
 2 
 
 
 90.94 
 
 17.05 
 
 13.39 
 
 8 
 
 323.3 
 
 215.6 
 
 169.3 
 
 2 
 
 
 95.99 
 
 19.00 
 
 14.92 
 
 8 
 
 
 333.4 
 
 229.3 
 
 180.1 
 
 2 
 
 
 101.0 
 
 21.05 
 
 16.53 
 
 g 
 
 
 343.5 
 
 243.4 
 
 191.1 
 
 2 
 
 
 106.1 
 
 23.21 
 
 18.23 
 
 8 
 
 
 353.6 
 
 247.9 
 
 202.5 
 
 2 
 
 
 111.2 
 
 25.47 
 
 20.01 
 
 9 
 
 363.8 
 
 272.8 
 
 214.3 
 
 2 
 
 
 116.2 
 
 27.84 
 
 21.87 
 
 9J 
 
 373.9 
 
 288.2 
 
 226.3 
 
 3 
 
 121.3 
 
 30.31 
 
 23.81 
 
 9 
 
 384.0 
 
 304.0 
 
 238.7 
 
 3* 
 
 126.3 
 
 32.89 
 
 25.83 
 
 9f 
 
 394.1 
 
 320.2 
 
 251.5 
 
 3 
 
 
 131.4 
 
 35.57 
 
 27.94 
 
 10 
 
 404.2 
 
 336.8 
 
 264.5 
 
 3 
 
 
 136.4 
 
 38.37 
 
 30.13 
 
 10* 
 
 414.3 
 
 353.9 
 
 277.9 
 
 3 
 
 
 141.5 
 
 41.26 
 
 32.41 
 
 10* 
 
 424.4 
 
 371.3 
 
 291.6 
 
 3 
 
 
 146.5 
 
 44.26 
 
 34.76 
 
 10f 
 
 434.5 
 
 389.2 
 
 305.7 
 
 3 
 
 
 151.6 
 
 47.37 
 
 37.20 
 
 11 
 
 444.6 
 
 407.5 
 
 320.1 
 
 3 
 
 
 156.6 
 
 50.57 
 
 39.72 
 
 11 
 
 . 
 
 454.7 
 
 426.3 
 
 334.8 
 
 4 
 
 161.7 
 
 53.89 
 
 42.33 
 
 11 
 
 ""*' 
 
 464.8 
 
 445.4 
 
 349.8 
 
 4 
 
 
 166.7 
 
 57.31 
 
 45.01 
 
 11 
 
 
 474.9 
 
 465.0 
 
 365.2 
 
 4 
 
 ; '' ! ; 
 
 171.8 
 
 60.84 
 
 47.78 
 
 12 
 
 485.0 
 
 485.0 
 
 380.9 
 
 *This table is for wrought iron. Multiply by .95 for weight of cast iron ; 
 by 1.02 for steel; by 1.16 for copper; by 1.09 for brass; by 1.48 for lead. 
 
 DIAMETER AND NUMBER OF WOOD SCREWS 
 
 Formulas for Wood 
 Screws 
 
 No. 
 
 Diameter 
 
 No. 
 
 Diameter 
 
 No. 
 
 Diameter 
 
 N = number 
 D = diameter 
 D = (N X. 01325) + .056 
 D-.056 
 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 10 
 
 .056 
 .069 
 .082 
 .096 
 .109 
 .122 
 .135 
 .149 
 .162 
 .175 
 .188 
 
 11 
 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 
 .201 
 .215 
 .228 
 .241 
 .255 
 .268 
 .281 
 .293 
 .308 
 .321 
 .334 
 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 
 .347 
 .361 
 .374 
 .387 
 .401 
 .414 
 .427 
 .440 
 .453 
 
 .01325 
 
SPIKES AND NAILS 
 
 Standard Steel-Wire Nails 
 
 Common Iron 
 
 Steel-Wire 
 
 
 I 
 
 Common 
 
 Finishing 
 
 Nails 
 
 Spikes 
 
 1 
 
 1,1 
 ft 
 
 1$ 
 
 || 
 
 {4 
 
 || 
 
 
 
 .| 8 
 
 2$ 
 
 S3 
 
 L 
 
 || 
 
 CO 
 
 V 
 
 % 
 
 3" 
 
 | 
 
 3 
 
 8(2 
 
 CO 
 
 1 
 
 If 
 
 I'l 
 
 li 
 
 e 
 
 2d 
 
 1 
 
 .0524 
 
 1,060 
 
 .0453 
 
 1,558 
 
 2d 
 
 1 
 
 800 
 
 3 
 
 .1620 
 
 41 
 
 3d 
 
 u 
 
 .0588 
 
 640 
 
 .0508 
 
 913 
 
 3d 
 
 u 
 
 400 
 
 3* 
 
 .1819 
 
 30 
 
 4d 
 
 If 
 
 .0720 
 
 380 
 
 .0508 
 
 761 
 
 4d 
 
 If 
 
 300 
 
 4 
 
 .2043 
 
 23 
 
 5d 
 
 11 
 
 .0764 
 
 275 
 
 .0571 
 
 500 
 
 5d 
 
 if 
 
 200 
 
 
 .2294 
 
 17 
 
 6d 
 
 2 
 
 .0808 
 
 210 
 
 .0641 
 
 350 
 
 6d 
 
 2 
 
 150 
 
 5 3 
 
 .2576 
 
 13 
 
 7d 
 
 2i 
 
 .0858 
 
 160 
 
 .0641 
 
 315 
 
 7d 
 
 21 
 
 120 
 
 51 
 
 .2893 
 
 11 
 
 8d 
 
 2i 
 
 .0935 
 
 115 
 
 .0720 
 
 214 
 
 8d 
 
 2* 
 
 85 
 
 6 
 
 .2893 
 
 10 
 
 9d 
 
 2f 
 
 .0963 
 
 93 
 
 .0720 
 
 195 
 
 9d 
 
 21 
 
 75 
 
 6* 
 
 .2249 
 
 7f 
 
 lOd 
 
 3 
 
 .1082 
 
 77 
 
 .0808 
 
 137 
 
 lOd 
 
 3 
 
 60 
 
 7 
 
 .2249 
 
 7 
 
 12d 
 
 3* 
 
 .1144 
 
 60 
 
 .0808 
 
 127 
 
 12d 
 
 31 
 
 50 
 
 8 
 
 .3648 
 
 5 
 
 16d 
 
 3i 
 
 .1285 
 
 48 
 
 .0907 
 
 90 
 
 16d 
 
 3* 
 
 40 
 
 9 
 
 .3648 
 
 4J 
 
 20d 
 
 4 
 
 .1620 
 
 31 
 
 .1019 
 
 62 
 
 20d 
 
 4 
 
 20 
 
 
 
 
 30d 
 
 4i 
 
 .1819 
 
 22 
 
 
 
 30d 
 
 41 
 
 16 
 
 
 
 
 40d 
 
 5 
 
 .2043 
 
 17 
 
 
 
 40d 
 
 6 
 
 14 
 
 
 
 
 50d 
 
 5i 
 
 .2294 
 
 13 
 
 
 
 50d 
 
 
 11 
 
 
 
 
 60d 
 
 6 
 
 .2576 
 
 11 
 
 
 
 60d 
 
 6* 
 
 8 
 
 
 
 
 WEIGHT OF 100 BOLTS WITH SQUARE HEADS AND NUTS 
 
 (The Carnegie Steel Co., Limited) 
 
 Length 
 
 Diameter of Bolts 
 
 TTnHpr 
 
 
 under 
 Head to 
 
 "D/-vi-nf 
 
 Un. 
 
 A In. 
 
 fin. 
 
 A In. 
 
 fin. 
 
 Un. 
 
 fin. 
 
 Jin. 
 
 1 In. 
 
 JrOint 
 Inches 
 
 Weight, in Pounds 
 
 li 
 
 4.0 
 
 7.0 
 
 10.5 
 
 15.2 
 
 22.5 
 
 39.5 
 
 63.0 
 
 
 
 H 
 
 4.4 
 
 7.5 
 
 11.3 
 
 16.3 
 
 23.8 
 
 41.6 
 
 66.0 
 
 
 
 2 
 
 4.8 
 
 8.0 
 
 12.0 
 
 17.4 
 
 25.2 
 
 43.8 
 
 69.0 
 
 109.0 
 
 163 
 
 21 
 
 5.2 
 
 8.5 
 
 12.8 
 
 18.5 
 
 26.5 
 
 45.8 
 
 72.0 
 
 113.3 
 
 169 
 
 2i 
 
 5.5 
 
 9.0 
 
 13.5 
 
 19.6 
 
 27.8 
 
 48.0 
 
 75.0 
 
 117.5 
 
 174 
 
 2i 
 
 5.8 
 
 9.5 
 
 14.3 
 
 20.7 
 
 29.1 
 
 50.1 
 
 78.0 
 
 121.8 
 
 180 
 
 3 
 
 6.3 
 
 10.0 
 
 15.0 
 
 21.8 
 
 30.5 
 
 52.3 
 
 81.0 
 
 126.0 
 
 185 
 
 3i 
 
 7.0 
 
 11.0 
 
 16.5 
 
 24.0 
 
 33.1 
 
 56.5 
 
 87.0 
 
 134.3 
 
 196 
 
 4 
 
 7.8 
 
 12.0 
 
 18.0 
 
 26.2 
 
 35.8 
 
 60.8 
 
 93.1 
 
 142.5 
 
 207 
 
 f 
 
 8.5 
 
 13.0 
 
 19.5 
 
 28.4 
 
 38.4 
 
 65.0 
 
 99.1 
 
 151.0 
 
 218 
 
 5 
 
 9.3 
 
 14.0 
 
 21.0 
 
 30.6 
 
 41.1 
 
 69.3 
 
 105.2 
 
 159.6 
 
 229 
 
 5i 
 
 10.0 
 
 15.0 
 
 22.5 
 
 32.8 
 
 43.7 
 
 73.5 
 
 111.3 
 
 168.0 
 
 240 
 
 6 
 
 10.8 
 
 16.0 
 
 24.0 
 
 35.0 
 
 46.4 
 
 77.8 
 
 117.3 
 
 176.6 
 
 251 
 
 6i 
 
 
 
 25.5 
 
 37.2 
 
 49.0 
 
 82.0 
 
 123.4 
 
 185.0 
 
 262 
 
 7 
 
 
 
 27.0 
 
 39.4 
 
 51.7 
 
 86.3 
 
 129.4 
 
 193.7 
 
 273 
 
 7| 
 
 
 
 28.5 
 
 41.6 
 
 54.3 
 
 90.5 
 
 135.0 
 
 202.0 
 
 284 
 
 8 
 
 
 
 30.0 
 
 43.8 
 
 59.6 
 
 94.8 
 
 141.5 
 
 210.7 
 
 295 
 
 9 
 
 
 
 
 46.0 
 
 64.9 
 
 103.3 
 
 153.6 
 
 227.8 
 
 317 
 
 10 
 
 
 
 
 48.2 
 
 70.2 
 
 111.8 
 
 165.7 
 
 224.8 
 
 339 
 
 11 
 
 
 
 
 50.4 
 
 75.5 
 
 120.3 
 
 177.8 
 
 261.9 
 
 360 
 
 12 
 
 
 
 
 52.6 
 
 80.8 
 
 128.8 
 
 1-89.9 
 
 278.9 
 
 382 
 
 13 
 
 
 
 
 
 86.1 
 
 137.3 
 
 202:0 
 
 296.0 
 
 404 
 
 14 
 
 
 
 
 
 91.4 
 
 145.8 
 
 214.1 
 
 313.0 
 
 426 
 
 15 
 
 
 
 
 
 96.7 
 
 154.3 
 
 226.2 
 
 330.1 
 
 448 
 
 16 
 
 
 
 
 
 102.0 
 
 162.8 
 
 238.3 
 
 347.1 
 
 470 
 
 17 
 
 
 
 
 
 107.3 
 
 171.0 
 
 250.4 
 
 364.2 
 
 492 
 
 18 
 
 
 
 
 
 112.6 
 
 179.5 
 
 262.6 
 
 381.2 
 
 514 
 
 19 
 
 
 
 
 
 117.9 
 
 188.0 
 
 274.7 
 
 398.3 
 
 536 
 
 20 ' 
 
 
 
 
 
 123.2 
 
 206.5 
 
 286.8 
 
 415.3 
 
 558 
 
 Per Inch 
 
 1.4 
 
 2.1 
 
 3.1 
 
 4.2 
 
 5.5 
 
 8.5 
 
 12.3 
 
 16.7 
 
 21.8 
 
 Additional 
 
 
 
 
 
 
 1 
 
 
 
 299 
 
300 
 
 PROPERTIES OF MATERIALS 
 
 PROPORTIONS OF THE UNITED STATES STANDARD SCREW 
 THREADS, NUTS, AND BOLT HEADS 
 
 Diam. 
 
 of 
 
 Screw 
 Inches 
 
 Threads 
 per 
 nch 
 
 20 
 
 18 
 
 16 
 
 14 
 
 13 
 
 12 
 
 11 
 
 10 
 
 9 
 
 8 
 
 7 
 
 7 
 
 Diam. 
 
 of 
 
 Core 
 Inch 
 
 Width 
 
 of 
 
 Flat 
 Inch 
 
 .185 
 
 .240 
 
 .294 
 
 .344 
 
 .400 
 
 .454 
 
 .507 
 
 .620 
 
 .731 
 
 .837 
 
 .940 
 
 1.065 
 
 1.160 
 
 1.284 
 
 1.389 
 
 1.490 
 
 1.615 
 
 1.712 
 
 1.962 
 
 2.175 
 
 2.425 
 
 2.628 
 
 2.878 
 
 3.100 
 
 3.317 
 
 3.566 
 
 3.798 
 
 4.027 
 
 4.255 
 
 4.480 
 
 4.730 
 
 4.953 
 
 5.203 
 
 5.423 
 
 .0062 
 .0070 
 .0078 
 .0089 
 .0096 
 .0104 
 .0113 
 .0125 
 .0140 
 .0156 
 .0180 
 .0180 
 .0210 
 .0210 
 .0227 
 .0250 
 .0250 
 .0280 
 .0280 
 .0310 
 .0310 
 .0357 
 .0357 
 .0384 
 .0410 
 .0410 
 .0435 
 .0460 
 .0480 
 .0500 
 .0500 
 .0526 
 .0526 
 .0555 
 
 Inside 
 Diam. 
 Inch 
 
 Outside 
 Diam. 
 Inch 
 
 Diagonal 
 Inch 
 
 Height 
 
 of 
 
 Head 
 Inches 
 
 The threads have an angle of 60, with flat tops and bottoms, and are of the 
 following proportions: 
 
 Notation of Letters, All Dimensions in Inches 
 
 D = outside diameter of screw; 
 
 d = diameter of root of thread, or of 
 
 hole in nut; 
 p = pitch of screw; 
 t = number of threads per inch; 
 /=flat top and bottom; 
 o = outside diameter of hexagon nut 
 
 or bolt head; 
 
 P = 
 
 Vl6D + 10 -2.909 
 
 = D- 
 
 1.299 
 
 16.64 
 
 3D , 1 
 
 = inside diameter of hexagon, or 
 side of square nut or bolt head ; 
 5 = diagonal of square nut or bolt 
 
 head; 
 h = height of rough or unfinished bolt 
 
 head. 
 
 The height of a finished nut or bolt 
 head is made equal to the diameter D 
 of the screw. 
 
 o=1.155* 
 
PROPERTIES OF MATERIALS 
 WEIGHT OF 1 LIN. FT. OF FLAT WROUGHT IRON* 
 
 301 
 
 Size 
 Inches 
 
 Weight 
 Pounds 
 
 Size 
 Inches 
 
 Weight 
 Pounds 
 
 Size 
 
 Inches 
 
 Weight 
 Pounds 
 
 1 Xi 
 
 .85 
 
 5iXf 
 
 6.65 
 
 4 X 
 
 
 8.45 
 
 HXi 
 
 1.06 
 
 six! 
 
 6.97 
 
 
 
 8.98 
 
 Hxi 
 
 1.27 
 
 SfXf 
 
 7.29 
 
 ix 
 
 
 9.51 
 
 HXi 
 
 1.48 
 
 6 X| 
 
 7.60 
 
 X 
 
 
 10.03 
 
 2^i 
 
 1.69 
 
 
 
 5 X 
 
 
 10.56 
 
 
 1.90 
 
 1 X 
 
 
 1.69 
 
 ix 
 
 
 11.09 
 
 2|Xi 
 
 2.11 
 
 HX 
 
 
 2.11 
 
 x 
 
 
 11.62 
 
 2fXi 
 
 2.32 
 
 HX 
 
 
 2.53 
 
 X 
 
 
 12.15 
 
 3 Xi 
 
 2.53 
 
 HX 
 
 
 2.96 
 
 6 XI 
 
 12.67 
 
 
 2.75 
 
 2 X 
 
 
 3.38 
 
 
 
 ix * 
 
 2.96 
 
 
 
 3.80 
 
 1 X 
 
 
 2.53 
 
 Xi 
 
 3.17 
 
 !x 
 
 
 4.22 
 
 HX 
 
 
 3.17 
 
 4 Xi 
 
 3.38 
 
 X 
 
 
 4.65 
 
 HX 
 
 
 3.80 
 
 4iXi 
 
 3.59 
 
 3 1 X I 
 
 5.07 
 
 
 
 4.44 
 
 
 3.80 
 
 
 5.49 
 
 2*X 
 
 
 5.07 
 
 4 a X i 
 
 4.01 
 
 3|X 
 
 
 5.92 
 
 !x 
 
 
 5.70 
 
 5 Xi 
 
 4.22 
 
 3fX 
 
 
 6.33 
 
 x 
 
 
 6.33 
 
 
 4.44 
 
 4 X 
 
 
 6.76 
 
 X j 
 
 
 6.97 
 
 s|xi 
 
 4.65 
 
 
 
 7.18 
 
 3 X 
 
 
 7.60 
 
 slxf 
 
 4.86 
 
 !x 
 
 
 7.60 - 
 
 3 jX 
 
 
 8.24 
 
 6 Xi 
 
 5.07 
 
 X 
 
 
 8.03 
 
 slxj 
 
 
 8.87 
 
 
 
 5 X 
 
 
 8.45 
 
 3|X- 
 
 
 9.51 
 
 1 X 
 
 
 1.27 
 
 six 
 
 
 8.87 
 
 
 
 10.14 
 
 HX 
 
 
 1.58 
 
 six 
 
 
 9.30 
 
 4iX ; 
 
 
 10.77 
 
 HX 
 
 
 1.90 
 
 six 
 
 
 9.72 
 
 4iX i 
 
 
 11.41 
 
 ifx 
 
 
 2.22 
 
 6 X 
 
 
 10.14 
 
 4f X '- 
 
 
 12.04 
 
 2 X 
 
 
 2.53 
 
 
 
 
 5 Xi 
 
 
 12.67 
 
 
 
 2.85 
 
 1 X 
 
 
 2.11 
 
 5iXi 
 
 
 13.31 
 
 2|X 
 
 
 3.17 
 
 HX 
 
 
 2.64 
 
 5JX i 
 
 
 13.94 
 
 2|X 
 
 
 3.49 
 
 HX 
 
 
 3.17 
 
 5fx! 
 
 
 14.57 
 
 3 X 
 
 
 3.80 
 
 ifx 
 
 
 3.70 
 
 6 Xi 
 
 15.21 
 
 
 
 4.12 
 
 2 X 
 
 
 4.22 
 
 
 
 3|X 
 
 
 4.44 
 
 
 
 4.75 
 
 HXI 
 
 5.07 
 
 3fX 
 
 
 4.75 
 
 2 A X 
 
 
 5.28 
 
 2 XI 
 
 6.76 
 
 4 X 
 
 
 5.07 
 
 2|X 
 
 
 5.81 
 
 3 XI 
 
 10.14 
 
 
 
 5.39 
 
 3 X 
 
 
 6.33 
 
 4 XI 
 
 13.52 
 
 4 * V 
 
 
 5.70 
 
 3iX 
 
 
 6.87 
 
 5 XI 
 
 16.90 
 
 4|X 
 
 
 6.02 
 
 six 
 
 
 7.39 
 
 6 XI 
 
 20.28 
 
 5 X 
 
 
 6.33 
 
 3fX 
 
 
 7.92 
 
 7 XI 
 
 23.66 
 
 TIMBER AND BOARD MEASURE 
 
 TIMBER MEASURE 
 
 Volume of Round Timber. The cubic contents of a round log are those 
 of a cylinder of the same dimensions. As logs usually taper throughout their 
 length, the diameter taken is the mean of the two end diameters. The cubic 
 contents of a cylinder are expressed by the formula, -^-l = ~^dl. From this 
 
 it is possible to deduce, for field use, the following: 
 
 Rule. The number of cubic feet in a round log is equal to one-quarter of the 
 
 mean girth (circumference or y) multiplied by the mean diameter multiplied by 
 the length. If, as is usually the case, the girth and diameter are given in inches, 
 the result obtained must be divided by 144- 
 
 *Multiply by .95 lor weight of cast iron; by 1.02 for weight of steel; by 1.16 
 for copper; by 1.09 for brass; by 1.48 for lead. 
 
302 
 
 PROPERTIES OF MATERIALS 
 
 When the accompanying table of quarter girths is used, it is only necessary 
 to measure the circumference of each end of the log and divide the sum by 2, 
 for the mean girth. Opposite one-quarter of this mean girth, find the area in 
 feet This multiplied by the length of the log, gives the cubic contents in feet. 
 
 EXAMPLE. The circumferences of a 20-ft. log are 48 and 60 in., respect- 
 ively. What is the cubic contents of the log? 
 
 SOLUTION. ( 48 + 60 ) -h 2 = 54 - mean girth. 54-7-4 = 13* = one-quarter 
 girth. The area corresponding to a quarter girth of 13* in. is 1.26 sq. ft. Hence, 
 1.26X20 = 25.20, number of cubic feet in the log. 
 
 TABLE OF QUARTER GIRTHS 
 
 Quarter 
 Girths 
 Inches 
 
 Area 
 Feet 
 
 Quarter 
 Girths 
 Inches 
 
 Area 
 Feet 
 
 Quarter 
 Girths 
 Inches 
 
 Area 
 Feet 
 
 6 
 
 .250 
 
 121 
 
 1.04 
 
 19 
 
 2.50 
 
 61 
 
 .272 
 
 12* 
 
 1.08 
 
 19* 
 
 2.64 
 
 el 
 
 .294 
 
 12f 
 
 1.12 
 
 20 
 
 2.77 
 
 61 
 
 .317 
 
 13 
 
 1.17 
 
 20* 
 
 2.91 
 
 7 
 
 .340 
 
 131 
 
 1.21 
 
 21 
 
 3.06 
 
 71 
 
 .364 
 
 13* 
 
 1.26 
 
 21* 
 
 3.20 
 
 7* 
 
 .390 
 
 131 
 
 1.31 
 
 22 
 
 3.36 
 
 7f 
 
 .417 
 
 14 
 
 1.36 
 
 22* 
 
 3.51 
 
 8 
 
 .444 
 
 141 
 
 1.41 
 
 23 
 
 3.67 
 
 81 
 
 8* 
 
 .472 
 .501 
 
 14* 
 141 
 
 1.46 
 1.51 
 
 23* 
 24 
 
 3.83 
 4.00 
 
 81 
 
 .531 
 
 15 
 
 1.56 
 
 24* 
 
 4.16 
 
 9 
 
 .562 
 
 151 
 
 1.61 
 
 25 
 
 4.34 
 
 91 
 
 .594 
 
 15* 
 
 1.66 
 
 25* 
 
 4.51 
 
 8* 
 
 .626 
 
 151 
 
 1.72 
 
 26 
 
 4.69 
 
 91 
 
 .659 
 
 16 
 
 1.77 
 
 26* 
 
 4.87 
 
 10 
 
 .694 
 
 161 
 
 1.83 
 
 27 
 
 5.06 
 
 101 
 
 .730 
 
 16* 
 
 1.89 
 
 27* 
 
 5.25 
 
 10* 
 
 .766 
 
 161 
 
 1.94 
 
 28 
 
 5.44 
 
 101 
 
 .803 
 
 17 
 
 2.00 
 
 28* 
 
 5.64 
 
 11 
 Hi 
 
 m 
 
 .840 
 .878 
 .918 
 
 171 
 17* 
 171 
 
 2.09 
 2.12 
 2.18 
 
 29 
 29* 
 30 
 
 5.84 
 6.04 
 6.25 
 
 111 
 
 .959 
 
 18 
 
 2.25 
 
 
 
 12 
 
 1.000 
 
 18* 
 
 2.37 
 
 
 
 BOARD MEASURE 
 
 The unit of board measure (B. M.) is the board foot, which is the contents 
 of a board 1 ft. square and 1 in. thick. When calculating board feet all thick- 
 nesses under 1 in. are counted as if 1 in., while all over 1 in. are counted at their 
 exact value. Thus, a 1-in. plank is counted as a 1-in. plank, and a li-in. 
 plank as 11 in. When estimating the number of board feet that should be cut 
 from a log, numerous rules have been devised, but the one in most general use 
 is known as Doyle's, Connecticut River, or Scribner's rule; it is as follows: 
 
 Rule. The diameter of the small end of the log, inside the bark, is first mea- 
 sured. From this diameter, 4 in. are deducted for slabbing and squaring up. The 
 square of one-fourth of this remainder, multiplied by the length, in feet, will give 
 the resultant board feet. 
 
 Table of Board Feet. The number of feet board measure for 1 ft. in length 
 of planks of all thicknesses, increasing by single inches, up to 12 in., and thence, 
 by each 2 in. up to 24 in., are given in the accompanying table. In the rare 
 cases where the thickness is not an even inch, the value for the board feet may 
 be found by interpolation. For timbers larger than 12X24, it is necessary 
 to take the board feet of two pieces each one-half the size of the stick under 
 consideration. Thus, the number of board feet in one piece 16X24 is twice 
 the number of board feet in a piece 8X24 or in one 16 X 12, 
 
 To economize space, the values have been carried to the first repeating 
 decimal only, which is marked with a (*). Unless the extension indicated is 
 
HYDROSTATICS 
 
 303 
 
 made, the final figure should be made 1 greater than in the table; thus, if the 
 figures in the table are 1.6*, this should be used as 1.7; or, better, as 1.67, or If, 
 because the correct value is 1.66666, repeating indefinitely. 
 
 TABLE OF BOARD FEET 
 
 D 
 
 Width of Plank, in Inches 
 
 o 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 1 
 
 Size of Plank, in Board Feet 
 
 1 
 
 .083* 
 
 .16* 
 
 .25 
 
 .3* 
 
 .416* 
 
 .5 
 
 .583* 
 
 .6* 
 
 .75 
 
 .83* 
 
 .916* 
 
 1 
 
 2 
 
 .166* 
 
 .33* 
 
 .50 
 
 .6* 
 
 .833* 
 
 1.0 
 
 1.166* 
 
 1.3* 
 
 1.50 
 
 1.66* 
 
 1.833* 
 
 2 
 
 3 
 
 .250 
 
 .50 
 
 .75 
 
 1.0 
 
 1.250 
 
 1.5 
 
 1.750 
 
 2.0 
 
 2.25 
 
 2.50 
 
 2.750 
 
 3 
 
 4 
 
 .333* 
 
 .66* 
 
 1.00 
 
 1.3* 
 
 1.666* 
 
 2.0 
 
 2.333* 
 
 2.6* 
 
 3.00 
 
 3.33* 
 
 3.666* 
 
 4 
 
 5 
 
 .416* 
 
 .83* 
 
 1.25 
 
 1.6* 
 
 2.083* 
 
 2.5 
 
 2.916* 
 
 3.3* 
 
 3.75 
 
 4.16* 
 
 4.583* 
 
 5 
 
 6 
 
 .500 
 
 1.00 
 
 1.50 
 
 2.0 
 
 2.500 
 
 3.0 
 
 3.500 
 
 4.0 
 
 4.50 
 
 5.00 
 
 5.500 
 
 6 
 
 7 
 
 .583* 
 
 1.16* 
 
 1.75 
 
 2.3* 
 
 2.916* 
 
 3.5 
 
 4.083* 
 
 4.6* 
 
 5.25 
 
 5.83* 
 
 6.416* 
 
 7 
 
 8 
 
 .666* 
 
 1.33* 
 
 2.00 
 
 2.6* 
 
 3.333* 
 
 4.0 
 
 4.666* 
 
 5.3* 
 
 6.00 
 
 6.66* 
 
 7.333* 
 
 8 
 
 9 
 
 .750 
 
 1.50 
 
 2.25 
 
 3.0 
 
 3.750 
 
 4.5 
 
 5.250 
 
 6.0 
 
 6.75 
 
 7.50 
 
 8.250 
 
 9 
 
 10 
 
 .833* 
 
 1.66* 
 
 2.50 
 
 3.3* 
 
 4.166* 
 
 5.0 
 
 5.833* 
 
 6.6* 
 
 7.50 
 
 8.33* 
 
 9.166* 
 
 10 
 
 11 
 
 .916* 
 
 1.83* 
 
 2.75 
 
 3.6* 
 
 4.583* 
 
 5.5 
 
 6.416* 
 
 7.3* 
 
 8.25 
 
 9.16* 
 
 10.833* 
 
 11 
 
 12 
 
 1.000 
 
 2.00 
 
 3.00 
 
 4.0 
 
 5.000 
 
 6.0 
 
 7.000 
 
 8.0 
 
 9.00 
 
 10.00 
 
 11.000 
 
 12 
 
 14 
 
 1.166* 
 
 2.33* 
 
 3.50 
 
 4.6* 
 
 5.833* 
 
 7.0 
 
 8.166* 
 
 9.3* 
 
 10.50 
 
 11.66* 
 
 12.833* 
 
 14 
 
 16 
 
 1.333* 
 
 2.66* 
 
 4.00 
 
 5.3* 
 
 6.666* 
 
 8.0 
 
 9.333* 
 
 10.6* 
 
 12.00 
 
 13.33* 
 
 14.666* 
 
 16 
 
 18 
 
 1.500 
 
 3.00 
 
 4.50 
 
 6.0 
 
 7.500 
 
 9.0 
 
 10.500 
 
 12.0 
 
 13.50 
 
 15.00 
 
 16.500 
 
 18 
 
 20 
 
 1.666* 
 
 3.33* 
 
 5.00 
 
 6.6* 
 
 8.333* 
 
 10.0 
 
 11.666* 
 
 13.3* 
 
 15.00 
 
 16.66* 
 
 18.333* 
 
 20 
 
 22 
 
 1.833* 
 
 3.66* 
 
 5.50 
 
 7.3* 
 
 9.166* 
 
 11.0 
 
 12.833* 
 
 14.6* 
 
 16.50 
 
 18.33* 
 
 20.166* 
 
 22 
 
 24 
 
 2.000 
 
 4.00 
 
 6.00 
 
 8.0 
 
 10.000 
 
 12.0 
 
 14.000 
 
 16.0 
 
 18.00 
 
 20.00 
 
 22.000 
 
 24 
 
 HYDROSTATICS 
 
 Hydrostatics treats of the equilibrium of liquids and of their pressures on 
 the walls of vessels containing them; the science depends on the way in which 
 the molecules of a liquid form a mass under the action of gravity and molecular 
 attraction, the latter of which is so modified in liquids as to give them their 
 state of liquidity. While the particles of a liquid cohere, they are free to slide 
 upon one another without the least apparent friction; and it is this perfect 
 mobility that gives them the mechanical properties considered in hydrostatics. 
 
 The fundamental property of hydrostatics is a physical axiom, and on it 
 are based nearly all the principles of hydrostatics; it is as follows: 
 
 When a pressure is exerted on any part of the surface of a liquid, that pressure 
 is transmitted undiminished to all parts of the mass, and in all directions. 
 
 Equilibrium of Liquids. The equilibrium of liquids is a property that can 
 be easily demonstrated, and examples are frequently seen. Thus, if two bar- 
 rels are connected at the bottom with a pipe, and water is poured in one until 
 it reaches within 1 ft. of the top, the water in the other will be found to have 
 attained the same height. 
 
 Pressure of Liquids on Surfaces. The general law governing the pressure 
 of liquids on surfaces is as follows: 
 
 Law. The pressure of a liquid on any surface immersed in it is equal to the 
 weight of a column of the liquid whose base is the surface pressed, and whose height 
 is the perpendicular depth of the center of gravity of the surface below the surface 
 of the liquid. 
 
 The pressure exerted by liquids is independent of the shape or size of the ves- 
 sel or cavity containing the liquid. The pressure of a liquid against any point 
 of any surface, either curved or plane, is always perpendicular to the surface 
 at that point. At any given depth, the pressure of a liquid is equal in every 
 direction, and is in direct proportion to the vertical depth below the surface. 
 
304 HYDROSTATICS 
 
 The weight of 1 cu. ft. of fresh water, at ordinary temperature of the atmos- 
 phere, that is, from 32 F. to 80 F., is usually assumed at 62.5 Ib. This is a 
 trifle more than the actual weight, but is sufficiently close for most practical 
 purposes. 
 
 To Find Pressure Exerted by Quiet W ater Against Side of Gangway or 
 Heading. Multiply the area of the side, in square feet, by the perpendicular 
 distance from the surface of the water to a point equidistant between the top 
 and bottom of the submerged heading or gangway, and multiply the product 
 by 62.5. The result will be the pressure, in pounds, exclusive of atmospheric 
 pressure; this latter need not be considered in ordinary mining work. 
 
 EXAMPLE. If an abandoned colliery, opened by a slope on a pitch of 25 
 and 100 yd. long, is allowed to fill with water, what is the average pressure 
 exerted on each square foot of the lower rib of the gangway, assuming that the 
 gangways were driven dead level, and that the length of the slope was measured 
 to a point on the lower rib equidistant between top and bottom of gangway? 
 
 SOLUTION. Perpendicular height of water is 300 X sin 25 =126.78 ft. 
 Then, the pressure on each square foot of the lower rib of gangway is 126.78 
 X 62.5 Ib. , = 7,923.75 Ib. , or over 3 3 gross tons. The total pressure exerted along 
 the gangway may readily be found by multiplying 7,923.75 Ib. by the number 
 of square feet in the lower rib against which it rests. 
 
 Pressure Against Dams, Etc. To find the total pressure of quiet water 
 against and perpendicular to any surface whatever, as a dam, embankment, 
 or the bottom, side, or top of any containing vessel, water pipe, etc., no matter 
 whether said surface is vertical, horizontal, or inclined; or whether it is flat or 
 curved ; or whether it reaches to the surface of the water or is entirely below it, 
 apply the following rule: 
 
 Rule. Multiply the area, in square feet, of the surface pressed by the vertical 
 depth, in feet, of its center of gravity below the surface of the water, and this product 
 by 62.5; the result will be the pressure in pounds. 
 
 Thus, assume that in Figs. 1, 2, and 3 the'depth of water in each dam is 
 12 ft., and. the wall or embankment is 50 ft. long. In Fig. 1 the total pressure 
 will equal 12 X 50 X 6 X 62.5 = 225,000 Ib. In Figs. 2 and 3, the walls or embank- 
 ments, being inclined, expose a greater surface to pressure, say, 18 ft. from A 
 to B. Then the total pressure equals 18X50X6X62.5 = 337,500 Ib. 
 
 The results obtained 
 are the total pressures 
 without regard to di- 
 rection. In Fig. 1 the 
 total pressure calcu- 
 late d, V 225,000 Ib., is 
 
 _ _ horizontal, tending 
 
 FIG. 1 FIG. 2 PIG. 3 either to overturn thi 
 
 wall or make it slide on its base. The center of pressure is at C, or one-third 
 of the vertical depth from the bottom. In Fig. 2, the pressure is exerted in 
 two directions; one pressure, acting horizontally, tends to overthrow or slide 
 the wall, while the other, acting vertically, tends to hold it in place. In Fig. 3, 
 the pressure is also exerted in two directions; one pressure, acting horizon- 
 tally, tends to overthrow or slide the wall, while the other tends to lift. So 
 long as the vertical depth of water remains the same, the horizontal pressure 
 remains the same, no matter what inclination is given the wall. Thus, in 
 Figs. 2 and 3, the horizontal pressure is the same as in Fig. 1, or 225,000 Ib. 
 
 Distribution of Pressure. The total pressure of the water is distributed 
 over the entire depth of the submerged part of the back of the wall, and is least 
 at the top, gradually increasing toward the bottom. But so far as regards the 
 united action of every portion of it, in tending to overthrow the wall, con- 
 sidered as a single mass of masonry incapable of being bent or broken, it may 
 all be assumed to be applied at C, which is one-third of the vertical depth from 
 the bottom in Fig. 1, or, what is the same thing, one-third of the slope distance 
 from the bottom in Figs. 2 and 3. 
 
 No matter how much water is in a dam or vessel, the pressure remains the 
 same, so long as the area pressed and the vertical depth of its center of gravity 
 below the level surface of the water remains unchanged. Thus, if the water 
 in dam shown in Fig. 1 extended back 1 m., it would exert no more pressure 
 against the wall than if it extended back only 1 ft. 
 
 In any two vessels having the same base, and containing the same depth 
 of water, no matter what quantity, the pressures on the bases are equal. Thus, 
 if Figs. 4 and 5 have the same base and are filled with water to the same depth, 
 the pressure on the bases will be equal. This fact, that the pressure on a given 
 
HYDROSTATICS 
 
 305 
 
 surface, at a given depth, is independent of the quantity of water, is called the 
 
 hydrostatic paradox. 
 
 As the pressure of water against any point is at right angles to the surface 
 
 at that point, props or other strengthening material for the bracing of 
 such structures as a sloping dam, should 
 be so placed as to offer the greatest re- 
 sistance in a line at right angles to the 
 sloping surf ace, and these supports should 
 be strongest and closest together at the 
 bottom. For the same reason, the hoops 
 on a circular tank should be strongest 
 and closest at the bottom. 
 
 Transmission of Pressure Through 
 Water. Water, in common with other 
 liquids, possesses the important property 
 of transmitting pressure equally in all 
 directions. Thus, if a vessel is constructed 
 
 FIG. 4 FIG. 5 
 
 
 FIG. 6 
 
 with two cylinders, the area of one being 10 sq. in., and that of the other 100 
 sq. in., and the vessel is filled with water, as in Fig. 6, and pistons are fitted to 
 the cylinders, a pressure of 100 Ib. applied at the smaller will balance 1,000 Ib. 
 at the larger. This is the principle of the hydrostatic press. Air and other 
 gaseous fluids transmit pressure equally in all directions, like liquids, but not as 
 rapidly. 
 
 To Find Pressure on Plane Surface at Any Given Depth of Water. For 
 pounds per square inch, multiply depth in feet by .434. For pounds per 
 square foot, multiply depth in feet by 62.5. For tons per square foot, multiply 
 
 PRESSURE AT DIFFERENT VERTICAL DEPTHS ALSO TOTAL 
 PRESSURE AGAINST A PLANE 1 FT. WIDE EXTEND- 
 ING VERTICALLY FROM SURFACE OF 
 WATER TO SAME DEPTHS 
 
 fl 
 
 Pressure 
 Pounds 
 per Sq. Ft. 
 
 Total 
 Pressure 
 Pounds 
 
 H 
 
 -d< 
 
 C/J rf 
 
 8 gw 
 
 ^ fe 
 
 Total 
 Pressure 
 Pounds 
 
 H 
 
 Pressure 
 Pounds 
 per Sq. Ft. 
 
 Total 
 Pressure 
 Pounds 
 
 1 
 
 62.5 
 
 31 
 
 27 
 
 1,687 
 
 22,781 
 
 65 
 
 4,062 
 
 132,031 
 
 2 
 
 125 
 
 125 
 
 28 
 
 1,750 
 
 24.500 
 
 70 
 
 4,375 
 
 153,125 
 
 3 
 
 187 
 
 281 
 
 29 
 
 1,812 
 
 26,281 
 
 75 
 
 4,687 
 
 175,781 
 
 4 
 
 250 
 
 500 
 
 30 
 
 1,875 
 
 28,125 
 
 80 
 
 5,000 
 
 200,000 
 
 5 
 
 312 
 
 781 
 
 31 
 
 1,937 
 
 30,031 
 
 85 
 
 5,312 
 
 225,781 
 
 6 
 
 375 
 
 1,125 
 
 32 
 
 2,000 
 
 32,000 
 
 90 
 
 5,625 
 
 253,125 
 
 7 
 
 437 
 
 1,531 
 
 33 
 
 2,062 
 
 34,031 
 
 95 
 
 5,937 
 
 282,031 
 
 8 
 
 500 
 
 2,000 
 
 34 
 
 2,125 
 
 36,125 
 
 100 
 
 6,250 
 
 312,500 
 
 9 
 
 562 
 
 2,531 
 
 35 
 
 2,187 
 
 38,281 
 
 110 
 
 6,875 
 
 378,125 
 
 10 
 
 625 
 
 3,125 
 
 36 
 
 2,250 
 
 40,500 
 
 120 
 
 7,500 
 
 450,000 
 
 11 
 
 687 
 
 3,781 
 
 37 
 
 2,312 
 
 42,781 
 
 130 
 
 8,125 
 
 528,100 
 
 12 
 
 750 
 
 4,500 
 
 38 
 
 2,375 
 
 45,125 
 
 140 
 
 8,750 
 
 612,500 
 
 13 
 
 812 
 
 5,281 
 
 39 
 
 2,437 
 
 47,531 
 
 150 
 
 9,375 
 
 703,125 
 
 14 
 
 875 
 
 6,125 
 
 40 
 
 2,500 
 
 50,000 
 
 160 
 
 10,000 
 
 800.000 
 
 15 
 
 937 
 
 7,031 
 
 41 
 
 2,562 
 
 52,531 
 
 170 
 
 10,625 
 
 903,125 
 
 16 
 
 1,000 
 
 8,000 
 
 42 
 
 2,625 
 
 55,125 
 
 180 
 
 11,250 
 
 1,012,500 
 
 17 
 
 1,062 
 
 9,031 
 
 43 
 
 2,687 
 
 57,781 
 
 190 
 
 11,875 
 
 1,128,125 
 
 18 
 
 1,125 
 
 10,125 
 
 44 
 
 2,750 
 
 60,500 
 
 200 
 
 12,500 
 
 1,250.000 
 
 19 
 
 1,187 
 
 11,281 
 
 45 
 
 2,812 
 
 63,281 
 
 225 
 
 14,062 
 
 1,582,031 
 
 20 
 
 1,250 
 
 12,500 
 
 46 
 
 2,875 
 
 66,125 
 
 250 
 
 15,625 
 
 1,953,125 
 
 21 
 
 1,312 
 
 13,781 
 
 47 
 
 2,937 
 
 69,031 
 
 275 
 
 17,187 
 
 2,363,281 
 
 22 
 
 1,375 
 
 15,125 
 
 48 
 
 3,000 
 
 72,000 
 
 300 
 
 18,750 
 
 2,812,500 
 
 23 
 
 1,437 
 
 16,531 
 
 49 
 
 3,062 
 
 75,031 
 
 350 
 
 21,875 
 
 3,828,125 
 
 24 
 
 1,500 
 
 18,000 
 
 50 
 
 3,125 
 
 78,125 
 
 400 
 
 25,000 
 
 5,000,000 
 
 25 
 
 1,562 
 
 19,531 
 
 55 
 
 3,437 
 
 94,531 
 
 450 
 
 28,125 
 
 6,328,125 
 
 26 
 
 1,625 
 
 21.12". 
 
 60 
 
 3.750 
 
 112,500 
 
 500 
 
 31,250 
 
 7,812,500 
 
306 
 
 HYDROSTATICS 
 
 depth in feet by .0279. The pressure per square foot at different depths 
 increases directly as the depths. The total pressure against a plane 1 ft. wide 
 at different depths increases as the square of the depths. 
 
 Pressure of Water in Pipes. As water exerts a pressure equally in all 
 directions, it is important that, in pipe lines, the pipe should be sufficiently 
 thick to assure strength enough to resist a bursting pressure. In ordinary 
 practice, the thickness of cast-iron water pipes of different bores is calculated 
 by Mr. J. T. Fanning's formula, given in his Hydraulic Engineering, which 
 is as follows, the thickness and bore being given in inches and the pressure in 
 pounds per square inch: 
 
 _,. , (pressure -f- 100) X bore ooov^/i b re \ 
 
 Thlckness = .4Xultimate tensile strength +' 333X ( l ~ w) 
 This formula, worked out for different heads and different sizes of bore, 
 yields the results given in the accompanying table. In this table, the ultimate 
 tensile strength of cast iron is taken at 18,000 Ib. per sq. in. The addition of 
 100 Ib. to the pressure is made to allow for water ram. The valves of water 
 pipes should be closed slowly, and especially as the pipes increase in diameter. 
 If this rule is not observed, the momentum of the water which is suddenly 
 stopped creates a great pressure against the pipes in all directions and 
 throughout the entire length of the line above the valve, even if it is many 
 miles long, and there is danger of the pipes bursting at any point. For this 
 reason, stop-gates are shut by screws, because they prevent any very sudden 
 closing; but in pipes of large diameters, even the screws must be worked 
 very slowly to prevent the pipes bursting. 
 
 THICKNESS OF PIPE FOR DIFFERENT HEADS AND PRESSURES 
 
 Head, in Feet 
 
 50 
 
 100 
 
 200 
 
 300 
 
 500 
 
 1,000 
 
 Pressure, in Pounds 
 per Square Inch 
 
 21.7 
 
 43.4 
 
 86.8 
 
 130 
 
 217 
 
 434 
 
 Bore 
 
 
 Inches 
 
 Thickness of Pipe, in Inches 
 
 2 
 
 .36 
 
 .37 
 
 .38 
 
 .39 
 
 .42 
 
 .48 
 
 3 
 
 .37 
 
 .38 
 
 .40 
 
 .42 
 
 .45 
 
 .54 
 
 4 
 
 .39 
 
 .40 
 
 .42 
 
 .45 
 
 .50 
 
 .61 
 
 6 
 
 .41 
 
 .43 
 
 .47 
 
 .50 
 
 .57 
 
 .75 
 
 8 
 
 .45 
 
 .47 
 
 .52 
 
 .57 
 
 .66 
 
 .90 
 
 10 
 
 .47 
 
 .50 
 
 .56 
 
 .62 
 
 .74 
 
 1.04 
 
 12 
 
 .49 
 
 .53 
 
 .60 
 
 .67 
 
 .82 
 
 1.18 
 
 16 
 
 .55 
 
 .60 
 
 .70 
 
 .79 
 
 .98 
 
 1.46 
 
 18 
 
 .57 
 
 .63 
 
 .74 
 
 .85 
 
 1.06 
 
 1.60 
 
 20 
 
 .61 
 
 .67 
 
 .79 
 
 .91 
 
 1.15 
 
 1.75 
 
 24 
 
 .66 
 
 .73 
 
 .87 
 
 1.02 
 
 1.30 
 
 2.03 
 
 30 
 
 .74 
 
 .83 
 
 1.01 
 
 1.19 
 
 1.55 
 
 2.46 
 
 36 
 
 .82 
 
 .93 
 
 1.15 
 
 1.36 
 
 1.80 
 
 2.88 
 
 48 
 
 .98 
 
 1.13 
 
 1.42 
 
 1.70 
 
 2.28 
 
 3.73 
 
 Wooden Pipe. The sizes of wooden pipes up to 6 in., and sometimes up 
 to 12 in. in diameter are commonly bored from a single log. The sizes up to 
 48 in. in diameter are made from a series of staves placed side by side and 
 wrapped with wire, steel bands, etc., and coated with tar or some similar pre- 
 servative. The sizes given in the accompanying table are made in the factories 
 and shipped to destination. Larger sizes 54-, 60-, 66-, 72-, 78-, 84-, 90-, 96-, 
 108-, and 120-in. pipes are made on the ground where used from staves of the 
 proper cross-section. As built, the staves break joint at least 24 in. so that 
 they interlock longitudinally, forming a continuous pipe. While being placed, 
 the completed pipe is wrapped with steel wire or bands. For heads up to 
 400 ft. (173 Ib. per sq. in.) wooden pipe has been used for many years and 
 possesses numerous advantages over cast- or wrought-iron pipe. Owing to the 
 smoothness of its interior, its carrying capacity for water is much greater 
 
HYDRAULICS 
 STANDARD SIZES OF WOOD PIPE 
 
 307 
 
 Inside Diameter 
 of Pipe 
 Inches 
 
 Outside Diameter 
 of Pipe 
 Inches 
 
 Weight per Foot 
 80-lb. Pressure 
 Pounds 
 
 Number of Feet a 
 40-Ft. Car 
 Will Hold 
 
 H 
 
 3 
 
 
 2 
 
 17,000 
 
 2 
 
 4 
 
 
 4 
 
 11,000 
 
 3 
 
 6 
 
 
 6* 
 
 6,000 
 
 4 
 
 7 
 
 
 7i 
 
 4,500 
 
 4 
 
 8 
 
 
 12 
 
 4,000 
 
 5 
 
 9 
 
 
 15 
 
 3,000 
 
 6 
 
 10 
 
 
 18 
 
 2,700 
 
 6 
 
 10 
 
 
 13 
 
 2,700 
 
 8 
 
 12 
 
 
 16 
 
 2,000 
 
 10 
 
 14 
 
 
 21 
 
 1,600 
 
 12 
 
 16 
 
 
 25 
 
 1,200 
 
 14 
 
 18 
 
 
 27 
 
 1,000 
 
 16 
 
 20 
 
 
 29 
 
 800 
 
 18 
 
 22 
 
 
 31 
 
 700 
 
 20 
 
 24 
 
 
 35 
 
 600 
 
 24 
 
 28 
 
 
 50 
 
 425 
 
 30 
 
 36, 
 
 
 90 
 
 200 
 
 36 
 
 42 
 
 
 110 
 
 175 
 
 48 
 
 54 J 
 
 160 
 
 65 
 
 than is that of cast or wrought pipe. This difference is estimated to be about 
 10% in favor of the wooden pipe when it and the iron pipe are new and as 
 much as 30 or 40% when both are old. Wooden pipe is not affected by acid 
 mine water or by electrolysis as is iron pipe, and for these reasons is in much 
 favor in many mines where the head is not too great. The standard thicknesses 
 are made to resist pressures due to 100 ft., 200 ft., 300 ft., and 400 ft. head, or 
 43 lb., 87 lb., 130 lb., and 173 |b. per sq. in. pressure. In exceptional cases, 
 wooden pipe has been built to work under 700-ft. head, say, under a pressure 
 of 300 lb. 
 
 Compressibility of Liquids. Liquids are not entirely incompressible, but 
 they are so nearly so, that for most purposes they may be considered as 
 incompressible. The bulk of water is diminished about y^nr by a pressure of 
 324 lb. per sq. in., or 22 atmospheres; varying slightly with its temperature. 
 It is perfectly elastic, regaining its original bulk when the pressure is 
 removed. 
 
 HYDRAULICS 
 
 DEFINITIONS 
 
 Hydraulics treats of liquids in motion, and in this, as in hydrostatics, water 
 is taken as the type. In theory, its principles are the same as those of falling 
 bodies, but in practice they are so modified by various causes that they can- 
 not be relied on except as verified by experiment. The discrepancy arises 
 from changes of temperature that vary the fluidity of the liquid, from friction, 
 the shape of the orifice, etc. When dealing with water only, the first cause 
 need not be considered. In theory the velocity of a jet is the same as that 
 of a body falling from the surface of the water. 
 
 To Find Theoretical Velocity of Jet of Water. Let v = velocity, g = acceler- 
 ation of gravity (32.16 ft.), and d = distance of orifice below surface of water. 
 Then, v=^2gd, 
 
 EXAMPLE. The depth of water above the orifice is 64 ft.; what is the 
 velocity? 
 
 SOLUTION. Substituting in the formula 64 for d and 32.16 for g, 
 
 v= V2X 32. 16X64 = 64. 16. 
 
308 HYDRAULICS ^ 
 
 To Find Theoretical Quantity of Water Discharged in Given Time. Multi- 
 ply the area of the orifice by the velocity of the water, and that product by 
 the number of seconds. 
 
 EXAMPLE. What quantity of water will be discharged in 5 sec. from an 
 orifice having an area of 2 sq. ft., at a depth of 16 ft.? 
 
 SOLUTION. 2X V2X 32. 16X16 = 64. 16 cu. ft., or the amount discharged 
 in 1 sec., and in 5 sec. the amount will be 5X64.16 = 320.8 cu. ft. 
 
 The foregoing rules are. only theoretical, and are only useful as foundations 
 on which to build practical formulas. 
 
 Flow of Water Through Orifices. The standard orifice, or an orifice so 
 arranged that the water when flowing from it touches only a line, as is the 
 case when flowing through a hole in a very thin plate, is used for the measure- 
 ment of water. The contraction of the jet, which always occurs when water 
 issues from a standard orifice, is due to the circumstance that the particles 
 of water as they approach the orifice move in conyerging directions, and that 
 these directions continue to converge for a short distance beyond the plane of 
 the orifice. This contraction causes only the inner corner of the orifice to be 
 touched by the escaping water, and takes place in orifices of any shape, its cross- 
 section being similar to the orifice until the place of greatest contraction is 
 passed. Owing to this contraction, the actual discharge from an orifice is 
 always less than the theoretical discharge. 
 
 Coefficient of Contraction. The coefficient of contraction is the number 
 by which the area of the orifice is to be multiplied in order to find the area 
 of the least cross-section of the jet. By experiment, this coefficient has been 
 found to be about .62 (Merriman's "Hydraulics"); or, in other words, the 
 minimum cross-section of the jet is 62% of the cross-section of the orifice. 
 
 Coefficient of Velocity. The coefficient of velocity is the number by which 
 the theoretical velocity of flow from the orifice is to be multiplied in order to 
 find the actual velocity at the least cross-section of the jet. This may be taken 
 for practical work as .98; or, in other words, the actual flow at the contracted 
 section is 98% of the theoretical velocity. 
 
 Coefficient of Discharge. The coefficient of discharge is the number by 
 which the theoretical discharge is to be multiplied in order to obtain the actual 
 discharge. This has been found by thousands of experiments to be equal to 
 the product of the coefficients of contraction .and velocity, and for practical 
 work it may be taken as .61; or, the actual discharge from standard orifices 
 is 61% of the theoretical discharge. 
 
 NOTE. While the coefficients for standard orifices with sharp edges have 
 been determined fairly close, those for the more complicated cases of weirs, 
 and especially for the flow of water through long pipes, are simply the nearest 
 approximation to the truth that it has been possible to obtain. In all cases, 
 the coefficient should be one that has been determined under cpnditions similar 
 to those in the problem in hand. For instance, it is not practicable to use the 
 C9efficient for small pipes in solving problems relating to large ones, or for short 
 pipes in solving problems relating to long ones. 
 
 Suppression of Contraction. When a vertical orifice has its lower edge 
 at the bottom of a reservoir, the particles of water flowing through its lower 
 portion move in lines nearly perpendicular to the plane of the orifice, and 
 the contraction of the jet does not form on the lower side. The same thing 
 occurs in a lesser degree when the lower edge of the orifice is within a distance 
 of three times its least diameter from the bottom. The suppression of con- 
 traction will occur on the side if it is placed within a distance of three times 
 its least diameter trom the side of a reservoir, the suppression of contraction 
 being the greater the nearer the orifice is to the side. By rounding the edge 
 of the orifice sufficiently, the contraction can be completely suppressed, and the 
 discharge can be increased. As stated before, the value of the coefficient of 
 contraction for a standard square-edged orifice is .62, but with a rounded 
 orifice it may have any value between .62 and 1. depending on the degree of 
 rounding 1 he coefficient of discharge for square-edged orifices has a mean 
 value of .61; this is increased with rounded edges and may have any value 
 between .51 and 1, although it is not probable that values greater than .95 
 can be obtained except by the most careful adjustment' of the rounded edges 
 to the exact curve of a completely contracted jet. A rounded interior orifice 
 s therefore always a source of error when the object of the orifice is the measure- 
 ment of the discharge. 
 
HYDRAULICS 
 
 309 
 
 GAUGING WATER 
 
 Water is sold by two methods; i. e., the flowing unit and the capacity unit. 
 The flowing unit is 1 cu. ft. per sec. In the western part of North America 
 the miners' inch has come into use quite largely, while in Australia and New 
 Zealand the cubic foot per second is the common measure; 1 cu. ft. per sec. 
 being 1 head, 10 heads of water is 10 cu. ft. per sec., regardless of the actual 
 hydrostatic head under which the water is delivered. Water is sometimes sold 
 for irrigation by the capacity unit, that is, so much land covered to a certain 
 depth, as, for instance, the acre-foot, which means that 1 A. has been covered 
 to a depth of 1 ft., or that 43,560 cu. ft. of water has been furnished. 
 
 Miners' Inch. The miners' inch may be roughly defined as the quantity of 
 water that will flow in 1 min. through a vertical standard orifice having a sec- 
 tion of 1 sq. in. and a head of 65 in. above the center of the orifice. This quan- 
 tity equals 1.53 cu. ft., and the mean quantity may be taken at, approximately, 
 1.5 cu. ft. per min. The laws or customs defining the miners' inch in different 
 districts vary so that the amount of water actually delivered varies from 1.2 to 
 1.76 cu. ft. per min. The principal reasons for these variations are the methods 
 adopted for measuring the water where large quantities are used; as, for 
 instance, at Smartsville, California, an opening 4 in. deep, 250 in. long, with a 
 head of 7 in. above the top edge, is said to furnish 1,000 miners' inches, while 
 it actually furnishes considerably over 1,000. In other places, the size of the 
 opening for measuring the amounts is restricted, and may actually furnish less 
 than the rated amount. In Montana the common method of measurement 
 was formerly through a vertical rectangle 1 in. high, with a head on the center 
 
 DUTY OF MINERS' INCH 
 
 (Risdon Iron Works, Evans's Elevator Catalogue) 
 
 North Bloomfield Mine 
 
 Years 
 
 Amount 
 of 
 Gravel 
 Washed 
 Cubic 
 Yards 
 
 Miners' 
 24-Hour 
 Inches 
 
 Grades 
 
 Amount 
 Washed 
 per 
 Miners' 
 Inch 
 Cubic 
 Yards 
 
 Water 
 Used per 
 Cubic 
 Foot of 
 Gravel 
 Moved 
 Cubic 
 Feet 
 
 Height 
 of 
 Bank 
 
 Feet 
 
 1870-74 
 
 3,250,000 
 
 710,987 
 
 6 in. to 12 ft. 
 
 4.60 
 
 18 
 
 100 
 
 1875 
 
 1,858,000 
 
 386,972 
 
 6 in. to 12 ft. 
 
 4.80 
 
 17 
 
 100 
 
 1876 
 
 2,919,700 
 
 700,000 
 
 6 in. to 12 ft. 
 
 4.17 
 
 20 
 
 200 
 
 1877 
 
 2,993,930 
 
 595,000 
 
 6 in. to 12 ft. 
 
 3.86 
 
 21 
 
 265 
 
 Totals 
 
 11,021,630 
 
 2,392,959 
 
 
 4.60 
 
 18 
 
 
 La Grange Mine 
 
 1874-76 
 
 676,968 
 
 624,745 
 
 4 in. to 16 ft. 
 
 1.08 
 
 74.0 
 
 10 to 48 
 
 1875-76 
 
 683,244 
 
 375,155 
 
 4 in. to 16 ft. 
 
 1.82 
 
 43.9 
 
 6 
 
 1874-76 
 
 284,932 
 
 207,010 
 
 4 in. to 16ft. 
 
 1.37 
 
 58.0 
 
 50 to 80 
 
 1875-78 
 
 459,570 
 
 302,960 
 
 4 in. to 16ft. 
 
 1.52 
 
 52.0 
 
 40 to 50 
 
 1880-81 
 
 329,120 
 
 203,325 
 
 4 in. to 16 It. 
 
 1.57 
 
 50.0 
 
 10 to 80 
 
 Totals 
 
 2,433,834 
 
 1,713,195 
 
 
 1.42 
 
 56.0 
 
 
310 
 
 HYDRAULICS 
 
 of the orifice of 4 in. The number of miners' inches discharged was considered 
 to be the same as the number of linear inches in the length of the orifice; thus, 
 under the given head, an orifice 1 in. deep and 60 in. long could discharge 
 60 miners' inches. 
 
 The State Legislature of Montana has now passed a law defining the miners' 
 inch as the number of gallons of water discharged in a given time, regardless 
 of the character of the openings or methods of measurement. The statement 
 is as follows: "Where water rights, expressed in miners' inches, have been 
 granted, 100 miners' inches shall be considered equivalent to a flow of 2 cu. 
 ft. per sec. (18.7 gal.), and this proportion shall be observed in determining 
 the equivalent flow represented by any number of miners' inches." If this 
 amount is reduced to cubic feet per minute, it will be found to be equal to a 
 flow of 1.5 cu. ft. per min., which is the value given for the miners' inch. 
 
 Duty or Work Performed by a Miners' Inch of Water. Few tests have been 
 made in regard to the duty of a miners' inch of water, but the North Bloom- 
 field mine and the La Grange mine, in California, have' carried on a series of 
 experiments extending over several years. At the La Grange mine, the obser- 
 vations were carried on simultaneously upon several different claims, hence 
 parallel dates appear. The following table gives the results of these experi- 
 
 Number of 
 
 Dimensions of Aperture, in Inches 
 
 Depth of Pressure 
 Board Above 
 
 Sluice Heads 
 
 
 
 Top of Aperture 
 
 
 Width 
 
 Depth 
 
 Inches 
 
 1 
 
 16 
 
 1 
 
 IT 
 
 2 
 
 16 
 
 2 
 
 4! 
 
 3 
 
 16 
 
 21 
 
 
 4 
 
 16 
 
 2 
 
 10 1 
 
 5 
 
 16 
 
 3; 
 
 91 
 
 6 
 
 32 
 
 2. 
 
 81 
 
 7 
 
 32 
 
 21 
 
 ftf 
 
 8 
 
 32 
 
 2' 
 
 10 
 
 9 
 
 32 
 
 3 
 
 10* 
 
 10 
 
 32 
 
 3| 
 
 Sf 
 
 ments. In general the duty is governed by the size, capacity, character 
 of pavement, and grade of sluices, together with the supply of water. A 
 heavy grade will compensate for a limited supply. With an abundant supply 
 of water and material, the capacity of the sluices will depend on the character 
 of the material washed, the size and minimum grade of the sluices, and the 
 character of the riffles used. In the North Bloomfield mine the sluices were 
 6 ft. wide, and 32 in. deep. The riffles were principally blocks (wood), but 
 rock riffles were used in the tail sluices. The larger portion of the material 
 moved was top gravel. In the La Grange mine the sluices were 4 ft. wide and 
 30 in. deep, and were paved with blocks. 
 
 Sluice Head. In Tasmania and the Australian Provinces, water is sold 
 by the sluice head. For the following information relating to Tasmania, we 
 are indebted to Roy Bamford, Esq., South Mt. Cameron, Tasmania. 
 
 "The sluice head as leased by mining companies from the Government at 
 a rental of 1 per yr. for each head, amounts to 24 cu. ft. per min. and is 
 measured as follows: 
 
 "A Government gauge box for measuring water is 12 ft. long, open on top, 
 
 and set truly horizontal. The 
 outlet end of the box is closed 
 with a board 1 in. in thickness 
 with the exception of an aper- 
 ture, which is always the full 
 width of the gauge box. In all 
 cases, the lower end of the 
 aperture is 2 in. above the 
 bottom of the gauge box. 
 FIG. 1 When measuring the discharge, 
 
 through the aperture, the water must stand on a level with the top of the 
 
HYDRAULICS 
 
 311 
 
 board. When more than ten sluice heads of water are required to be 
 measured, two or more of such gauge boxes shall be used." 
 
 Gauging by V Notch. The right-angled V notch is frequently used for gaug- 
 ing the flow of comparatively small streams. The notch is usually fitted into 
 a box provided with baffle boards, Fig. 1, or, where this is not practicable, 
 the water should be so impounded above the notch as to remove all possibility 
 of surface currents producing a perceptible velocity of approach. The dis- 
 tance a of the surface of the water below the top of the box is taken at a 
 point some distance back from the notch (at least 18 to 20 in.), where the sur- 
 
 DISCHARGE OF WATER THROUGH A RIGHT-ANGLED V NOTCH 
 
 
 >v 
 
 
 >> 2 
 
 
 jj 0) 
 
 H "3 
 
 
 *3 
 
 
 >,- 
 
 "S "' 
 
 I| 
 
 w Jj 
 
 1|| 
 
 sl 
 
 II 
 
 H 
 
 1 J 
 
 .(J 4> 3 
 
 ||| 
 
 1J 
 
 1 -SS 
 3 1* w 
 
 h 
 
 Q* 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 1.05 
 
 .3457 
 
 3.25 
 
 5.827 
 
 5.45 
 
 21.22 
 
 7.65 
 
 49.53 
 
 9.85 
 
 93.18 
 
 1.10 
 
 .3884 
 
 3.30 
 
 6.054 
 
 5.50 
 
 21.71 
 
 7.70 
 
 50.34 
 
 9.90 
 
 94.37 
 
 1.15 
 
 .4340 
 
 3.35 
 
 6.285 
 
 5.55 
 
 22.20 
 
 7.75 
 
 51.16 
 
 9.95 
 
 95.56 
 
 1.20 
 
 .4827 
 
 3.40 
 
 6.523 
 
 5.60 
 
 22.70 
 
 7.80 
 
 51.99 
 
 10.00 
 
 96.77 
 
 1.25 
 
 .5345 
 
 3.45 
 
 6.765 
 
 5.65 
 
 23.22 
 
 7.85 
 
 52.83 
 
 10.05 
 
 97.98 
 
 1.30 
 
 .5896 
 
 3.50 
 
 7.012 
 
 5.70 
 
 23.74 
 
 7.90 
 
 53.67 
 
 10.10 
 
 99.20 
 
 1.35 
 
 .6480 
 
 3.55 
 
 7.266 
 
 5.75 
 
 24.26 
 
 7.95 
 
 54.53 
 
 10.15 
 
 100.43 
 
 1.40 
 
 .7096 
 
 3.60 
 
 7.524 
 
 5.80 
 
 24.79 
 
 8.00 
 
 55.39 
 
 10.20 
 
 101.67 
 
 1.45 
 
 .7747 
 
 3.65 
 
 7.788 
 
 5.85 
 
 25.33 
 
 8.05 
 
 56.26 
 
 10.25 
 
 102.92 
 
 1.50 
 
 .8432 
 
 3.70 
 
 8.058 
 
 5.90 
 
 25.87 
 
 8.10 
 
 57.14 
 
 10.30 
 
 104.18 
 
 1.55 
 
 .9153 
 
 3.75 
 
 8.332 
 
 5.95 
 
 26.42 
 
 8.15 
 
 58.03 
 
 10.35 
 
 105.45 
 
 .60 
 
 .9909 
 
 3.80 
 
 8.613 
 
 6.00 
 
 26.98 
 
 8.20 
 
 58.92 
 
 10.40 
 
 106.73 
 
 .65 
 
 1.0700 
 
 3.85 
 
 8.899 
 
 6.05 
 
 27.55 
 
 8.25 
 
 59.82 
 
 10.45 
 
 108.02 
 
 .70 
 
 1.1530 
 
 3.90 
 
 9.191 
 
 6.10 
 
 28.12 
 
 8.30 
 
 60.73 
 
 10.50 
 
 109.31 
 
 .75 
 
 1.2400 
 
 3.95 
 
 9.489 
 
 6.15 
 
 28.70 
 
 8.35 
 
 61.65 
 
 10.55 
 
 110.62 
 
 .80 
 
 1.3300 
 
 4.00 
 
 9.792 
 
 6.20 
 
 29.28 
 
 8.40 
 
 62.58 
 
 10.60 
 
 111.94 
 
 .85 
 
 1.4240 
 
 4.05 
 
 10.100 
 
 6.25 
 
 29.88 
 
 8.45 
 
 63.51 
 
 10.65 
 
 113.26 
 
 .90 
 
 1.5220 
 
 4.10 
 
 10.410 
 
 6.30 
 
 30.48 
 
 8.50 
 
 64.45 
 
 10.70 
 
 114.60 
 
 .95 
 
 1.6250 
 
 4.15 
 
 10.730 
 
 6.35 
 
 31.09 
 
 8.55 
 
 65.41 
 
 10.75 
 
 115.94 
 
 2.00 
 
 1.7310" 
 
 4.20 
 
 11.060 
 
 6.40 
 
 31.71 
 
 8.60 
 
 66.37 
 
 10.80 
 
 117.29 
 
 2.05 
 
 1.8410 
 
 4.25 
 
 11.390 
 
 6.45 
 
 32.33 
 
 8.65 
 
 67.34 
 
 10.85 
 
 118.65 
 
 2.10 
 
 1.9550 
 
 4.30 
 
 11.730 
 
 6.50 
 
 32.96 
 
 8.70 
 
 68.32 
 
 10.90 
 
 120.02 
 
 2.15 
 
 2.0740 
 
 4.35 
 
 12.070 
 
 6.55 
 
 33.60 
 
 8.75 
 
 69.30 
 
 10.95 
 
 121.41 
 
 2.20 
 
 2.1960 
 
 4.40 
 
 12.420 
 
 6.60 
 
 34.24 
 
 8.80 
 
 70.30 
 
 11.00 
 
 122.81 
 
 2.25 
 
 2.3230 
 
 4.45 
 
 12.780 
 
 6.65 
 
 34.89 
 
 8.85 
 
 71.30 
 
 11.05 
 
 124.21 
 
 2.30 
 
 2.4550 
 
 4.50 
 
 13.140 
 
 6.70 
 
 35.56 
 
 8.90 
 
 72.31 
 
 11.10 
 
 125.61 
 
 2.35 
 
 2.5900 
 
 4.55 
 
 13.510 
 
 6.75 
 
 36.23 
 
 8.95 
 
 73.33 
 
 11.15 
 
 127.03 
 
 2.40 
 
 2.7300 
 
 4.60 
 
 13.890 
 
 6.80 
 
 36.89 
 
 9.00 
 
 74.36 
 
 11.20 
 
 128.45 
 
 2.45 
 
 2.8750 
 
 4.65 
 
 14.270 
 
 6.85 
 
 37.58 
 
 9.05 
 
 75.40 
 
 11.25 
 
 129.90 
 
 2750 
 
 3.0240 
 
 4.70 
 
 14.650 
 
 6.90 
 
 38.27 
 
 9.10 
 
 76.44 
 
 11.30 
 
 131.35 
 
 2.55 
 
 3.1770 
 
 4.75 
 
 15.040 
 
 6.95 
 
 38.96 
 
 9.15 
 
 77.49 
 
 11.35 
 
 132.81 
 
 '2. (30 
 
 3.3350 
 
 4.80 
 
 15.440 
 
 7.00 
 
 39.67 
 
 9.20 
 
 78.55 
 
 11.40 
 
 134.27 
 
 2.65 
 
 3.4980 
 
 4.85 
 
 15.850 
 
 7.05 
 
 40.38 
 
 9.25 
 
 79.63 
 
 11.45 
 
 135.75 
 
 2.70 
 
 3.6660 
 
 4.90 
 
 16.260 
 
 7.10 
 
 41.10 
 
 9.30 
 
 80.71 
 
 11.50 
 
 137.23 
 
 2.75 
 
 3.8380 
 
 4.95 
 
 16.680 
 
 7.15 
 
 41.83 
 
 9.35 
 
 81.80 
 
 11.55 
 
 138.73 
 
 2.80 
 
 4.0140 
 
 5.00 
 
 17.110 
 
 7.20 
 
 42.56 
 
 9.40 
 
 82.90 
 
 11.60 
 
 140.23 
 
 2.85 
 
 4.1960 
 
 5.05 
 
 17.540 
 
 7.25 
 
 43.30 
 
 9.45 
 
 84.01 
 
 11.65 
 
 141.75 
 
 2.90 
 
 4.3820 
 
 5.10 
 
 17.970 
 
 7.30 
 
 44.06 
 
 9.50 
 
 85.12 
 
 11.70 
 
 143.28 
 
 2.95 
 
 4.5740 
 
 5.15 
 
 18.420 
 
 7.35 
 
 44.82 
 
 9.55 
 
 86.24 
 
 11.75 
 
 144.82 
 
 3.00 
 
 4.7700 
 
 5.20 
 
 18.870 
 
 7.40 
 
 45.58 
 
 9.60 
 
 87.37 
 
 11.80 
 
 146.36 
 
 3.05 
 
 4.9710 
 
 5.25 
 
 19.320 
 
 7.45 
 
 46.36 
 
 9.65 
 
 88.52 
 
 11.85 
 
 147.91 
 
 3.10 
 
 5.1780 
 
 5.30 
 
 19.790 
 
 7.50 
 
 47.14 
 
 9.70 
 
 89.67 
 
 11.90 
 
 149.48 
 
 o.l5 
 
 5.3880 
 
 5.35 
 
 20.260 
 
 7.55 
 
 47.92 
 
 9.75 
 
 90.83 
 
 11.95 
 
 151.05 
 
 3.20 
 
 5.6050 
 
 5.40 
 
 20.730 
 
 7.60 
 
 48.72 
 
 9.80 
 
 92.00 
 
 12.00 
 
 152.64 
 
 *1 cu. ft. contains 7.48 U. S. gal.; 1 U. S. gal. weighs 8.34 Lb. 
 
312 
 
 HYDRAULICS 
 
 in which Q = quantity, in cut 
 h = '. 
 
 feet per minute; 
 
 face of the water is unaffected by the flow through the notch. The distance 
 a, subtracted from the total depth of the notch H, gives the head h of the 
 water passing over the notch. The discharge, in cubic feet per second, may 
 be found by the formula 
 
 = .306VP= 
 ubic 
 
 head, in inches. 
 
 The accompanying table gives the discharge, in cubic feet per minute, 
 through a right-angled V notch, as shown in Fig. 1, for heads varying from 
 
 1.05 in. to 12 in. 
 
 Gauging by Weirs. A weir is 
 an obstruction placed across a 
 stream for the purpose of diverg- 
 ing the water so as to make it flow 
 through a desired channel, which 
 may be a notch or opening in the 
 weir itself. The term usually ap- 
 _Ji plies to rectangular notches in 
 z^^=: which the water touches only the 
 bottom and ends, the opening 
 
 being a notch without any upper 
 
 %zggp3!gH:3 edge. Weirs are of two general 
 classes: weirs with end contractions, 
 
 p g ' **' Fig. 2 (a) , and weirs without end 
 
 contractions, as in (6). The crest 
 and edges of the weir with end contractions should be sharp, as shown in 
 (c) and (J). The head of water H producing the flow over the weir should 
 be measured at a sufficient distance from the crest to avoid the effects of the 
 curve of the surface as it flows over the crest. The water above the weir 
 should be motionless, or 
 if it has any perceptible 
 current toward the weir, 
 this should be determined 
 and taken into account in 
 the formula. Fig. 3 illus- 
 trates a weir constructed ~ 
 across a small stream for 
 measuring its flow. The 
 head is measured from the 
 stake some distance back 
 of the weir, the top of the 
 stake being level with the 
 crest of the weir B. The 
 discharge over the weir 
 may be calculated from 
 the following formula: 
 
 Let 1 = length of weir, in feet; 
 # = head, in feet; 
 
 v = velocity with which water approaches weir, in feet; 
 h = head equivalent to velocity with which water approaches weir; 
 e = coefficient of discharge; 
 
 Q = theoretic discharge, in cubic feet per second; 
 Q' = actual discharge, in cubic feet per second. 
 
 For weirs with end contractions and a velocity of approach, the actual 
 discharge is 
 
 Where the water has no velocity of approach, 
 
 Q' = 5.347 C/V7/3 
 
 For weirs without end contractions, but with a velocity of approach, the 
 actual discharge is 
 
 = 5.347 cl 
 
 p IG 3 
 
 Where the water has no velocity of approac 
 Q' = 5.347 cl^l~H* 
 
 The velocity with which the water approaches the weir may be found by 
 determining the approximate discharge from the stream without any allowance 
 for velocity of approach, and then dividing this discharge, in cubic feet per 
 
HYDRAULICS 
 
 313 
 
 second, by the area of the stream, in square feet, where it approaches the 
 
 weir, which will give the velocity of approach, in feet per second. Having 
 
 obtained the value of v, the equivalent head h may be found by the formula 
 
 fc = . 01555^2 
 
 As v is small in a properly constructed weir, it is usually neglected unless 
 great accuracy is required. 
 
 The values of coefficients of discharge, as determined from experiments, 
 for weirs with end and for weirs without end contractions are given in the 
 accompanying tables. In the first two tables, the values of the coefficients 
 are given in feet and tenths. When only a close approximatioh is required, 
 it is desired to take all of the measurement in feet and inches. The third 
 table should not be used unless the length of the crest is at least three or four 
 times the depth of water passing over the weir, for if this is not the case, there 
 will be serious errors caused by end contractions. 
 
 COEFFICIENT OF DISCHARGE FOR WEIRS WITH END 
 CONTRACTIONS 
 
 
 Length of Weir, in Feet 
 
 Effective Head 
 
 .66 
 
 1 2 
 
 3 
 
 5 
 
 10 
 
 19 
 
 Feet 
 
 
 1 
 
 
 
 
 
 
 Value of Coefficient 
 
 .10 
 
 .632 
 
 .639 
 
 .646 
 
 .652 
 
 .653 
 
 .655 
 
 .656 
 
 .15 
 
 .619 
 
 .625 
 
 .634 
 
 .638 
 
 .640 
 
 .641 
 
 .642 
 
 .20 
 
 .611 
 
 .618 
 
 .626 
 
 .630 
 
 .631 
 
 .633 
 
 .634 
 
 .25 
 
 .605 
 
 .612 
 
 .621. 
 
 .624 
 
 .626 
 
 .628 
 
 .629 
 
 .30 
 
 .601 
 
 .608 
 
 .616 
 
 .619 
 
 .621 
 
 .624 
 
 .625 
 
 .40 
 
 .595 
 
 .601 
 
 .609 
 
 .613 
 
 .615 
 
 .618 
 
 .620 
 
 .50 
 
 .590 
 
 .596 
 
 .605 
 
 .608 
 
 .611 
 
 .615 
 
 .617 
 
 .60 
 
 .587 
 
 .593 
 
 .601 
 
 .605 
 
 .608 
 
 .613 
 
 .615 
 
 .70 
 
 
 .590 
 
 .598 
 
 .603 
 
 .606 
 
 .612 
 
 .614 
 
 Qf\ 
 
 
 
 .595 
 
 .600 
 
 .604 
 
 .611 
 
 .613 
 
 .90 
 
 
 
 .592 
 
 .598 
 
 .603 
 
 .609 
 
 .612 
 
 1.00 
 
 
 
 .590 
 
 .595 
 
 .601 
 
 .608 
 
 .611 
 
 1.20 
 
 
 
 .585 
 
 .591 
 
 .597 
 
 .605 
 
 .610 
 
 1.40 
 
 
 
 .580 
 
 .587 
 
 .594 
 
 .602 
 
 .609 
 
 1.60 
 
 
 
 
 .582 
 
 .591 
 
 .600 
 
 .607 
 
 COEFFICIENT OF DISCHARGE FOR WEIRS WITHOUT END 
 CONTRACTIONS 
 
 
 Length of Weir, in Feet 
 
 Effective Head 
 Feet 
 
 19 
 
 10 
 
 7 
 
 5 
 
 4 
 
 3 
 
 2 
 
 
 Value of Coefficient 
 
 .10 
 
 .657 
 
 .658 
 
 .658 
 
 .659 
 
 
 
 
 .15 
 
 .643 
 
 .644 
 
 .645 
 
 .645 
 
 .647 
 
 .649 
 
 .652 
 
 .20 
 
 .635 
 
 .637 
 
 .637 
 
 .638 
 
 .641 
 
 .642 
 
 .645 
 
 25 
 
 .630 
 
 .632 
 
 .633 
 
 .634 
 
 .636 
 
 .638 
 
 .641 
 
 .30 
 
 .626 
 
 .628 
 
 .629 
 
 .631 
 
 .633 
 
 .636 
 
 .639 
 
 .40 
 
 .621 
 
 .623 
 
 .625 
 
 .628 
 
 .630 
 
 .633 
 
 .636 
 
 .50 
 
 .619 
 
 .621 
 
 .624 
 
 .627 
 
 .630 
 
 .633 
 
 .637 
 
 .60 
 
 .618 
 
 .620 
 
 .623 
 
 .627 
 
 .630 
 
 .634 
 
 .638 
 
 .70 
 
 .618 
 
 .620 
 
 .624 
 
 .628 
 
 .631 
 
 .635 
 
 .640 
 
 .80 
 
 .618 
 
 .621 
 
 -.625 
 
 .629 
 
 .633 
 
 .637 
 
 .643 
 
 .90 
 
 .619 
 
 .622 
 
 .627 
 
 .631 
 
 .635 
 
 .639 
 
 645 
 
 1.00 
 
 .619 
 
 .624 
 
 .628 
 
 .633 
 
 .637 
 
 .641 
 
 648 
 
 1.20 
 
 .620 
 
 .626 
 
 .632 
 
 .636 
 
 .641 
 
 .646 
 
 
 1.40 
 
 .^22 
 
 .629 
 
 .634 
 
 .640 
 
 .644 
 
 
 
 1.60 
 
 .623 
 
 .631 
 
 .637 
 
 .642 
 
 .647 
 
 
 
314 
 
 HYDRAULICS 
 
 DISCHARGE PER MINUTE FOR EACH INCH IN LENGTH OF WEIR 
 FOR DEPTHS FROM 1-8 IN. TO 25 IN. 
 
 
 Depth of Water, in Inches 
 
 
 
 
 i 
 
 i 
 
 1 
 
 i 
 
 ! 
 
 I 
 
 I 
 
 
 Discharge per Inch of Length per Minute, in Cubic Feet 
 
 
 
 
 .01 
 
 .05 
 
 .09 
 
 .14 
 
 .20 
 
 .26 
 
 .33 
 
 1 
 
 .40 
 
 .47 
 
 .55 
 
 .65 
 
 . .74 
 
 .83 
 
 .93 
 
 1.03 
 
 2 
 
 1.14 
 
 1.24 
 
 1.36 
 
 1.47 
 
 1.59 
 
 1.71 
 
 1.83 
 
 1.96 
 
 3 
 
 2.09 
 
 2.23 
 
 2.36 
 
 2.50 
 
 2.63 
 
 2.78 
 
 2.92 
 
 3.07 
 
 4 
 
 3.22 
 
 3.37 
 
 3.52 
 
 3.68 
 
 3.83 
 
 3.99 
 
 4.16 
 
 4.32 
 
 5 
 
 4.50 
 
 4.67 
 
 4.84 
 
 5.01 
 
 5.18 
 
 5.36 
 
 5.54 
 
 5.72 
 
 6 
 
 5.90 
 
 6.09 
 
 6.28 
 
 6.47 
 
 6.65 
 
 6.85 
 
 7.05 
 
 7.25 
 
 7 
 
 7.44 
 
 7.64 
 
 7.84 
 
 8.05 
 
 8.25 
 
 8.45 
 
 8.66 
 
 8.86 
 
 8 
 
 9.10 
 
 9.31 
 
 9.52 
 
 9.74 
 
 9.96 
 
 10.18 
 
 10.40 
 
 10.62 
 
 9 
 
 10.86 
 
 11.08 
 
 11.31 
 
 11.54 
 
 11.77 
 
 12.00 
 
 12.23 
 
 12.47 
 
 10 
 
 12.71 
 
 13.95 
 
 13.19 
 
 13.43 
 
 13.67 
 
 13.93 
 
 14.16 
 
 14.42 
 
 11 
 
 14.67 
 
 14.92 
 
 15.18 
 
 15.43 
 
 15.67 
 
 15.96 
 
 16.20 
 
 16.46 
 
 12 
 
 16.73 
 
 16.99 
 
 17.26 
 
 17.52 
 
 17.78 
 
 18.05 
 
 18.32 
 
 18.58 
 
 13 
 
 18.87 
 
 19.14 
 
 19.42 
 
 19.69 
 
 19.97 
 
 20.24 
 
 20.52 
 
 20.80 
 
 14 
 
 21.09 
 
 21.37 
 
 21.65 
 
 21.94 
 
 22.22 
 
 22.51 
 
 22.79 
 
 23.08 
 
 15 
 
 23.38 
 
 23.67 
 
 23.97 
 
 24.26 
 
 24.56 
 
 24.86 
 
 25.16 
 
 25.46 
 
 16 
 
 25.76 
 
 26.06 
 
 26.36 
 
 26.66 
 
 26.97 
 
 27.27 
 
 27.58 
 
 27.89 
 
 17 
 
 28.20 
 
 28.51 
 
 28.82 
 
 29.14 
 
 29.45 
 
 29.76 
 
 30.08 
 
 30.39 
 
 18 
 
 30.70 
 
 31.02 
 
 31.34 
 
 31.66 
 
 31.98 
 
 32.31 
 
 32.63 
 
 32.96 
 
 19 
 
 33.29 
 
 33.61 
 
 33.94 
 
 34.27 
 
 34.60 
 
 34.94 
 
 35.27 
 
 35.60 
 
 20 
 
 35.94 
 
 36.27 
 
 36.60 
 
 36.94 
 
 37.28 
 
 37.62 
 
 37.96 
 
 38.31 
 
 21 
 
 38.65 
 
 39.00 
 
 39.34 
 
 39.69 
 
 40.04 
 
 40.39 
 
 40.73 
 
 41.09 
 
 22 
 
 41.43 
 
 41.78 
 
 42.13 
 
 42.49 
 
 42.84 
 
 43.20 
 
 43.56 
 
 43.92 
 
 23 
 
 44.28 
 
 44.64 
 
 45.00 
 
 45.38 
 
 45.71 
 
 46.08 
 
 46.43 
 
 46.81 
 
 24 
 
 47.18 
 
 47.55 
 
 47.91 
 
 48.28 
 
 48.65 
 
 49.02 
 
 49.39 
 
 49.76 
 
 CONVERSION FACTORS 
 
 Cubic Feet Into Gallons. 1 cu. ft. = 1,728 cu. in. = 1,728-^-231 gal. 
 = 7.4805194 gal. 
 
 Gallons Into Cubic Feet. 1 U. S. liq. gal. = 231 cu. in. = 23 1-5-1, 728 cu. ft. 
 = .133680555 cu. ft 
 
 Feet per Second Into Miles per Hour. 1 ft. per sec. = 3,600 ft. per hr. 
 -=*. ormi. perhr. 
 
 Miles per Hour Into Feet per Second. 1 mi. per hr. = 5,280 ft. per hr. 
 = , or if feet per sec. 
 
 Second-Feet per Day Into Gallons. 1 sec.-ft., or 7.4805194 gal. per sec. for 
 1 da., or 86,400 sec. = 646,316.87616 gal. 
 
 Millions of Gallons Into Second-Feet per Day. 1,000,000 gal. per 24 hr. 
 
 ~1 728X86400 CU * **' per Se " Or 1>5472286 sec - ft - 
 
 Second-Feet per Day Into Acre-Feet. 1 sec.-ft. flow for 1 da. = 86,400 cu. 
 ft. = 86,400 + 43,560 = 1.983473 A.-ft. 
 
 Acre-Feet Into Second-Feet Flow for 24 Hours. 1 A.-ft. each 24 hr. 
 = 43,560 cu. ft. each 86,400 sec. = 43 ,560-^86,400, or fflt sec.-ft. flow for 24 hr. 
 
 Acre-Feet Into Gallons. 1 A.-ft. = 43,560 cu. ft. (43.560X 1,728) -h 231 
 = 325,851.428 gal. 
 
 Millions of Gallons Into Acre-Feet. 1,000,000 U. S. liq. gal., or 231,000,000 
 cu. in. - 133,680.555 cu. ft. = 133,680.555^-43,560 = 3.0688832 A.-ft. 
 
HYDRAULICS 
 
 315 
 
 Second-Feet Into Minute Gallons. 1 cu. ft. contains 1,728 cu. in.; 1 gal. has 
 a capacity of 231 cu. in.; 1 sec.-ft. equals [(1,728-4- 231) X 60] gal. per min. 
 = 448.831164 min.-gal. 
 
 Minute-Gallons Into Second-Feet. 1 gal. contains 231 cu. in.; 1 cu. ft. con- 
 tains 1,728 cu. in.; 1 gal. per min. equals [ (231-5-1,728)-^ 60] sec.-ft., 
 = .0022280092 sec.-ft. 
 
 FLOW OF WATER IN OPEN CHANNELS 
 
 Ditches. In the case of hydraulic mining and irrigation, water is usually 
 conveyed through ditches. The ditch line should be carefully surveyed and 
 all brush and trees removed, and the underbrush cut away and burned, before 
 beginning to excavate the ditch. The form of ditch and its grade will depend 
 largely on the amount of water to be conveyed and the character of the soil 
 in the section under consideration. As a general rule, the average flow of water 
 in a ditch should not be less than 2 ft. per sec., and under most circumstances 
 should not exceed 4 ft., though in rare cases where the formation is suitable, 
 mean velocities of 5 ft. per sec. are employed. Sand will deposit from a current 
 flowing at the rate of 1 j ft. per sec., and if the current does not have a velocity 
 of at least 2 ft. per sec., vegetation is liable to block the ditch line. 
 
 The following letters will be used in the formulas for determining the 
 various factors relating to ditches: 
 
 h = difference in level between ends of canal or ditch, or between two 
 
 points under consideration; 
 / = horizontal length of portion of canal or ditch under consideration; 
 
 s = slope = ratio j = sine of slope ; 
 
 a = area of water cross-section in square feet; 
 
 p = wet perimeter = portion of outline of cross-section of stream in contact 
 with channel, in feet; 
 
 r = hydraulic radius, or hydraulic mean depth = ratio -; 
 
 c' = coefficient, depending on nature of surface of ditch; 
 
 c = coefficient depending on nature of surface of ditch, as determined by 
 Kutter's formula; 
 
 = mean velocity of flow, in feet per second; 
 
 v' = surface velocity of a stream; 
 
 v b = bottom velocity of a stream; 
 
 x = bottom or one side of a section the form of which is one-half a 
 regular hexagon, in feet; 
 
 Q = quantity of water flowing, in cubic feet per second; 
 
 n = coefficient of roughness in Kutter's formula. 
 
 Safe Bottom Velocity. The bottom velocity of a stream may be obtained 
 from the average velocity by the formula 
 
 v b = v- 10.87 Vrs 
 
 The accompanying table gives values of safe bottom and mean velocities, 
 corresponding with certain materials, as given by Ganguillet and Kutter: 
 
 SAFE BOTTOM AND MEAN VELOCITIES OF STREAMS 
 
 Material of Channel 
 
 Safe Bottom 
 Velocity v b 
 Feet per Second 
 
 Mean Velocity v 
 Feet per Second 
 
 Soft brown earth 
 Soft loam 
 
 .249 
 .499 
 
 .328 
 656 
 
 Sand 
 
 1.000 
 
 1 312 
 
 Gravel 
 
 1.998 
 
 2.625 
 
 Pebbles 
 
 2.999 
 
 3.938 
 
 Broken stone, flint 
 Conglomerate, soft slate 
 Stratified rock 
 Hard rock 
 
 4.003 
 4.988 
 6.006 
 10009 
 
 5.579 
 6.564 
 8.204 
 13 127 
 
 
 
 
316 . HYDRAULICS 
 
 Resistance of Soils to Erosion by Water. The following resistances of 
 various soils to erosion by water have been selected from the experiments of 
 W. A. Burr: 
 
 Soil Feet per Second 
 
 Pure sand resists erosion by flow 9f ..................... 1.10 
 
 Sandy soil. 15% clay, resists erosion by flow of .......... 1.20 
 
 Sandy loam, 40% clay, resists erosion by flow of ........ 1.80 
 
 Loamy soil, 65% clay, resists erosion by flow of .......... 3.00 
 
 Clay loam, 85% clay, resists erosion by flow of .......... 4.80 
 
 Agricultural clay, 95% clay, resists erosion by flow of ..... 6.20 
 
 Clay, resists erosion by flow of ........................ 7.35 
 
 Carrying Capacity of Ditches. Ditches should never be run full, but should 
 be constructed large enough so that they will carry the desired amount of 
 water when from three-fourths to seven-eighths full. For any given cross- 
 section, the greatest flow will be attained when the hydraulic radius or hydraulic 
 mean depth is equal to one-half of the actual depth of the channel. The 
 cross-section of a ditch or conduit that has the greatest possible carrying capac- 
 ity is a half circle, and the nearest practical approach to this is a half hexagon. 
 Knowing the cross-section of a ditch, its dimensions may be found by the 
 formula: 
 
 As the obtuse angle between the side and bottom of the ditch is 120, the 
 form can be easily laid off. The carrying capacity of ditches generally increases 
 after they have been in use some time, as the ditch becomes lined with a fine 
 scum that closes the pores in the soil and prevents leakage; this may increase 
 the amount by as much as 10%. 
 
 Grade. The grade of the ditch must be sufficient to create the desired 
 velocity of flow, and depends largely on the character of the material com- 
 posing the surface of the ditch. If the surface is smooth, as, for instance, 
 where the ditch is cut through clay or is lined with masonry, the grade can 
 be considerably less than where the surface is rough, or when cut through 
 coarse gravel or when lined with rough stone. In mountainous countries, 
 where the ground is hard, deep narrow ditches with steep grades are gener- 
 ally preferred to larger channels with gentle slopes, as the cost of excavation 
 is considerably less; but steep grades and narrow ditches are suitable only 
 when the banks can resist the rapid flow. In California, grades of from 16 to 
 20 ft. per mi. are used, and 10 ft. per mi. is quite common. Water channels 
 of a uniform cross-section should have a uniform grade; otherwise, the flow 
 will be checked in places, which will result in deposits of sand or silt in some 
 portions of the ditch, which are liable to cause the banks to be overflowed 
 and the ditch to be ultimately destroyed. When designing any given ditch, 
 the grade is generally assumed to correspond to the formation of the country 
 and the velocity figured from the grade. In case v is found to be so great 
 that it will cut the banks, it will be necessary either to reduce the grade or to 
 change the form of the ditch so as to reduce the velocity. 
 
 Ditch Banks, when possible, should be composed of solid material, but when 
 necessary to use excavated material care must be taken to see that the material 
 is so placed as to avoid settling and cracking as much as possible. All stumps, 
 roots, etc. should be separated from the material to be used for embankments. 
 If artificial banks are necessary, they should be built of masonry if the expense 
 is not too great ; or, the water may be carried across depressions in pipes or 
 flumes. When the character of the material through which the ditch is con- 
 structed is not sufficiently firm to resist the desired current vetocity, it is neces- 
 sary to line the ditch. In some locations the ditches are simply smoothed 
 on the inside and lined with from f in. to 1 in. of cement mortar, made up 
 of Portland cement and sharp sand. In other cases, they are lined with dry 
 stonework laid up in order and carefully bonded together. Sometimes the 
 stonework is pointed with cement or mortar on the inside, so as to present a 
 more uniform surface to the flow. In other cases, the sides are simply revetted 
 with stone. 
 
 Influence of Depth on Ditch. The depth of the flow in a ditch has consider- 
 able influence on the scouring or eroding of the bottom and the banks, owing 
 to the fact that a much greater average velocity can be attained in a deep 
 stream than in a shallow stream, without causing an excessive velocity of the 
 water in contact with the wet perimeter. For this reason, in cases where 
 banks will stand it, it is best to use narrow deep ditches rather than wide flat 
 
HYDRAULICS 
 
 317 
 
 ditches, though each location has to be treated in accordance with its own 
 special conditions, and no general rule can be laid down. 
 
 Measuring the Flow of Water in Channels. The laws for the resistance to 
 the flow may be expressed by the relation ha = c'lpv 2 ; or 
 
 VS3- 
 
 If c \/ , the formula becomes 
 
 The coefficient c is usually found by means of Kutter's formula, one form 
 of which is as follows: 
 
 23+ l +; 00155 
 
 The values for n, the coefficient of roughness under various conditions, 
 are given in the accompanying table: 
 
 COEFFICIENT OF ROUGHNESS UNDER VARIOUS CONDITIONS 
 
 Character of Channel 
 
 Value of 
 
 Clean, well-planed timber 
 
 Clean, smooth, glazed iron, and stoneware pipes 
 
 Masonry, smoothly plastered with cement, and for very clean, 
 
 smooth, cast-iron pipe 
 
 Unplaned timber, ordinary cast-iron pipe, and selected pipe 
 
 sewers, well laid and thoroughly flushed 
 
 Rough iron pipes and ordinary sewer pipes, laid under usual 
 
 conditions 
 
 Dressed masonry and well-laid brickwork 
 
 Good rubble masonry and ordinary rough or fouled brickwork . . . 
 
 Coarse rubble masonry and firm, compact gravel 
 
 Well-made earth canals in good alinement 
 
 Rivers and canals in moderately good order and perfectly free 
 
 from stones and weeds 
 
 Rivers and canals in rather bad condition and somewhat 
 
 obstructed by stones and weeds 
 
 Rivers and canals in bad condition, overgrown with vegetation 
 
 and strewn with stones and other detritus, according to 
 
 condition . . . 
 
 .009 
 .010 
 
 .011 
 .012 
 
 .013 
 .015 
 .017 
 .020 
 .0225 
 
 .025 
 .030 
 
 .035 to .05 
 
 As it is quite difficult to obtain the value of c by Kutter's formula, the 
 following three approximate formulas for v are given: 
 For canals with earthen banks, 
 
 9r+35 
 
 If the ditch is lined with dry stonework, 
 
 if the ditch is lined with rubble masonry, 
 
 IQO.OOOr^ 
 7.3r+6 
 
 To find the quantity Q of water flowing through any channel in a given 
 time, multiply the velocity by the area, or Q = av. 
 
 Flow in Brooks and Rivers. When a stream is so large that it becomes 
 impracticable to employ a weir for measuring its flow, fairly accurate results 
 may be arrived at by determining the velocity of the current at various points 
 
318 HYDRAULICS 
 
 in a carefully surveyed cross-section of the stream, thus determining both v 
 and o. The greatest velocity of current occurs at a point some distance below 
 the surface, in the deepest part of the channel. When determining the current 
 velocities in the different portions of a stream, it is frequently advantageous 
 to divide the stream into divisions. This may be accomplished by stretching 
 a wire across and tying strings or rags about the wire at various points. The 
 mean velocity of the current between these points can be determined by 
 current meters, or by floats. The points for observation should be chosen 
 where the channel is comparatively straight and the current uniform. Surface' 
 floats may be used, in which case the mean velocity of the point where the float 
 is used may be found as follows: If v' equals the observed velocity, then the 
 mean velocity will be v = .9'. 
 
 By taking observations of the velocity of the current in each section of 
 a stream, the amount of water flowing may be determined for each separate 
 section. The total amount of water flowing in the stream will be the sum 
 of the amounts in each section. The average velocity of the entire stream 
 may be found by dividing the total amount of water flowing by the total area of 
 the cross-section of the stream. The correction necessary to reduce surface 
 velocity to mean velocity may be made as follows: Measure off nine-tenths 
 of the ordinary distance, and figure the time as though for the full distance. 
 For instance, if only 90 ft. is employed, the time will be taken and the problem 
 figured as though it were 100 ft., because the mean velocity is only nine-tenths 
 of the surface velocity. 
 
 FLUMES 
 
 Flumes are used for conveying water when a ditch line would be abnormally 
 long, or when the material to be excavated is very hard. They may be 
 constructed of timber or of metal, but metal flumes are comparatively rare, 
 as piping can be used instead. The line of the proposed flume should be 
 carefully cleared of all standing timber, and the brush burned for at least 
 20 ft. each side of the flume line to prevent danger from fire. The life of an 
 ordinary flume, which is supported on or constructed of timber, is always 
 short, varying, as a rule, from 10 to 20 yr., depending on whether the flume is 
 allowed to run dry a portion of the year or is always full of water, the care 
 with which it was originally constructed, and the attention paid to repairs. 
 -Grade and Form of Flumes. Flumes are usually set on a much steeper 
 grade than is possible in ditches, the grade frequently being as much as 25 to 
 30 ft. per mi., and in special cases even more. The result of this is that the 
 carrying capacity of flumes is much greater than that of ditches of the same size. 
 The form of flume depends largely on the material of which it is constructed. 
 Metal flumes may have a semicircular form, while wooden flumes are either 
 rectangular or V-shaped. The former is used almost exclusively for con- 
 veying water, and the latter quite extensively for fluming timber or cord 
 wood from the mountains to the shipping point in the valley. 
 
 Timber flumes should be so constructed that the water will meet with but 
 small resistance, and the bottom and side should be enclosed in a frame of 
 
 timbers so braced or secured 
 
 that there is no possible chance 
 
 of the sides spreading or lifting 
 
 from the bottom, and thus 
 
 causing leakage. As a rule, all 
 
 mortised-and-tenoned joints 
 | should be avoided in flume con- 
 struction. Fig. 1 shows a tim- 
 ber flume in which no joints 
 
 are cut; the bottoms of the 
 
 posts are kept in place by 
 
 stringers spiked on the sills and 
 
 the tops are tied together by 
 
 pieces bolted on. Fig. 2 shows 
 PIG. 1 a construction in which the p IGi 2 
 
 posts are let into the sills and 
 
 supported by diagonal braces. The ties across the top of the posts are also 
 notched to receive the upper ends of the posts. As a rule, these ties are only 
 placed on every third or fourth frame, the diagonal braces being depended 
 on to hold the other posts in place. The joints between the planking may be 
 battened on the inside with strips of $-in. lumber, 4 or 5 in. wide, or the edges 
 
HYDRAULICS 319 
 
 of the planking may be dressed and painted before they are put together, so 
 as to form a tight joint. 
 
 Connection With Ditches. Where flumes connect with ditches or dams, 
 the posts for several boxes should be made longer, so that they may receive 
 another sideboard to prevent the water from splashing over the sides. The 
 flume should also be widened out or flared, both at its entry and discharge ends. 
 Where the flume passes through a bank of earth, an outer siding may be nailed 
 on the outside of the posts, to protect the flume from rotting. 
 
 Trestles. Where flumes are carried on trestles, the individual frames 
 supporting the flume are usually placed on heavy stringers, which in turn are 
 supported upon trestle bents from 12 to 16 ft. apart, the frames supporting 
 the flume being placed about 4 ft. apart. 
 
 Curves. Where flumes are laid around curves, the outer edge of the flume 
 should be elevated so as to prevent splashing and to cause the flowing water 
 to have a uniform depth across the width of the flume. It is impossible to 
 give any definite rule as to the amount that the outer edge of the flume should 
 be raised, but this is usually accomplished by judging the amount when the 
 flume is first constructed, and correcting this by wedging up after the water 
 is flowing. The individual boxes of the flume may have to be cut into two 
 or three portions on curves, and at times the side planks are sawed partly 
 through, so as to enable them to be bent to the desired curve. 
 
 Waste Gates. Waste gates should be placed every 5 mi., to empty the 
 flume for repairs, or in case of accident. They are also useful for flushing 
 snow out of a flume. In snowy regions, flumes are frequently protected by sheds 
 over their exposed portions. 
 
 Flow of Water Through Flumes. As smooth wooden surfaces offer consider- 
 ably less resistance to the flow of water than earth or stone canals, the coeffi- 
 cients must necessarily be somewhat reduced, and the following formula is 
 useful in giving the flow of water through flumes; 
 
 /100.000i*f 
 \6.6r+0.46 
 
 That flumes may have their full carrying capacity, they have to be of 
 sufficient length to get the water in motion, or, as it is technically expressed, 
 "to put the water in train." It is largely on this account that flumes have 
 to be made of a larger cross-section at both the entrance and the exit. 
 
 In cold countries it may be best to construct the flume narrower than it is 
 deep, as in cold weather the ice in the narrow flume freezes a crust entirely 
 across the surface, thus protecting the water from further action of the elements 
 and frequently prolonging the flow through the flume for several weeks, while 
 wide shallow flumes will not freeze on the surface so quickly, but will freeze 
 in from the bottom and sides until they are practically a solid mass of ice. 
 
 When a flume is laid on the ground along a bank, it should be laid as close 
 to the bank as possible, so as to protect it from snow or landslides, and so that 
 in the winter the snow will drift in under and behind it, thus preventing the 
 circulation of the air about the flume. This will protect the flume, and may 
 prolong the flow for some time after cold weather sets in. 
 
 TUNNELS 
 
 Tunnels are sometimes used for conveying water, in connection with flume 
 or ditch lines. Where a tunnel is unlined, it is best to give the roof the shape 
 of the Gothic arch, because this stands better and resists scaling to a greater 
 extent than the round arch, which usually scales off until it has the form of the 
 Gothic arch. If tunnels are to be used as water conduits, without lining, care 
 should be taken to make the inside of the tunnel as smooth as possible. In 
 some cases, in order to increase the carrying capacity, the tunnel has been 
 lined with wooden-stave pipe, backed with concrete, the pipe requiring no 
 metal bands, but depending on the concrete to keep it in place. When such 
 linings are employed, it is not practicable to have them exposed to the alternate 
 action of the water and the atmosphere; hence, the tunnel should be kept 
 continually full of water. To accomplish this, the tunnel may be dropped 
 below the grade of the ditch or flume line, so that it is always under a slight 
 hydrostatic pressure, and even if the water is turned off from the line, the 
 tunnel will remain fu 1 ! of water, the same as an inverted siphon. Sometimes 
 tunnels are lined with cement, being given either a circular or oval form, or 
 they may have a flat bottom, with flat sides and an arched roof. The cement 
 
320 
 
 HYDRAULICS 
 
 may be placed directly on the country rock composing the walls of the tunnel 
 or the tunnel may be lined with brick or stone, and then cemented on the inside. 
 Flow Through Tunnels. The flow of water through tunnels, when they are 
 only partly filled, is calculated by the formulas for flow in open channels, 
 while in the case of lined tunnels that are run full, the flow is calculated by 
 formulas for calculating the flow through pipes. 
 
 PIG. 1 
 
 FLOW THROUGH PIPES 
 
 Hydraulic Gradient. If a pipe of uniform cross-section is connected with 
 a reservoir, and water is allowed to discharge through its open end, the pressure 
 on the pipe at any point is equal to the vertical distance from the center of the 
 pipe at that point to an imaginary line, called the hydraulic gradient or hydraulic 
 grade line. This is a line drawn from a point slightly below the surface of the 
 
 water in the reservoir to 
 the outlet of the pipe, as 
 ab, Fig. 1. The distance 
 from the surface of the 
 water to the point a is equal 
 to the head lost in over- 
 coming the friction at the 
 entrance to the pipe, and 
 is rarely over 1 ft. A pipe 
 laid along the line ab will 
 carry exactly the same 
 amount of water as when 
 laid horizontally, as shown, 
 but there will be practically 
 no pressure tending to burst 
 the pipe at any point along 
 this line; while if it is laid 
 along the line from the 
 point a' (the reservoir being made deeper), it will still deliver exactly the 
 same amount of water, but the pressure tending to burst the pipe will be 
 greatly increased. In order that a pipe may have a maximum discharge, no 
 point in the line must rise above the hydraulic gradient ; it makes no difference 
 in the discharge how far below the gradient it may fall. 
 
 In Fig. 2, the pipe rises above the hydraulic gradient ac; in this case a new 
 hydraulic gradient ab must be established and the flow calculated for this head. 
 The pipe be simply acts to carry off the water delivered to it at b. If the 
 upper side of the pipe is open at the point b, the water will have no tendency 
 to escape, but, on the contrary, air will probably enter and the pipe flow only 
 partly full from b to c. 
 
 Flow in Pipes. Darcy, a French engineer, made a series of experiments on 
 different diameters of cast-iron pipe, with different degrees of internal rough- 
 ness, from which he calculated 
 a series of formulas. The fol- 
 lowing are some of these for- 
 mulas, as arranged by the late 
 E. Sherman Gould, C.E..E.M. 
 Darcy found that the character 
 of the inside surface of the pipe 
 played a very important part 
 in its discharge, and he deduced 
 
 a formula and determined a p IG 2 
 
 series of coefficients for it, but 
 
 Mr. Gould calls attention to the fact that the coefficients for pipes from 8 to 48 in. 
 in diameter practically cancel the numerical factor employed in Darcy 's formula, 
 and that a slightly different factor applies to pipes from 3 to 8 in., so that the 
 following simple formulas, in which the factors given apply, may be obtained: 
 Q = discharge, in cubic feet per second; 
 q = discharge, in U. S. gallons per minute; 
 D diameter of pipe, in feet; 
 d = diameter of pipe, in inches; 
 H = total head, in feet; 
 h = head per 1,000 ft.; 
 V = velocity, in feet per second. 
 
HYDRAULICS 321 
 
 Pipes Between_3 and 8 In. in Diameter 
 Rough inside surface, Q = .89^~D*h = .89D*TJ'Dh; V = 
 Smooth inside surface, Q = .89 V2ZWz = 1.25D 2 VD/Z; V 
 Pipes Above 8 In. in Diameter 
 Rough inside surface, Q = VZW* = D^T)h; V = 1.27 ^Dh 
 
 Rough inside surface, d in inches, Q = o7^\/T 
 
 ^oo \ o 
 
 Smooth inside surface, Q=lArWi = lAD*^jDh; V = 
 
 As a rule, it is best to calculate any pipe line by the formula for pipes having 
 a rough internal surface, for if this is not done the results are liable to be 
 disappointing, as all pipes become more or less rough with use. 
 Eytelwein's Formtfia for Delivery of Water in Pipes: 
 D = diameter of pipe, in inches; 
 // = head of water, in feet; 
 L = length of pipe, in feet; 
 W = water discharged per minute, in cubic feet. 
 
 Hawksley's Formula: 
 
 G number of gallons delivered per hour; 
 
 L = length of pipe, in yards; 
 
 /Z = head of water, in feet; 
 
 D = diameter of pipe, in inches. 
 
 *L 
 
 Neville's General Formula: 
 
 v velocity, in feet per second; 
 
 r = hydraulic mean depth, in feet; 
 
 5 = sine of inclination, or total fall divided by total length 
 
 In cylindrical pipes, vX 47. 124<2 2 = discharge per minute, in cubic feet, 
 or vX 293. 7286d 2 = discharge per minute in gallons, d being the diameter of the 
 pipe in feet. 
 
 Comparison of Formulas. The various formulas for velocity are as follows: 
 
 R = mean hydraulic depth, in f eet = area -4- wet perimeter = - for circular 
 
 section of pipe; 
 5 = sine of slope = y ; 
 
 v velocity, in feet per second; 
 
 d = diameter of pipe, in feet; 
 L = length of pipe, in feet; 
 # = head of water, in feet. 
 Prony, v = 97.05 V/J5-. 08 
 
 Eytelwein, = 
 
 Eytelwein, = 108V^5-.13 
 
 Hawksley, " ? . 
 
 Neville, i 
 
 Darcy, v = C ^RS 
 
 For the value of C see the following table. The maximum value of C for 
 very large pipes is 113.3. 
 
 Kutter, v = C ^RS 
 
 in which C = 
 
322 
 
 HYDRAULICS 
 
 Weisbach, h = ~ 
 
 ~\v ' " 6 
 
 in which /* = head necessary to overcome friction in the pipe; 
 r = mean radius of pipe, in feet; 
 g = gravity = 32.2. 
 
 . .02L/,, 1 \ 
 
 , Darcy ' ht T\ l +Wd)2g 
 
 VALUE OF C IN DARCY'S FORMULA 
 
 Diameter of Pipes, in Inches 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 Value of C. 
 
 05 
 
 80 
 
 93 
 
 99 
 
 102 
 
 103 
 
 105 
 
 106 
 
 107 
 
 108 
 
 109 
 
 109.5 
 
 110 
 
 110.5 
 
 110.7 
 
 111 
 
 111.5 
 
 111.5 
 
 Loss of Head in Pipe by Friction. In each 100 ft. in length the loss of head, 
 by friction, in pipes of different diameters, when discharging various quantities 
 of water per minute is given in the accompanying table, which has been 
 prepared by the Pelton Water Wheel Co. 
 
 O/AOffAAf Of FftlCTIONM. HEADS IN WATCff HPf flf/f 1000 FT. LENGTH. 
 
 FIG. 3 
 
 EXAMPLE. Having 200-ft. head and 600 ft. of 11-in. pipe, carrying 119 cu. 
 ft. of water per minute, what is the effective head? 
 
 SOLUTION. In right-hand column, under 11-in. pipe, find 119 cu. ft. 
 Opposite this will be found the coefficient of friction for this amount of water, 
 which is .444. Multiplying this by the number of hundred feet of pipe, which 
 
HYDRAULICS 
 
 323 
 
 is 6, gives 2.66 ft., which is the loss of head. Therefore, the effective head 
 is 200 -2.66 = 197.34. 
 
 The following formula, deduced by William Cox, gives practically the 
 same results as the accompanying table, and will be found useful in many 
 instances: 
 
 in which F = friction head ; 
 
 L = length of pipe, in feet; 
 D = diameter of pipe, in inches; 
 V = velocity, in feet per second. 
 
 The diagram shown in Fig. 3 gives the frictional heads in 1,000 ft. of water 
 pipe. It shows the flow, in gallons per minute, of the common sizes and gives 
 the frictional heads in both feet of water and pounds per square inch. 
 
 Friction of Knees and Bends. To obtain the friction of knees and bends, 
 the following formulas may be taken as giving close approximate results. 
 It is well to bear in mind that right angles should be avoided whenever possi- 
 ble, and that bends should be made with as large a radius as circumstances 
 will allow. The position of the angle A is shown in Fig. 4. 
 Let A = angle of bend or knee with forward 
 
 line of direction; 
 
 V = velocity of water, in feet per second; 
 R = radius of center line of bend; 
 r radius of bore of pipe (or f diameter); 
 K = coefficient for angles of knees; 
 L = coefficient for curvature of bends; 
 // = head of water, in feet, necessary to 
 
 overcome friction of bends, or knees. FlG 4 
 
 (a/ 
 
 The value of K is as follows for different angles: 
 
 A... 
 
 20 I 40 
 
 60 | 80 
 
 90 
 
 100 
 
 120 
 
 K 
 
 .046 [ .139 
 
 .364 1 .74 
 
 98 
 
 1 26 
 
 1 86 
 
 
 
 
 
 
 
 For bends, 
 
 Values of L for various ratios of the radius of bend to radius of bore: 
 
 When -| = 
 
 K. 
 
 ' 
 
 .2 
 
 .3 
 
 .4 
 
 .5 
 
 .6 
 
 .7 
 
 .8 
 
 .9 
 
 1.0 
 
 Circular sec- 
 tion L 
 Rectangular 
 section L . . . 
 
 .131 
 .124 
 
 .138 
 .135 
 
 .158 
 .18 
 
 .206 
 .25 
 
 .294 
 .4 
 
 .44 
 .64 
 
 .66 
 1.01 
 
 .98 
 1.55 
 
 1.4 
 2.3 
 
 2.0 
 3.2 
 
 RELATIVE QUANTITIES OF WATER DELIVERED IN 24 HOURS, IN 
 1 HOUR, AND IN 1 MINUTE 
 
 Gal. 
 in 
 24 Hr. 
 
 Gal. 
 in 
 1 Hr. 
 
 Gal. 
 in 
 1 Min. 
 
 Gal. 
 in 
 24 Hr. 
 
 Gal. 
 in 
 IHr. 
 
 Gal. 
 in 
 1 Min. 
 
 Gal. 
 in 
 24 Hr. 
 
 Gal. 
 in 
 1 Hr. 
 
 Gal. 
 in 
 1 Min. 
 
 2,500,000 
 2,000,000 
 1,500,000 
 1,000,000 
 950,000 
 900,000 
 850,000 
 800,000 
 750,000 
 700,000 
 
 104,166.6 
 83,333.3 
 62,500.0 
 41,666.6 
 39,583.3 
 37,500.0 
 35,416.6 
 33,333.3 
 31,250.0 
 29,166.6 
 
 1,736.0 
 
 1,388.8 
 1,041.7 
 694.4 
 659.7 
 625.0 
 590.2 
 555.5 
 520.8 
 486.1 
 
 650,000 
 600,000 
 550,000 
 500,000 
 450,000 
 400,000 
 350,000 
 300,000 
 250,000 
 200,000 
 
 27,083.3 
 25,000.0 
 22,916.6 
 20,833.3 
 18,750.0 
 16,666.6 
 14,583.3 
 12,500.0 
 10,416.7 
 8,333.3 
 
 451.3 
 
 416.7 
 381.9 
 347.2 
 312.5 
 277.7 
 243.0 
 208.3 
 173.6 
 138.8 
 
 150,000 
 100,000 
 75,000 
 60,000 
 50,000 
 25,000 
 20.000 
 15,000 
 10,000 
 5,000 
 
 6,250.0 
 4,166.6 
 3,125.0 
 2,500.0 
 2,083.3 
 1,041.6 
 833.3 
 625.0 
 416.6 
 208.3 
 
 104.1 
 69.4 
 52.1 
 41.6 
 34.7 
 17.3 
 13.8 
 10.4 
 6.9 
 3.4 
 
324 
 
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HYDRAULICS 
 
 327 
 
 RESERVOIRS 
 
 When selecting a site for a reservoir, the following points should be observed: 
 
 1. A proper elevation above the point at which the water is required. 
 
 2. The total supply available, including observations as to the rainfall 
 and snowfall. 
 
 3. The formation and character of the ground, with reference to the 
 amount of absorption and evaporation. 
 
 The most desirable formation of ground for a reservoir site is one of com- 
 pact rock, like granite, gneiss, or slate; porous rocks, like sandstones and 
 limestones, are not so desirable. Steep bare slopes are best for the country 
 surrounding a reservoir, as the water escapes from them quickly. The presence 
 of vegetation above the reseryoir causes a considerable amount of absorption ; 
 but, at the same time, the rainfall is usually greater in a region covered with 
 vegetation than in a barren region, hence the streams have a more uniform 
 flow. A reservoir must be made large enough to hold a supply capable of 
 meeting the maximum demand. The area of a reservoir should be determined, 
 and a table made showing its contents for every foot in depth, so that the 
 amount of water available can always be known. 
 
 MINE DAMS 
 
 Dams may be constructed in mines to isolate a portion of the workings so 
 that they can be flooded to extinguish fires, or, where an extremely wet formation 
 has been penetrated, they may be constructed to prevent the water flowing 
 into the workings. Mine dams should be of sufficient strength to resist any 
 column of water that will be likely to come against them. The dam should 
 be arched toward the direction from which the pressure comes, and should be 
 given a good firm bearing in both walls 
 and in the floor and roof. Fig. 1 illus- 
 trates a brick dam that was constructed 
 in Kehley's Run Colliery, at Shenandoah, 
 Pennsylvania, to isolate a portion of the 
 seam so that it might be flooded to extin- 
 guish a mine fire. This is one of the largest 
 mine dams that has ever been constructed. 
 It is composed of three brick arches, each 
 having a thickness of 5 ft., placed one 
 against the other so that they act as one 
 solid structure. The gangway at this point 
 is about 20 ft. wide, and the distance to 
 the next upper level is about 119 ft. It 
 was intended that this should be the maxi- 
 mum head of water that the dams would 
 ever have to resist, though they were made 
 sufficiently strong to resist a head of water 
 reaching to the surface. The separate walls 
 were constructed one at a time, and the 
 cement allowed to set before the next wall 
 was placed. The back wall was carried to 
 a greater.depth and height than the others, 
 so as to make sure of the fact that all slips 
 or partings had been closed. The total 
 pressure upon the dam when the water 
 was in the mine was about 70,000 lb. 
 per sq. ft. 
 
 Dams constructed to permit the flood- 
 ing of a mine usually require no passages 
 through them, but where dams are con- FIG. 1 
 
 structed to confine the water to certain 
 
 parts of the workings, and so reduce pumping charges, it may be necessary 
 to provide both manways and drain pipes through the dams. Fig. 2 
 illustrates a plan and cross-section of a dam in the Curry Mine, at Norway, 
 Michigan, constructed to keep out of the mine workings the water that came 
 from some exploring drifts. As originally constructed, it was a sandstone 
 dam 10 ft. thick and arched on the back face with a radius of 6 ft. A piece 
 of 20-in. pipe provided a manway through the masonry and was held in place 
 
328 
 
 HYDRAULIC&- 
 
 by three sets of clamps and bolts passing through the stonework. A 5-in. 
 drain pipe was also carried through the dam and secured by clamps. When 
 the pressure came upon the dam it was found to leak, so the water was drained 
 off and a 22-in. brick wall built 2 ft. 4 in. back of the dam, the space between 
 being filled with concrete, and the manway and drain pipe extended through 
 the brick wall. Before closing the drain pipe, horse manure was fastened 
 against the face of the brick wall by means of a plank partition. After this 
 
 the manway and drain pipe were 
 closed, and when the pressure came 
 on, the dam was found to leak a 
 small amount, but this soon prac- 
 tically ceased, showing that the 
 manure had closed the leaks. A 
 gauge in the head, of the manway on 
 this dam showed a pressure of 211 
 lb., which corresponded to a static 
 head of 640 ft. of water. The total 
 pressure against the dam was some- 
 thing over 800 T., which it success- 
 fully resisted. 
 
 Dams are now successfully made 
 of concrete, which may be used 
 alone or as a support to and sur- 
 rounding an inner framing of wooden 
 or steel beams, steel rods, etc. The 
 roof and floor as well as the two 
 ribs should be notched deeply . so 
 that the dam on all four sides may 
 have ample bearing in order that 
 it may not be bodily pushed for- 
 wards by the weight of the water 
 behind it. 
 
 OUTSIDE DAMS 
 
 Dams are used for retaining 
 water in reservoirs, for diverting 
 streams in mining, and for storing 
 d6bris coming from coal washeries 
 in canons or narrow valleys. 
 
 Foundations for dams must be 
 p IG solid to prevent settling, and water- 
 
 tight to prevent leakage under the 
 
 base of the dam. Whenever possible, the foundation should be solid rock. 
 Gravel is better than earth, but when gravel is employed it will be neces- 
 sary to drive sheet piling under the upper toe of the dam, to prevent water 
 from seeping through the formation under the dam. Vegetable soil should be 
 avoided, and all porous material, such as sand, gravel, etc. should be stripped 
 off until hard pan or solid rock is reached. In case springs occur in the area 
 covered by the foundation of the dam, they must be traced; and if they 
 originate on the upper side their flow must be confined to that side of the dam, 
 so that they will have no tendency to become passageways for water from the 
 upper to the lower face of the dam, thus providing holes that may ultimately 
 destroy the entire foundation of the structure. 
 
 Wooden Dams. Wooden dams are constructed of round, sawed, or hewn 
 logs. The timbers are usually at least 1 ft. square, or, if round, from 18 to 
 24 in. in diameter. A series of cribs from 8 to 10 ft. square are constructed by 
 building up the logs in log-house fashion and securing them together with tree- 
 nails. The individual cribs are secured to one another with treenails or by 
 means of bolts. The cribs are usually filled with loose rock to keep them in 
 place, and in many cases are secured to the foundation by means of bolts. 
 A layer of planking on the upper face of the dam makes it watertight, and when 
 the spillway is over the crest of the dam the top of the cribs must be planked. 
 In most cases, it is also necessary to provide an apron for the water to fall 9n. 
 The apron may be set on small cribs, or on timbers projecting from the cribs 
 of the dam itself. 
 
 Abutments and Discharge Gates. Abutments are structures at the ends of a 
 dam. They may be constructed from timber, masonry, or dry stonework. 
 
HYDRAULICS 329 
 
 If possible, abutments should have a curved outline, and should be so placed 
 that there is no possibility of the water overflowing them, or getting behind 
 them during floods. If the regular discharge from a dam takes place from the 
 main face, the gates may be arranged in connection with one of the abutments, 
 or by means of a tunnel and culvert through the dam. In either case, some 
 structure should be constructed above the outlet so as to prevent driftwood, 
 brush, and other material from stopping the discharge gates. When the 
 discharge gates are placed at one side of the dam, they are usually arranged 
 outside of the regular abutment, between it and a special abutment, the dis- 
 charge being through a series of gates into a flume, ditch, or pipe. 
 
 Spillways, or Waste Ways. Spillways, or waste ways are openings pro- 
 vided in a dam for the discharge of water during floods or freshets, or for the 
 discharge of a portion not being used at any time. The spillway may be over 
 the crest of the dam; though, where the topography favors such a construction, 
 the main dam may be of sufficient height to prevent water from passing its 
 crest and the spillway arranged at another outlet over a lower dam. Waste 
 ways, proper, are openings through the dam, and are intended for the discharge 
 of the large quantities of water that come do.wn during freshets or floods. In 
 the case of timber dams, the waste ways are usually surrounded by heavy 
 cribs, and have an area of from 40 to 50 sq. ft. each. 
 
 There are two general forms of construction employed for waste ways. 
 One consists of a comparatively narrow opening in the dam, extending to a 
 considerable depth (8 or 10 ft.). Water is allowed to discharge through this 
 during flood time, but when it is desired to stop the flow, planks are placed 
 across the up-stream face of the opening in such a manner as to close it. The 
 opening, which is usually not over 3 or 4 ft. wide, is provided with guides on 
 the upper face of the dam; between these the planks are slid down, the indi- 
 vidual pieces of planking being at least 1 ft. longer than the opening that they 
 are to cover. The other device frequently used consists in providing the 
 waste way, at one side of the regular spillway, with a crest 2 or 3 ft. lower 
 than the regular spillway. The crest of this waste way is composed of heavy 
 timber, and 4 or 5 ft. above there is placed a parallel timber; the space between 
 the two is then closed by flash boards, which are pieces of 2- in. or 3-in. plank, 
 6 or 8 in. wide, and long enough to extend from 1 to 2 ft. above the upper 
 timber. The planks are placed against both timbers so as to close the space. 
 Through the upper end of each plank is bored a hole through which a piece 
 of rope is passed and a knot tied in the end of the rope; these ropes are secured 
 by staples to the upper timber. When it becomes necessary to open the 
 waste way, men go under with peevies, cant hooks, or pinch bars, and pry 
 up the planks in such a way as to draw the longer end out of contact with 
 the lower timber, when the force of the water will immediately carry the 
 plank down the stream as far as the rope will allow. After the first plank 
 has been loosened, the succeeding ones can be pulled up with comparative 
 ease, and two men can open a 25-ft. or 30-ft. section of waste way in a very 
 few minutes. The ropes keep the plank from being lost, and the opening 
 can be closed again by passing the planks down into the water to one side of 
 the opening and moving them into the current. Some skill is required both 
 in opening and closing the waste ways. 
 
 Stone Dams. Where cement or lime is expensive, but where suitable 
 rubble stone can be obtained, dams are frequently constructed without the use 
 of mortar. In such cases, the upper and lower faces of the dam should be of 
 hammer-dressed stone, carefully bonded, and sometimes the stones in the 
 lower face of the dam are anchored by means of bolts. The dam can be made 
 watertight by placing a skin of planking on the upper face. In case water 
 should ever pass over the crest of such a dam, much of it will settle through 
 the openings in the stone into the interior of the dam, and subject the stones 
 in the lower portion of the face to a hydrostatic pressure, provided an opening 
 has not been made for the escape of such water. For this reason, culverts or 
 "openings should be made through the lower portion of the dam, to discharge 
 any such water. When such dams as this are constructed, the regular spillway 
 is not placed over the face of the dam, but at some other point, and usually 
 over a timber dam. 
 
 Earth Dams. Earth dams are used for reservoirs of moderate height. 
 They should be at least 10 ft. wide on top, and a height of more than 60 ft. is 
 unusual. When the material of which the dam is composed is not water- 
 tight, as for instance, gravel, sand, etc., it is sometimes necessary to construct 
 a puddle wall of clay in the center of the regular dam. This consists of a 
 narrow dam of clay mixed with a certain proportion of sand. The puddle wall 
 
HYDRAULICS 
 
 should not be less than from 6 to 8 ft. thick at the top of the dam, and should 
 be given a slight batter on each side. It is constructed during the building 
 of the dam, and should be protected from contact with the water by a con- 
 siderable thickness of earth on the upper face. The upper face of an earthen 
 dam is frequently protected by means of plank or a pavement of stone. The 
 lower face is frequently protected by means of sod, or sod and willow trees. 
 Sometimes earth dams are provided with a masonry core in place of the puddle 
 
 wall, to render them water-tight. This consists of a masonry wall carried to 
 an impervious stratum, and up through the center of the dam. The masonry 
 core should never be less than 2 or 3 ft. thick at the top, and should be given 
 a batter of at least 10% on each side. At the regular water level, earthen dams 
 are liable to have a small bench or shelf formed, and on this account, during 
 the construction, such a bench or shelf is sometimes built into the earth dam. 
 The accompanying figure shows a dam with a masonry core, with the upper 
 face covered with rubble and the lower face covered with grass. 
 
 IRRIGATION QUANTITY TABLES 
 
 Amount of Water 
 Required to Cover 
 1 A. to Given Depths 
 
 Second-Feet Reduced to 
 Gallons and Acre-Feet* 
 
 Gallons Required 
 to Cover a Given 
 Number of Acres 
 to Depth of 1 Ft. 
 
 Depth 
 
 11JS 
 
 1 
 
 1 
 
 *o 
 
 i 
 
 fa 
 
 U 
 
 |P 
 
 sf 
 
 $2% 
 
 I 
 
 o 
 
 Ft. 
 
 In. 
 
 if!! 
 
 13 
 O 
 
 
 i 1 
 
 Jl* a 
 
 
 111 
 
 <&< 
 
 1 
 
 
 1 
 
 3.630 
 
 27,154 
 
 ~~ 
 
 112.2 
 
 80,790 
 
 .2479 
 
 1 
 
 325,851 
 
 
 2 
 
 7,260 
 
 54,309 
 
 i 
 
 224.4 
 
 161,579 
 
 .4959 
 
 2 
 
 651,703 
 
 
 3 
 
 10,890 
 
 81,463 
 
 
 
 336.6 
 
 242,369 
 
 .7438 
 
 3 
 
 977,554 
 
 
 4 
 
 14,520 
 
 108,617 
 
 i 
 
 448.8 
 
 323,158 
 
 .9917 
 
 4 
 
 1,303,406 
 
 
 5 
 
 18,150 
 
 135,771 
 
 it 
 
 561.0 
 
 403,948 
 
 1.2397 
 
 5 
 
 1,629,257 
 
 
 6 
 
 21,780 
 
 162,926 
 
 H 
 
 673.2 
 
 484,738 
 
 1.4876 
 
 6 
 
 1,955,109 
 
 
 7 
 
 25,410 
 
 190,080 
 
 if 
 
 785.5 
 
 565,527 
 
 1.7355 
 
 7 
 
 2,280,960 
 
 
 8 
 
 29,040 
 
 217,234 
 
 2 
 
 897.7 
 
 646,317 
 
 1.9835 
 
 8 
 
 2,606,812 
 
 
 9 
 
 32,670 
 
 244,389 
 
 2* 
 
 1122.1 
 
 807.896 
 
 2.4793 
 
 9 
 
 2,932,663 
 
 
 10 
 
 36,300 
 
 271,542 
 
 3 
 
 1346.5 
 
 969,475 
 
 2.9752 
 
 10 
 
 3,258,515 
 
 
 11 
 
 39,930 
 
 298,697 
 
 4 
 
 1795.3 
 
 1,292,634 
 
 3.9669 
 
 15 
 
 4,887,772 
 
 
 00 
 
 43,560 
 
 325,851 
 
 5 
 
 2244.2 
 
 1.615,792 
 
 4.9586 
 
 20 
 
 6,517,029 
 
 
 2 
 
 50,820 
 
 380,160 
 
 6 
 
 2693.0 
 
 1,938,951 
 
 5.9503 
 
 25 
 
 8,146,286 
 
 
 4 
 
 58,080 
 
 434,469 
 
 7 
 
 3141.8 
 
 2,262,109 
 
 6.9421 
 
 30 
 
 9,775,544 
 
 
 6 
 
 65,340 
 
 488,777 
 
 8 
 
 3590.6 
 
 2,585,268 
 
 7.9338 
 
 40 
 
 13,034,058 
 
 
 8 
 
 72,600 
 
 543,086 
 
 9 
 
 4039.5 
 
 2,908,426 
 
 8.9255 
 
 60 
 
 19,551,087 
 
 1 
 
 10 
 
 79,860 
 
 597,394 
 
 10 
 
 4488.3 
 
 3,231,585 
 
 9.9173 
 
 80 
 
 26,068,116 
 
 2 
 
 00 
 
 87,120 
 
 651,703 
 
 20 
 
 8976.6 
 
 6,463,170 
 
 19.8345 
 
 160 
 
 52,136,232 
 
 *One cubic foot of water per second (exact 7.48052 gal.) constant flow is 
 known as the second-foot. 
 
 The acre-foot is the quantity of water required to cover 1 A. to a depth 
 
HYDRAULICS 331 
 
 Refuse Dams. Refuse dams are placed across the bed of streams to hold 
 back refuse from mines and washeries, and to prevent damage to the valleys 
 below. They are made of stone, timber, or brush. No attempt is made to 
 render the refuse dam water-tight, the only object being that it should retard 
 the flow of the stream and give it a greater breadth of discharge, so that the 
 water naturally drops and deposits the sediment that it is carrying. The 
 sediment soon silts or fills up against the face of the dam, the area above the 
 dam becoming a flat expanse or plain over which the water finds its way to 
 the dam. When these dams are constructed of stone, the individual stones 
 on the lower face and crest of the dam should be so large that the current will 
 be unable to displace them, while the upper face and core of the dam may be 
 composed of finer material. In case a breach should occur in the refuse dam, 
 it will not necessarily endanger the region farther down the stream, as is the 
 case when a break occurs in a water dam. The reason for this is that the 
 refuse dam is not made watertight, and hence there is never much pressure 
 against it, or a large volume of water held back that can rush suddenly down 
 the stream should a break occur. The only result of the break would be that 
 more or less of the gravel, sand, slate, etc., behind the dam would be washed 
 through the breach. 
 
 Wing Dams. Wing dams are used for turning streams from their courses, 
 so as to expose all or a portion of the bed for placer mining or other purposes. 
 They are usually of a temporary nature, and are constructed of brush and 
 stones, light cribs filled with stones, and of large stones, or timber. Some- 
 times the course of a stream is turned by an obstruction made of sand bags 
 and a wing dam constructed behind this of frames of timber, the intervening 
 space being filled with gravel or earth; in some cases, the timber is covered with 
 stone and the surface riprapped so that if the flow ever comes over the top 
 of the structure it will not destroy it. 
 
 Masonry and Concrete Dams. When high masonry or concrete dams are 
 to be employed they should be designed by a competent hydraulic engineer. 
 Masonry or concrete dams are not, as a rule, used around coal mines, owing 
 to the fact that the length of time during which the dam is required rarely 
 warrants such expensive construction. 
 
 WATER-POWER 
 
 Theoretical Efficiency of Water-Power. The gross power of a fall of 
 water is the product of the weight of water discharged in a unit of time, and 
 the total head or difference in elevation of the surface of the water, above 
 and below the fall. The term head, used in connection with waterwheels, 
 is the difference in height between the surface of water in the penstock and 
 that in the tailrace, when the wheel is running. 
 
 If Q = cubic feet of water discharged per minute; 
 W = weight of 1 cu. ft. of water = 62.5 lb.; 
 H = total head, in feet; 
 
 WQH = gross power, in foot-pounds per minute; 
 WQH 
 
 Substituting the value for W, gives 
 
 . 00189Q#, as horsepower of a fall. 
 
 The total power can never be utilized by any form of motor, because there 
 is a loss of head, both at the entrance to, and exit from, the wheel, and 
 there are also, losses of energy due to friction of the water in passing through 
 the wheel. The ratio of the power developed by the wheel to the gross 
 power of the fall, is the efficiency of the wheel. A head of water can be made 
 use of in any one of the following ways: 
 
 1. By its weight, as in the water balance, or overshot wheel. 
 
 2. By its pressure, as in the hydraulic engine, hydraulic presses, cranes, 
 etc., or in a turbine water wheel. 
 
 3. By its impulse, as in the undershot and impulse wheels, such as 
 Peltons, etc. 
 
 4. By a combination of these. 
 
 Horsepower of a Running Stream. The gross horsepower is 
 
 QHX62.5 
 H ' P< 33,000" 
 
332 HYDRAULICS 
 
 in which Q = quantity actually impinging on float or bucket, in cubic feet 
 
 per minute; 
 H = theoretical head added to velocity of stream. 
 
 in which v = velocity, in feet per second. 
 
 For example, if the floats of an undershot waterwheel are 2 ft.XlO ft., and 
 the stream has a velocity of 3 ft, per sec., i. e., z> = 3, # = 9-^64.4 = .139, and Q 
 = 2X10X3X60 = 3,600 cu. ft. per min. 
 
 From this, H. P. = 3,600 X. 139 X. 00189 = .945 H. P., or a gross horsepower 
 for practically .05 sq. ft. of wheel surface; but, under ordinary circumstances, 
 it is impossible to attain more than 40% of this, or practically .02 H. P. per 
 sq. ft. of surface, which requires 50 sq. ft. of float surface to each horsepower 
 furnished. 
 
 Current Motors. A current motor fully utilizes the energy of a stream 
 only when it is so arranged that it can take all the velocity out of the water; 
 that is, when the water leaves the floats or vanes with no velocity. In practice, 
 it is impossible to obtain even a close approximation to these results, and hence 
 only a small fraction of the energy of a running stream can be utilized by the 
 current motor. 
 
 Current motors are frequently used to obtain small amounts of power from 
 a large stream, as, for instance, for pumping a limited amount of water for 
 irrigation. For this work, an ordinary undershot wheel having radial paddles 
 is usually employed. At one end of the wheel a series of small buckets are 
 placed, and so arranged that each bucket will dip up water at the bottom of the 
 wheel and discharge it into the launder, near the top of the wheel. The shape 
 of the buckets should be such that only the amount of water that the bucket 
 is capable of carrying to the launder will be dipped up, for, if the bucket is 
 constantly slopping or pouring water as it ascends, a large amount of useless 
 work is performed in raising this extra water and then pouring it out again, 
 as only the portion that reaches the launder can be of any service. Current 
 motors are not practicable for furnishing large amounts of power. 
 
 Utilizing Power of Waterfall. The power of a waterfall may be utilized by 
 a number of different styles of motors, but each has certain advantages. 
 
 When the head is low (not over 5 or 6 ft.), breast or undershot wheels are 
 frequently employed. If these are properly proportioned, it is possible to 
 realize from 25% to 50% of the theoretical power of the fall, but the wheels 
 are large and cumbersome compared with the duty they perform, and are not 
 often installed at present, especially near manufacturing centers. 
 
 For falls up to 40 or 50 ft., overshot wheels are very commonly employed, 
 and they have been used for even greater heads than this. The overshot wheel 
 derives its power both from the impulse of the water entering the buckets, and 
 from the weight of the water as it descends on one side of the wheel in the 
 buckets; the latter factor is by far the more important of the two. When 
 properly proportioned, overshot wheels may realize from 70% to 90% of the 
 power of the waterfall, but they are large and cumbersome compared with the 
 power that they give, and are not often installed except in isolated regions, 
 where they are made from timber by local mechanics. 
 
 For heads varying from 50 ft. up, impulse wheels are very largely used. 
 These are also sometimes called hurdy gurdies, and are usually of the Pelton 
 type, consisting of a wheel provided with buckets, so arranged about its peri- 
 phery that they receive an impinging jet of water and turn it back upon itself, 
 discharging it with practically no velocity, and converting practically all the 
 energy into useful work. The efficiency of these wheels varies from 85% to 
 90% under favorable circumstances. This style of wheel is especially adapted 
 for very high heads and comparatively small amounts of water. There are a 
 number of instances where wheels are operating under a head of as much as 
 2,000 ft. This style of impulse wheel is an American development; in Europe, 
 a style of impulse turbine has been used to some extent, but has not found 
 very much favor in the United States. 
 
 Turbines, or reaction wheels, are very largely employed, especially for 
 moderate heads. When properly designed to fit the working conditions, they 
 can be used for heads varying from 4 to 5 ft. up to considerably over 100 ft., 
 and when properly placed are capable of utilizing the entire head, a factor 
 that gives them a decided advantage over any other style of waterwheel. 
 Turbines are capable of returning 85% to 90% of the theoretical energy as 
 useful power, and are largely used, especially where a considerable volume of 
 water at a low head, or a smaller volume at a moderate head, can be obtained. 
 
HYDRAULICS 
 
 333 
 
 PUMP MACHINERY 
 
 CLASSIFICATION OF PUMPS 
 
 f Pumps are employed for unwatering mines, handling water at placer mines, 
 irrigation, water-supply systems, boiler feeds, etc. For unwatering mines, 
 two general systems of pumping are employed: (1) The pump is placed in 
 the mine and is operated by a motor on the surface, the power being trans- 
 mitted through a line of moving rods. (2) Both the motor and pump are 
 placed in the mine, the motor being an engine driven by steam, compressed 
 air, hydraulic motor, or an electric motor. 
 
 Cornish Pumps. Any method of operating pumps by rods is commonly 
 called a Cornish system. Formerly, the motor in the Cornish system consisted 
 of a steam engine placed over the shaft head, which operated the pump by a 
 direct line of rods. With this arrangement, there is great danger of accident 
 to the engine from the settling of the ground around the shaft, or from fire in 
 the shaft; also, the position of the motor renders access to the shaft difficult. 
 To overcome these objections, the engine is frequently placed at one side of 
 the shaft, and the rods operated by a bob; this has become the common prac- 
 tice, and is generally called the Cornish rig. The engine employed in the most 
 modern plants is generally of the Corliss type, and is provided with a governor 
 to guard against the possibility of the engine running away, in case the rods 
 should break. 
 
 This system requires no steam line down the shaft, and is independent of 
 the depth of water in the mine, so that the pump is not stopped by the drown- 
 ing of a mine, but the moving rods are a great inconvenience in the shaft, and 
 they absorb a great amount of power by friction. 
 
 Simple and Duplex Pumps. In the simple pumps a steam cylinder is con- 
 nected directly to a water cylinder, and the steam valves are operated by 
 tappets. Such a pump is more or less dependent on inertia at certain points 
 of the stroke to insure the motion of the valves, hence will not start from 
 any place, but is liable to become stalled at times. 
 
 In the duplex pump, two steam cylinders and two water cylinders are 
 arranged side by side, and the valves so placed that when one piston is at mid- 
 stroke it throws the steam valve for the other cylinder, etc. With this arrange- 
 ment, the pump will start from any point, and can never be stalled for lack of 
 steam, due to the position of the valves. Ordinarily, duplex pumps are to be 
 preferred for mine work. 
 
 The pa ' ' 
 Any form 
 
 or surrounding the ram, 
 and so situated that any 
 wear will allow communi- 
 cation between the op- 
 posite ends of the cylin- 
 der, is called inside pack- 
 ing. It may consist simply 
 of piston rings about the 
 piston, as in the case of 
 an ordinary steam : engine 
 piston G, Fig. 1, 'or sta- 
 tionary rings may be em- 
 ployed about the outside 
 of a moving ram, or long 
 piston P. In either case, the cylinder heads have to be removed before the 
 condition of the packing can be inspected, and any leak does not make itself 
 visible. 
 
 When outside packing is employed, separate rams are used in opposite 
 ends of the cylinder, there being no internal communication between the 
 chambers in which the rams work. The rams are packed by ordinary 
 outside stuffingboxes and glands. The arrangement consists practically of 
 two single-acting pumps arranged to work alternately, so that one is forcing 
 water while the other is drawing water. Fig. 2 shows a horizontal section 
 of a cylinder so arranged, together with the yoke rods that operate the ram 
 at the farther end of the cylinder. 
 
 As a rule, inside-packed pumps should be avoided in mines, because acid 
 or gritty waters are liable to cut the packing, and make the pumps leak in a 
 
 packing for the water piston of a pump may be either inside or outside, 
 m of packing that is inside the cylinder, either upon a moving piston 
 
 FIG. 1 
 
334 HYDRAULICS 
 
 very short time. For dipping work in single stopes or entries, small single 
 or duplex outside-packed pumps may be employed. It is generally best to 
 operate such pumps by compressed air, for the exhaust will then be beneficial 
 
 to the mine air. If steam 
 iFThm *dl? is employed, it is fre- 
 
 I, T;~ f i^'"_ ---- -~-.-7r?zzjm, I _ quently necessary to 
 
 f~ =ia^^^^^3)BO O O Sbji^^^^^^a j|^^ introduce a trap and 
 
 c: ^^M^^^J^M^^ J ^J^ remove entrailed water 
 
 f K.U ' *u ^ from the steam before 
 
 p ir o it enters the pump, and 
 
 to dispose of the exhaust 
 
 by piping it out or condensing it. Such isolated steam pumps are about the 
 most wasteful form of steam-driven motor in existence. 
 
 For sinking, center-packed single or duplex pumps are usually employed, 
 the duplex style being the better. For station work, where much water is to 
 be handled, large compound, or triple-expansion, condensing, duplex pumping 
 engines are empk>yed. They may, or may not, be provided with cranks and 
 a flywheel. Engineers differ greatly upon this point, and, as a rule, for very 
 high lifts and great pressures, the flywheel is employed. , 
 
 The main points in consideration are the first cost of the pump, and the 
 amount that will be saved by using the more expensive engine. The large 
 flywheel pumping engines are several times as expensive as the direct-acting 
 steam pumps, and the question is as to whether their greater efficiency will 
 more than counterbalance the increased outlay. Most engineers favor fly- 
 wheel pumps for handling large volumes of water where the work is approxi- 
 mately constant, and direct-acting pumps, without flywheels or cranks, for 
 handling small amounts of water, or for very irregular service, owing to the 
 fact that if the flywheel pump is driven below its normal speed it does not 
 govern properly, nor work economically. Until recently, water was removed 
 from mines in lifts of about 300 to 350 ft., pumps being placed at stations along 
 the shaft. 
 
 While a series of station pumps are still employed in some cases, they are 
 generally intended to take care of water coming into the shaft, or workings 
 at or near their level, and are not employed for handling water in successive 
 stages or lifts. For handling the bulk of the water from the bottom of the 
 shaft, large pumping engines are employed that frequently force the water 
 to the surface from depths of over 1,000 ft. These high-duty pumping plants, 
 when near the shaft and operated by steam with a condenser, frequently show 
 a very high efficiency. When air is employed to operate such a plant, a much 
 higher efficiency can be obtained if the compressed air is heated before it is 
 used in the high-pressure cylinder and during its passage from the high-pressure 
 to the low-pressure cylinder. This has been very successfully accomplished 
 by means of a steam reheater, the small amount of steam necessary being 
 conveyed to the station in the small pipe, and entirely condensed in the reheater, 
 from which it is trapped as water. 
 
 The duty of steam pumps is approximately as follows: For small-sized 
 steam pumps, the steam consumption is from 130 to 200 Ib. per H. P. per hr., 
 when operating in the workings of a mine at some distance from the boiler. 
 For larger sizes of simple steam pumps, the consumption runs from 80 to 
 130 Ib. per H. P. per hr. Compound-condensing pumps, such as are commonly 
 used as station pumps, consume from 40 to 70 Ib. per H. P. per hr. Triple- 
 expansion, condensing, high-class pumping engines consume from 24 to 26 Ib. 
 per H. P. per hr. The Cornish pump consumes varied amounts of steam in 
 proportion to the water delivered, depending largely on the friction of the 
 gearing, bobs, rods, etc., but its efficiency is usually considerably below the 
 best class of pumping engines. 
 
 Speed of Water Through Valves, Pipes, and Pump Passages. The speed of 
 water through the valves and passages of a pump should not exceed 250 ft. per 
 min., and care should be taken to see that the passages are not too abruptly 
 deflected. The flow of water through the discharge pipe should not exceed 
 500 ft. per min., and for single-cylindered pumps it is usually figured at between 
 250 and 400 ft. per min. In the case of very large pumps, greater velocities 
 may be allowed. The suction pipe for the pump should be larger than the 
 discharge pipe. Ordinarily the suction pipe for a pump should not exceed 
 250 ft. in length, and should not contain more than two elbows. The following 
 formula gives the diameter of the suction and discharge pipes of a pump: 
 
 G = United States gallons per minute; 
 
 d' = diameter of suction pipe, in inches; 
 
HYDRAULICS 
 
 335 
 
 d" = diameter of discharge pipe, in inches; 
 
 v' = velocity of water, in feet per minute, in suction pipe = from .50" to ,75v" 
 v" = velocity of water, in feet per minute, in discharge pipe. 
 
 = 4.( 
 
 RATIO OF STEAM AND WATER CYLINDERS 
 DIRECT-ACTING PUMP 
 
 Let A =area of steam cylinder; 
 
 D = diameter of steam cylinder ; 
 F = steam pressure, in pounds per square inch; 
 tf = head of water = 2.309; 
 a = area of pump cylinder; 
 d = diameter of pump cylinder; 
 p = pressure per square inch, corresponding to head 
 
 IN A 
 
 E = efficiency of pump = 
 
 EAP 
 
 work done in pump cylinder 
 work done in steam cylinder' 
 
 .433/7 
 EP 
 
 EAP 
 
 2.30QEPX~. 
 a 
 
 75%, then # = 1.732PX J 
 
 E is commonly taken at from .7 to .8 for ordinary direct-acting pumps. 
 For the highest class of pumping engines it may amount to .9. The steam 
 pressure P is the mean effective pressure, according to the indicator diagram; 
 the pressure p is the mean total pressure acting on the pump plunger or piston, 
 including the suction, as would be shown by the indicator diagram of the 
 water cylinder. The pressure on the pump cylinder is frequently much greater 
 than that due to the height of the lift, on account of the friction in the valves 
 and passages, which increases rapidly with the velocity of the flow. 
 
 Piston Speed of Pumps. For small pumps, it is customary to assume a 
 speed of 100 ft. per min., but, in the case of very small short-stroke pumps, 
 this is too high, owing to the fact that the rapid reverses make the flow 
 through the valves and change in the direction of the current too frequent. 
 When the stroke of the pump is somewhat longer (18 in. or more), higher speeds 
 can be employed, and in the case of large pumping engines having long strokes, 
 speeds of as much as 200 to 250 ft. per min. are successfully used without jar 
 or hammer. 
 
 STROKES FOR PISTON SPEED OF 100 FT. PER MIN. 
 
 Length of 
 Stroke 
 Inches 
 
 Number 
 of 
 Strokes 
 
 Length of 
 Stroke 
 Inches 
 
 Number 
 of 
 Strokes 
 
 Length of 
 Stroke 
 Inches 
 
 Number 
 of 
 Strokes 
 
 4 
 5 
 6 
 7 
 8 
 10 
 
 300 
 240 
 200 
 172 
 150 
 120 
 
 12 
 14 
 16 
 18 
 20 
 22 
 
 100 
 86 
 75 
 67 
 60 
 55 
 
 24 
 26 
 28 
 30 
 36 
 40 
 
 50 
 46 
 43 
 40 
 33 
 30 
 
 Boiler Feed-Pumps. In practice, it has been shown that a piston speed 
 greater than 100 ft. per min. results in excessive wear and tear on a boiler 
 feed-pump, especially when the water is warm. This is because vapor forms in 
 the cylinders, and results in a water hammer. In determining the proper 
 size of a pump for feeding a steam boiler, not only the steam employed in 
 running the engine, but that necessary for the pumps, heating system, etc. 
 must be taken into consideration. 
 
336 
 
 HYDRAULICS 
 
 THEORETICAL CAPACITY OF PUMPS AND HORSEPOWER REQUIRED 
 TO RAISE WATER 
 
 Let Q = cubic feet of water per minute; 
 G = United States gallons per minute; 
 G' = United States gallons per hour; 
 d = diameter of cylinder, in inches; 
 1 = stroke of piston, in inches; 
 2V = number of single strokes per minute; 
 v = speed of piston, in feet per minute; 
 
 RATIOS OF AREAS TO DIAMETERS 
 
 
 Diameter of Steam Cylinder, in Inches 
 
 TV t 
 
 
 of Water 
 Cylinders 
 Inches 
 
 5 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 
 Ratios of Areas 
 
 I 
 
 64,00 
 
 92.16 
 
 163.84 
 
 256.00 
 
 368.64 
 
 501.76 
 
 1 
 
 44.44 
 
 64.00 
 
 113.77 
 
 177.77 
 
 256.00 
 
 348.44 
 
 1 
 
 32.65 
 
 47.02 
 
 83.59 
 
 130.61 
 
 188.10 
 
 256.00 
 
 1 
 
 25.00 
 
 36.00 
 
 64.00 
 
 100.00 
 
 144.00 
 
 196.00 
 
 H 
 
 19.75 
 
 28.44 
 
 50.56 
 
 79.01 
 
 113.78 
 
 154.86 
 
 
 16.00 
 
 23.04 
 
 40.96 
 
 64.00 
 
 92.16 
 
 125.44 
 
 ij 
 
 13.22 
 
 19.04 
 
 33.85 
 
 52.89 
 
 76.17 
 
 103.66 
 
 i; 
 
 11.11 
 
 16.00 
 
 28.44 
 
 44.44 
 
 64.00 
 
 87.11 
 
 tj 
 
 9.46 
 
 13.63 
 
 24.23 
 
 37.87 
 
 54.53 
 
 74.22 
 
 li 
 
 8.16 
 
 11.75 
 
 20.90 
 
 32.65 
 
 47.02 
 
 64.00 
 
 11 
 
 7.11 
 
 10.24 
 
 18.20 
 
 28.44 
 
 40.96 
 
 55.75 
 
 2 
 
 6.25 
 
 9.00 
 
 16.00 
 
 25.00 
 
 36.00 
 
 49.00 
 
 2i 
 
 4.93 
 
 7.11 
 
 12.64 
 
 19.75 
 
 28.44 
 
 38.71 
 
 21 
 
 4.00 
 
 5.76 
 
 10.24 
 
 16.00 
 
 23.04 
 
 31.36 
 
 2f 
 
 3.30 
 
 4.76 
 
 8.46 
 
 13.22 
 
 19.04 
 
 25.91 
 
 3 
 
 2.77 
 
 4.00 
 
 7.11 
 
 11.11 
 
 16.00 
 
 21.77 
 
 3i 
 
 2.37 
 
 3.40 
 
 6.06 
 
 9.46 
 
 13.63 
 
 18.56 
 
 3 
 
 2.04 
 
 2.93 
 
 5.22 
 
 8.16 
 
 11.75 
 
 16.00 
 
 3! 
 
 1.77 
 
 2.56 
 
 4.55 
 
 7.11 
 
 10.24 
 
 13.93 
 
 4 
 
 1.56 
 
 2.25 
 
 4.00 
 
 6.25 
 
 9.00 
 
 12.25 
 
 4J 
 
 1.38 
 
 1.99 
 
 3.54 
 
 5.53 
 
 7.97 
 
 10.85 
 
 4f 
 
 1.23 
 
 1.77 
 
 3.15 
 
 4.93 
 
 7.11 
 
 9.67 
 
 4| 
 
 1.10 
 
 1.59 
 
 2.83 
 
 4.43 
 
 6.38 
 
 8.68 
 
 5 
 
 1.00 
 
 1.44 
 
 2.56 
 
 4.00 
 
 5.76 
 
 7.84 
 
 5* 
 
 .82 
 
 1.19 
 
 2.11 
 
 3.30 
 
 4.76 
 
 6.47 
 
 6 
 
 .69 
 
 1.00 
 
 1.77 
 
 2.77 
 
 4.00 
 
 5.44 
 
 61 
 
 .59 
 
 .85 
 
 1.51 
 
 2.37 
 
 3.40 
 
 4.63 
 
 7 
 
 .51 
 
 .73 
 
 1.30 
 
 2.04 
 
 2.93 
 
 4.00 
 
 71 
 
 .44 
 
 .64 
 
 1.13 
 
 1.77 
 
 2.56 
 
 3.48 
 
 8 
 
 .39 
 
 .56 
 
 1.00 
 
 1.56 
 
 2.25 
 
 3.06 
 
 |J 
 
 .34 
 
 .49 
 
 .88 
 
 1.38 
 
 1.99 
 
 2.71 
 
 9 
 
 .30 
 
 .44 
 
 .79 
 
 1.23 
 
 1.77 
 
 2.42 
 
 9* 
 
 .27 
 
 .39 
 
 .70 
 
 1.11 
 
 1.59 
 
 2.17 
 
 10 
 
 
 .36 
 
 .64 
 
 1.00 
 
 1.44 
 
 1.96 
 
 11 
 
 
 .29 
 
 .52 
 
 .82 
 
 1.19 
 
 1.62 
 
 12 
 
 
 .25 
 
 .44 
 
 .69 
 
 1.00 
 
 1.36 
 
 13 
 
 
 
 .37 
 
 .59 
 
 .85 
 
 1.16 
 
 14 
 
 
 
 .33 
 
 .51 
 
 .73 
 
 1.00 
 
 15 
 
 
 
 .28 
 
 .44 
 
 .64 
 
 .87 
 
 16 
 
 
 
 .25 
 
 .39 
 
 .56 
 
 .76 
 
 17 
 
 
 
 
 .34 
 
 .49 
 
 .67 
 
 18 
 
 
 
 
 .30 
 
 .44 
 
 .60 
 
HYDRAULICS 
 
 337 
 
 W 
 P 
 p 
 H 
 H. P. 
 
 Then, 
 
 weight moved, in pounds per minute ; 
 pressure, in pounds per square foot = 62.5ff; 
 pressure, in pounds per square inch = .433H; 
 height of lift, in feet; 
 horsepower. 
 
 OF STEAM AND WATER CYLINDERS 
 
 Diameter of Steam Cylinders, in Inches 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 
 
 28 
 
 30 
 
 Ratios of Areas 
 
 455.11 
 
 
 
 
 
 
 
 
 334 . 37 
 
 
 
 
 
 
 
 
 256 . 00 
 
 324.00 
 
 400.00 
 
 
 
 
 
 
 202 . 27 
 
 256 . 00 
 
 316.05 
 
 
 
 
 
 
 163.84 
 
 207.36 
 
 256.00 
 
 309 . 76 
 
 
 
 
 
 135.41 
 
 171.37 
 
 211.57 
 
 256 . 00 
 
 
 
 
 
 113.77 
 
 144.00 
 
 177.77 
 
 215.11 
 
 256.00 
 
 
 
 
 96.95 
 
 122.70 
 
 151.48 
 
 183.29 
 
 218.11 
 
 
 
 
 83.59 
 
 105.79 
 
 130.61 
 
 158.05 
 
 188.10 
 
 220 . 73 
 
 
 
 72.82 
 
 92.16 
 
 113.78 
 
 137.67 
 
 163.85 
 
 192.29 
 
 
 
 64.00 
 
 81.00 
 
 100.00 
 
 121.00 
 
 144.00 
 
 169.00 
 
 196.00 
 
 225.00 
 
 50.56 
 
 64.00 
 
 79.01 
 
 95.60 
 
 113.78 
 
 133.53 
 
 154.86 
 
 177 .77 
 
 40.96 
 
 51.84 
 
 64.00 
 
 77.44 
 
 92.16 
 
 108.16 
 
 125.44 
 
 144.00 
 
 33.81 
 
 42.84 
 
 52.89 
 
 64.00 
 
 76.17 
 
 89.39 
 
 103.66 
 
 119.01 
 
 28.44 
 
 36.00 
 
 44.44 
 
 53.77 
 
 64.00 
 
 75.11 
 
 87.11 
 
 100.00 
 
 24.23 
 
 30.67 
 
 37.87 
 
 45.82 
 
 54.53 
 
 64.00 
 
 74.22 
 
 85.21 
 
 20.90 
 
 26.44 
 
 32.65 
 
 39 . 51 
 
 47.02 
 
 55.18 
 
 64.00 
 
 73.47 
 
 18.20 
 
 23.04 
 
 28.44 
 
 34.42 
 
 40.96 
 
 48.07 
 
 55.75 
 
 64.00 
 
 16.00 
 
 20.25 
 
 25.00 
 
 30.25 
 
 36.00 
 
 42,25 
 
 49.00 
 
 56.25 
 
 14.22 
 
 17.93 
 
 22.14 
 
 26.79 
 
 31.89 
 
 37.43 
 
 43.41 
 
 49.83 
 
 12.64 
 
 16.00 
 
 19.75 
 
 23.90 
 
 28.44 
 
 33.38 
 
 38.71 
 
 44.44 
 
 11.34 
 
 14.36 
 
 17.73 
 
 21.45 
 
 25.53 
 
 29.96 
 
 34.75 
 
 39.89 
 
 10.24 
 
 12.96 
 
 16.00 
 
 19.36 
 
 23.04 
 
 27.04 
 
 31.36 
 
 36.00 
 
 8.46 
 
 10.71 
 
 13.22 
 
 16.00 
 
 19.04 
 
 22.35 
 
 25.01 
 
 29.75 
 
 7.11 
 
 9.00 
 
 11.11 
 
 13.44 
 
 16.00 
 
 18.77 
 
 21.77 
 
 25.00 
 
 6.06 
 
 7.66 
 
 9.46 
 
 11.45 
 
 13.63 
 
 16.00 
 
 18.56 
 
 21.30 
 
 5.22 
 
 6.61 
 
 8.16 
 
 9.87 
 
 11.75 
 
 13.79 
 
 16.00 
 
 18.37 
 
 4.55 
 
 5.76 
 
 7.11 
 
 8.60 
 
 10.24 
 
 12.00 
 
 13.93 
 
 16.00 
 
 4.00 
 
 5.06 
 
 6.25 
 
 7.56 
 
 9.00 
 
 10 . 56 
 
 12.25 
 
 14.06 
 
 3.54 
 
 4.48 
 
 5.53 
 
 6.69 
 
 7.97 
 
 9.35 
 
 10.85 
 
 12.45 
 
 3.15 
 
 4.00 
 
 4.93 
 
 5.98 
 
 7.11 
 
 8.34 
 
 9.67 
 
 11.11 
 
 2.83 
 
 3.59 
 
 4.43 
 
 5.36 
 
 6.38 
 
 7.49 
 
 8.68 
 
 9.97 
 
 2 . 56 
 
 3.24 
 
 4.00 
 
 4.84 
 
 5.76 
 
 6.76 
 
 7.84 
 
 9.00 
 
 2.11 
 
 2.67 
 
 3.30 
 
 4.00 
 
 4.76 
 
 5.58 
 
 6.47 
 
 7.43 
 
 .77 
 
 2.25 
 
 2.77 
 
 3.36 
 
 4.00 
 
 4.69 
 
 5.44 
 
 6.25 
 
 .51 
 
 1.91 
 
 2.37 
 
 2.86 
 
 3.40 
 
 4.00 
 
 4.63 
 
 5.32 
 
 .30 
 
 1.65 
 
 2.04 
 
 2.46 
 
 2.93 
 
 3.44 
 
 4.00 
 
 4.59 
 
 .13 
 
 1.44 
 
 1.77 
 
 2.15 
 
 2.56 
 
 3.00 
 
 3.48 
 
 4.00 
 
 .00 
 
 1.26 
 
 1.56 
 
 1.89 
 
 2.25 
 
 2.64 
 
 3.06 
 
 3.51 
 
 .88 
 
 1.12 
 
 1.38 
 
 1.67 
 
 1.99 
 
 2.34 
 
 2.71 
 
 3.11 
 
 .79 
 
 1.00 
 
 1.23 
 
 1.49 
 
 1.77 
 
 2.08 
 
 2.41 
 
 2.77 
 
338 HYDRAULICS 
 
 The diameter of piston required for a given capacity per minute will be 
 
 The actual capacity of a pump will vary from 60% to 95% of the theoretical 
 capacity, depending on the tightness of the piston, valves, suction pipe, etc. 
 HP QP = Q#X144X.433^ QH = Gp 
 
 "33,000, 33,000 " 529.2 1,714.5 
 
 The actual horsepower required will be considerably greater than the 
 theoretical, on account of the friction in the pump; hence, at least 20% should 
 be added to the power for friction and usually about 50% more is added to 
 cover leaks, etc., so that the actual horsepower required by the pump is about 
 70% more than the theoretical. 
 
 EXAMPLE 1. What size of pump will throw 30 gal. of water per min. up 
 125 ft., from the bottom of a pit or prospect shaft to the station pump at the 
 main shaft? 
 
 SOLUTION. An allowance of probably 25% should be made with a small 
 pump of this character, to overcome slippage or leaking through the valves, 
 past the piston, etc., and hence the total amount of water to be handled is 
 
 40 gal. per min. The formula for the diameter of piston is d = 4.95\/ ; 
 
 therefore, assuming that v = 100 ft. per min., d = 4.95 VH = 4.95 X. 63 = 3. 12. In 
 practice,- a 3j-in. pump will probably be employed. 
 
 EXAMPLE 2. Find the approximate horsepower necessary to lift 30 gal. 
 per min. in Example 1. 
 
 SOLUTION. 
 
 TT _ Gp 30X.433X125 ,. , , TT _ 
 
 H " R - Tjlb IjfO ' 95 ' or P ractlcallv 1 H - p - 
 
 In order to cover leakage through valves, friction, etc., an addition of at 
 least 75% should be made to a very small pump like this, and so If H. P. would 
 be counted on. 
 
 The table on page 339 gives theoretical horsepowers only. Approxi- 
 mately the actual horsepower for a 100-ft. lift may be found by multiplying 
 the tabular figures by 1.7; for a 200-ft. lift, by 1.45; and for a 300-ft. lift, by 1.3. 
 for triplex pumps. 
 
 Depth of Suction. Theoretically, a perfect pump will raise water to a 
 height of nearly 34 ft. at the sea level; but, owing to the fact that a perfect 
 vacuum can never be attained with the pump, that the water always contains 
 more or less air, and that more or less watery vapor will form below the piston, 
 it is never possible to reach this theoretical limit, and, in practice, it is not 
 possible to draw water much, if any, over 30 ft. at the sea level, even when the 
 water is cold. Warm water cannot be lifted as high as cold Water because a 
 larger amount of watery vapor forms. With boiler feed-pumps handling hot 
 water, the water should flow to the pumps by gravity. 
 
 For pumps and connections in the best possible condition, it is generally 
 figured that the suction lift will be three-fourths of that theoretically possible. 
 However, pumps are very commonly out of order to a certain degree so that the 
 lifts given in the following table agree very well with actual practice. 
 
 SUCTION LIFT OF PUMPS AT DIFFERENT ALTITUDES 
 
 Altitude Above Sea Level 
 
 Atmospheric 
 Pressure at Altitude 
 
 Theoretical 
 
 Practical 
 
 Miles 
 
 Feet 
 
 Pounds per 
 Square Inch 
 
 Lift 
 Feet 
 
 Lift 
 Feet 
 
 
 
 14.70 
 
 33.95 
 
 22 
 
 1 
 
 1,320 
 
 14.02 
 
 32.38 
 
 21 
 
 S 
 
 2,640 
 
 13.33 
 
 30.79 
 
 20 
 
 1 
 
 3,960 
 
 12.66 
 
 29.24 
 
 18 
 
 1 
 
 5,280 
 
 12.02 
 
 27.76 
 
 17 
 
 U 
 
 6,600 
 
 11.42 
 
 26.38 
 
 16 
 
 H 
 
 7,920 
 
 10.88 
 
 25.13 
 
 15 
 
 2 
 
 10,560 
 
 9.88 
 
 22.82 
 
 14 
 
HYDRAULICS 339 
 
 S8S8S8S8S88S88S8S888888 
 
 ' 
 
 
 i-coooc v codi 
 
 1-1 1-H i-H rH IM 01 CO 
 
 rHC^TtliOCO^O5Oi-NiOa><NO' it-^CXNiOt^-O'O 
 CO CD O5 <N 1C 00 i-J lO 00 T-J t> CO CD <N GO CO O5 >O 1> I> GO O CN 
 
 i-l i-l i-l T-I (N (N CO 
 
 _ 
 
 iCO'OO'OO'OOiCOO'OOO'OOiOO 
 Ci"5t^pC^lOl>;p<Ntf3pt^Op<NiOt^.O 
 
 *' 
 
 5Tj5io'cdi>o6d<N 
 
 rH 1- TH rH M IN IN CO CO ^ "2 CO t^ OS -< 
 
 O5 O3 00 t^- t>- CO CO iO * * IN O 00 t^ Tt* i-l 00 >O Oi (N CD O t>- 
 O >-; C<J CO rj< 1C C3 1> 00 O5 i-H -^ CD GO CO GO (N t>- CO CO O O CO 
 
 .......... 
 
 1-< r-< T- c CN co co T to co t> o 
 
 (N>O^C<iOcDt-O5OC<lOt^O' 
 CO l> O5 iH C^ C GO i-J >C i-H t>- CO O C 
 
 '''' 
 
 OiCO'COiCO'OOO'OOOiCOiC 
 
 iCOiOOiCO'OO'OOO'COO'OOiC 
 
 OO'COO'OOiCOOOOC 
 OOI>iOO<NOI v -OiOO>OC 
 
 ,_| ,_( ,_( r-| (N IN 
 
 - 
 
 CO CO - 
 OO 
 
 > H (N iO 00 i-t >O i-H t>. CO O (N 
 
340 
 
 HYDRAULICS 
 
 Amount of Water Raised by a Single-Acting Lift Pump. In the case of all 
 pumps having a piston or ram, the amount of water lifted is usually con- 
 siderably less than the piston displacement, owing to the leakage through 
 the valves, etc., but with single-acting lift pumps, having bucket plungers 
 with a clack valve in the plunger, the amount lifted may actually exceed the 
 plunger displacement; that is, the volume of water may actually be greater 
 than the length of the stroke multiplied by the number of strokes, for, during 
 the up-stroke, the water both above and below the piston is set in motion, and 
 during the down-stroke, the inertia of the water actually carries more water 
 through the valve than would pass through it on account of the space passed 
 through. This increases as the speed or number of strokes increases. 
 
 Capacity of Pumps. In the accompanying table are given the capacities 
 of pumps; these values are for single strokes; to find the capacity for one 
 revolution the capacity for a stroke must be multiplied by 2. 
 
 CAPACITY OF PUMPS 
 
 Diameter 
 of Piston 
 or Plun- 
 ger, Inches 
 
 Length of Piston or Plunger Stroke, in Inches 
 
 2 
 
 3 
 
 ,..| j 
 
 e , 
 
 12 
 
 13 
 
 Displacement per Stroke of Pump, in Gallons 
 
 1 
 
 .0106 
 
 .0159 
 
 .0212 
 
 .0266 
 
 .0319 
 
 .0372 
 
 .0638 
 
 .0691 
 
 1 
 
 .0129 
 
 .0193 
 
 .0257 
 
 .0321 
 
 .0386 
 
 .0450 
 
 .0771 
 
 .0835 
 
 1 
 
 .0153 
 
 .0229 
 
 .0306 
 
 .0382 
 
 ,0459 
 
 .0535 
 
 .0918 
 
 .0994 
 
 1 
 
 .0208 
 
 .0312 
 
 .0416 
 
 .0521 
 
 .0625 
 
 .0729 
 
 .1249 
 
 .1353 
 
 2 
 
 .0272 
 
 .0408 
 
 .0544 
 
 .0680 
 
 .0816 
 
 .0952 
 
 .1632 
 
 .1768 
 
 2i 
 
 .0344 
 
 .0516 
 
 .0688 
 
 .0860 
 
 .1033 
 
 .1205 
 
 .2065 
 
 .2238 
 
 24 
 
 .0425 
 
 .0638 
 
 .0850 
 
 .1063 
 
 .1275 
 
 .1488 
 
 .2550 
 
 .2763 
 
 2f 
 
 .0514 
 
 .0771 
 
 .1029 
 
 .1286 
 
 .1543 
 
 .1800 
 
 .3086 
 
 .3343 
 
 3 
 
 .0612 
 
 .0918 
 
 .1224 
 
 .1530 
 
 .1836 
 
 .2142 
 
 .3672 
 
 .3978 
 
 3 
 
 .0718 
 
 .1077 
 
 .1437 
 
 .1796 
 
 .2154 
 
 .2514 
 
 .4310 
 
 .4668 
 
 3 
 
 .0833 
 
 .1249 
 
 .1666 
 
 .2082 
 
 .2499 
 
 .2915 
 
 .4997 
 
 .5414 
 
 > 3 
 
 .0956 
 
 .1484 
 
 .1913 
 
 .2391 
 
 .2869 
 
 .3347 
 
 .5738 
 
 .6216 
 
 4 
 
 .1088 
 
 .1632 
 
 .2176 
 
 .2720 
 
 .3264 
 
 .3808 
 
 .6530 
 
 .7072 
 
 4J 
 
 .1228 
 
 .1843 
 
 .2457 
 
 .3071 
 
 .3684 
 
 .4300 
 
 .7370 
 
 .7984 
 
 4, 1 
 
 .1377 
 
 .2065 
 
 .2754 
 
 .3443 
 
 .4131 
 
 .4819 
 
 .8262 
 
 .8950 
 
 42- 
 
 .1534 
 
 .2301 
 
 .3068 
 
 .3835 
 
 .4603 
 
 .5370 
 
 .9205 
 
 .9972 
 
 5 
 
 .1700 
 
 .2550 
 
 .3400 
 
 .4250 
 
 .5100 
 
 .5950 
 
 .0200 
 
 1 . 1050 
 
 5| 
 
 .1874 
 
 .2811 
 
 .3749 
 
 .4686 
 
 . 5623 
 
 .6560 
 
 .1245 
 
 1.2183 
 
 5 
 
 .2057 
 
 .3086 
 
 .4114 
 
 .5143 
 
 .6171 
 
 .7200 
 
 .2342 
 
 1 . 3370 
 
 5 
 
 .2248 
 
 .3373 
 
 .4497 
 
 .5621 
 
 .6745 
 
 .7870 
 
 .3490 
 
 1.4614 
 
 6 
 
 .2448 
 
 .3672 
 
 .4896 
 
 .6120 
 
 .7344 
 
 .8568 
 
 .4690 
 
 1.5912 
 
 6 
 
 .2656 
 
 .3984 
 
 .5312 
 
 .6641 
 
 .7969 
 
 .9297 
 
 .5940 
 
 1 . 7270 
 
 6 
 
 .2872 
 
 .4309 
 
 .5745 
 
 .7182 
 
 .8618 
 
 1.0050 
 
 .7240 
 
 1 . 8674 
 
 6J 
 
 .3099 
 
 .4648 
 
 .6197 
 
 .7747 
 
 .9296 
 
 1.0850 
 
 1.8590 
 
 2.0140 
 
 7 
 
 .3332 
 
 .4999 
 
 .6665 
 
 .8331 
 
 .9997 
 
 1.1660 
 
 1.9990 
 
 2.1660 
 
 71 
 
 .4084 
 
 .6126 
 
 .8168 
 
 1.0210 
 
 1.2250 
 
 1.4290 
 
 2 . 4500 
 
 2 . 6540 
 
 8 
 
 .4352 
 
 .6529 
 
 .8704 
 
 1.0890 
 
 1.3060 
 
 1.5230 
 
 2.6110 
 
 2 . 8290 
 
 9 
 
 .5508 
 
 .8263 
 
 .1020 
 
 1.3770 
 
 1 . 6520 
 
 1 . 9280 
 
 3 . 3050 
 
 3 . 5800 
 
 10 
 
 .6800 
 
 .0200 
 
 .3600 
 
 1.7000 
 
 2.0400 
 
 2 . 3800 
 
 4.0800 
 
 4 . 4200 
 
 10* 
 
 .7497 
 
 .1250 
 
 .4990 
 
 1 . 8740 
 
 2.2490 
 
 2.6240 
 
 4.4980 
 
 4.8730 
 
 11 
 
 .8228 
 
 .2340 
 
 .6460 
 
 2.0570 
 
 2.4680 
 
 2.8800 
 
 4.9370 
 
 5 . 3480 
 
 12 
 
 .9792 
 
 .4690 
 
 .9580 
 
 2.4480 
 
 2.9380 
 
 3.4270 
 
 5 . 8750 
 
 6.3650 
 
 13 
 
 1.1490 
 
 .7230 
 
 2 . 2970 
 
 2.8720 
 
 3.4450 
 
 4.0220 
 
 6 . 8940 
 
 7.4670 
 
 14 
 
 1.3320 
 
 .9980 
 
 2 . 6650 
 
 3.3310 
 
 3.9970 
 
 4 . 6640 
 
 7.9940 
 
 8.6610 
 
 15 
 
 1 . 5300 
 
 2.2950 
 
 3.0600 
 
 3.8250 
 
 4 . 5900 
 
 5.3540 
 
 9.1800 
 
 9.9430 
 
 16 
 
 1 . 7400 
 
 2.6100 
 
 3.4800 
 
 4.3500 
 
 5.2200 
 
 6.0900 
 
 10.4400 
 
 11.3100 
 
 18 
 
 2.2030 
 
 3.3050 
 
 4.4060 
 
 5 . 5080 
 
 6.6100 
 
 7.7110 
 
 13.2200 
 
 14.3200 
 
 20 
 
 2.7200 
 
 4.0800 
 
 5.4400 
 
 6 . 8000 
 
 8.1600 
 
 9.5200 
 
 16.3200 
 
 17.6800 
 
 22 
 
 3.2910 
 
 4.9360 
 
 6 . 5820 
 
 8.2280 
 
 9.8740 
 
 11.5200 
 
 19.7500 
 
 21.3900 
 
 24 
 
 3.9160 
 
 5.8750 
 
 7.8330 
 
 9 . 7920 
 
 11.7500 13.7100 
 
 1 
 
 23 . 5000 25 . 4600 
 
HYDRAULICS 341 
 
 TABLE (CONTINUED) 
 
 Diam- 
 
 Length of Piston or Plunger Stroke, in Inches 
 
 eter of 
 
 
 Piston 
 
 
 
 
 
 
 
 
 or 
 
 1C 
 
 18 
 
 20 
 
 24 
 
 25 
 
 33 
 
 36 
 
 38. 
 
 Plun- 
 
 
 
 
 
 
 
 
 
 ger, 
 
 
 Inches 
 
 Displacement per Stroke of Pump, in Gallons 
 
 11 
 
 .0850 
 
 .0956 
 
 .1062 
 
 .1275 
 
 .1328 
 
 .1753 
 
 .1912 
 
 .2019 
 
 If 
 
 .1029 
 
 .1157 
 
 .1286 
 
 .1543 
 
 .1607 
 
 .2121 
 
 .2314 
 
 .2442 
 
 H 
 
 .1224 
 
 .1377 
 
 .1530 
 
 .1836 
 
 .1912 
 
 .2524 
 
 .2754 
 
 .2907 
 
 1| 
 
 .1666 
 
 .1874 
 
 .2082 
 
 .2499 
 
 .2603 
 
 .3436 
 
 .3748 
 
 .3956 
 
 2 
 
 .2176 
 
 .2448 
 
 .2720 
 
 .3264 
 
 .3400 
 
 .4488 
 
 .4896 
 
 .5168 
 
 21 
 
 .2754 
 
 .3098 
 
 .3442 .4131 
 
 .4303 
 
 .5680 
 
 .6196 
 
 .6541 
 
 2J 
 
 .3400 
 
 .3825 
 
 .4250 
 
 .5100 
 
 .5313 
 
 .7013 
 
 .7650 
 
 .8075 
 
 21 
 
 .4114 
 
 .4628 
 
 .5143 
 
 .6171 
 
 .6428 
 
 .8485 
 
 .9257 
 
 .9771 
 
 3 
 
 .4896 
 
 .5508 
 
 .6120 
 
 .7344 
 
 .7650 
 
 .0100 
 
 1.1020 
 
 1.1630 
 
 31 
 
 .5746 
 
 .6464 
 
 .7183 
 
 .8619 
 
 .8978 
 
 .1851 
 
 1.2930 
 
 1.3647 
 
 3^- 
 
 .6664 
 
 .7497 
 
 .8330 
 
 .9996 
 
 1.0410 
 
 .3744 
 
 1.4994 
 
 1 . 5830 
 
 3 1 
 
 .7650 
 
 .8610 
 
 .9562 
 
 1.1480 
 
 1.1953 
 
 .5778 
 
 1.7212 
 
 1.8169 
 
 4 
 
 .8704 
 
 .9792 
 
 .0880 
 
 1.3060 
 
 1 . 3600 
 
 .7952 
 
 1.9584 
 
 2.0672 
 
 41 
 
 .9826 
 
 1.1054 
 
 .2282 
 
 1.4740 
 
 1.5353 
 
 2.0270 
 
 2.2110 
 
 2.3336 
 
 41 
 
 .1010 
 
 1.2393 
 
 .3770 
 
 1 . 6524 
 
 1.7212 
 
 2.2720 
 
 2.4786 
 
 2.6163 
 
 4f 
 
 .2274 
 
 1.3780 
 
 .5340 
 
 1.8410 
 
 1.9180 
 
 2.5310 
 
 2.7620 
 
 2.9150 
 
 5 
 
 .3600 
 
 1 . 5300 
 
 .7000 
 
 2.0400 
 
 2.1250 
 
 2.8050 
 
 3.0600 
 
 3.2300 
 
 51 
 
 .5000 
 
 1.6870 
 
 .8740 
 
 2.2490 
 
 2.3430 
 
 3.0930 
 
 3.3740 
 
 3 . 5610 
 
 5* 
 
 .6460 
 
 1.8510 
 
 2.0570 
 
 2.4680 
 
 2.5710 
 
 3.3940 
 
 3.7030 
 
 3.9080 
 
 s| 
 
 .7990 
 
 2.0230 
 
 2.2480 
 
 2.6980 
 
 2.8110 
 
 3.7100 
 
 4.0470 
 
 4 . 2720 
 
 6 
 
 .9580 
 
 2.2030 
 
 2.4480 
 
 2.9380 
 
 3.0600 
 
 4.0380 
 
 4.4060 
 
 4.6500 
 
 61 
 
 2.1250 
 
 2.3900 
 
 2 . 6560 
 
 3.1880 
 
 3.3200 
 
 4.3830 
 
 4.7810 
 
 5.0470 
 
 6* 
 
 2.2980 
 
 2.5850 
 
 2.8730 
 
 3.4470 
 
 3.5910 
 
 4.7400 
 
 5.1710 
 
 5 . 4580 
 
 6f 
 
 2.4790 
 
 2.7880 
 
 3.0990 
 
 3.7180 
 
 3.8730 
 
 5.1130 
 
 5.5780 
 
 5 . 8870 
 
 7 
 
 2.6660 
 
 2.9990 
 
 3 . 3320 
 
 3.9990 
 
 4.1650 
 
 5.4990 
 
 5.9980 
 
 6.3320 
 
 7i 
 
 3.2670 
 
 3.6750 
 
 4.0840 
 
 4.9000 
 
 5.1050 
 
 6.7390 
 
 7.3510 
 
 7.7590 
 
 8 
 
 3.4820 
 
 3.9170 
 
 4.3520 
 
 5.2230 
 
 5.4400 
 
 7.1810 
 
 7.8340 
 
 8 . 2690 
 
 9 
 
 4.4060 
 
 4.9570 
 
 5 . 5080 
 
 6.6100 
 
 6.8850 
 
 9.0890 
 
 9.9150 
 
 10.4600 
 
 10 
 
 5.4400 
 
 6.1200 
 
 6.8000 
 
 8.1600 
 
 8.5000 
 
 11.2200 
 
 12.2400 
 
 12.9200 
 
 i(H 
 
 5.9980 
 
 6.7470 
 
 7.4970 
 
 8.9960 
 
 9.3700 
 
 12.3700 
 
 13.4900 
 
 14.2400 
 
 11 
 
 6.5820 
 
 7.4050 
 
 8.2280 
 
 9.8730 
 
 10.2800 
 
 13.5800 
 
 14.8100 
 
 15.6300 
 
 12 
 
 7.8340 
 
 8.8130 
 
 9 . 7920 
 
 11.7500 
 
 12.2400 
 
 16.1600 
 
 17.6300 
 
 18.6000 
 
 13 
 
 9 . 1920 
 
 10.3400 
 
 11.4900 
 
 13.7800 
 
 14.3600 
 
 18.9600 
 
 20 . 6900 
 
 21.8300 
 
 14 
 
 10 . 6600 
 
 11.9900 
 
 13.3200 
 
 15.9800 
 
 16.6600 
 
 21.9900 
 
 23.9900 
 
 25.3200 
 
 15 
 
 12.2300 
 
 13.7700 
 
 15.2900 
 
 18.3600 
 
 19.1200 
 
 25.2400 
 
 27 . 5400 
 
 29.0700 
 
 16 
 
 13.9200 
 
 15.6600 
 
 17.4000 
 
 20 . 8800 
 
 21.7600 
 
 28.7200 
 
 31.3300 
 
 33.0700 
 
 18 
 
 17.6200 
 
 19.8200 
 
 22.030026.440027.5400 
 
 36.3500 
 
 39 . 6600 
 
 41.8600 
 
 20 
 
 21.7600 
 
 24.4800 
 
 27 . 2000 32 . 6400 34 . 0000 
 
 44.8800 
 
 48:9600 
 
 51.6800 
 
 22 
 
 26.3300 
 
 29 . 6200 
 
 32.9100 39.490041.1400 
 
 54 . 3000 
 
 59.2400 
 
 62.5300 
 
 24 
 
 31.330035.2500 
 
 39.160047.000048.9600 
 
 64 . 6300 
 
 70 . 5000 
 
 74.4200 
 
 Pump Valves. As a rule, a large number of small valves having a compara- 
 tively small opening are preferable to a small number of large valves with 
 a greater opening, and most modern pumps are built on these lines. A small 
 valve represents a proportionately larger surface of discharge with the same 
 lift than the large valve, hence whatever the total area of the valve-seat open- 
 ing, its full contents can be discharged with less lift through numerous small 
 valves than through one large valve. 
 
 large metal valve. 
 
 Cornish pumps generally have one 
 
 POWER PUMPS 
 
 In a power pump the reciprocating motion is transmitted to the water 
 plunger or piston by means of a crank driven by belting or gearing, instead of 
 in a straight line directly from the steam or air piston. Power pumps are not 
 
342 
 
 HYDRAULICS 
 
 generally used for pumping against heavy pressures. They may be single, 
 duplex, or triplex, single-acting or double-acting, and either of piston or plunger 
 types, although double-acting and triple-acting plunger pumps are the most 
 common. The triplex pump consists of three single-acting plunger pumps 
 driven by cranks 120 apart on a single shaft. A tight and a loose pulley 
 provide the means for starting and stopping the pump without disturbing 
 the engine on the main shaft. The pulley shaft is geared to the crank-shaft 
 by a pinion and spur wheel. By setting the cranks 120 apart, the strokes 
 follow and overlap one another giving a uniform flow of water and a uniform 
 expenditure of power. In the case of duplex single-acting pumps, the cranks 
 are placed 180 apart and the discharge is the same as from one double-acting 
 pump of the same diameter of plunger and length of stroke. Duplex, double- 
 
 ring and discharging 
 these pumps is sometimes supplied with gears at each end to equalize the 
 strain, particularly when heavy pressures are to be overcome. 
 
 Electrically Driven Power Pumps. Where water is to be delivered from 
 isolated workings to the sumps for the large station pumps, electrically driven 
 power pumps are far more efficient than steam pumps. In some cases, it is 
 probably best to equip the entire mine with electric pumps, both in the isolated 
 workings and at the stations, because they can be driven by a high-class 
 compound-condensing engine on the surface, directly connected to a generator, 
 and furnishing electricity through conductors to the various pumps. 
 
 The total efficiency of a series of small electric pumps that aggregate a 
 sufficient amount of power to enable this arrangement to be used, is very 
 much higher than the total efficiency of a number of small isolated steam or 
 compressed-air pumps introduced into the workings. With compound- 
 condensing engines upon the surface, operating electric pumps underground, 
 the steam consumption per pump horsepower per hour, for the smaller sizes, 
 would only be about 40 Ib. per H. P. per hr.; for medium-sized electric pumps, 
 about 30 Ib. per hr., and larger sizes from 20 to 30 Ib. per H. P. per hr. These 
 figures show that for pumping from isolated portions of the mine the electric 
 pump is much more efficient than the steam pump, as the current can fre- 
 quently be obtained from the lines operating the underground haulage 
 system, furnishing light, etc. 
 
 An efficiency of at least 50% should be obtained in any well-designed, 
 well-built pump, so that a close approximation to "the actual current consump- 
 tion can be obtained by doubling the theoretical consumption given in the 
 accompanying table. 
 
 THEORETICAL CONSUMPTION OF ELECTRIC CURRENT FOR 
 PUMPING WATER PER 1,000 GAL. 
 
 Total 
 Elevation 
 
 Equivalent 
 Pressure 
 
 Kilowatts 
 
 Total 
 Elevation 
 
 Equivalent 
 Pressure 
 
 Kilowatts 
 
 Feet 
 
 per 
 Square Inch 
 
 1,000041. 
 
 Feet 
 
 per 
 Square Inch 
 
 per 
 1,000 Gal. 
 
 10 
 
 4.33 
 
 .0312 
 
 160 
 
 69.29 
 
 .500 
 
 20 
 
 8.66 
 
 .0624 
 
 170 
 
 73.63 
 
 .531 
 
 30 
 
 12.99 
 
 .0937 
 
 180 
 
 77.96 
 
 .562 
 
 40 
 
 17.32 
 
 .124 
 
 190 
 
 82.29 
 
 .593 
 
 60 
 
 21.65 
 
 .156 
 
 200 
 
 86.62 
 
 .624 
 
 60 
 
 25.99 
 
 .187 
 
 210 
 
 91.14 
 
 .655 
 
 70 
 
 30.32 
 
 .218 
 
 220 
 
 95.48 
 
 .686 
 
 80 
 
 34.65 
 
 .249 
 
 230 
 
 99.82 
 
 .717 
 
 90 
 
 38.95 
 
 .281 
 
 240 
 
 104.16 
 
 .748 
 
 100 
 
 43.31 
 
 .312 
 
 250 
 
 108.50 
 
 .779 
 
 110 
 
 47.64 
 
 .343 
 
 260 
 
 112.84 
 
 .813 
 
 120 
 
 51.97 
 
 .374 
 
 270 
 
 116.91 
 
 .841 
 
 130 
 
 56.30 
 
 .406 
 
 280 
 
 121.24 
 
 .875 
 
 140 
 
 60.63 
 
 .437 
 
 290 
 
 125.57 
 
 .903 
 
 150 
 
 64.96 
 
 .468 
 
 300 
 
 129.90 
 
 .934 
 
HYDRAULICS 343 
 
 Precautions Necessary With Electrically Driven Mine Pumps. Where 
 electricity is used in mining, the prevailing tendency is to lay the blame for 
 troubles of various kinds to its use, because electricity is the least understood 
 and most mysterious force employed. It is especially important, therefore, 
 that every precaution be taken to minimize the possibility of accident from 
 electric causes, either by shock or by fire. While bare wires are necessarily 
 employed as trolley wires, all wires used as feeders, on the headings, and wires 
 leading to the pump should be well insulated, as even a slight shock received 
 by the attendant working at or near the pump, or trackmen, or timbermen 
 working on the entries, may prove fatal should the man receiving the shock 
 fall against the exposed wire. Whenever possible, a dry, wooden platform 
 should be provided about the pump; or, if this is considered objectionable 
 on account of the fire risk, a good, dry, cement floor should be laid in the 
 pump room. A small stool with insulator pins and glasses for legs forms a 
 safeguard and should be used whenever it is necessary to adjust or change 
 brushes or work on the commutator while running. 
 
 It is hardly surprising that a fire should originate in a mine when a small 
 electric pump is placed on a wooden floor in a frame pump house and the 
 attendant has a seat or bunk with straw mattress, where he reclines and smokes; 
 or when oil and waste are thrown about and the fuse boxes and rheostat are 
 fastened to a board placed against an inflammable partition, while a strong 
 draft passing through the place, and no available means at hand of extinguish- 
 ing a fire adds to the danger. 
 
 The following precautions are advised in placing an electric pump: Place 
 the pump, if possible, in a special room excavated for the purpose. Where 
 a break-through or passage between two rooms must be used, it should be 
 closed with brick or stone and not with wooden brattice. Make the place 
 fireproof; allow no wooden boxes or furnishings of inflammable material; 
 enforce strict regulations in regard to oil and waste used about the pump; 
 have a dry, cement floor and keep it clean. Matches must not be left in or 
 around the pump house, or any illuminating oil kept therein, and lubricating 
 oils should be carried to the pump house only in small quantities and in closed 
 cans. Cotton waste when saturated with oil is liable to spontaneous com- 
 bustion, and should be thrown into a tight can and taken out of the mine each 
 day. The discharge pipe of the pump should be tapped with 1-in. connections, 
 and a length of hose with a nozzle kept in the pump house ready for use in 
 case of fire. 
 
 The pump house should be well lighted by incandescent lamps. Where 
 lamps are used in series, at least two circuits should be run, since one burn-out 
 will extinguish an entire series. The transmission wire for the pump should 
 be strung on glass or porcelain insulators and care taken to prevent contact 
 with the pump frame or the mine timbers. The line should be taken as directly 
 as possible to the switch and fuses, and should be protected against a series 
 ground or a short circuit. 
 
 The following table gives the gallons per minute delivered from various 
 sized pumps operating at different piston speeds. 
 
 Centrifugal Pumps. In mining practice, centrifugal pumps commonly 
 driven by an electric motor placed on the same shaft, have been used for many 
 years in raising water from local dips and swamps into the main sump. The 
 absence of valves makes them well adapted to pumping dirty or gritty water 
 and the fact that the moving parts have a rotatory instead of a reciprocating 
 motion makes them especially suitable where electric power is available. 
 Their small size, and consequent portability, is a commending feature for 
 underground work. Where the water is strongly acid these pumps probably 
 wear out sooner than ordinary reciprocating pumps unless made of special 
 acid-resisting metal. 
 
 The original form of single-stage centrifugal pump was designed for handling 
 large volumes of water under small heads, say, from 60 to 100 ft. In modern 
 installations, heads of 500 ft., 750 ft., and even more, are overcome by the use 
 of multistage pumps, so that this type is now frequently used in pumping from 
 the main sump to the surface in one operation. 
 
 The pump consists of a series of revolving, turbine-like wheels or impellers, 
 set side by side on the same shaft. The water thrown off by the first wheel is 
 taken up by the second and by it passed on to the third, and similarly, accord- 
 ing to the number of stages. If there is but one revolving part or impeller, 
 which throws the water into the discharge pipe, the pump is single-stage; if 
 there are two revolving parts, the second discharging the water forced into it 
 by the first, it is a two-stage pump, and similarly for each additional revolving 
 
344 
 
 HYDRAULICS 
 
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HYDRAULICS 345 
 
 part. These pumps are designated by the size of their outlet as, for instance, 
 a 2-in. or 4-in. pump, meaning with a 2-in. or a 4-in. discharge pipe. 
 
 The height of lift depends on the quantity of water to be discharged and the 
 circumferential velocity of the revolving disk and is proportional to the area 
 of the discharge orifices at the circumference of the disk. The circumferential 
 velocity depends on the diameter of the disks as well as on the number of 
 revolutions per minute. As the number of revolutions per minute is com- 
 monly limited by those of the electric driving motor, the diameter of the disks, 
 that is, the size of the wheel or pump, is varied to suit the head against which 
 the machine is working. For a given lift, the total efficiency of centrifugal 
 pumps increases with the size of .the pump, being about .45 to .50 for the 
 smallest sizes of single stage pumps, and .70 to .75 for the largest, the mul- 
 tistage pumps giving better results. 
 
 One of the most important points to investigate when selecting a centri- 
 fugal pump is the total head against which it will have to work, as this head 
 determines the speed at which the pump can most economically run and the 
 speed determines the size necessary to throw a given volume of water. The 
 horsepower may be determined by the same formula used for reciprocating 
 pumps, 
 
 BHP = (GFMXhead in feet) 4- (3, 960 X efficiency of pump), 
 in which, BHP = brake horsepower; 
 
 GPM = number of gallons to be delivered per minute. 
 
 In this formula, if the efficiency is made equal to unity, the horsepower 
 determined will be the net horsepower theoretically required to raise the given 
 number of gallons the given height. As stated, the efficiency varies widely, 
 and may be taken at .50 for small wheels operating under low heads and .75 for 
 large multistage wheels operating under high heads. However, the determi- 
 nation of the proper size of pump had better be left to the manufacturer who, 
 on receipt of the proper data, will supply the right kind and size of pump and 
 will guarantee its efficiency. The data required are the quantity of water to 
 be pumped per minute and its kind (clean, acid, muddy, gritty, etc., size of 
 grains of impurity, etc.), the suction lift, or distance from the water level in 
 the sump to the center line of the pump, the discharge lift, or difference in 
 elevation between the center line of the pump and the point of discharge, 
 together with a sketch showing a plan of the discharge line with its length and 
 size and the number, location, and radius of the various bends. The pressure, 
 in pounds per square inch, of steam or compressed air, or voltage of electric 
 current should be given, all estimates being made for the power available at 
 the point of its application. 
 
 When bolting the pump to the foundation, care must be taken not to spring 
 the bedplate. Every joint in the suction pipe should be air-tight. The pump 
 should be installed to run in the direction indicated by the arrow, wording, or 
 other instruction stamped or cast on the casing. The stuffingboxes should be 
 properly packed and the water-seal ring should be in the proper position. 
 The bearings should be cleaned and filled with a good grade of engine oil. 
 Long sweep elbows only, and as few of them as possible, should be used in the 
 suction and discharge piping. It is also advisable to use large pipe lines, as 
 this reduces the power necessary to drive the pump and will save money in 
 the long run. To prevent freezing in cold weather, the pump should always 
 be drained when not in use by unscrewing the plug in .the bottom of the 
 pump casing. 
 
 All centrifugal pumps that do not operate with pressure on the suction 
 side (that is, all pumps drawing water from a sump that is below the level 
 of the center of the pump) must have the casing and suction pipe filled with 
 water before starting. This may 'be accomplished in various ways. Where 
 steam or compressed air is the power an ejector is used, but this method of 
 priming is not available in mining practice where electricity is used. If a 
 hand primer is used, the air cock on the top of the pump is opened and the 
 primer, which is a small hand pump, is worked until water flows through this 
 cock. Then the pump is started. 
 
 If there is a foot-valve on the bottom of the suction pipe, the pump can be 
 primed by running water into it from an overhead tank, or any other source 
 of supply, as the valve will hold the water in the pump. In the event of the 
 column pipe being full of water, as is commonly the case when the pump has 
 been shut down temporarily (as during the night shift), a by-pass may be 
 arranged by which the water in the column pipe may be drawn off in sufficient 
 quantity to prime the 'pump. After priming, the pump can be started and, 
 when full speed has been attained, the discharge valve opened. 
 
346 HYDRAULICS 
 
 PUMPS FOR SPECIAL PURPOSES 
 
 Sinking Pumps. Sinking pumps may be either single or duplex in their 
 action, and may be inside or outside packed. Outside-packed single-acting 
 pumps are in many ways preferable, owing to the fact that they are less liable 
 to get out of order. One requisite of any sinking pump is that it should have 
 as few exposed parts as possible, and that these parts should be so placed that 
 they will be protected to as great an extent from injury by blasting as possible. 
 Sinking pumps are usually provided with a telescopic section in the suction 
 pipe, and sometimes also in the discharge pipe, so that they can be moved 
 down several feet without having to break the joints of the piping. 
 
 Pumps for Acid Waters. Where mine waters are acid in their nature, 
 bronze, bronze-lined, or lead lined pumps are usually employed, and in some 
 cases even wooden pumps have been used, as, 
 for instance, in the Swedish copper mines, 
 though this practice is disappearing in favor of 
 the use of bronze or copper linings. The pipes 
 for such pumps should be of bronze or copper 
 tubing, or should be lined with some sub- 
 stance that will not be affected by the acid 
 of the water. Sometimes wooden linings are 
 employed, placed as shown in Figs. 1 and 2, 
 Fig. 1 being a section of the pipe with the lining 
 complete, and Fig. 2 a cross-section of one 
 of the individual boards used in the lining. 
 These are usually made of pine about f in. 
 thick, and are gro9ved on each end as shown. 
 FIG. 1 r IG. 2 They are sprung in so as to complete a circle 
 
 on the inside of the pipe, and then long, thin, wooden keys driven into the 
 grooves. When the water is allowed to go into the pipes, the linings swell 
 and make all joints perfectly tight. Elbows and other crooked sections are 
 lined with sheet lead beaten in with a mallet. Concrete-lined pumps have 
 been recently introduced in mines where there is acid water. 
 
 PUMP FOUNDATIONS 
 
 The foundation for pumping machinery depends entirely on the type of 
 pump. Direct-acting duplex pumps probably require the least foundation, for 
 the piston and plunger moving in 9pposite directions almost balance the 
 machine in line with the plunger motion and the strains due to reversing are 
 contained almost wholly within the machine itself. Small duplex-pump 
 foundations are made of a solid mass of brick or concrete, while large pumps are 
 often set on separate piers, one for the water end and one for the steam end. 
 The foundations must go down to sufficiently hard material to bear the weight 
 of the pump; or, if the substratum consists of loose sand or gravel, the founda- 
 tion must be spread so that the pressure does not exceed 1 T. per sq. ft. Single 
 pumps require a somewhat heavier foundation than duplex pumps, owing to 
 the greater shocks to which they are subjected. 
 
 Foundations should be built of hard brick laid in cement mortar, or of 
 concrete; or, in the case of large pumps, stone may be used. The pump should 
 be secured to foundation bolts anchored to plates underneath the masonry. 
 If. solid rock exists at the place where the pump is to be located, the surface 
 of the rock is leveled to suit the bedplate or footings of the pump; holes for the 
 foundation bolts are then drilled to a sufficient depth, and the bolts, which 
 should have a good length and a roughened shank, are placed in the holes and 
 fastened by pouring molten lead around them. 
 
 Pump houses, or pump stations as they are often called, are generally placed 
 near the foot of a shaft or slope in a room excavated for the purpose in the solid 
 rock or coal. If the roof needs support, timbers or steel supports may be used. 
 
 PUMP MANAGEMENT 
 
 All pumps, when new, should be run slowly until the parts have become 
 thoroughly adjusted to their bearings, when the speed may be increased. 
 Because a new pump works stiffly is no cause for alarm, for, while a machinist 
 can properly construct the parts, he cannot always forsee the strains caused 
 by the action of the pump, when the parts are assembled and which require 
 certain adjustments to be made after the pump is at work. By running the 
 pump slowly with the parts properly lubricated and making such adjustments 
 as may be necessary, stiffness will gradually disappear and the highest efficiency 
 
HYDRAULICS 347 
 
 of the pump will be attained, provided other matters on which the pump's 
 action depend have received proper attention. 
 
 The causes that affect a pump, impair its efficiency, and prevent it from 
 performing its full duty are: wear; the improper adjustment of valves, valve 
 stems, and levers; the improper packing of plungers and stuffingboxes; draw- 
 ing up the stuffingbox glands too tightly; lost motion due to permitting the 
 working parts to wear and not adjusting them to the new conditions; accumu- 
 lations of foreign matter under the valves or in the strainer; broken valves and 
 valve springs; leakage in valves; taking air in the suction pipe; clogged or 
 broken discharge pipes; and the use of poor gaskets. 
 
 At many mines, the pumps are capable of a larger capacity than is obtained 
 by the low speed at which they are run, but it is important that such pumps 
 be run continuously, as any serious interruption in pumping might cause trouble 
 elsewhere. It is customary, therefore, to keep on hand a supply of duplicate 
 valves, moving parts, and packing, in order that when it becomes necessary 
 to make repairs they may be made without great loss of time. 
 
 A common cause of pumps refusing to work properly is due to their taking 
 air below the suction valves. Small leaks will cause the piston to jump, owing 
 to the water not entering through the suction valves soon enough to fill the 
 entire chamber. This trouble may be remedied by seeing that all joints in the 
 suction pipe and between the pipe and the pump are air-tight. Leaks may 
 sometimes be detected by the hearing or by the flame from a candle being 
 drawn toward the hole. If the leaks are small and not at the pipe joints, a 
 coat of asphalt paint may stop them; if large, they should be drilled larger, the 
 hole threaded, and a screw plug inserted. If the leak is at the joint between 
 two pipes, the pipes should be uncoupled and screwed together again, using 
 graphite pipe grease for a lubricant; or, if the joint is a flanged one, a new 
 gasket should be placed between the flanges, and the pipes lined up before the 
 bolts are tightened. 
 
 Sometimes, a pump fails to catch the water when started owing to leakage 
 of the valves in the suction chamber. The trouble may be caused by the 
 valve and valve seat being corroded; by chips or gravel getting under the 
 valves and preventing them from seating properly; or by the valves and seats 
 becoming worn so that leakage cannot be prevented without changing the 
 parts. 
 
 Many pumps that will not raise water in the suction pipe when empty, 
 owing to the pump having been idle for some time, will continue to draw 
 water after once being started. In such cases, it is necessary to prime the 
 pump, by which is meant filling the suction pipe and part of the suction cham- 
 ber, if there is one, and in some cases, also, the pump barrel, with water, so that 
 the pump may start under conditions similar to those under which it must 
 work. To prime the pump, it is simply necessary to open the cock, or valve, 
 in the priming pipe and allow water from the column pipe to flow down into 
 the suction pipe and the pump. When these are full, the valve is again closed 
 and the pump is ready to start. 
 
 Pumps sometimes fail to raise the water when the full head is resting on the 
 valves in the discharge chamber. This may be due to air accumulating 
 between the suction and the discharge decks, which air is compressed and 
 expanded by the motion of the plunger. Air valves should be provided in the 
 water cylinder for the purpose of allowing this confined air' to escape. Violent 
 jarring and trembling often take place if the discharge chamber is not provided 
 either with an air chamber where the lift is not above 150 ft., or with an allevi- 
 ator, for lifts above that distance. This jarring is due to the column of 
 water in the discharge pipe coming to rest suddenly between strokes and 
 having to be again put in motion. 
 
 In case the pump column is filled with water and the pump is stopped, 
 the water will run back through the pump if the foot-valve is not tight. To 
 prevent this, a gate valve or a check-valve is placed a short distance from the 
 pump in the column pipe. A gate valve wears less than a check-valve, and 
 presents no obstruction to the flow of water when the valve is open. This 
 valve is useful in the column pipe to keep the pressure off the valves when the 
 pump is not at work, and also for keeping water from running back into the 
 pump chamber when the valves are being repaired. 
 
 When starting compound pumps, the steam on the high-pressure-cylinder 
 piston is not always powerful enough to move the plungers against the resis- 
 tance of the water in the discharge pipe; but, by opening the gate valve in the 
 by-pass piping, the pressure on the plungers is relieved for a sufficient num- 
 ber of strokes to allow the steam to reach the low-pressure piston, when the 
 
348 HYDRAULICS 
 
 combined force of the two pistons will do the work and the by-pass pipe can 
 be closed. 
 
 Valves in the steam end sometimes wear unevenly or the valve stems by 
 continual action wear and cause lost motion, thus causing a back pressure 
 and irregular action. Anything wrong in the steam end can usually be deter- 
 mined by the irregular exhaust, but even this may be deceptive in case the 
 water-end valves are leaking. If the steam valves are suspected, the steam- 
 chest cover may be raised for their inspection, but the valves should not be 
 disturbed until it has been determined, by moving the water piston backwards 
 and forwards several times, that they do not open and close properly. The 
 trouble may be in the levers or toggles that throw them, and the adjustments 
 may be properly made without disturbing the valves. In many duplex 
 pumps, there are very slight differences between the two sides, and the amount 
 of lost motion between the valve stem and the valve should be carefully 
 adjusted. Too little lost motion will cause short stroking, while too much will 
 allow the pistons to strike the heads. The adjustment requires skill. 
 
 Sometimes, the valve seat or the valve has soft spots that wear faster than 
 the rest of the valve and seat. Through these slight depressions, steam will 
 blow and cut both valve and seat if attention is not given them; back pressure 
 will then seriously interfere with the working of the pump. If the defect is 
 in the valve, a new one can take its place; but the valve seat, if a part of the 
 steam cylinder, will require an entirely new cylinder, and hence it is economy 
 to scrape the seat until the depressions are removed. A try plate made of steel 
 having a perfectly level surface is covered with chalk and carefully rubbed 
 over the valve seat; the elevations will have chalk on them, the depressions will 
 not. The elevations are scraped with a chisel made of the best steel until they 
 are worn down so that chalk sticks to every part of the seat alike. The valve 
 is treated in the same way if it can be done without too much expense. The 
 valve and the valve seat when removable should be sent to the shop to be 
 reground. 
 
 The first step after a pump has been erected is to clean out the steam 
 piping. In order that this may be done without carrying foreign matter into 
 the pump, the piping is left disconnected from the pump and steam at full 
 boiler pressure is allowed to blow freely through the piping and valves for a 
 few minutes. Steam is then shut off and the piping is connected to the pump. 
 
 The next step is to blow out the steam cylinders. To do this, the cylinder 
 heads should be put on, leaving the pistons and valves out of the cylinders. 
 The stuffingboxes should be closed, which is most conveniently done by placing 
 a piece of board between the stuffingbox and the reversed gland and then 
 setting up the nut on the stuffingbox studs. When the gland is drawn home 
 by a nut outside of it, a circular piece of pine board may be placed between 
 the end of the gland and the inside of the nut in order to close the opening 
 through which the piston rod passes. Steam may now be turned on the 
 main steam pipe leading to the pump; by opening the throttle valve wide at 
 short intervals, the sand and scale in the ports and other passages and spaces 
 of the steam end can be blown out. After the cylinders have been blown out, 
 the heads and covers should be removed and all foreign matter blown into the 
 corners and chambers of the cylinders removed by hand. The pistons, valves, 
 cylinder heads, and other covers can then be put in place. The blowing out 
 of the pipes and cylinders after erection is often neglected or but imperfectly 
 done, with serious consequences to the machine; it cannot be too thoroughly 
 done, particularly in that type of pump where the steam ports and exhaust 
 ports are on top, for in this particular case the sand and grit are deposited in 
 the bottom of the cylinder for the piston to ride on. 
 
 The packing of all rods and stems is the next step. If fibrous- packing is 
 used, the boxes should be filled full and the glands tightened down very moder- 
 ately. The tightening of the glands can best be done when steam is on and the 
 machine is in motion, when they should be tightened only sufficiently to stop 
 leakage and no more. When excessive tightening is required to stop leakage, 
 the packing should be completely renewed. Some pumps are fitted with 
 metallic packing; this packing is usually prepared by specialists and fully 
 guaranteed, and their directions for use should be carefully followed. In case 
 of failure or unsatisfactory results, the makers should be consulted. 
 
 The piling of the machinery is the next step and is a very important one. 
 All rubbing surfaces should be provided with suitable oiling devices appropriate 
 to the particular place and service. The quality of oil should be carefully 
 selected to suit the velocity and pressure of the rubbing surfaces on which it 
 is used. For use within the steam cylinder, heavy mineral oil is the only oil 
 
HYDRAULICS 349 
 
 capable of withstanding the high temperature; and when starting up new 
 pumps only the best quality should be used, regardless of price. A liberal 
 use of this oil for the first month will go far toward reducing subsequent oil bills. 
 
 The pumping engine must often run continuously or without interruption 
 for a month or even longer. This requires that all oiling devices be so arranged 
 that they can be supplied and adjusted while the machine is in motion. It 
 is a good plan to provide two sets of oiling systems for all the principal journals, 
 so that if one fails the other can be used while the disabled one is being over- 
 hauled. All oil holes are generally stopped with wooden plugs or bits of waste 
 twisted into the hole, or are otherwise protected while the machine is being 
 erected. These should now be removed and the oil holes and oil channels 
 thoroughly cleaned. Bearings should be flooded with oil at first to wash out 
 any dust or grit that may have reached the rubbing surfaces. 
 
 The steam end is then ready to be warmed up, and it may be mentioned 
 that from now on the method of starting a pump is the same whether the 
 pump is a new one or an old one. To warm up the steam end, the throttle is 
 opened just a little and with the drain cocks opened wide, steam is allowed 
 to blow through the cylinder until no more water passes out of the drain cocks, 
 using the steam by-pass pipes in case of multiple-expansion pumps. If the 
 pump has a valve gear that can be operated by hand, the warming up can be 
 hastened by working the valve back and forth slowly. While the steam end 
 is warming up, the water end should be made ready by opening the stop-valve 
 in the delivery pipe and otherwise seeing to it that the pump has a free delivery. 
 If a stop-valve is fitted to the suction pipe, this should be opened. If the 
 machine is compound or triple expansion, the water by-pass valves must be 
 opened until the machine has made a sufficient number of strokes to bring the 
 intermediate and low-pressure cylinders into action, when the by-pass valves 
 should be closed. If the pump is fitted with dash-relief valves, these should 
 be closed before starting, in order to keep the pistons as far from the heads 
 as possible in starting. Should the pump exhaust into an independent con- 
 denser, this should be started and a vacuum obtained before starting the 
 pumps. 
 
 To start the pump, open the throttle slowly and let the pistons work back 
 and forth very slowly a few times, gradually increasing the velocity until full 
 speed is attained. After the pump has been running a few minutes, close the 
 drain cocks. If the pump has dash-relief valves, the length of stroke may now 
 be carefully adjusted. 
 
 To stop the pump, close the throttle, open the drain cocks, and close the 
 gate valve in the discharge pipe, if one is fitted. Afterwards, shut down the 
 condenser. 
 
 MISCELLANEOUS FORMS OF WATER ELEVATORS 
 Jet Pump. In the jet pump, the energy of a jet of water is utilized for 
 raising a larger volume through a small distance, or a mixture of water and 
 solid material through a short distance. 
 
 Vacuum Pump. The pulsometer, which is the most important representa- 
 tive of the vacuum pumps, consists of two chambers in a large casting, with 
 suitable automatic valves arranged at the top and bottom of the chambers. 
 Steam is introduced into one of the chambers, then the valve at the top closed. 
 This steam will condense, forming a vacuum that draws water from the suction 
 into the chamber. When the chamber is filled with water, steam is again 
 introduced and forces the water out through the discharge pipe. The oper- 
 ation is then repeated, more water being drawn in by the condensation of 
 the steam. The two chambers work alternately, one being engaged in draw- 
 ing water in while the other forces it out. The total steam efficiency of this 
 form of pump is small, though it may actually be above that of small steam 
 pumps employed in isolated portions of a mine. The advantages are that 
 the pump possesses no intricate mechanism nor reciprocating parts, requires 
 no lubrication, and is not injured by gritty or acid materials. On this account 
 it may be employed for pumping water in concentration works, coal-washing 
 plants, and similar places where the water is liable to contain grit or dirt. 
 
 Air-Lift Pumps. By introducing compressed air at the bottom of a pipe 
 submerged in any liquid, the air in the pipe rises as bubbles, and so reduces 
 the specific gravity of the fluid in the pipe. This causes the fluid in the pipe 
 to rise above the level of that surrounding the pipe. The difference in specific 
 gravity can never be great, and hence the fluid can never be elevated to any 
 considerable height without having the lower end immersed to a correspond- 
 ingly great depth. On this account it is frequently necessary to drill a well 
 
350 HYDRAULICS 
 
 considerably below the water-bearing strata, so as to pbtain the proper ratio 
 between the submerged portion of the pipe and the height to which the water 
 is to be lifted. Some advantages of this form of pump are that there are no 
 moving parts, no lubrication is required, and gritty material does not inter- 
 fere with the operation. If the pump is constructed of suitable material, it 
 may be employed for handling acids or solutions in electrolytic or chemical 
 works. This style of pump is also quite extensively employed for pumping 
 water from Artesian wells. It has not been successful as a mine pump, owing 
 to the ratio between the part immersed and the lift. 
 
 Water Buckets. Where only a limited amount of water collects in the 
 mine workings, it is frequently removed by means of a special water bucket 
 or water car during the hours that the hoisting engine would otherwise be 
 idle Where very large amounts of water are to be removed from deep 
 shafts, it has been found economical to do this with special water buckets. 
 
 One of the best illustrations of this class of work is the Gilberton water 
 shaft which has been equipped at the Gilberton Colliery of the Philadelphia 
 and Reading Coal and Iron Co. The collieries draining to this shaft require 
 the removal of 6,000,000 gal. of water per 24 hr. during the wet season, and 
 this has to be lifted from a depth of 1,100 ft. In order to accomplish the work 
 by means of steam pumps, it required a number of pump stations in different 
 parts of the mine, each of which had to be attended by a pumpman, and a 
 large number of steam lines were required in the mine. In order to remove the 
 danger of fire caused by these steam lines, and to dispense with the large 
 amount of labor otherwise necessary, it was decided to hoist the water, and a 
 shaft 22 ft.X26 ft. 8 in. outside of timbers, was sunk. This shaft contains 
 two compartments 7 ft.X7 ft., in which the water buckets are operated, and 
 two compartments 7 ft.X 11 ft. 8 in. that are utilized for cages to lower men, 
 timber, and other supplies. The water tanks employed in the special water 
 compartments are 5 ft. 6 in. in diameter, and 14 ft. long. They are provided 
 with special devices, sliding on regular cage guides, and empty themselves 
 automatically at the surface by means of a trip or sliding valve. Two pairs 
 of direct-acting hoisting engines, with 45-in. X 60-in. cylinders, operating 
 drums 14 ft. 8 in. in diameter by 15-ft. face, are employed. These operate the 
 water buckets in cages by means of 2-in. crucible steel ropes, at 50 rev. per 
 min., which is equivalent to a piston speed of 500 ft. per min. The drums will 
 hoist two tanks of 2,400 gal. per min. This gives an output of 7,000,000 gal. 
 per 24 hr. By slightly increasing the speed of the engine, this amount can 
 be increased 10%, which is 25% in excess of the calculated maximum demand 
 on the shaft. The cages in the cage compartments are so arranged that they 
 can be disconnected, and water buckets substituted for them. This would be a 
 total output of over 14,000,000 gal. per 24 hr. at the normal speed of the 
 engine. One great advantage of this style of pumping plant is that there is 
 absolutely no fear of drowning the pumps. 
 
 The following figures by Mr. F. E. Brackett give the cost of operation 
 and the efficiency of the water hoist at the Coleman shaft, Cambria County, 
 Pennsylvania. The Coleman shaft is about 660 ft. deep and the water hoist 
 consists of two Wellman-Seaver-Morgan boiler-shaped automatic skips of 
 1,200 gal. capacity each, with the customary valves, etc. "The bailing of the 
 water was carried on intermittently by the main hoisting engine. It was 
 found that bailing from 20 to 30 min. per hr. was sufficient to keep the water 
 down. 
 
 "When bailing with one skip, one skip of water was delivered every 75 sec. 
 but by a slight effort a skip could be delivered in 60 sec. When two skips 
 were in use, the time necessary to deliver a skip was from 31 to 38 sec., averag- 
 ing 34 sec. Of this time. 20 sec. were occupied in hoisting the skip 700 ft. and 
 the remaining 14 sec. were occupied in slowing down and dumping. The 
 actual dumping only occupied about 5 sec. The capacity of the two skip hoists 
 was, therefore, (1,200-H 34) X 60 = 2,120 gal. per min. 
 
 "The amount of coal consumed in hoisting the 800 gal. per min. made by 
 the mine at this time was 23 gross T. per da. of 24 hr. It was estimated that 
 85% of this, or 19 T., was consumed in hoisting the water. The consumption 
 of steam by the hoisting engine, as computed from its dimensions, was 74 Ib. 
 per useful H. P. per hr. As it requires 141 H. P. to hoist 800 gal. of water 
 per min. 700 ft., the amount of steam required was 250,416 Ib. per da. Divid- 
 ing the water by the coal, the efficiency of the boilers on this kind of inter- 
 mittent work is only 6 Ib. of steam per Ib. of coal. The duty of the plant, as 
 computed from these data, is about 15,400,000 ft.lb. of work per 100 Ib. of 
 coal, which is extremely low.*' 
 
HYDRAULICS 
 
 351 
 
 Mr. Brackett reaches the conclusion of other mining engineers that water 
 hoisting from shallow depths is very uneconomical "as there is very little 
 opportunity to use the steam expansively. Even should an attempt be made 
 to do so, the time occupied in getting up speed, when the steam must be 
 admitted at nearly full stroke, occupies a large percentage, sometimes all, of 
 the total time under steam. In the second place, there is a large amount of 
 power wasted during every winding by the application of brakes to bring the 
 load to rest. Besides these, the intermittent use of steam necessarily inter- 
 feres with the economical operation of the boilers. Enough steam cannot be 
 raised during the demand for it without wasting fuel during the time there is 
 little or no demand for it. By careful design, especially on windings of greater 
 length, no doubt these losses can be reduced to some extent, but as a general 
 proposition the plan of hoisting water instead of pumping it should not be 
 adopted, unless there exists some other reason that is of greater weight than 
 the economical side of the question." 
 
 Some years ago the Hamilton iron mine, in Michigan, was drowned by 
 a sudden inrush of water that drove the pumpmen from the pumps. In order 
 to remove this large volume of water, special bailing buckets were substituted 
 for the ordinary mine skips. These bailing buckets ran on the inclined skip 
 road, and unwatered the mine in a remarkably short time. 
 
 Siphons. The principle on which the siphon works is shown in the accom- 
 panying figure. The atmospheric pressure on the surface of the water in the 
 upper basin will force the water up the short leg I to the crown or summit, 
 from whence it will flow by gravity through the long leg h into the lower 
 basin. The vertical height h is called the lift, and the vertical fall hi, the fall 
 of the siphon. The difference between these heights (hi h) may be called the 
 siphon head. The pressure of the atmosphere on the water in each basin acts 
 to keep the pipes /, h filled with water. 
 
 The conditions required for the successful operation of a siphon may be 
 stated as follows: 
 
 1. The height of the summit of the siphon above the surface of the water 
 in the upper basin, or the vertical lift of the siphon, must not exceed a practical 
 limit to which the atmpsphere will force the water. This height is theoretically 
 34 ft. at sea level, but is less at points above the sea level. A safe rule to apply 
 in determining the vertical height to which the atmosphere will force the 
 water in the suction pipe of a pump, or in the short leg of a siphon, is to take .8 
 
 of the barometric height, expressed in inches, for the vertical lift of the pump, 
 or siphon, in feet. Thus, if the barometer stands at 30 in., the lift of the pump 
 or siphon, may be taken as 30 X. 8 = 24 ft. Where the suction pipe is nearly 
 vertical, and consequently of shorter length, this height may be somewhat 
 increased; but where the suction pipe is inclined and its length therefore 
 considerable, the vertical lift should be decreased proportionately. 
 
 2. The longer leg, or the discharge pipe of the siphon, must fall through a 
 greater vertical height than the short leg, or draft pipe. 
 
 3. When the fall hi of the siphon exceeds the practical limit to which the 
 atmosphere will force the water, care must be taken to arrange the fall of the 
 siphon relative to its lift, or to increase the length of the long leg, or to use a 
 pipe of a smaller diameter, or to throttle the discharge by means of a valve, 
 so as to prevent the siphon from running empty in a few hours, which it will do 
 whenever the fall is so great that the water in the long leg runs away from 
 the crown faster than the atmospheric pressure forces it up the short leg. 
 
352 HEAT AND FUELS 
 
 Another important condition requisite to the successful operation of a 
 siphon, is the submerging of both ends of the siphon pipe in their respective 
 basins, in order to prevent air from being drawn into the pipe and reaching the 
 crown, or summit, of the siphon. This takes place more readily in the short 
 leg of the siphon than in the long leg, due to the direction of the flow of the water. 
 The submergence of the discharge end of the siphon, however, is important 
 in order to insure a full flow in the pipe. Air carried into a siphon by the water 
 will gradually accumulate at the highest point of the siphon pipe and will 
 interfere with the working unless an air trap is provided at that point through 
 which the air can be let off from time to time. 
 
 In order that a siphon may operate successfully without a throttling valve, 
 its length, diameter, lift, and fall must bear a certain relation to one another, 
 or fulfil certain conditions, without which the pipe has a tendency to empty 
 itself. Referring to the accompanying figure, and calling the head, length, 
 and diameter of pipe, h, I, and d, respectively, on the suction end; and hi, li, 
 and d\ on the discharge end, as the flow is uniform throughout the pipe, 
 hd 6 hidi 6 
 
 1 IT 
 
 But the pressure of the atmosphere acts on both ends; at sea level, this will 
 support a water column of 14.7 -f-. 434 = 34 ft., practically. Hence, the head 
 producing the flow of water from the suction end to the crown is 34 h, while 
 the head causing the flow from the crown to the discharge end is hi 34. There- 
 fore, the formula when applied to siphons at sea level, becomes 
 
 I li 
 
 Whenever the second member of this formula, which represents the flow 
 in the discharge end of the siphon, becomes greater than the first member, 
 which represents the suction end, the pipe will tend to empty itself, because 
 the water will then flow away from the crown faster than the atmospheric 
 pressure can supply the waste. 
 
 Whenever the foregoing equation is satisfied, the siphon needs no throttling 
 valve to restrict its flow, although a valve at each end of the siphon is necessary 
 for filling the pipe. The discharge is then given by the following formula, 
 
 EXAMPLE. A siphon pipe 4 in. in diameter and 1,000 ft. long, has a rise 
 
 of 15 ft. and a fall of 40 ft.; how may gallons of water will it discharge in 1 hr.? 
 
 SOLUTION. Assuming that, for mine work, /=.Q1. and substituting the 
 
 given values in the formula, G = 2.83X4*X \ OIX*!^)? = 143+ gal ' per min ' 
 The quantity discharged in 1 hr. is then 60 X 143 = 8,580 gal. 
 
 HEAT AND FUELS 
 
 Heat is a form of energy produced by the rapid vibrations of the molecules 
 of a body. All bodies are assumed to be built up of molecules that are held 
 together by cohesion but yet are in a state of rapid movement in relation to 
 one another. The application of heat to a body causes a more rapid vibration 
 of the molecules, and the withdrawal of heat causes a less rapid vibration, 
 thereof; it is to the rate of vibration that the sense of hotness or coldness is due. 
 
 Thermometers. Changes in the temperature of a body are commonly 
 measured by a thermometer, although very high temperatures are measured 
 in other ways as by means of a pyrometer, etc. Because of its uniform expan- 
 sion and its sensitiveness to heat, mercury is commonly used in the construction 
 of thermometers, provided the temperatures to be measured range between, 
 say, - 35 P. and + 625 F. This is because mercury freezes at about - 38 F. 
 and volatilizes at +675 P., beginning to give off some vapor at even a lower 
 temperature. For measuring temperatures below the freezing point of mercury, 
 alcohol is commonly employed although the United States Bureau of Standards 
 prefers toluene. 
 
 In all thermometers, the freezing and boiling points of water under mean 
 atmospheric pressure at sea level determine two fixed points, but the division 
 of the scale between these points is made in one of three different ways. In 
 
HEAT AND FUELS 
 
 353 
 
 the Fahrenheit thermometer, which is in universal use in the United States and 
 Great Britain, the boiling point of water is called 212 and the freezing point 32, 
 the of the scale being 32 below the freezing point and at what was then 
 supposed to be the lowest temperature attainable. In the centigrade ther- 
 mometer, in use in those countries that employ the metric system and in 
 England and the United States in scientific work, the freezing point of water 
 is called and the boiling point 100. In the Reaumur thermometer, in use 
 in Russia and in Germany (for domestic purposes), the freezing point of water 
 is called and its boiling point 80. The following formulas serve to convert 
 the readings of one scale into those of the others: 
 
 F = f C+32 = fR+32 
 
 C = t(F-32)=f R 
 
 R = (F-32) = |C 
 
 Thus, 1,000 C. is equal to 1X1,000 + 32 = 1,832 F., and, similarly, 490 F. 
 is equal to f X (490 32) = 254.5 C. However, when the relation between a 
 given number of degrees of the scales is desired other formulas must be used. 
 Because between the freezing and boiling points of water there are 100 on 
 the centigrade scale and 180 on the Fahrenheit scale, 1 C. = 1.8 F., and 1 
 F. = .555+C. Thus, a range of temperature represented by 1,000 C. is equal 
 to a range of 1,800 F. 
 
 COMPARISON OF THERMOMETER SCALES 
 
 
 Fahrenheit 
 Degrees 
 
 Centigrade 
 Degrees 
 
 Reaumur 
 Degrees 
 
 Absolute zero 
 Zero, Fahrenheit 
 Freezing point 
 Maximum density of water 
 
 -459.64 
 0.00 
 32.00 
 39.10 
 
 -273.13 
 
 - 17.78 
 0.00 
 3.94 
 
 -218.51 
 - 14.22 
 0.00 
 3 15 
 
 Boiling point 
 
 212.00 
 
 100.00 
 
 80.00 
 
 Absolute Zero. At 32 F., a perfect gas expands -- part of its volume 
 
 4" l.t>4 
 
 if its temperature is increased 1, the pressure remaining unchanged. Con- 
 sequently, at 32+491. 64 = 523.64 the gas will occupy double its original 
 volume; and if the temperature is reduced to 491.64 32= 459.64, the 
 gas will disappear. Presumably some change in the rate of contraction takes 
 place before the minimum temperature is reached, but the law may con- 
 veniently be used within the range of temperature where it is known to hold 
 good. This temperature of -459.64 F. (commonly taken as -460 F.) is 
 known as absolute zero. On the centigrade scale, this point is reached at 
 273.13, usually taken as 273. From this, any perfect gas expands ^ 5 
 or 5 f 3 of its volume for each 1 increase in temperature above that of absolute 
 zero, depending on whether the Fahrenheit or centigrade thermometer is used. 
 
 Temperatures reckoned from the absolute zero are known as absolute 
 temperatures. To find the absolute temperature on the Fahrenheit scale, 
 add 460 to the reading of the thermometer. Thus, 62 F. = 460 + 62 = 522 
 absolute F., and -54 F. = 460-54 = 406 absolute F. Similarly, in the 
 centigrade scale, 62 C. = 273 + 62 = 335 absolute C., and -54 C. = 273-54 
 = 219 absolute C. 
 
 British Thermal Unit. The quantitative measure of heat in use by English- 
 speaking nations is known as the British thermal unit, commonly written 
 B. T. U. It is the quantity of heat required to raise the temperature of 
 1 Ib. of water lat 62 F.; that is, from 62 to 63. For accurate work, it 
 is necessary to specify the particular degree at which the temperature is 
 measured for the amount of heat required to raise the temperature of 1 Ib. 
 of water is not the same for all parts of the thermometric scale. British 
 thermal units were at one time referred to the temperature of the maximum 
 density of water, 39.1 F., but recent practice uses 62 F. as being nearer the 
 mean value. 
 
 The heating value of a fuel is commonly expressed in the number of British 
 thermal units per pound of coal, oil, etc., it will yield on burning. Thus, 
 it may be stated that a certain coal has a fuel or heat value of 12,000 B. T. U. 
 
354 HEAT AND FUELS 
 
 This means that 1 Ib. of the fuel when burned under perfect conditions will 
 yield sufficient heat to raise the temperature of 12,000 Ib. of water 1 F., or 
 will raise the temperature of 1 Ib. of water 12,000 F. 
 
 Calorie. The calorie is the equivalent in the metric system of the British 
 thermal unit. It is the amount of heat required to raise the temperature of 
 1 kilogram of pure water from 15 to 16 C. As in the case of the British 
 thermal unit, the calorie was at one time referred to as the temperature of water 
 at its maximum density, or 3.94 C. The French and English systems are 
 not exactly equivalent or interchangeable because the quantity of heat required 
 to raise the temperature of a given mass of water from 59 F. (15 C.) to 60.8 F. 
 (16 C.) is not exactly the same as that required to raise its temperature from 
 62 F. to 63 F. This difference, however, is very little, but .03%. 
 
 There are two calories in common use. The one just defined, in which the 
 unit weight is the kilogram, is in use commercially and is known as the large 
 calorie. Chemists use the small calorie, -nfer of the former, being the amount 
 of heat required to raise the temperature of 1 gram of water from 15 C. to 
 16 C. These are also known as the kilogram-calorie and gram-calorie, 
 respectively. 
 
 Pound Calorie. The pound calorie is the quantity of heat required to 
 raise the temperature of 1 Ib. of water from 15 to 16 C. This unit is not 
 infrequently employed in stating the calorific power or heat value of coals and 
 in metallurgical calculations where the weights of the substances involved are 
 given in pounds. 
 
 Equivalence of Heat Units. Neglecting the difference in the specific heat 
 of water at different temperatures (as noted before), the relations between the 
 different thermal units may be determined as follows: 
 
 1 B. T. U. = .252 large cal. = 252 small cal. = .0555 Ib.-cal. 
 1 large cal. = 1,000 small cal. = 3.968 B. T. U. = 2.2046 Ib.-cal. 
 1 small cal. = .001 large cal. = .003968 B. T. U. = .0022046 Ib.-cal. 
 1 Ib.-cal. = 1.8 B. T. U. = .4536 large cal. =453.6 small cal. 
 
 When calories are expressed per kilogram and it is desired to find the 
 equivalent number of British thermal units per pound, the factor for multiply- 
 ing is 1.8 as will appear from the following fractions, which show the relation 
 between the units of the two systems: 
 
 B. T. U. per Ib. = Ib. raised deg. F. 
 Cal. per kg. kg. raised deg. C. 
 
 As pounds are in each numerator and kilograms are in each denominator 
 
 they may be canceled, and B " ^- U - Beg. ^ because X o F> = 1 . 8 o c> 
 
 From this B. T. U. (per pound) = 1.8 cals. (per kilo). 
 
 Mechanical Equivalent of Heat. Heat being a form of energy is capable 
 of performing work. Joule's investigations showed that 1 B. T. U. was equiva- 
 lent to 772 ft.-lb. of work, but later determinations indicate that the true 
 mechanical equivalent of 1 B. T. U. is 777.52 ft.-lb., which is commonly taken 
 as 778 ft.-lb. Thus, if 1 Ib. of Pocahontas coal has a fuel value of 15,000 B. 
 T. U., it is capable of doing 15,000X778 = 11,670,000 ft.-lb. of work, The 
 unit of work in the metric system is the meter-kilogram (often called the kilo- 
 gram-meter) and is equal to 1 kg. raised through a height of 1 m. One calorie 
 is equal to 426.8028 rn.-kg. One B. T. U. = 107.5614 m.-kg., and 1 cal. is 
 equal to 3,087.3531 ft.-lb. The number 778 is called the mechanical equivalent 
 of heat, or, sometimes, Joule's equivalent. 
 
 Expansion by Heat. All bodies change in volume as the temperature to 
 which they are subjected is changed; they commonly expand as they are heated 
 and contract as they are cooled. The rate of expansion is commonly expressed 
 as a coefficient, which indicates the relative amount the substance expands 
 in length for an increase of 1 in temperature. The rate of expansion is not 
 the same at all temperatures, as it increases slightly, in the case of metals, as 
 higher temperatures are reached. 
 
 In the first table on page 359 are given the coefficients of linear expansion 
 for 1 F. of some of the more common materials. The coefficients of surface 
 expansion are twice the values in the table; and the coefficients of cubic expan- 
 sion, or expansion in volume, are three times the tabular values. Thus, a bar 
 of wrought iron 60 in. long, if heated from 60 F. to 460 F., or through 400, 
 will expand 60 X. 00000677X400 = .16248 in. In a similar way, a sphere of 
 brass measuring 1,000 cu. in. at 32 F., will have its volume increased by 1,000 
 X300X (3X. 0000104) =9.36 cu. in. if heated to 332 F. 
 
HEAT AND FUELS 355 
 
 EQUIVALENT TEMPERATURES BY THE FAHRENHEIT AND 
 CENTIGRADE THERMOMETERS 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 -459.64 
 
 -273.13 
 
 2 
 
 16.7 
 
 62 
 
 16.7 
 
 122 
 
 50.0 
 
 400 
 
 240.0 
 
 3 
 
 16.1 
 
 63 
 
 17.2 
 
 123 
 
 50.6 
 
 350 
 
 212.2 
 
 4 
 
 15.6 
 
 64 
 
 17.8 
 
 124 
 
 51.1 
 
 300 
 
 184.4 
 
 5 
 
 15.0 
 
 65 
 
 18.3 
 
 125 
 
 51.7 
 
 250 
 
 156.7 
 
 6 
 
 14.5 
 
 66 
 
 18.9 
 
 126 
 
 52.2 
 
 200 
 
 128.9 
 
 7 
 
 13.9 
 
 67 
 
 19.5 
 
 127 
 
 52.8 
 
 150 
 
 101.1 
 
 8 
 
 13.3 
 
 68 
 
 20.0 
 
 128 
 
 53.3 
 
 100 
 
 73.3 
 
 9 
 
 12.8 
 
 69 
 
 20.6 
 
 129 
 
 53.9 
 
 50 
 
 45.6 
 
 10 
 
 12.2 
 
 70 
 
 21.1 
 
 130 
 
 54.5 
 
 49 
 
 45.0 
 
 11 
 
 11.7 
 
 71 
 
 21.7 
 
 131 
 
 55.0 
 
 48 
 
 44.4 
 
 12 
 
 11.1 
 
 72 
 
 22.2 
 
 132 
 
 55.6 
 
 47 
 
 43.9 
 
 13 
 
 10.6 
 
 73 
 
 22.8 
 
 133 
 
 56.1 
 
 46 
 
 43.3 
 
 14 
 
 10.0 
 
 74 
 
 23.3 
 
 134 
 
 56.7 
 
 45 
 
 42.8 
 
 15 
 
 9.5 
 
 75 
 
 23.9 
 
 135 
 
 57.2 
 
 44 
 
 42.2 
 
 16 
 
 8.9 
 
 76 
 
 24.5 
 
 136 
 
 57.8 
 
 43 
 
 41.7 
 
 17 
 
 8.3 
 
 77 
 
 25.0 
 
 137 
 
 58.3 
 
 42 
 
 41.1 
 
 18 
 
 7.8 
 
 78 
 
 25.6 
 
 138 
 
 58.9 
 
 41 
 
 40.6 
 
 19 
 
 7.2 
 
 79 
 
 26.1 
 
 139 
 
 59.5 
 
 40 
 
 40.0 
 
 20 
 
 6.7 
 
 80 
 
 26.7 
 
 140 
 
 60.0 
 
 39 
 
 39.4 
 
 21 
 
 6.1 
 
 81 
 
 27.2 
 
 141 
 
 60.6 
 
 38 
 
 38.9 
 
 22 
 
 5.6 
 
 82 
 
 27.8 
 
 142 
 
 61.1 
 
 37 
 
 38.3 
 
 23 
 
 5.0 
 
 83 
 
 28.3 
 
 143 
 
 61.7 
 
 36 
 
 37.8 
 
 24 
 
 4.5 
 
 84 
 
 28.9 
 
 144 
 
 62.2 
 
 35 
 
 37.2 
 
 25 
 
 3.9 
 
 85 
 
 29.5 
 
 145 
 
 62.8 
 
 34 
 
 36.7 
 
 26 
 
 3.3 
 
 86 
 
 30.0 
 
 146 
 
 63.3 
 
 33 
 
 36.1 
 
 27 
 
 2.8 
 
 87 
 
 30.6 
 
 147 
 
 63.9 
 
 32 
 
 35.6 
 
 28 
 
 2.2 
 
 88 
 
 31.1 
 
 148 
 
 64.5 
 
 31 
 
 35.0 
 
 29 
 
 1.7 
 
 89 
 
 31.7 
 
 149 
 
 65.0 
 
 30 
 
 34.4 
 
 30 
 
 1.1 
 
 90 
 
 32.2 
 
 150 
 
 65.6 
 
 29 
 
 33.9 
 
 31 
 
 -.6 
 
 91 
 
 32.8 
 
 151 
 
 66.1 
 
 28 
 
 33.3 
 
 32 
 
 .0 
 
 92 
 
 33.3 
 
 152 
 
 66.7 
 
 27 
 
 32.8 
 
 33 
 
 + .6 
 
 93 
 
 33.9 
 
 153 
 
 67.2 
 
 26 
 
 32.2 
 
 34 
 
 1.1 
 
 94 
 
 34.5 
 
 154 
 
 67.8 
 
 25 
 
 31.7 
 
 35 
 
 1.7 
 
 95 
 
 35.0 
 
 155 
 
 68.3 
 
 24 
 
 31.1 
 
 36 
 
 2.2 
 
 96 
 
 35.6 
 
 156 
 
 68.9 
 
 23 
 
 30.6 
 
 37 
 
 2.8 
 
 97 
 
 36.1 
 
 157 
 
 69.5 
 
 22 
 
 30.0 
 
 38 
 
 3.3 
 
 98 
 
 36.7 
 
 158 
 
 70.0 
 
 21 
 
 29.4 
 
 39 
 
 3.9 
 
 99 
 
 37.2 
 
 159 
 
 70.6 
 
 20 
 
 28.9 
 
 40 
 
 4.5 
 
 100 
 
 37.8 
 
 160 
 
 71.1 
 
 19 
 
 28.3 
 
 41 
 
 5.0 
 
 101 
 
 38.3 
 
 161 
 
 71.7 
 
 18 
 
 27.8 
 
 42 
 
 5.6 
 
 102 
 
 38.9 
 
 162 
 
 72.2 
 
 17 
 
 27.2 
 
 43 
 
 6.1 
 
 103 
 
 39.5 
 
 163 
 
 72.8 
 
 16 
 
 26.7 
 
 44 
 
 6.7 
 
 104 
 
 40.0 
 
 164 
 
 73.3 
 
 15 
 
 26.1 
 
 45 
 
 7.2 
 
 105 
 
 40.6 
 
 165 
 
 73.9 
 
 14 
 
 25.6 
 
 46 
 
 7.8 
 
 106 
 
 41.1 
 
 166 
 
 74.5 
 
 13 
 
 25.0 
 
 47 
 
 8.3 
 
 107 
 
 41.7 
 
 167 
 
 75.0 
 
 12 
 
 24.4 
 
 48 
 
 8.9 
 
 108 
 
 42.2 
 
 168 
 
 75.6 
 
 11 
 
 23.9 
 
 49 
 
 9.5 
 
 109 
 
 42.8 
 
 169 
 
 76.1 
 
 10 
 
 23.3 
 
 50 
 
 10.0 
 
 110 
 
 43.3 
 
 170 
 
 76.7 
 
 9 
 
 22.8 
 
 51 
 
 10.6 
 
 111 
 
 43.9 
 
 171 
 
 77.2 
 
 8 
 
 22.2 
 
 52 
 
 11.1 
 
 112 
 
 44.5 
 
 172 
 
 77.8 
 
 7 
 
 21.7 
 
 53 
 
 11.7 
 
 113 
 
 45.0 
 
 173 
 
 78.3 
 
 6 
 
 21.1 
 
 54 
 
 12.2 
 
 114 
 
 45.6 
 
 174 
 
 78.9 
 
 5 
 
 20.6 
 
 55 
 
 12.8 
 
 115 
 
 46.1 
 
 175 
 
 79.5 
 
 4 
 
 20.0 
 
 56 
 
 13.3 
 
 116 
 
 46.7 
 
 176 
 
 80.0 
 
 3 
 
 19.4 
 
 57 
 
 13.9 
 
 117 
 
 47.2 
 
 177 
 
 80.6 
 
 2 
 
 18.9 
 
 58 
 
 14.5 
 
 118 
 
 47.8 
 
 178 
 
 81.1 
 
 1 
 
 18.3 
 
 59 
 
 15.0 
 
 119 
 
 48.3 
 
 179 
 
 81.7 
 
 
 
 17.78 
 
 60 
 
 15.6 
 
 120 
 
 48.9 
 
 180 
 
 82.2 
 
 + 1 
 
 17.2 
 
 61 
 
 16.1 
 
 121 
 
 49.5 
 
 181 
 
 82.8 
 
356 
 
 HEAT AND FUELS 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 182 
 
 83.3 
 
 244 
 
 117.8 
 
 306 
 
 152.2 
 
 368 
 
 186.7 
 
 183 
 
 83.9 
 
 245 
 
 118.3 
 
 307 
 
 152.8 
 
 369 
 
 187.2 
 
 184 
 
 84.5 
 
 246 
 
 118.9 
 
 308 
 
 153.3 
 
 370 
 
 187.8 
 
 185 
 
 85.0 
 
 247 
 
 119.5 
 
 309 
 
 153.9 
 
 371 
 
 188.3 
 
 186 
 
 85.6 
 
 248 
 
 120.0 
 
 310 
 
 154.5 
 
 372 
 
 188.9 
 
 187 
 
 86.1 
 
 249 
 
 120.6 
 
 311 
 
 155.0 
 
 373 
 
 189.5 
 
 188 
 
 86.7 
 
 250 
 
 121.1 
 
 312 
 
 155.6 
 
 374 
 
 190.0 
 
 189 
 
 87.2 
 
 251 
 
 121.7 
 
 313 
 
 156.1 
 
 375 
 
 190.6 
 
 190 
 
 87.8 
 
 252 
 
 122.2 
 
 314 
 
 156.7 
 
 376 
 
 191.1 
 
 191 
 
 88.3 
 
 253 
 
 122.8 
 
 315 
 
 157.2 
 
 377 
 
 191.7 
 
 192 
 
 88.9 
 
 254 
 
 123.3 
 
 316 
 
 157.8 
 
 378 
 
 192.2 
 
 193 
 
 89.5 
 
 255 
 
 123.9 
 
 317 
 
 158.3 
 
 379 
 
 192.8 
 
 194 
 
 90.0 
 
 256 
 
 124.5 
 
 318 
 
 158.9 
 
 380 
 
 193.3 
 
 195 
 
 90.6 
 
 257 
 
 125.0 
 
 319 
 
 159.5 
 
 381 
 
 193.9 
 
 196 
 
 91.1 
 
 258 
 
 125.6 
 
 320 
 
 160.0 
 
 382 
 
 194.5 
 
 197 
 
 91.7 
 
 259 
 
 126.1 
 
 321 
 
 160.6 
 
 383 
 
 195.0 
 
 198 
 
 92.2 
 
 260 
 
 126.7 
 
 322 
 
 161.1 
 
 384 
 
 195.6 
 
 199 
 
 92.8 
 
 261 
 
 127.2 
 
 323 
 
 161.7 
 
 385 
 
 196.1 
 
 200 
 
 93.3 
 
 262 
 
 127.8 
 
 324 
 
 162.2 
 
 386 
 
 196.7 
 
 201 
 
 93.9 
 
 263 
 
 128.3 
 
 325 
 
 162.8 
 
 387 
 
 197.2 
 
 202 
 
 94.5 
 
 264 
 
 128.9 
 
 326 
 
 163.3 
 
 388 
 
 197.8 
 
 203 
 
 95.0 
 
 265 
 
 129.5 
 
 327 
 
 163.9 
 
 389 
 
 198.3 
 
 204 
 
 95.6 
 
 266 
 
 130.0 
 
 328 
 
 164.5 
 
 390 
 
 198.9 
 
 205 
 
 96.1 
 
 267 
 
 130.6 
 
 329 
 
 165.0 
 
 391 
 
 199.5 
 
 206 
 
 96.7 
 
 268 
 
 131.1 
 
 330 
 
 165.6 
 
 392 
 
 200.0 
 
 207 
 
 97.2 
 
 269 
 
 131.7 
 
 331 
 
 166.1 
 
 393 
 
 200.6 
 
 208 
 
 97.8 
 
 270 
 
 132.2 
 
 332 
 
 166.7 
 
 394 
 
 201.1 
 
 209 
 
 98.3 
 
 271 
 
 132.8 
 
 333 
 
 167.2 
 
 395 
 
 201.7 
 
 210 
 
 98.9 
 
 272 
 
 133.3 
 
 334 
 
 167.8 
 
 396 
 
 202.2 
 
 211 
 
 99.5 
 
 273 
 
 133.9 
 
 335 
 
 168.3 
 
 397 
 
 202.8 
 
 212 
 
 100.0 
 
 274 
 
 134.5 
 
 336 
 
 168.9 
 
 398 
 
 203.3 
 
 213 
 
 100.6 
 
 275 
 
 135.0 
 
 337 
 
 169.5 
 
 399 
 
 203.9 
 
 214 
 
 101.1 
 
 276 
 
 135.6 
 
 338 
 
 170.0 
 
 400 
 
 204.5 
 
 215 
 
 101.7 
 
 277 
 
 136.1 
 
 339 
 
 170.6 
 
 401 
 
 205.0 
 
 216 
 
 102.2 
 
 278 
 
 136.7 
 
 340 
 
 171.1 
 
 402 
 
 205.6 
 
 217 
 
 102.8 
 
 279 
 
 137.2 
 
 341 
 
 171.7 
 
 403 
 
 206.1 
 
 218 
 
 103.3 
 
 280 
 
 137.8 
 
 342 
 
 172.2 
 
 404 
 
 206.7 
 
 219 
 
 103.9 
 
 281 
 
 138.3 
 
 343 
 
 172.8 
 
 405 
 
 207.2 
 
 220 
 
 104.5 
 
 282 
 
 138.9 
 
 344 
 
 173.3 
 
 406 
 
 207.8 
 
 221 
 
 105.0 
 
 283 
 
 139.5 
 
 345 
 
 173.9 
 
 407 
 
 208.3 
 
 222 
 
 105.6 
 
 284 
 
 140.0 
 
 346 
 
 174.5 
 
 408 
 
 208.9 
 
 223 
 
 106.1 
 
 285 
 
 140.6 
 
 347 
 
 175.0 
 
 409 
 
 209.5 
 
 224 
 
 106.7 
 
 286 
 
 141.1 
 
 348 
 
 175.6 
 
 410 
 
 210.0 
 
 225 
 
 107.2 
 
 287 
 
 141.7 
 
 349 
 
 176.1 
 
 411 
 
 210.6 
 
 226 
 
 107.8 
 
 288 
 
 142.2 
 
 350 
 
 176.7 
 
 412 
 
 211.1 
 
 227 
 
 108.3 
 
 289 
 
 142.8 
 
 351 
 
 177.2 
 
 413 
 
 211.7 
 
 228 
 
 108.9 
 
 290 
 
 143.3 
 
 352 
 
 177.8 
 
 414 
 
 212.2 
 
 229 
 
 109.5 
 
 291 
 
 143.9 
 
 353 
 
 178.3 
 
 415 
 
 212.8 
 
 230 
 
 110.0 
 
 292 
 
 144.5 
 
 354 
 
 178.9 
 
 416 
 
 213.3 
 
 231 
 
 110.6 
 
 293 
 
 145.0 
 
 355 
 
 179.5 
 
 417 
 
 213.9 
 
 232 
 
 111.1. 
 
 294 
 
 145.6 
 
 356 
 
 180.0 
 
 418 
 
 214.5 
 
 233 
 
 111.7 
 
 295 
 
 146.1 
 
 357 
 
 180.6 
 
 419 
 
 215.0 
 
 234 
 
 112.2 
 
 296 
 
 146.7 
 
 358 
 
 181.1 
 
 420 
 
 215.6 
 
 235 
 
 112.8 
 
 297 
 
 147.2 
 
 359 
 
 181.7 
 
 421 
 
 216.1 
 
 236 
 
 113.3 
 
 298 
 
 147.8 
 
 360 
 
 182.2 
 
 422 
 
 216.7 
 
 237 
 
 113.9 
 
 299 
 
 148.3 
 
 361 
 
 182.8 
 
 423 
 
 217.2 
 
 238 
 
 114.4 
 
 300 
 
 148.9 
 
 362 
 
 183.3 
 
 424 
 
 217.8 
 
 239 
 
 115.0 
 
 301 
 
 149.5 
 
 363 
 
 183.9 
 
 425 
 
 218.3 
 
 240 
 
 115.6 
 
 302 
 
 150.0 
 
 364 
 
 184.5 
 
 426 
 
 218.9 
 
 241 
 
 116.1 
 
 303 
 
 150.6 
 
 365 
 
 185.0 
 
 427 
 
 219.5 
 
 242 
 
 116.7 
 
 304 
 
 151.1 
 
 366 
 
 185.6 
 
 428 
 
 220.0 
 
 243 
 
 117.2 
 
 305 
 
 151.7 
 
 367 
 
 186.1 
 
 429 
 
 220.6 
 
HEAT AND FUELS 
 TABLE (Continued) 
 
 357 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 430 
 
 221.1 
 
 459 
 
 237.2 
 
 488 
 
 253.3 
 
 925 
 
 496.1 
 
 431 
 
 221.7 
 
 460 
 
 237.8 
 
 489 
 
 253.9 
 
 950 
 
 510.0 
 
 432 
 
 222.2 
 
 461 
 
 238.3 
 
 490 
 
 254.5 
 
 975 
 
 523.9 
 
 433 
 
 222.8 
 
 462 
 
 238.9 
 
 491 
 
 255.0 
 
 1,000 
 
 537.8 
 
 434 
 
 223.3 
 
 463 
 
 239.5 
 
 492 
 
 255.6 
 
 1,050 
 
 565.6 
 
 435 
 
 223.9 
 
 464 
 
 240.0 
 
 493 
 
 256.1 
 
 1,100 
 
 593.3 
 
 436 
 
 224.5 
 
 465 
 
 240.6 
 
 494 
 
 256.7 
 
 1,150 
 
 621.1 
 
 437 
 
 225.0 
 
 466 
 
 241.1 
 
 495 
 
 257.2 
 
 1,200 
 
 648.9 
 
 438 
 
 225.6 
 
 467 
 
 241.7 
 
 496 
 
 257.8 
 
 1,250 
 
 696.7 
 
 439 
 
 226.1 
 
 468 
 
 242.2 
 
 497 
 
 258.3 
 
 1,300 
 
 704.4 
 
 440 
 
 226.7 
 
 469 
 
 242.8 
 
 498 
 
 258.9 
 
 1,350 
 
 732.2 
 
 441 
 
 227.2 
 
 470 
 
 243.3 
 
 499 
 
 259.5 
 
 1,400 
 
 760.0 
 
 442 
 
 227.8 
 
 471 
 
 243.9 
 
 500 
 
 260.0 
 
 1,450 
 
 787.8 
 
 443 
 
 228.3 
 
 472 
 
 244.4 
 
 525 
 
 273.9 
 
 1,500 
 
 815.6 
 
 444 
 
 228.9 
 
 473 
 
 245.0 
 
 550 
 
 287.8 
 
 1,600 
 
 871.1 
 
 445 
 
 229.5 
 
 474 
 
 245.6 
 
 575 
 
 301.7 
 
 1,700 
 
 926.7 
 
 446 
 
 230.0 
 
 475 
 
 246.1 
 
 600 
 
 315.6 
 
 1,800 
 
 982.2 
 
 447 
 
 230.6 
 
 476 
 
 246.7 
 
 625 
 
 329.4 
 
 1,900 
 
 1,036.7 
 
 448 
 
 231.1 
 
 477 
 
 247.2 
 
 650 
 
 343.3 
 
 2,000 
 
 ,093.3 
 
 449 
 
 231.7 
 
 478 
 
 247.8 
 
 675 
 
 357.2 
 
 2,100 
 
 ,148.9 
 
 450 
 
 232.2 
 
 479 
 
 248.3 
 
 700 
 
 371.1 
 
 2,200 
 
 ,204.4 
 
 451 
 
 232.8 
 
 480 
 
 248.9 
 
 725 
 
 385.0 
 
 2,300 
 
 ,260.0 
 
 452 
 
 233.3 
 
 481 
 
 249.5 
 
 750 
 
 398.9 
 
 2,400 
 
 ,315.6 
 
 453 
 
 233.9 
 
 482 
 
 250.0 
 
 775 
 
 412.8 
 
 2,500 
 
 ,371.1 
 
 454 
 
 234.5 
 
 483 
 
 250.6 
 
 800 
 
 426.7 
 
 2,600 
 
 ,426.7 
 
 455 
 
 235.0 
 
 484 
 
 251.1 
 
 825 
 
 440.6 
 
 2,700 
 
 ,482.2 
 
 456 
 
 235.6 
 
 485 
 
 251.7 
 
 850 
 
 454.4 
 
 2,800 
 
 ,537.8 
 
 457 
 
 236.1 
 
 486 
 
 252.2 
 
 875 
 
 468.3 
 
 2,900 
 
 ,593.3 
 
 458 
 
 236.7 
 
 487 
 
 252.8 
 
 900 
 
 482.2 
 
 3,000 
 
 ,648.9 
 
 EQUIVALENT TEMPERATURES BY THE CENTIGRADE AND 
 FAHRENHEIT THERMOMETERS 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 -273.13 
 
 -459.64 
 
 33 
 
 27.4 
 
 7 
 
 19.4 
 
 19 
 
 66.2 
 
 250 
 
 418.0 
 
 32 
 
 25.6 
 
 6 
 
 21.2 
 
 20 
 
 68.0 
 
 225 
 
 373.0 
 
 31 
 
 23.8 
 
 5 
 
 23.0 
 
 21 
 
 69.8 
 
 200 
 
 328.0 
 
 30 
 
 22.0 
 
 4 
 
 24.8 
 
 22 
 
 71.6 
 
 175 
 
 283.0 
 
 29 
 
 20.2 
 
 3 
 
 26.6 
 
 23 
 
 73.4 
 
 150 
 
 238.0 
 
 28 
 
 18.4 
 
 2 
 
 28.4 
 
 24 
 
 75.2 
 
 125 
 
 193.0 
 
 27 
 
 16.6 
 
 -1 
 
 30.2 
 
 25 
 
 77.0 
 
 100 
 
 148.0 
 
 26 
 
 14.8 
 
 
 
 32.0 
 
 26 
 
 78.8 
 
 75 
 
 103.0 
 
 25 
 
 13.0 
 
 + 1 
 
 33.8 
 
 27 
 
 80.6 
 
 50 
 
 58.0 
 
 24 
 
 11.2 
 
 2 
 
 35.6 
 
 28 
 
 82.4 
 
 49 
 
 56.2 
 
 23 
 
 9.4 
 
 3 
 
 37.4 
 
 29 
 
 84.2 
 
 48 
 
 54.4 
 
 22 
 
 7.6 
 
 4 
 
 39.2 
 
 30 
 
 86.0 
 
 47 
 
 52.6 
 
 21 
 
 5.8 
 
 5 
 
 41.0 
 
 31 
 
 87.8 
 
 46 
 
 50.8 
 
 20 
 
 4.0 
 
 6 
 
 42.8 
 
 32 
 
 89.6 
 
 45 
 
 49.0 
 
 19 
 
 2.2 
 
 7 
 
 44.6 
 
 33 
 
 91.4 
 
 44 
 
 47.2 
 
 18 
 
 -.4 
 
 8 
 
 46.4 
 
 34 
 
 93.2 
 
 43 
 
 45.4 
 
 17 
 
 + 1.4 
 
 9 
 
 48.2 
 
 35 
 
 95.0 
 
 42 
 
 43.6 
 
 16 
 
 3.2 
 
 10 
 
 50.0 
 
 36 
 
 96.8 
 
 41 
 
 41.8 
 
 15 
 
 5.0 
 
 11 
 
 51.8 
 
 37 
 
 98.6 
 
 40 
 
 40.0 
 
 14 
 
 6.8 
 
 12 
 
 53.6 
 
 38 
 
 100.4 
 
 39 
 
 38.2 
 
 13 
 
 8.6 
 
 13 
 
 55.4 
 
 39 
 
 102.2 
 
 38 
 
 36.4 
 
 12 
 
 10.4 
 
 14 
 
 57.2 
 
 40 
 
 104.0 
 
 37 
 
 34.6 
 
 11 
 
 12.2 
 
 15 
 
 59.0 
 
 41 
 
 105.8 
 
 36 
 
 32.8 
 
 10 
 
 14.0 
 
 16 
 
 60.8 
 
 42 
 
 107.6 
 
 35 
 
 31.0 
 
 9 
 
 15.8 
 
 17 
 
 62.6 
 
 43 
 
 109.4 
 
 34 
 
 29.2 
 
 8 
 
 17.6 
 
 18 
 
 64.4 
 
 44 
 
 111.2 
 
HEAT AND FUELS 
 TABLE (Continued) 
 
 Degrees 
 Cent. 
 
 Degrees 
 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 Fahr. 
 
 Degrees 
 Cent. 
 
 Degrees 
 
 Fahr. 
 
 45 
 
 113.0 
 
 108 
 
 226.4 
 
 171 
 
 339.8 
 
 234 
 
 453.2 
 
 46 
 
 114.8 
 
 109 
 
 228.2 
 
 172 
 
 341.6 
 
 235 
 
 455.0 
 
 47 
 
 116.6 
 
 110 
 
 230.0 
 
 173 
 
 343.4 
 
 236 
 
 456.8 
 
 48 
 
 118.4 
 
 111 
 
 231.8 
 
 174 
 
 345.2 
 
 237 
 
 458.6 
 
 49 
 
 120.2 
 
 112 
 
 233.6 
 
 175 
 
 347.0 
 
 238 
 
 460.4 
 
 50 
 
 122.0 
 
 113 
 
 235.4 
 
 176 
 
 348.8 
 
 239 
 
 462.2 
 
 51 
 
 123.8 
 
 114 
 
 237.2 
 
 177 
 
 350.6 
 
 240 
 
 464.0 
 
 52 
 
 125.6 
 
 115 
 
 239.0 
 
 178 
 
 352.4 
 
 241 
 
 465.8 
 
 53 
 
 127.4 
 
 116 
 
 240.8 
 
 179 
 
 354.2 
 
 242 
 
 467.6 
 
 54 
 
 129.2 
 
 117 
 
 242.6 
 
 180 
 
 356.0 
 
 243 
 
 469.4 
 
 55 
 
 131.0 
 
 118 
 
 244.4 
 
 181 
 
 357.8 
 
 244 
 
 471.2 
 
 56 
 
 132.8 
 
 119 
 
 246.2 
 
 182 
 
 359.6 
 
 245 
 
 473.0 
 
 57 
 
 134.6 
 
 120 
 
 248.0 
 
 183 
 
 361.4 
 
 246 
 
 474.8 
 
 58 
 
 136.4 
 
 121 
 
 249.8 
 
 184 
 
 363.2 
 
 247 
 
 476.6 
 
 59 
 
 138.2 
 
 122 
 
 251.6 
 
 185 
 
 365.0 
 
 248 
 
 478.4 
 
 60 
 
 140.0 
 
 123 
 
 253.4 
 
 186 
 
 366.8 
 
 249 
 
 480.2 
 
 61 
 
 141.8 
 
 124 
 
 255.2 
 
 187 
 
 368.6 
 
 250 
 
 482.0 
 
 62 
 
 143.6 
 
 125 
 
 257.0 
 
 188 
 
 370.4 
 
 251 
 
 483.8 
 
 63 
 
 145.4 
 
 126 
 
 258.8 
 
 189 
 
 372.2 
 
 252 
 
 485.6 
 
 64 
 
 147.2 
 
 127 
 
 260.6 
 
 190 
 
 374.0 
 
 253 
 
 487.4 
 
 65 
 
 149.0 
 
 128 
 
 262.4 
 
 191 
 
 375.8 
 
 254 
 
 489.2 
 
 66 
 
 150.8 
 
 129 
 
 264.2 
 
 192 
 
 377.6 
 
 255 
 
 491.0 
 
 67 
 
 152.6 
 
 130 
 
 266.0 
 
 193 
 
 379.4 
 
 256 
 
 492.8 
 
 68 
 
 154.4 
 
 131 
 
 267.8 
 
 194 
 
 381.2 
 
 257 
 
 494.6 
 
 69 
 
 156.2 
 
 132 
 
 269.6 
 
 195 
 
 383.0 
 
 258 
 
 496.4 
 
 70 
 
 158.0 
 
 133 
 
 271.4 
 
 196 
 
 384.8 
 
 259 
 
 498.2 
 
 71 
 
 159.8 
 
 134 
 
 273.2 
 
 197 
 
 386.6 
 
 260 
 
 500.0 
 
 72 
 
 161.6 
 
 135 
 
 275.0 
 
 198 
 
 388.4 
 
 275 
 
 527.0 
 
 73 
 
 163.4 
 
 136 
 
 276.8 
 
 199 
 
 390.2 
 
 300 
 
 572.0 
 
 74 
 
 165.2 
 
 137 
 
 278.6 
 
 200 
 
 392.0 
 
 325 
 
 617.0 
 
 75 
 
 167.0 
 
 138 
 
 280.4 
 
 201 
 
 393.8 
 
 350 
 
 662.0 
 
 76 
 
 168.8 
 
 139 
 
 282.2 
 
 202 
 
 395.6 
 
 375 
 
 707.0 
 
 77 
 
 170.6 
 
 140 
 
 284.0 
 
 203 
 
 397.4 
 
 400 
 
 752.0 
 
 78 
 
 172.4 
 
 141 
 
 285.8 
 
 204 
 
 399.2 
 
 425 
 
 797.0 
 
 79 
 
 174.2 
 
 142 
 
 287.6 
 
 205 
 
 401.0 
 
 450 
 
 842.0 
 
 80 
 
 176.0 
 
 143 
 
 289.4 
 
 206 
 
 402.8 
 
 475 
 
 887.0 
 
 81 
 
 177.8 
 
 144 
 
 291.2 
 
 207 
 
 404.6 
 
 500 
 
 932.0 
 
 82 
 
 179.6 
 
 145 
 
 293.0 
 
 208 
 
 406.4 
 
 550 
 
 1,022.0 
 
 83 
 
 181.4 
 
 146 
 
 294.8 
 
 209 
 
 408.2 
 
 600 
 
 1,112.0 
 
 84 
 
 183.2 
 
 147 
 
 296.6 
 
 210 
 
 410.0 
 
 650 
 
 1,202.0 
 
 85 
 
 185.0 
 
 148 
 
 298.4 
 
 211 
 
 411.8 
 
 700 
 
 1,292.0 
 
 86 
 
 186.8 
 
 149 
 
 300.2 
 
 212 
 
 413.6 
 
 750 
 
 1,382.0 
 
 87 
 
 188.6 
 
 150 
 
 302.0 
 
 213 
 
 415.4 
 
 800 
 
 1,472.0 
 
 88 
 
 190.4 
 
 151 
 
 303.8 
 
 214 
 
 417.2 
 
 850 
 
 1,562.0 
 
 89 
 
 192.2 
 
 152 
 
 305.6 
 
 215 
 
 419.0 
 
 900 
 
 1,652.0 
 
 90 
 
 194.0 
 
 153 
 
 307.4 
 
 216- 
 
 420.8 
 
 950 
 
 1,742.0 
 
 91 
 
 195.8 
 
 154 
 
 309.2 
 
 217 
 
 422.6 
 
 1,000 
 
 1,832.0 
 
 92 
 
 197.6 
 
 155 
 
 311.0 
 
 218 
 
 424.4 
 
 1,100 
 
 2,012.0 
 
 93 
 
 199.4 
 
 156 
 
 312.8 
 
 219 
 
 426.2 
 
 1,200 
 
 2,292.0 
 
 94 
 
 201.2 
 
 157 
 
 314.6 
 
 220 
 
 428.0 
 
 1,300 
 
 2,372.0 
 
 95 
 
 203.0 
 
 158 
 
 316.4 
 
 221 
 
 429.8 
 
 1,400 
 
 2,552.0 
 
 96 
 
 204.8 
 
 159 
 
 318.2 
 
 222 
 
 431.6 
 
 1,500 
 
 2,732.0 
 
 97 
 
 206.6 
 
 160 
 
 320.0 
 
 223 
 
 433.4 
 
 1,600 
 
 2,912.0 
 
 98 
 
 208.4 
 
 161 
 
 321.8 
 
 224 
 
 435.2 
 
 1,700 
 
 3,092.0 
 
 99 
 
 210.2 
 
 162 
 
 323.6 
 
 225 
 
 437.0 
 
 1,800 
 
 3,272.0 
 
 100 
 
 212.0 
 
 163 
 
 325.4 
 
 226 
 
 438.8 
 
 1,900 
 
 3,452.0 
 
 101 
 
 213.8 
 
 164 
 
 327.2 
 
 227 
 
 440.6 
 
 2,000 
 
 3,632.0 
 
 102 
 
 215.6 
 
 165 
 
 329.0 
 
 228 
 
 442.4 
 
 2,100 
 
 3,812.0 
 
 103 
 
 217.4 
 
 166 
 
 330.8 
 
 229 
 
 444.2 
 
 2,200 
 
 3,992.0 
 
 104 
 
 219.2 
 
 167 
 
 332.6 
 
 230 
 
 446.0 
 
 2,300 
 
 4,172.0 
 
 105 
 
 221.0 
 
 168 
 
 334.4 
 
 231 
 
 447.8 
 
 2,400 
 
 4,352.0 
 
 106 
 
 222.8 
 
 169 
 
 336.2 
 
 232 
 
 449.6 
 
 2,500 
 
 4,532.0 
 
 107 
 
 224.6 
 
 170 
 
 338.0 
 
 233 
 
 451.4 
 
 2,600 
 
 4,712.0 
 
HEAT AND FUELS 
 COEFFICIENTS OF LINEAR EXPANSION PER 1 F. 
 
 359 
 
 Substance 
 
 Coefficient 
 
 Substance 
 
 Coefficient 
 
 Aluminum 
 Brass 
 
 .00001140 
 .00001040 
 .00000306 
 .00000550 
 .00000780 
 .00000961 
 .00000399 
 .00000521 
 .00000841 
 .00000460 
 .00000587 
 .00000677 
 .00001580 
 
 Marble 
 
 .00000400 
 .00000206 
 .00000490 
 .00003334 
 .00000494 
 .00000200 
 .00000400 
 .00000670 
 .00000599 
 .00000702 
 .00001160 
 .00000276 
 .00001634 
 
 Mac , /from 
 
 Brick 
 
 Masonry | to 
 
 Mercury 
 Platinum 
 
 Cement, concrete |^ om 
 
 Porcelain 
 
 Glass . . . . (f rom 
 
 Sandstone { om 
 
 Steel, untempered 
 Steel, tempered 
 
 I to 
 Gold 
 
 Granite 
 
 Iron cast 
 
 Tin 
 
 
 Wood pine 
 
 Lead 
 
 Zinc 
 
 
 
 It should be noted that if the length of a bar that has been heated is deter- 
 mined, and then its length is found after its temperature has been reduced by 
 the amount it has been heated, the value obtained for the contraction in length 
 will not be the same as first obtained for the expansion. Thus, in the case of 
 the wrought iron bar, its final length is 60.16248 in., the expansion from 60 
 to 460 being .16248 in. If the same bar is cooled from 460 to 60, the con- 
 traction will be 60. 16248 X. 00000677X400 = .16292 in., or .00044 in. more than 
 the expansion from 60 to 460. 
 
 The reason for this difference is purely a mathematical one. If C is the 
 coefficient of expansion and Ti, Tz, L\, and Lz, are, respectively, the initial and 
 final temperatures and the initial and final lengths, the formula becomes, 
 
 Conduction of Heat. The progress of heat from places of higher to places 
 of lower temperature in the same body is called conduction. Good conductors 
 are those through which the heat wave moves rapidly; poor conductors are 
 those in which this movement is slow. The relative heat conductivities of 
 some of the metals are given in an accompanying table. 
 
 RELATIVE HEAT CONDUCTIVITIES OF METALS 
 
 Metal 
 
 Conductivity 
 
 Metal 
 
 Conductivity 
 
 Silver 
 
 100.0 
 
 Iron 
 
 11.9 
 
 Copper 
 Gold 
 
 73.6 
 53.2 
 
 Steel 
 Lead 
 
 11.6 
 
 8.5 
 
 
 31.3 
 
 Platinum 
 
 8.4 
 
 
 28 1 
 
 Bismuth 
 
 1.8 
 
 Tin 
 
 15.2 
 
 Mercury 
 
 1.3 
 
 
 
 
 
 A non-conductor is a substance that will not conduct heat. No perfectly 
 non-conducting substances are known, although a number of substances are 
 such poor conductors that they are commonly classed as non-conductors. 
 The metals are the best conductors, silver ranking first, while liquids and 
 gases are very poor conductors. Organic substances, as cotton, wool, straw, 
 bran, etc., and rocks and earths, like magnesia, asbestos, etc., are very poor 
 conductors; this quality is taken advantage of in the manufacture of boiler 
 and steam-pipe coverings. 
 
 Radiation of Heai. The communication of heat from a hot body to a 
 colder one across an intervening space is called radiation. The best example 
 of radiated heat is that received from the sun. The intensity of heat radiation 
 from a given source: Varies as the temperature of the source; varies inversely 
 
360 
 
 HEAT AND FUELS 
 
 as the square of the distance from the source; and grows less as the inclination 
 of the rays to the surface grows less. 
 
 The radiating power of heated surfaces depends greatly on the form, shape, 
 and material of which they are composed. Thus, in the case of a cubic vessel, 
 filled with hot water, having its vertical sides coated, respectively, with polished 
 silver, tarnished lead, mica, and lampblack, the radiating power of the sides 
 was experimentally determined to be as 25 : 45 : 80 : 100. From this, bright 
 surfaces radiate less heat than dark ones having the same temperature. 
 
 Those bodies or surfaces that reflect heat readily do not absorb it to any 
 extent, and conversely. Thus, lampblack, which reflects few of the heat rays 
 impinging upon it, absorbs nearly all; and polished silver absorbs but about 
 2.5% of the heat rays, reflecting 97.5%. 
 
 Specific Heat. The specific heat of a substance is the ratio between the 
 quantity of heat required to raise or lower the temperature of that substance 1 
 and the quantity 9f heat required to raise or lower an equal weight of water 1. 
 Thus, if the specific heat of lead is .0299, the amount of heat expressed in 
 British thermal units required to raise a certain weight of this metal 1 will 
 raise the same weight of water only .0299 of 1, or, what is the same thing, 
 as 1 B. T. U. will raise the temperature of 1 Ib. of water 1 F., .0299 B. T. U. 
 will raise the temperature of 1 Ib. of lead 1 F. 
 
 For strict accuracy, the temperature should be noted at which the specific 
 heat is measured, because it has been found that the specific heat is variable 
 for high temperatures. For ordinary temperatures, however, the values given 
 in the accompanying tables may be considered constant. As stated before, 
 the specific heat of water varies with the temperature. 
 
 SPECIFIC HEAT OF WATER AT VARIOUS TEMPERATURES 
 
 Temperature 
 
 
 Temperature 
 
 
 
 Specific 
 
 
 Specific 
 
 
 
 
 
 Degrees 
 
 Degrees 
 
 Heat 
 
 Degrees 
 
 Degrees 
 
 Heat 
 
 Centigrade 
 
 Fahrenheit 
 
 
 Centigrade 
 
 Fahrenheit 
 
 
 
 
 32 
 
 1.0094 
 
 50 
 
 122 
 
 .9980 
 
 5 
 
 41 
 
 1.0053 
 
 55 
 
 131 
 
 .9985 
 
 10 
 
 50 
 
 1.0023 
 
 60 
 
 140 
 
 .9994 
 
 15 
 
 59 
 
 1.0003 
 
 65 
 
 149 
 
 1.0004 
 
 16.11 
 
 61 
 
 1.0000 
 
 70 
 
 158 
 
 1.0015 
 
 20 
 
 68 
 
 .9990 
 
 75 
 
 167 
 
 1.0028 
 
 25 
 
 77 
 
 .9981 
 
 80 
 
 176 
 
 1.0042 
 
 30 
 
 86 
 
 .9976 
 
 85 
 
 185 
 
 1.0056 
 
 35 
 
 95 
 
 .9974 
 
 90 
 
 194 
 
 1.0071 
 
 40 
 
 104 
 
 .9974 
 
 95 
 
 203 
 
 1.0086 
 
 45 
 
 113 
 
 .9976 
 
 100 
 
 212 
 
 1.0101 
 
 SPECIFIC HEATS OF SOLIDS 
 
 Substance 
 
 Specific 
 Heat 
 
 Substance 
 
 Specific 
 Heat 
 
 Aluminum . . 
 
 2143 
 
 
 1152 
 
 Ashes 
 
 2100 
 
 
 0299 
 
 Brass 
 
 .0883 
 
 Platinum 
 
 .0323 
 
 Charcoal 
 
 .2410 
 
 Steel', soft 
 
 .1175 
 
 Copper. . . 
 
 0951 
 
 Steel hard 
 
 1165 
 
 Glass 
 
 .1937 
 
 
 2026 
 
 Ice 
 
 .5040 
 
 Tin 
 
 0518 
 
 Iron, cast 
 
 .1189 
 
 Zinc 
 
 .0935 
 
 
 
 
 
HEAT AND FUELS 
 SPECIFIC HEATS OF LIQUIDS 
 
 361 
 
 Substance 
 
 Specific 
 Heat 
 
 Substance 
 
 Specific 
 Heat 
 
 Alcohol, 32 
 Alcohol, 176 
 Benzene, 50 
 Benzene, 122 
 Glycerine 
 Lead, melted 
 Mercury, 32 
 
 .5475 
 .6794 
 .4066 
 .4502 
 .5760 
 .0410 
 .0335 
 
 Petroleum 
 Sea water, 64 
 Sulphur, melted 
 Sulphuric acid 
 Tin, melted 
 Turpentine, Oil of 
 
 .4980 
 .9800 
 .2350 
 .3363 
 .0637 
 .4110 
 
 
 
 
 
 In the table of the specific heats of certain gases, it will be noted that two 
 values are given for these. This is because it requires less heat to raise the 
 temperature of a gas when the volume remains constant than when the pressure 
 is constant and the volume varies. 
 
 SPECIFIC HEATS OF GASES 
 
 Substance 
 
 Specific 
 Heat at 
 Constant 
 Pressure 
 
 Specific 
 Heat at 
 Constant 
 Volume 
 
 Substance 
 
 Specific 
 Heat at 
 Constant 
 Pressure 
 
 Specific 
 Heat at 
 Constant 
 Volume 
 
 Air 
 Carbon dioxide .... 
 Carbon monoxide. . 
 Hydrogen 
 
 .2375 
 .2170 
 .2479 
 3.4090 
 
 .1690 
 .1535 
 .1758 
 2.4123 
 
 Methane 
 Nitrogen 
 Oxygen 
 
 .5929 
 .2438 
 .2175 
 .4805 
 
 .4505 
 .1727 
 .1551 
 .3460 
 
 Superheated steam 
 
 EXAMPLE. Assuming that all the heat of combustion is utilized, how many 
 pounds of cast iron, which has a specific heat of .1189, may be raised from 60 
 to 260 in temperature, by the burning of 1 Ib. of Pocahontas coal with a heat- 
 ing value of 14,500 B. T. U.? 
 
 SOLUTION. The number of British thermal units required to raise the 
 temperature of 1 Ib. of cast iron from 60 to 260 is (260-60) X.I 189 
 = 23.78 B. T. U. As 1 Ib. of the coal yields 14,500 B. T. U., it will raise 14,500 
 -=-23.78 = 610 (about) Ib. of cast iron from 60 to 260. 
 
 The specific heat of an alloy or of a mixture of gases, etc., is found by 
 multiplying the percentage by weight of each one of the several constituents 
 by its specific heat and dividing the sum of these products by 100. 
 
 EXAMPLE 1. What is the specific heat of an alloy composed of 21% of 
 copper, 40% of tin, and 39% of zinc? 
 
 SOLUTION. Copper 21 X .0951 = 1.9971 
 
 Tin 40X. 0518 = 2.0720 
 
 Zinc 39 X. 0935 = 3.6465 
 
 100 7.7156 
 
 Hence, the specific heat is 7.7156 -MOO = .077156. 
 
 EXAMPLE 2. What is the specific heat of an afterdamp composed of 4.5% 
 COi, 1.5% CO, 80.0% N, and 14% O, by weight? 
 SOLUTION. AT 80.0 X. 2438 = 19.50400 
 
 O 14.0 X. 2 175= 3.04500 
 COz 4.5 X. 2 170= .97650 
 CO 1.5X .2479 = .37185 
 100.0 23.89735 
 
 Hence the specific heat is 23.89735 -MOO = .2389735, say, 2390. 
 Sensible and Latent Heat. The heat that serves only to increase the 
 temperature of a body to which it is imparted, and which may be measured by 
 means of a thermometer, is known as sensible heat. For illustration, the heat 
 required to raise the temperature of a volume of water from the freezing 
 point at 32 to the boiling point at 212, or through 180 is sensible heat. In 
 steam engineering, the amount of heat in the water above that at 32 is com- 
 monly called the heat of the liquid. 
 
362 HEAT AND FUELS 
 
 However, heat may be applied to ice at 32 and to water at 212 without 
 increasing the temperature of either. In the one case the ice is changed to 
 water at the same temperature, 32, and in the other case the water is changed 
 into steam at the same temperature, 212. In neither case can the heat added 
 be measured by the thermometer until all the ice is converted into water and 
 all the water changed into steam. This heat that is absorbed in changing the 
 state or condition of a body, which does work in overcoming the cohesion of 
 the molecules, is called latent heat. This heat is given up when the body 
 resumes its original liquid or solid state. 
 
 The heat absorbed in melting a body is called the latent heat of fusion and in 
 the case of melting ice into water is equal to 144 B. T. U. The heat absorbed 
 in changing a body from the liquid to the gaseous state is known as the latent 
 heat of volatilization. In the case of water this is called the latent heat of 
 evaporation, and is commonly taken as being equal to 965.8 B. T. U. Later 
 investigations by Marks and Davis indicate that the true value of the latent 
 heat of evaporation of water is 970.4 B. T. U. Using the former value, the 
 number of British thermal units required to change 1 Ib. of ice at 32 F. into 
 steam at 212 F., may be divided as follows: 
 
 Latent heat of fusion = 144.0 
 
 Sensible heat from 32 to 212= 180.0 
 
 Latent heat of evaporation = 965.8 
 
 1,289.8 
 
 Should the ice have been at a temperature below the freezing point there 
 must be added to the 1,289.8 B. T. U. thus obtained the amount of heat 
 required to raise the ice to the melting point. Thus, if the ice is at 0, the 
 amount of heat required to raise it to 32 will be equal to (32 0) X specific 
 heat of ice = 32 X. 504 = 16. 13 B. T. U., and the total heat required to convert 
 1 Ib. of ice at into steam at 212 will be equal to 16.13 + 1,289.8=1,305.93 
 B. T. U. Should the water have been at, say, 60, the total heat required- to 
 evaporate it into steam at 212 will b'e: 
 
 Sensible heat from 60 to 212= 152.0 B. T. U. 
 
 Latent heat of evaporation = 965.8 B. T. U. 
 
 1,117.8 B. T. U. 
 
 In those cases where it is necessary to calculate the heat of formation of 
 steam at a higher temperature than 212, Regnault's formula may be used. 
 This gives the number of heat units required to convert water at 32 into 
 steam at any temperature, T. 
 
 Heat units = 1,081.4 +.305 T 
 
 EXAMPLE 1. How many British thermal units are required to convert 
 1 Ib. of water at 60 into steam at 400? 
 
 SOLUTION. From the formula, heat units = 1,081.4 +(.305X400) = 1,203.4 
 B. T. U. But the initial temperature of the water was 60 or 60-32 = 28 
 above the freezing point. Inasmuch as a rise of 1 in the temperature of the 
 water requires the expenditure of 1 B. T. U., 28 heat units must be deducted 
 from the total previously obtained, and the required number is 1,203.4 28 
 = 1,175.4 B. T. U. 
 
 EXAMPLE 2. How many pounds of water at 60 may be evaporated into 
 steam at 400 by the burning of 1 Ib. of Pocahontas coal yielding 14,500 B. T. U. 
 per Ib.? 
 
 SOLUTION. From example 1, it will require 1,175.4 B. T. U. to convert 
 1 Ib. of water into steam under the assumed conditions. Consequently, 1 Ib. of 
 coal will evaporate 14,5004-1,175.4 = 12.3 Ib. of water at 60 into steam at 400. 
 
 MELTING POINTS AND LATENT HEAT OF FUSION OF METALS 
 
 
 Fusing 
 
 Latent 
 
 
 Fusing 
 
 Latent 
 
 Metal 
 
 Point 
 Degrees 
 
 Heat 
 Fusion 
 
 Metal 
 
 Point 
 Degrees 
 
 Heat 
 Fusion 
 
 
 F. 
 
 B. T. U. 
 
 
 F. 
 
 B. T. U. 
 
 Aluminum 
 
 1,157 
 
 180.0 
 
 Nickel 
 
 2,642 
 
 111.6 
 
 Copper 
 
 1,985 
 
 77.9 
 
 Platinum 
 
 3,227 
 
 49.0 
 
 Gold. 
 
 1,946 
 
 29.3 
 
 Silver 
 
 1,764 
 
 43.8 
 
 Iron, wrought. . 
 
 2,912 
 
 126.0 
 
 Sulphur 
 
 237 
 
 16.8 
 
 Lead 
 
 619 
 
 7.2 
 
 Tin 
 
 446 
 
 24.9 
 
 Mercury 
 
 -38 
 
 5.1 
 
 Zinc... 
 
 788 
 
 40.7 
 
HEAT AND FUELS 
 
 363 
 
 The boiling point of water decreases as the altitude above sea level increases, 
 as is shown in an accompanying table. 
 
 BOILING POINT OF WATER AT VARIOUS ALTITUDES 
 
 Boiling 
 Point 
 
 Eleva- 
 tion 
 Above 
 
 Atmos- 
 pheric 
 Pressure 
 
 Barom- 
 eter at 
 
 Boiling 
 Point 
 
 Eleva- 
 tion 
 Above 
 
 ..Atmos- 
 pheric 
 Pressure 
 
 Barom- 
 eter at 
 
 Degrees 
 
 Sea 
 
 Pounds 
 
 32 F. 
 
 Degrees 
 
 Sea 
 
 Pounds 
 
 32 F. 
 
 Fahren- 
 heit 
 
 Level 
 Feet 
 
 per 
 Square 
 Inch 
 
 Inches 
 
 Fahren- 
 heit 
 
 Level 
 Feet 
 
 per 
 Square 
 Inch 
 
 Inches 
 
 184 
 
 15,221 
 
 8.20 
 
 16.70 
 
 199 
 
 6,843 
 
 11.29 
 
 22.99 
 
 185 
 
 14,649 
 
 8.38 
 
 17.06 
 
 200 
 
 6,304 
 
 11.52 
 
 23.47 
 
 186 
 
 14,075 
 
 8.57 
 
 17.45 
 
 201 
 
 5,764 
 
 11.76 
 
 23.95 
 
 187 
 
 13,498 
 
 8.76 
 
 17.83 
 
 202 
 
 5,225 
 
 12.01 
 
 24.45 
 
 188 
 
 12,934 
 
 8.95 
 
 18.22 
 
 203 
 
 4,697 
 
 12.26 
 
 24.96 
 
 189 
 
 12,367 
 
 9.14 
 
 18.61 
 
 204 
 
 4,169 
 
 12.51 
 
 25.48 
 
 190 
 
 11,799 
 
 9.34 
 
 19.02 
 
 205 
 
 3,642 
 
 12.77 
 
 26.00 
 
 191 
 
 11,243 
 
 9.54 
 
 19.43 
 
 206 
 
 3,115 
 
 13.03 
 
 26.53 
 
 192 
 
 10,685 
 
 9.74 
 
 19.85 
 
 207 
 
 2,589 
 
 13.30 
 
 27.08 
 
 193 
 
 10,127 
 
 9.95 
 
 20.27 
 
 208 
 
 2,063 
 
 13.57 
 
 27.63 
 
 194 
 
 9,579 
 
 10.17 
 
 20.71 
 
 209 
 
 1,539 
 
 13.85 
 
 28.19 
 
 195 
 
 9,031 
 
 10.39 
 
 21.15 
 
 210 
 
 1,025 
 
 14.13 
 
 28.76 
 
 196 
 
 .481 
 
 10.61 
 
 21.60 
 
 211 
 
 512 
 
 14.41 
 
 29.33 
 
 197 
 
 7,932 
 
 10.83 
 
 22.05 
 
 212 
 
 
 
 14.70 
 
 29.92 
 
 198 
 
 7,381 
 
 11.06 
 
 22.57 
 
 
 
 
 
 Combustion. In dealing with the burning of fuels, whether solid, liquid, 
 or gaseous, combustion may be defined as the rapid chemical combination of 
 carbon, hydrogen, and sulphur, or their compounds, with the oxygen of the 
 air, the reaction being accompanied by the production of light and heat. 
 When the combustible or burnable element unites with all the oxygen it is 
 capable of absorbing, the combustion is perfect; otherwise it is imperfect. 
 
 The more common chemical reactions in the burning of fuels are here given. 
 The Roman numerals above the symbols employed in expressing the reaction 
 give the relative volumes of the gaseous substances involved, and the Arabic 
 numerals below the reactions are the approximate molecular weights of these 
 substances. The actual weights concerned in the reactions are proportional 
 to the molecular weights. 
 
 In the complete combustion of carbon to carbon dioxide, the reaction is 
 
 C+0 2 = C0 2 
 12+32= 44 
 giving 14,544 B. T. U. per Ib. of carbon burned. 
 
 In the incomplete burning of carbon to carbon monoxide, the reaction is 
 
 24 + 32= 56 
 giving 4,450 B. T. U. per Ib. of carbon burned. 
 
 In the combustion of carbon monoxide to carbon dioxide, the reaction is 
 II I II 
 
 56 +32= 88 
 giving 4,325 B. T. U. per Ib. and 347 B. T. U. per cu. ft. of CO burned. 
 
 In the complete combustion of hydrogen to form water, the reaction is 
 II I II 
 
 4 +32= 36 
 
 giving 62,028 B. T. U per Ib. and 349 B. T. U. per cu. ft. of hydrogen burned. 
 In the complete combustion of hydrogen sulphide to carbon dioxide and 
 sulphur dioxide, the reaction is 
 
 II III II II 
 2HzS + 3O 2 = 2HsO + 25O 2 
 .68 + 96= 36 +128 
 
364 HEAT AND FUELS 
 
 giving by calculation 7.459 B. T. U. per Ib. and 709 B. T. U. per cu. ft. of 
 hydrogen sulphide burned. 
 
 In the complete combustion of methane to form carbon dioxide and water, 
 the reaction is 
 
 16 -j- 64 = 44 + 36 
 giving 23.513 B. T. U. per Ib. and 1,053 B. T. U. per cu. ft. of methane burned. 
 In the complete combustion of acetylene to form carbon dioxide and water, 
 the reaction is n y _ jy n 
 
 2C 2 # 2 +50 2 = 4C0 2 +2# 2 
 
 52 +160= 176 + 36 
 
 giving 21,465 B. T. U. per Ib. and 1,556 B. T. U. per cu. ft. of acetylene burned. 
 In the complete combustion of olefiant gas to carbon dioxide and water, 
 the reaction is 
 
 28 + 96= 88 -f- 36 
 giving 21,344 B. T. U. per Ib. and 1,675 B. T. U. per cu. ft. of plefiant gas burned. 
 In the complete combustion of ethane to carbon dioxide and water, the 
 reaction is 
 
 II VII IV VI 
 
 2CzH 6 + 7O 2 = 4C0 2 + 6# 2 O 
 
 60 +224= 176 + 108 
 
 giving 22,230 B. T. U. per Ib. and 1,862 B. T. U. per cu. ft. of ethane burned. 
 In the complete combustion of sulphur to sulphur dioxide, the reaction is 
 I I 
 
 32+32= 64 
 giving 4,050 B. T. U. per Ib. of sulphur burned. 
 
 The following reactions are important in dealing with fuels, particularly 
 of the gaseous type, as one or all of them are concerned in the manufacture of 
 producer or water gas. 
 
 If carbon dioxide is forced through a bed of incandescent coke, it absorbs 
 a certain amount of carbon to form carbon monoxide according to the reaction 
 
 I II 
 
 C0 2 +C = 2CO 
 44 +12= 56 
 
 This reaction is not accompanied by the generation of heat but by its 
 absorption at the rate of 10,150 B. T. U. per Ib. of carbon burned. 
 
 If steam is injected into white-hot coke, the vapor is decomposed into 
 carbon monoxide and hydrogen. The temperature must be very high and the 
 steam supply partial, the reaction being 
 
 I I I 
 
 12+ 18 =28 + 2 
 
 In this case, also, there is an absorption of heat and to the extent of 5,883 B. 
 T. U. per Ib. of carbon involved. 
 
 If in the last case the steam supply is increased and the temperature lowered, 
 the reaction is 
 
 II I II 
 
 12+ 36 =44+4 
 
 In this case the absorption of heat is 6,066 B. T. U. per Ib. of carbon consumed. 
 When using any of the foregoing equations as a basis for calculating the 
 volumes and weights of the gaseous substances entering into a reaction, it must 
 be remembered that the same is assumed to have taken place at standard 
 temperature and pressure, viz.: 32 P., and 29.92 in. of mercury. Further 
 discussion of the nature and products of combustion will be found near the 
 end of this section and in the section on Mine Ventilation. 
 
FUELS 365 
 
 FUELS 
 
 FUELS IN GENERAL 
 
 Substances that are burned for the purpose of generating heat for com- 
 mercial purposes are called fuels. As regards their physical state they are 
 divided into solid, liquid, and gaseous fuels. The solid fuels include wood, 
 charcoal, coal, peat, coke, sawdust, and other substances of vegetable origin. 
 Liquid fuels include petroleum and its derivatives, naphtha, gasoline, and 
 other oils, and grain, wood, and denatured alcohol. Caseous fuels include 
 natural gas and various manufactured gases, such as coal gas, water gas, 
 producer gas, coke-oven gas, blast-furnace gas, etc. The products of com- 
 bustion, or gases, from beehive coke ovens are frequently used for steam 
 raising, but can hardly be called fuels as they contain no combustible con- 
 stituents, their value being in their actual, sensible heat. 
 
 The chief combustible element in all fuels is carbon, which has a heat 
 value of 14,544 B. T. U. per Ib. In most solid fuels, carbon chiefly exists as 
 such, but in the liquid and gaseous fuels and to a less extent in coal, it occurs 
 as a hydrocarbon, that is, as a gaseous compound of carbon and hydrogen. The 
 heat value per pound of gas is given under the head of Combustion in the 
 discussion of the combustion of the various hydrocarbon gases. 
 
 The second important combustible element is hydrogen, which has a heat 
 value of 62,028 B. T. U. per Ib. of gas. It exists in the free, or uncombined, 
 state in natural gas and in certain manufactured fuel gases, such as water gas, 
 but is more commonly present in the form of a hydrocarbon, or combined 
 with oxygen to form water. If both hydrogen and oxygen exist in a fuel, it 
 is assumed that all the oxygen is combined with the hydrogen in the form of 
 water, HzO. The hydrogen thus combined has no fuel value and must there- 
 fore be deducted from the total amount of hydrogen present in calculating the 
 heating value of the fuel. The hydrogen left after deducting what is combined 
 with the oxygen is called the available hydrogen. As the weight of hydrogen 
 in water is one-eighth the weight of the oxygen, the percentage of available 
 
 hydrogen is obtained from the formula, h = H. in which h, H, and O, are, 
 
 o 
 
 respectively, the percentages of available hydrogen, total hydrogen, and oxygen, 
 in the fuel. 
 
 WOOD AS FUEL 
 
 Wood is composed of woody fiber, or cellulose, CtHioOs, which makes up the 
 chief part of its bulk; the constituents of the sap; and water. The most 
 important of the sap constituents is a soluble gum, lignine, amounting, on the 
 average, to 13% of the wood. The cellulose and lignine are both combustible, 
 whereas the water is not only not combustible, but its evaporation absorbs 
 a good portion of the heat generated by the burning of the other constituents. 
 Dry wood is, therefore, a much better fuel than undried wood. 
 
 Newly felled wood contains from 25 to 50% of water, the amount varying 
 greatly with different kinds, but averaging about 40%. Exposed to the air 
 at ordinary temperatures, wood loses a large part of its moisture and shrinks, 
 reaching a minimum of about 20% of moisture after about 2 yr. of air drying, 
 but it absorbs water and swells in air highly charged with moisture. 
 
 Ordinary air-dried wood may be considered as having the following com- 
 position: hygroscopic water, 20%; oxygen and hydrogen in the proportion in 
 which they unite to form water, 40%; and charcoal, including 1% of ash, 40%. 
 
 The effective value of all kinds of wood per pound, when dry, is substan- 
 tially the same, and is v'ommonly estimated at 40% of that of the same weight 
 of average coal. In the accompanying tables are given the weight per 
 cord of air-dried woods arranged in the order of their fuel value per cord, the 
 weight of coal equivalent to 1 cord of air-dried wood, and Gottlieb's values 
 for the composition and calorific value per pound of different varieties of wood. 
 
366 
 
 FUELS 
 
 WEIGHTS PER CORD OF DRY WOOD ARRANGED ACCORDING TO 
 FUEL VALUES 
 
 Wood 
 
 Weight 
 Pounds 
 
 Wood 
 
 Weight 
 Pounds 
 
 Hickory (shell bark) 
 
 4,469 
 
 Beech 
 
 3,126 
 
 Hickory (red heart) .... 
 White oak 
 
 3,705 
 3,821 
 
 Hard maple 
 Southern pine 
 
 2,878 
 3,375 
 
 Red oak 
 
 3,254 
 
 Virginia pine 
 
 2,680 
 
 Spruce 
 
 2,325 
 2 137 
 
 Yellow pine 
 White pine 
 
 1,904 
 1 868 
 
 yp 
 
 
 
 
 WEIGHT OF COAL EQUIVALENT TO 1 CORD OF AIR-DRIED WOOD 
 
 Kind of Wood 
 
 Weight of 
 1 Cord 
 Pounds 
 
 Weight of Coal Equiv- 
 alent to 1 Cord 
 of Wood 
 Pounds 
 
 
 4 500 
 
 1,800 to 2,000 
 
 White oak 
 
 3,850 
 
 1,540 to 1,715 
 
 Beech red and black oak . . 
 
 3250 
 
 1,300 to 1,450 
 
 Poplar, chestnut, and elm 
 
 2,350 
 
 940 to 1,050 
 
 Pine average 
 
 2,000 
 
 800 to 925 
 
 
 
 
 COMPOSITION AND CALORIFIC VALUE PER POUND OF WOOD 
 
 (Gottlieb) 
 
 Kind of Wood 
 
 Composition 
 
 Calorific Value 
 
 C 
 
 H 
 
 N 
 
 o 
 
 Ash 
 
 Calories 
 
 B. T. U. 
 
 Oak 
 
 50.16 
 49.18 
 48.99 
 49.06 
 48.88 
 50.36 
 50.31 
 
 6.02 
 6.27 
 6.20 
 6.11 
 6.06 
 5.92 
 6.20 
 
 .09 
 .07 
 .06 
 .09 
 .10 
 .05 
 .04 
 
 43.36 
 43.91 
 44.25 
 44.17 
 44.67 
 43.39 
 43.08 
 
 .37 
 .57 
 .50 
 .57 
 .29 
 .28 
 .37 
 
 4,620 
 4,711 
 4,728 
 4,774 
 4,771 
 5,035 
 5,085 
 
 8,316 
 8,480 
 8,510 
 8,591 
 8,586 
 9,063- 
 9,153 
 
 Ash 
 Elm 
 
 Beech 
 
 Birch 
 Fir 
 
 Pine 
 
 
 It is safe to assume that from 2.25 to 2.5 Ib. of dry wood are equivalent 
 in fuel value to 1 Ib. of soft (bituminous) coal of average quality and that, as 
 stated, the fuel value of the same weight of different woods is very nearly the 
 same; that is, 1 Ib. of hickory is worth no more for fuel than 1. Ib. of pine, 
 assuming both to be dry. 
 
 The efficiency of wood fuel depends largely on whether it is wet (as cut) 
 or dry and in a measure as to whether it is fired as cord wood, in 4-ft. lengths, 
 or as sawdust or hogeed wood, the latter term being applied to the fine and 
 shredded material produced by running slabs and logs through a macerator or 
 hogging machine. Such refuse may contain as much as 60% of moisture and 
 requires that a large combustion chamber be provided as well as a large area of 
 heated firebrick to radiate heat to the fuel in order to evaporate the water. 
 To secure this extra space, extension furnaces are commonly used, and added 
 room in the firebox may be had by dropping the grate to the level of the boiler- 
 house floor with an ashpit below. When cord wood is fired, extension furnaces 
 are not generally necessary, although the grates should be dropped. Babcock 
 
FUELS 367 
 
 & Wilcox, in "Steam," state that "with proper draft conditions, 150 Ib. of this 
 fuel (sawdust and hogged chips) containing about 30 to 40% of moisture can 
 be burned per square foot of grate surface per hour, and in a properly designed 
 furnace 1 sq. ft. of grate surface can develop from 5 to 6 boiler H. P. Where 
 the wood contains 50% of moisture or over, it is not usually safe to figure on 
 obtaining more than 3 to 4 H. P. per sq. ft. of grate surface." 
 
 PEAT AS FUEL 
 
 Peat, or as it is sometimes called, turf, results from the accumulation, in 
 place, of partly decomposed and disintegrated vegetable matter, chiefly of 
 varieties of moss (sphagnum), where the ordinary decay and decomposition 
 of such material has been more or less suspended, although the form and a 
 considerable part of the structure of the plant organs are more or less destroyed. 
 It is found in bogs and marshes, where periodic overflows or times of saturation 
 by water are favorable to the growth of plant life and the preservation of its 
 remains under water. According to its origin and the conditions under which 
 it has accumulated, peat may vary in color from brown to black. In texture it 
 may vary from light, spongy matter, that is porous, coarse, fibrous, or even 
 woody, and easily falls to pieces when flry, to forms that are nearly or quite 
 devoid of structure, and which, when wet, are as plastic as clay, and when dry 
 form dense, hard masses resembling lignite. In all cases peat is nearly or quite 
 saturated with water, containing, under usual natural conditions, from 80 to 95%. 
 
 When dry, peat is generally lighter colored than when freshly dug and will 
 usually float if placed in water, although this is not always true of the dark- 
 colored, plastic kinds that are high in ash and when thoroughly dry are as 
 compact and nearly as hard as coal. Except for such types, raw or untreated 
 peat is easily crumbled to powder when handled, and makes bulky and unsub- 
 stantial fuel that does not bear transportation well. The name muck is com- 
 monly applied to black impure peats of the more completely decomposed types. 
 
 It is estimated that the 12,000 sq. mi. of workable peat bogs in the United 
 States contain 13,000,000,000 T. of marketable peat. These deposits are 
 mostly found in the colder and moister sections of the country, in New Eng- 
 land and westwards from close to the southern boundary of New York nearly 
 to the ninetieth meridian and thence northwards to Canada. This is supple- 
 mented by a narrow strip of bog land extending down the Atlantic coast to 
 Florida, includes all of that state, and reaches westwards, probably across 
 Texas, to the Mexican border. Areas of unknown extent are met along the 
 Pacific coast in California, Oregon, and Washington. The Canadian deposits 
 of peat are estimated to cover 35,000 sq. mi. 
 
 Peat is commonly prepared by cutting the material (after the bog has 
 been properly drained) into regular shaped pieces somewhat larger than an 
 ordinary building brick, which are subsequently stacked with air spaces between 
 and dried in the open or under sheds. In some cases, the peat is subjected to 
 a process of grinding or macerating and pressing before being pressed into 
 bricks and is known as machine peat, pressed peat, condensed peat, or machine- 
 formed peat. Peat, after being air-dried, may be ground to a powder, further 
 dried, and pressed into briquettes under a pressure of 18,000 to 30,000 Ib. per 
 sq. in. Either charcoal or coke may be made from peat in suitably designed 
 furnaces or retorts. In the producer, air-dried peat yields large volumes of 
 fuel gas of the most excellent quality; this seems the most satisfactory way 
 of using it in manufacturing operations. 
 
 According to the United States Geological Survey, freshly dug peat from 
 Bethel, Conn., gave by analysis, moisture, 88.72%; volatile matter, 6.54%; 
 fixed carbon, 3.13%; ash, 1.61%; and sulphur (separately determined), .08%. 
 The calorific value of this freshly dug peat was but 927 B. T. U. per Ib. 
 
 A consignment of compressed or machine peat from near Orlando, Fla., 
 and tested at the St. Louis Exposition contained by analysis, moisture, 21%; 
 volatile matter, 51.72%; fixed carbon, 22.11%; ash, 5.17%; and sulphur (separ- 
 ately determined), .4-5%. The ultimate analysis of the same peat was carbon, 
 46.57%; hydrogen, 6.51%; nitrogen, 2.33%; oxygen, 38.97%; ash, 5.17%; and 
 sulphur, .45%. The calorific value of the peat was 8,127 B. T. U. per Ib. 
 
 As a general rule c rdinary air-dried peat has about one-half the fuel value of 
 bituminous coal, say, from 4,000 to 5,500 B. T. U. per Ib.; the calorific value 
 of machined peat being much higher. The cost of machine peat will range 
 between $.75 to $1.50 per T., so that in fuel value it is about equivalent to 
 bituminous coal at $3 per T. 
 
368 
 
 FUELS 
 
 COAL 
 
 CONSTITUENTS OF COAL 
 
 Coal consists of the finely comminuted remains of vegetable matter that 
 have been preserved, under water, from complete decay. Whether it has 
 resulted from the accumulation of drift material, as at the mouths of large 
 rivers, or from the growth of trees, shrubs, and mosses in place in bogs, is 
 an undecided question. The accompanying table shows the theoretical change 
 from wood to anthracite. 
 
 CHANGES IN CHEMICAL COMPOSITION FROM WOOD TO 
 ANTHRACITE 
 
 Substance 
 
 Carbon 
 Per Cent. 
 
 Hydrogen 
 Per Cent. 
 
 Oxygen 
 Per Cent. 
 
 Woody fiber 
 
 52.65 
 
 5.25 
 
 42.10 
 
 Peat from Vulcaire .*. . . 
 
 59.57 
 
 5.96 
 
 34.47 
 
 
 66.04 
 
 5.27 
 
 28.69 
 
 Earthy brown coal - 
 
 73.18 
 
 5.58 
 
 21.14 
 
 Coal from Belestat secondary 
 
 75.06 
 
 5.84 
 
 19.10 
 
 
 89.29 
 
 5.05 
 
 5.66 
 
 Anthracite, Mayenne, transition formation 
 
 91.58 
 
 3.96 
 
 4.46 
 
 The chemical elements present in coal are the carbon, hydrogen, oxygen, 
 and nitrogen of the original vegetable matter, together with the ash thereof, 
 and some sulphur and phosphorus. There are other elements and their combi- 
 nations present, but the ones named are those commonly determined by the 
 chemist. The carbon exists separately and, known as fixed carbon, is the chief 
 combustible substance in most coals. A certain amount of the carbon is com- 
 bined with some of the hydrogen in various gases called hydrocarbons. The 
 nitrogen exists as a gas, and while part of the oxygen may also exist as a gas 
 and a small portion is probably combined with the carbon as carbon dioxide, 
 the bulk of it is combined with hydrogen in the proportions necessary to form 
 water. The water is. commonly called moisture, and the other gaseous con- 
 stituents are called volatile matter, volatile combustible matter, or volatile hydro- 
 carbons. 
 
 Chemists report the composition of coal in the form either of a proximate 
 analysis or of an ultimate analysis. In the former, the constituents are 
 reported in the various combinations in which they occur in the coal, as mois- 
 ture, fixed carbon, volatile matter, and ash, the percentages of which should 
 add up 100. Both the sulphur and phosphorus are separately determined; 
 that is, their amounts are not included to make up the 100% of the four chief 
 constituents. In an ultimate analysis, the constituents are determined in their 
 elementary or ultimate form and the percentages of carbon, hydrogen, oxygen, 
 nitrogen, sulphur, phosphorus if determined, and ash should add up 100. 
 Numerous comparisons of proximate and ultimate analyses of the same coals 
 ( are given in an accompanying table. 
 
 Moisture in coal consists of two portions, first, surface moisture, or that 
 which is on the exterior surface of each lump, and which may be dried off in 
 ordinary dry air; second, the hygroscopic moisture, or that which is held by 
 capillary attraction in the pores of the coal and can only be driven out of a 
 lump of coal by heating it considerably above 212 P. The percentage of 
 surface moisture that may be held in a pile of coal depends on the size of the 
 pieces; the smaller the coal, the greater is the amount of moisture that it will 
 hold. Thus, buckwheat anthracite, or slack bituminous coal, after exposure 
 to rain, may hold as much as 8 or 10%. 
 
 The amount of hygroscopic moisture depends on the kind of coal; thus, 
 anthracite contains practically none, or less than 1%; semibituminous coal 
 rarely over 1%; bituminous coal from Pennsylvania, between 1 and 2%; 
 from Ohio, about 4%; from Illinois, 8 to 14%; while lignite may contain 20% 
 or more. A sample of Illinois coal originally containing 14% of moisture, 
 and thoroughly dried by heating to from 240 F. to 280 F., reabsorbed the 
 same amount of moisture when exposed to ordinary air for 2 mo. 
 
FUELS 369 
 
 In addition to representing 20 Ib. per T. of worthless material for each 
 1% present, moisture causes an actual loss of heat from the fact that every 
 pound of water has to be evaporated into steam at 212 and the steam then 
 raised to an uncertain temperature, which is approximately that of the fire 
 and may be from 1,500 to 2,500. Thus, the water contained in a coal 
 analyzing 10% moisture will be 200 Ib. per T. and will require to raise it from, 
 say, 60 to 1,500, 200X[1,117.8 + (1,500-32)X.48] = 364,488 B. T. U., which 
 is all the heat generated by the combustion of about 33 Ib. of ordinary coal 
 having a calorific value of 11,000 B. T. U. per Ib. 
 
 Fixed carbon is the chief heat-producing constituent of coal, and, the 
 amount of impurities remaining the same, the relative heating values of coals 
 are fairly well determined by a comparison of their content of this substance. 
 Although the fixed carbon of a coal evaporates much less water than an equiva- 
 lent weight of the volatile hydrocarbons when properly burned, in ordinary 
 practice so much of the latter is lost through careless firing or improper furnace 
 construction, that the relative heating value of a coal may be fairly approxi- 
 mated by assuming that the fixed carbon is the only useful constituent. 
 
 Volatile matter is that part of the coal that is driven off as a combustible 
 gas when the coal is heated. When a large percentage of volatile matter is 
 present, coals ignite easily and burn with a long yellow flame, and, in ordinary 
 methods of combustion, give off dense smoke. The relative proportions of 
 volatile matter and fixed carbon in a coal, other things being equal, determine 
 its adaptability to any particular purpose, as appears under the Classification 
 of Coals. 
 
 The volatile combustible matter in coal consists of carbon, hydrogen, and 
 oxygen in various proportions, differing with the character of the coal. It is 
 found that, with the exception of cannel coal, the larger the percentage of 
 volatile matter in a coal, the greater, usually, is the proportion of oxygen in 
 the volatile matter. It also appears that in the semibituminpus coals, after 
 deducting as much of the hydrogen as is needed to form water with the oxygen, 
 that is, one-eighth as much as the oxygen, the remainder, or the available 
 hydrogen, is combined with carbon in about the proportion forming methane, 
 or marsh gas, C7/4, or three parts, by weight, of carbon to one part of hydrogen; 
 while in the bituminous coals it is combined in about the proportions of five 
 parts, by weight, of carbon to one part of hydrogen. The low heating values 
 per pound of combustible in coals that are high in volatile matter and in 
 oxygen, are thus accounted for. 
 
 The following calculations made on coals having the ultimate analyses 
 given in the table on pages 382 to 385 illustrate the increase in moisture and 
 the decrease in available hydrogen and calorific power of American coals in pro- 
 ceeding westwards from the New. River field of West Virginia by way of 
 Pittsburg, Pa., to Illinois. 
 
 No. 114, New River, available H = 4.66-^4^ =4.14; B. T. U. = 14,765 
 
 O 
 
 No. 85, Pittsburg, available tf = 4.63-^ =3.70; B. T. U.= 13,952 
 
 o 
 
 No. 28, Illinois, available # = 5.44-^^ = 3.10; B. T. U. = 10,719 
 
 The ash of coal comes partly from that properly belonging to the vege- 
 table matter from which it was formed and partly from sediments washed 
 into the coal swamp during times of flood. Just what proportion of coal ash 
 represents that of the original plant growth will, naturally, depend on the 
 composition of that growth, something impossible to determine, but it would 
 seem that any ash in coal to the extent of more than 2%, is due to extraneous 
 mineral matter. In composition, coal ash approximates that of fireclay, with 
 the addition of ferric oxide, sulphate of lime, magnesia, potash, and phosphoric 
 acid. 
 
 White-ash coals are generally freer from sulphur than red-ash coals, which 
 contain iron pyrites, but there are exceptions, as in a certain Peruvian coal, 
 which contains more than 10% of sulphur and yields not a small percentage 
 of white ash. 
 
 The fusibility of ash varies according to its composition. It is the more 
 infusible the more nearly its composition approaches fireclay, or silicate of 
 alumina, and becomes more fusible with the addition of other substances, 
 such as iron, lime, etc. Coals high in sulphur usually give a very fusible ash, 
 on account of the iron with which the sulphur is in combination. A fusible 
 ash tends to form a clinker on the grate bars, and therefore is objectionable. 
 
370 FUELS 
 
 The quantity of ash in different coals as they are sent to market differs 
 greatly according to the quality of the coal itself and the care taken to remove 
 the slate, dirt, etc. that accompany them as they come from the mine. A 
 lump of coal may contain only 5% of ash, while the average of the coal, includ- 
 ing slate and dirt as it is mined, may contain 15%. A considerable part of 
 the slate may be removed from the larger sizes by picking after screening, and 
 from the smaller sizes by washing. 
 
 In the case of anthracite, the table on page 386 brings out the increase in ash 
 and decrease in calorific power as the sizes grow smaller. The table on page 387 
 is of value in showing the actual commercial ash present in bituminous coals, 
 many of which, in the case of carefully selected lumps, will yield by analysis 
 less than one-half the ash given in the table. 
 
 Sulphur, having a calorific value of 4,050 B. T. U. per lb., is always present 
 in coal. While some few coals, notably the Georges Creek-Cumberland 
 semibituminous, occasionally contain but a trace of this element, it is com- 
 monly present to the extent of .5 to 5% and even more. Sulphur is generally 
 classed as an impurity in coals because of the corroding action of its fumes 
 upon metals. The terms low sulphur and high sulphur as applied to coals, 
 are generally relative, although a coal containing less than 1% sulphur would 
 everywhere be placed among the former and one having 5% among the latter. 
 The amount of this element that will render a coal unfit for any particular 
 service is discussed under the Classification of Coals. 
 
 Sulphur exists in coal in at least three forms. It usually occurs in combina- 
 tion with iron as the bisulphide, FeSi, which is known by various names as 
 fool's gold, brasses, etc., and very commonly only as sulphur. In pyrites, 
 sulphur has about one-half the heating value per pound of carbon. The 
 pyrites may occur in minute crystalline grains disseminated through the mass 
 of the coal or segregated in small patches upon the cleavage planes; as sheets 
 or plates, of considerable area in proportion to their thickness, that are parallel 
 to the bedding; as regular layers interstratified with the coal; and as lense- 
 shaped masses, sometimes weighing 100 lb., known as sulphur balls. Sulphur 
 balls, when pure, contain 53.33% sulphur and are a source of income at some 
 mines where they are placed in the gob and from time to time gathered up and 
 shipped to the chemical works, where they are employed in the manufacture 
 of sulphuric acid. X 
 
 Sulphur may be present as a sulphate, usually that of calcium or lime, 
 CaSOt, less commonly as magnesium sulphate, MgSOt, and sometimes as 
 the salt of other metals. The sulphates are commonly found in thin whitish 
 or grayish plates on the vertical joint planes of the coal; in this combination, 
 sulphur has no fuel value. 
 
 Sulphur may also be present in combination with the organic constituents 
 of the coal, in which form it is known as vegetable sulphur and has a fuel value. 
 
 Phosphorus, as a natural constituent of the original vegetable matter, is 
 always found in coal. The amount of phosphorus is always very small and 
 does not affect the heating value of the coal, and is only of importance if the 
 coal is destined to make coke for use in furnaces working on Bessemer iron. 
 Phosphorus probably exists as a single or double phosphate of lime and alumina. 
 Mr. Charles Catlett notes, in the Big seam near Columbiana, Ala., the existence 
 of light-colored, resinous grains of evansite, hydrous aluminum phosphate, 
 
 Phosphorus is commonly segregated near both the roof and floor of the 
 seam and by rejecting a few inches of the top and bottom coal, the coke made of 
 the remainder may often be brought within the Bessemer limits. Its amount 
 also varies as the workings are extended and analyses of the coal should be 
 made weekly or monthly as the headings advance. 
 
 CLASSIFICATION OF COALS 
 
 The most convenient commercial classification of coals is based on the 
 relative amounts of combustible matter therein, both fixed carbon and volatile 
 hydrocarbons, as determined by a proximate analysis; this is shown in the 
 accompanying table. 
 
 It must be remembered that this classification is decidedly arbitrary and 
 that the coals of any one group overlap at either end of the scale into those 
 of the other groups. This is particularly true of the lignites, many varieties 
 of which cannot be. distinguished from bituminous coal of the better grades 
 if the proximate analysis is made the criterion. Many of the coals of Arkansas 
 are low in volatile matter and may be grouped with either the semianthracite 
 or semibituminous. Similarly, the low-volatile coals of, say, Somerset County 
 
FUELS 
 
 371 
 
 CLASSIFICATION OF COALS BASED ON THEIR CONTENT OF FIXED 
 CARBON AND VOLATILE MATTER 
 
 Kind of Coal 
 
 Fixed 
 Carbon 
 Per Cent. 
 
 Volatile 
 Matter 
 Per Cent. 
 
 Anthracite 
 
 97.0 to 92.5 
 
 3.0 to 7.5 
 
 Semianthracite 
 
 92.5 to 87.5 
 
 7.5 to 12.5 
 
 Semibituminous 
 
 87 5 to 75 
 
 12 5 to 25 
 
 Bituminous, Eastern United States 
 Bituminous, Western United States . 
 
 75.0 to 60.0 
 65.0 to 50.0 
 
 25.0 to 40.0 
 35 to 50.0 
 
 
 undr 50 
 
 over 50 
 
 
 
 
 and Cambria County, Pa., may be classed as either bituminous or 
 semibituminous. 
 
 Owing to this overlapping of the different groups in the scale, a classi- 
 fication based on calorific values is also unsatisfactory. Likewise, geological 
 age fails to furnish a satisfactory basis of classification. As a general rule, 
 the younger the coal geologically, the higher is its content of moisture and 
 volatile matter and, consequently, the lower is it in fixed carbon. Thus, the 
 coals of the Tertiary age are all lignites and commonly of the brown-coal type; 
 the coals of the underlying Cretaceous are commonly black lignites (subbitu- 
 minous) with spme'true bituminous coals among them; and the true bitumin- 
 ous, semibituminous, semianthracite, and anthracite coals are almost entirely 
 confined to the true coal measures of the Carboniferous age, in which, the 
 lower volatile coals are found near the base of the series. This rule appears 
 to hold good in regions where the rocks have either remained undisturbed or 
 at best have been but slightly folded, but metamorphism has played an 
 important part in changing the characteristics of seams in mountain districts. 
 The Cretaceous of Colorado is marked by beds of subbituminous lignite and 
 bituminous coals in the level country and foot-hills, which the metamorphism 
 incident to mountain building has altered to anthracite in the midst of the 
 Rockies; therefore, the same seam may present the characteristics of bitu- 
 minous coal in flat unbroken regions, of semibituminous coal in the foot-hills, 
 and of semianthracite and possibly of true anthracite in the higher and more 
 disturbed mountains. 
 
 Anthracite. Anthracite, or hard coal, as it is frequently called, is the 
 densest, hardest, and most lustrous of all varieties. It has a conchoidal 
 fracture, frequently displays iridescence, and is characterized both in the lump 
 and in the bed by the absence of cleavage planes. Its specific gravity ranges 
 from 1.3 to 1.8 with an average value of about 1.5. It contains from 3 to 7% 
 of volatile matter, does not coke, is kindled slowly and with difficulty, requires 
 a strong draft through the firebox, and burns with a short almost colorless 
 flame, which is smokeless or essentially so. Practically all the anthracite 
 mined in the United States comes from a small area in northeastern Pennsyl- 
 vania. A series of analyses of anthracite from that state are given in the 
 table on page 386. These are commercial analyses made on large shipments 
 and show that on account of the uniformly high ash content, the calorific value 
 of anthracite is rather low in comparison with standard bituminous coals. 
 It will also be observed that the smaller sizes (pea, barley, rice, etc.) are much 
 less efficient than the larger broken, egg, and the like. The high content of 
 ash in the smaller sizes is due very largely to imperfect preparation. 
 
 An analysis of the so-called anthracite from Cranston, R. I., is No. 92 of 
 the table on pages 382 to 385. The coal is highly graphitic in character and of 
 far more geological interest than commercial value. Its existence has been 
 known for many years, during which time the numerous attempts to exploit 
 it have always ended in failure. 
 
 An analysis of anthracite from the Cretaceous seam near Crested Butte, 
 Colo., and from the same formation at Madrid, N. Mex., are given in the 
 table on page 387. 
 
 Analyses of anthracite from Alaska will be found in the table on page 390, 
 from New Zealand in the table on page 391, and of the so-called anthracites 
 (more properly semianthracites) from Banff, Alberta, Canada, in the table on 
 page 388. 
 
372 FUELS 
 
 In the Pocono formation of the Subcarboniferous in the Sleepy Creek 
 and Third Hill Mountains of Berkley and Morgan Counties, W. Va., are 
 found a series of deposits of anthracite that are so irregular in thickness, uncer- 
 tain in area, and so crushed and otherwise disturbed as to be commercially 
 worthless. Their content 9f volatile matter is about 10%, which more properly 
 groups them with the semianthracites. 
 
 The so-called anthracites of Blacksburg, Montgomery County, W. Va., 
 an analysis of which is No. 105 of the table on pages 382 to 385, are really 
 semi-anthracites and commercially, are of but little more value than those 
 from Sleepy Creek Mountains, W. Va., or Cranston, R. I. 
 
 Semianthracite. Semianthracite contains from 7.5% to 12.5% of volatile 
 matter and passes by insensible gradations on the one hand into anthracite 
 and on the other hand into semibituminous coal. It is not so hard or dense 
 as true anthracite, is not so lustrous, and, when freshly broken, will leave 
 soot upon the hands, something anthracite will not do. It is somewhat 
 lighter than anthracite, ignites quite readily, and burns more freely than 
 hard coal. 
 
 A series of proximate analyses of Pennsylvania semianthracites mined in 
 the northward extension of the anthracite region is given in the table on 
 page 386. The average of eleven analyses of Semianthracite from Alaska will 
 be found in the table on page 390, and an analysis of this grade of coal from 
 Banff, Alberta, Canada, is given in the table on page 388. Several proximate 
 analyses of Semianthracite from Arkansas, and one from Virginia will be found 
 in the table on page 387, and complete analyses and calorific values of the 
 same in the table on pages 382 to 385. 
 
 Semibituminous Coals. The semibituminous coals containing from 12.5 
 to 25% of volatile matter, and, neglecting the ash and moisture, from 75 to 
 87.5% of fixed carbon are everywhere trie favorites for steam raising. Typical 
 examples are the well-known Pocahontas and New River coals of West Virginia, 
 the Georges Creek-Cumberland coal of Maryland, the Broad Top coals of 
 Pennsylvania, and the Kittanning coals of Cambria, Clearfield, and Somerset 
 Counties in the latter state. All these coals contain about 18% of volatile 
 matter, from 5% to 10% of ash and water and from 70 to 80% of fixed carbon, 
 with sulphur little if any over 1% and have a calorific value of 14,000 B. T. U. 
 per lb., in some cases even more. Some of the coals in this group are fairly 
 hard and blocky, a structure noticeable in those from the Pittsburg seam in the 
 Georges Creek-Cumberland and Broad Top regions, while others are very soft, 
 as typified in the P9cahontas and New River coals. The Kittanning coals 
 of Pennsylvania are intermediate between the Pocahontas and Georges Creek 
 in hardness. Containing more volatile matter than anthracite, these coals 
 kindle more readily and burn more rapidly with a steady fire. 
 
 Complete analyses and calorific values of these coals from Arkansas (so- 
 called Semianthracite) , Pennsylvania, Maryland, West Virginia, and Oklahoma 
 are given in the table on pages 382 to 385. Other, and shorter analyses of 
 these coals from Maryland, Pennsylvania, and West Virginia are given in the 
 table on page 387. Coals of this type from Alaska are -noted in the table on 
 page 390, and some foreign and Canadian semibituminous coals are listed in 
 the tables on pages 388 and 389, respectively. 
 
 Bituminous Coals. The bituminous coals include about 75% of the output 
 of the mines of the United States. Those produced in the eastern states contain 
 from 25% to a maximum of 40% of volatile matter, or, say, 30 to 32% as an 
 average. Those mined in the central basin and west thereof range as high as 
 50% in volatile matter, a general average being about 40%. The western 
 bituminous coals are generally characterized by a very much higher content 
 of water than their eastern namesakes, which frequently runs up to 10%, and 
 usually contain more sulphur. These coals vary from hard to soft and from 
 blocky to columnar in structure. Their specific gravity is normally about 1.3. 
 They burn with a yellow flame and much smoke, and, on distillation, yield 
 hydrocarbon oils, tar, etc. According to the use to which they are put or to 
 certain physical and chemical characteristics, theyare subdivided into numerous 
 groups. 
 
 Subbituminous Coals. The very convenient term subbituminous coals, 
 which originated with Dr. M. R. Campbell, of the United States Geological 
 Survey, is given to that large and valuable group of coals, that possesses some 
 of the undesirable features of the true lignites or brown-coals, together with 
 many of the desirable features of the true bituminous coals. They are some- 
 times called black lignites from their color, which is often highly lustrous and 
 not to be' distinguished from that of bituminous coals proper. They have a 
 
FUELS 373 
 
 brown streak and a specific gravity of 1.22 to 1.25. They burn with a long, 
 bright flame, with considerable smoke like bituminous coals but do not coke. 
 In composition and calorific power, they closely resemble and are, in some 
 cases, even superior to, the true bituminous coals of the Central Basin, as 
 will be seen by comparing the analyses, in the table on pages 382 to 385 of 
 subbituminous coal No. 14, from Lafayette, Colo., or Np. 125, from Hanna, 
 Wyo., with analysis No. 28, of bituminous coal from Livingston, 111., or with 
 No. 35, from Linton, Ind. 
 
 The distinction between the two groups lies in their different behavior on 
 weathering. True bituminous coals break down under atmospheric action 
 into smaller and smaller cubes or prisms, the faces of which are more or less 
 parallel to the cleavage planes (butt, face, etc.) of the coal in the bed. As 
 Doctor Campbell remarks, "Exception is to be noted, however, in the case of 
 cannel coal, splint coal, and many forms of block coal, of which the Brazil 
 block of Indiana may be considered the type. Such coals always show cleavage 
 faces on large blocks, but the blocks do not split readily. These coals generally 
 have other characteristics by which they may be identified without recourse 
 to their weathering properties." 
 
 On the other hand, subbituminous coal, on weathering, breaks up into 
 irregularly shaped fragments, and, in particular, separates along the bedding 
 planes into plates. This latter peculiarity is the sole distinction between -the 
 two groups of coals. To quote further from Doctor Campbell: "In applying 
 these criteria (weathering, etc.) some coals will be classed as bituminous which 
 have a brown streak, are young geologically, and generally have been regarded 
 as lignites or lignitic coals; but they resist the weather, stand shipment well, 
 and have a high calorific value, which makes them to all intents and purposes 
 bituminous coal." 
 
 Lignite. Primarily, the distinction between subbituminous coal and 
 lignite is one of color alone; the former is black and the latter brown. As the 
 subbituminous coals have been segregated from the lignites and given a dis- 
 tinctive name, the original term is now confined to the typical lignite, or brown- 
 coal. Lignites are generally inferior as fuels, compared to the subbituminous 
 coals, are usually higher in moisture and volatile matter and lower in fixed 
 carbon, usually show their vegetable origin more plainly, weather more rapidly, 
 and are less well adapted to transportation. It should be noted that many 
 subbituminous coals and lignites, even in the dry climate of the Rocky Moun- 
 tain region where they are largely mined, will completely disintegrate into 
 slack within 2 to 4 mo. 
 
 Bituminous coals, for trade purposes, are subdivided into many groups 
 with distinctive names, depending on the use to which they are put or to 
 which they are best adapted, or depending on some peculiarity of structure 
 or composition. Some of these varieties are here noted. 
 
 Gas Coals. The coals suitable for the manufacture of illuminating gas 
 in closed retorts by the destructive distillation of the coal itself without the 
 admission of either air or steam are termed gas coals. These coals yield the 
 original type of gas used for lighting, a type now quite largely superseded by 
 water gas made by forcing steam through incandescent anthracite or coke. 
 Probably the best, and, in any event, the earliest used gas coals in the United 
 States are those mined along the line of the Pennsylvania Railroad near Irwin 
 and along the Baltimore & Ohio Railroad on the Youghiogheny River, in 
 Westmoreland County, Pa. As there produced, these coals commonly contain 
 as much as 37% of volatile matter, from 6 to 8% of ash with considerably 
 less than 1% of sulphur, and being hard and blocky, bear transportation well. 
 Their yield is rather more than 10,000 cu. ft. of gas per T. of coal charged into 
 the retorts, the gas being of 17 to 21 c. p. The residual coke amounts to about 
 60% of the weight of the original coal and is shiny, fairly strong, and well 
 adapted to domestic purposes or steam raising. Their yield of nitrogenous 
 products, such as ammonia, is also high. These characteristics of Westmore- 
 land coal, particularly the low- content of sulphur, are those demanded of 
 standard gas coals. 
 
 Domestic Coals. The term domestic, as applied to coal, refers as much 
 to its size as to its composition or other features. In the anthracite consuming 
 sections of the eastern states, the domestic sizes are stove and chestnut adapted 
 to burning in ranges and small heaters, and egg suitable for use in furnaces. 
 In the bituminous regions, there is frequently sold a domestic lump, which 
 may mean a coal specially screened over bars, say, 3 in. apart, or it may refer 
 to coal that will pass over a 3-in. bar screen and through one with bars set, 
 say, 6 in. apart. In any case, coals for domestic use are well screened and 
 
374 FUELS 
 
 usually over bars much more widely spaced than those used in preparing coal 
 for steam raising. While it is true that domestic coals are classified more by 
 size than anything else, the possession of certain qualities will make one coal 
 more desirable than another for household purposes. The coal that sustains 
 a mild, steady combustion, and remains ignited at a low temperature with a 
 comparatively feeble draft, is the best. A coal burning with a smoky flame 
 is objectionable as producing much soot and dirt, especially for open grates or 
 cooking purposes. For self-feeding stoves, or for base burners, a dry non- 
 coking coal is necessary. A very free and fiercely burning coal is not desirable, 
 particularly in stoves, as the temperature cannot be easily regulated. A 
 sulphurous coal is also bad, as it produces stifling gases with a defective draft, 
 and corrodes the grates and fire-bowls. The difficulty from clinkering is not 
 so great in domestic uses, as the temperature is not generally high enough to 
 fuse the ash. A stony, hard ash that will not pass between the grate bars is 
 bad, and light pulverulent ash is best. 
 
 Blacksmith, or Smithing, Coals. A coal suitable for blacksmith purposes 
 should have a high heating power, should contain as much less than 1% of 
 sulphur as possible, should be low in ash, and should coke sufficiently to form 
 a hollow fire, that is, should form an arch on the forge. The semibituminous 
 coals from the Ne,w River and Pocahontas regions of West Virginia, that from 
 the Georges Creek-Cumberland district of Maryland, and the Broad Top (Hunt- 
 ingdon County) field of Pennsylvania, make excellent blacksmith coals as 
 mined. The slack of many coking coals, if washed to reduce the content of 
 sulphur (especially) and ash, serve excellently as smithing coal. The best 
 known blacksmith coal of the east and the one formerly used for this purpose 
 to the practical exclusion of all others is known by the name of Blossburg from 
 the town of that name in Tioga County, Pa., where it was first mined. An 
 average analysis of this coal (commercial sample) from the Morris Run mines, 
 wher.e the coal is at its best gave moisture, 1.12%; volatile matter, 18.57%; 
 fixed carbon, 72.10%; ash, 7.63%; and sulphur, .583%. It will be noted that 
 this is a semibituminous coal essentially the same as those already described. 
 
 Steam Coals In the Eastern states and where anthracite is concerned, 
 the term steam refers entirely to the size of the fuel. Thus, if (as noted under 
 that title) the domestic sizes of anthracite are chestnut, stove, and egg, the 
 steam sizes are smaller than these and include pea, buckwheat, barley, rice, 
 etc. The term steam coal is also often used to indicate any coal, anthracite 
 or bituminous, that is too poor to be used for any purpose except steam 
 raising; the idea being that anything that will burn is good enough to find 
 place in the firebox. 
 
 For steam making, the superiority of coals high in combustible constituents 
 is admitted, and those with the higher percentage of fixed carbon are the most 
 desirable. But the consideration of the steaming qualities of a coal involves, 
 also, a consideration of the form of furnace and of all the conditions of com- 
 bustion. The evaporative power of a coal in practice cannot be stated without 
 reference to the conditions of combustion, and every practical test of a coal, 
 to be thorough, should lead to a determination of the best form of furnace 
 for that coal, and should furnish knowledge as to what class of furnaces in 
 actual use such coal is specially adapted. It is not sufficient that in compara- 
 tive tests of coals the same conditions should exist with each, but there should 
 also be determined the best conditions for each coal. 
 
 Of coals high in fixed carbon, the semianthracites and the semibituminous 
 rank as high as the anthracite in meeting the various requirements of a quick 
 and efficient steaming coal. 
 
 For railway use, these coals have been found to excel anthracites in evapo- 
 rating power. The comparative absence, in semibituminous coals, of smoke, 
 which means loss of combustible matter as well as discomfort to the traveler, 
 is sufficient to suggest their superiority over bituminous coals for such use. 
 
 Steaming coal should kindle readily and burn quickly but steadily, and 
 should contain only enough volatile matter to insure rapid combustion. It 
 should be low in ash and sulphur, should not clinker, and when it is to be 
 transported should not easily crumble and break. 
 
 Coking Coals. Coking coals are those that become pasty or semiviscid 
 in the fire and produce, if the burning or heating is carried on with the partial 
 or entire exclusion of air and the process is not allowed to proceed too far, a 
 hard or porous mass known as coke, which consists, essentially, of the fixed 
 carbon and the ash of the original coal, the peculiar structure being due to 
 the escape from the partly melted mass of individual bubbles of gas driven off 
 by the heat. 
 
FUELS 375 
 
 Commercial coke making is carried on in firebrick structures known as 
 coke ovens, which are of two general and very distinct types. The original 
 form of oven and still the chief type used in the United States consists of a 
 hemispherical shell of firebrick into which air sufficient to burn the escaping 
 gases is admitted over the door during the coking process. This is called, 
 from the marked similarity in form, a beehive coke oven. The modern type, 
 called a retort oven, usually consists of a long (18 to 40 ft.) and narrow (18 to 
 30 in.) rectangular chamber placed like a book on edge, the height being 10, 12, 
 or more ft. In this chamber the coal is heated without access of air, the 
 process being analogous to the production of illuminating gas. Ovens of this 
 type are frequently called by-product ovens as they are well adapted to the 
 recovery from the gases of the tar, ammonia, etc., which are commonly wasted 
 in coking in the beehive oven. 
 
 Neither anthracite nor semianthracite on one end of the scale will coke, 
 nor will the subbituminous and lignite coals on the other. This limits the 
 possible possession of coking qualities to the semibituminous and bituminous 
 coals, ranging between 12.5 and 50% in volatile matter. In the United States, 
 those semibituminous coals so low in volatile matter as to approximate the 
 semianthracite in composition either will not coke at all or but very indiffer- 
 ently. The same is true at the other end of the scale of the bituminous coals 
 very high in volatile matter, as these coals in the Western states are almost 
 invariably non-coking. The difficulty in making any coke at all, or at best 
 but a very indifferent one, from Western bituminous coals seems to be due to 
 the large amount of water they contain. Probably 90 or 95% of American 
 coke is made from coal containing between 18 and 35% of volatile matter. 
 But all coals falling within these limits will not coke, and the reason why, of 
 two coals having essentially the same analytic composition, one should coke 
 and the other not, is a much disputed question. 
 
 Even if a coal will make some kind of a coke, whether this is of value or not 
 depends on the use to which it is to be put. For the manufacture of pig iron 
 in the blast furnace, the coke must be firm and tough and not dense, but with a 
 pronounced cellular structure and a hard cell wall. If the pig iron from the 
 blast furnace is to be used in the manufacture of steel by the Bessemer process, 
 the makers prefer a coke containing from 1 to 3% of volatile matter and 
 moisture combined, 10 to 12% of ash, and 89 to 85% of fixed carbon with 
 sulphur and phosphorus not over 1% and .02%, respectively. This is the 
 composition of the standard so-called Bessemer coke. Unfortunately, very 
 little coke is now obtainable that possesses both this purity and the proper 
 physical qualities. The objection to sulphur in the coke is that it enters the 
 iron and, not being removed in the Bessemer converter, remain^ in the steel, 
 which it makes red short or brittle when hot. Similarly, phosphorus is not 
 removed in this process, but it makes the steel cold short, or brittle when cold, 
 a very serious objection in structures subject to shock, as rails. Further, low- 
 phosphorus iron ores are becoming more and more difficult to obtain, so that 
 the lower the content of this impurity in the coke, the higher may it be in the 
 ore. If the pig iron is to be used for making steel by the basic open-hearth 
 process, phosphorus and to a less extent sulphur are not so objectionable in 
 the coke, as they are largely removed in the furnace. 
 
 For use in the foundry in the manufacture of castings, the coke should 
 possess the same physical qualities demanded of good blast-furnace coke, 
 but the percentage of both sulphur and phosphorus may be much higher. In 
 fact, many foundry managers prefer a high phosphorus coke, as the presence of 
 this element in the metal makes it very fluid when melted so that it readily 
 fills the smallest openings in the mold. It is generally demanded that coke 
 for foundry purposes shall be capable of melting 10 Ib. of iron per pound of fuel. 
 Such a result is not often obtained and in ordinary practice 1 Ib. of coke will 
 melt but 8 Ib. of iron. f 
 
 In smelting operations where the metals are recovered as matte (sulphide of 
 iron, etc.) large amounts of sulphur in the coke are not objectionable, as the 
 element is essential to the process. 
 
 For domestic use, it is desirable that the coke be hard so that it will bear 
 crushing and screening to the proper sizes and subsequent transportation to 
 market. The amount of sulphur and phosphorus in domestic coke is not of 
 great importance, but the percentage of ash should be as low as is consistent 
 with due strength, and the ash should not clinker. 
 
 From the foregoing, it is evident that a coal that will make a coke suitable 
 for one purpose will not make a coke suitable for another. The fusibility of 
 the carbon, the amount of disposable hydrogen, the tenacity with which the 
 
376 FUELS 
 
 gaseous constituents are held, the amounts of sulphur and phosphorus in the 
 coal, the rapidity and temperature of the coking process, the state of the coal 
 when charged into the oven (whether as run of mine or slack), even the process 
 itself, all affect in one way and another the physical and chemical qualities of 
 the coke and, consequently, the use to which it is best adapted. More or less 
 weathered coal from near the outcrop will not make as good coke as that mined 
 under more cover; many coals that will coke but indifferently as run of mine 
 coke excellently in the fine state; and others, which make a poor showing in 
 the beehive oven, are well adapted to use in retort ovens. 
 
 Ordinary analyses do not indicate whether or not a coal is a good coking 
 coal, and they indicate simply by giving the amount of carbon, ash, and sul- 
 phur, what will be the probable purity of the coke formed. To produce a stand- 
 ard Bessemer coke in the beehive oven, the typical coal has essentially the 
 analysis of No. 18, of the table on pages 382 to 385, mined from the Pittsburg 
 seam in the Connellsville region of Pennsylvania. Other analyses of this seam 
 show the volatile matter to be as high as 32%, with the fixed carbon, ash, and 
 sulphur as low as 59%, 7%, and .5%, respectively. Coals having analyses 
 that differ materially from this give most excellent cokes that are in every way 
 equal to that from the Connellsville region. As illustrations of this may be 
 cited the cokes made from the semibituminous coals from the New River and 
 Pocahontas fields of West Virginia, which coals contain only about 18% of 
 volatile matter, as well as coke made from the coal mined from the Freeport 
 seam, which often contains over 35% of volatile matter. Coke made from 
 coals containing less than 5 or 6% of ash, while pure, is not generally desirable 
 as blast-furnace fuel , as it lacks the strength to support the burden, and break- 
 ing up before burning tends to be blown out the stack by the blast. It must 
 be remembered that coals that will not yield a satisfactory coke from either 
 the chemical or physical view point in the beehive oven, often will do so in 
 the retort oven. Thus, when investigating the coking qualities of the coal 
 from any field carload lots should be shipped to both beehive and retort oven 
 plants for tests under actual working conditions. 
 
 Yield of Coke. There are several methods used by field engineers in 
 arriving at an estimate of the quantity and quality of coke that a given coal 
 will produce. It is obvious that if there is no loss of fixed carbon in the proc- 
 ess, all this element will be in the coke together with all the ash. In the 
 Connellsville region, it is found that about 40% of the sulphur is volatilized, 
 60% remaining in the coke. With this understanding, what is called the 
 theoretic coke obtainable from a coal such as No. 85 from Connellsville may 
 be figured as follows: 
 
 ; '-r* Original Remaining Analysis 
 
 Coal in Coke of Coke 
 
 Moisture 97 
 
 Volatile matter 29.09 
 
 Fixed carbon 60.85 60.85 87.00 
 
 Ash 9.09 9.09 13.00 
 
 100.00 69.94 100.00 
 
 Sulphur, separate 90 X .60 .54 .77 
 
 The figures in the third column are arrived at by dividing those in the 
 second column by .6994, which figure is often spoken of as the theoretic yield 
 and which means simply, that the coal in question should yield under perfect 
 conditions 69.94% of its weight as coke, which should have the composition 
 given in the third column. These results agree very closely with those obtained 
 in actual practice in the Connellsville region; in fact, there is frequently a 
 greater yield than the theoretic one due to the deposition of carbon in the pores 
 of the coke during the process. 
 
 Many engineers assume that under average conditions 1.5 T. of coal are 
 required to make 1 T. of coke, and that there is enough sulphur volatilized 
 to insure that the percentage of this impurity in the coke shall not exceed that 
 in the original coal. Using the foregoing coal, the figures follow: 
 
 Analysis 
 of Coke 
 Per Cent. 
 
 Ash in coke 9.09X1.5= 13.63 
 
 Fixed carbon by difference 100.00- 13.63 = 86.37 
 
 100.00 
 Sulphur, separate 90 
 
FUELS 377 
 
 As the coking process, in the beehive oven at least, is by no means a per- 
 fect one, the analysis will be affected by the volatile matter in the coke due to 
 imperfect burning and to the moisture resulting from watering down the charge. 
 The sum of these should not exceed 2% in fairly good practice. 
 
 Either of the foregoing methods of estimating the yield and composition 
 of coke 'give good results if the coal contains enough volatile matter to furnish 
 the necessary heat for the coking process. It fails in the case -of the semi- 
 bituminous coals, as a certain amount of their fixed carbon is burned in sup- 
 plying the heat for the coking operation. Using the analysis of Pocahontas 
 coal, the theoretic yield of coke is, of course, the sum of the fixed carbon 
 and ash or 73.87 + 5.25 = 79.12%, and its composition, using the first method 
 given, should be, fixed carbon, 93.36%; ash, 6.64%; and sulphur (separately) 
 .48%. But it is found that the yield in the beehive oven from coals of this 
 type is commonly about 63% of the weight of the coal charged. Because all 
 the ash remains in the coke and the fixed carbon alone is consumed, using a ton 
 of 2,000 Ib. as a basis, the composition of the coke is as follows: 
 
 2,000 Ib. of coal yields 2.000X. 6300= 1,260 Ib.; fixed carbon+ash 
 2,000 Ib. of coal yields 2,000 X. 0525= 105 Ib.; ash 
 2,000 Ib. of coal yields 1,260-105 = 1,155 Ib.; fixed carbon 
 Hence, 2,000 Ib. of coal will yield 63%, or 1,260 Ib., of coke, which con- 
 tains 1,155 Ib., or 91.67%, of fixed carbon and 105 Ib., or 8.33%, of ash. The 
 sulphur may be estimated to be from .64 as in the coal to .48% as determined 
 by the first method. 
 
 If the coal is coked in a retort oven, the yield of coke will exceed the theo- 
 retic, and a fair average may be taken as 78% of the weight of the charge. 
 Using the Connellsville coal mentioned,' the yield and composition of coke in a 
 retort oven will be about as follows: 
 
 2,000 Ib. of coal yields 2.0QOX. 7800 = 1,560 Ib.; fixed carbon+ash 
 2,000 Ib. of coal yields 2,000 X. 0909= 182 Ib.; ash 
 2,000 Ib. of coal yields 1,560-182 = 1,378 Ib.; fixed carbon 
 Hence 2,000 Ib. of coal will yield 78%, or 1,560 Ib.. of coke, which contains 
 1,378 Ib., or 88.33%, of fixed carbon and 182 Ib., or 11.67% of ash. It is 
 apparent that coking in a retort oven gives more and better coke than coking 
 in the beehive oven. The increased output is particularly noticeable in coking 
 semibituminous coals. 
 
 Of the total coke produced in the beehive oven, between 95 and 96% will 
 be of large size suitable for shipment to any market; 3 to 4% will be fine or 
 small coke (breeze or braise) which may be separated from the ash by screen- 
 ing and sold for domestic use; and about 1% of ashes, which is usually worth- 
 less but is sometimes ground and used for foundry facings. The foregoing 
 represents what may be called Connellsville practice; if semibituminous coal 
 is used, the resultant coke is softer and the amount of fine coke and ashes is 
 considerably greater. 
 
 Pishel's Test for Coking Qualities of Coal. There has recently been 
 developed, by Mr. Max. A. Pishel, a simple field test for determining the 
 coking or non-coking properties of coals which should have extensive 
 application. As described by Mr. Pishel in the columns of the Colliery 
 Engineer, the procedure is: "Pulverize in a mortar a small quantity of the 
 coal to be tested until it will pass through a 100-mesh sieve. Pour out the 
 loose material and note the amount that adheres to the mortar. With 
 some coals, the mortar and pestle will be deeply coated with coal dust that 
 adheres so strongly that it can be removed with difficulty; with other coals, 
 there will be only a thin film of coal dust adhering to the mortar and pestle; 
 while with still others both mortar and pestle will be nearly as clean after the 
 operation is completed as they were before it began. The degree of adhesion 
 depends on the grade of the coal with" reference to its coking qualities. If it 
 adheres strongly, the coal will make a good coke; if it adheres only partly, 
 the coal will make an inferior grade of coke; and if it does not adhere, the coal 
 is non-coking." Porcelain, glass, earthenware, iron, or agate mortars may be 
 used, the desideratum being that the material is hard and smooth. The results 
 may be obtained as well with a small mortar that may be carried in the pocket 
 as with a large one. 
 
 The structure of the coal in the bed affords some clue to its coking quali- 
 ties; at least, it has been often noted that where the Pittsburg and Freeport 
 seam coals, as well as those from the Pocahontas and New River districts, 
 make a good coke, the coal shows a distinct columnar structure and tends to 
 break out of the bed in long prisms or fingers. 
 
378 FUELS 
 
 Non-Coking Coals. The term non-coking coals is applied to those bitu- 
 minous coals that do not coke even when highly heated but which retain the 
 shape of the original lump until reduced to ashes. There are numerous varieties 
 known by distinctive names, and all are valuable domestic fuels. 
 
 Fat and Dry, or Lean, Coals. Fat coals are those that possess a large 
 amount of volatile matter and consequently burn with a long oily flame. Dry, 
 or lean, coals are, obviously, the reverse of fat coals and burn with short flame 
 and little smoke. Cannel coal affords an illustration of the first and Poca- 
 hontas of the second of these groups. 
 
 Free-Burning Coal. The term free-burning is applied to those coals that 
 burn easily with a light draft. The term is rather loosely used, being applied 
 by some to non-coking coals, by others to semibituminous coals as opposed 
 to anthracite, and by still others to coals containing a larger amount of volatile 
 matter. 
 
 Cannel Coal. Cannel coal is a variety of bituminous coal that is very rich 
 in volatile matter, which makes it a very valuable gas coal. It kindles readily 
 and burns with a dense smoky flame. It is compact, with little or no luster and 
 without any appearance of banded structure, breaking with a conchoidal 
 fracture. Its content of volatile is commonly about 50%, its color is dull 
 black to grayish black, and its specific gravity is about 1.23. Certain varieties 
 show what appear to be small concretions about the size of a dime scattered 
 over the surface of a fresh fracture; these are called birds-eye cannel from the 
 fancied resemblance of these structures. The name cannel coal is a corruption of 
 the term candle coal given to it because long splints of it readily ignite and burn 
 with a long flame, spitting and sputtering like a candle burning in a draft. 
 It was at one time a popular grate fuel but, although extensive deposits exist, 
 is now little mined. 
 
 Splint Coal. Splint coal has a dull black color, and is much harder and less 
 breakable than ordinary bituminous coal. It is readily fissile, like slate, but 
 breaks with difficulty on cross-fracture. It ignites less readily than ordinary 
 bituminous coal, but makes a hot fire, and is a good house coal, although its 
 content of ash is usually high. Both it and cannel coal, while occurring in 
 distinct seams, are very commonly found as a layer or layers interstratified 
 in seams of ordinary coal. 
 
 PROXIMATE ANALYSIS OF COAL 
 
 The following is the outline of the method recommended for the proximate 
 analysis of coal by a committee of the American Chemical Society, Messrs. 
 W. F. Hillebrand, C. B. Dudley, W. A. Noyes. 
 
 Sampling. At least 5 Ib. of coal should be taken for the original sample, 
 with care to secure pieces that represent the average. These should be broken 
 up and quartered down to obtain the smaller sample, which is to be reduced 
 to a fine powder for analysis. The quartering and grinding should be carried 
 out as rapidly as possible, and immediately after the original sample is taken, 
 to prevent gain or loss of moisture. The powdered coal should be kept in a 
 tightly stoppered tube, or bottle, until analyzed. Unless the coal contains 
 less than 2% of moisture, the shipment of large samples in wooden boxes 
 should be avoided. 
 
 In boiler tests, shovelfuls of coal should be taken at regular intervals and 
 put in a tight covered barrel, or some air-tight covered receptacle, and the 
 latter should be placed where it is protected from the heat of the furnace. 
 
 In sampling from a mine, the map of the mine should be carefully exam- 
 ined and points for sampling located in such a manner as to represent fairly 
 the body of the coal. These points should be placed close to the working face. 
 Before sampling, a fresh cut of the face should be made from top to bottom 
 to a depth that will insure the absence of possible changes or of sulphur 
 and smoke from the blasting powders". The floor should be cleaned and a 
 piece of canvas spread to catch the cuttings. Then, with a chisel, a cutting 
 from floor to roof, say 3 in. wide and about 1 in. deep should be made. The 
 shale or other impurities that it is the practice at that mine to reject should not 
 be chiseled out, however. The length of the cutting made should then be 
 measured, but the impurities should not be included in this measurement. 
 With a piece of flat iron and a hammer, all pieces should be broken to $-in. 
 cubes or less, without removing from the cloth, then quartered, and trans- 
 ferred to a sealed bottle or jar. For the " run-of-mine " sample, samples taken 
 at several points in this manner should be mixed and quartered down. If the 
 vein varies in thickness at different points, the samples taken at each point 
 should correspond in amount to the thickness of the vein. For instance, a 
 
FUELS 379 
 
 small measure may be filled as many times with the coal of the sample as the 
 vein is feet in thickness. Should there appear differences in the nature of the 
 coal, it will be more satisfactory to take, in addition to the general sample, 
 samples of such portions of the vein as may display these differences. 
 
 Moisture. Dry 1 g. of the coal in an open porcelain or platinum crucible 
 at 104 to 107 C. for 1 hr., best in a double- walled bath containing pure 
 toluene. Cool in a desiccator and weigh covered. 
 
 Volatile Combustible Matter. Place 1 g. of fresh, undried coal in a platinum 
 crucible weighing 20 to 30 g., and having a tightly fitting cover. Heat over 
 the full flame of a Bunsen burner for 7 min. The crucible should be supported 
 on a platinum triangle with the bottom 6 to 8 cm. above the top of the burner. 
 The flame used should be fully 20 cm. high when burning free, and the determi- 
 nation made in a place free from drafts. The upper surface of the cover should 
 burn clear but the under surface should remain covered with carbon. To 
 find volatile combustible matter, subtract the percentage of moisture from the 
 loss found here. 
 
 Ash. Burn the portion of coal used for the determination of moisture at 
 first over a very low flame, with the crucible open and inclined, until free from 
 carbon. If properly treated, this sample can be burned much more quickly 
 than the dense carbon left from the determination of volatile matter. 
 
 Fixed Carbon. The fixed carbon is found by subtracting the percentage 
 of ash from the percentage of coke. 
 
 Sulphur (Eschka's Method). Mix thoroughly 1 g. of the finely powdered 
 coal with 1 g. of magnesium oxide and 5 g. of dry sodium carbonate, in a thin 
 75 to 100 c. c. platinum dish or crucible. The magnesium oxide should be 
 light and porous, not a compact, heavy variety. Heat the dish on a triangle 
 over an alcohol lamp, held in the hand at first; gas must not be used, because 
 of the sulphur it contains. Stir the mixture frequently with a platinum wire 
 and raise the heat very slowly, especially with soft coals. Keep the flame in 
 motion and barely touching the dish, at first, until strong glowing has ceased, 
 and then increase gradually until, in 15 min., the bottom of the dish is at a low 
 red heat. When the carbon is burned, transfer the mass to a beaker and 
 rinse the dish, using about 50 c. c. of water. Add 15 c. c. of saturated bromine 
 water and boil for 5 min. Allow to settle, decant through a filter, boil a second 
 and a third time with 30 c. c. of water, and wash until the filtrate gives only 
 a slight opalescence with silver nitrate and nitric acid. The -volume of the 
 filtrate should be about 200 c. c. Add 1| c. c. of concentrated hydrochloric 
 acid, or a corresponding amount of dilute acid (8. c c. of an acid of 8%). Boil 
 until the bromine is expelled, and add to the hot solution, drop by drop, especi- 
 ally at first, and with constant stirring, 10 c. c. of a 10% solution of barium 
 chloride. Digest on the water bath, or over a low flame, with occasional 
 stirring" until the precipitate settles clear quickly. Filter and wash, using 
 either a Gooch crucible or a paper filter; the latter may be ignited moist in a 
 platinum crucible, using a low flame until the carbon is burned. 
 
 In the case of coals containing much pyrites or calcium sulphate, the 
 residue of magnesium oxide should be dissolved in hydrochloric acid and the 
 solution tested for sulphuric acid. 
 
 When the sulphur in the coal is in the form of pyrites, that compound is 
 converted almost entirely into ferric oxide in the determination of ash, and, 
 as three atoms of oxygen replace four atoms of sulphur, the weight of the ash 
 is less than the weight of the mineral matter in the coal by five-eighths the 
 weight of the sulphur. While the error from this source is sometimes con- 
 siderable, a correction for proximate analyses is not recommended. When 
 analyses are to be used as a basis for calculating the heating effect of the coal, 
 a correction should be made. 
 
 FORMS OF REPORTING ANALYSES 
 
 The proximate analysis of a coal may be reported in one of several ways. 
 
 An analysis designated as received refers to the fact that the sample received 
 no preliminary drying before analysis and usually represents the coal exactly 
 as mined or as loaded on the railroad car, etc. 
 
 An analysis marked as fired refers to the fact that the sample for analysis 
 was taken from the fuel in the boiler room, usually at the time of a test, and 
 represents the coal as fired into the furnace. 
 
 An analysis denoted air dried refers to the fact that the sample was dried 
 at a uniform temperature, usually the standard one of 62 F., for a number of 
 hours before being analyzed. 
 
380 
 
 FUELS 
 
 In the first two cases, the moisture in the sample is commonly reported 
 as moisture, or water, although the temperature at which the water is driven 
 off is sometimes given. Thus, there are such expressions as "moisture at 
 212," or "at 100," "at 221," or "at 105," depending on the temperature 
 and thermometric scale employed. 
 
 In the third case, the water is reported in two parts. The first, which rep- 
 resents the difference in the amount of water in the sample as received and after 
 being dried in the laboratory at 62 F. is known as air drying loss, or as loss on 
 drying. The second part represents the difference between the water in the 
 air-dried sample and that given off on heating at 105 C. This is commonly 
 reported as explained in connection with the first two cases, the temperature 
 usually being stated. 
 
 An analysis reported moisture free, or as of dry coal, is one in which the sum 
 of the percentages of fixed carbon, volatile matter, and ash equal 100. The 
 moisture is reported as a separate item like the sulphur, and usually as, say, 
 "moisture at 105 C." 
 
 An analysis reported as dry and free from ash, or as ash and moisture free, 
 and even, although wrongly, as pure coal, is one in which the percentages of 
 fixed carbon and volatile matter equal 100, the moisture and ash being reported 
 separately. 
 
 Analyses reported in one form may readily be reduced to another. A 
 proximate analysis made on a sample as received, as fired, or air-dried, may be 
 reduced to a moisture-free basis by dividing each of the constituents, except 
 the moisture, by 100 - moisture. If it is desired to reduce the analysis to a 
 moisture- and ash-free basis, all the constituents except the moisture and ash, 
 which are dropped, are divided by 100 (moisture + ash). These divisors are 
 applicable to the sulphur and calorific value (British thermal units) as well. 
 
 An ultimate analysis may, also, be reduced from the as received to the 
 moisture free, or to the ash- and moisture-free basis by using the same divisors 
 as before, provided the amount of moisture in the coal is known. The ash, 
 sulphur, carbon, and nitrogen are divided in the regular way, but from the 
 hydrogen must be deducted one-ninth of the moisture and from the oxygen, 
 eight-ninths of the moisture. 
 
 COAL 114 FROM SEWELL SEAM, McDONALD, W. VA. 
 
 
 
 IH (U 
 <g 
 
 Divisor 
 
 Moisture 
 Free 
 
 1 
 s 
 
 Ash and 
 Moisture 
 Free 
 
 
 Moisture 
 Volatile matter . . 
 
 .68 
 23.28 
 
 .9932 
 
 23.43 
 
 .9418 
 
 24.71 
 
 4J M 
 
 
 70.91 
 
 .9932 
 
 71.40 
 
 .9418 
 
 75.29 
 
 gl 
 
 Ash 
 
 5.14 
 
 .9932 
 
 5.17 
 
 
 
 P3 
 
 Total 
 
 100.00 
 
 
 100.00 
 
 
 100.00 
 
 ft* 
 
 
 
 
 
 
 
 
 Sulphur, separate 
 
 91 
 
 .9932 
 
 .92 
 
 .9418 
 
 .97 
 
 
 
 
 
 
 
 
 
 Carbon 
 
 83 56 
 
 .9932 
 
 84.13 
 
 .9418 
 
 88.71 
 
 
 Hydrogen ( - moisture) 
 Nitrogen 
 Oxygen ( f moisture) 
 
 4.66 
 1.60 
 4 13 
 
 .9932 
 .9932 
 .9932 
 
 4.62 
 1.61 
 3.55 
 
 .9418 
 .9418 
 .9418 
 
 4.86 
 1.70 
 3.74 
 
 a '35 
 
 Sulphur 
 
 91 
 
 9932 
 
 .92 
 
 .9418 
 
 .97 
 
 6^ 
 
 Ash 
 
 5 14 
 
 9932 
 
 5 17 
 
 
 
 11 
 
 
 
 
 
 
 
 b<! 
 
 Total 
 
 100 00 
 
 
 10000 
 
 
 100.00 
 
 
 
 
 
 
 
 
 
 Calorific power 
 
 14,765 
 
 .9932 
 
 14,866 
 
 .9418 
 
 15,680 
 
FUELS . * 381 
 
 The calculation shown in the table on page 380 is made upon a typical coal 
 from the New River field, No. 114 of the table on pages 382 to 385, mined from 
 the Sewell seam, at McDonald, W. Va. The second C9lumn contains both the 
 proximate and the ultimate analyses and the calorific value, or power, in 
 British thermal units per pound. The divisor in the third column is obtained 
 by deducting the moisture from 100 and dividing by 100, or divisor = (100 
 
 .68) -T- 100 = .9932. By dividing all the figures in the second column by this 
 divisor, those in the fourth column are obtained, and these represent the 
 composition of the coal on a moisture-free, or dry-coal basis. The second 
 divisor, that in the fifth column, is obtained by deducting the sum of the 
 moisture and ash from 100 and dividing the result by 100, or divisor = (100 
 
 .68 5. 14) -T- 100 = .94 18. The figures in the second column (as before) 
 excepting the ash and moisture if divided by this factor will give the figures 
 in the sixth column, which represent the composition of the coal on an ash- 
 and moisture-free, or on the dry-and-free-from-ash basis. 
 
 In dealing with the ultimate analysis, before applying either divisor, there 
 must be deducted from the hydrogen and oxygen one-ninth and eight-ninths, 
 respectively, of the moisture (.68) as given in the proximate analysis. The 
 two dividends will be, respectively, 4.66 (.68-7-9) =4.5844, and 4.13 (.68 -5- 9) 
 X8 = 3.5256. 
 
 Should it be desired to give the percentage of moisture on a moisture-free 
 basis, that is, as a separate determination similar to the sulphur, it may be 
 obtained by dividing the moisture in the original sample by the factor in the 
 third column, or moisture, separately determined = . 68 -4-.. 9932 = .684. If the 
 moisture and ash are desired on the ash- and moisture-free basis, they may be 
 had by dividing the percentage of these constituents in the second column by 
 the divisor in the fifth column, and are, respectively, .68-7- .94 19 = .72, and 
 5. 14 -T- .94 19 = 5.45. 
 
 ANALYSES OF TYPICAL COALS 
 
 The table on pages 382 to 385 gives the proximate and the ultimate analyses 
 and the calorific values, in British thermal units per pound, of a number of 
 typical American coals, selected largely from the Reports of the Fuel Testing 
 Plant at the St. Louis Exposition of 1904. Other anaylses are taken from 
 various reports of the United States Geological Survey and the United States 
 Bureau of Mines. Except as noted, all the analyses and heat determinations 
 represent carload lots and were made on samples air-dried at the same temper- 
 ature. For this reason, the relative values of the different coals are indicated 
 by their calorific power as given in British thermal units. . The exceptions are: 
 The proximate and the ultimate analyses and the heating values of coals 105, 
 110, and 111 were made upon samples marked "as received"; that is, the pre- 
 liminary air-drying was omitted, and the analyses indicate more moisture and 
 a lower calorific value in these coals than if they had been air-dried. Also, 
 the ultimate analyses, but not the calorific values, of coals 15, 16, 17, 18, and 
 19, were made upon samples as received. 
 
 In the column headed Kind, A = anthracite; B= bituminous; B. L. = black 
 lignite, the subbituminous coal of the United States Geological Survey; G. A. 
 = graphitic anthracite; L = lignite, the true lignite or brown coal; P = peat; 
 S. A. = semianthracite; S. B. = semibituminous. 
 
 In the column headed Grade, L = lump; N = nut; P = pea; R = run of mine; 
 S=^lack or culm. L. N. refers to a mixture of lump and nut; S. N. refers to a 
 mixture of slack and nut; and, similarly, for other combinations of the letters. 
 
 In the proximate analyses, the sums of the moisture, volatile matter, fixed 
 carbon, and ash should equal 100%. The sulphur is separately determined. 
 In the ultimate analyses, the sums of the carbon, hydrogen, nitrogen, oxygen, 
 sulphur, and ash should equal 100%. 
 
 In the table on page 386 is given a series of proximate analyses of Penn- 
 sylvania anthracite and semianthracite. Those marked C were made on 
 samples of the coal as received or as fired, and represent a series of monthly 
 or semimonthly shipments, usually extending over a year and in some cases 
 aggregating 15,000 T. in weight. They were made with great care in order 
 to determine the proper price to be paid for the coal, which was sold on analysis. 
 The analyses marked D were made on air-dried samples previously collected 
 in the mine by breaking down a full section of the working face. In all cases, 
 regardless of the origin or preliminary treatment of the sample before analysis, 
 the calorific values were determined on air-dried samples. 
 
 In the table on page 387, there is given a series of proximate analyses and 
 calorific values of some important coals not contained in the table on pages 
 
382 
 
 FUELS 
 
 R 
 
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 M 
 
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FUELS 383 
 
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 tOlNCOCO rt< i-l CO 00 Oi CO CO CT> O5 O i-l O CO CO IN iO O CO OS * >O O5 O5 Tjn IN l> t- O 
 
 i >OCO O t- 
 
 q o> <*oococo<N_o 
 
 rH C\i CDi-HOd'-5o 
 
 CO >O COOCO^QCQi 
 
 OOiO t^ OfNOSCOOO'O * O< 
 (Ni-I> CO <NiOC5>O-^HO rH TlHl 
 
 iMCO'-icOC3iCOi-t(Mi-lCOOO 
 
 t^t>-OTt< t CO i-l Ttl O5 IN (M i-H iOO'-lO001>C 
 
 coqiNcp oq t^iqt^ciiNio q N>oi>.o6qNO.. 
 
 O5i-5cor-i 06 to CD -5 06 -5 rjJ d -5 >o co co t> cd co co o i> 06 >o co 06 o> os >o * 06 >o 
 
 COTj<T}<Tt< CO ^^T><CO-^Ti< tp >O Tft IQ T^I tp -^ T}< r}< >O Tt< IQ >Q 1> CO CO CO CO -^ CO -^ 
 
 IClOt^^H 1C CO<l(N<H>rH ^4 O05lOOO05O0005OCOO>Tj<^HCOTt<(N^H^CO 
 
 Tjjooqco oo oot>-qo5(Ni> *-t oo co co q o os o> q os q q * rn T-H us co rn o; * co 
 
 ICCOINCO CO t>rH|>dl^lN CO COOi'-HlvcdoOCDcddiOCDCDOOcd'^COOJ^iOIN 
 
 COCOCOCO IM COCOCO'^COCO CO CO IN CO CO CO CO CO CO CO CO CO CO rH i-l CO CO IN Tt< Tft CO 
 
 O * O l> (N O O TJH CD O O <N Tj* CO TtN CO CT> Oi CO 
 
 03 
 
 CO ^ 
 
 PQPQ 
 
 pq pqpqpqpqpqpq pq pqpqpqpqpqpqfqpqpqpqpqpq . . pq fq pq pq pq ,_) 
 
 I I 
 g5 jggg g a 
 
 ^ z 
 
 .5^5 0000 
 
 rHCNWH IO COt^OOOSO--! <N CO rj< 10 CO t^ 00 O> O i-< CN CO * iO CO t^ 00 O> O ^ IN 
 COCOCOCO CO COCOCOCO^Tt< T^ rt ^ Tj< ^ rti rj< T}< O O O O O tO O "5 iO O CO CO CO 
 
384 
 
 FUELS 
 
 r4(N r-T rHO> O> CO CO"HrH 
 
 
 cQpg.cQ.pq.pQ-<3 
 
 os 3* 3 
 
 I 
 
 
FUELS 385 
 
 id^^^t^oidr)5iotdTi5(x5^dNNtO(x3do6toT)5iodTjHdo6odt^di>i>cocico 
 
 iO to r^ >O CO IO rj5 tQ tQ ^ Tji to to ^ tQ TJ^ -^ lOiO^H^iOTJHtfjtOtOTjH 
 
 Si^i^8^2isSi^^gS^S^S5feS^Si^ 
 
 <N 06 cd * to -<^ ci co oJ 06 o IN' t>^ vi *$ to 06 d *-* to oi d d <N rj5 <>i <N' N" -i to oi t <N r-J t^ co oi 
 
 'lOi 
 
 ...pq....h-3 pq.pcjpq hjt-j.ij^ 
 
 pq pq pq pq pq pq j i-4 >-l oq .pq<pqpq .pqpqpqprpq .pq . . pq pq pq pq pq pq pq . .pq . . 
 w pq c/2 coco pqpq pqpq 
 
 i 2-S ciow'v^-i 
 
 d d w w 
 
 
 
 d O 0,0 
 
 ..... !>'>!>J>'t>>J>!>i>J>i>i> , 
 
 25 
 
386 FUELS 
 
 PROXIMATE ANALYSES AND HEATING VALUES OF PENNSYLVANIA 
 ANTHRACITES 
 
 (United States Bureau of Mines) 
 
 
 
 
 Moisture 
 
 Volatile 
 Matter 
 
 ll 
 
 &CJ 
 
 1 
 
 1 
 
 1 
 
 t> 
 H 
 PQ 
 
 
 Morea broken 
 
 c 
 
 338 
 
 4.86 
 
 8245 
 
 9 31 
 
 60 
 
 13 057 
 
 
 Deringer, egg 
 
 c 
 
 3.67 
 
 5.29 
 
 81.42 
 
 9 62 
 
 .66 
 
 13,009 
 
 
 Kingston, grate 
 
 c 
 
 3.34 
 
 4.74 
 
 81.08 
 
 10 84 
 
 65 
 
 12,717 
 
 
 Wilkes-Barre, screenings. . 
 Nanticoke, barley 
 
 c 
 c 
 
 4.17 
 5.45 
 
 5.95 
 8.43 
 
 79.02 
 72.12 
 
 10.86 
 14 00 
 
 .70 
 64 
 
 12,654 
 12,045 
 
 
 Mid Valley, pea 
 
 r 
 
 395 
 
 7.38 
 
 72 85 
 
 15 82 
 
 92 
 
 11 989 
 
 1 
 
 Deringer, pea 
 Pittston, pea . ... 
 
 C 
 r 
 
 5.11 
 3 62 
 
 4.99 
 5.82 
 
 74.87 
 7340 
 
 15.03 
 17 16 
 
 .62 
 
 82 
 
 11,831 
 11 798 
 
 1' 
 
 Mt. Hope, mammoth 
 screenings 
 
 r 
 
 560 
 
 6.61 
 
 71 62 
 
 16 17 
 
 75 
 
 11 581 
 
 c 
 
 Newcastle, pea 
 
 r 
 
 4.93 
 
 5.21 
 
 72.96 
 
 1690 
 
 .65 
 
 11,574 
 
 < 
 
 Schuylkill, rice 
 
 r 
 
 507 
 
 4.99 
 
 71 58 
 
 18 32 
 
 75 
 
 11 382 
 
 
 Pittston, No. 2 buckwheat 
 Girard, mammoth, buck- 
 wheat 
 
 C 
 
 r 
 
 5.93 
 6 21 
 
 6.72 
 564 
 
 70.35 
 70 70 
 
 16.80 
 17 45 
 
 .95 
 56 
 
 11,359 
 11 141 
 
 
 Mt. Hope, barley 
 Tower City, Lykens Valley 
 Bernice egg 
 
 C 
 
 r 
 
 6.55 
 3.33 
 2 12 
 
 5.26 
 3.27 
 8 80 
 
 70.83 
 
 84.28 
 73 43 
 
 17.36 
 9.12 
 15 65 
 
 .69 
 .60 
 58 
 
 11,132 
 13,351 
 12 575 
 
 .-tt 
 
 Bernice, Randall & Shaad 
 mine . 
 
 p 
 
 50 
 
 9 go 
 
 7790 
 
 12 03 
 
 83 
 
 13 510 
 
 1 
 
 Bernice, O'Boyle & Fay 
 mine 
 
 p 
 
 60 
 
 9 50 
 
 77 40 
 
 12 49 
 
 1 41 
 
 13 425 
 
 1 
 
 Bernice, Connell mine 
 Lopez, Northern Anthra- 
 cite Company 
 
 D 
 p 
 
 .70 
 .60 
 
 8.65 
 9.10 
 
 76.75 
 7895 
 
 13.90 
 11 35 
 
 .66 
 65 
 
 13,185 
 13 605 
 
 1 
 
 Loyalsock 
 
 
 1.49 
 
 11.07 
 
 78.88 
 
 7.09 
 
 .86 
 
 
 382 to 285. Those analyses marked C are of commercial lots delivered to the 
 various government departments and represent the coal as received or, as 
 fired. The analyses marked D were made from air-dried samples; in some 
 cases they represent carload lots, and in others they are samples taken in the 
 mine. The calorific values were determined upon air-dried samples except 
 those given in italics, which were calculated from the analysis by means of 
 Kent's formula. The analyses that are not marked with a C or a D are 
 believed to represent air-dried samples, but those reporting them failed to 
 state the facts in the case. 
 
 One of the accompanying tables gives a series of analyses of Alaskan coals 
 taken from the reports of the United States Geological Survey. Among them 
 are three analyses of coals from the Yukon Territory of Canada. The report 
 does not state whether the analyses are of air-dried or as-received samples; 
 judging from the amount of water in some specimens, it is presumed that they, 
 at least, were of samples as received. The sulphur is separately determined. 
 
 A series of proximate analyses of foreign coals, many of which are used on 
 the Pacific coast of the United States, is given in the table on page 391. 
 JLhe sample of coal from Argentine and the one from Rio Grande do Sul, 
 Brazil, were tested at the United States Fuel Testing Plant, St. Louis, Missouri. 
 They were treated in the same way as the samples of American coal given in 
 the table on page 387. These two analyses are of air-dried samples and the 
 heating values are 6.320 and 9,058 B. T. U., respectively. The heating value 
 of the Victoria coal from Windmill shaft is given as 12,871 B. T. U. The 
 other analyses are taken from numerous authorities, who fail to state whether 
 they were made on air-dried or on as-received samples; judging from the small 
 amount of water in most of them, the samples appear to have been air-dried 
 before analysis. The sulphur is usually separately determined. 
 
FUELS 
 
 387 
 
 PROXIMATE ANALYSES OF MISCELLANEOUS AMERICAN COALS 
 
 (United States Geological Survey) 
 
 State 
 
 Kind of Coal 
 
 
 Moisture 
 
 Volatile 
 Matter 
 
 ll 
 *0 
 
 i 
 
 & 
 13 
 
 CO 
 
 S> 
 H 
 
 
 
 Ala. 
 Ark. 
 Ark. 
 Ark. 
 Ariz. 
 Ariz. 
 Ariz. 
 Cal. 
 Cal. 
 Cal. 
 Cal. 
 Col. 
 Col. 
 Col. 
 Col. 
 111. 
 111. 
 Kans. 
 Ky. 
 Ky. 
 Ky. 
 Ky. 
 Md. 
 Mich. 
 Mich. 
 Mich. 
 Mont. 
 Mont. 
 Mont. 
 N. Mex. 
 Ore. 
 Ore. 
 Ore. 
 Pa. 
 Pa. 
 Pa. 
 Utah 
 Utah 
 Utah 
 Va. 
 Va. 
 Va. 
 Va. 
 W. Va. 
 
 W. Va. 
 
 W. Va. 
 W. Va. 
 W. Va. 
 W. Va. 
 
 W. Va. 
 
 
 D 
 D 
 D 
 D 
 D 
 D 
 D 
 D 
 D 
 
 D 
 D 
 D 
 D 
 C 
 C 
 C 
 D 
 D 
 D 
 D 
 
 D 
 D 
 D 
 D 
 D 
 D 
 
 D 
 
 D 
 C 
 C 
 C 
 D 
 D 
 D 
 
 D 
 D 
 D 
 
 C 
 C 
 C 
 
 C 
 C 
 
 1.33 
 1.12 
 1.03 
 .68 
 7.80 
 8.10 
 9.89 
 4.86 
 18.02 
 12.20 
 11.32 
 6.80 
 6.60 
 5.50 
 2.80 
 7.93 
 7.08 
 3.50 
 1.62 
 1.78 
 1.44 
 1.68 
 .70 
 8.71 
 3.78 
 10.67 
 1.00 
 .60 
 1.10 
 5.70 
 9.60 
 10.41 
 9.49 
 2.42 
 3.04 
 2.56 
 3.10 
 4.04 
 4.37 
 2.98 
 1.11 
 1.01 
 1.07 
 
 .75 
 
 .73 
 2.50 
 3.18 
 2.36 
 
 3.08 
 2.63 
 
 30.55 
 11.54 
 10.53 
 9.93 
 33.80 
 33.30 
 39.07 
 47.74 
 39.22 
 35.20 
 45.09 
 36.50 
 35.30 
 37.80 
 5.05 
 34.23 
 34.94 
 33.73 
 32.68 
 34.27 
 31.80 
 33.20 
 18.81 
 38.45 
 41.18 
 33.59 
 20.00 
 30.30 
 28.20 
 2.18 
 36.30 
 46.15 
 23.87 
 20.31 
 29.79 
 16.47 
 40.58 
 43.23 
 41.84 
 10.94 
 31.79 
 32.70 
 32.83 
 
 38.16 
 
 17.43 
 20.58 
 30.57 
 18.56 
 
 17.56 
 18.25 
 
 58.88 
 78.62 
 80.06 
 79.94 
 44.50 
 47.80 
 46.95 
 41.03 
 26.39 
 41.40 
 35.91 
 50.28 
 52.44 
 48.49 
 77.55 
 49.78 
 48.60 
 52.43 
 57.39 
 55.55 
 56.84 
 61.35 
 72.96 
 41.16 
 49.34 
 53.80 
 55.19 
 57.75 
 50.57 
 86.13 
 40.90 
 36.85 
 32.54 
 70.13 
 60.85 
 71.58 
 48.10 
 47.27 
 47.77 
 64.14 
 61.36 
 60.39 
 58.68 
 
 54.63 
 
 77.71 
 71.70 
 59.40 
 71.70 
 
 74.79 
 73.87 
 
 9.24 
 
 8.72 
 8.38 
 9.43 
 13.90 
 10.84 
 4.05 
 6.37 
 16.37 
 11.20 
 7.68 
 6.42 
 5.66 
 8.21 
 14.60 
 8.06 
 9.38 
 10.34 
 8.31 
 8.40 
 9.92 
 3.77 
 7.26 
 11.68 
 5.70 
 1.94 
 23.81 
 11.35 
 20.13 
 5.99 
 13.20 
 6.59 
 34.10 
 7.14 
 6.32 
 9.39 
 8.22 
 5.46 
 6.02 
 21.94 
 5.74 
 5.90 
 7.42 
 
 6.45 
 
 4.63 
 5.22 
 6.85 
 7.38 
 
 4.57 
 5.25 
 
 2.10 
 2.01 
 2.51 
 
 1.76 
 1.30 
 1.14 
 .42 
 4.26 
 3.07 
 4.58 
 
 .44 
 .98 
 .53 
 .60 
 1.79 
 2.19 
 4.60 
 1.07 
 .83 
 .56 
 .60 
 1.01 
 2.72 
 2.50 
 1.01 
 .44 
 .87 
 1.37 
 .69 
 
 1.02 
 1.18 
 1.10 
 1.23 
 .93 
 .54 
 .58 
 .89 
 .68 
 1.48 
 .85 
 .67 
 
 2.30 
 
 .62 
 
 .74 
 .92 
 .81 
 
 .66 
 .64 
 
 13,884 
 13,853 
 13,965 
 13,896 
 10,650 
 11,020 
 12,101 
 12,727 
 8,105 
 10,130 
 
 11,833 
 12,001 
 10,885 
 12,563 
 12,215 
 12,151 
 12,989 
 18,664 
 13,357 
 13,473 
 14,228 
 14,626 
 12,359 
 13,489 
 12,868 
 11,420 
 13,610 
 11,790 
 13,268 
 9,720 
 
 7,683 
 14,087 
 14,040 
 13,748 
 11,956 
 11,729 
 11,908 
 11,669 
 14,276 
 14,203 
 13,910 
 
 13,509 
 
 15,032 
 14,533 
 13,849 
 14,135 
 
 14,557 
 14,528 
 
 Semianthracite, Spadra 
 Semianthracite, Clarksvil],e 
 Semianthracite, Russelville. 
 Tuba, Black Mesa Field 
 Oraibi, Black Mesa Field . . . 
 St. Michael 
 
 Stone Canon 
 
 Tesla 
 
 Trafton 
 
 Mean of ten analyses 
 
 Canon City, Chandler 
 Canon City Nonac 
 
 Colorado Springs, Cell 
 Crested Butte 
 
 Pawnee, washed nut 
 Pana, washed nut 
 Cherokee lump 
 Elkhorn Field. Millard 
 Elkhorn Field, Flatwoods. . . 
 Elkhorn Field, L. Elkhorn . . 
 Elkhorn Field, U. Elkhorn . . 
 Georges Creek, av. 53 anal. . . 
 Bay City, Lower Verne .... 
 Bay City, Upper Verne .... 
 Saginaw 
 
 Electric Field 
 
 Electric Field 
 
 Electric Field 
 
 Madrid 
 Coos Bay average. . 
 
 Coos Bay, average 
 Rogue Riv. Valley, Medford 
 Cambria Co., Beech Creek. . 
 Reynoldsville 
 
 Somerset County, C' bed . . . 
 Castle Gate -. 
 Price 
 
 Winter Quarters 
 Blacksburg . . 
 
 Dante, Widow Kennedy. . . . 
 Dante, Lower Banner 
 Dante Upper Banner 
 
 Fairmont, average of sixty- 
 three mines 
 Pocahontas, " average of 
 thirty-eight mines 
 Piney, Raleigh County 
 Kanawha Gas. 
 
 Pocahontas, No. 3, 3-in. 
 
 Pocahontas, No. 3, M.R 
 
388 
 
 FUELS 
 
 CN CO tO CNCO 
 .-ICN CO CO CN 
 
 <J4 rJH -t * 00 CN CD CD 00 iO ^J CO 00 CO CO C T* CO CO CO CO O O O5 
 
 qsy 
 
 ^ gj ^H r-H q t-; O5 CO lO TjJ 00 CN CO CN O5 
 I-H O 00 * I-H O5 1~ d id CO C CO CN CN >O 
 
 i-H CN 
 ^ CO C 
 
 S 6 "? . ""3 - *5 c 5 t> : c ^P i: 1 a ?'^ o 3 
 rH I-* r-i rMi-'cOrHCN-<j'<Ni-'Tj3(N 
 CNCNW I-H 
 
 6666 
 
 CNCO 00 
 
 odd 
 
 C WTJ *o + rj 
 
 i|ijiil,iiJ 
 
 
 
 COt^OO 
 
 6 6 6 
 
 i ^ odd 
 
 J 5; S S ooo 
 
 c56 
 
 
 000 - 
 
 o 
 
 2S2 
 
 G af^c 
 
 >?**' 
 
 1*3 1 
 
 :^i :^s :, : g g 
 
 ::: f|^p^ 
 :pq -pq -cq -6^,^ 
 
 S|S|S|wx^^ 
 
 aj c3 -52 t-t IH ^t tn 
 
 O O ' 
 
OO^^OOOCO 
 tO CO t- b- t^ O 
 
 FUELS 
 
 CM OOOOOCM <*< OCM CO 
 iCMOOt^OOiOt-.CMCO'Ot^. 
 
 Hi>i>cq I-HI> OCM XI-H 
 
 ' 
 
 COQCOCN CM 00 
 iOtOCM 
 
 cj'-i oo 
 
 CO CM CM CM CM -H CM 
 
 & CD tO CM 
 
 co OCO<N 
 
 *"" 
 
 i-Hi-H OO CM.-HCM 
 
 T^ r^ t>. CO tO OO C5 to O Ci CO * 
 CD CM CO i-H CM I-H CM CM CO t^ i-5 ' tH 
 
 C> Ci iO CD 00 TJJ t>. TI< CD to to iO 5 
 ' ' CM rH rH CO CD 1C 
 
 r-JCOOiOJOSO * CO O5 OS fl i-H 00 CM t> r^ CO CO CO l> 10 CM O CM tO CO tO CD rH 00 O CM CM 
 
 00 5 CO - t 
 
 OJOOCOCOOCM CO COt^tOoit 
 ^ r^ -^ to CO Tt< to tO tO to to t 
 
 o; rji co CD M cq -* 10 r-H oq oq io q i> oc oq oiCM 
 t^io^cj3o6c>iO'Oo6T)5oo6io>oo6-^ CM' co 
 
 1Q iQ >Q ^y Tt< >O iO >C tQ CO CO IQ O T>< -^ r}< rj< -^ 
 
 
 j'O^COt^'-HCO CDOOTjJOOOOCOOOCO COO5 
 MCO c6rHi-HCM"CMCOCO'-< OOCO 
 CM CO 
 
 & 
 
 <U O 
 
 ' 
 
 ^ a 
 
 
 ^00^^ 
 
 ZZ 6 6^ 
 
 'in <u <uZZ rt 
 
 CT3T) . . 3 
 
 D rt rt cj c cr 
 e o ^ 
 Mj^-S'S^ 
 W &^t 
 
 a 
 S IJ 
 
 rt rt cfl 
 
 -4-> -M 4J 
 
 o o o 
 OOO( 
 
 .CJCJOCJCJ 
 
 o 
 
 _0 
 
 6 
 
 . ** <s^ 
 
 Pcj 
 
 
 
 SS 
 
 3 1 S S 3? 8 gllllilll 1 |.H.a.y.y.a.'E'E 
 
 ^> ^> ^> ^ ^, ^>, > fh ^ ^K ^75 ^7? V7\ r75 r7\ J-7\ rR .H . H A . IS. rt . A . n. n: ^/^^/t 
 
 cJ5 g 
 
FUELS 
 
 A series of proximate analyses and heating values of Canadian coals arranged 
 by provinces, coal fields, mines, etc., is given in the table on pages 388 and 389. 
 The analyses and heating- value determinations were made on samples dried at 
 212 P., consequently the sum of the volatile matter, fixed carbon, and ash 
 equals 100. Both the moisture and sulphur were separately determined and 
 do not enter in this total. By reason of the analyses, etc. being made on dry 
 samples, the values in the table are higher than if made on air-dried samples 
 and cannot be compared with those given in the table on pages 382 to 385. The 
 samples were collected at the mine either at the working face or from coal being 
 shipped and represent several tons in each case. The following abbreviations 
 
 PROXIMATE ANALYSES OF ALASKAN COALS 
 
 (United States Geological Survey) 
 
 District and Kind of Coal 
 
 Mois- 
 ture 
 
 Volatile 
 Matter 
 
 Fixed 
 Carbon 
 
 Ash 
 
 Sul- 
 phur 
 
 Anthracite 
 Bering River, average of seven 
 analyses 
 
 7.88 
 
 6.15 
 
 78.23 
 
 7.74 
 
 1.30 
 
 Matanuska River 
 
 2.55 
 
 7.08 
 
 84.32 
 
 6.05 
 
 .57 
 
 Semianthracite 
 Bering River, average of eleven 
 
 5.80 
 
 887 
 
 7606 
 
 9 27 
 
 1 08 
 
 Semibituminous 
 Bering River, average of twenty- 
 eight analyses 
 
 4.18 
 
 14.00 
 
 72.42 
 
 9.39 
 
 1.73 
 
 Cape Lisburne, average of three 
 analyses 
 
 3.66 
 
 17.47 
 
 75.95 
 
 2.92 
 
 .96 
 
 Matanuska River, average of six- 
 teen analyses . . . 
 
 2.71 
 
 20 23 
 
 6539 
 
 11.60 
 
 57 
 
 Bituminous 
 Lower Yukon, average of eleven 
 analyses 
 
 4.68 
 
 31.14 
 
 56.62 
 
 7.56 
 
 .48 
 
 Subbituminous, or black lignite 
 Matanuska River, average of four 
 analyses 
 
 6.56 
 
 3543 
 
 49.44 
 
 8.57 
 
 .37 
 
 Koyukuk River 
 
 4 47 
 
 34 32 
 
 48 26 
 
 12.95 
 
 
 
 1 39 
 
 40 02 
 
 55 55 
 
 3 04 
 
 2 98 
 
 Alaska Peninsula, average of five 
 analyses 
 
 234 
 
 38 68 
 
 49 75 
 
 9 22 
 
 1 07 
 
 Cape Lisburne, average of eleven 
 analyses 
 
 9 35 
 
 3801 
 
 47 19 
 
 5 45 
 
 35 
 
 
 6 85 
 
 36 39 
 
 43 38 
 
 13 38 
 
 54 
 
 Port Graham 
 
 16 87 
 
 37 48 
 
 39 12 
 
 6.53 
 
 .39 
 
 Southeast Alaska, average of five 
 analyses 
 Wain wright Inlet . . . 
 
 1.97 
 10 65 
 
 37.84 
 42 99 
 
 35.18 
 42 94 
 
 24.23 
 3 42 
 
 .57 
 62 
 
 Colville River 
 
 11 50 
 
 30 23 
 
 30 27 
 
 27 90 
 
 50 
 
 Upper Yukon, Canada, average of 
 thirteen analyses ' 
 
 13 08 
 
 39 88 
 
 39 28 
 
 7 72 
 
 1 26 
 
 Upper Yukon, Circle Province, 
 average of three analyses 
 
 10 45 
 
 41 81 
 
 40 49 
 
 7 27 
 
 1 30 
 
 Upper Yukon, Rampart Province, 
 average of six analyses 
 
 11 42 
 
 41 15 
 
 36 95 
 
 1048 
 
 .33 
 
 Seward Peninsula 
 
 24 92 
 
 38 15 
 
 33 58 
 
 3 35 
 
 68 
 
 Chitistone River. . 
 
 1 65 
 
 51 50 
 
 40 75 
 
 6 10 
 
 
 Katchemak Bay, average of six 
 analyses 
 
 19 85 
 
 40 48 
 
 30 99 
 
 8 68 
 
 35 
 
 N en ana River . . 
 
 13 02 
 
 48 81 
 
 32 40 
 
 5 77 
 
 16 
 
 Kodiak Island 
 Unga Island, average of two analy- 
 ses 
 
 12.31 
 10 92 
 
 51.48 
 53 36 
 
 33.80 
 28 25 
 
 2.41 
 
 7 47 
 
 .17 
 1 36 
 
 Tyonck, average of four analyses. . . 
 Chistochina River . . 
 
 8.55 
 15 91 
 
 54.20 
 60 35 
 
 30.92 
 19 46 
 
 6.53 
 4 28 
 
 3.38 
 
 
 
 
 
 
 
FUELS 
 
 391 
 
 are used: L, lump; R, run of mine; B, buckwheat (anthracite); P, pea (anthra- 
 cite); Sa, mine sample; A. Ry. & I. Co., Alberta Railway and Irrigation Co.: 
 B. Mines, Bankhead Mines, Ltd.; C. C. & Ry. Co., Cumberland Coal and 
 Railway Co.; C. P. C. Co., Crowsnest Pass Coal Co.; C. W. C. Co., Canada 
 West Coal Co.; Dom. C. Co., Dominion Coal Co.; E. C. & B. Co., Eureka 
 Coal and Brick Co.; H. C. & C. Co., Hillcrest Coal and Coke Co.; H. M., 
 Hosmer Mines, Ltd.; I. C. & C. Co., International Coal and Coke Co.; I. C. 
 
 PROXIMATE ANALYSES OF FOREIGN COALS 
 
 (Various Authorities) 
 
 Coal 
 
 Mois- 
 ture 
 
 Vola- 
 tile 
 Matter 
 
 Fixed 
 Carbon 
 
 Ash 
 
 Sul- 
 phur 
 
 Argentine, Province of Mendoza 
 Brazil, Rio Grande do Sul 
 Brazil, Pernambuco 
 British Columbia, Crowsnest Pass, 
 
 7.67 
 10.96 
 1.90 
 
 1 09 
 
 18.39 
 26.78 
 18.82 
 
 21 07 
 
 31.00 
 
 38.82 
 58.73 
 
 7054 
 
 42.85 
 23.44 
 20.55 
 
 7 29 
 
 1.21 
 2.94 
 
 37 
 
 British Columbia, Comox, average . . . 
 British Columbia, Nanaimo, average . 
 Chili, Straits of Magellan 
 England, Durham, coking average 
 England, South Durham, Brockwell. . 
 England, South Durham, Busty seam . 
 England, Bearspark colliery 
 
 1.18 
 2.12 
 1.64 
 .91 
 1.12 
 .86 
 .85 
 4 84 
 
 28.41 
 34.07 
 24.85 
 13.12 
 22.05 
 25.24 
 27.06 
 34 07 
 
 62.91 
 55.94 
 69.52 
 81.54 
 72.17 
 68.24 
 68.97 
 46.33 
 
 7.49 
 7.93 
 3.99 
 4.43 
 4.66 
 5.66 
 3.12 
 14.76 
 
 1.54 
 .64 
 .97 
 .92 
 1.22 
 1.30 
 .78 
 1.08 
 
 
 6 00 
 
 34 00 
 
 4304 
 
 1696 
 
 1 20 
 
 ndia Johilla 
 
 5 76 
 
 33.03 
 
 44.22 
 
 16.99 
 
 .42 
 
 fapan, average eight analyses 
 apan Yubari mine 
 
 2.62 
 1.22 
 
 42.49 
 42.43 
 
 50.07 
 51.75 
 
 4.82 
 4.60 
 
 .92 
 .47 
 
 
 1 63 
 
 30 14 
 
 6072 
 
 7 51 
 
 .27 
 
 apan, Poronai mine, Seam 2 
 
 2.59 
 1 77 
 
 36.83 
 4796 
 
 56.32 
 42 62 
 
 4.26 
 7 65 
 
 .60 
 .16 
 
 Mexico, Sabinas Coal Co., Sabinas . . . 
 Mexico, Coahuila Coal Co., Coahuila. 
 New South Wales, Southern Field, 
 
 .69 
 .39 
 
 97 
 
 22.46 
 19.91 
 
 23 10 
 
 58.05 
 64.93 
 
 56 26 
 
 18.80 
 14.77 
 
 10 67 
 
 .86 
 .46 
 
 ^ew South Wales, Western, average. . 
 ^ew South Wales, Northern, average, 
 ^ew South Wales, Killingworth mine . 
 New Zealand, Lake Coleridge 
 
 1.87 
 1.92 
 1.24 
 1 80 
 
 31.49 
 35.09 
 38.82 
 1 96 
 
 52.61 
 51.08 
 32.46 
 84.12 
 
 14.03 
 8.91 
 27.48 
 12.12 
 
 .63 
 .54 
 3.50 
 
 sTew Zealand, Millerton Mines 
 New Zealand, Paparoa, Beds 1, 2, 3. . 
 slew Zealand, Paparoa, Beds 4, 5 
 New Zealand, Xaitongata mines 
 
 1.16 
 1.03 
 
 .78 
 20.06 
 
 20.50 
 16.38 
 23.55 
 28.93 
 
 74.83 
 78.78 
 72.77 
 44.60 
 
 3.51 
 3.81 
 2.90 
 6.41 
 
 .29 
 .48 
 
 New Zealand Westport mines 
 
 2 60 
 
 37 17 
 
 5601 
 
 4.22 
 
 
 Nova Scotia, Sydney, average 
 
 10.60 
 
 39.20 
 
 56.70 
 
 5.10 
 
 1.20 
 
 Philippines, Compostella, Cebu 
 Philippines Mt. Uling Cebu 
 
 7.80 
 6 30 
 
 37.56 
 35 30 
 
 51.96 
 53 55 
 
 2.68 
 4 45 
 
 .40 
 
 3 hilippines, average nine analyses, 
 Cebu 
 
 1400 
 
 31 08 
 
 5035 
 
 4.58 
 
 
 Philippines Batan 
 
 5 82 
 
 40 29 
 
 52 40 
 
 1 49 
 
 66 
 
 Philippines, Batan 
 
 4.53 
 
 45.89 
 
 46.96 
 
 2.62 
 
 .39 
 
 Philippines Batan 
 
 5 62 
 
 38 68 
 
 54 42 
 
 1.36 
 
 .14 
 
 Philippines, Batan 
 
 6.08 
 
 40.36 
 
 51.24 
 
 2.32 
 
 .40 
 
 Philippines, Batan, average five 
 
 13 57 
 
 3691 
 
 44 92 
 
 4 60 
 
 
 Scotland, Lanarkshire splint 
 Pransvaal, Brugspruit 
 Transvaal Bethel 
 
 6.86 
 .80 
 30 
 
 34.42 
 28.02 
 41 23 
 
 55.53 
 64.62 
 52 16 
 
 3.19 
 6.56 
 631 
 
 .70 
 .86 
 Trace 
 
 Transvaal, Springs 
 Victoria, Coal Creek, Bed 2 
 Victoria Windmill shaft 
 
 .57 
 7.00 
 594 
 
 14.10 
 21.60 
 33 67 
 
 63.00 
 55.66 
 55 23 
 
 22.00 
 12.35 
 5 16 
 
 
 
 
 
 
 
 
392 FUELS 
 
 & Ry. Co., Inverness Coal and Railway Co.; I. C. Co., Intercolonial Coal Co.; 
 L. B. C. Co., Lund Breckenridge Coal Co.; Leitch, Leitch Collieries, Ltd.; 
 M. Coal Co., Minudie Coal Co.; No. Atl. Cols., North Atlantic Collieries, 
 Ltd.; N. S. S. & C. Co., Nova Scotia Steel and Coal Co.; N. V. C. & C. Co., 
 Nicola Valley Coal and Coke Co.; P. C. Co., Parkdale Coal Co.; P. C. C. Co., 
 Pacific Coast Coal Co.; P. H., R. Ry. & C. Co., Port Hood, Richmond, Rail- 
 way and Coal Co.; S. C. Co., Strathcona Coal Co.; St. C. Co., Standapd Coal 
 Co.; W. C. Co., Wellington Colliery Co.; W. C. Cols., West Canadian Col- 
 lieries; W. D. Cols. Co., Western Dominion Collieries Co.; W. F. Co., Western 
 Fuel Co.; W. P. & Y. Ry. Co., White Pass and Yukon Railway Co., Ltd. 
 
 DETERMINATION OF HEATING VALUE OF COAL FROM A 
 PROXIMATE ANALYSIS 
 
 A very good idea of the calorific power of a coal , from a commercial stand- 
 point at least, may be obtained from a proximate analysis by some simple cal- 
 culations. Of the two methods of doing this, that devised by William Kent 
 and known by his name has a fairly general application. A method devised 
 by Lord and Haas is restricted to a given field, but for the coals within that 
 field it is probably more accurate than Kent's. 
 
 Kent's Method. According to Kent, a relation exists between the amount 
 of fixed carbon in the combustible portion of a coal (coal ash-and-moisture 
 free, according to the fifth column in the calculation given under the head 
 Proximate Analysis of Coal ante) and its calorific value per pound of combus- 
 tible, which is shown in the following table. 
 
 These figures are correct within 2% for all coals containing more than 63% 
 of fixed carbon in the combustible, but for coals containing less than 60% 
 fixed carbon or more than 40% volatile matter in the combustible they are 
 liable to an error, in either direction, of about 4%. The greater variation 
 in the coals low in fixed carbon and high in volatile matter is due to the fact 
 that they differ considerably in the percentage of oxygen in the volatile matter. 
 
 APPROXIMATE HEATING VALUE OF COALS 
 
 Per Cent, of Fixed Carbon 
 
 Heating Value per Pound Combustible 
 
 in Coal Dry tind. Free 
 
 
 From Ash 
 
 B. T. U. 
 
 Calories 
 
 100 
 
 14,580 
 
 8,100 
 
 97 
 
 14,940 
 
 8,300 
 
 94 
 
 15,210 
 
 8,450 
 
 90 
 
 15,480 
 
 8,600 
 
 87 
 
 15,660 
 
 8,700 
 
 80 
 
 15,840 
 
 8,800 
 
 72 
 
 15,660 
 
 8,700 
 
 68 
 
 15,480 
 
 8,600 
 
 ;.V 63 
 
 15,120 
 
 8,400 
 
 60 
 
 14,760 
 
 8,200 
 
 57 
 
 14,220 
 
 7,900 
 
 55 
 
 13,860 
 
 7,700 
 
 53 
 
 13,320 
 
 7,400 
 
 51 
 
 12,420 
 
 6,900 
 
 B T U 
 
 Method of Lord and Haas. The following formula is based on extensive 
 experiments made at the Ohio State University by Messrs. Lord and Haas 
 and the results calculated by it have been found to agree very closely with those 
 obtained with the Mahler calorimeter. 
 
 >-^A-5-M) + (5X4.050) 
 
 100 
 
 A, sulphur 5, and moisture M are expressed as percentages, 
 and K is a constant determined from a number of chemical and calorimetric 
 determinations by the following formula, in which the values substituted are 
 the averages of a number of analyses: 
 
 K _ B. T. U.- (sulphur X 4,050) 
 
 100- (ash + sulphur + moisture) 
 
FUELS 393 
 
 These gentlemen found that the value of K, which depends on the amount 
 of moisture, ash, and sulphur in the coal, is practically constant for the same 
 coal in the same field, regardless of any local variation in the relative propor- 
 tions of these constituents. The value of K as determined by them for various 
 coals from Ohio, Pennsylvania, and West Virginia is given in the following 
 table. 
 
 VALUE OF K FOR VARIOUS COALS 
 
 Coal 
 
 Value of K 
 
 Upper Preeport, Ohio and Pennsylvania 
 
 15,116 
 
 Pittsburg, Pennsylvania -. 
 
 15,183 
 
 Middle Kittanning (Darlington coal), Pennsylvania 
 
 15062 
 
 Middle Kittanning (Hocking Valley coal), Ohio. . . 
 
 14,265 
 
 Thacker, West Virginia 
 
 15,410 
 
 Pocahontas, West Virginia 
 
 15 829 
 
 Fairmount, West Virginia 
 
 15,675 
 
 ILLUSTRATION 1. Lord and Haas' Method. Using coal No. 103 from Poca- 
 hontas, Va., as the sulphur is separately determined in the usual way, the per- 
 centages of ash and moisture must be recalculated, to what they would be if 
 the sulphur were included. This is done by dividing them by (100 +S) -f- 100 
 = 1.0074, as the coal contains .74% of sulphur. Prom this the adjusted 
 moisture and ash are, respectively, 1.62% and 5.82%. The value of K to 
 be used, 15,829, is taken from the table. Substituting in formula 1: 
 B T U = 15.829X(100-5.82-.74- 
 
 As the true calorific value is 14,672, the difference is 108 B. T. U., or .736%. 
 
 Kent's Method. Using the same coal as before, No. 103, from the Poca- 
 hontas field in Virginia, the heating value of which has been determined by 
 calorimeter to be 14,672 B. T. U. per lb., the proximate analysis is: Mois- 
 ture, 1.63%; volatile matter, 17.17%; fixed carbon, 75.34%; and ash, 5.86%; 
 the sum of these four constituents is 100%. The coal dry and free from ash 
 is made up of 75.34-1- (75.34 + 17.17 = 92.51) =81.44% of fixed carbon, and 
 17.17^7- (75.34 + 17.17 = 92.51) = 18.56% of volatile matter. By interpolating 
 in the second column of the table, the heating value per pound of combustible 
 of a coal dry and free from ash, and containing 81.44% of fixed carbon, is found 
 to be 15,803 B. T. U. As just shown, the total combustible (the sum of the fixed 
 carbon and volatile matter) in the coal is 92.51. Hence, the calorific value 
 of this coal is 15,803 X. 9251 = 14,619 B. T. U. This agrees very closely with 
 the calorimetric value, the difference being but 48 B. T. U., or .361%. 
 
 ILLUSTRATION 2. Kent's Method. Using coal No. 78, of the table given 
 on pages 382 to 385, from Henryetta, Okla., the heating value of which is 
 12,620 B. T. U., and which contains by analysis: Moisture, 3.87%; volatile 
 matter, 35.73%; fixed carbon, 50.05%; and ash, 10.35%. The fixed carbon 
 in the coal dry and free from ash is 58.35% and the volatile matter is 41.65%. 
 By interpolating in the second column of the table giving the approximate 
 heating value of coals, the calorific value of a coal per pound of combustible and 
 containing 58.35% of fixed carbon on a dry and ash-free basis, is 14,463 B. T. U. 
 But the total combustible (fixed carbon + volatile matter) in this coal is 
 50.05+35.73 = 85.78%, hence its heating value is 14,463 X. 8578= 12,406 
 B. T. U. This differs from the true calorific value by 214 B. T. U., or 1.6%. 
 It will be noted, however, that this coal contains less than 60% of fixed carbon, 
 and is, thence, within the group in which the formula does not apply within 4%. 
 
 Lord and Haas' Method. Taking the coal just used and recalculating the 
 analysis to include the sulphur, the analysis is: Moisture, 3.80%; ash, 10.15%: 
 and sulphur, 1.95%. The recalculated volatile matter is 35.03%, and fixed 
 carbon 49.07%. This coal is not included in the table of those for which 
 the value of K has been determined. It is possible, however, for illustrative 
 purposes only, to assume a value for this constant. 
 
 In content of volatile matter this coal is not unlike No. 82 from the Pitts- 
 burg seam, at Ellsworth, Pa., 35.73% as against 34.83%. Using the value 
 of K, 15,183, for the Pittsburg seam, and substituting in formula 1, gives for 
 the calorific value of this coal 12,848 B. T. U. per lb. This is 228 B. T. U., 
 or 1.80%, greater than the true value, 12,620 B. T. U. 
 
394 FUELS 
 
 In the amount of fixed carbon, 49.07%, this coal is not unlike No. 75, a 
 Hocking coal from Dixie, Ohio, carrying 46.08% of fixed carbon. Using the 
 value of K, 14,265, for Hocking coal, and substituting in the formula, gives 
 the calorific value of coal No. 78 to be 12,076 B. T. U. This is 544 B. T. U., 
 or 4.31% less than the true value. 
 
 The illustrations show that while this method gives excellent results with 
 those coals for which the value of K has been experimentally determined, it 
 cannot be relied on to give good results where K is unknown. Nor do Messrs. 
 Lord and Haas make any such claim for it. 
 
 DETERMINATION OF HEATING VALUE OF COAL FROM AN 
 
 ULTIMATE ANALYSIS 
 
 Dulong's Formula. The available method of determining the heating 
 value of coal from an ultimate analysis is based on the formula devised by 
 Dulong and known by his name. The amount of heat obtained in the burning 
 of 1 Ib. of coal under theoretically perfect conditions is expressed as follows: 
 
 Lb. Cal. = 8,080C+34,462(tf-~) +2,2505 
 
 in which C, H, O, and 5 are the percentages of the elements the symbols repre- 
 sent and the coefficients are the calories evolved in burning 1 Ib. of carbon, 
 hydrogen, and sulphur, respectively. The figures within the parenthesis 
 
 (H ) represent the available hydrogen, i. e., the amount of that element over 
 
 and above that required to combine with the oxygen to form water. American 
 engineers commonly employ the British thermal unit in place of the pound- 
 calorie. However, if calculations are made in pound-calories, they may 
 readily be reduced to British thermal units by multiplying by 1.8. 
 
 In terms of the British thermal unit, the formula becomes, 
 B. T. U. = 14,544C+62,032.ff +4,0505 
 
 In this formula C, H, O, and 5 are the percentages of carbon, hydrogen, 
 oxygen, and sulphur, respectively, as determined by an ultimate analysis, and 
 14,544, 62,032, and 4,050, are the number of British thermal units evolved in 
 burning 1 Ib. of those of the foregoing elements that are combustible. 
 
 ILLUSTRATIONS. Using coal No. 103 from Pocahontas, Va., 
 
 B. T. U. = 14,544X.8314+62,032X(.0458-^|^)+4,050X.0075 = 
 
 This is within 69 B. T. U., or .470% of the calorimeter value. 
 In the case of coal No. 78, from Henryetta, Okla., 
 
 B. T. U. = 14,544X.6985+62,028x(.0514- 1 i^p)+4,050X.0199 = 
 
 which is 73 B. T. U., or .58%, too low. 
 
 Dulong's formula may be relied on to give results within 2% of the true 
 calorimetrically determined value, and the agreement is generally much closer, 
 as has been shown. It should be remembered that if the more accurate values 
 for the calorific powers of the combustible elements are substituted in the for- 
 mula, the results obtained are lower than those had through the use of the 
 earlier and approximate ones. 
 
 A comparison of the results obtained in calculating the heating values of 
 coals No. 103 and No. 78, by the different methods available is here given in 
 tabular form. 
 
 No. 103 No. 78 
 Method Employed B. T. U. B. T. U. 
 
 Actual value by calorimeter 14,672 12,620 
 
 Dulong's formula 14,603 12,547 
 
 Kent's formula 14,619 12,406 
 
 Lord and Haas' formula 14,564 
 
 Lord and Haas' formula, K for Pittsburg coal, in 
 
 No. 78 12,848 
 
 Lord and Haas' formula, K for Hocking coal, in 
 
 No. 78 12,076 
 
FUELS 
 
 PETROLEUM AS FUEL 
 
 Next to natural gas, petroleum is the ideal fuel, 1 Ib. of it having a heating 
 value about 50% greater than 1 Ib. of average coal. Of the 209,556,048 bbl. 
 produced in the United States in 1910, 24,586,108 bbl. were used for fuel by 
 the railroads along the Pacific coast and in the Southwest, displacing, say, 
 some 7,000,000 T. of coal. If to the consumption of the railroads is added that 
 of steamships, central-station power plants, and other large industrial con- 
 cerns, it is probable that the amount of oil used as fuel in the regions named 
 is equivalent to about 20,000,000 T. of coal. 
 
 Petroleum is a dark greenish-black to light-brown oil produced by the 
 decomposition of organic matter contained in the rocks, but whether the 
 organic matter is of vegetable or animal origin is undetermined. The oil con- 
 sists of a series of hydrocarbons that may^be distilled off in a series of gradually 
 increasing density as the temperature is increased. The residue, consisting of 
 the least volatile portion, which comnwnly remains as a solid known as the 
 base, affords a means of classifying oils into three groups: paraffin oils, asphalt 
 oils, and qlefin oils. 
 
 The oils in the first group are those produced in the eastern and middle 
 western states and being limited in production and high in yield of very valu- 
 able light oils (gasoline, kerosene, etc.) are too high in cost to be used as fuel. 
 In the second group come the oils of California and Texas, produced in large 
 quantities and at low cost, and furnishing the vast bulk of the fuel oil used 
 in the West and Southwest. In the third group are the oils of Baku, Russia, 
 on the Caspian Sea, and, except in so far as they possibly displace American 
 coal in foreign markets, are of no especial interest to the mining engineer. 
 
 Composition of Crude Petroleum. Petroleum in the fo rm in which it issues 
 from the earth is known as crude oil. It usually contains from 83 to 87% of 
 carbon; from 10 to 16% of hydrogen; and small amounts of oxygen, nitrogen, 
 and sulphur. Crude oil contains from less than 1% to over 30% of water. 
 The amount of wa,ter depends largely on the care with which the oil is pumped 
 from the well. The oil from old producing wells commonly contains more 
 water than that from wells newly drilled. In fact, in many districts, the per- 
 centage of water gradually increases during the life of the well, eventually the 
 entire output being salt water. As the amount of water in the crude oil is 
 uncertain and variable and as it separates out if left undisturbed, allowance 
 must be made therefor in providing storage or, as more commonly called, 
 tankage. The accompanying table gives the ultimate analyses of oils from 
 various sources. 
 
 As stated, the various hydrocarbons composing crude petroleum may be 
 separated by distillation at different temperatures; thus, gasoline is driven off 
 by heating from 140 to 158 P.; a light benzine or naphtha at from 158 to 
 248 P.; heavier benzines at 248 to 347 P.; kerosene, or ordinary illuminating 
 oil, at 338 P. and upwards; lubricating oils at 482 P. and above; paraffin 
 wax at a higher temperature; leaving a tarry residuum that may be further 
 distilled until nothing but a small quantity of coke remains in the still. If the 
 distillation is stopped after the kerosene has been driven off, the residue may 
 be used for fuel oil. 
 
 Flash Point and Firing Point. If a sample of fuel oil or of crude oil is 
 placed in an open cup and heat is applied, the oil will begin to vaporize and 
 inflammable gases will be driven off. If, while the heating proceeds, a lighted 
 match is passed at intervals over the surface of the oil and about f in. from it, 
 a point will be reached at which the vapor rising from the oil will ignite and 
 burn with a flicker of blue flame. The temperature of the oil when this flame 
 first becomes apparent is termed the flash point of the oil. If the heating of the 
 sample is continued, the vapors will be given off more rapidly and eventually 
 they will ignite and burn continuously at the surface of the oil when the lighted 
 " match is brought near. The temperature of the oil when the burning becomes 
 continuous is termed the firing point of the oil. The flash point and the firing 
 point of an oil depend on the composition, specific gravity, and source of the oil. 
 As a general rule, the heavier oils have a much higher flash point than the 
 lighter ones and an attempt has been made to use this as a basis for classifying 
 them. A specific giavity of .85 is taken as the basis, oils heavier than this 
 having a flash point above 60 P., and oils lighter than this having a flash point 
 lower than 60 P., although this is very far from always being true. It is 
 obvious that a high flash point is very desirable in a fuel oil in order to avoid 
 danger of explosion. 
 
FUELS 
 ULTIMATE ANALYSES OF CRUDE PETROLEUM 
 
 
 c 
 U 
 
 Hydrogen 
 
 c 
 
 | 
 
 5 
 
 1 
 1 
 
 fc 
 
 I 
 
 If 
 SB 
 
 wO 
 
 Flash Point 
 Degrees 
 
 Calorific 
 Power per 
 Pound 
 B. T. U. 
 
 United States 
 California 
 
 85.04 
 
 11.52 
 
 .99 1 
 
 2.45 
 
 1.40 
 
 
 
 17,871 
 
 California 
 Kentucky 
 
 81.52 
 85.20 
 
 11.51 
 13.36 
 
 6.92i 
 l.ll 2 
 
 0.55 
 
 
 
 230 
 
 18,667 
 20,6353 
 
 Ohio 
 
 83.40 
 
 14.70 
 
 1.30 
 
 0.60 
 
 
 
 
 19,580 
 
 Ohio 
 
 8420 
 
 13 10 
 
 70 2 
 
 
 
 .887 
 
 
 19 539 3 
 
 Ohio, Mecca 
 Pennsylvania, 
 Franklin 
 
 86.30 
 84.90 
 
 13.07 
 14.10 
 
 .632 
 1.40 
 
 
 
 .886 
 
 
 20,6603 
 19,210 
 
 Pennsylvania, O i 1 
 Creek 
 
 82 00 
 
 14 80 
 
 3 20 2 
 
 
 
 816 
 
 
 20 590 3 
 
 Texas, Beaumont . . 
 Texas, Beaumont . . 
 Texas, Beaumont. . 
 Texas 
 
 84.60 
 83.30 
 86.10 
 87 15 
 
 10.90 
 12.40 
 12.30 
 1233 
 
 2.87 
 3.83 
 .92 
 
 1.63 
 0.50 
 1.75 
 032 
 
 
 .924 
 .926 
 
 .908 
 
 180 
 216" 
 
 370 
 
 19,060 
 19,481 
 19,060 
 19338 
 
 West Virginia 
 
 84 30 
 
 14 10 
 
 1 60 2 
 
 
 
 841 
 
 
 21 240 
 
 West Virginia 
 Foreign Countries 
 Austria, Galicia. . . . 
 Austria, Galicia 
 Borneo 
 
 83.20 
 
 85.30 
 82.20 
 85 70 
 
 13.20 
 
 12.60 
 12.10 
 11 00 
 
 3.602 
 
 2.102 
 5.70 2 
 3 31 
 
 
 
 .857 
 
 .855 
 .870 
 
 
 20,0523 
 
 20,1053 
 18,416 
 19 240 
 
 Burmah 
 
 83 80 
 
 12 70 
 
 3 50 2 
 
 
 
 875 
 
 
 19 835 3 
 
 Canada, West 
 
 81.30 
 
 13.40 
 
 2.30 2 
 
 
 
 .857 
 
 
 19,998 3 
 
 Canada, Petrolia... 
 China, Fu-li-fu 
 Germany, Hanover 
 Germany, Pechel- 
 bronn 
 
 84.50 
 83.50 
 80.40 
 
 85 70 
 
 13.50 
 12.90 
 12.70 
 
 12 00 
 
 2.00 2 
 3.602 
 6.902 
 
 2 3Q2 
 
 
 
 .870 
 .860 
 .892 
 
 892 
 
 
 20,5523 
 19,9103 
 19,0793 
 
 19 772 3 
 
 Germany, Schwab- 
 weiler 
 
 8620 
 
 13 30 
 
 50 2 
 
 
 
 861 
 
 
 20 794 s 
 
 Italy, Parma 
 
 8400 
 
 1340 
 
 1 80 2 
 
 
 
 786 
 
 
 20 436 s 
 
 Java, Rembang. . . 
 Java, Tjabados. .. 
 Java, Gagor 
 
 87.10 
 83.60 
 8500 
 
 12.00 
 14.00 
 11 20 
 
 .902 
 2.402 
 2 80 2 
 
 
 
 .923 
 
 .827 
 927 
 
 
 19,7073 
 20,7003 
 19 137 3 
 
 Roumania 
 Russia, Baku 
 Russia, Baku 
 Russia, Baku 
 
 83.00 
 87.40 
 86.60 
 85.30 
 
 12.20 
 12.60 
 12.30 
 11.60 
 
 4.802 
 
 .102 
 1.102 
 
 3.102 
 
 
 
 .901 
 .882 
 .938 
 .954 
 
 
 19,3503 
 20,5663 
 20,1873 
 19.4043 
 
 . Calorific Value of Fuel Oil. The combustible elements in oil are the same 
 as those m coal, namely, carbon and hydrogen, and usually some sulphur. 
 The calorific value per pound may be determined by means of Dulong's for- 
 mula, which is applied exactly as in the case of an ultimate analysis of coal. 
 This formula v/as used to calculate the greater number of the calorific powers 
 given in the accompanying table. From the results of available tests, it is 
 found that the heat of combustion per pound of fuel oil varies from 17,000 to 
 21,000 B. T. U., California oil averaging about 18,600 B. T. U., and Texas oil 
 some 1,000 B. T. U. higher. At 18,600 B. T. U. per Ib. and assuming an aver- 
 age specific gravity of .885, 1 gal. of oil weighs 7.37 Ib., and will yield 137,082 
 B- T. U., and a barrel of 42 gal. will weigh 310 Ib. and will yield 5,766,000 
 B. T. U. Using the same specific gravity and a calorific value of 19,600 B. T. U. 
 per Ib. 1 gal. of oil will develop 144,452 B. T. U.,'and a barrel 6,076,000 B. T. U. 
 rhe theoretical comparative fuel values of coals of different heating powers 
 
 1 Includes nitrogen. 
 
 2 Oxygen, by difference. 
 
 Calculated by means of Dulong's formula. 
 
FUELS 
 
 397 
 
 and of fuel oil yielding, respectively, 18,600 and 19,600 B. T. U., per Ib. are 
 given in the following table. 
 
 This table, however, is of more theoretical than practical interest, as it is 
 based on the assumption that combustion is perfect whether oil or coal is used, 
 and that, in consequence, the efficiency of an oil-burning and of a coal-burning 
 boiler is the same. This is far from the case, as the efficiency of a properly 
 designed oil-burning boiler is the greater. To this must be added the advan- 
 tages outlined, so that only an actual test of the two fuels will determine which 
 is the more economical under a given set of conditions. 
 
 COMPARATIVE VALUE OF COAL AND OIL AS FUEL 
 
 
 At 18,600 B. T. U. per Lb. 
 
 At 19,600 B. T. U. per Lb. 
 
 Thermal 
 Value of 
 
 Pounds 
 
 Pounds 
 
 Barrels 
 
 Pounds 
 
 Pounds 
 
 Barrels 
 
 Different 
 
 of Coal 
 
 of Coal 
 
 of Petro- 
 
 of Coal 
 
 of Coal 
 
 of Petro- 
 
 Coals 
 B. T. U. 
 
 Equiva- 
 lent to 
 
 Equiva- 
 lent to 
 
 leum 
 Equiva- 
 
 Equiva- 
 lent to 
 
 Equiva- 
 lent to 
 
 leum 
 Equiva- 
 
 per Pound 
 
 1 Lb. of 
 
 1 Bbl. of 
 
 lent to 
 
 1 Lb. of 
 
 1 Bbl. of 
 
 lent to 
 
 
 Petro- 
 
 Petro- 
 
 1 T. of 
 
 Petro- 
 
 Petro- 
 
 1 T. of 
 
 
 leum 
 
 leum 
 
 Coal 
 
 leum 
 
 leum 
 
 Coal 
 
 10,000 
 
 1.860 
 
 577 
 
 3.47 
 
 1.960 
 
 608 
 
 3.29 
 
 11,000 
 
 1.691 
 
 524 
 
 3.82 
 
 1.782 
 
 552 
 
 3.62 
 
 12,000 
 
 1.550 
 
 481 
 
 4.16 
 
 1.633 
 
 506 
 
 3.95 
 
 13,000 
 
 1.431 
 
 444 
 
 4.51 
 
 1.508 
 
 467 
 
 4.28 
 
 14,000 
 
 1.329 
 
 412 
 
 4.85 
 
 1.400 
 
 434 
 
 4.61 
 
 15,000 
 
 1.240 
 
 384 
 
 5.21 
 
 1.307 
 
 405 
 
 4.95 
 
 Advantages and Disadvantages of Oil Fuel. Babcock and Wilcox sum- 
 marize the advantages of fuel oil as follows: 
 
 1. The cost of handling is much lower, the oil being fed by simple mechani- 
 cal means, resulting in 
 
 2. A general labor saving throughout the plant in the elimination of 
 stokers, coal passers, ash handlers, etc. 
 
 3. For equal heat value, oil occupies very much less space than coal. 
 This storage space may be at any distance from .the boiler without detriment. 
 
 4. Higher efficiencies and capacities are obtainable with oil than with 
 coal. The combustion is more perfect as the excess air is reduced to a 
 minimum; the furnace temperature may be kept practically constant, as the 
 furnace doors need not be opened for cleaning or working fires; smoke may be 
 eliminated with the consequent increased cleanliness of the heating surfaces. 
 
 5. The intensity of the fire can be almost instantaneously regulated to 
 meet load fluctuations. 
 
 6. Oil, when stored, does not lose in calorific value as does coal, nor are 
 there any difficulties arising from disintegration, such as may be found where" 
 coal is stored. 
 
 7. Cleanliness and freedom from dust and ashes in the boiler room with 
 a consequent saving in wear and tear on machinery; little or no damage to 
 surrounding property due to such dust. 
 
 The disadvantages of oil are: 
 
 1. The necessity that the oil have a reasonably high flash point to mini- 
 mize the danger of explosions. 
 
 2. City or town ordinances may impose burdensome conditions relative 
 to location and isolation of storage tanks, which in the case of a plant situated 
 in a congested portion of the city, might make the use of this fuel prohibitive. 
 
 3. Unless the boilers and furnaces are especially adapted for the use of 
 this fuel, the boiler upkeep cost will be higher than if coal is used. 
 
 The relative cost of the two fuels per unit of power produced is, of course, 
 the deciding factor in the premises, and this varies so greatly in such short 
 intervals of time, even from day to day, that current quotations of the 
 delivered cost of both fuels must always be used in making calculations of the 
 savings possible when substituting oil for coal, and vice versa. 
 
FUELS 
 
 GASEOUS FUELS 
 
 Kinds of Gas. The different gases used as fuel are the following, arranged 
 in the order of their heating value: (1) Natural gas, which is obtained from 
 wells in different parts of the world; (2) illuminating gas, or coal gas, which is 
 made either by distilling coal in retorts or by enriching water gas with the 
 volatile matter distilled from cannel coal or with vapors distilled from petro- 
 leum; (3) coke-oven gases, which are mainly those coming from by-product 
 ovens, although occasionally the gases from the beehive ovens are used under 
 boilers; (4) water gas, which is made by blowing steam through a bed of glow- 
 ing anthracite or coke, by the reaction C-f- #20 = CO +2tf; (5) producer gas, 
 which is made by blowing air into burning bituminous coal, in which case the 
 volatile matter, including condensible tarry vapors, is distilled, and the coke 
 is burned to carbon monoxide; producer gas is also made by blowing air into 
 burning anthracite, thus producing carbon monoxide; (6) combined water gas 
 and producer gas, which is made by blowing air mixed with steam into a pro- 
 ducer charged with burning bituminous coal; (7) blast-furnace gas, which is 
 the waste gas coming from the top of a blast furnace, and which contains a 
 certain amount of carbon monoxide available as fuel. 
 
 The composition and heating value of different gases, as given by H. A. 
 Humphrey in the Proceedings of the Institution of Civil Engineers of Great 
 Britain, are shown in the following table. 
 
 ANALYSES AND HEATING VALUES OF VARIOUS GASES 
 
 Constituent Gases 
 
 II 
 
 
 
 I 
 
 S& 
 
 P. BO. 
 
 N*3 <U 
 
 *e I 
 
 PI 
 
 Hydrogen, H 
 
 Marsh gas (methane), CH* 
 
 CnHzn gases 
 
 Carbon monoxide, CO 
 
 Carbon dioxide, C02 
 
 Nitrogen, AT 
 
 Total volume (approxi- 
 mate) 
 
 Total combustible gases . . 
 
 Heating value (B. T. U. 
 per cubic foot at 64 F.) 
 
 22.0 
 
 67.0 
 
 6.0 
 
 .6 
 
 .6 
 
 3.0 
 
 100.0 
 95.6 
 
 892.4 
 
 48.0 
 
 39.5 
 
 3.8 
 
 7.5 
 
 .5 
 
 100.0 
 98.8 
 
 686.0 
 
 56.9 
 22.6 
 3.0 
 8.7 
 3.0 
 5.8 
 
 100.0 
 91.2 
 
 511.0 
 
 20.0 
 
 4.0 
 21.0 
 
 5.0 
 49.5 
 
 100.0 
 45.0 
 
 207.5 
 
 18.7 
 
 !a 
 
 25.1 
 
 6.6 
 
 49.0 
 
 100.0 
 160.0 
 
 8.6 
 2.4 
 
 24.4 
 5.2 
 
 59.4 
 
 100.0 
 35.4 
 
 134.5 
 
 24.8 
 2.3 
 
 13.2 
 12.9 
 46.8 
 
 100.0 
 154.6 
 
 Some additional analyses of natural, producer, and coke-oven gases, 
 together with their average heating values, are given in another table. 
 
 The heating value per pound and per cubic foot, measured at 32 F., and 
 atmospheric pressure of the several constituents of a mixed fuel are given in 
 the table on page 400. The figures in the first column are those of Favre and 
 Silbermann except in the two cases noted. Other heating values differing 
 slightly from these are given by different authorities, owing to a difference 
 in the experiments by which the values have been determined. In the third 
 column are shown approximate figures, giving the British thermal units per 
 pound of combustible, that are within the limits of error of chemical analysis. 
 
 Blast-Furnace Gases. Blast-furnace gas varies greatly in its composition , 
 and in six analyses made in 1 da., the carbon dioxide varied from 6.6 to 7.7%, 
 the carbon monoxide from 20.1 to 31.7%, and the nitrogen and hydrocarbons 
 
FUELS 
 
 o a? 
 #11 
 
 
 883 3 38 
 
 ^0 ' CO COO^ 
 
 qq^w woqi 
 
 OS MT-lO T}<COi-H 
 
 oo 
 cooo 
 
 ooo 
 
 ooo 
 ^H5oo 
 
 as 
 
 !.i 
 
 I 
 
 uoowwSwiS <J 
 
400 
 
 FUELS 
 HEATING VALUE OF GASES AT 32 F. 
 
 Substance 
 
 Burned in Oxygen 
 
 Approxi- 
 mate 
 Values 
 per Pound 
 B. T. U. 
 
 Per Pound 
 B. T. U. 
 
 Per Cubic 
 Foot 
 B. T. U. 
 
 Hydrogen to HzO 
 Carbon to carbon dioxide, COz 
 
 62,032 
 14,544 
 4,451 
 
 4,325 
 
 23,513 
 
 21,344 
 17.847 
 18,196* 
 4,050t 
 
 346.75 
 338.00 
 
 1,050.00 
 1,568.00 
 1,351.60 
 
 62,000 
 14,600 
 4,450 
 
 4,300 
 10,150 
 
 4,000 
 
 Carbon to carbon monoxide, CO 
 Carbon monoxide, CO, to carbon dioxide 
 COz per unit of CO 
 
 Carbon monoxide, CO, to carbon dioxide, 
 COz per unit of carbon C 
 
 Marsh gas (methane), CHi, to HzO and 
 COz.. 
 
 Ethvlene (olefiant-gas) , CzH t , to HzO and 
 COz 
 
 Benzole gas, CeHe, to HzO and COz 
 
 Acetylene, CzHz, to HzO and COz 
 
 Sulphur to SOz 
 
 
 from 60.5 to 72.2% by volume. The heating value calculated from the aver- 
 age analyses was 1,175 B. T. U. per lb., and at the temperature of 584 P., at 
 which it entered the steam boiler furnace, it carried 140 B. T. U. per lb. 
 additional heat. The 1,175 B. T. U. per lb. are equal to about 94 B. T. U. 
 per cu. ft., measured at 32 P., or only about one-tenth of the value of 1 cu. 
 ft. of natural gas. 
 
 Modern blast furnaces, working on Bessemer iron, will produce about 
 8,500 lb. of available gas per ton of pig iron made. This gas will have an aver- 
 age composition of about COz, 10.80%; CO, 28.00%; H, 2.50%; CHt, .2%; 
 and N, 58.50%; and will yield 85 to 100 B. T. U. per cu. ft., or 1,050 to 1,250 
 B. T. U. per lb., assuming that the weight of 1 cu. ft. thereof is .081 lb. The 
 heat from the waste gases of the blast furnaces in the United States, which 
 produced about 26,700,000 T. of pig iron in 1910, was sufficient, if entirely util- 
 ized, to have displaced 10,400,000 T. of coal having a fuel value of 12,000 
 B. T. U. per lb. 
 
 Natural Gas. Natural gas, produced from drilled wells, usually in or near 
 the oil fields, is a valuable fuel in many states. The total production in 
 1910 was 509,155,309,000,000 cu. ft. The value is placed at $70,756,158, or 
 13.90 c. per 1,000 cu. ft., varying from 7.16 c. per cu. ft. in West Virginia to 
 73.77 c. in South Dakota. Assuming a fuel value of 1,000 B. T. U. per cu. ft., 
 this gas displaced 21,000,000 T. of coal rated at 12,000 B. T. U. per lb. 
 The 1,327,722 domestic consumers used 169,823,030,000.000 cu. ft. of gas, 
 for which they paid an average price of 24.4 c. per 1,000 cu. ft., the rate 
 charged varyingf rom 16.9 c. per 1,000 ft. in Oklahoma to $1 in Michigan. 
 The 18,267 industrial establishments used 339,332,279,000,000 cu. ft., for 
 which they paid an average price of 8.63 c. per 1,000 cu. ft., the rate charged 
 varying from 5.1 c. per 1,000 cu. ft. in West Virginia to 69.5 c. in South Dakota. 
 > The great variation in the composition of natural gas from different fields 
 is shown in the table on page 399. Assuming a calorific value of 1,000 B. T. U. 
 per cu. ft., 24,000 cu. ft. of gas will yield as much heat as 1 T. of coal rated at 
 12,000 B. T. U. per lb. To displace 1 T. of high-grade Pocahontas or New 
 River coal rated at, say, 14,750 B. T. U. per lb., will require 29,500 cu. ft. of 
 gas. The number of cubic feet of gas required to displace 1 T. of coal when the 
 calorific powers of each are known, may be found by dividing twice the calorific 
 power of the coal per pound by the ratio the calorific power of the gas bears 
 to 1,000 B. T. U. 
 
 EXAMPLE. (a) How many thousand cubic feet of gas having a calorific 
 power of 925 B. T. U. per cu. ft., will be required to displace 1 T. of coal rated 
 at 13,965 B. T. U. per lb.? (b) How many cubic feet will be required if the 
 heating value of the gas is 1,155 B. T. U. per lb.? 
 
 *Calculated. fN. W. Lord. 
 
FUELS 401 
 
 SOLUTION. (a) It is assumed that the efficiency of the boiler is the same 
 regardless of the fuel used. 13 ' 9 6 5 _ X2 = 30.195 cu. ft. 
 
 ,VAU 
 
 - = 24,181 cu. ft. 
 
 It is possible, also, to deduce from this that 1,000 cu. ft. of the first gas 
 = 2,000-^-30.195 = 66.23 Ib. of the coal, and 1,000 cu. ft. of the second gas 
 = 2,000-7-24.181 = 82.71 Ib. of the coal. Likewise, 1 Ib. of the coal is equal 
 to 1,000 -=-66.23 = 15.09 cu. ft. of the first gas, and is equal to l.OOO-r-82.71 
 = 12.10 cu. ft. of the second gas. 
 
 In the matter of natural gas in the Pittsburg, Pa., district, a committee of 
 the Western Society of Engineers report that 1 Ib. of good coal is equal to 
 7| cu. ft. of natural gas. When burned with just enough air, its temperature 
 of combustion is 4.200 F. The Westinghouse Air Brake Company found from 
 experiment that 1 Ib. of Youghiogheny coal is equal 12 \ cu. ft. of natural gas, 
 or 1,000 cu. ft. of natural gas is equal 81.6 Ib. of coal. Indiana natural gas 
 gives 1,000,000 B. T. U. per 1,000 cu. ft., and weighs .045 Ib. per cu. ft. 
 
 Natural gas, when used for steam raising, is commonly under a pressure 
 of about 8 oz. and is fired through a large number of small burners to prevent 
 what is known as lancing, or the issuing of the flame in a long jet similar in 
 appearance and largely in action to that of a blow-pipe. 
 
 By-Product Gas. By-product gas, so called, is given off in large amount 
 in connection with the numerous by-product processes of coking. When the 
 coking plant is situated at a steel works, the gas is used for the generation of 
 steam; if situated in or near a city, the gas is enriched and used for illuminating 
 and general fuel purposes, as is done at the plant of the New England Gas and 
 Coke Company at Everett, near Boston, Mass. 
 
 In 1910 there were 4,078 by-product ovens in the United States, of which 
 all but 27 were in blast. They consumed 9,529,042 T. of coal and produced 
 7,138,734 T. of coke, an average yield of 74.9%. A certain amount of the gas 
 given off by the coking coal is required to furnish the heat demanded by the 
 process; the gas not so used, the surplus or available gas, amounted, in 1910, 
 to 27,692,858,000 cu. ft., valued at $3,017,908, or about 11 c. per 1,000 cu. ft. 
 The production appears to be, from these statistics, at the rate of 2,900 cu. ft. 
 per T. of coal charged, or 3,880 cu. ft. per T. of coke drawn. These figures 
 are approximate and to be used with caution because at a small number of 
 plants no attempt was made to save the gas, and at another, the yield of gas 
 had to be estimated. 
 
 The amount of gas available depends on so many factors that it is impossible 
 to predicate just how much and what grade of gas a given coal will yield. 
 Obviously, the amount of gas available from coking 1 T. of high-volatile Con- 
 nellsville coal is much greater than that to be had from a lean semibituminous 
 coal. The composition of the gas will vary with the composition of the coal 
 and with the process employed in coking. The gas will also depend, in a very 
 great measure, on whether the ovens are designed primarily for coke making, 
 as at a steel or iron plant, or whether intended for the manufacture of illuminat- 
 ing gas and the recovery of by-products (in this case, the coke being a by- 
 product), as at Everett, near Boston. 
 
 In regard to the yield of gas per ton of coal charged, the 280 Koppers regen- 
 erative ovens at Joliet, 111., when charged with a mixture of 80% Pocahontas 
 and 20% high -volatile coal, yielded 84% of the coal charged as coke and 
 10,000 cu. ft. of gas per T., of which rather more than 5,000 cu. ft. was surplus 
 and available as fuel. The same oven, operating in Germany on a coal not 
 dissimilar to the Connellsville, Pa., yields between 5,000 and 6,000 cu. ft. of 
 available gas per T. Mr. P. E. Lucas, superintendent of the coke-oven depart- 
 ment of the Dominion Iron and Steel Co., Sydney, N. S., estimates the average 
 yield of surplus gas from average coal in by-product ovens as 5,000 cu. ft. per T. 
 of coal charged, and that this gas has a fuel value of from 450 to 500 B. T. U. 
 per cu. ft. At Mulheim-on-the-Ruhr, Germany, a plant of 50 Koppers ovens 
 supplies that city and Barmen, 40 mi. distant, with gas; these ovens take 8 to 
 10 T. of coal at a cha-ge. The time of coking is 24 hr. but only the richer 
 portion of the gas, that evolved from the second to the twelfth hour, which 
 is about 50% of the yield, is distributed. During these 10 hr., each oven 
 produces 70,600 cu. ft. of gas of a calorific value well over 600 B. T. U. per 
 cu. ft., with the average composition: COt, 1.2%; CO, 6.8%; H, 49.5%; 
 CHt, 38.3%; and N, 4.2%. Mr. Edwin A. Moore, estimates that a plant of 
 100 United-Otto ovens consuming 750 T. of coal will produce 3,472,000 cu. ft. 
 
402 FUELS 
 
 of available gas, or at the rate of 4,630 cu. ft. of gas per T. of coal charged. 
 Mr. Moore calls attention to the fact that the gases given off during the early 
 portion of the coking process (first 10 hr.) have a fuel value of 650 B. T. U. 
 per cu. ft., and during the latter period, but 525 B. T. U. It would appear that 
 the average coal will yield about 4,500 cu. ft. of available gas per T., and 
 that the gas has a heating value of some 500 B. T. U. per cu. ft.; on which 
 basis the gas has about 8.5% of the heating value of the coal from which it is 
 made, assuming the latter to be rated at around 13,000 B. T. U. per Ib. 
 
 On the basis of containing 500 B. T. U. per cu. ft., the 27,692,858,000 cu. ft. 
 of by-product gas marketed in 1910 displaced about 580,000 T. of coal with a 
 fuel value of 12,000 B. T. U. per Ib. 
 
 As this gas is highly charged with moisture, arrangements must be made 
 for getting rid of the condensed water. Further, as the gas carries large 
 amounts of tar and heavy hydrocarbons that clog the burners, arrangements 
 must be made whereby they may be cleaned out by blowing steam through 
 them. 
 
 Coke-Oven Gas. Beehive coke-oven gases are used at numerous mines 
 for the generation of the necessary steam for operating the power plant con- 
 nected therewith. As these gases do not contain any combustible portion, 
 their value lies in their sensible heat. Ihe total horsepower available may be 
 
 obtained from the formula, HP = 
 
 in which W= weight of gases passing per hour; T ' 
 
 T = temperature of gases entering boiler; 
 t = temperature of gases leaving boiler; 
 s = specific heat of gases. 
 
 As the temperature of the gases entering the boiler is rarely as great as 
 2,000 F., and as with coal firing the furnace temperature ranges from 2,500 
 to 3,000, the heating surface first passed over will not absorb as much heat 
 in the waste-heat boilers, and, consequently, the heating surface per boiler 
 horsepower should be increased. From 12 to 15 ft. in water-tube boilers is 
 about right, and from 15 to 20 ft. in return tubular and shell boilers. 
 
 In a series of tests with a high-class water-tube boiler, the following results 
 were obtained with the waste heat from the coke ovens: Temperature of the 
 gases entering the boiler, 1,720 F.; temperature of gases leaving the boiler, 
 650 F.; boiler heating surface, 1,611 sq. ft.; water evaporated per hour from 
 and at 212 F., mean result, 6,465 Ib.; water evaporated from and at 212 per 
 oven per hour, 294 Ib.; water evaporated from and at 212 per Ib. of coal 
 coked, 1.7 Ib.; water evaporated from and at 212 per sq. ft. of heating surface, 
 4 Ib. 
 
 At the Sydney Mines of the Nova Scotia Steel and Coal Company, the waste 
 heat from coke ovens of the Bauer type is used in the generation of steam. In 
 referring to a test run made upon a single boiler, Mr. Thomas J. Brown, the 
 superintendent, obtained these results: Average horsepower per hour, 331; 
 maximum horsepower per hour, 436; minimum horsepower per hour, 179; 
 evaporation from and at 212 per Ib. of coal charged into the ovens, 1.18 Ib. 
 of water; coal charged into the ovens per boiler horsepower, 29.23 Ib. Mr. Brown 
 further states, that the boilers have 3,140 sq. ft. of heating surface, with a 
 flue temperature at the rear of the boilers of between 600 and 700, and that 
 the proportion of about 9.5 sq. ft. of heating surface per horsepower developed 
 seems to be about right for this class of fuel. 
 
 At Marianna, Pa., 2,000 H. P. are developed from a battery of 75 beehive 
 ovens at a cost of $2.50 per da. as opposed to a cost of $63.50 if coal were used. 
 At the Stag Canon Mines, Dawson, N. Mex., 2,400 H. P. are developed from the 
 waste gases of 218 beehive ovens, the gases being delivered under the boilers 
 at temperatures ranging from 1,800 F. to 2,600 F. and leaving the stack at 
 from 600 to 1,150 F. Mr. R. D. Martin, referring to the waste heat ovens 
 in use at Agujita and Lampacitos, Coahuila, Mex., estimates that each oven 
 is capable of developing 12 boiler H. P. from a coal containing, volatile matter, 
 21.1%; fixed carbon, 67.4%; and ash, 11.5%. Here the temperature in 
 the firebox, as determined with Saeger cones, was as high as 2,600 F. 
 Mr. Howard N. Eavenson, in connection with the Continental Coke Co., 
 No. 1 plant, estimates that the waste heat from 6 T. of coal charged into a 
 coke oven will yield as many boiler horsepower as 1 T. of coal directly fired. 
 
 Coal Gas. Coal gas, frequently called illuminating gas from the use to 
 which it is ordinarily put, is made by heating bituminous coal high in volatile 
 matter in fireclay retorts of a semielliptic cross-section. The retorts are about 
 
FUELS 
 
 403 
 
 15 in. high by 26 in. wide inside, and 9 to 10 ft. long if single-ended, or 18 to 20 ft. 
 long if double-ended. The retort walls are about 4 in. thick and each retort is 
 connected with a pipe that allows the gases to escape as fast as formed. After 
 passing through various devices to remove the ammonia, tar, and sulphur, the 
 gas passes into a gas holder and is ready for distribution. 
 
 Analyses of typical gas coals from the Pittsburg, Pa., field are given in the 
 following table. 
 
 ANALYSES OF GAS COALS 
 
 Constituents 
 
 Westmoreland Coal 
 Company 
 
 Pennsylvania Gas Coal 
 Company 
 
 South 
 Side 
 Mine 
 
 Foster 
 
 Mine 
 
 Larri- 
 mer 
 No. 2 
 
 Irwin 
 
 No. 1 
 
 Irwin 
 
 Sewick- 
 ley 
 
 Water 
 Volatile matter. . . . 
 Fixed carbon 
 Sulphur 
 Ash 
 
 1.410 
 37.655 
 54.439 
 .636 
 5.860 
 
 1.310 
 37.100 
 55.004 
 .636 
 5.950 
 
 1.560 
 39.185 
 54.352 
 .643 
 4.260 
 
 1.78 
 35.36 
 59.29 
 .68 
 2.89 
 
 1.280 
 38.105 
 54.383 
 .792 
 5.440 
 
 1.490 
 37.153 
 58.193 
 .658 
 2.506 
 
 
 Total 
 
 100.000 
 
 100.000 
 
 100.000 
 
 100.00 
 
 100.000 
 
 100.000 
 
 Under ordinary conditions 1 T. of such coal should produce about 10,000 
 cu. ft. of gas of 17 c. p., 1,400 Ib. of coke, 12 gal. of tar, and 4 Ib. of ammonia. 
 The following may be considered as the average composition of purified 
 coal gas: 
 
 Per Cent. 
 
 Hydrocarbon vapors .6 
 
 Heavy hydrocarbons 4.4 
 
 Carbon dioxide, COz 3.4 
 
 Carbon monoxide. CO 10.1 
 
 Marsh gas, CH\ 30.6 
 
 Oxygen, O 3 
 
 Hydrogen, H 45.9 
 
 Nitrogen, N 4.7 
 
 Total 100.0 
 
 The use of illuminating gas as fuel for steam-raising is limited by its cost 
 which, while sometimes as low as 80 c. per 1,000 cu. ft., is usually about $1. 
 A certain amount is used directly in small gas engines in the larger cities, but 
 the larger amount is used for illumination or in cooking ranges, domestic 
 heating stoves, and the like. Coal gas made from gas coals in retorts is being 
 largely displaced by water gas. 
 
 Water Gas. Water gas contains the same combustible constituents as coal 
 gas but not in the same proportions. ^ It is made commercially by the contact 
 of steam with incandescent carbon, in the form of anthracite or coke, which 
 decomposes the steam separating the hydrogen from the oxygen. The oxygen 
 takes up carbon from the coal or coke and forms carbon monoxide, along with 
 a small amount of carbon dioxide. The resultant gases therefore are mainly 
 hydrogen and carbon monoxide mechanically mixed together. This is what 
 is called blue, or uncarbureted, water gas. It burns with a non-luminous flame 
 and is consequently useless for lighting purposes, except in incandescent lamps 
 of the Welsbach type. In actual practice, this water gas is always enriched 
 with oil gas, which furrishes the hydrocarbons necessary to make a luminous 
 flame. The oil gas was made separately in many of the older forms of ap- 
 paratus, but it is now commonly produced in the same apparatus in which the 
 water gas is made. 
 
 The only impurity that must be removed from water gas is hydrogen 
 sulphide, which is formed from the sulphur that is always present in varying 
 amounts in the coal or coke and sometimes in the oil. The hydrogen sulphide 
 
404 
 
 FUELS 
 
 is removed by purification with lime or iron oxide in the same way that the 
 purification of coal gas is accomplished. 
 
 Carbon dioxide, which is formed either by imperfect contact of the steam 
 with the incandescent carbon, or because the temperature of the carbon is too 
 low, is not a dangerous impurity, but is merely an inert gas incapable of com- 
 bustion. It, however, absorbs heat when the gas is burned, and is conse- 
 quently injurious to the heating and lighting power. It can be removed by 
 purification with lime, but this is not necessary if the generating apparatus is 
 handled properly, as the quantity made will be very small. No ammonia 
 is produced. 
 
 The following is a volumetric analysis of purified water gas: 
 
 Per Cent. 
 
 Hydrocarbon vapors 
 
 Heavy hydrocarbons 
 
 Carbon dioxide, COz . . 
 
 Carbon monoxide, CO 
 
 Marsh gas, CHt 
 
 Oxygen, O 
 
 Hydrogen, H 
 
 Nitrogen, N 
 
 Total.., 
 
 1.2 
 12.6 
 3.0 
 28.0 
 20.2 
 
 4 
 
 31.4 
 
 3.2 
 
 . 100.0 
 
 Water gas requires from 30 to 40 Ib. of coal or coke per 1,000 cu. ft. of gas 
 made, and from 4 to 5 gal. of oil, depending on the candlepower required. 
 Usually between 5 and 6 c. p. is obtained from each gallon of oil used. The 
 specific gravity of 24 c. p. water gas is about .625, air being taken as unity. 
 
 Pure uncarbureted water gas has no perceptible odor, but the carbureted 
 gas has an odor fully as strong as coal gas. This is mainly due to the hydro- 
 carbons from the oil that is used for enriching. It should be noted that these 
 hydrocarbons are not added if the gas is to be used for heating or in gas engines. 
 
 Producer Gas. Producer gas is made in a cylindrical riveted shell of boiler 
 plate, lined with firebrick. A thick bed of fuel is maintained in the bottom of 
 the producer and through this is passed a moderate supply of air, with or 
 without water vapor or steam. By properly regulating the air supply, a partial 
 or incomplete combustion of the fuel is maintained, resulting in the gradual 
 consumption of all the combustible matter. The coke, instead of remaining as 
 a by-product, as in the manufacture of coal gas or in by-product or retort coke 
 ovens, is all consumed in making the gas. When dry air alone is forced through 
 the fire, the resulting gas is known as air gas and is the true producer gas; when 
 the air is mixed with steam or water vapor the resulting gas is called mixed gas, 
 and is frequently made in producers; and when air is not used at all and steam 
 alone is forced through the fire, the product is called water gas as previously 
 explained. 
 
 The quantity of producer gas derivable from 1 T. of fuel will vary according 
 to the fuel used, the type of producer plant, and the method of operating. 
 The United States Geological Survey, at its Fuel Testing Plant at the Louisiana 
 Purchase Exposition, held in St. Louis, in 1904, made an exhaustive series of 
 tests of American coals used in gas producers, and from its reports the follow- 
 ing tables, etc., are taken. 
 
 QUANTITY OF GAS PRODUCED PER POUND OF FUEL IN AN 
 UP-DRAFT PRESSURE PRODUCER 
 
 Fuel 
 
 Maximum 
 
 Minimum 
 
 Average 
 
 As Fired 
 Cubic 
 Feet 
 
 Dry 
 Cubic 
 Feet 
 
 As Fired 
 Cubic 
 Feet 
 
 Dry 
 
 Cubic 
 Feet 
 
 As Fired 
 Cubic 
 Feet 
 
 Dry 
 Cubic 
 Feet 
 
 Bituminous coal . . . 
 Lignite . . . 
 
 100.8 
 45.9 
 
 100.3 
 52.8 
 
 37.0 
 26.1 
 
 40.9 
 38.8 
 
 60.5 
 35.8 
 30.3 
 
 64.7 
 45.7 
 38.3 
 
 Peat 
 
FUELS 
 
 405 
 
 The yield of gas, in cubic feet per pound of dry fuel, which may be expected 
 in the up-draft producer from various fuels is, roughly, as follows: Coke or 
 charcoal, 90; anthracite, 75; bituminous coal, 65; lignite, 46; and peat, 38. 
 On the basis of the Survey's tests the yield of gas and the heat value of the 
 gas per ton of fuel as fired are approximately as in the table here given. 
 
 YIELD AND HEAT VALUE OF GAS PER TON OF FUEL AS FIRED IN 
 AN UP-DRAFT PRESSURE PRODUCER 
 
 Kind of Fuel 
 
 Cubic Feet 
 of Gas per 
 Ton of Fuel 
 as Fired 
 
 British 
 Thermal Units 
 in Gas, per 
 Cubic Foot 
 
 British 
 Thermal Units 
 in Gas, per 
 Ton of Fuel 
 as Fired 
 
 Coke or charcoal 
 
 170,000 
 
 140 
 
 23,800,000 
 
 Anthracite 
 Bituminous coal 
 
 140,000 
 120000 
 
 135 
 152 
 
 19,000,000 
 18300000 
 
 Lignite 
 Peat 
 
 72,000 
 60000 
 
 158 
 175 
 
 11,400,000 
 10 000,000 
 
 
 
 
 
 It will be noted from this table that while the inferior fuels yield less gas 
 per ton, as might be expected, the heating value of the gas, in British thermal 
 units per cubic foot, is greater than in gas made from high-class coals. 
 
 Gas Producers. There are three general types of gas producer in use. In 
 the suction type, the drawing of the air and steam through the fire and, con- 
 sequently, the generation of the gas, is accomplished by the suction in the 
 engine cylinder in which the gas is used. While the gases are scrubbed, etc., 
 to get rid of the tar that otherwise would clog the cylinders, the absence of 
 storage tanks for the gas and the fact that the suction of the engine causes the 
 operation of the producer, renders absolute separation of the tar difficult if 
 not impossible. Hence, only low volatile coals are adapted to use in this type 
 of producer, and because the price of such coals is always high, suction plants, 
 though numerous, are of comparatively small power, few exceeding 300 H. P. 
 each, and most of them not exceeding 100 H. P. 
 
 The up-draft pressure producer is the common American type in which 
 the gas is developed under a slight pressure due to the introduction of the air 
 and steam blasts, and the gas is stored in holders until required by the engine. 
 As the generation of the gas is independent of the suction stroke of the engine, 
 tar and other impurities may be removed by suitable devices and hence the use 
 of bituminous coal, lignite, and peat is possible. This form of producer is 
 offered in many types, some of which are without gas holders and are proving 
 eminently satisfactory. If the holder is omitted, automatic devices must be 
 introduced for controlling the pressure and the supply of gas to the engine. 
 
 TYPICAL ANALYSES BY VOLUME OF PRODUCER GAS 
 
 
 From 
 
 
 
 
 Bituminous 
 
 From Lignite 
 
 From Peat 
 
 
 Coal 
 
 Per Cent. 
 
 Per Cent. 
 
 
 Per Cent. 
 
 
 
 
 U. D. 
 
 D. D. 
 
 U. D. 
 
 D. D. 
 
 U. D. 
 
 D. D. 
 
 Carbon dioxide, COz 
 
 9.84 
 
 6.22 
 
 10.55 
 
 11.87 
 
 12.40 
 
 10.94 
 
 
 .04 
 
 .13 
 
 .16 
 
 .01 
 
 
 .41 
 
 Ethylene, CiH* 
 
 .18 
 
 .01 
 
 .17 
 
 
 .40 
 
 .06 
 
 Carbon monoxide, CO. . . . 
 
 18.28 
 
 21.05 
 
 18.72 
 
 16.01 
 
 21.00 
 
 16.91 
 
 Hydrogen, Hz 
 
 12.90 
 
 12.01 
 
 13.74 
 
 14.66 
 
 18.50 
 
 10.19 
 
 Methane, CH* 
 
 3.12 
 
 .49 
 
 3.44 
 
 .98 
 
 2.20 
 
 .66 
 
 Nitrogen, Nz 
 
 55.64 
 
 60.09 
 
 53.22 
 
 56.37 
 
 45.50 
 
 60.83 
 
 
406 BOILERS 
 
 In both the foregoing types of producer, the extraction of the tar removes 
 a large part of the heat value of the gas. If the tar can be sold at a good price 
 this may not make much difference, but where the tar is thrown away the loss 
 is sufficient to warrant the attempt to devise some means of converting this 
 tar into gas of suitable quality for engine use. To this end down-draft producers 
 are coming into general use and in them the gases are drawn down through the 
 bed of coal and the tar is thereby decomposed into fixed, combustible gases. 
 
 Typical analyses of gases made from the same fuels in the up-draft (U. D). 
 and down-draft (D. D.) producer, the percentages being by volume, are given 
 in the preceding table. 
 
 In the matter of steam raising it is questionable if better results are obtained 
 by using the gas made from the coal than by firing the coal directly under the 
 boilers, especially in the case of good grades of coal from subbituminous to 
 anthracite, but many fuels, notably peat and some of the true lignites, that 
 give indifferent results when fired directly under a steam boiler, give most 
 excellent results when fired as gas. Further, almost any material containing 
 carbon will yield fuel gas in the producer, even bituminous shale, saw-dust, 
 wood pulp, cornstalks, and the like. It is practically impossible to predicate 
 the yield of gas and the quality thereof of a coal from its analysis. Tests in 
 the various types of producers are required for this purpose. 
 
 Strictly speaking, the gaseous fuels previously described are all producer 
 gases, except natural gas, coal gas (illuminating gas), and the waste heat gases 
 from beehive coke ovens. These various producer gases are not commonly 
 used for steam raising under boilers, but are a direct source of power in internal 
 combustion engines. It must be noted that as carbon monoxide is one of the 
 most important heat-producing constituents of all these gases, extreme caution 
 must be observed in inhaling them owing to their highly poisonous nature. 
 
 BOILERS 
 
 STEAM 
 
 PROPERTIES OF STEAM 
 
 Saturated Steam. If water is put in a closed vessel and heat is applied until 
 boiling occurs and steam is given off, the pressure and the temperature of the 
 steam will be the same as those of the water. The steam thus produced is 
 known as saturated steam; that is, saturated steam is steam whose temperature 
 is the same as that of boiling water subjected to the same pressure. Its 
 nature is such that any loss of heat will cause some of the steam to condense, 
 provided the pressure is not changed. Saturated steam that carries no water 
 particles with it is called dry saturated steam; if it contains moisture it is called 
 wet steam. At every different pressure, saturated steam has certain definite 
 values for the temperature, the weight per cubic foot, the heat per pound, and 
 so on. These various values, collected and arranged in order, form the table 
 of the Properties of Saturated Steam, more commonly termed the Steam 
 Table, which is given on the following pages. 
 
 The various properties of steam, with their symbols, as given in the Steam 
 Table, are as follows: 
 
 The temperature, t, of the steam, which is the boiling point of the water 
 from which the steam is formed. 
 
 The heat of the liquid, q, which is the number of British thermal units required 
 to raise the temperature of 1 Ib. of water from 32 F. to the boiling point corre- 
 sponding to the given pressure. 
 
 The latent heat of vaporization, r, often termed the latent heat, which is the 
 number of British thermal units required to change 1 Ib. of water at the boiling 
 point into steam at the same temperature. 
 
 The total heat of vaporization, H, often termed the total heat, which is the 
 number of British thermal units required to raise 1 Ib. of water from 32 F. to 
 the boiling point for any given pressure and to change it into steam at that 
 pressure. It is the sum of the heat of the liquid and the latent heat. 
 
 The specific volume, V, which is the volume, in cubic feet, of 1 Ib. of steam 
 at the given pressure. 
 
 The density, w, which is the weight, in pounds, of 1 cu. ft. of steam at the 
 given pressure. It is the reciprocal of the specific volume. 
 
BOILERS 
 PROPERTIES OF SATURATED STEAM 
 
 407 
 
 p 
 
 t 
 
 q 
 
 H 
 
 r 
 
 V 
 
 w 
 
 1 
 
 101.99 
 
 70.0 
 
 1,113.1 
 
 1,043.0 
 
 334.6 
 
 .00299 
 
 2 
 
 126.27 
 
 94.4 
 
 1,120.5 
 
 1,026.1 
 
 173.6 
 
 .00576 
 
 3 
 
 141.62 
 
 109.8 
 
 1,125.1 
 
 1,015.3 
 
 118.4 
 
 .00844 
 
 4 
 
 153.09 
 
 121.4 
 
 1,128.6 
 
 1,007.2 
 
 90.31 
 
 .01107 
 
 5 
 
 162.34 
 
 130.7 
 
 1,131.5 
 
 1,000.8 
 
 73.22 
 
 .01366 
 
 6 
 
 170.14 
 
 138.6 
 
 1,133.8 
 
 995.2 
 
 61.67 
 
 .01622 
 
 7 
 
 176.90 
 
 145.4 
 
 1,135.9 
 
 990.5 
 
 53.37 
 
 .01874 
 
 8 
 
 182.92 
 
 151.5 
 
 1,137.7 
 
 986.2 
 
 47.07 
 
 .02125 
 
 9 
 
 188.33 
 
 156.9 
 
 1,139.4 
 
 982.5 
 
 42.13 
 
 .02374 
 
 10 
 
 193.25 
 
 161.9 
 
 1,140.9 
 
 979.0 
 
 38.16 
 
 .02621 
 
 11 
 
 197.78 
 
 166.5 
 
 1,142.3 
 
 975.8 
 
 34.88 
 
 .02866 
 
 12 
 
 201.98 
 
 170.7 
 
 1,143.6 
 
 972.9 
 
 32.14 
 
 .03111 
 
 13 
 
 205.89 
 
 174.6 
 
 1,144.7 
 
 970.1 
 
 29.82 
 
 .03355 
 
 14 
 
 209.57 
 
 178.3 
 
 1,145.8 
 
 967.5 
 
 27.79 
 
 .03600 
 
 14.7 
 
 212.0 
 
 180.8 
 
 1,146.6 
 
 965.8 
 
 26.60 
 
 .03760 
 
 16 
 
 216.32 
 
 185.1 
 
 1,147.9 
 
 962.8 
 
 24.59 
 
 .04067 
 
 18 
 
 222.40 
 
 191.3 
 
 1,149.8 
 
 958.5 
 
 22.00 
 
 .04547 
 
 20 
 
 227.95 
 
 196.9 
 
 1,151.5 
 
 954.6 
 
 19.91 
 
 .05023 
 
 22 
 
 233.06 
 
 202.0 
 
 1,153.0 
 
 951.0 
 
 18.20 
 
 .05495 
 
 24 
 
 237.79 
 
 206.8 
 
 1,154.4 
 
 947.6 
 
 16.76 
 
 .05966 
 
 26 
 
 242.21 
 
 211.2 
 
 1,155.8 
 
 944.6 
 
 15.55 
 
 .06432 
 
 28 
 
 246.36 
 
 215.4 
 
 1.157.1 
 
 941.7 
 
 14.49 
 
 .06899 
 
 30 , 
 
 250.27 
 
 219.4 
 
 1,158.3 
 
 938.9 
 
 13.59 
 
 .07360 
 
 32 
 
 253.98 
 
 223.1 
 
 1,159.4 
 
 936.3 
 
 12.78 
 
 .07820 
 
 34 
 
 257.50 
 
 226.7 
 
 1,160.4 
 
 933.7 
 
 12.07 
 
 .08280 
 
 36 
 
 260.85 
 
 230.0 
 
 1,161.5 
 
 931.5 
 
 11.45 
 
 .08736 
 
 38 
 
 264.06 
 
 233.3 
 
 1,162.5 
 
 929.2 
 
 10.88 
 
 .09191 
 
 40 
 
 267.13 
 
 236.4 
 
 1,163.4 
 
 927.0 
 
 10.37 
 
 .09644 
 
 42 
 
 270.08 
 
 239.3 
 
 1,164.3 
 
 925.0 ' 
 
 9.906 
 
 .1009 
 
 44 
 
 272.91 
 
 242.2 
 
 1,165.2 
 
 923.0 
 
 9.484 
 
 .1054 
 
 46 
 
 275.65 
 
 245.0 
 
 1,166.0 
 
 921.0 
 
 9.097 
 
 .1099 
 
 48 
 
 278.30 
 
 247.6 
 
 1,166.8 
 
 919.2 
 
 8.740 
 
 .1144 
 
 50 
 
 280.85 
 
 250.2 
 
 1,167.6 
 
 917.4 
 
 8.414 
 
 .1188 
 
 52 
 
 283.32 
 
 252.7 
 
 1,168.4 
 
 915.7 
 
 8.110 
 
 .1233 
 
 54 
 
 285.72 
 
 255.1 
 
 1,169.1 
 
 914.0 
 
 7.829 
 
 .1277 
 
 56 
 
 288.05 
 
 257.5 
 
 1,169.8 
 
 912.3 
 
 7.568 
 
 .1321 
 
 58 
 
 290.31 
 
 259.7 
 
 1,170.5 
 
 910.8 
 
 7.323 
 
 .1366 
 
 60 
 
 292.51 
 
 261.9 
 
 1,171.2 
 
 909.3 
 
 7.096 
 
 .1409 
 
 62 
 
 294.65 
 
 264.1 
 
 1,171.8 
 
 907.7 
 
 6.882 
 
 .1453 
 
 64 
 
 296.74 
 
 266.2 
 
 1,172.4 
 
 906.2 
 
 6.680 
 
 .1497 
 
 66 
 
 298.78 
 
 268.3 
 
 1,173.0 
 
 904.7 
 
 6.490 
 
 .1541 
 
 68 
 
 300.76 
 
 270.3 
 
 1,173.6 
 
 903.3 
 
 6.314 
 
 .1584 
 
 70 
 
 302.71 
 
 272.2 
 
 1,174.3 
 
 902.1 
 
 6.144 
 
 .1628 
 
 72 
 
 304.61 
 
 274.1 
 
 1,174.9 
 
 900.8 
 
 5.984 
 
 .1671 
 
 74 
 
 306.46 
 
 276.0 
 
 1,175.4 
 
 899.4 
 
 5.834 
 
 .1714 
 
 76 
 
 308.28 
 
 277.8 
 
 1,176.0 
 
 898.2 
 
 5.691 
 
 .1757 
 
 78 
 
 310.06 
 
 279.6 
 
 1,176.5 
 
 896.9 
 
 5.554 
 
 .1801 
 
 80 
 
 311.80 
 
 281.4 
 
 1,177.0 
 
 895.6 
 
 5.425 
 
 .1843 
 
 82 
 
 313.51 
 
 283.2 
 
 1,177.6 
 
 894.4 
 
 5.301 
 
 .1886 
 
 85 
 
 316.02 
 
 285.8 
 
 1,178.3 
 
 892.5 
 
 5.125 
 
 .1951 
 
 90 
 
 320.04 
 
 290.0 
 
 1,179.6 
 
 889.6 
 
 4.858 
 
 .2058 
 
 95 
 
 323.89 
 
 294.0 
 
 1,180.7 
 
 886.7 
 
 4.619 
 
 .2165 
 
 100 
 
 327.58 
 
 297.9 
 
 1,181.9 
 
 884.0 
 
 4.403 
 
 .2271 
 
 105 
 
 331.13 
 
 301.6 
 
 1,182.9 
 
 881.3 
 
 4.206 
 
 .2378 
 
 110 
 
 334.56 
 
 305.2 
 
 1,184.0 
 
 878.8 
 
 4.026 
 
 .2484 
 
 115 
 
 337.86 
 
 308.7 
 
 1,185.0 
 
 876.3 
 
 3.862 
 
 .2589 
 
 120 
 
 341.05 
 
 312.0 
 
 1,186.0 
 
 874.0 
 
 3.711 
 
 .2695 
 
 125 
 
 344.13 
 
 315.2 
 
 1,186.9 
 
 871.7 
 
 3.572 
 
 .2800 
 
 130 
 
 347.12 
 
 318.4 
 
 1,187.8 
 
 869.4 
 
 3.444 
 
 .2904 
 
 135 
 
 350.03 
 
 321.4 
 
 1,188.7 
 
 867.3 
 
 3.323 
 
 .3009 
 
 140 
 
 352.85 
 
 324.4 
 
 1,189.5 
 
 865.1 
 
 3.212 
 
 .3113 
 
408 
 
 BOILERS 
 TABLE (Continued) 
 
 p 
 
 / 
 
 Q 
 
 H 
 
 r 
 
 V 
 
 w 
 
 145 
 
 355.59 
 
 327.2 
 
 1,190.4 
 
 863.2 
 
 3.107 
 
 .3218 
 
 150 
 
 358.26 
 
 330.0 
 
 ,191.2 
 
 861.2 
 
 3.011 
 
 .3321 
 
 155 
 
 360.86 
 
 332.7 
 
 ,192.0 
 
 859.3 
 
 2.919 
 
 .3426 
 
 160 
 
 363.40 
 
 335.4 
 
 ,192.8 
 
 857.4 
 
 2.833 
 
 .3530 
 
 165 
 
 365.88 
 
 338.0 
 
 ,193.6 
 
 855.6 
 
 2.751 
 
 .3635 
 
 170 
 
 368.29 
 
 340.5 
 
 ,194.3 
 
 853.8 
 
 2,676 
 
 .3737 
 
 175 
 
 370.65 
 
 343.0 
 
 ,195.0 
 
 852.0 
 
 2.603 
 
 .3841 
 
 180 
 
 372.97 
 
 345.4 
 
 ,195.7 
 
 850.3 
 
 2.535 
 
 .3945 
 
 185 
 
 375.23 
 
 347.8 
 
 ,196.4 
 
 848.6 
 
 2.470 
 
 .4049 
 
 190 
 
 377.44 
 
 350.1 
 
 ,197.1 
 
 847.0 
 
 2.408 
 
 .4153 
 
 195 
 
 379.61 
 
 352.4 
 
 ,197.7 
 
 845.3 
 
 2.349 
 
 .4257 
 
 200 
 
 381.73 
 
 354.6 
 
 ,198.4 
 
 843.8 
 
 2.294 
 
 .4359 
 
 205 
 
 383.82 
 
 356.8 
 
 ,199.0 
 
 842.2 
 
 2.241 
 
 .4461 
 
 210 
 
 385.87 
 
 358.9 
 
 ,199.6 
 
 840.7 
 
 2.190 
 
 .4565 
 
 215 
 
 387.88 
 
 361.0 
 
 ,200.2 
 
 839.2 
 
 2.142 
 
 .4669 
 
 220 
 
 389.84 
 
 363.0 
 
 ,200.8 
 
 837.8 
 
 2.096 
 
 .4772 
 
 225 
 
 391.79 
 
 365.1 . 
 
 ,201.4 
 
 836.3 
 
 2.051 
 
 .4876 
 
 230 
 
 393.69 
 
 367.1 
 
 ,202.0 
 
 834.9 
 
 2.009 
 
 .4979 
 
 235 
 
 395.56 
 
 369.0 
 
 ,202.6 
 
 833.6 
 
 1.968 
 
 .5082 
 
 240 
 
 397.41 
 
 371.0 
 
 ,203.2 
 
 832.2 
 
 1.928 
 
 .5186 
 
 250 
 
 400.99 
 
 374.7 
 
 ,204.2 
 
 829.5 
 
 1.854 
 
 .5393 
 
 260 
 
 404.47 
 
 378.4 
 
 1,205.3 
 
 826.9 
 
 1.785 
 
 .5601 
 
 275 
 
 409.50 
 
 383.6 
 
 1,206.8 
 
 823.2 
 
 1.691 
 
 .5913 
 
 300 
 
 417.42 
 
 391.9 
 
 1,209.3 
 
 817.4 
 
 1.554 
 
 .644 
 
 325 
 
 424.82 
 
 399.6 
 
 1,211.5 
 
 811.9 
 
 1.437 
 
 .696 
 
 The pressures, p, given in the first column are absolute pressures. The 
 pressure registered by the gauge on the boiler is the gauge pressure, or 
 the pressure of the steam above that of the atmosphere. The pressure of the 
 atmosphere at sea level, with the barometer at about 30 in., is approximately 
 14.7 Ib. per sq. in. Therefore, the absolute pressure at sea level is equal to the 
 gauge pressure plus 14.7. In using the Steam Table, the atmospheric pressure, 
 14.7 Ib. per sq. in., must always be added to the gauge pressure. 
 
 Use of Steam Table. For any absolute pressure p given in the first column 
 of the Steam Table, the corresponding temperature t, total heat H, or other 
 property is found in the same horizontal line, under the proper column heading ; 
 but if the pressure lies between two of the values given in the first column, 
 the corresponding temperature, total heat, etc. must be found by interpolation, 
 as illustrated in the following examples: 
 
 EXAMPLE 1. Find the temperature corresponding to a pressure of 147 Ib. 
 per sq. in., absolute. 
 
 SOLUTION. Referring to the Steam Table, 
 
 for p = 150 Ib., * = 358.26 
 
 and for p = 145 Ib., t = 355.59 
 
 Difference, 5 Ib., 2.67 
 
 Difference for 1 Ib. difference of pressure is 2.67 -^ 5 = .534. 147 Ib. - 145 Ib. 
 = 2 Ib., the given difference of pressure; and for this, the difference in 
 temperature is 2X. 534= 1.068 or 1.07, taking two decimal places. Hence, 
 the increase of 2 Ib. from 145 Ib. -to 147 Ib. is accompanied by an increase in 
 temperature of 1.07. Therefore, adding the increase 1.07 to the tempera- 
 ture 355.59 corresponding to 145 Ib., the temperature for 147 Ib. is 355.59 
 + 1.07 = 356.66. 
 
 EXAMPLE 2. The pressure in a steam boiler as shown by the gauge is 
 87 Ib. per sq. in. What is the temperature of the steam? 
 
 SOLUTION. The absolute pressure is 87+14.7 = 101.7 Ib. per sq. in. This 
 
 ssure, in the Steam Table, lies between the values 100 and 105. 
 
 pressure 
 
 for = 1051b., * = 331.13 
 for p = 100 Ib.. * = 327.58 
 Difference, 5 Ib., 3.55 
 
BOILERS 409 
 
 For 1 Ib. change of pressure, the difference in temperature is 3.55 -i-5 = .71. 
 From 100 Ib. to 101.7 Ib., the change of pressure is 1.7 Ib., and the corresponding 
 change of temperature is .71 X 1.7 = 1.207, or 1.21 as the values in the 
 Steam Table contain but two decimal places. For 101.7 Ib., therefore, the 
 temperature is 327.58+ 1.21 = 328.79. 
 
 EXAMPLE 3. What is the pressure of steam at a temperature of 285 P.? 
 SOLUTION. From the Steam Table, 
 
 for t = 285.72, p = 54 Ib. 
 
 for t = 283.32, p = 52 Ib. 
 
 Difference, 2.40, 2 Ib. 
 
 From t = 283.32 to t = 285, the increase of temperature is 1.68. Now, as 
 an increase of temperature of 2.40 gives an increase of pressure of 2 Ib., the 
 increase of 1.68 must give an increase of pressure of 
 
 ^|X2 Ib.- 1.4 Ib, 
 
 Hence, the required pressure is 52 lb. + 1.4 lb. = 53.4 Ib. 
 
 EXAMPLE 4. Find, from the Steam Table, the total heat of 1 Ib. of satu- 
 rated steam at a pressure of 63 Ib. per sq. in., gauge. 
 
 SOLUTION. The absolute pressure is 63 + 14.7 = 77.7 Ib. per sq. in. From 
 the Steam Table, 
 
 for = 78 Ib., # = 1,176.5 B. T. U. 
 
 for = 76 Ib., #=1. 176.0 B. T. U. 
 
 Difference, 2 Ib., .5 B. T. U. 
 
 Difference, 1 Ib., .25 B. T. U. 
 
 The difference between the given pressure and 76 Ib. is 77.7 76 = 1.7 Ib. 
 For a difference of 1.7 Ib., the change of total heat is 1.7 X. 25 = .425 B. T. U. 
 Hence, for 77.7 Ib., H = l,176.0+.425 = 1,176.425, say 1,176.4 B. T. U. 
 
 EXAMPLE 5. Find the volume occupied by 14 Ib. of steam at 30 Ib. gauge 
 pressure. 
 
 SOLUTION. Absolute pressure = 30 +14.7 = 44.7 Ib. per sq in. From the 
 Steam Table, 
 
 for = 44 Ib., V = 9.484 cu. ft.* 
 
 for p = 46 Ib. , V = 9.Q97cu. ft. 
 
 Difference, 2 Ib., .387 cu. ft. 
 
 The difference for 1 Ib. is .387 + 2 = . 1935. 44.7 - 44 = .7 Ib. actual difference 
 in pressure. .1935X .7 = .135 difference in volume. As the pressure increases, 
 the volume decreases; and to obtain the volume at 44.7 Ib., it is necessary 
 to subtract the difference .135 from the volume at 44 Ib.; thus, for = 44.7, 
 V = 9.484 -.135 = 9.349 cu. ft. The volume of 14 Ib. is 14X9.349 cu. ft. 
 = 130.89 cu. ft. 
 
 EXAMPLE 6. Find the weight of 40 cu. ft. of steam at a temperature of 
 254 F. 
 
 SOLUTION. From the Steam Table, the weight w of 1 cu. ft. of steam at 
 253.98 is .07820 Ib. 254 -253.98 = .02. Neglecting the .02, the weight of 
 40 cu. ft. is therefore .07820X40 = 3.128 Ib. 
 
 EXAMPLE 7. How many pounds of steam at 64 Ib. pressure, absolute, are 
 required to raise the temperature of 300 Ib. of water from 40 to 130 F., the 
 water and steam being mixed together? 
 
 SOLUTION. The number of heat units required to raise 1 Ib. from 40 to 
 130 is 130 -40 = 90 B. T. U. Actually, a little more than 90 would be 
 required but the above is near enough for all practical purposes. Then, to 
 raise 300 Ib. from 40 to 130 requires 90X300 = 27,000 B. T. U. This quan- 
 tity of heat must necessarily come from the steam. Now, 1 Ib. of steam at 
 64 Ib. pressure gives up, in condensing, its latent heat of vaporization, or 
 906.2 B. T. U.; but, in additipn to its latent heat, each pound of steam<on con- 
 densing must give up an additional amount of heat in falling to 130. As the 
 original temperature of the steam was 296.74 F. (see Steam Table), each pound 
 gives up by its fall of temperature 296.74-130 = 166.74 B. T. U. Conse- 
 quently, each pound o f the steam gives up a total of 906.2 + 166.74 = 1,072.94 
 B. T. U., and 27,000-M,072.94 = 25.16 Ib. of steam will therefore be required 
 to accomplish the desired result. 
 
 SUPERHEATED STEAM 
 
 If saturated steam in contained in a vessel, out of contact with water, and 
 heat is added to it, its temperature will begin to rise and its weight per cubic 
 
410 BOILERS 
 
 foot will begin to decrease, provided the pressure remains constant. As more 
 heat is added, the temperature rises farther above that of saturated steam at 
 that pressure, and the steam is then called superheated steam. Superheated 
 steam cannot exist in contact with water. 
 
 The following distinction is usually made between saturated and super- 
 heated steam: For a given pressure, saturated steam has one temperature 
 and one weight per cubic foot, neither of which can change so long as the 
 steam remains in immediate contact with water. Superheated steam at the 
 same pressure has a greater temperature and less weight per cubic foot than 
 saturated steam, and both the temperature and weight per cubic foot may vary 
 while the pressure remains constant if the volume increases or decreases accord- 
 ingly. In other words, both the pressure and the volume of superheated steam 
 must be constant in order to maintain a constant temperature and a constant 
 weight per cubic foot. 
 
 QUALITY OF STEAM 
 
 Moisture in Steam. The steam furnished by the average steam boiler 
 is not dry saturated steam, but is usually wet steam. A good boiler should 
 not show more than 2 or 3% of water in the steam. In a quantity of wet 
 steam, or a mixture of steam and water, the percentage of dry steam, expressed 
 as a decimal, is called the quality of the steam. For example, suppose that a 
 certain boiler generates wet steam that contains 3%, or .03, of moisture; then 
 the quality of the steam, or the percentage of dry steam, is .97. In other 
 words, the quality of the steam is equal to 1 minus the percentage of moisture, 
 expressed decimally, or Q = \ m, 
 
 in which Q = quality of steam; 
 
 m = percentage of moisture, expressed decimally. 
 
 EXAMPLE. What is the quality of steam that contains 2.7% of moisture? 
 
 SOLUTION. Expressed as a decimal, 2.7% = .027. Then, substituting this 
 value for m in the formula, Q = 1 .027 = .973. 
 
 Heat in Wet Steam. The total heat contained in 1 Ib. of dry steam is the 
 sum of the heat required to raise 1 Ib. of water from 32 F. to the boiling point 
 and the heat required to change the boiling water into steam of the same tem- 
 perature. That is, in the Steam Table, each value given in the fourth column 
 is the sum of the values given in the third and fifth columns and lying in the 
 same horizontal row. In a mixture of 1 Ib. of steam and water at the same 
 temperature there is less heat than in 1 Ib. of dry steam at the same temper- 
 ature; for all the water has not been changed to steam, and consequently the 
 latent heat of 1 Ib. of steam has not been utilized. Instead, there is present 
 only that part of the latent heat which is used to evaporate the portion of the 
 mixture that is dry steam, which is represented by the quality of the steam. 
 Thus, using the symbols given in the Steam Table, 
 
 H = q+r (1) 
 
 which is the formula for the total heat of 1 Ib. of dry steam. But if the steam 
 is wet, and Q represents the quality of the steam, expressed decimally, the 
 total heat of 1 Ib., represented by Hi, is 
 
 Hi = q+Qr (2) 
 
 EXAMPLE. What is the total heat of 10 Ib. of steam at 150 Ib. gauge 
 pressure, if the steam contains 5% of moisture? 
 
 SOLUTION. From the Steam Table, the heat of the liquid of 1 Ib. of dry 
 steam at 150 Ib., gauge, or 150 + 14.7 = 164.7 Ib., absolute, is q = 337.84 B. T. U.. 
 and the latent heat of 1 Ib. at the same pressure is r = 855.71 B. T. U. As the 
 moisture is 5%, the quality of the steam is 1.00 .05 = .95. Then, applying 
 formula 2, fli = 337.84 + .95X855.71 = l,150.76 B. T. U. 
 FLOW OF STEAM 
 
 Weight of Steam Discharged. The number of pounds of steam that will 
 flow continuously through a pipe of given diameter in 1 min. at specified pres- 
 sure may be calculated by the formula 
 
 in which W= weight of steam discharged, in pounds per minute; 
 
 w = weight of 1 cu. ft. of steam at pressure Pi; 
 
 Pi = pressure of steam at entrance to pipe, in pounds per square inch; 
 Pa = pressure of steam at discharge, in pounds per square inch; 
 
 L = length of pipe, in feet; 
 
 d = diameter of pipe, in inches. 
 
BOILERS 
 
 411 
 
 In applying the preceding formula in determining the diameter of the steam 
 pipe for an engine, it must be remembered that, in steam-engine work, the 
 steam is drawn intermittently from the pipe. Thus, assume that an engine 
 of 100 H. P., consuming 30 Ib. of steam per H. P. per hr., cuts off at one-fourth 
 stroke. In that case, the steam consumption per hour would be 100X30 
 = 3,000 Ib. But as the steam used at each stroke is drawn into the cylinder 
 during only one-fourth of the time required to complete the stroke, the 3,000 Ib. 
 of steam flows through the pipe in { hr. Then, in order to determine the 
 quantity of steam that would now continuously at the same velocity at which 
 it flows during admission to the cylinder, the actual steam consumption per 
 hour should be divided by the fraction representing the cut-off and the quotient 
 should be taken as the weight of steam discharged per hour. This value, 
 divided by 60, should be substituted for w in the formula. Thus, in the case 
 mentioned, the amount of steam discharged per hour, flowing continuously 
 at the same velocity as during the admission period, is 3,000-^ = 12,000, and 
 the value of W to be used in the formula is therefore 12,000-7-60 = 200 Ib. per 
 min. Knowing the pressures, the length of pipe, and the weight of the enter- 
 ing steam per cubic foot, different values of d may be assumed, until a value is 
 found that will give the necessary discharge W. This is the required pipe 
 diameter. 
 
 WEIGHT OF STEAM DELIVERED PER MINUTE THROUGH 100 FT. 
 OF PIPE WITH 1 LB. DROP OF PRESSURE 
 
 Initial 
 Gauge 
 Pressure 
 Pounds per 
 Square Inch 
 
 Nominal Diameter of Pipe, in Inches 
 
 3 
 
 3* 
 
 4 
 
 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 Weight, in Pounds, of Steam Delivered per Minute 
 Through 100 Ft. of Pipe with 1 Lb. Drop of Pressure 
 
 70 
 80 
 90 
 100 
 110 
 120 
 130 
 140 
 150 
 
 43.2 
 45.5 
 47.6 
 49.7 
 51.7 
 53.6 
 55.4 
 57.2 
 58.9 
 
 64.5 
 68.0 
 71.2 
 74.3 
 77.3 
 80.2 
 82.9 
 85.5 
 88.1 
 
 91.7 
 96.6 
 101.2 
 105.7 
 109.9 
 113.9 
 117.8 
 121.5 
 125.2 
 
 124.3 
 130.9 
 137.2 
 143.2 
 148.9 
 154.4 
 159.7 
 164.7 
 169.6 
 
 168.7 
 177.7 
 186.3 
 194.4 
 202.1 
 209.5 
 216.7 
 223.6 
 230.2 
 
 277.2 
 292.1 
 306.0 
 319.8 
 332.2 
 344.3 
 356.1 
 367.4 
 378.3 
 
 410.5 
 432.5 
 453.3 
 473.0 
 491.8 
 509.9 
 527.4 
 544.6 
 560.2 
 
 577.2 
 608.2 
 637.3 
 665.1 
 691.5 
 717.0 
 741.6 
 765.7 
 787.7 
 
 793.3 
 835.8 
 875.9 
 914.1 
 950.4 
 985.4 
 1,019.6 
 1,052.9 
 1,082.6 
 
 1.051.7 
 1,108.4 
 1,161.3 
 1,211.8 
 1,259.9 
 1,306.3 
 1,351.1 
 1,393.9 
 1,428.1 
 
 The approximate weights of steam delivered per minute through 100 ft. of 
 pipe of various diameters, with a drop of pressure of 1 Ib., are given in the 
 foregoing table. On the whole, these values are slightly higher than those 
 that would be obtained by the foregoing formula for the same conditions. If 
 the drop of pressure is more or less than 1 Ib., the value in the table must be 
 multiplied by the square root of the drop, to obtain the discharge. Also, 
 if the length of the pipe is more or less than 100 ft., divide 100 by the length, 
 in feet, and multiply the square root of this quotient by the value given in the 
 table. The following example illustrates this point. 
 
 EXAMPLE. How many pounds of steam will be discharged per minute, 
 with an initial gauge pressure oi 120 Ib. per sq. in., through a pipe 3 in. in 
 diameter and 400 ft. long, with a drop of pressure of 2 Ib.? 
 
 SOLUTION. From the table, the amount discharged through 100 ft. of 3-in. 
 pipe with a drop of 1 Ib. and an initial pressure of 120 Ib. per sq. in., is_53.6 Ib. 
 per min. But as the drop is 2 Ib., the table value isjnultiplied by V2 and as 
 the length is 400 ft., it must also be multiplied^ "N/H8- Hence, the discharge 
 for the given conditions will be 53.6X V2X Vi88 = 37.9 Ib. per min. 
 
 Resistance of Elbows and Valves. The presence of elbows, bends, and 
 valves in a steam pipe increases the resistance to the flow of steam and thus 
 increases the drop of pressure between the inlet and outlet ends. It has been 
 found that the resistance caused by an elbow or a sharp bend is approximately 
 
412 BOILERS 
 
 the same as the resistance of a length of pipe equal to 60 times the diameter, 
 and that a stop- valve has a resistance equal to that of a length ot pipe ol 
 40 diameters. In using the foregoing formula for the weight of steam dis- 
 charged, therefore, the value of L should be the equivalent length of pipe, 
 taking into account the bends and valves. 
 
 EXAMPLE. What is the equivalent length of 300 ft. bf 3-in. pipe containing 
 four elbows and six stop- valves? 
 
 SOLUTION. Each elbow has a resistance the same as that of 60 diameters 
 of pipe, or 60X3 = 180 in. = 15 ft., and four elbows have the resistance of 
 4X16 = 60 ft. of pipe. Each stop-valve has a resistance that is equivalent to 
 adding 40X3 = 120 in. = 10 ft. of pipe, and, as there are six valves, their com- 
 bined resistance is that of 6X10 = 60 ft. of pipe. The equivalent length of 
 pipe is, therefore, 300+60+60 = 420 ft. 
 
 Steam Pipes for Engines. In practice, the velocity of flow of steam in the 
 supply pipes of engines and pumps is usually not greater than 6,000 ft. per 
 min., although it is increased to as much as 8,000 ft. per mm. in some cases. 
 For exhaust pipes, a common value is 4,000 ft. per mm. The assumptions 
 made are that the cylinder is filled with steam at boiler pressure at each stroke 
 and that a volume of steam equal t9 the volume of the cylinder is released at 
 each stroke, so that the flow is practically continuous. The areas of the steam 
 and exhaust pipes may then be calculated by the formula 
 
 AS 
 a = - , 
 
 5 
 
 in which a = area of steam or exhaust pipe, in square inches; 
 A = area of cylinder, in square inches; 
 5 = piston speed, in feet per minute; 
 s = velocity of steam in pipe, in feet per minute. 
 
 EXAMPLE. Find the areas of the steam and exhaust pipes _for an engine 
 whose cylinder is 20 in. in diameter and whose piston speed is 450 ft. per mm. 
 SOLUTION. By the formula, the area of the steam pipe, assuming that s 
 -6,000 ft. per min., is 
 
 .7854X202X450 
 
 = 6^00 23.6 sq.m 
 
 Similarly, for the exhaust pipe, assuming that 5 = 4,000, the area is 
 
 BOILER PIPING 
 
 Principal Considerations. The piping of an engine and boiler plant requires 
 that careful attention be paid to all the details as well as to the general design, 
 not only in order to make it suitable for the purpose, but also in order to reduce 
 the likelihood of a breakdown. The main considerations regarding steam 
 piping are the size of the pipes, the arrangement and construction of the piping 
 system, the method of providing for expansion, and proper drainage. 
 
 Materials for Pipes. Most of the piping for steam and water is built up of 
 wrought-iron or steel pipe of standard size. The various grades of wrought- 
 iron and steel pipe are known as standard, extra strong, and double extra strong. 
 Both wrought-iron and steel pipe are used in the piping systems of power 
 plants. Formerly, wrought iron was chiefly used, but of late steel has been 
 employed, especially for the larger sizes of steam pipes. The two kinds are 
 equally reliable when made into expansion bends, copper bends as a general 
 
 rule being used only for very heavy work. 
 Expansion Joints. In installing steam 
 piping, provision must be made for ex- 
 ^\ pansion and contraction, which ordinarily 
 1 amounts to about lj in. per 100 ft. of pipe. 
 ""^ Generally, this may be provided for in the 
 arrangement of the piping, but for great 
 lengths that are straight, or nearly so, it 
 is necessary to use expansion joints, which 
 may be made in various ways. One form, shown in Fig. 1, is called the 
 slip joint. The ends a and b of the sections of pipe come together in a stuf- 
 fingbox c in order to make a steam-tight joint. The stud bolts are extra 
 long, so as to extend through holes in a flange d riveted to the pipe b. 
 
 = 
 
BOILERS 
 
 413 
 
 ^- -^ 
 
 Check-nuts e on the ends of the studs prevent the two ends of the pipe from 
 
 being forced apart by the steam pressure. The nuts e are not intended 
 
 ordinarily to be in contact with the flange; their 
 
 distance from the flange is adjusted so that the 
 
 proper expansion may occur. 
 
 In Fig. 2 is shown a corrugated expansion 
 
 joint, which is sometimes used on large exhaust p IG 2 
 
 pipes. It consists of a short section of flanged 
 
 corrugated pipe, usually copper, which is put in the steam pipe wherever 
 
 necessary. The elasticity of this section, due to the corrugations, permits 
 
 expansion and contraction. 
 
 Expansion Bends. The best way of allowing for expansion is by using 
 
 expansion bends, or bent pipes; but the 
 space they occupy often limits their 
 use. The forms of bends more com- 
 monly used are shown in Fig. 3, the 
 trade name being given below each 
 bend. Where a bent pipe is used, the 
 radius r of the bend should not be less 
 than six times the diameter of the pipe, 
 for wrought iron or steel; to secure the 
 proper spring in bends used on long 
 lines of piping, the radius should be 
 greater than this. Bends of copper pipe 
 may be of shorter radius, as copper 
 yields more readily than iron or steel. 
 
 Bends made from iron or steel pipe 
 must be bent while red hot. Iron and 
 steel pipe bends generally have iron 
 flanges fastened on; copper bends either 
 have composition flanges riveted and 
 brazed on, or have steel flanges, the 
 edges of the pipe being turned over. 
 The piping is usually installed so that it 
 is under a slight tension when cold; 
 when filled with steam, the expansion 
 of the pipes removes the tension, and 
 there is no stress on the pipe except 
 that due to the steam pressure. 
 
 Arrangement of Piping. The pipes 
 and fittings must be so proportioned 
 as to permit of free flow of steam or 
 water. Water pockets should be 
 avoided; and where such pockets are 
 unavoidable, they must be drained to 
 free them from water. By-pass pipes 
 should be arranged around feedwater 
 heaters, economizers, pumps, etc. The 
 system must be so designed as to give 
 perfect freedom for expansion and 
 contraction. 
 
 Perfect drainage must be provided 
 in order that all water of condensation 
 shall be fully separated from the steam. 
 Reliability is insured by careful 
 design and superior workmanship, com- 
 bined with the use of high-class mate- 
 rials and fittings and the judicious 
 S'acing of cut-out and by-pass valves, 
 rainage is best effected by arranging 
 the piping so that all the water of 
 condensation will flow by gravity to- 
 ward a point close to the delivery end 
 of the pipe, and then providing a drip 
 
 pipe at that point. A trap may be placed at the end of the drip pipe for 
 
 automatic draining. 
 
414 
 
 BOILERS 
 
 BOILER FITTINGS 
 
 SAFETY VALVES 
 
 The safety valve is a device attached to the boiler to prevent the steam 
 pressure from rising above a certain point. When _ steam is made more 
 rapidly than it is used, its pressure must necessarily rise; and if no means of 
 escape is provided for it, the result must be an explosion. Briefly described, 
 the safety valve consists of a plate, or disk, fitting over a hole in the boiler 
 shell and held to its place by a dead weight, by a weight on a lever, or by a 
 j. The weight or the spring is so adjusted that when the steam reaches 
 desired pressure the disk is raised from its seat, and the surplus steam 
 escapes through the opening in the shell. 
 
 rl 
 
 n 
 
 B j 
 
 H 
 
 G 
 
 
 FIG. 1 
 
 Weight of Ball for Lever Safety Valve. A simple diagram of a lever safety 
 valve is shown in Fig. 1. The valve stem and the ball are attached to the 
 lever at C and B, respectively, and the fulcrum is at F. 
 Let d = FB = distance from fulcrum to weight, in inches; 
 
 c = FG = distance from fulcrum to center of gravity of lever, in inches; 
 a = FC distance from fulcrum to center line of valve, in inches; 
 A =area of orifice beneath bottom of valve, in square inches; 
 W= weight of ball P, in pounds; 
 Wi = weight of valve and stem, in pounds; 
 Wz = weight of lever, in pounds; 
 
 p = blow-off pressure, in pounds per square inch. 
 
 Then, if the position of the ball P on the lever is fixed, the required weight 
 of the ball may be found by the formula 
 
 ,,,_a(PA-Wi)-W* 
 
 d 
 
 EXAMPLE. The area of the orifice is 10 sq. in., the distance from the valve 
 to the fulcrum is 3 in., and the length of the lever is 32 in. The valve and 
 stem weigh 5 lb., the lever weighs 12 lb., and the gauge pressure is 90 Ib. 
 What should be the weight W, if placed 2 in. from the end of the lever, assuming 
 the lever to be straight? 
 
 SOLUTION. In this case, c = 32-J-2 = 16 in., and d = 32-2 = 30 in. Then, 
 substituting in the formula, 
 
 TT/_ 3XQOX10 -5) -12X16 __ 
 
 -83. lib. 
 
 Position of Ball for Lever Safety Valve. If the ball of a lever safety valve 
 has a known weight and it is desired to find at what distance from the fulcrum 
 it must be placed so as to give a required blow-off pressure, the formula to be 
 used is 
 
 ,_a(pA-Wi)-W z c 
 
 W 
 in which the various letters have the same meanings as before. 
 
 EXAMPLE. Suppose all the quantities to remain the same as in the solution 
 of the preceding example, except that it is desired that the boiler should blow 
 off at 75. lb. gauge pressure, instead of 90 lb. What will be the distance of 
 the weight from the fulcrum? 
 
 SOLUTION. Applying the formula 
 
 , 3X(75X10-5)-12X16 , 
 o = gg^ = 24.58 in. 
 
 Roper's Safety-Valve Rules. Some inspectors of the United States Steam- 
 boat Inspection Service prefer to have lever safety-valve problems worked 
 
BOILERS 415 
 
 out by the rules that follow, known among American marine engineers as 
 Roper's rules. 
 
 Let A = area of valve, in square inches; 
 
 D distance from center line of valve to fulcrum, in inches; 
 
 L = distance of weight from fulcrum, in inches; 
 
 P = steam pressure, in pounds per square inch; 
 
 W = weight of load or weight on lever, in pounds; 
 
 V = weight of valve and stem, in pounds; 
 
 w = weight of lever, in pounds; 
 
 / = distance from fulcrum to center of gravity of lever, in inches. 
 Then, the pressure at which the safety-valve will blow off is found by the 
 formula 
 
 If the distance L is known, the weight W to be hung on the lever is found 
 by the formula 
 
 w = APD-(wl+VD) (2) 
 
 The distance L from the fulcrum to the point at which the weight W is 
 hung is found by the formula 
 
 T APD-(wl+VD) (3 ) 
 
 W 
 
 Area of Safety Valve. By area of safety valve is meant the area of the 
 opening in the valve seat; that is, the area of the surface of the valve in con- 
 tact with steam when the valve is closed. The size of the valve relative to the 
 size of the boiler and the working pressure is prescribed by law in many locali- 
 ties, and must be made to conform to the law wherever such law is in existence. 
 In localities having no law governing this matter, the size of the safety valve 
 may be calculated by the accompanying formulas, which are based on practice 
 and recommended by leading authorities. 
 
 For natural draft, 
 
 For artiacial draft, 
 
 (2) 
 
 in which G = grate surface, in square feet ; 
 
 p = steam, gauge pressure, in pounds per square inch; 
 10 = weight of coal burned per hour, in pounds; 
 A = least area of safety valve, in square inches. 
 
 Location of Safety Valve. The safety valve should be placed in direct con- 
 nection with the boiler, so that there can be no possible chance of cutting off 
 the communication between them. A stop-valve placed between the boiler 
 and the safety valve is a very fruitful cause of boiler explosions. Again, the 
 safety valve must be free to act, and to prevent it from corroding fast to its 
 seat, it should be lifted from the seat occasionally. Care must be taken to 
 prevent persons ignorant of the importance of safety valves from raising the 
 blow-off pressure by adding to the weights or increasing the tension of the 
 spring. To this end, the weights of lever safety valves are often locked in 
 position by the boiler inspector. 
 
 FUSIBLE PLUGS 
 
 Fusible plugs are devices placed in the crown sheets of furnaces, or in 
 similar places, to obviate danger from overheating through lack of water. 
 The plug often consists of an alloy of tin, lead, and bismuth, which melts at a 
 comparatively low temperature. In many localities, the law requires that 
 fusible plugs shall be attached to all high-pressure boilers. 
 
 The fusible plugs in common use are shown in section, on the next 
 page. They consist of brass or iron shells threaded on the outside with a 
 standard pipe thread. The plugs have some form of conical filling, the larger 
 end of the filling receiving the steam pressure. The conical form of the filling 
 prevents it from being blown out by the pressure of the steam. Fusible plugs 
 applied from the outside differ from those applied from the inside, as shown. 
 
 Location of Fusible Plugs. In the absence of local laws, the following 
 rules issued by the Board of Boiler Rules of the State of Massachusetts may 
 be adopted. Fusible plugs must be filled with pure tin, and the least diameter 
 
416 BOILERS 
 
 shall not be less than \ in., except for working pressures over 175 lb., gauge, 
 or when it is necessary to place a fusible plug in a tube, in which cases the least 
 diameter of fusible metal shall not be less than 
 | in. The location of fusible plugs shall be as 
 follows: 
 
 In horizontal return-tubular boilers, in the 
 back head, not less than 2 in. above the upper 
 row of tubes and projecting through the sheet 
 not less than 1 in. 
 
 In horizontal flue boilers, in the back head, 
 on a line with the highest part of the boiler 
 exposed to the products of combustion, and 
 
 projecting through the sheet not less than 1 in. 
 
 Sns/afe Type Oute/de Type j n i OCO motive-type or star water-tube boil- 
 
 ers, in the highest part of the crown sheet and projecting through the sheet 
 
 In vertical fire-tube boilers, in an outside tube, placed not less than one- 
 third the length of the tube above the tower tube-sheet. 
 
 In vertical submerged-tube boilers, in the upper tube-sheet. 
 
 In water-tube boilers of the Babcock & Wilcox type, in the upper drum, not 
 less than 6 in. above the bottom of the drum and projecting through the sheet 
 
 In Stirling boilers of standard type, in the front side of the middle drum 
 not less than 6 in. above the bottom of the drum and projecting through the 
 sheet not less than 1 in. 
 
 In Stirling boilers of the superheated type, in the front drum, not less than 
 6 in. above the bottom of the drum, and exposed to the products of combustion, 
 projecting through the sheet not less than 1 in. 
 
 In water-tube boilers of the Heine type, in the front course of the drum, 
 not less than 6 in., from the bottom of the drum, and projecting through the 
 sheet not less than 1 in. 
 
 In Robb-Mumford boilers of standard type, in the bottom of the steam and 
 water drum, 24 in. from the center of the rear neck, and projecting through the 
 sheet not less than 1 in. 
 
 In water-tube boilers of the Almy type, in a tube directly exposed to the 
 products of combustion. . 
 
 In vertical boilers of the Climax or Hazleton type, in a tube or center drum, 
 not less than one-half the height of the shell, measuring from the lowest circum- 
 ferential seam. 
 
 In Cahall vertical water-tube boilers, in the inner sheet of the top drum, 
 not less than 6 in. above the upper tube sheet. 
 
 In Scotch marine-type boilers, in the combustion-chamber top, and pro- 
 jecting through the sheet not less-than 1 in. 
 
 In dry-back Scotch-type boilers, in the rear head, not less than 2 in. above 
 the top row of tubes, and projecting through the sheet not less than 1 in. 
 
 In Economic-type boilers, in the rear head, above the upper row of tubes. 
 
 In cast-iron sectional heating boilers, in a section over and in direct contact 
 with the products of combustion in the primary combustion chamber. 
 
 In other types and new designs, fusible plugs shall be placed at the lowest 
 permissible water level, in the direct path of the products of combustion, as 
 near the primary combustion chamber as possible. 
 
 CONNECTION OF STEAM GAUGE 
 
 A steam gauge should be connected to the boiler in such a manner that it 
 will neither be injured by heat nor indicate incorrectly the pressure to which 
 it is subjected. To prevent injury from heat, a so-called siphon is placed 
 between the gauge and the boiler. This siphon in a short time becomes filled 
 with water of condensation, which protects the spring of the gauge from the 
 injury the hot steam would cause. Care should be taken not to locate the 
 steam-gauge pipe near the main steam outlet of the boiler, as this may cause 
 the gauge to indicate a lower pressure than really exists. In locating the steam 
 gauge, care must also be taken not to run the connecting pipe in such a manner 
 that the accumulation of water in it will cause an extra pressure to be shown. 
 
 BLOW-OFFS 
 
 For the double purpose of emptying the boiler when necessary and of 
 discharging the loose mud and sediment that collect from the feed water, every 
 boiler is provided with a pipe that enters the boiler at its lowest point. This 
 
BOILERS 417 
 
 pipe, which is provided with a valve or a cock, is commonly known as the 
 bottom blow-off. The position of the blow-off pipe varies with the design of 
 the boiler; in ordinary return-tubular boilers, it is usually led from the bottom 
 of the rear end of the shell through the rear wall. Where the boiler is fitted 
 with a mud-drum, the blow-off is attached to the drum. 
 
 Blow-Off Cocks and Valves. While in many boiler plants globe valves 
 are used on the blow-off pipe, they have the disadvantage that the valve 
 may be kept from closing properly by a chip of incrustation or similar matter 
 getting between the valve and its seat, with the result that water may leak out 
 of the boiler unnoticed. Plug cocks packed with asbestos are widely used, 
 the asbestos packing obviating the objectionable features of the ordinary plug 
 cock. Gate valves are also used to some extent, but have the same disadvant- 
 age as globe valves. In the best modern practice, the blow-off pipe is fitted 
 with two shut-off devices. The one shut-off may be an asbestos-packed cock 
 and the other some form of valve, or both may be cocks or valves, the idea 
 underlying this practice being that leakage past the shut-off nearest the boiler 
 will be arrested by the other. 
 
 Protection of Blow-Off Pipe. When exposed to the gases of combustion, 
 the bottom blow-off pipe should always be protected by a sleeve made of pipe, 
 by being bricked in, or by a coil of plaited asbestos packing. If this precaution 
 is neglected, the sediment and mud collecting in the pipe, in which there is no 
 circulation, will rapidly become solid. The blow-off pipe should lead to some 
 convenient place entirely removed from the boiler house and at a lower level 
 than the boiler. Sometimes it may be connected to the nearest sewer. In 
 many localities, however, ordinances prohibit this practice; the blow-off is then 
 connected to a cooling tank, whence the water may be discharged into the sewer. 
 
 FURNACE FITTINGS 
 
 Bridge Wall. The bridge, also termed the bridge wall, is a low wall at the 
 back end of the grate; it forms the rear end of the furnace and causes the flame 
 to come into close contact with the heating surface of the boiler. It is usually 
 built of common brick and faced with firebrick. The passage between the 
 bridge and the boiler shell should not be too small; its area may be approx- 
 imately one-sixth the area of the grate. The space between the grate and the 
 shell should be ample for complete combustion, and the distance between 
 the grate and the boiler shell may be made about one-half the diameter 
 of the shell. 
 
 Fixed Grates. The grate, which is nearly always made of cast iron, fur- 
 nishes a support for the fuel to be burned and must be provided with spaces 
 
 for the admission of air. The area 
 of the solid portion of the grate is 
 usually made nearly equal to the 
 combined area of the air spaces. 
 
 [ ri r i The common type of fixed grate 
 
 I *-^_^^ a I ^ * ' is made of single bars a, Fig. 1, 
 
 "~~ LL "* placed side by side in the furnace. 
 
 PJQ * The thickness of the lugs cast on 
 
 the sides of the bars determines the 
 
 width of the open spaces of the grate. It is the general practice to make the 
 thickness across the lugs twice the thickness of the top of the bar. For long 
 furnaces, the bars are generally made in two lengths of about 3 ft. each, with 
 a bearing bar in the middle of the grate. Long grates are generally set with a 
 downward slope toward the bridge wall of about f in. per ft. of length. 
 
 For the larger sizes of anthracite and bituminous coal, the air space may 
 be from f to f in. wide, and the grate bar may have the same width. For 
 pea and nut coal, the air space may 
 be from f to in., and for finely 
 divided fuel, like buckwheat, rice, 
 bird's-eye, culm, and slack, air spaces 
 from & to f in. may be used. 
 
 The grate bar shown in Fig. 2, p IG 2 
 
 and known as the herring-bone grate 
 
 bar, has in many places superseded the ordinary grate bar, because it will usually 
 far outlast a set of ordinary grate bars. Herring-bone grate bars can be 
 obtained in a great variety of styles and with different widths of air spaces. 
 They are usually supported on cross-bars, and, like many other forms of grate 
 27 
 
418 
 
 BOILERS 
 
 bars, may be arranged with trunnions, so as to rock the individual bars by means 
 of hand levers. 
 
 A form of cast-iron grate bar for the burning of sawdust is shown in Fig. 3. 
 The bar is semicircular in cross-section and is provided with circular openings 
 
 for the introduction of air. Lugs 
 are cast on each side of the bar 
 to serve as distance pieces in pro- 
 vid ing air spaces between the bars. 
 Dead Plate. The front ends 
 of the grate bars are usually sup- 
 -TIG- 6 ported on the dead plate, which 
 
 is a flat cast-iron plate placed across the furnace just inside the boiler front 
 and on a level with the bottom of the furnace door. The purpose of the 
 dead plate is twofold: It forms a support for the firebrick lining of the boiler 
 front, and a resting place on which bituminous coal may be coked before it is 
 placed on the fire. To support the grate bars, the inner edge of the dead plate 
 is either beveled or a lip is provided, as at a, Fig. 4. 
 
 Objection to Stationary Grate Bars. The greatest objection to stationary 
 grate bars is that with them the furnace door must be kept open for a con- 
 siderable length of time when the fire is being cleaned. Cleaning fires when the 
 boiler has a stationary grate not only severely taxes the fireman, but the inrush 
 of cold air chills the boiler plates, thus producing stresses that in the course 
 of time will crack them. 
 
 Shaking Grates. There are on the market many designs of shaking grates 
 for large steam boilers, differing chiefly in detail and arrangement. Usually 
 the grate bars are hung on trunnions at each 
 end and are connected together with bars to 
 which are attached shaking rods that extend 
 forwards through the furnace front. Levers or 
 handles are attached to the shaking rods, and 
 by working them back and forth the grate bars rlG. 4 
 
 receive a rocking motion that breaks up the bed of coal on the grate and serves 
 to shake the ashes through into the ash-pit. The fires may thus be kept clean 
 without the necessity of opening the fire-doors. 
 
 Classes of Mechanical Stokers. A mechanical stoker is a power-driven 
 rocking grate arranged so as to give a uniform feed of coal and: to rid itself 
 continuously of ashes and clinkers. The principal designs of mechanical 
 stokers and automatic furnaces may be divided into 
 two general classes, overfeed and underfeed. 
 
 Overfeed Stoker. In overfeed stokers the 
 fixed carbon of the coal is burned on inclined 
 grates. The coal is pushed on to these grates, 
 which are given a sufficiently rapid vibratory mo- 
 tion to feed it down at such a rate that practically 
 all the carbon is burned before reaching the lower 
 end, where the ashes and clinkers are discharged. 
 In Fig. 5 is shown a sectional view of a stoker of 
 this class. The 
 coal is fed into 
 the hopper a, 
 from which it is 
 pushed by the 
 pusher plate 6 
 on to the dead 
 plate c, where 
 it is heated. 
 From c it passes 
 to the grate d. 
 Each bar is sup- 
 ported at its 
 
 __ _ ends by trunn- 
 
 FlG - 5 ions and is con- 
 
 nected by an arm to a rocker bar , which is slowly moved to and fro by an 
 eccentric on the shaft s, so as to rock the grates back and forth; the grates 
 thus gradually move the burning fuel downwards. The ashes and clinkers 
 are discharged from the lower grate bar on to the dumping grate e. A guard / 
 may be raised, as shown by the dotted lines, so as to prevent coke or coal from 
 falling from the grate bars into the ash-pit when the dumping grate is lowered. 
 
BOILERS 
 
 419 
 
 Air for burning the gases is admitted in small jets through holes in the air 
 tile g, and the mixture of gas and air is burned in the hot chamber between the 
 firebrick arch h and the bed of burning coke below. 
 
 Underfeed Stoker. The stoker shown in Fig. 6 illustrates the principle of 
 operation and the construction of the underfeed stoker. Coal is fed into the 
 hopper a, from which it is drawn by the spiral conveyer b and forced into the 
 magazine d. The incoming supply of fresh coal forces the fuel upwards to the 
 surface and over the sides of the magazine on the grates, where it is burned. 
 A blower forces air through a pipe / into the chamber g surrounding the maga- 
 
 
 FIG. 6 
 
 zine. From g the air passes upwards through hollow-cast iron tuyere blocks 
 and out through the openings, or tuyeres e. The gas formed in the magazine, 
 mixed with the jets of air from the tuyeres, rises through the burning fuel 
 above, where it is subjected to a sufficiently high temperature to secure its 
 combustion. Nearly all the air for burning the coal is supplied through the 
 tuyeres, only a very small portion of the supply coming through the grate. 
 The ashes and clinkers are gradually forced to the sides of the grate against 
 the side walls of the furnace, from which they are removed from time to time 
 through doors in the furnace front similar to the fire-doors of an ordinary 
 furnace. In other words, owing to the construction of the underfeed stoker, 
 the fire must periodically be cleaned from clinkers and the ashes removed 
 by hand. 
 
 COVERING FOR BOILERS, STEAM PIPES, ETC. 
 
 The losses by radiation from uncovered pipes and vessels containing steam 
 are considerable, and in the case of pipes leading to steam engines, are mag- 
 nified by the action of the condensed water in the cylinder. It therefore is 
 important that such pipes should be well protected. The accompanying 
 table gives the loss of heat from steam pipes naked, and covered with wool or 
 hair felt of different thickness, the steam pressure being assumed at 75 lb., 
 and the exterior air at 60. 
 
 There is a wide difference in the value of different substances for protection 
 from radiation, their values varying nearly in the reverse ratio to their con- 
 ducting power for heat, up to their ability to transmit as much heat as the 
 surface of the pipe will radiate, after which they become detrimental, rather 
 than useful, as covering. This point is reached nearly at baked clay or brick. 
 
420 
 
 8 
 
 BOILERS 
 
 
 
 t- OOO 
 O CO i-l 
 
 O N 
 
 ^ eo 
 
 00 COM<NOC<3 
 
 >o O t^ c< oo i-^ co 
 
 oo o; <N O5 1>; i-; * 
 
 (NOOi-ilNO'* 
 CC 00 Tf< CO <N O 
 
 O t^ t^ 00 * 00 
 
BOILERS 
 
 421 
 
 A smooth or polished surface is of itself a good protection, polished tin or 
 Russia iron having a ratio, for radiation, of 53 to 100 for cast iron. Mere 
 color makes but little difference. 
 
 CONDUCTING POWER OF VARIOUS SUBSTANCES 
 
 (From Peclet) 
 
 Substance 
 
 Conducting 
 Power 
 
 Substance 
 
 Conducting 
 Power 
 
 
 .274 
 
 Wood, across fiber 
 
 83 
 
 Eiderdown 
 Co'tton or wool, any 
 
 .314 
 
 Cork 
 Coke, pulverized ... 
 
 1.15 
 1.29 
 
 density 
 
 .323 
 
 India rubber 
 
 1.37 
 
 
 .418 
 
 Wood, with fiber 
 
 1.40 
 
 
 .523 
 
 Plaster of Paris 
 
 3 86 
 
 Wood ashes 
 
 .531 
 
 Baked clay 
 
 4.83 
 
 Straw 
 
 .563 
 
 Glass . . 
 
 660 
 
 Charcoal powder 
 
 .636 
 
 Stone 
 
 13.68 
 
 
 
 
 
 Hair or wool felt has the disadvantage of becoming soon charred from 
 the heat of steam at high pressure, and sometimes of taking fire therefrom. 
 This has led to a variety of cements for covering pipes composed generally 
 of clay mixed with different substances, as asbestos, paper fiber, charcoal, 
 etc. A series of careful experiments, made at the Massachusetts Institute 
 of Technology showed the condensation of steam in a pipe covered by one 
 of them, as compared with a naked pipe, and one covered with hair felt, was 
 100 for the naked pipe, 67 for the cement covering, and 27 for the hair felt. 
 
 The presence of sulphur in the best coverings and its recognized injurious 
 effects make it imperative that moisture be kept from the coverings, for, if 
 present, it will surely combine with the sulphur, thus making it active. Stated 
 in other words, the pipes and coverings must be kept in good repair. Much 
 of the inefficiency of coverings is due to the lack of attention given them; 
 they are often seen hanging loosely from the pipe that they are supposed 
 to protect. 
 
 RELATIVE VALUE OF NON-CONDUCTORS 
 
 (From Chas. E. Emery, Ph. D.) 
 
 Material 
 
 Value 
 
 Material 
 
 Value 
 
 
 3.35 
 
 Wood across the grain 
 
 .40 to .55 
 
 Loose lampblack 
 Goose feathers 
 
 1.12 
 1.08 
 
 Loam, dry and open . . . 
 Chalk ground 
 
 .55 
 .51 
 
 Pelt, hair or wool 
 
 1.00 
 
 Coal ashes 
 
 .35 to .49 
 
 Carded cotton ... . 
 
 1.00 
 
 Gas-house carbon 
 
 .47 
 
 Charcoal from cork .... 
 
 .87 
 
 Asbestos paper 
 
 .47 
 
 Mineral wool 
 
 .68 to .83 
 
 Paste of fossil meal and 
 
 
 Fossil meal 
 
 .66 to .79 
 
 
 .47 
 
 Straw rope, wound spir- 
 ally 
 
 .77 
 
 Asbestos, fibrous 
 Plaster of Paris, dry 
 
 .36 
 .34 
 
 Rice chaff, loose 
 
 .76 
 
 Clay, with vegetable 
 
 
 Carbonate of magnesia 
 
 .67 to .76 
 
 fiber 
 
 .34 
 
 Charcoal from wood . . . 
 Paper 
 
 .63 to .75 
 .50 to .74 
 
 Anthracite powdered. . . 
 Coke, in lumps 
 
 .29 
 .27 
 
 Cork 
 
 .71 
 
 Air space, undivided . 
 
 .14 to .22 
 
 Sawdust 
 
 .61 to .68 
 
 Sand 
 
 .17 
 
 Paste of fossil meal and 
 
 .63 
 
 Baked clay, brick 
 Glass 
 
 .07 
 .05 
 
 Wood ashes 
 
 .61 
 
 Stone 
 
 .02 
 
 
 
 
 
422 
 
 BOILERS 
 
 The preceding table is deduced from tests of raw materials contained 
 in commercial pipe coverings and does not indicate the relative values of cover- 
 ings into whose composition they enter. Mineral wool, a fibrous material made 
 from blast-furnace slag, is a good protection, and is incombustible. Cork 
 chips, cemented together with water glass make one of the best coverings 
 known. 
 
 A cheap jacketing for steam pipes, but a very efficient one, may be applied 
 as follows: First, wrap the pipe in asbestos paper, though this may be dis- 
 pensed with; then lay from 6 to 12 strips of wood lengthwise, according to 
 size of pipe, binding them in position with wire or cord, and around the frame- 
 work thus constructed wrap roofing paper, fastening it by paste or twine. 
 For flanged pipe, space may be left for access to the bolts, which space should 
 be filled with felt. If exposed to weather, tarred paper should be used or the 
 exterior should be painted. A French plan is to cover the surface with a rough 
 flour paste, mixed with sawdust until it forms a moderately stiff dough. It 
 should be applied with a trowel, in four or five layers each \ in. thick. If iron 
 surfaces are well cleaned from grease, the adhesion is perfect; for copper, a 
 hot solution of clay in water should be applied. A coating of tar renders the 
 composition impervious to the weather. 
 
 BOILER FEEDING AND FEEDWATER 
 
 INJECTORS 
 
 Classification of Injectors. Injectors may be divided into two general 
 classes, namely, non-lifting and lifting injectors. Non-lifting injectors are 
 intended for use where there is a head of water available. When the water 
 comes to a non-lifting injector under pressure, as from a city main, it can be 
 placed in almost any convenient position close to the boiler. Lifting injectors 
 are of two distinct types, called automatic injectors and positive injectors. As 
 positive injectors generally have two sets of tubes, they are frequently called 
 double-tube injectors. Automatic injectors are so called from the fact that they 
 will automatically start again in case the jet of water is broken by jarring or 
 other means. Positive, or double-tube injectors are provided with two sets of 
 tubes, one set of which is used for lifting the water, and the other set for forcing 
 the water thus delivered to it into the boiler. A positive injector has a wider 
 range than an automatic injector and will handle a hotter feed- water supply; 
 it will also lift water to a greater height than the automatic injector. 
 
 Advantages and Disadvantages of Injectors. The advantages of the injec- 
 tor as a boiler feeding apparatus are its cheapness, compared with a pump of 
 equal capacity; it occupies but little space; the repair bills are low, owing to the 
 absence of moving parts; no exhaust piping is required, as with a steam pump; 
 it delivers hot water to the boiler. 
 
 The disadvantages of the injector are that it will not start with a steam pres- 
 sure less than that for which it is designed, and that it will stand but little 
 abuse, being poorly adapted for handling water containing grit or other matter 
 liable to cut the nozzles. 
 
 Size of Injector. Most engineers prefer to select a size of injector having 
 a capacity per hour about one-half greater than the maximum evaporation 
 per hour in order to have some reserve capacity. The maximum evaporation, 
 
 WATER DELIVERED BY INJECTORS 
 
 Diameter of 
 Throat 
 Decimals of an 
 Inch 
 
 Delivery, in Gallons per Hour, with a Pressure 
 per Square Inch of 
 
 30 Lb. 
 
 45 Lb. 
 
 60 Lb. 
 
 75 Lb. 
 
 90 Lb. 
 
 .10 
 .15 
 .20 
 .25 
 .30 
 
 56 
 127 
 226 
 354 
 505 
 
 69 
 156 
 278 
 434 
 624 
 
 80 
 180 
 321 
 502 
 722 
 
 89 
 201 
 360 
 561 
 
 807 
 
 98 
 221 
 393 
 615 
 
 884 
 
BOILERS 
 
 when not known, may be estimated in United States gallons by one of the fol- 
 lowing rules, which hold good for ordinary combustion rates under natural 
 draft: 
 
 Rule I. For plain cylindrical boilers, multiply the product of the length and 
 diameter in feet by 1 .3. 
 
 Rule. II. For tubular boilers, either horizontal or vertical, multiply the product 
 of the square of the diameter, in feet, and the length, in feet, by 1.9. 
 
 Rule III. For water-tube boilers, multiply the heating surface, in square feet, 
 by .4. 
 
 Rule IV. For boilers not covered by the foregoing rules, multiply the grate 
 surface, in square feet, by 12. 
 
 Rule V. // the coal consumption, in pounds per hour, is known, it may be 
 taken as representing the number of gallons evaporated per hour, 
 
 No standard method of designating the size of an injector is followed by 
 all makers; therefore, such an instrument must be selected from the lists of 
 capacities published by the different makers. 
 
 WATER REQUIRED PER MINUTE TO FEED BOILERS 
 
 fe 
 
 " 
 
 fe^ 
 
 ' 
 
 &u 
 
 
 
 
 
 ^ 
 
 <L> 
 
 
 o5 
 
 ^> to 
 
 
 Sfi\ 
 
 M 
 
 ^3 W 
 
 isfc 
 
 J^^ 
 
 M 
 
 & 03 
 
 8,-s 
 
 <i>m 
 
 a) g 
 
 & 
 
 & 
 
 *rl ^ 
 
 
 || 
 
 ga 
 
 
 
 rt G 
 1 ^ 
 
 gvM 
 
 ft O 
 
 tk 
 
 r 
 
 1 
 
 F 
 
 |.3 
 
 F 
 
 1 O 
 
 PCi 
 
 F 
 
 I 3 
 
 20 
 
 1.2 
 
 60 
 
 3.6 
 
 110 
 
 6.6 
 
 190 
 
 11.4 
 
 400 
 
 24.0 
 
 25 
 
 1.5 
 
 65 
 
 3.9 
 
 120 
 
 7.2 
 
 200 
 
 12.0 
 
 450 
 
 27.0 
 
 30 
 
 1.8 
 
 70 
 
 4.2 
 
 130 
 
 7.8 
 
 225 
 
 13.5 
 
 500 
 
 30.0 
 
 35 
 
 2.1 
 
 75 
 
 4.5 
 
 140 
 
 8.4 
 
 250 
 
 15.0 
 
 600 
 
 36.0 
 
 40 
 
 2.4 
 
 80 
 
 4.8 
 
 150 
 
 9.0 
 
 275 
 
 16.5 
 
 700 
 
 42.0 
 
 45 
 
 2.7 
 
 85 
 
 5.1 
 
 160 
 
 9.6 
 
 300 
 
 18.0 
 
 800 
 
 48.0 
 
 50 
 
 3.0 
 
 90 
 
 5.4 
 
 170 
 
 10.2 
 
 325 
 
 19.5 
 
 900 
 
 54.0 
 
 55 
 
 3.3 
 
 100 
 
 6.0 
 
 180 
 
 10.8 
 
 350 
 
 21.0 
 
 1,000 
 
 60.0 
 
 NOTE. A. S. M. E. standard of 30 lb., or 3.6 gal., per H. P. per hr., evapo- 
 rated from 100 F., to 70 lb. steam pressure per square inch. 
 
 Location of Injector. An injector must always be placed in the position 
 recommended by the maker. There must always be a stop- valve in the steam- 
 supply pipe to the injector. While lifting injectors, when working as such, 
 scarcely need a stop-valve in the suction pipe, it is advisable to supply it. 
 When the water flows to the injector under pressure, a stop- valve in the water- 
 supply pipe is a necessity. A stop-valve and a check- valve must be placed in 
 the feed-delivery pipe, with the stop-valve next to the boiler. The check- 
 valve should never be omitted, even if the injector itself is supplied with one. 
 No valve should ever be placed in the overflow pipe, nor should the overflow 
 be connected directly to the overflow pipe, but a funnel should be placed on 
 the latter so that the water can be seen. This direction does not apply to the 
 inspirator or to any other injector that has a hand-operated, separate over- 
 flow valve. In the inspirator, the overflow pipe is connected directly to the 
 overflow, but the end of the pipe must be open to the air. In general, where 
 the injector lifts water it is not advisable to have a foot-valve in the suction 
 pipe, as it is desirable that the injector and pipe may drain themselves when not 
 in use. A strainer should be placed on the end of the suction pipe. 
 
 Steam Supply to Injector. The steam for the injector must be taken from 
 the highest part of the boiler, as it must be supplied with dry steam. Under 
 no consideration should the steam be taken from another steam pipe. The 
 suction pipe should be as straight as possible and must be air-tight. When 
 connecting up an injector, the pipes should be cleaned by being blown out with 
 steam before the connection is made, because if a small bit of dirt gets into the 
 injector it will interfere seriously with its operation. 
 
 Injector Troubles. In the following discussion of injector troubles, the 
 suction pipe, strainer, feed-delivery pipe, and check-valve are considered as 
 parts of the injector. When searching for the cause of a trouble, therefore, 
 
424 BOILERS 
 
 the suction and delivery pipes should be carefully inspected as well as the 
 
 1 . Failure to Raise Water The causes that prevent an injector from raising 
 water are: 
 
 Suction pipe stopped up, due, generally, to a clogged strainer or to the pipe 
 itself being stopped at some point. In case the suction pipe is clogged, steam 
 should be blown back through the pipe to force out the obstruction. 
 
 Leaks in suction pipe, which prevent the injector forming the vacuum 
 'required to raise the water. To test the suction pipe for air leaks, plug up the 
 end and turn the full steam pressure on the pipe; leaks will then be revealed 
 by the steam issuing therefrom. Have the suction pipe full of water before 
 steam is turned on, as the presence of small leaks will be revealed better by 
 water than by steam. 
 
 Water in the suction pipe too hot; a leaky steam valve or leaky boiler check- 
 valve and leaky injector check- valve may allow hot water or steam to enter 
 the source of supply and heat the water until the injector refuses to handle it. 
 
 Obstruction in the lifting or combining tubes; or, the spills (or openings) in 
 the tubes through which the steam and water escape to the overflow may be 
 clogged up with dirt or lime. 
 
 2. Injector Primes But Will Not Force In some cases an injector will lift 
 water, but will not force it into the boiler; or, it may force part of it into the 
 boiler and the rest out of the overflow. When it fails to force, the trouble 
 may be due to one or the other of the following causes: 
 
 Choked Suction Pipe or Strainer. If the suction pipe or strainer is partly 
 choked, the injector will be prevented from lifting sufficient water to condense all 
 the steam issuing from the steam valve. The uncondensed steam, therefore, will 
 gradually decrease the vacuum in the combining tube until it is reduced so much 
 that the injector will not work. The remedy, when the supply valve is partly 
 closed, is to open it; when the suction pipe is choked, blow out the obstruction. 
 
 Suction Pipe Leaking. The leak may not be sufficient to prevent the 
 injector from lifting water, but the quantity lifted may be insufficient to con- 
 dense all the steam, which, therefore, destroys the vacuum in the combining 
 tube. A slight leak will pimply cut down the capacity of the injector. In 
 such a case an automatic injector will work noisily, on account of the overflow 
 valve seating and unseating itself as the pressure in the combining tube varies, 
 due to the leak. 
 
 Boiler Check-Valve Stuck Shut. If the boiler check-valve is completely 
 closed, the injector may or may not continue to raise water and force it out 
 of the overflow; this depends on the design of the injector. If the boiler check 
 is partly open, the injector will force some of the water into the boiler and the 
 remainder out of the overflow. In case the check-valve cannot be opened 
 wide, water may be saved by throttling both steam and water until the over- 
 flow diminishes, or, if possible, ceases. The steam should be throttled at the 
 valve in the boiler steam connection. If a check-valve sticks, it can sometimes 
 be made to work again by tapping lightly on the cap or on the bottom of the 
 valve body. 
 
 Obstruction in Delivery Tube. Any obstruction in the deliverv tube w411 
 cause a heavy waste of water from the overflow. To remedy this, the tube 
 will have to be removed and cleaned. 
 
 Leaky Overflow Valve. A leaky overflow valve is indicated by the boiler 
 check chattering on its seat. To remedy this defect, grind the valve on its 
 seat until it forms a tight joint. 
 
 Injector Choked With Lime. It is essential to the proper working of an 
 injector that the interior of the tubes be perfectly smooth and of the proper 
 bore. As in course of time the tubes become clogged with lime, the capacity 
 of the injector decreases until, finally, it refuses to work at all. If the water 
 used is very bad, it is frequently necessary to cleanse the tubes of the accumu- 
 lated lime. This may be done by putting the parts in a bath consisting of 
 1 part of muriatic acid to 10 parts of water. The tubes should be removed 
 from it as soon as the gas bubbles cease to be given off. 
 
 INCRUSTATION AND CORROSION 
 
 Incrustation. Broadly speaking, any deposit that is formed on the plates 
 and tubes of a boiler is termed scale, or incrustation; it is caused by impurities 
 that enter with the water and that are left behind in the boiler when the water 
 is evaporated. In passing through the soil, water dissolves certain mineral 
 substances, the most important of which are carbonate of lime and sulphate 
 of lime. Other substances frequently present in small quantities are chloride 
 
BOILERS 425 
 
 of sodium, or common salt, and chloride of magnesium. The water also often 
 contains other troublesome substances. 
 
 Impurities in Feedwater. Some of the more common impurities found in 
 feedwater, together with their properties, are as follows: 
 
 Carbonate of lime will not dissolve in pure water, but will dissolve in water 
 that contains carbonic-acid gas. It becomes insoluble and is precipitated 
 in the solid form when the water is heated to about 212 F.; the carbonic-acid 
 gas is driven off by the heat. 
 
 Sulphate of lime dissolves readily in cold water, but not in hot water. It 
 precipitates in the solid form when the water is heated to about 290 P., corre- 
 sponding to a gauge pressure of 45 Ib. 
 
 Chloride of sodium will not be precipitated by the action of heat unless the 
 water has become saturated with it. As it generally is present in but very 
 small quantities in fresh water, it will take a very long time for the water in 
 a boiler to become troublesome, and with the ordinary blowing down of a boiler 
 once a week or every 2 wk., there is little danger of the water becoming satu- 
 rated with it. Consequently, it is one of the least troublesome scale-forming 
 substances contained in fresh water. 
 
 Chloride of magnesium is one of the worst impurities in water intended for 
 boilers, for while not dangerous as long as the water is cold, it makes the water 
 very corrosive when heated, and when present in large quantities, it attacks 
 the metal and rapidly destroys it. 
 
 Organic matter by itself may or may not cause the water to become corrosive, 
 but will often cause foaming; when it is present in small quantities in water 
 containing carbonate or sulphate of lime, or both, it usually serves to keep 
 the deposits from becoming hard. 
 
 Earthy matter, like organic matter, is not dissolved in the water, but is in 
 mechanical suspension. It is very objectionable, especially when it is clay, 
 and when other scale-forming substances are present is liable to form a hard 
 scale resembling Portland cement. 
 
 Acids, such as sulphuric acid, nitric acid, tannic acid, and acetic acid, are 
 often present in the feedwater. The sulphuric acid is the most dangerous 
 one of these acids, attacking the metal of which the boiler is composed and 
 corroding it very rapidly. The other acids, while not so violent in their action 
 as the sulphuric acid, are also dangerous, and water containing any one should 
 be neutralized when it must be used. 
 
 Formation of Scale. The small solid particles due to precipitation of sub- 
 stances in solution or matter in mechanical suspension, remain for a time 
 suspended in the water, especially the carbonate of lime which will float on the 
 surface of the water. These particles will gradually settle on the plates, tubes, 
 and other internal surfaces. A large part of the impurities will be carried by 
 the circulation of the water to the most quiet part of the boiler and there settle 
 and form a scale. In a few weeks, if no means of prevention are used, the inner 
 parts of the boiler may be covered with a crust from & to 5 in. in thickness. 
 
 Danger of Scale. A scale & in. or less in thickness is thought by many to 
 be an advantage, as it protects the plates from the corrosive action of acids 
 in the water. When, however, the scale becomes i in. thick or more, heat is 
 transmitted through the plates and tubes with difficulty, more fuel is required, 
 and there is danger of overheating the plates. The chief danger from a heavy 
 incrustation is the liability of overheating the plates and tubes. Scale also 
 prevents a proper examination of the inside of the boiler, as it may hide a 
 dangerously corroded piece of plate or a defective rivet head. 
 
 Scale Containing Lime. The carbonate of lime forms a soft, muddy scale, 
 which when dry, becomes fluffy and flourlike. This scale may be easily swept 
 or washed out of the boiler by a hose, provided it is not baked hard and fast. 
 A carbonata scale is much harder to deal with when grease is allowed to enter 
 the boiler. The grease settles and mixes with the floury scale, making a spongy 
 crust that remains in contact with the plates, being too heavy to be carried 
 off by the natural circulation of the water. The sulphate of lime forms a 
 scale that soon bakes to the plates. 
 
 Kerosene as Scale Remover. Some substances seem to soften and aid in 
 detaching scale. Of these, kerosene oil has met with much favor. Its action 
 appears to be mechanical rather than chemical, the oil penetrating or soaking 
 through the scale and softening and loosening it. It is somewhat useful, too, 
 in preventing the formation of scale, enveloping the fine particles of the scale- 
 forming substances that, after precipitation, float on the surface of the water 
 for a little while. It seems that this prevents the particles from adhering 
 firmly to one another and to the metal when they finally settle. 
 
426 
 
 BOILERS 
 
 Removal of Scale by Chipping. A hard scale, when once formed, is gen- 
 erally removed by chipping it off with scaling hammers and scaling bars; soft 
 scale can be largely removed during running by a periodic use of the bottom 
 and surface blow-offs, and the remainder can usually be washed out and raked 
 out when the boiler is blown down and opened. In order to prevent the scale- 
 forming substances deposited on the metal from baking hard, it is advisable 
 to let the boiler cool down slowly until entirely cold preparatory to blowing 
 off, whenever circumstances permit this to be done. This cooling process 
 will generally take from 24 to 36 hr. 
 
 Removal of Mud. Mud and earthy matter by itself will not form any 
 hard scale, but will often do so when carbonate of lime and sulphate of lime 
 are present. An accumulation of such matter can be prevented, and most of. 
 it can be removed, by a periodic use of the bottom blow-off, removing any 
 remainder whenever the boiler is opened. 
 
 Internal Corrosion. Corrosion of boiler plates may be denned as the eating 
 away or wasting of the plates due to the chemical action of water. Corrosion 
 may be internal and external. Internal corrosion may present itself as uniform 
 corrosion, pitting or honeycombing, and groov- 
 ing. In cases of uniform corrosion large areas 
 of plate are attacked and eaten away. There 
 is no sharp line of division between the cor- 
 roded part and the sound plate. Corrosion 
 often violently attacks the staybolts and rivet 
 heads. 
 
 Pitting or Honeycombing. Pitting or honey- 
 combing of the boiler plates is readily per- 
 ceived. The plates are indented in spots with 
 holes and cavities from -fa to i in. deep. The 
 appearance of a pitted plate is shown in Fig. 1. 
 On the first appearance of pitting, the 
 surface so affected should be thoroughly 
 cleaned and a good coating of thick paint 
 made of red lead and boiled linseed oil shpuld 
 be applied. This treatment should be given 
 
 FIG. 1 
 
 from time to time to insure protection to the metal. 
 
 Grooving. Grooving, which means the formation of a distinct groove, is 
 generally caused by the buckling action of the plates when under pressure. 
 Thus, the ordinary longitudinal lap joint of a boiler slightly distorts the shell 
 from a truly cylindrical form, and the steam pressure tends to bend the plates 
 at the joint. This bending action is liable to start a small crack along the 
 lap, which, being acted on by corrosive agents in the water, 
 soon deepens into a groove, as shown in Fig. 2. 
 
 External Corrosion. External corrosion frequently attacks 
 stationary boilers, particularly those set in brickwork. The 
 causes of external corrosion are dampness, exposure to weather, 
 leakage from joints, moisture arising from the waste pipes or 
 blow-off, etc. External corrosion should be prevented by 
 keeping the boiler shell free from moisture, and the stoppage of 
 all leaks as soon as they appear. 
 
 Leakage at rivets and the calking edges of seams may be 
 caused by the delivery of the cold feed water on to the hot plates ; 
 another cause is the practice of emptying the boiler when hot 
 and then filling it with cold water. The leakage in both cases 
 is due to the sudden contraction of the plates. 
 
 In horizontal water-tube boilers of the inclined-tube type, 
 external corrosion principally attacks the ends of the tubes, 
 especially the back ends, close up to the headers into which 
 they are expanded. In the course of time this will cause 
 the tubes to leak around the expanded portion in the headers. 
 
 If leaks are attended to as soon as they occur, no corrosion will take place, 
 as the gases of combustion are harmless unless acting in conjunction with 
 water or dampness, or unless the coal is rich in sulphur. Should, however, 
 the ends of several tubes be found badly corroded but not yet leaking from that 
 cause, the tubes should by all means be removed and replaced. 
 
 Lamination. Sometimes what is called lamination, or the splitting of a 
 plate into thin layers, is revealed by the action of the fire in causing a bag or 
 blister to appear. Laminations due to slag and other impurities in the metal 
 which become flattened out when the plates are rolled, are shown at a, Fig. 3. 
 
 FIG. 2 
 
BOILERS 
 
 427 
 
 Under the action of the heat the part exposed to the fire will form a blister 
 which may finally open at the point 6 or c. If the laminated portion of the 
 plate is small, it may 
 be cut out and a patch 
 
 laminations in the same 
 plate, it is advisable 
 to put in a new plate. 
 
 Overheating. The heating of a plate beyond its normal temperature is 
 called overheating, and may be caused by low water or by incrustation. When 
 the plate is covered by a heavy scale, the plate becomes overheated, so that 
 it yields to the steam pressure, forming a pocket, as shown in Fig. 4, which 
 represents the shell sheet, or the sheet of a horizontal return-tubular boiler 
 directly oyer the fire. If the pogket is not discovered in time for the plate 
 to be repaired, it stretches until finally the material becomes too thin to with- 
 stand the steam pressure; the pocket then bursts with more or less liability 
 of an explosion. The vegetable or animal oils carried into the boiler from a 
 surface condenser are particularly liable to cause the formation of pockets. 
 Prevention of Incrustation and Corrosion. Incrustation can best be pre- 
 vented by purifying the feedwater prior to its entering the boiler, but can be 
 
 fairly satisfactorily prevented 
 by a chemical treatment of the 
 water in the boiler. When the 
 water contains large quantities 
 of substances that float on the 
 surface, mechanical means may 
 be resorted to, using the surface 
 blow-off at frequent intervals 
 or some equivalent skimming 
 device. Corrosion is prevented 
 
 FIG. 4 
 
 by neutralizing the acids in the 
 
 water by an alkali. Corrosion due to a perfectly fresh water can be prevented 
 by giving a protective coating to the metal, which may be a thick red-lead 
 paint made up with boiled linseed oil. Sometimes organic substances con- 
 taining tannic acid, such as oak bark, hemlock, or sumac, are used to loosen 
 or prevent scale. They should not be used, as they are liable to injure the 
 plates by corrosion. The accompanying table gives a list of scale-forming 
 substances and the means of preventing or neutralizing them. 
 
 SCALE-FORMING SUBSTANCES AND THEIR REMEDIES 
 
 Troublesome Substance 
 
 Trouble 
 
 Remedy or Palliation 
 
 Sediment, mud, clay, etc. 
 
 Incrustation 
 
 Filtration 
 
 
 
 Blowing off 
 
 Readily soluble salts 
 
 Incrustation 
 
 Blowing off 
 
 
 
 Heating feed 
 
 Bicarbonates of lime, magnesia, iron 
 
 Incrustation 
 
 Addition of caustic soda, 
 
 
 
 lime, or magnesia 
 
 Sulphate of lime 
 
 Incrustation 
 
 Addition of carbonate of 
 
 
 
 soda or barium chloride 
 
 Chloride and sulphate of magnesium 
 
 Corrosion 
 
 Addition of carbonate of 
 
 
 
 soda, etc. 
 
 Carbonate of soda in large amounts 
 
 Priming 
 
 Addition of barium chlo- 
 
 
 
 ride 
 
 Acid (in mine water) 
 
 Corrosion 
 
 Alkali 
 
 
 
 Heating feed 
 
 Dissolved carbonic acid and oxygen 
 
 Corrosion 
 
 Addition of caustic soda, 
 
 
 
 slaked lime, etc. 
 
 Grease (from condensed water) 
 
 Corrosion 
 
 Slaked lime and filtering 
 
 
 
 Carbonate of soda 
 
 
 
 Substitute mineral oil 
 
 Organic matter (sewage) 
 
 Priming 
 
 Precipitate with alum or 
 chloride of iron and filter 
 
 Organic matter 
 
 Corrosion 
 
 Same as last 
 
428 BOILERS 
 
 Use of Zinc in Boilers. Zinc is much used in marine boilers for the pre- 
 vention of both incrustation and corrosion. The zinc is distributed through 
 the boiler in the form of slabs. About 1 sq. in. of zinc surface should Be 
 supplied for every 50 Ib. of water in the boiler. 
 
 TESTING OF FEEDWATER 
 
 Testing for Corrosiveness. It is a good plan to occasionally test the feed- 
 water and also the water in the boiler for corrosiveness. This may be done by 
 B'acing a small quantity in a glass and adding a few drops of methyl orange, 
 the sample of water is acid, and hence corrosive, it will turn pink. If it is 
 alkaline, and hence harmless, it will remain yellow. The acidity may also be 
 tested by dipping a strip of blue litmus paper in the water. If it turns red, the 
 water is acid. This method is not so sensitive as the previous one, which 
 should be used in preference. If litmus paper is kept in stock, it should be 
 kept in a bottle with a glass stopper, as exposure to the atmosphere will cause 
 the paper to deteriorate. If the water in the" boilers has become corrosive and 
 corrosion has set in, the water in the gauge glass will show red or even black. 
 As soon as the color is beyond a dirty gray or straw color, it is advisable to 
 introduce lime or soda to neutralize the acid. 
 
 Testing for Carbonate of Lime. Pour some of the water to be tested into 
 an ordinary tumbler. Add a little ammonia and ammonium oxalate, and then 
 heat to the boiling point. If carbonate of lime is present, a precipitate will 
 be formed. 
 
 Testing for Sulphate of Lime. Pour some of the feed water into a tumbler 
 and add a few drops of hydrochloric acid. Add a small quantity of a solution 
 of barium chloride and slowly heat the mixture. If a white precipitate is 
 formed, which will not redissolve when a little nitric acid is added, sulphate 
 of lime is present. 
 
 Testing for Organic Matter. Add a few drops of pure sulphuric acid to the 
 sample of water. Then add enough of a pink-colored solution of potassium 
 permanganate to make the whole mixture a faint rose color. If the solution 
 retains its color after standing a few hours, no organic substances are present. 
 
 Testing for Matter in Mechanical Suspension. Keep a tumblerful of the 
 feedwater in a quiet place. If no sediment is formed in the bottom of the 
 tumbler after standing for a day, there is no mechanically suspended matter 
 in the water. 
 
 PURIFICATION OF FEEDWATER 
 
 Means of Purification. Water intended for boilers may be purified by 
 settlement, by filtration, by chemical means, and by heat. Filtration will 
 remove impurities in mechanical suspension, such as oil and grease, and earthy 
 matter, but will not remove substances dissolved in the water. Chemical 
 treatment of the water will render the scale-forming substances and corrosive 
 acids harmless, and may be applied either before or after the water enters the 
 boilers, but preferably the former. Purification by heat is based on the fact 
 that most of the scale-forming substances become insoluble and are precipi- 
 tated when the water containing them is heated to a high temperature. 
 
 Purification by Settlement. For feedwater containing much matter in 
 mechanical suspension, one of the simplest methods of purifying it is to provide 
 a relatively large reservoir, or a large tank for small steam plants, where the 
 impurities can settle to the bottom. While this method is fairly satisfactory 
 in removing earthy matter, it will not clear the water of finely divided organic 
 matter, which is usually lighter than the water and often so finely divided 
 as to be almost dissolved it in. 
 
 Purification by Filtration. Organic and earthy matter in mechanical sus- 
 pension is most satisfactorily removed by a filter, passing the water through 
 layers of sand, gravel, hay, or equivalent substances, or through layers of 
 cloth. Hay and cloth are of service, especially where the feedwater contains 
 oil or grease, as is the case where a surface condenser is used and the condensed 
 steam is used over again. 
 
 Purification by Chemicals. Chemical purification may take place before 
 or after the water enters the boiler, the former method being somewhat more 
 expensive. However, the purification is better carried out before the water 
 enters the boiler, as the amount of impurities entering the boiler will be greatly 
 reduced. The process adopted depends on the impurities. 
 
 Use of Quicklime. When the water contains only carbonate of lime, it 
 may be treated with slaked quicklime, using 28 gr. of lime for every 50 gr. of 
 lime present in the water, the quicklime precipitating the carbonate of lime and 
 being transformed into carbonate of lime itself during the process. 
 
BOILERS 429 
 
 Use of Caustic Soda. Water containing carbonate of lime may be treated 
 with caustic soda, which precipitates the former and leaves carbonate of soda, 
 which is harmless. For every 100 gr. of carbonate of lime 80 gr. of caustic 
 soda should be added. 
 
 Use of Sal Ammoniac. Sal ammoniac is sometimes added to water con- 
 taining carbonate of lime and will cause the latter to precipitate. Its use is 
 not advisable, however, because if used in excess there is danger of forming 
 hydrochloric acid, which will attack the boiler. 
 
 Treatment for Sulphate of Lime. While slaked lime will precipitate car- 
 bonate of lime, it will nave no effect on sulphate of lime, and water containing 
 the latter, either alone or in conjunction with carbonate of lime, must be treated 
 with other chemicals. The most available chemicals for water containing 
 both are carbonate of soda and caustic soda. These are often fed into the 
 boiler and will precipitate the carbonate and sulphate of lime, requiring the 
 sediment to be blown out or otherwise removed periodically. 
 
 Quantity of Chemicals to Use. When treating water containing carbonate 
 and sulphate of lime, caustic soda may be used either by itself or in combina- 
 tion with carbonate of soda, depending on the relative proportions of the 
 lime compounds present in the water. The amount of caustic soda or car- 
 bonate of soda to be used per gallon of feed water can be found as follows: 
 
 Rule I. Multiply the number of grains of carbonate of lime per gallon by 1.36. 
 If this product is greater than the number of grains of sulphate of lime per gallon, 
 only caustic soda is to be used. To find the quantity of caustic soda required per 
 gallon, multiply the number of grains of carbonate of lime in 1 gal. by .8. 
 
 Rule II. Multiply the number of grains of carbonate of lime per gallon 
 by 1.36. If this product is less than the number of grains of sulphate of lime per 
 gallon, multiply the difference by .78 to obtain the number of grains of carbonate 
 of soda required per gallon. To find the amount of caustic soda required per 
 gallon, multiply the number of grains of carbonate of lime in 1 gal. by .8. 
 
 EXAMPLE. A quantitative analysis of a certain feedwater shows it to 
 contain 23 gr. of sulphate of lime and 14 gr. of carbonate of lime per gallon. 
 How much caustic soda and carbonate of soda should be used per gallon to 
 precipitate the scale-forming substances? 
 
 SOLUTION. By rule I, 14X1.36 = 19 gr. As this product is less than the 
 number of grains of sulphate of lime per gallon, rule II is to be used. Applying 
 rule II, (23 - 19) X. 78 = 3. 12 gr. of carbonate of soda, and 14X.8 = 11.2 gr. of 
 caustic soda. 
 
 Use of Carbonate of Soda. Water containing sulphate of lime, but no 
 carbonate of lime, may be treated with carbonate of soda. The amount of the 
 latter that is required per gallon to precipitate the sulphate of lime is found by 
 multiplying the number of grains per gallon by .78. When using soda, it is 
 well to keep in mind that it will not remove deposited lime from the inside of a 
 boiler. All that the soda can do is to facilitate the separating of the lime, that 
 is, cause it to deposit in a soft state. This sediment must be removed 
 periodically. 
 
 Use of Trisodium Phosphate. For decomposing sulphate of lime, tribasic 
 sodium phosphate, more commonly known as trisodium phosphate, is often 
 used. This is claimed to act on the sulphate of lime, forming sulphate of 
 sodium and phosphate of lime, the former of which remains soluble and is 
 harmless, and the latter of which is a loose, easily removed deposit. Trisodium 
 phosphate also acts on carbonate of lime and carbonate of magnesia, forming 
 phosphate of lime and phosphate of magnesia, at the same time neutralizing 
 the carbonic acid released from the carbonate of lime and magnesia, and the 
 sulphuric acid released from the sulphates. 
 
 Neutralization of Acids. Acid water can be neutralized by means of an 
 alkali, soda probably being the best one. The amount of soda to be used can 
 best be found by trial, adding soda until the water will turn red litmus paper 
 blue. 
 
 Purification by Heat. Carbonate of lime and sulphate of lime become 
 insoluble if the water is heated, the former precipitating at about 212 F. and 
 the latter at about 290 F. This fact is taken advantage of in devices that 
 may be called combined feedwater heaters and purifiers; as they generally use 
 live steam, they are also called live-steam feedwater heaters. As no feedwater 
 heater can effect a direct saving of fuel except when the heat is taken from a 
 source of waste, a live-steam feedwater heater can affect the fuel C9nsumption 
 but indirectly. This it does by largely preventing the accumulation of scale 
 in the boiler and the attendant loss in economy due to the lowering of the 
 rate of heat transmission through a plate heavily covered with incrustation. 
 
430 BOILERS 
 
 FEEDWATER HEATING 
 
 The feedwater furnished to steam boilers must be raised from its normal 
 temperature to that of steam before evaporation can commence, and if not 
 otherwise accomplished, it will be done at the expense of fuel that should be 
 utilized in making steam. At 75 Ib. gauge pressure, the temperature of boiling 
 water is about 320 F., and if 60 is taken as the average temperature of feed- 
 water, 320-60 = 260 B. T. U. is required to raise 1 Ib. of water from 60 to 320. 
 It requires 1,151.5 B. T. U. to convert 1 Ib. of water at 60 into steam at 75 Ib. 
 gauge pressure, so that the 260 B. T. U. required for heating the water rep- 
 resents 260-r-l,151.5 = 22.6% of the total. All heat taken from a source of 
 waste, therefore, that can be imparted to the feedwater before it enters the 
 boilers is just so much saved, not only in cost of fuel but in boiler capacity. 
 
 Types of Exhaust-Steam Feedwater Heaters. The impurities contained 
 in the water will largely determine the type of exhaust-steam heater to be used 
 in any given plant. These heaters are divided into two general classes, namely, 
 open heaters and closed heaters. 
 
 An open heater is one in which the water space is open to the atmosphere. 
 In a direct-contact open heater, the exhaust steam comes in contact with the 
 water, which, by means of some one of a number of suitable devices, is broken 
 into spray or thin sheets so that it will readily absorb the heat of the steam. 
 In a coil heater, the exhaust steam passes through coils of pipe submerged in 
 a vessel containing the water to be heated, and open at the top. 
 
 A closed heater is a heater in which the feedwater is not exposed to the 
 atmosphere, but is subjected to the full boiler pressure. The steam does not 
 come in contact with the water; the latter is heated through contact with 
 metallic surfaces, generally those of tubes, that are heated by the exhaust 
 steam. 
 
 Selection of Heater. When the boiler feedwater is free from acids, salts, 
 sulphates, and carbonates, so that no scale is formed at a high temperature 
 the closed feedwater heater will be found satisfactory. Heaters of the coil 
 type may be used with pure water, but should not be used with water that 
 will precipitate sediment or scale-forming matter of any kind. The coil 
 heater is very efficient as a heater, as the water circulating through the coils 
 is a long time in contact with the surface surrounded and heated by the exhaust 
 steam. Heaters of the closed type with straight tubes and a sediment chamber 
 can be cleaned more readily than those having curved tubes, but the curved 
 tubes allow more freedom for expansion and contraction. Heaters of the 
 tubular type should have ample sediment chambers and may be used with 
 water that contains organic or earthy matter, but not with water containing 
 scale-forming ingredients. Carbonate of lime is likely to combine with earthy 
 matter and form an exceedingly hard scale. 
 
 Heaters of the open exhaust-steam type have the advantage of bringing 
 the exhaust steam in direct contact with the feedwater; some of the exhaust 
 steam is condensed, thus effecting a saving in feedwater, and sediment and 
 scale-forming ingredients, except sulphates of lime and magnesia, are precipi- 
 tated or will settle to the bottom of the heater. The oil in the exhaust steam 
 must be intercepted by special oil extractors, filters, or skimmers, generally 
 combined with the heater and, by automatic regulation, sufficient fresh feed- 
 water must be added to make up the total quantity required. When the 
 system is properly arranged, all live-steam drips and discharges from traps 
 are led to the heater. 
 
 BOILER TRIALS 
 
 Purposes of Boiler Trials. A boiler trial, or boiler test, as it is often called, 
 may be made for one or more of several purposes, the method of conducting 
 the trial depending largely on its purpose. The boiler trial may vary from the 
 simplest one, in which the only observations are the fuel burned and the water 
 fed to the boiler in a stated period of time, to the elaborate standard boiler trial, 
 in which special apparatus and several skilled observers are essential. The 
 object of a boiler trial may be to determine the efficiency of the boiler under 
 given conditions; the comparative value of different boilers working under 
 the same conditions; the comparative value of fuel; or the evaporative power, 
 or horsepower, of the boiler. 
 
 Observations During Trial. The essential operations of a boiler trial are 
 the weighing of the feedwater and fuel, and the observation of the steam 
 pressure, temperature of feedwater, and various other less important pressures 
 
BOILERS 431 
 
 and temperatures. These observations should be made simultaneously at 
 intervals of about 15 min. 
 
 Weighing the Coal. The coal supplied to the furnace is weighed out in lots 
 of 500 or 600 Ib. It is a convenient plan to have a box with one side open 
 placed on a platform scale. A weight is then placed on the scale beam sufficient 
 to balance the box. The scale may then be set at 500 or 600 Ib., the coal 
 shoveled in until the beam rises, and then fed directly from the box to the 
 furnace. After the test, the ashes and clinkers must be raked from the ash-pit 
 and grate and weighed. This weight subtracted from the weight of the coal 
 used gives the amount of combustible. 
 
 Measurement of Feedwater. The amount of water evaporated in a test 
 for comparative fuel values may be taken as equal to the amount of feedwater 
 supplied without introducing any serious error. The most reliable method 
 of measuring the feedwater delivered to the boilers is to weigh it. 
 
 Standard of Boiler Horsepower. When making a horsepower or an 
 efficiency test, a more elaborate method of procedure is required than for a 
 comparative fuel-value test. The reason for this is that different boilers 
 generate steam at different pressures, different feedwater temperatures, and 
 different degrees of dryness; hence, to compare the performances of boilers so 
 as to determine their comparative efficiencies, it is necessary to reduce the 
 actual evaporation to an equivalent evaporation from and at 212 F. per Ib. of 
 combustible. 
 
 A committee of the American Society of Mechanical Engineers has recom- 
 mended as a commercial horsepower an evaporation of 30 Ib. of water per hr. 
 from a feedwater temperature of 100 F. into steam at 70 Ib. gauge pressure, which 
 is equivalent to 34f units of evaporation; that is, to 34 Ib. of water evaporated 
 from a feedwater temperature of 212 F. into steam at the same temperature. 
 
 As 965.8 B. T. U. is required to evaporate 1 Ib. of water from and at 212, a 
 boiler horsepower is equal to 965.8X34^ = 33,320 B. T. U. per hr. 
 
 Equivalent Evaporation. The equivalent evaporation is readily deter- 
 mined by means of the formula 
 
 w _W(H-t+32) 
 965.8 ' 
 in which W = actual evaporation, in pounds of water per hour; 
 
 H = total heat of steam above 32 F. at observed pressure of evap- 
 oration; 
 
 t = observed feedwater temperature; 
 
 W\ = equivalent evaporation, in pounds of water per hour, from and 
 at 212 F. 
 
 EXAMPLE. A boiler generates 2,200 Ib. of dry steam per hr. at a pressure 
 of 120 Ib. gauge; the temperature of the feedwater being 70 F.: (a) What is 
 the equivalent evaporation? (b) What is the horsepower of the boiler? 
 
 SOLUTION. (a) According to the Steam Table, the total heat H correspon- 
 ding to a gauge pressure of 120 Ib. is 1,188.6 B. T. U. Applying the formula, 
 
 _ 
 
 (b) The horsepower is obtained by dividing the total equivalent evapora- 
 tion by 34.5, the equivalent of 1 H. P., and is 
 
 2,621 -=-34.5 = 76 H. P., nearly 
 
 Factor of Evaporation. The quantity that changes the actual 
 
 96o.o 
 
 evaporation of 1 Ib. of water to the equivalent evaporation from and at 212 F. 
 is called the factor of evaporation. To facilitate the calculating of equivalent 
 evaporation, the accompanying table of factors of evaporation is inserted. 
 The equivalent evaporation is found by multiplying the actual evaporation 
 by the factor of evaporation taken from the table. 
 
 EXAMPLE 1. A boiler is required to furnish 1,800 Ib. of steam per hr. at 
 a gauge pressure of 80 Ib.; if the temperature of the feedwater is 48 F., what 
 will be the rated horsepower of the boiler? 
 
 SOLUTION. From the table, the factor of evaporation for 80-lb. pressure 
 and a feedwater temperature of 40 is 1.214, and for the same pressure and a 
 feedwater temperature of 50 it is 1.203; the difference is 1.214 1.203 = .011. 
 The difference of temperature is 50 40 =10, and the difference between 
 the lower temperature and the required temperature is 48 40 = 8. Then, 
 10 : 8=.011 : x, or x=.009; 1.2 14 -.009 = 1.205. 1,800X1.205 = 2,169 Ib., 
 and 2,169-7-34.5 = 63 H. P., nearly. 
 
432 
 
 BOILERS 
 
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BOILERS 433 
 
 EXAMPLE 2. What is the factor of evaporation when the feedwater tem- 
 perature is 122 F. and the gauge pressure 72? 
 
 SOLUTION. In the table, under the column headed 70 and opposite 120 in 
 the left-hand column is found 1.128; in column headed 80 and opposite 120 is 
 found 1.131; difference is .003. In the same vertical columns and opposite 130 
 are found 1.117 and 1.120; difference is .003, same as before. Hence, for an 
 increase of 10 Ib. in gauge reading, there is an increase of .003 in the factor of 
 evaporation, or an increase of .0003 for 1 Ib. and of .0003 X 2 = .0006 for 2 Ib. 
 Therefore, for a feedwater temperature of 120 and 72 Ib. pressure, the factor 
 of evaporation is 1.128 + . 0006 = 1.1286. The difference between the numbers 
 opposite 120 and 130 in the two columns headed 70 and 80, respectively, is 
 1. 128-1. 117 = .011, and 1.31-1. 120 = .011, showing that, for an increase of 
 temperature in the feedwater of 10, there is a decrease in the factor of .011 
 and for 1 a decrease of .0011, or for 2 of .0022. Hence, the value of the 
 factor for a temperature of 122 and a gauge pressure of 72 Ib. is 1.1286 .0022 
 = 1.126. 
 
 Boiler Efficiency. The efficiency of a boiler may be denned as the ratio of 
 the heat utilized in evaporating water to the total heat supplied by the fuel. 
 The efficiency thus calculated is really the combined efficiency of the furnace and 
 boiler, as it is not easily possible to determine separately the efficiency of each. 
 
 The amount of heat supplied is determined by first accurately weighing 
 the fuel 'used during the test and deducting all the ash and unconsumed por- 
 tions. This weight, in pounds, is multiplied by the total heat of combustion 
 of 1 Ib. of the fuel, as determined by an analysis, the product being the total 
 number of heat units supplied during the test under the assumpton that com- 
 bustion was perfect. The heat usefully expended in evaporating water is 
 obtained by first weighing the feedwater and correcting this weight according 
 to the quality of the steam ; the corrected weight is then multiplied by the num- 
 ber of heat units required to change water at the temperature of the feed into 
 steam at the observed pressure. The efficiency of the boiler, expressed as a 
 per cent., may be found by the formula 
 
 in which E = efficiency of boiler; 
 
 A = heat utilized in evaporating water ; 
 B = total heat supplied by fuel. 
 
 EXAMPLE. A boiler trial shows a useful expenditure of 186,429,030 B. T. U. 
 and a total supply of 270,187,000 B. T. U. What is the efficiency of the 
 boiler? 
 
 SOLUTION. Applying the formula, 
 
 186.429 .030 _ fiq _ fiw 
 E ~ 270,187,000 ~- 69 >9% 
 
 Standard Code. For elaborate boiler trials, the standard code recom- 
 mended by the American Society of Mechanical Engineers should be used. 
 
 BOILER MANAGEMENT 
 
 FILLING BOILERS 
 
 Preparation for Filling Boiler. Before starting the flow of water into the 
 boiler, the manhole plates or handhole plates that were removed preparatory 
 to cleaning and overhauling must be replaced, and the blow-off valve must 
 be closed. The gaskets, and also the surfaces with which they come in contact, 
 should be examined to see that they are in good condition. It is customary 
 to place a mixture of cylinder oil and graphite on the outer surface of each 
 gasket, so that it may be removed without tearing. It is important that the 
 manhole plates and handhole plates be properly replaced and secured in order 
 to prevent leakage. 
 
 Height of Water. In some cases the water can flow in and fill the boiler 
 to the required height by means of the pressure that exists in the main supply 
 pipe. In other cases, it may be necessary to use a hose or to fill the boiler 
 with a steam pump or a hand pump. The boiler should be filled until the water 
 shows half way up in the gauge glass. 
 
 Escape of Air. While filling a boiler it is necessary to make provision for 
 the escape of the contained air, as otherwise the pressure caused by the com- 
 pression of the air may prevent the boiler from being filled to the proper height. 
 
 28 
 
434 BOILERS 
 
 Most boilers have some valve that can be used for this purpose; a gauge-cock 
 may be left open until water issues therefrom, when it may be closed, borne- 
 times the manhole plate, if the manhole is on top, is left off while filling a boiler. 
 
 MANAGEMENT OF FIRES WHEN STARTING 
 
 Precautions in Starting. After the boiler has been filled and before start- 
 ing the fire, the attendant should see that the water column and connections 
 are perfectly clear and free, that is, that the valves in the connections and 
 the gauge-glass valves are open so that the water level may show in the glass; 
 he should also see that the gauge-cocks are in good working order and should 
 open the top cock or the safety valve; he should take care that the stress on the 
 stop-valve spindle is relieved by just unscrewing the valve from the seat 
 without actually opening it. He should make sure that the pump, or injector, 
 or whatever device is used to feed the boiler, is in good working order, and 
 ready to start when required. 
 
 Starting the Fires. It is customary to coyer the grates with a layer of coal 
 first, and then to add the wood, among which may be thrown oily waste or 
 other combustible material that may be at hand. To start the fire, light the 
 waste or other easily ignited material and open the damper and ashpit doors 
 to produce draft. Then close the furnace door. After the wood has started 
 to burn well, spread it evenly over the grate and add a fine sprinkling of coal, 
 until this in turn begins to glow, when more coal may be added and the fire 
 occasionally leveled until the proper thickness of fuel has been obtained. 
 Should the chimney refuse to draw, the draft can generally be started by 
 building a small fire in the base of the chimney. 
 
 Value of Slow Fires. When getting up steam, the fire should not be forced 
 but, instead, should be allowed to burn up gradually. By forcing the fire, 
 the plates or tubes that are nearest the fire suffer extreme expansion, while 
 those parts that are remote from the fire are still cold; under such conditions 
 the seams and rivets, and also the tube ends, which are expanded into the tube 
 plates, are liable to be severely strained, and, possibly, permanently injured. 
 It is not desirable to raise steam in any boiler, except in steam fire-engines, in 
 less than from 2 to 4 hr., according to the size, from the time the fire is first 
 started. When steam begins to issue from the opened top gauge-cock or the 
 raised safety valve, as the case may be, the cock or the valve may be closed 
 and the pressure still allowed to rise slowly until the desired pressure has been 
 reached. 
 
 Trying the Fittings. After the pressure at which the boiler is to run has 
 been reached, and before cutting it into service, all the valves and cocks should 
 be tried. The safety valve should be raised and its action noted; the water 
 column should be blown out and the gauge-cocks tested ; the feeding apparatus 
 should be tried ; and it should be noted particularly whether the check- valves 
 seat properly and the valve in the feedpipe is open. All the accessible parts 
 should be examined for leaks. 
 
 CONNECTING BOILERS 
 
 Cutting Boiler Into Service. Cutting a boiler into service is accomplished 
 by opening the stop-valve, thus permitting the steam to flow to the engine 
 or other destination. The stop-valve should be opened very slowly to prevent 
 a too sudden change in the temperature and consequent expansion of the piping 
 through which the steam flows, and also to prevent water hammer. The steam- 
 pipe drain should be kept open until the pipe is thoroughly warmed up. In 
 large plants with many boilers and long steam mains, it takes several hours to 
 warm these pipes thoroughly by the slow circulation of the steam, but the main 
 stop-valve should not be fully opened until these pipes are warm. 
 
 Connecting Boilers to Main. Before connecting the different boilers of a 
 battery to the same steam main, the precaution of equalizing the pressures in 
 the different boilers must be observed in order to prevent a sudden rush of 
 steam from one boiler to another. All the pressures should be within about 
 2 Ib. before an attempt is made to connect the boilers. 
 
 Changing Over. In plants where there are duplicate sets of boilers, one set 
 being in operation while the other is undergoing repairs, overhauling, and 
 cleaning, the method of changing over, or connecting, is as follows: Start the 
 fires and raise steam in the boilers that are to be cut into service. Allow the 
 pressure to rise in all to within 5 Ib. of that which is in the boilers in operation. 
 All arrangements before changing over should be made with a view of getting 
 all the heat that can be obtained from the fires in the boilers that are to be cut 
 
BOILERS 435 
 
 out. This can be accomplished by running until the fires have given up all 
 their available heat for making steam, as indicated by the gradual fall in 
 pressure when the dampers are wide open, and then making the change. 
 While the fires in one set of boilers are burning low and the pressure is falling, 
 the pressure in the boilers to be cut in is gradually rising and meeting, so to 
 speak, the falling pressure of the set in operation. When the difference of 
 5 Ib. is reached, change over. A man should be stationed at each stop-valve, 
 and while pne is being opened the other should be closed; the engine will con- 
 tinue running uninterruptedly while the change is being made. 
 
 EQUALIZING THE FEED 
 
 When the boilers of a battery have been cut into service and hence are all 
 connected together through the steam main, the regulation and equalization 
 of the feedjvater becomes an important factor. Each boiler has its own check- 
 valve and Teed stop-valve, and generally all the boilers are supplied from one 
 pump, which is running constantly. The quantity of water admitted to each 
 boiler is regulated by its feed stop-valve. When the w'ater gets low in any boiler 
 the feed stop-valve should be opened wider, while at the same time the feed 
 stop-valves on one or more of the other boilers in operation may be closed 
 partly and thus divert the feedwater to the one most requiring it. Some boiler 
 plants have check-valves with an adjustable lift; in that case the feed is equal- 
 ized by adjusting the lifts of the check-valves, the stop-valves being left wide 
 open while running. It will be understood from the foregoing that the object 
 in view is the maintaining of an equal water level in all the boilers through 
 the manipulation of the feed stop-valves or check-valves. A boiler that is 
 not doing its legitimate share in generating steam may be known by the fact 
 that the feed stop-valve or check-valve on that boiler will be nearly, if not 
 entirely, closed most of the time. 
 
 FIRING WITH SOLID FUEL 
 
 The safe and economical operation of steam boilers calls for careful and 
 intelligent management. The fires should be kept in such condition as to 
 maintain the desired pressure and to burn the fuel with economy. Different 
 fuels require different handling and hence only general rules can be given; 
 much will depend on the skill and judgment of the attendant, who must him- 
 self discover in each case by actual trial the best method to pursue. The fires 
 must be cleaned at intervals; the time and method of cleaning depend on the 
 nature of the fuel and the rapidity with which it is being consumed, the style 
 of grate in use, and the construction of the furnace. 
 
 Cleaning of Fires. There are two methods employed in cleaning the fires: 
 first, that of cleaning the front half and then the rear half; second, that of cleaning 
 one side of the fire and then the other side. In the first method, previous to 
 cleaning, green fuel is thrown on and allowed to burn partly until it glows 
 over the entire surface. The new and glowing fuel is then pushed to the 
 back of the furnace with a hoe, leaving nothing on the front half of the 
 grate but the ashes and clinkers, which are then pulled out, leaving the front 
 end of the grate entirely bare. The new fire, which was pushed back, is drawn 
 forwards and spread over the bare half of the grate. The ashes and clinkers 
 that are on the rear half of the grate are then pulled over the top of the front 
 half of the fire and out through the furnace door; this leaves the rear half of 
 the grate bare, which must be covered by pushing back some of the new front 
 fire. The clean fire having been spread evenly, some new fuel must be spread 
 over the entire surface. 
 
 The second method is substantially the same in principle, but the fire is 
 pushed to one side instead of to one end of the furnace. The condition of the 
 fires themselves and the nature of the service of the plant will determine just 
 how often and at what time the cleaning of fires should take place. In general, 
 the fires in stationary boilers require cleaning at intervals of from 8 to 12 hr. 
 Fires require cleaning more often when forced draft is used than when working 
 with natural draft. 
 
 Rapidity in cleaning fires is of great importance, as during the operation 
 a large volume of cold air enters the furnace and chills the metallic surfaces 
 with which it comes in contact; consequently, the boiler is damaged, however 
 slightly. It is the greatest advantage of shaking grates that they allow the 
 fire to be cleaned without opening the furnace door; the inrush of cold air and 
 consequent chilling of the plates, etc. is thus avoided. 
 
 Before starting to clean fires, the steam pressure and the water level should 
 be run up as high as is safe and the feed should be shut off in order to reduce 
 
436 BOILERS 
 
 the loss in pressure while cleaning. The condition of the fire during cleaning 
 and the opening of the furnace doors cause the pressure to drop quite rapidly, 
 but the rapidity and the amount of drop will be reduced by taking the precau- 
 tions mentioned and cleaning quickly. 
 
 The amount of drop in pressure while cleaning fires depends on several 
 conditions. For example, with a boiler that has a small steam space and, 
 in addition, is. too small for the work required of it without forcing, it is to be 
 expected that the drop in pressure will be much more than if the reverse con- 
 ditions exist. Furthermore, it may be necessary to clean fires while steam is 
 being drawn from the boiler, instead of being able to clean at a time when 
 the engine is stopped. In that case a greater drop must be expected than 
 when cleaning while no steam is being drawn from the boiler. It is advisable 
 when possible to do the cleaning at a time when no steam is being drawn from 
 the boiler or when the demand for steam is light. t 
 
 UNIFORM STEAM PRESSURE 
 
 Desirability of Uniform Pressure. The attendant should aim to carry the 
 pressure in the boiler as uniform as possible. A steady steam pressure and a 
 steady water level are conducive to economy in the use of a fuel because, with 
 these conditi9ns, in a properly designed plant there will be a fairly steady 
 temperature in the furnace, which, under normal conditions, is sufficiently 
 high to insure a thorough ignition of the volatile matter in the coal. With a 
 constant demand for steam, a fluctuation in the steam pressure is caused by 
 a change in the furnace temperature, assuming the feedwater supply to be 
 constant, and whenever the steam pressure is down, the furnace temperature 
 is low at the same time. In consequence of this, large quantities of the volatile 
 matter in the coal often escape unconsumed and cause a serious loss of heat. 
 Furthermore, with a steady steam pressure the stresses on the boiler are 
 constant, and hence the life of the boiler will be increased and repair bills will 
 be smaller than otherwise. 
 
 Maintenance of Uniform Pressure. During the period of time between the 
 cleaning of the fires, the pressure may be carried nearly uniform by manipu- 
 lating the feed apparatus so that just the necessary amount of water constantly 
 enters the boiler. Intermittent feeding is practiced under certain local con- 
 ditions, as, for example, where there is an injector or a pump that is so large 
 that it is impossible to run it continuously without increasing the height of 
 the water level. In such a case, the feeding must be stopped just before firing, 
 and is not resumed until the new fire begins to make steam, as indicated by 
 the rise of pressure on the gauge. If the pressure tends to rise above the 
 standard or normal the dampers must be partly closed and the quantity of 
 feed increased, assuming in this case that no damper regulator is fitted and 
 that, hence, the damper is regulated by hand. A damper regulator, system- 
 atic firing, and proper feeding are essential for carrying a practically uniform 
 pressure. Should the pressure continue to rise, more green fuel must be 
 thrown on, the damper closed, the feed increased, and only as a last resort 
 should the furnace door be opened. 
 
 A uniform steam pressure cannot be kept without proper firing. To 
 maintain such a pressure the following directions should be observed: Keep 
 the fire uniformly thick; allow no air holes in the bed of fuel; fire evenly and 
 regularly; be careful not to fire too much at a time; keep the fire free from 
 ashes and clinkers; and do not neglect the sides and corners while keeping 
 the center clean. Do not, however, clean the fires oftener than is necessary. 
 Keep the ash-pit clear. 
 
 Keeping Water Level Constant. In connection with the maintenance of a 
 constant water level, the following instructions should be followed: On start- 
 ing to work, remember that the first duty of the fireman is to examine the 
 water level. Try the gauge-cocks, as the gauge glass is not always reliable. 
 If there is a battery of boilers, try the gauge-cocks on each boiler. 
 
 PRIMING AND FOAMING 
 
 Priming. The phenomenon called griming is analogous to boiling over; 
 the water is carried into the steam pipes and thence to the engine, where 
 considerable damage is liable to take place if the trouble is not checked in time. 
 There are several causes for priming, the most common ones of which are: 
 insufficient boiler power, defective design of boiler, water level carried too 
 high, irregular firing, and sudden opening of stop-valves. 
 
 When the boiler power is insufficient, the best remedy is to increase the 
 boiler plant; the next best thing to do is to put in a separator, which, obviously, 
 
BOILERS 437 
 
 will only prevent the entrained water from reaching the engine, and will not 
 stop the priming. 
 
 Defective design of a boiler generally consists of a steam space that is too 
 small or a bad arrangement of the tubes, which may be spaced so close in an 
 effort to obtain a large heating surface as to interfere seriously with the circu- 
 lation. In horizontal return-tubular boilers, a sufficiently large steam space 
 can be obtained by the addition of a steam drum; sometimes the top row of 
 tubes can be taken out to advantage, which permits a lower water level. 
 Defective circulation in horizontal fire-tube boilers is difficult to detect and 
 to remedy; if it is due to a too close spacing of the tubes, a marked betterment 
 may be effected by the removal of one or two vertical rows of tubes. The 
 remedy for a water level that is too high is to carry the water at a lower level. 
 
 Evidences of Priming. Priming manifests itself first by a peculiar clicking 
 sound in the cylinder of the engine, due to water thrown against the heads. 
 In cases of very violent priming, the water will suddenly rise several inches in 
 the gauge glass, thus showing more water in the boiler than there really is. 
 When priming takes place, it can be checked temporarily as follows: Close 
 the damper, and thereby check the fires until the water is quiet; the engine 
 stop-valve should also be partly closed to check the inrush of water. Observe 
 whether the water drops in the gauge glass, and then, if more feed is needed, 
 increase the feed. To prevent damage to the engine, open the cylinder drains. 
 Regular and even firing tends to prevent priming. 
 
 Foaming. The phenomenon called foaming is not the same as priming, 
 though frequently considered so. Foaming is the result of flirty or greasy 
 water in the boiler; the water foams and froths at the surface, but does not 
 lift. A boiler may prime and foam simultaneously, but a foaming boiler does 
 not always prime. Foaming while taking place is visible in the gauge glass 
 and is best remedied by using the surface blow-off. If no surface blow-off is 
 fitted, the bottom blow-off may be used in order to get rid of the dirty water. 
 Like priming, foaming will cause a wrong level to be shown, and hence the 
 first thing to do in case of foaming is to quiet the water by checking the outrush 
 of steam, either by slowing the engine down or by checking the fire, or by both. 
 
 SHUTTING DOWN AND STARTING UP 
 
 Preparations for Shutting Down. Before shutting down for the night it is 
 advisable to fill the boiler to the top of the glass, so as to be sure to have suffi- 
 cient water to start with in the morning. The presence of possible leaks 
 through the valves, tube ends, or seams necessitates this course of action. 
 Even if no leaks exist, it is good practice to dp this, if for no other reason than 
 to admit of blowing out a portion before raising steam in the morning. All 
 the gauge-cocks should be tried and the water column should be blown out to 
 insure their being free and clear. 
 
 Banking of Fires. The fires may be banked at such a time that there will 
 be about enough steam to finish the day's run, thus shutting down under a 
 reduced pressure with only a remote possibility of its rising again through 
 the night. If the fires are properly banked and the steam worked off while 
 the feed is on, it will be remotely possible for the pressure to rise during the 
 night to a dangerous extent. To bank the fires they should be shoved to the 
 back of the grate and well covered with green fuel, leaving the front part of 
 the grate bare, thus preventing any possibility of the banked fire burning up 
 through the night. 
 
 Closing Valves and Damper. The steam stop-valve, feed stop-valve, 
 whistle valve, and other steam valves should be closed; the valves at the top 
 and bottom of the gauge glass also should be shut off to prevent loss of water, 
 etc. in case the glass should break during the night. If there is a damper 
 regulator, it should be so arranged that the damper may be left closed, but 
 not quite tight, because a small opening must be left to permit the collecting 
 gases from the banked fire to escape up the chimney; otherwise, there is danger 
 that the gas will ignite and cause an explosion. It is very important to take 
 this precaution and also to make a mark by means of which the distance 
 the damper is open can be ascertained at a glance. In fact, a damper should 
 be so made that when shut to the full extent of its travel there will be still 
 sufficient space around it to allow the gas to escape. The damper regulator 
 should be rendered positivelv inoperative in any manner permitted by its 
 design so that when closed it will remain in that position until connected prop- 
 erly by the attendant in the morning. 
 
 Starting the Fires. On entering the boiler room in the morning, the quan- 
 tity of water in the boiler should first be noted. The gauge glass and the 
 
438 BOILERS 
 
 gauge-cocks should be tried and the water level determined. After it has been 
 found that the water is not too low, the banked fires may be pulled down and 
 spread over the grates and allowed to burn up slowly, the damper regulator, 
 if one is fitted, in the meantime having been connected. 
 
 Blowing Down. While the fires are burning up and before the pressure 
 begins to rise, the blow-off cock or valve should be opened and the boiler blown 
 down; that is, a small quantity of the water should be blown out. This should 
 be done every morning, so that any impurities in mechanical suspension in the 
 water that settled during the night may be removed. Great care should be 
 exercised while doing this so that too much water is not blown out; from 3 to 
 4 in. as shown by the gauge glass, is sufficient. Under no circumstances should 
 the attendant leave the blow-off while it is open. Disaster to the boiler is 
 liable to follow a disregard of this injunction. Next, all the valves, except 
 the stop- valve, which were shut the night before should be opened and tried 
 to see that they are free and in good working order. 
 
 CARE OF BOILERS 
 
 Safety Valves. Great care should be exercised to see that the safety valves 
 are ample in size and in working order. Overloading or neglect frequently 
 lead to the most disastrous results. Safety valves should be tried at least 
 once every day, to see that they act freely. 
 
 Pressure Gauge. The steam gauge should stand at zero when the pres- 
 sure is off, and it should show the same pressure as that at which the safety 
 valve is set when that is blowing off. If the. pressures do not agree, the 
 gauge should be compared with one known to be correct. 
 
 Water Level. The first duty of an engineer before starting, or at the begin- 
 ning of his watch, is to see that the water is at the proper height. He should 
 not rely on glass gauges, floats, or water alarms, but try the gauge-cocks. 
 If they do not agree with the water gauge, the cause should be learned and the 
 fault corrected. 
 
 Gauge-Cocks and Water Gauges. All gauge-cocks and water gauges must 
 be kept clean. Water gauges should be blown out frequently, and the glasses 
 and passages to them kept clean. The Manchester, England, Boiler Associa- 
 tion attributes more accidents to inattention to water gauges than to all other 
 causes put together. 
 
 Feed-Pump or Injector. The feed-pump or injector should be kept in 
 perfect order, and be of ample size. No make of pump can be expected 
 to be continuously reliable without regular and careful attention. It is 
 always safe to have two means of feeding a boiler. Check- valves and self- 
 acting feed-valves should be frequently examined and cleaned. The attend- 
 ant should satisfy himself frequently that the valve is acting when the 
 feed-pump is at work. 
 
 Low Water. In case of low water, immediately cover the fire with ashes 
 (wet if possible) or any earth that may be at hand. If nothing else is handy, 
 use fresh coal. Draw fire as soon as it can be done without increasing the heat. 
 Neither turn on the feed, start nor stop engine, nor lift safety valve until fires 
 are out and the boiler cooled down. 
 
 Blisters and Cracks. Blisters and cracks are liable to occur in the best 
 plate iron. When the first indication appears, there must be no delay in having 
 the fault carefully examined and properly cared for. 
 
 Fusible Plugs. When used, fusible plugs must be examined when the boiler 
 is cleaned, and carefully scraped clean on both the water and fire sides, or they 
 are liable not to act. 
 
 Firing. Fire evenly and regularly, a little at a time. Moderately thick 
 fires are most economical, but thin firing must be used where the draft is poor. 
 Take care to keep grates evenly covered, and allow no air holes in the fire. 
 Do not clean fires oftener than necessary. With bituminous coal, a coking 
 fire, i. e., firing in front and shoving back when coked, gives best results, if 
 properly managed. 
 
 Cleaning. All heating surfaces must be kept clean outside and in, or 
 there will be a serious waste of fuel. The frequency of cleaning will depend 
 on the nature of fuel and water. When a new feed water supply is intro- 
 duced, its effect on the boiler should be closely observed, as this new supply 
 may be either an advantage or a detriment as compared with the working of 
 the boiler previous to its introduction. As a rule, never allow over f in. of 
 scale or soot to collect on surfaces between cleanings. Handholes should be 
 frequently removed and surfaces examined, particularly in the case of a new 
 boiler, until proper intervals have been established by experience. 
 
BOILERS 439 
 
 The exterior of tubes can be kept clean by the use of blowing pipe and 
 hose through openings provided for that purpose. When using smoky fuel, 
 it is best to occasionally brush the surfaces when steam is off. 
 
 Hot Feedwater. Cold water should never be fed into any boiler when 
 it can be avoided, but when necessary it should be caused to mix with the 
 heated water before coming in contact with any portion of the boiler. 
 
 Foaming. When foaming occurs in a boiler, checking the outflow of steam 
 will usually stop it. If caused by dirty water, blowing down and pumping up 
 will generally cure it. In cases of violent foaming, the draft and fires should 
 be checked. 
 
 Air Leaks. Be sure that all openings for admission of air to boiler or flues, 
 except through the fire, are carefully stopped ; this is frequently an unsuspected 
 cause of serious Waste of fuel. 
 
 Blowing Off. If feedwater is muddy or salt, blow off a portion frequently, 
 according to condition of water. Empty the boiler every week or two, and 
 fill up afresh. When surface blow cocks are used, they should be often opened 
 for a few minutes at a time. Make sure no water is escaping from the blow-off 
 cock when it is supposed to be closed. Blow-off cocks and check- valves should 
 be examined every time the boiler is cleaned. Never empty the boiler while 
 the brickwork is hot. 
 
 Leaks. When leaks are discovered, they should be repaired as soon as 
 possible. 
 
 Filling Up. Never pump cold water into a hot boiler. Many times leaks, 
 and, in shell boilers, serious weaknesses, and sometimes explosions are the 
 result of such an action. 
 
 Dampness. Take care that no water comes in contact with the exterior 
 of the boiler, as it tends to corrode and weaken it. Beware of all dampness 
 in seatings and coverings. 
 
 Galvanic Action. Examine frequently parts in contact with copper or 
 brass, where water is present, for signs of corrosion. If water is salt or acid, 
 some metallic zinc placed in the boiler will usually prevent corrosion, but it 
 will need attention and renewal from time to time. 
 
 Rapid Firing. In boilers with thick plates or seams exposed to the fire, 
 steam should be raised slowly, and rapid or intense firing avoided. With thin 
 water tubes, however, and adequate water circulation, no damage can come 
 from that cause. 
 
 Standing Unused. If a boiler is not required for some time, empty and 
 dry it thoroughly. If this is impracticable, fill it quite full of water, and put 
 in a quantity of common washing soda. External parts exposed to dampness 
 should receive a coating of linseed oil. 
 
 Repair of Coverings. All coverings should be looked after at least once 
 a year, given necessary repairs, refitted to the pipe, and the spaces due to 
 shrinkage taken up. Little can be expected from the best non-conductors if 
 they are allowed to become saturated with water, or if air-currents are per- 
 mitted to circulate between them and the pipe. 
 
 General Cleanliness. All things about the boiler room should be kept 
 clean and in good order; negligence tends to waste and decay. 
 
 BOILER INSPECTION 
 
 NATURE OF INSPECTION 
 
 The inspection of a boiler usually consists in an external examination of 
 the complete structure, and of the setting if the boiler is externally fired, and 
 an internal inspection. The examination of the boiler consists of an ocular 
 inspection for visible defects, and a hammer test or sounding for hidden defects 
 of plates, stays, braces, and other boiler parts. The hammer test is made 
 by tapping the suspected parts with a light hammer and judging the existence 
 and extent of defects from the sound produced by the blow. If the examina- 
 tion discloses marked wear and tear, a series of calculations is often required 
 to find the safe pressure that may be allowed on the worn parts, using such 
 formulas or rules as laws, ordinances, and regulations may prescribe. In the 
 absence of officially prescribed formulas and rules, the inspector should use 
 such rules as he deems in best accordance with good practice. The inspection 
 is usually, but not always, completed by a so-called hydrostatic test, which is 
 generally prescribed by official regulations. 
 
440 BOILERS 
 
 EXTERNAL INSPECTION 
 
 Preparation. Before a boiler that has been in use can be inspected, it must 
 be blown out and must be allowed to cool off. As soon as the water has been 
 removed, the manhole covers, handhole covers, and washout plugs should be 
 taken out and all loose mud and scale washed out with a hose. If the boiler 
 is externally fired, the tubes must be swept and the furnace, the ash-pit, the 
 smokebox, and the space back of the bridge wall must be cleaned out. Any 
 removable insulating covering that prevents the inspector from having free 
 access to the exterior of the boiler must be removed to the extent deemed 
 necessary by him; it may even be necessary to take down some of the bricks 
 of the setting. 
 
 Inspection of Externally Fired Boilers. In the inspection of an externally 
 fired fire-tube or flue boiler, the exterior is first examined. The seams are 
 gone over inch by inch; the rivet heads and calking edges of the plates are care- 
 fully scrutinized for evidence of leaks; and possible cracks are looked for 
 between the rivet heads, especially in the girth seams and on the under side of 
 the boiler. The plates must also be examined for corrosion, bulges, blisters, and 
 cracks. The heads are inspected for cracks between the tubes or flues, cracks 
 in the flanges, leaky tubes, and leaks in the seams. The condition of the fire- 
 brick lining of the furnace and bridge and the top of the rear combustion cham- 
 ber is noted while making the exterior examination of the underside of the 
 boiler. Every defect that is found should be clearly marked. Attention must 
 also be paid to the condition of the grate bars and their supports. 
 
 Inspection of Internally Fired Boilers. The inspection of the shell and 
 heads must be followed by examination of the fire-box or furnace tubes or 
 flues, and of the combustion chambers if these are fitted inside the boiler. 
 In fire-boxes, special attention must be paid to the crown sheet. The ends of 
 the staybolts require close examination; if such ends are provided with nuts, 
 these must be examined, as they are liable to loosen and are also liable to be 
 burned off in time. Each staybolt should be tested for breakage, which is 
 done by holding a sledge against the outside end of the staybolt and striking 
 the inner, or fire-box, end with a light hammer; in making this test on the 
 boilers of locomotives it is customary, when practical, to subject the boiler 
 to an internal air pressure of from 40 to 50 Ib. per sq. in. The internal pressure, 
 by bulging the sheets, separates the ends of a broken staybolt, which renders 
 it comparatively easy to find them by the hammer test. 
 
 Inspection of New Boilers. As made in boiler shops, the external inspection 
 of new boilers, whether they are internally or externally fired, and whether 
 they are of the water-tube or the fire-tube type, usually consists in a thorough 
 examination for visible defects and testing under water pressure to locate 
 leaks. If a new boiler subject to official inspection during construction 
 successfully passes such a hydrostatic test as the regulations prescribe, it will 
 usually be permitted the working pressure it was designed for, the design 
 having been approved officially before construction. The working pressure 
 will be reduced, however, if the inspection discloses poor workmanship. 
 
 In the external inspection of water-tube boilers that have been in use, the 
 tubes that are exposed directly to the heat of the fire must be particularly 
 well examined for evidence of overheating. The plugs or handholes placed 
 in headers to permit the insertion of the tubes and the cleaning of them are 
 inspected for leakage, and the headers are inspected for cracks. Steam drums 
 and mud-drums should be examined as carefully and for the same defects as 
 the shells of externally fired fire-tube boilers. The fire-brick lining of the 
 furnace, and the interior of the brick setting in general, as well as the baffle 
 plates controlling the direction of flow of the gases of combustion, must be 
 examined for cracks and any other defects. The external inspection of the 
 setting can usually be made very rapidly, as everything is in plain sight. 
 
 INTERNAL INSPECTION 
 
 Preparation. Before the internal inspection is begun all loose mud should 
 be washed out with a hose. In a horizontal return-tubular boiler and flue 
 boiler, the shell plates and heads should be examined for corrosion and pitting; 
 if the boiler has longitudinal lap seams, these should be inspected at the inside 
 calking edere for incipient grooving and cracks. All seams should be examined 
 for cracks between the rivet holes. Obviously, if the boiler is scaled to an 
 appreciable degree, the scale must be removed before inspection. The tubes 
 or flues should be examined for pitting, as well as for uniform corrosion. All 
 braces should be inspected by sounding them with a hammer, and if they are 
 attached by cotter pins, it should be seen to that these are firmly in place. 
 
BOILERS 441 
 
 All defects found should be marked; it is good practice to make a memorandum 
 of them as well. If any of the bracing seems to have worn considerably, it 
 should be measured at the smallest part in order that the safe working pressure 
 thereon may be calculated afterwards. To determine to what thickness a 
 plate attacked by uniform corrosion has been reduced the inspector will have 
 one or more holes drilled through the plate in the worn part to enable him to 
 measure the thickness. These holes are afterwards plugged, generally by 
 tapping out and then screwing in a plug. 
 
 Inspection of Locomotive-Type Boilers. In internally fired boilers of the 
 fire-box and locomotive type, particular attention must be paid to the crown 
 bars, crown bolts, and sling stays; in boilers having the crown sheet stayed 
 by radial staybolts, special attention is also paid to these. As a general rule, 
 the inspector can make only an ocular inspection of most of them, as they are 
 beyond his reach; where the outer sheets of the firebox contain inspection or 
 washout holes above the level of the crown sheet, a lighted candle tied or 
 otherwise fastened to a stick can usually be introduced through these holes 
 from the outside by a helper. In inspecting above the crown sheet, the inspec- 
 tor should look for mud betv/een the crown sheet and crown bars and sight 
 over the top of the bars to see if any have been bent. As the inspector can 
 reach from the inside of the boiler only a few of the staybolts staying the sides 
 of the firebox, he must rely on the hammer test applied from the inside of the 
 furnace for finding broken staybolts. 
 
 Flues and Combustion Chambers. In boilers having circular furnace flues 
 and internal combustion chambers, the top of the furnace flues must be care- 
 fully inspected for deposits of grease and scale, which are especially liable to 
 be found if the feedwater is obtained from a surface condenser. Even a light 
 deposit of grease on the furnace flue is liable to lead to overheating and sub- 
 sequent collapse of the top. The tops of the combustion chambers, together 
 with their supports, are usually easily inspected, there being ample space to 
 reach every part. 
 
 Inspection of Vertical Boilers. Vertical boilers as a general rule, except in 
 the largest sizes, have no manhole to admit a person to the inside, and such 
 internal inspection as is possible must be made through the handholes. Defects 
 to be looked for are pitting and uniform corrosion of the shell and tubes near 
 the usual water-line, and cracks in the heads between the tubes, the lower 
 head being especially liable to show this injury. 
 
 INSPECTION OF FITTINGS 
 
 Inspection of Safety Valve. The safety valve requires very careful inspec- 
 tion. If this valve is known to leak, it should be reseated and reground before 
 the hydrostatic test is made. After a boiler passes the hydrostatic test, the 
 clamp locking the safety valve is removed, and by running the pressure up 
 once more, the point at which the safety valve opens can be noted by watching 
 the steam gauge, which is supposed to have been tested and corrected. If the 
 safety valve does not open at the working pressure allowed or opens too soon, 
 it is readjusted. If the safety valve is locked by a seal, as is often required 
 by official regulations, the seal is applied after adjustment of the valve. 
 
 Testing of Steam Gauge. The steam gauge should be tested before the 
 hydrostatic test and at each inspection with a so-called boiler inspector's test- 
 ing outfit. If the gauge under test is more than 5% incorrect most inspectors 
 will condemn it although some will condemn gauges showing a much smaller 
 error. In most cases the gauge can be repaired at small expense by the makers. 
 
 Inspection of Water Gauge and Blow-off. The connections of water 
 column and water-gauge glasses require examination in order to see that they 
 are clear throughout their whole length. The blow-off pipe also requires 
 examination in order to see that it is clear. 
 
 SELECTION OF BOILERS 
 
 General Requirements. When choosing a boiler, the facts to be kept in 
 mind are: 
 
 1. The grate surface must be sufficient to burn the maximum quantity of 
 coal expected to be used at any time, taking into consideration the available 
 draft, the quality of coal, its percentage of ash, whether or not the ash tends 
 to run into clinker, and the facilities, such as shaking grates, for getting rid of 
 the ash or clinker. 
 
 2. The furnace must be adapted to burn the particular kind of coal used. 
 
442 BOILERS 
 
 3. The heating surface must be sufficient to absorb so much of the heat 
 generated that the gases escaping into the chimney will be not over 450 F. 
 with anthracite, and 550 F. with bituminous coal. 
 
 4. The gas passages must be so designed and arranged as to compel the gas 
 to traverse at a uniform rate the whole of the heating surface, being not so 
 large at any point as to allow the gas to find a path of least resistance, or short- 
 circuiting, or, on the other hand, so contracted at any point as to cause an 
 obstruction to the draft. 
 
 When these elements are found in any boiler and they may be found in 
 boilers of many of the common types the relative merits of the different 
 types may be C9nsidered with reference to their danger of explosion; their 
 probable durability; the character and extent of repairs that may be needed 
 from time to time, and the difficulty, delay, and expense that these may entail; 
 the accessibility of every part of the boiler to inspection, internal and external; 
 the facility for removal of mud and scale from every portion of the inner sur- 
 face, and of dust and soot from the exterior; the water and steam capacity; 
 the steadiness of water level; and the arrangements for securing dry 
 
 Liability to Explosion. All boilers may be exploded by overpressure, such 
 as might be caused by the combination of an inattentive fireman and an inopera- 
 tive safety valve, or by corrosion weakening the boiler to such an extent as 
 to make it unable to resist the regular working pressure; but some boilers are 
 much more liable to explosion than others. When selecting a boiler, it is well 
 to see whether or not it has any of the features that are known to be dangerous. 
 
 The plain cylinder boiler is liable to explosion from strains induced by its 
 method of suspension, and by changes of temperature. Alternate expansion 
 and contraction may produce a line of weakness in one of the rings, which 
 may finally cause an explosion. A boiler should be so suspended that all its 
 parts are free to change their position under changes of temperature without 
 straining any part. The circulation of water in the boiler should be sufficient 
 to keep all parts at nearly the same temperature. Cold feedwater should 
 not come in contact with the shell, as this will cause contraction and strain. 
 
 The horizontal tubular boiler, and all externally fired shell boilers, are 
 liable to explosion from overheating of the shell, due to accumulation of mud, 
 scale, or grease, on the portion of the shell lying directly over the fire, to c. 
 double thickness of iron with rivets, together with some scale, over the fire, 
 or to low water uncovering and exposing an unriveted part of the shell directly 
 to the hot gases. 
 
 Vertical tubular boilers are liable to explosion from deposit 9f mud, scale, 
 or grease, upon the lower tube-sheet, and from low water allowing the upper 
 part of the tubes to get hot and cease to act as stays to the upper tube-sheet. 
 
 Locomotive boilers may explode from deposits on the crown sheet, from 
 low water exposing the dry crown sheet to the hot gases, and from corrosion 
 of the staybolts. 
 
 Double-cylinder boilers, such as the French elephant boiler, and the boilers 
 used at some American blast furnaces, have exploded on account of the forma- 
 tion of a steam pocket on the upper portion of the lower drum, the steam 
 being prevented from escaping from out of the rings of the drum by the lap 
 joint of the adjoining ring, thus making a layer of steam about J in. thick 
 against the shell, which was directly exposed to the hot gases. In the case of 
 vertical or inclined tubes acting as stays to an upper sheet, the upper part 
 of the tubes may become overheated in case of low water; also, when there 
 are stayed sheets, the stays are liable to become corroded. 
 
 In addition to these features of design, all boilers are liable to explosion due 
 to corrosion. Internal corrosion is usually due to acid feedwater, and all 
 boilers are equally liable to it. External corrosion, however, is more liable 
 to take place in some designs of boilers than others, and in some locations 
 rather than others. If any portion of a boiler is in a cold and damp place, it 
 is liable to rust out. For this reason the mud-drums of many modern forms of 
 boilers are made of cast iron, which resists rusting better than either wrought 
 iron or steel. If any part of a boiler, other than a part made of cast iron, is 
 liable to be exposed to a cold and damp atmosphere, or covered with damp 
 soot or ashes, or exposed to drip from rain or from leaky pipes, and especially 
 if such part is hidden by brickwork or otherwise so that it cannot be seen, 
 that part is an element of danger. 
 
 The causes of boiler explosions may be summarized as follows: (1) Bad 
 materials; (2) bad workmanship; (3) bad water, which eats away the plates 
 by internal corrosion; (4) water lying upon plates, bringing about external 
 
BOILERS 443 
 
 corrosion; (5) overpressure; (6) safety valves sticking; (7) water .getting too 
 low; (8) excessive firing; (9) hot gases, acting on plates above water level; 
 (10) choking of feedpipes; (11) insufficient provision for expansion and con- 
 traction; (12) insufficient steam room and too sudden a withdrawal of a large 
 quantity of steam; (13) getting up steam, or knocking off a boiler too suddenly; 
 (14) allowing wet ashes to lie in contact with plates. The probable causes 
 suggest their several remedies. 
 
 Durability. The question of durability is partly covered by that of danger 
 of explosion, but it also is related to the question of incrustation and scale. 
 The plates and tubes of a boiler may be destroyed by internal or external 
 corrosion and by being burned out. It may be regarded as impossible to 
 burn a plate or tube of iron or steel, no matter how high the temperature of 
 the flame, provided one side of the metal is covered with water. However, 
 if a steam pocket is formed, or if there is a layer of grease or hard scale, so 
 that the water does not touch the metal, the plate or tube may be burned. 
 In a water tube that is horizontal, or nearly so, and in which the circulation 
 of water is defective, it is possible to form a mass of steam that will drive the 
 water away from the metal, and&thus al^w the tube to burn out. When 
 considering the probable durability of a boiler, it is necessary to consider the 
 same things as when investigating the danger of explosion. There are, how- 
 ever, many chances of burning out a minor part of a_boiler without serious 
 danger, to one chance of a disastrous explosion. Thus the tubes of a water- 
 tube boiler, if allowed to become thickly covered with scale, might be burned 
 out again and again without causing any further destruction at any one time 
 than the rupture of a single tube. A new type of boiler should be considered 
 with regard to the likelihood of frequent small repairs being necessary, as well 
 as with regard to its liability to complete destruction. The most important 
 of these considerations are: The circulation through all parts of the boiler 
 must be such that the water cannot be driven out of any tube or from any 
 portion of a plate, so as to form a steam pocket exposed to high temperature; 
 there must be proper facilities for removing the scale from every portion ot 
 the plates and tubes. 
 
 Repairs. The questions of durability and of repairs are, in some respects, 
 related to each other; the more infrequent and the less extensive the repairs, 
 the greater the durability. The tubes of a boiler, where corroded or burnt 
 out, may be replaced and made as good as new. The shell, when it springs 
 a leak, may be patched, but is then likely to be far from as good as new. When 
 the shell corrodes badly it must be replaced, and to replace the shell is the 
 same as getting a new boiler. Herein is the advantage of the sectional water- 
 tube boilers. The sections, or parts of a section, may be renewed easily, and 
 made as good as new, while the shell, being far removed from the fire and easily 
 kept dry externally, is not liable either to burning out or to external corrosion. 
 When considering the merits of a new style of boiler, with reference to repairs, 
 it may be asked what parts of the boiler are most likely to give out and need 
 to be repaired or replaced? Are these repairs easily effected, how long will 
 they require, and, after they are made, is the boiler as good as new? 
 
 Facility for Removal of Scale and for Inspection. The matter of facility 
 for the removal of scale and for inspection has already been discussed to some 
 extent under the head of durability. Some early water-tube boilers had no 
 facilities for the removal of scale, it being claimed that they did not need any, 
 because their circulation was so rapid. If there is scale-forming material in 
 the water it will be deposited when the water is evaporated, and no amount or 
 kind of circulation will keep it from accumulating on every part of the boiler, 
 and in every kind of tubes, vertical, horizontal, or inclined. The nearly vertical 
 circulating tubes of a water-tube boiler, in which the circulation is nine times 
 as fast as the average circulation in the inclined tubes, have been found nearly 
 full of scale; that is, a 4-in. tube had an opening in it of less than 1 in. in diam- 
 eter. This was due to carelessness in blowing off the boiler, or to exceptionally 
 bad feedwater, or both. 
 
 Water and Steam Capacity. It is claimed for some forms of boilers that 
 they are better than others because they have a larger water or steam capacity. 
 Great water capacity is useful where the demands for steam are extremely 
 fluctuating, as in a rolling mill or a sugar refinery, where it is desirable to store 
 up heat in the water in the boilers during the periods of the least demand 
 to be given out during periods of greatest demand. Large water capacity is 
 usually objectionable in boilers for factories, especially if they do not run at 
 night and the boilers are cooled down, because there is a large quantity of water 
 to be heated before starting each morning. If rapid steaming, or the ability 
 
444 
 
 BOILERS 
 
 to get up steam quickly from cold water, or to raise the pressure quickly, is 
 desired, large water capacity is a detriment. 
 
 The advantage of large steam capacity is usually overrated. It is useful to 
 enable the steam to be drained from water before it escapes into the steam 
 pipe, but the same result can be effected by means of a dry pipe, as in loco- 
 motive and marine practice, in which the steam space in the boiler is very small 
 in proportion to the horsepower. Large steam space in the boiler is of no 
 importance for storing energy or equalizing the pressure during the stroke 
 of an engine. The water in the boiler is the place to store heat, and if the 
 steam pipe leading to an engine is of such small capacity that it reduces the 
 pressure, the remedy is a steam reservoir close to the engine or a large steam pipe. 
 
 To secure steadiness of water level requires either a large area of water 
 surface, so that the level may be changed slowly by fluctuations in the demand 
 for steam or in the delivery of the feed-pump, or else constant, and preferably 
 automatic, regulation of the feedwater supply to suit the steam demand. _ A 
 rapidly lowering water level is apt to expose dry sheets or tubes to the action 
 of the hot gases, and thus be a source of danger. A rapidly rising level may, 
 before it is seen by the fireman, cause water to be carried over into the steam 
 pipe, and endanger the engine. 
 
 Water Circulation. Positive and complete circulation of the water in a 
 boiler is necessary to keep all parts of the boiler at a uniform temperature, 
 and to prevent the adhesion of steam bubbles to the surface, which may cause 
 overheating of the metal. It is claimed by some manufacturers that the 
 extremely rapid circulation of water in their boilers tends to make them more 
 economical than others. However, proof is lacking that increased rapidity 
 of circulation of water beyond that usually found in any boiler will give increased 
 
 RATIO OF HEATING SURFACE TO HORSEPOWER AND TO 
 GRATE AREA 
 
 
 Ratij Heating Surface 
 
 ^ 4 _. Heating Surface 
 
 
 Horsepower 
 
 Grate Area 
 
 Plain cylindrical 
 Flue 
 
 6 to 10 
 8 to 12 
 
 12 to 15 
 20 to 25 
 
 Return-tubular 
 Vertical 
 
 14 to 18 
 15 to 20 
 
 25 to 35 
 25 to 30 
 
 Water-tube 
 Locomotive 
 
 10 to 12 
 Ito 2 
 
 35 to 40 
 50 to 100 
 
 economy. It is known that increased rate of flow of air over radiating surfaces 
 increases the amount of heat transmitted through the surface, but this is 
 because by the increased circulation, cold air is continually brought into con- 
 tact with the surface, making an increased difference of temperature on the 
 two sides, which causes increased transmission. But by increasing the rapidity 
 of circulation in a steam boiler, it is not possible to vary the difference of 
 temperature to any appreciable extent, for the water and the steam in the 
 boiler are at about the same temperature throughout. The ordinary or 
 "Scotch" form of marine boiler shows an exception to the general rule of 
 uniformity of temperature of water throughout the boiler, but the temperature 
 above the level of the lower fire-tubes is practically uniform. 
 
 Heating Surface. In the various types of boilers, there is a nearly constant 
 ratio between the water-heating surface and the horsepower, and also between 
 the heating surface and the grate area. These ratios are given in an accompany- 
 ing table. If the heating surface of a boiler is known, the horsepower can be 
 found roughly; thus, if a return-tubular boiler has a heating surface of 900 sq. ft., 
 its horsepower lies between 900-^18 = 50 H. P. and 900-^14 = 64.3 H. P., say 
 about 57 H. P. 
 
 The heating surface of a boiler is the portion of the surface exposed to the 
 action of flames and hot gases. This includes, in the case of a multitubular 
 boiler, the portions of the shell below the line of brickwork, the exposed heads 
 of the shell, and the interior surface of the tubes. In the case of a water-tube 
 boiler, the heating surface comprises the portion of the shell below the brick- 
 work, the outer surface of the headers, and the outer surface of the tubes. In 
 any given case, the heating surface may be calculated by the rules of mensuration. 
 
BOILERS 
 
 445 
 
 The following example will show the method of calculating the heating surface 
 of a return-tubular boiler: 
 
 EXAMPLE. What is the heating surface of a horizontal return -tubular 
 boiler that has the following dimensions: Diameter, 60 in.; length of tubes, 
 12 ft.; internal diameter of tubes, 3 in.; number of tubes, 82. 
 
 SOLUTION. Assume that two-thirds of the shell is in contact with hot 
 gases or flame, and two-thirds of the two heads are heating surface. 
 
 Circumference of shell is 60X3.1416 = 188.496 = 188.5 in., say. 
 
 Length of shell is 12 X 12 = 144 in. 
 
 Heating surface of shell is 188.5 X 144 X ? = 18,096 sq. in. 
 
 Circumference of tube is 3X3.1416 = 9.425 in., nearly. 
 
 Heating surface of tubes is 82X144X9.425 = 111,290.4 sq. in. 
 
 Area of one head is 60' X. 7854 = 2,827.44 sq. in. 
 
 Two-thirds area of both heads is 1X2X2,827.44 = 3,769.92 sq. in. 
 
 From the heads must be subtracted twice the area cut out by the tubes; 
 this is 82X3 2 X.7854X2 = 1,159.26 sq. in. 
 
 Total heating surface in square feet is 
 
 18,096 + 111,290.4+3,769.92-1,159.26 
 
 144 
 
 = 916.64 sq. ft. 
 
 PROBABLE MAXIMUM WORK OF A PLAIN CYLINDRICAL BOILER OP 
 
 120 SQ. FT. HEATING SURFACE AND 12 SQ. FT. GRATE 
 
 SURFACE 
 
 Rate of driving; 
 
 
 
 
 
 
 
 
 
 
 pounds of wa- 
 
 
 
 
 
 
 
 
 
 
 ter evapor- 
 
 
 
 
 
 
 
 
 
 
 ated per sq. ft. 
 
 
 
 
 
 
 
 
 
 
 of heating 
 
 
 
 
 
 
 
 
 
 
 surface per 
 
 
 
 
 
 
 
 
 
 
 hour 
 
 2 
 
 3 
 
 3.5 
 
 4 
 
 4.5 
 
 5 
 
 6 
 
 7 
 
 8 
 
 Total water 
 
 
 
 
 
 
 
 
 
 
 evaporated 
 
 
 
 
 
 
 
 
 
 
 by 120 sq. ft. 
 
 
 
 
 
 
 
 
 
 
 heating s u r- 
 
 
 
 
 
 
 
 
 
 
 face per hour, 
 pounds 
 
 240.00 
 
 360.00 
 
 420.0O 
 
 480.00 
 
 540.00 
 
 600.00 
 
 720.00 
 
 840.00 
 
 960.00 
 
 Horsepower 
 
 
 
 
 
 
 
 
 
 
 34.5 Ib. per 
 
 
 
 
 
 
 
 
 
 
 hour=l H.P. 
 
 6.96 
 
 10.43 
 
 12.17 
 
 13.91 
 
 15.65 
 
 17.39 
 
 20.87 
 
 24.35 
 
 27.83 
 
 Pounds water 
 
 
 
 
 
 
 
 
 
 
 evaporated 
 
 
 
 
 
 
 
 
 
 
 per pound 
 
 
 
 
 
 
 
 
 
 
 combustible . 
 
 10.88 
 
 11.30 
 
 11.36 
 
 11.29 
 
 11.20 
 
 11.05 
 
 10.48 
 
 9.48 
 
 8.22 
 
 Pounds combus- 
 
 
 
 
 
 
 
 
 
 
 tible burned 
 
 
 
 
 
 
 
 
 
 
 per hour 
 
 22.10 
 
 31.90 
 
 37.00 
 
 42.50 
 
 48.20 
 
 54.30 
 
 68.70 
 
 88.60 
 
 116.80 
 
 Pounds combus- 
 
 
 
 
 
 
 
 
 
 
 tible per hour 
 
 
 
 
 
 
 
 
 
 
 per square 
 foot of grate . 
 
 1.85 
 
 2.65 
 
 3.08 
 
 3.55 
 
 4.02 
 
 4.52 
 
 5.72 
 
 7.38 
 
 9.73 
 
 Pounds combus- 
 
 
 
 
 
 
 
 
 
 
 tible per hour 
 
 
 
 
 
 
 
 
 
 
 per horse- 
 
 
 
 
 
 
 
 
 
 
 power 
 
 3.17 
 
 3.05 
 
 3.04 
 
 3.06 
 
 3.08 
 
 3.12 
 
 3.30 
 
 3.64 
 
 4.16 
 
 
 
 
 
 
 
 
 
 
 The figures in the last line show that the amount of fuel required for a 
 given horsepower is nearly 37% greater when the rate of evaporation is 8 Ib. 
 than when it is 3.5 Ib. 
 
 The figures in the foregoing table that represent the economy of fuel, 
 viz., Pounds water evaporated per pound combustible and Pounds combustible 
 per hour per horsepower, are what may be called maximum results, and they 
 are the highest that are likely to be obtained with anthracite, with the most 
 skillful firing and with every other condition most favorable. Unfavorable 
 conditions, such as poor firing, scale on the inside of the heating surface, dust 
 
446 BOILERS 
 
 or soot on the outside, imperfect protection of the top of the boiler from radi- 
 ation, leaks of air through the brickwork, or leaks of water through the blow-off 
 pipe, may greatly reduce these figures. 
 
 CHIMNEYS 
 
 Products of Combustion. The weight and volume of the various gases 
 that enter into problems relating to combustion when measured at 32 F. and 
 the average atmospheric pressure at sea level of approximately 14.7 Ib. per 
 sq. in., corresponding to a height of the mercurial barometer of 29.92 in. are 
 given under the subject of Ventilation. To find the volume at any other 
 temperature and pressure, the following formula is used, 
 
 ft-P. 
 
 piTz 
 in which vz = volume corresponding to absolute pressure Pz and absolute 
 
 temperature T* (or 460 +< 2 ); 
 />2 = any given absolute pressure; 
 vi = volume at any other pressure pi and absolute temperature Ti 
 
 (or46Q+/i). 
 
 EXAMPLE. What is the volume of 4 Ib. of dry air at 75 F. and under an 
 absolute pressure of 20 Ib. per sq. in.? 
 
 SOLUTION. From the table, it is found that 1 Ib. of air, at 32 F. and 14.7 Ib. 
 per sq. in. absolute pressure, occupies 12.388 cu. ft., hence, under the same 
 conditions, 4 Ib. occupies 4X12.388 = 49.552 cu. ft. Substituting, in the 
 formula, the values vz = 49. 552, pz = 14. 7 Ib. per sq. in., pi = 20 Ib. per sq. in., 
 fa-75" P., we get , 1 = 49 . 552XX = 3 9 . 6 cu . ft . 
 
 Hitherto it has been considered that the fuel was burned in oxygen. When 
 burning with air, the chemical reactions are the same, for the nitrogen in the air 
 passes through the furnace unchanged. In calculations of temperature, how- 
 ever, account must be taken of the nitrogen, as it is heated by the combustion 
 and therefore absorbs heat and causes the furnace to have a lower temperature 
 than if oxygen alone were used. 
 
 The first table on page 447 gives the weights -of air, water vapor, and 
 saturated mixtures of air and water vapor at different temperatures, under the 
 ordinary atmospheric pressure of 14.7 Ib. per sq. in., or 29.92 in. of mercury. 
 
 EXAMPLE. A coal whose heating value is 12,000 B. T. U. per Ib., is burned 
 with 20 Ib. of air (not including water vapor) per Ib. of coal. The relative 
 humidity of the air is 90%, and its temperature is 92 F. How much heat is 
 lost in the chimney gases on account of the moisture in the air, if the chimney 
 gases escape at 512 F.? 
 
 SOLUTION. From the table, it is found that 1 Ib. of air will hold, when fully 
 saturated, .03289 Ib. of water vapor at 92 F.; hence, 20 Ib. of air will hold 20 
 X .03289 = .6578 Ib. of water vapor; at 90% relative humidity, it will hold 
 .6578 X. 90 = .59202 Ib. water vapor. 
 
 The amount of heat absorbed in heating 1 Ib. of water from 92 F. to 512 F. 
 is: (a) From 92 to 212, or through 120, is 120 X.1 (specific heat of water) 
 = 120 B. T. U.; (6) from 212 to 512, or through 300, is 300X.48 (specific 
 heat of superheated steam) = 144 B. T. U. The total absorption is 120+144 
 = 264 B. T. U. .59202 Ib. water will absorb 264 X. 59202 = 156.29 B. T. U. 
 
 or 156 1 | 9 ( ^ ) 100 = 1.3%. of the heating value of the coal. 
 
 EXAMPLE. How many cubic feet of dry air per pound of coal are used in 
 the preceding example, if the air is at the mean atmospheric pressure of 14.7 Ib. 
 per sq. in.? 
 
 SOLUTION. From the table, by calculation, it is found that 1 Ib. of air 
 at 32 and at the mean atmospheric pressure occupies 1 ^ .0807 = 12.39 cu. ft. 
 
 no I 4.AA 
 
 At 92 it occupies 12.39X ^ =13.9 cu. ft.; 20 Ib. will occupy 13.9X20 
 = 278cu. ft. 
 
 EXAMPLE. How many cubic feet of air must be delivered per minute by 
 a fan, to drive 1.000 H. P. of boilers under the conditions of the preceding 
 examples, if 4 Ib. of coal is burned per H. P. per hr.? 
 
 SOLUTION.- 4 * 1,000X278 = 18t533 cu ft per min 
 
BOILERS 
 
 447 
 
 WEIGHT OF AIR, WATER VAPOR, AND SATURATED MIXTURES AT 
 DIFFERENT TEMPERATURES 
 
 
 
 
 Mixtures of Air Saturated With Vapor 
 
 
 Weight 
 of 1 Cu. 
 
 Elastic 
 
 Elastic 
 
 Weight of 1 Cu. Ft. of 
 
 
 
 Ft. of 
 
 Force of 
 
 Force of 
 
 Mixture of Air and 
 
 
 Temper- 
 ature 
 Degrees 
 P. 
 
 Dry Air 
 at 
 Different 
 Temper- 
 
 Water 
 Vapor 
 Inches 
 of 
 
 Air in 
 Mixture 
 of Air 
 and 
 
 Water Vapor 
 
 Weight 
 of Vapor 
 Mixed 
 With 
 
 
 
 Total 
 
 
 atures 
 
 Mercury 
 
 Vapor 
 
 Weight 
 
 Weight 
 
 Weight 
 
 1 Lb. 
 
 of Air 
 
 
 Pound 
 
 
 Inches 
 
 of 
 
 of 
 
 of 
 
 
 
 
 
 of 
 
 Air 
 
 Vapor 
 
 Mixture 
 
 Pounds 
 
 
 
 
 Mercury 
 
 Pound 
 
 Pound 
 
 Pound 
 
 
 
 
 .0864 
 
 .044 
 
 29.877 
 
 .0863 
 
 .000079 
 
 .086379 
 
 .00092 
 
 12 
 
 .0842 
 
 .074 
 
 29.849 
 
 .0840 
 
 .000130 
 
 .084130 
 
 .00155 
 
 22 
 
 .0824 
 
 .118 
 
 29.803 
 
 .0821 
 
 .000202 
 
 .082302 
 
 .00245 
 
 32 
 
 .0807 
 
 .181 
 
 29.740 
 
 .0802 
 
 .000304 
 
 .080504 
 
 .00379 
 
 42 
 
 .0791 
 
 .267 
 
 29.654 
 
 .0784 
 
 .000440 
 
 .078840 
 
 .00561 
 
 52 
 
 .0776 
 
 .388 
 
 29.533 
 
 .0766 
 
 .000627 
 
 .077227 
 
 .00819 
 
 62 
 
 .0761 
 
 .556 
 
 29.365 
 
 .0747 
 
 .000881 
 
 .075581 
 
 .01179 
 
 72 
 
 .0747 
 
 .785 
 
 29.136 
 
 .0727 
 
 .001221 
 
 .073921 
 
 .01680 
 
 82 
 
 .0733 
 
 1.092 
 
 28.829 
 
 .0706 
 
 .001667 
 
 .072267 
 
 .02361 
 
 92 
 
 .0720 
 
 1.501 
 
 28.420 
 
 .0684 
 
 .002250 
 
 .070717 
 
 .03289 
 
 102 
 
 .0707 
 
 2.036 
 
 27.885 
 
 .0659 
 
 .002997 
 
 .068897 
 
 .04547 
 
 112 
 
 .0694 
 
 2.731 
 
 27.190 
 
 .0631 
 
 .003946 
 
 .067046 
 
 .06253 
 
 122 
 
 .0682 
 
 3.621 
 
 26.300 
 
 .0599 
 
 .005142 
 
 .065042 
 
 .08584 
 
 132 
 
 .0671 
 
 4.752 
 
 25.169 
 
 .0564 
 
 .006639 
 
 .063039 
 
 .11771 
 
 142 
 
 .0660 
 
 6.165 
 
 23.756 
 
 .0524 
 
 .008473 
 
 .060873 
 
 .16170 
 
 152 
 
 .0649 
 
 7.930 
 
 21.991 
 
 .0477 
 
 .010716 
 
 .058416 
 
 .22465 
 
 162 
 
 .0638 
 
 10.099 
 
 19.822 
 
 .0423 
 
 .013415 
 
 .055715 
 
 .31713 
 
 172 
 
 .0628 
 
 12.758 
 
 17.163 
 
 .0360 
 
 .016682 
 
 .052682 
 
 .46338 
 
 182 
 
 .0618 
 
 15.960 
 
 13.961 
 
 .0288 
 
 .020536 
 
 .049336 
 
 .71300 
 
 192 
 
 .0609 
 
 19.828 
 
 10.093 
 
 .0205 
 
 .025142 
 
 .045642 
 
 1.22643 
 
 202 
 
 .0600 
 
 24.450 
 
 5.471 
 
 .0109 
 
 .030545 
 
 .041445 
 
 2.80230 
 
 212 
 
 .0591 
 
 29.921 
 
 .000 
 
 .0000 
 
 .036820 
 
 .036820 
 
 Infinite 
 
 OXYGEN AND AIR REQUIRED FOR THE COMBUSTION OF CARBON, 
 HYDROGEN, ETC. 
 
 Fuel 
 
 Chemical Reaction 
 
 Carbon to COt 
 
 Carbon to CO i 
 
 Carbon monoxide toCO 2 j 
 
 Hydrogen to H^O | 
 
 Marsh gas (methane), 1 ! 
 
 Sulphur to SO 2 ! 
 
 C+O = 
 
 CO + 0: 
 
 = CO 
 = C0 2 
 
 5+2O = SOz 
 
 I? 
 
 8.85 
 
 4.43 
 
 1.90 
 
 26.56 
 
 13.28 
 3.33 
 
 fe-gx 
 
 " 
 
 11.52 
 5.76 
 2.47 
 
 34.56 
 
 17.28 
 4.32 
 
 12.52 
 6.76 
 3.47 
 
 35.56 
 
 18.28 
 5.32 
 
 The preceding table contains, in convenient form, the reactions involved 
 in the combustion of various fuels, as explained more in detail before, as well 
 as the weight of air, oxygen, and nitrogen, required to burn 1 Ib. of the fuel, 
 
448 
 
 BOILERS 
 
 and the weight of the products of combustion resulting therefrom. It is found, 
 in practice, that if air is blown through a bed of hot anthracite or coke, and the 
 resulting gases are analyzed, they always contain some carbon monoxide, 
 showing imperfect combustion, unless they contain a considerable quantity of 
 uncombined oxygen, or air. The excess of air required to effect complete 
 combustion to carbon dioxide is usually not less than 50% of that theoretically 
 necessary, so that about 17 Ib. of air is required to insure the complete com- 
 bustion of 1 Ib. of carbon instead of 11.52 Ib., the figure given in the table. 
 It is probable, also, that more than 34.56 Ib. of air is required to effect the 
 combustion of each pound of hydrogen in a furnace, although, experimentally, 
 one volume of oxygen and two volumes of hydrogen mixed together, or eight 
 parts by weight of oxygen to one of hydrogen may be exploded by a spark, and 
 converted into water vapor. The excess of air required in furnaces may^be 
 due to the presence of the great volumes of nitrogen and carbon dioxide, which 
 dilutes the oxygen and makes it less active in causing combustion. 
 
 EXAMPLE. How much air is required for the complete combustion of 
 1 Ib. of coal containing 5% moisture, 20% volatile matter, 60% fixed carbon, 
 15% ash, assuming the volatile matter to be of the composition of marsh gas 
 (methane), CU? 
 
 SOLUTION. The molecular weight of marsh gas is 12+4 = 16; hence, three- 
 fourths of the weight of the volatile matter is carbon and one-fourth hydrogen. 
 The carbon of the volatile matter is | X 20 = 15% of the fuel. The fixed carbon 
 is given as 60%. The total carbon is 15+60 = 75%. The hydrogen of the 
 volatile matter is iX20 = 5% of the fuel. 
 
 As, from the table, 11.52 Ib. of air is required to burn 1 Ib. of carbon to COi, 
 and 34.56 Ib. of air is required to burn 1 Ib. of hydrogen, the theoretical amount 
 of air required to burn the fuel will be: For the carbon .75X 11.52 = 8.640 Ib.; 
 for the hydrogen .05X34.56 = 1.728 Ib.; making a total of 10.368 Ib. If an 
 excess of 50% of air is allowed, the amount will be 1.5 X 10.368= 15.552 Ib. 
 
 EXAMPLE. How many cubic feet of dry air at 62 F. will be required 
 in the preceding example? 
 
 SOLUTION. The weight of 1 cu. ft. of air at a temperature of 62 F. and a 
 barometric pressure of 29.92 is .0761 Ib.; hence, 10.368 Ib. = 10.368-7- .0761 
 = 136.24 cu. ft. and 15.552 lb. = 15.552 -=-.0761 = 204.36 cu. ft. 
 
 Temperature of Ignition. Every combustible must be heated to a certain 
 temperature, known as the temperature of ignition, or kindling point, before 
 it will combine with oxygen, or burn. The accompanying table gives the 
 temperatures of ignition of various fuels as determined by different authorities. 
 It appears from this table that it requires a considerably higher temperature 
 to ignite the gases distilled from coal than to ignite the coal itself, the 
 temperature of ignition of the carbon being lower than that of the gases. 
 
 TEMPERATURE OF IGNITION OF VARIOUS FUELS 
 
 Fuel 
 
 Temperature of 
 Ignition 
 Degrees F 
 
 Marsh gas (methane), CHt 
 
 1,202* 
 
 Carbon monoxide, CO. , . 
 
 1 202 to 1 211 
 
 Carbon monoxide, CO, in presence of a large quantity of 
 carbon dioxide COz 
 
 1 292 
 
 Ethylene (olefiant gas), C^^i^ 
 
 1 022 
 
 Hydrogen 
 
 1 031 to 1 130 
 
 Anthracite 
 
 925 
 
 Semibituminous coal 
 
 870 
 
 Bituminous coal 
 
 766 
 
 Cannel coal 
 
 668 
 
 Soft charcoal, prepared at 500 F 
 
 650 
 
 Sulphur 
 
 470 
 
 
 
 *The temperature of ignition of marsh gas diluted with carbon dioxide and 
 nitrogen in the proportions ordinarily found in a furnace is given by the French 
 Coal Commission as 1,436 F. 
 
Temperature of 
 Fire. Assuming that a 
 pure fuel, such as car- 
 bon, is thoroughly 
 burned in a furnace, all 
 the heat generated will 
 be transferred to the 
 gaseous products of 
 combustion, raising 
 their temperature above 
 that at which the_ fuel 
 and the oxygen or air are 
 supplied to the furnace. 
 Suppose that 1 Ib. of 
 carbon is burned with 
 2f Ib. of oxygen, form- 
 ing 3 | Ib. of carbon 
 dioxide, both the carbon 
 and the oxygen being 
 supplied at F. The 
 combustion of 1 Ib. of 
 carbon generates 
 14,600 B. T. U., which 
 will all be contained in 
 the 3f Ib. of carbon 
 dioxide. The specific 
 heat of carbon dioxide 
 is .217 at constant pres- 
 sure; that is, it requires 
 .217 B. T. U. to raise 
 the temperature of 1 Ib. 
 of carbon dioxide 1 F. 
 To raise 3| Ib. of car- 
 bon dioxide 1 F. will 
 require 3 |X. 2 17 = .7957 
 B. T. U., and 14,600 B. 
 T. U. will therefore raise 
 its temperature 14,600 
 -4- .7957 = 18,348.6 F. 
 (approximately 18,350 
 F.) above the tempera- 
 ture at which the car- 
 bon and the oxygen were 
 supplied. The tempera- 
 tures thus calculated 
 are known as theoret- 
 ical temperatures, and 
 are based on the assump- 
 tions of perfect com- 
 bustion and no loss by 
 radiation. The temper- 
 ature of 18,350 is far 
 beyond any tempera- 
 ture known, and it is 
 probable that long be- 
 fore it could be reached, 
 the phenomenon of dis- 
 sociation would take 
 place; that is, the car- 
 bon dioxide would be 
 split into carbon and 
 oxygen, and the ele- 
 ments would lose their 
 affinity for each other. 
 
 The theoretical ele- 
 vation of temperature 
 of the fare may be calcu- 
 lated by the formula 
 
 29 
 
 BOILERS 
 
 S99J39Q 
 -UI9J, JO UOI^BA9[g 
 
 449 
 
 ! 
 
 tJ a 
 
 6^ 
 
 ^o 
 
 13 
 
 11 
 
 f 
 
 spunoj 
 
 COMCOCO'-it^ 
 
 co" co" co" co" co* <N" 
 
 06 ION O 06 co 
 
 O3 o; psua 
 
 (uoqjBQ PUB jiy) 
 
 spunoj 
 
 uoqjBQ 
 
 jo puno<j J3d aiy 
 
 J9<J 
 
 spunoj 
 
 ^ S99J33Q 
 
 -UI9X 
 
 n *x 'a 
 
 p9^BJ3U9Q 
 
 -a 
 
 ZQ3 SuiuiJO^j 
 
 spuno^ 
 
 spunoj 
 
 uoqjBQ 
 
 jo puno j aad Jiy 
 
 OOOlOO r-t i-( 
 >O <N t- CO Tt* T-H 
 O3COOO IOOI> 
 
 coeoeicfwi-i 
 
 O 00 CD-^ O<O 
 rt< (N i-H O 00 O 
 
 >OO O 
 l>O iO 
 
 00 CO 00 Tt< CO CO 
 ^V-* CO* CON 
 
 000 
 
 ( rH 00 >O 
 
 CO ^ C^J 
 t-OOO 
 
 oooo 
 
 TjtcC 00 O 
 
 l^M 
 CO (M 
 
 spuno 
 
 j gg- 
 
 ddn 
 
450 BOILERS 
 
 B. T. U. generated by the combustion 
 Elevation of temperature - 
 
 Weight of gaseous products X their specific heats 
 It is evident from this formula that the rapidity of the combustion, or the 
 time required to burn a given weight of fuel, has nothing to do with the tem- 
 perature that may theoretically be attained. In practice, the temperature 
 of a bed of coal in a furnace and that of the burning gases immediately above 
 the coal are reduced, to some extent, by radiation; and as the quantity of heat 
 radiated from a given mass of fuel is a function of the time during which it 
 takes place, a considerable portion of the heat generated may be lost by radi- 
 ation when the combustion is very slow. With ordinary rates of combustion, 
 however, that is, of about 10 Ib. of coal per square foot of grate surface 
 per hour, and firebrick furnaces, the percentage of loss of heat by radiation 
 is 1% or less, and the actual temperature that may be attained will be very 
 nearly as high with that rate of combustion as witri a rate of 20 or 40 Ib. 
 
 The elevations of temperature given in the foregoing table were deter- 
 mined by means of the preceding formula, the specific heat of the chimney gases 
 being taken as .24. 
 
 To burn 1 Ib. of hydrogen, 8 Ib. of oxygen is required, and there is also 
 present 8X3.32 = 26.56 Ib. of nitrogen, which is mixed with the oxygen in the 
 air. The gaseous products are 9 Ib. of water, in the shape of superheated steam 
 (specific heat .48), and 26.56 Ib. of nitrogen (specific heat .2438). The heat 
 produced is 62,000 B. T. U. If the temperature of the atmosphere is 62 F., 
 150 B. T. U. is absorbed during the combustion in heating 1 Ib. of water, HiO, 
 from 62 to 212 F. per Ib., 965.8 B. T. U. in evaporating it at that temper- 
 ature, and .48 (T+t 212) in superheating it from 212 to the temperature T 
 +/ of the fire, T being the increase of temperature and t the temperature of 
 the atmosphere, which in this case is 62 F. All this heat may be recovered 
 by condensing the steam and cooling the water of condensation to 62. There- 
 fore, the following equation is obtained : 
 
 which, being solved, gives T = 4,873 F. T+t = 4,935 F. Showing that hydro- 
 gen and carbon, when perfectly burned, give about the same maximum theo- 
 retical temperature. 
 
 By a process of reasoning similar to the preceding, the following formula 
 is derived, to obtain the maximum theoretical temperature of the fire, when the 
 fuel contains hydrogen and moisture with a varying supply of air: 
 616C+2,220fl-327Q-44PF 
 
 f+.02W+A8H 
 
 in which T = elevation of temperature above that of atmosphere; 
 C = percentage of carbon in fuel; 
 H = percentage of hydrogen in fuel; 
 O = percentage of oxygen in fuel; 
 W= percentage of water in fuel; 
 /= pounds of dry gases of combustion (HiO excluded) 
 
 per pound of fuel. 
 EXAMPLE. What would be the temperature of the fire, the temperature 
 of the atmosphere being 62 P., when burning a coal having the composition 
 excluding ash and sulphur, carbon 75%, hydrogen 5%, oxygen 10%, moisture 
 10%; the dry chimney gases amount to 20 Ib. per Ib. of this combustible 
 including the moisture? 
 
 SOLUTION. Applying the formula, 
 
 r _616X75+2.220X5-327X10-44X10 
 20 + .02X10+.18X5 
 T+/ = 2,540 -r-62 = 2,602 F. 
 EXAMPLE. What is the maximum temperature attainable by burning 
 moist wood of the composition carbon 38%, hydrogen 5%, oxygen 32%, nitro- 
 gen and ash 1%, moisture 24% ; the dry gases are 15 Ib. per Ib. of wood, and the 
 temperature of the atmosphere is 62 P.? 
 SOLUTION. Applying the formula, 
 
 616X38+2,220X5-327X32-44X24 
 15+.02X24+.18X5 
 r+* = l,403+62 = 1,465 F. 
 EXAMPLE. What will be the temperature of a fire of Pocahontas coal 
 analyzing carbon 84.22%, hydrogen 4.26%, oxygen 3.48%, nitrogen .84%, 
 sulphur .59%, ash 5.85%, water .76%; the dry gases are 20 Ib. per Ib. of com- 
 bustible, the heating value of the sulphur being neglected? 
 
BOILERS 451 
 
 SOLUTION. The combustible, carbon and hydrogen, is 88.48% of the coal, 
 hence /= 20 X .8848 = 17.69. Applying the formula, 
 
 616X84.22+2.220X4.26-327X3.48-44X.76 
 
 17.69 + .02X. 76 + . 18X4.26 SM ' 
 
 r+* = 3,257 +62 = 3,319 F. 
 
 When the combustion is perfect, and the furnace is entirely enclosed in walls 
 of firebrick, highly heated, the temperatures calculated by the formula are 
 nearly attained, the only loss being that due to external radiation. In ordinary 
 practice, with the boiler immediately above the fire, the temperature is lowered 
 by radiation, and also, when soft coal is used, by imperfect combustion. 
 
 Estimation of Air Supply. The theoretical amounts of air required to burn 
 the several combustible elements in a fuel were given in the table on page 447, 
 but when burning coal in a furnace only a rough estimate of the quantity of 
 air supplied may be obtained by direct measurement by an anemometer, or by 
 counting the revolutions of a fan. The only available method of closely 
 approximating the amount of air supplied, is by making a proximate analysis 
 of the gases of combustion, taken from a point close to the furnace, but 
 beyond the point of visible flame. If taken from the chimney, the gas may 
 be of different composition on account of inward leaks of air through cracks 
 in the brickwork. 
 
 The analysis of the gases gives the percentage of carbon dioxide, oxygen, 
 and carbon monoxide, in this order, the quantity of these gases being deter- 
 mined by absorption; nitrogen is determined by difference; that is, the remain- 
 der after subtracting the sum of the other three gases from 100. Unburned 
 hydrogen or hydrocarbon gases cannot be conveniently determined by ordinary 
 analysis. If the combustion is complete, the percentage of nitrogen will 
 always be found between 79 and 80. If it exceeds 80%, unburned hydrogen, 
 or hydrocarbons are present, an error has been made in the analysis, or, possibly, 
 the hydrogen of a gaseous fuel has been burned leaving the carbon unburned. 
 Thus, in burning marsh gas (methane), CHt, with an insufficient supply of air, 
 the hydrogen only may be burned to water, HzO, leaving the carbon unburned 
 in the shape of soot, which is caught in a filter attached to the gas-collecting 
 apparatus. The water, or water vapor, is condensed, and is not determined 
 in the analysis, leaving the nitrogen that accompanied the oxygen alone to 
 be determined. In this manner, the nitrogen in the gases may actually 
 exceed 80%. 
 
 The following formula may be used for calculating the air supply: 
 
 3.032.ZV 
 Pounds of dry air per pound of carbon = -. \ C Q 
 
 in which COt, CO, and N are percentages, by volume, of the dry gas. 
 
 EXAMPLE. How many pounds of air are supplied per pound of carbon in 
 burning a coal, if the gases analyze carbon dioxide 11.74%, carbon monoxide 
 .10%, oxygen 7.71%, nitrogen 80.45%? 
 
 SOLUTION. Substituting in the formula, 
 3.032X80.45 
 
 Production and Measurement of Draft. It is well known that any volume 
 of gas is lighter when heated than the same volume of gas when cool. When 
 hot gases pass into the chimney they have a temperature of from 400 to 600 F., 
 while the air outside the chimney has a temperature of from 40 to 90 F. 
 Roughly speaking, the air weighs twice as much, bulk for bulk, as the hot 
 gases. Naturally, then, the pressure in the chimney is less than the pressure 
 of the outside air. The production of draft and the satisfactory operation of 
 a chimney depend on this pressure difference. The pressure of the draft 
 depends on the temperature of the furnace gases and the height of the chimney. 
 Chimney draft is affected by so many varying conditions that no absolutely 
 reliable rules can be given for proportioning chimneys to give a certain desired 
 draft pressure. The rules given for chimney proportions are based on successful 
 practice rather than on pure theory. 
 
 The intensity of the draft may be measured by means of a water gauge 
 such as is shown in the accompanying illustration. This is a glass tube open 
 at both ends, bent to the shape of the letter U ; the left leg communicates with 
 the chimney. The difference in the two water levels H and Z in the legs 
 represents the intensity of the draft, and is expressed in inches of water. 
 
 The draft produced by a chimney may vary from J in. to 2 in. of water, 
 depending on the temperature of the chimney gases and on the height of the 
 chimney. Generally speaking, it is advantageous to use a high chimney and 
 
452 
 
 BOILERS 
 
 as low a chimney temperature as possible. The draft pressure required 
 depends on the kind of fuel used. Wood requires but little draft, say, $ in. of 
 water or less; bituminous coal generally requires less draft than anthracite. 
 To burn anthracite slack, or culm, the draft pressure should be 
 about 1 1 in. of water. 
 
 Erection of Chimneys. The form of a chimney has a pro- 
 nounced effect on its capacity. A round chimney has a greater 
 capacity for a given area than a square one. If the flue is taper- 
 ing, the area for calculation is measured at its smallest section. 
 The flue through which the gases pass from the boilers to the chim- 
 ney should have an area equal to, or a little larger than, the area 
 of the chimney. Abrupt turns in the flue or contractions of its 
 area should be carefully avoided. Where one chimney serves 
 several boilers, the branch flue from each furnace to the main flue 
 must be somewhat larger than its proportionate part of the area 
 of the main flue. 
 
 Chimneys are usually built of brick, though concrete, iron, 
 and steel are often used for those of moderate height. Brick 
 chimneys are usually built with a flue having parallel sides and a 
 taper on the outside of the chimney of from ^g to i in. per ft. of 
 height. A round chimney gives greater draft area for the same 
 amount of material in its structure and exposes less surface to the 
 wind than a square chimney. Large brick stacks are usually made 
 with an inner core and an outer shell, with a space between them. 
 Such chimneys are usually constructed with a series of internal 
 pilasters, or vertical ribs, to give rigidity. The top of the chim- 
 ney should be protected by a coping of stone or a cast-iron plate 
 to prevent the destruction of the brickwork by the weather. 
 
 Iron or steel stacks are made of plates varying from | to in. thick. The 
 larger stacks are made in sections, the plates being about 1 in. thick at the top 
 and increasing to | in. at the bottom; they are lined with firebrick about 18 in. 
 thick at the bottom and 4 in. at the top. Sometimes no lining is used on 
 account of the likelihood of corrosion and the difficulty of inspection, and also 
 because the inside of lined stacks cannot be painted. 
 
 On acdount of the great concentration of weight, the foundation for a 
 chimney should be carefully designed. Good natural earth will support from 
 2,000 to 4,000 Ib. per sq. ft. The footing beneath the chimney foundation 
 should be made of large area, in order to reduce the pressure due to the weight 
 of the chimney and its foundation to a safe limit. 
 
 Height and Area of Chimneys. The relation between the height of the 
 chimney and the pressure of the draft, in inches of water, is given by the 
 formula = fl /T.6 _ 7.9\ 
 
 in which . p = draft pressure, in inches of water; 
 
 H = height of chimney, in feet; 
 T a and T c = absolute temperatures of outside air 
 and of chimney gases respectively. 
 
 EXAMPLE. What draft pressure will be produced by a chimney 120 ft. 
 high, the temperature of the chimney gases being 600 F., and of the external 
 air 60 P.? 
 
 SOLUTION. Substituting in the formula, 
 
 To find the height of chimney to give a specified draft pressure, the preced- 
 ing formula may be transformed. Thus, 
 
 H 
 
 6_.9x 
 T a T c ) 
 
 EXAMPLE. Required, the height of the chimney to produce a draft of \\ in. 
 of water, the^temperature of the gases and of the external air being, respectively, 
 
 SOLUTION. Substituting in the formula, 
 
 n 
 ti 
 
 7.6 
 522' 
 
 167 ft. 
 
 _ 
 1,010 
 
BOILERS 453 
 
 In determining the height of a chimney in cities, it should be borne in 
 mind that the chimney must almost always be carried to a height above the 
 roofs of surrounding buildings, partly in order to prevent a nullification of the 
 draft by opposing air-currents and partly to prevent the commission of a 
 nuisance. 
 
 The height of the chimney being decided on, its cross-sectional area must 
 be sufficient to carry off readily the products of combustion. The following 
 formulas for finding the dimensions of chimneys are in common use: 
 Let H = height of chimney, in feet; 
 
 H .P. = horsepower of boiler or boilers; 
 
 A = actual area of chimney, in squa're feet; 
 E = effective area of chimney, in square feet; 
 5 = side of square chimney, in inches; 
 d = diameter of round chimney, in inches. 
 
 Then, E = = A-.6A (1) 
 
 Vfl 
 
 (2) 
 (3) 
 
 d= 13.54 VE+4 (4) 
 
 The table on page 454 has been computed from these formulas. 
 EXAMPLE. What should be the diameter of a chimney 100 ft. high that 
 furnishes draft for a 600-H. P. boiler? 
 
 SOLUTION. Substituting in formula 1, E = '- =18. Now, using 
 
 VlOO 
 formula 4, d = 13.54V 18+4 = 61.44 in. 
 
 EXAMPLE. For what horsepower of boilers will a chimney 64 in. sq. and 
 125 ft. high furnish draft? 
 
 SOLUTION. By simply referring to the table, the horsepower is found 
 to be 934. 
 
 Maximum Combustion Rate. The maximum rates of combustion attain- 
 able under natural draft are given by the following formulas, which have been 
 deduced from the experiments of Isherwood: 
 
 Let F weight of coal per hour per square foot of grate area, in pounds; 
 H = height of chimney or stack, in feet, 
 
 Then, for anthracite burned under the most favorable conditions, 
 
 F = 2V#-1 (1) 
 
 and under ordinary conditions, 
 
 F = 1.5V#-1 (2) 
 
 For best semianthracite and bituminous coals, 
 
 F = 2.25Vfl (3) 
 
 and for less valuable soft coals, 
 
 F = 3Vfl (4) 
 
 The maximum rate of combustion is thus fixed by the height of the 
 chimney; the minimum rate may be anything less. 
 
 EXAMPLE. Under ordinary conditions, what is the maximum rate of com- 
 bustion of anthracite if the chimney is 120 ft. high? 
 
 SOLUTION. By formula 2, _ 
 
 F = 1.5X Vl20 - 1 = 15| Ib. per sq. ft. per hr. 
 
 Forced Draft. The use of forced draft as a substitute for, or as an aid to, 
 natural chimney draft is becoming quite common in large boiler plants. Its 
 advantages are that it enables a boiler to be driven to its maximum capacity 
 to meet emergencies without reference to the state of the weather or to the 
 character of the coal; that the draft is independent of the temperature of the 
 chimney, gases, and that, therefore, lower flue temperatures may be used than 
 with natural draft; and in many cases that it enables a poorer quality of coal 
 to be used than is required with natural draft. Forced draft may be obtained: 
 
 (1) by a steam jet in the chimney, as in locomotives and steam fire-engines; 
 
 (2) by a steam-jet blower under the grate bars; (3) by a fan blower delivering air 
 under the grate bars, the ash-pit doors being closed; (4) by a fan blower deliver- 
 ing air into a closed ftreroom, as in the closed stake-hold system used in some 
 ocean-going vessels; and (5) by a fan placed in the flue or chimney drawing 
 the gases of combustion from the boilers, commonly called the induced-draft 
 system. Which one of these several systems should be adopted in any special 
 
454 STEAM ENGINES 
 
 SIZE OF CHIMNEYS AND HORSEPOWER OF BOILERS 
 
 1 1 
 
 to 
 
 d m 
 
 Height of Chimney, in Feet 
 
 ct 
 
 
 pi 
 
 1 
 
 
 
 2 | 
 
 1 
 
 00 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 110 
 
 125 
 
 150 
 
 175 
 
 200 
 
 > 4> 
 
 a 8 
 
 JT 
 
 " 
 fe ^ 
 
 
 t co 
 
 < CO 
 
 |l 
 
 IE 
 
 Commercial Horsepower 
 
 
 
 cog 
 
 &s 
 
 23 
 
 25 
 
 27 
 
 
 
 
 
 
 
 
 
 .97 
 
 1.77 
 
 16 
 
 18 
 
 35 
 
 38 
 
 41 
 
 
 
 
 
 
 
 
 
 1.47 
 
 2.41 
 
 19 
 
 21 
 
 49 
 
 54 
 
 58 
 
 62 
 
 
 
 
 
 
 
 
 2.08 
 
 3.14 
 
 22 
 
 24 
 
 65 
 
 72 
 
 78 
 
 83 
 
 
 
 
 
 
 
 
 2.78 
 
 3.98 
 
 24 
 
 27 
 
 84 
 
 92 
 
 100 
 
 107 
 
 113 
 
 
 
 
 
 
 
 3.58 
 
 4.91 
 
 27 
 
 30 
 
 
 115 
 
 125 
 
 133 
 
 141 
 
 
 
 
 
 
 
 4.47 
 
 5.94 
 
 30 
 
 33 
 
 
 141 
 
 152 
 
 163 
 
 173 
 
 182 
 
 
 
 
 
 
 5.47 
 
 7.07 
 
 32 
 
 36 
 
 
 
 183 
 
 196 
 
 208 
 
 219 
 
 
 
 
 
 
 6.57 
 
 8.30 
 
 35 
 
 39 
 
 
 
 216 
 
 231 
 
 245 
 
 258 
 
 271 
 
 
 
 
 
 7.76 
 
 9.62 
 
 38 
 
 42 
 
 
 
 
 311 
 
 330 
 
 348 
 
 365 
 
 389 
 
 
 
 
 10.44 
 
 12.57 
 
 43 
 
 48 
 
 
 
 
 402 
 
 427 
 
 449 
 
 472 
 
 503 
 
 551 
 
 
 
 13.51 
 
 15.90 
 
 48 
 
 54 
 
 
 
 
 505 
 
 r>3', 
 
 565 
 
 593 
 
 632 
 
 692 
 
 748 
 
 
 16.98 
 
 19.64 
 
 54 
 
 60 
 
 
 
 
 
 658 
 
 694 
 
 728 
 
 776 
 
 849 
 
 918 
 
 981 
 
 20.83 
 
 23.76 
 
 59 
 
 66 
 
 
 
 
 
 792 
 
 835 
 
 876 
 
 934 
 
 1,203 
 
 1,105 
 
 1,181 
 
 25.08 
 
 28.27 
 
 64 
 
 72 
 
 
 
 
 
 
 995 
 
 1,038 
 
 1,107 
 
 1,212 
 
 1,310 
 
 1,400 
 
 29.73 
 
 33.18 
 
 70 
 
 78 
 
 
 
 
 
 
 1,163 
 
 1,214 
 
 1,294 
 
 1,418 
 
 1,531 
 
 1,637 
 
 34.76 
 
 38.48 
 
 75 
 
 84 
 
 
 
 
 
 
 1,344 
 
 1,415 
 
 1,496 
 
 1,639 
 
 1,770 
 
 1,893 
 
 40.19 
 
 44.18 
 
 80 
 
 90 
 
 
 
 
 
 
 1,537 
 
 1,616 
 
 1,720 
 
 1,876 
 
 2,027 
 
 2,167 
 
 46.01 
 
 50.27 
 
 86 
 
 96 
 
 case will usually depend on local conditions. The steam jet has the advantage 
 of lightness and compactness of apparatus, and is therefore most suitable for 
 locomotives and steam fire-engines, but it also is the most wasteful of steam, 
 and therefore should not be used when one of the fan-blower systems is avail- 
 able, except for occasional or temporary use, or when very cheap fuel, such as 
 anthracite culm at the mines, is used. 
 
 STEAM ENGINES 
 
 PRINCIPLES AND REQUIREMENTS 
 
 A good steam engine should be as direct acting as possible; that is, the 
 connecting parts between the piston and the crank-shaft should be few in 
 number, as each part wastes some power. The movin g parts of an engine should 
 be strong, to resist strains, and light, so as to offer no undue resistance to 
 motion; parts moving upon each other should be well, truly, and smoothly 
 finished, to reduce resistances to a minimum; the steam should get into the 
 cylinder easily at the proper time, and the exhaust should leave the cylinder as 
 exactly and as easily. The steam pipes supplying steam should have an 
 area one-tenth the combined areas of the cylinders they supply, and exhaust 
 pipes should be somewhat larger. The cylinder and the steam pipes and the 
 boiler should be well protected. The engine should be capable of being started 
 and stopped and reversed easily and quickly. 
 
 Clearance. The term clearance is used in two senses in connection with the 
 steam engine. It may be the distance between the piston and the cylinder 
 head when the piston is at the end of its stroke, or it may represent the volume 
 between the piston and the valve when the engine is on dead center. To avoid 
 confusion, the former is called piston clearance, and the latter is termed simply 
 clearance. Piston clearance is always a measurement, expressed in parts of 
 an inch. Clearance, however, is a volume. 
 
STEAM ENGINES 455 
 
 The clearance of an engine may be found by putting the engine on a dead 
 center and pouring in water until the space between the piston and the cylinder 
 head, and the steam port leading into it, is filled. The volume of the water 
 poured in is the clearance. The clearance may be expressed in cubic feet or 
 cubic inches, but it is more convenient to express it as a percentage of the 
 volume swept through by the piston. For example, suppose that the clearance 
 volume of a 12"X18" engine is found to be 128 cu. in. The volume swept 
 through by the piston per stroke is 12* X. 7854X18 = 2,035.8 cu. in. Then, 
 the clearance is 128-^2,035.8 = .063 = 6.3%. The clearance may be as low as 
 i% in Corliss engines, and as high as 14% in high-speed engines. 
 
 Theoretically, there should be no clearance, because the steam that fills 
 the clearance space does no work except during expansion; it is exhausted 
 from the cylinder during the return stroke, and represents so much dead loss. 
 This is remedied, to some extent, by compression. If the compression were 
 carried up to the boiler pressure, there would be very little, if any, loss, as the 
 steam would then fill the entire clearance space at boiler pressure, and the 
 amount of fresh steam needed would be the volume displaced by the piston 
 up to the point of cut-off, the same as if there were no clearance. In practice, 
 however, the compression is made only sufficiently great to cushion the recipro- 
 cating parts and bring them to rest quietly. 
 
 It is not practicable to build an engine without any clearance, on account 
 of the formation of water in the cylinder due to the condensation of steam, 
 particularly when starting the engine. Automatic cut-off high-speed engines 
 of the best design, with shaft governors, usually compress to about half the 
 boiler pressure, and have a clearance of from 7 to 14%. Corliss engines require 
 but very little compression, owing to their low rotative speeds; they also have 
 very little clearance, as the ports are short and direct. 
 
 Cut-Off . The apparent cut-off is the ratio between the portion of the stroke 
 completed by the piston at the point of cut-off, and the total length of the stroke. 
 For example, if the length of stroke is 48 in., and the steam is cut off from the 
 cylinder just as the piston has completed 15 in. of the stroke, the apparent 
 cut-off is if = -f e . 
 
 The real cut-off is the ratio between the volume of. steam in the cylinder 
 at the point of cut-off and the volume at the end of the stroke, both volumes 
 including the clearance of the end of the cylinder in question. If the volume 
 of steam in the cylinder, including the clearance, at the point of cut-off is 
 
 4 cu. ft., and the volume, including the clearance, at the end of the stroke is 
 6 cu. ft., the real cut-off is = |. 
 
 Ratio of Expansion. The ratio of expansion, also called the real number of 
 expansions, is the ratio between the volume of steam, including the steam in 
 the clearance space, at the end of the stroke, and the volume, including the 
 clearance, at the point of cut-off. It is the reciprocal of the real cut-off. For 
 example, if the volume at the end of the stroke is 8 cu. ft., and the cut-off is 
 
 5 cu. ft., the ratio of expansion is 8-j-5 = 1.6; in other words, the steam would 
 be said to have one and six-tenths expansions. The corresponding real cut-off 
 will be f . 
 
 Let e =real number of expansions; 
 
 * = clearance, expressed as a per cent, of stroke; 
 k =real cut-off; 
 
 ki = apparent cut-off; j 
 
 r = apparent number of expansions = . 
 
 KI 
 
 Then, =|andfe = - (1) 
 
 K 6 
 
 *4 <*> 
 
 EXAMPLE. The length of stroke is 36 in.; the steam is cut off when the 
 piston has completed 16 in. of the stroke; the clearance is 4%. Find the 
 apparent cut-off, the real cut-off, and the real number of expansions. 
 
 SOLUTION. Apparent cut-off = | = $ = .444. 
 ki+i .444 + .04 .484 
 
 Real number of expansions = e = r = -j-^ = 
 
 Mean Effective Pressure. In order to find the horsepower of an engine, 
 it is necessary to know the mean effective pressure (abbreviated M. E. P.), 
 
456 
 
 STEAM ENGINES 
 
 which is defined as the average pressure urging the piston forwards during its 
 entire stroke in one direction, less the pressure that resists its progress. If an 
 indicator is not available, so that diagrams may be taken in order to determine 
 the mean effective pressure of an engine, the value of this pressure may be 
 estimated by the formula 
 
 P = .Q[C(p+ 14.7) 17], 
 
 in which P = M. E. P., in pounds per square inch; 
 
 C = constant corresponding to cut-off, taken from 
 
 following table; 
 
 p = boiler pressure, in pounds per square inch, gauge. 
 
 The foregoing formula applies only to a simple noncondensing engine. If the 
 engine is a simple condensing engine, the formula should be altered by sub- 
 stituting for 17 the pressure existing in the condenser, in pounds per square 
 inch. 
 
 CONSTANTS USED IN CALCULATING MEAN EFFECTIVE 
 PRESSURE 
 
 Cut-off 
 
 Constant 
 
 Cut-off 
 
 Constant 
 
 Cut-off 
 
 Constant 
 
 1 
 
 .545 
 .590 
 .650 
 .705 
 .737 
 
 I 
 
 1 
 
 .773 
 .794 
 .864 
 .916 
 .927 
 
 .7 
 
 1 
 
 .943 
 .954 
 .970 
 .981 
 .993 
 
 In this table, the fraction indicating the point of cut-off is obtained by divid- 
 ing the distance that the piston has traveled when the steam is cut off by the 
 whole length of the stroke; that is, it is the apparent cut-off. It is to be 
 observed that this rule cannot be applied to a compound engine or to any other 
 engine in which the steam is expanded in successive stages in several cylinders. 
 
 EXAMPLE. Find the approximate mean effective pressure of a non-con- 
 densing engine cutting off at one-half stroke, if the boiler pressure is 80 lb., 
 
 SOLUTION. According to the table, the constant corresponding to cut-off 
 at one-half stroke is C = .864. Then, applying the formula, P = .9X[.864 
 X (80+14.7) - 171 = 58.34 lb. per sq. in. 
 
 Horsepower. The indicator furnishes the most ready method of measuring 
 the pressures on the piston of a steam engine and, in consequence, of determin- 
 ing the amount of work done in the cylinder and the corresponding horsepower. 
 The power measured by the use of the indicator is called the indicated horse- 
 power. It is the total power developed by the action of the net pressures of the 
 steam on the two sides of the moving piston. The indicated horsepower is 
 generally represented by the initials I. H. P. 
 
 The part of the indicated horsepower that is absorbed in overcoming the fric- 
 tional resistances of the moving parts of the engine is termed the friction horse- 
 power. If the engine is running light, or with no load, all the power developed 
 in the cylinder is absorbed in keeping the engine in motion, and the friction 
 horsepower is equal to the indicated horsepower. This principle furnishes a 
 simple approximate method of finding the friction horsepower of a given engine; 
 as, however, the friction between the surfaces increases with the pressure, the 
 power absorbed in overcoming the engine will be greater as the load on the 
 engine is increased. 
 
 The difference between the indicated horsepower and the friction horse- 
 power is the net horsepower. This is the power that the engine delivers through 
 the flywheel or shaft to the belt or the machine driven by it, and is sometimes 
 called the delivered horsepower. As the power that an engine is capable of 
 delivering when working under certain conditions is often measured by a 
 device known as a Prony brake, the net horsepower is frequently called the 
 brake horsepower, abbreviated B. H. P. 
 
 Finding the Indicated Horsepower. Knowing the dimensions and speed 
 of the engine and the mean effective pressure on the piston, all the data for find- 
 ing the rate of work done in the engine cylinder expressed in horsepower are 
 at hand. 
 
STEAM ENGINES 457 
 
 Let H = indicated horsepower of engine; 
 
 P = mean effective pressure of the steam, in 
 
 pounds per square inch; 
 A = area of piston, in square inches; 
 L length of stroke, in feet; 
 N = number of working strokes per minute. 
 
 In a double-acting engine, or one in which the steam acts alternately on both 
 sides of the piston, the number of working strokes per minute is twice the 
 number of revolutions per minute. For example, if a double-acting engine 
 runs at a speed of 210 R. P. M. there are 420 working strokes per minute. 
 A few types of engines, however, are single-acting; that is, the steam acts on 
 only one side of the piston. Such are the Westinghouse, the Willans, and 
 others. In this case, only one stroke per revolution does work, and, conse- 
 quently, the number of strokes per minute to be used in the foregoing formula 
 is the same as the number of revolutions per minute. Unless it is specifically 
 stated that an engine is single-acting, it is always understood, when the dimen- 
 sions of a steam engine are given, that a double-acting engine is meant. 
 
 EXAMPLE. The diameter of the piston of an engine is 10 in. and the length 
 of stroke 15 in. It makes 250 R. P. M., with a mean effective pressure of 
 40 Ib. per sq. in. What is the horsepower? 
 
 SOLUTION. As it is not stated whether the engine is single or double acting, 
 assume that it is double acting; then, the number of strokes is 250X2 = 500 per 
 min. Hence, 
 
 T w P P L A N 40Xf|X(10 2 X.7854)X500 
 LH - P ' = 33,000 = 33,000 
 
 The indicated horsepower of a compound or triple-expansion engine may be 
 calculated from the indicator diagrams in exactly the same manner as with 
 any simple engine, considering each cylinder as a simple engine and adding the 
 horsepowers of the several cylinders together. In taking the indicator cards 
 from a compound engine, the precaution of taking the cards simultaneously 
 from all cylinders must be observed, especially when the engine runs under a 
 variable load, because, otherwise, an entirely wrong distribution of power may 
 be shown, and there may also be a great variation between the indicated horse- 
 power really existing and that calculated from diagrams taken at different 
 times. 
 
 The indicated horsepower of compound engines is sometimes found by refer- 
 ring the mean effective pressure of the high-pressure cylinder to the low-pressure 
 cylinder and calculating the horsepower of the engine on the assumption that 
 all the work is done in the low-pressure cylinder. To do this, the mean effective 
 pressures of the two cylinders are found from indicator diagrams; the mean 
 effective pressure of the high-pressure cylinder is then divided by the ratio of 
 the volume of the low-pressure cylinder to that of the high-pressure cylinder; 
 and the quotient is added to the mean effective pressure of the low-pressure 
 cylinder, the sum being the referred mean effective pressure. This sum is then 
 taken as the mean effective pressure of the engine, and the area of the low- 
 pressure piston as the piston area; with these data, the length of stroke and the 
 number of strokes, the horsepower is computed as for any simple engine. In 
 the case of a triple-expansion engine, the mean effective pressures of the high- 
 pressure and intermediate cylinders are referred to the low-pressure cylinder 
 and added to its mean effective pressure. Thus, suppose that in a 12", 
 20", and 34"X30" engine the mean effective pressures are 82.3 Ib., 27.8 Ib., 
 and 10.6 Ib., respectively. Then, the referred mean effective pressure is 
 &*i 2 27 8 106 
 f^+^^H - = 10.4 + 10 + 10.6 = 31 Ib., and this value must be substituted 
 
 o.Uo ^./o I 
 
 for P in finding the horsepower of the engine. While this method shortens the 
 labor of computing the horsepower, it obviously does not show the distribution 
 of work between the cylinders. 
 
 Stating Sizes of Engines. The size of a simple engine, that is, an engine 
 having but one cylinder, is commonly stated by giving the diameter of the 
 cylinder, followed by the length of the stroke, both in inches. Thus, a simple 
 engine having a cylinder 12 in. in diameter and a stroke of 24 in. would be 
 referred to as a 12"X24" engine, the multiplication sign in this case serving 
 merely to separate the two numbers. The sizes of compound and multiple- 
 expansion engines are designated in a similar fashion. Thus, a compound 
 engine with a high-pressure cylinder 11 in. in diameter, a low-pressure cylinder 
 
458 STEAM ENGINES 
 
 20 in. in diameter, and a stroke of 15 in. would be referred to as an 11* and 20* 
 X15" compound engine. In the same way, a 14", 22", and 34"X18" triple- 
 expansion engine would be one in which the diameters of the cylinders are 
 14 in., 22 in., and 34 in., and the stroke is 18 in. 
 
 Mechanical Efficiency. The mechanical efficiency of an engine is the ratio 
 of the net horsepower to the indicated horsepower; or it is the percentage of 
 the mechanical energy developed in the cylinder that is utilized in doing useful 
 work. To find the efficiency of an engine, when the indicated and net horse- 
 powers are known, divide the net horsepower by the indicated horsepower. 
 
 Piston Speed. The total distance traveled by the piston in 1 min. is called 
 the piston speed. As it is customary to take the stroke in inches, to find the 
 piston speed, multiply the stroke in inches by the number of strokes and divide 
 
 IN 
 by 12; or, letting 5 represent the piston speed, S = , where / is the stroke in 
 
 inches. But N = 2R, where R represents the number of revolutions per 
 minute. Hence, 
 
 ^ 
 12 12 6 
 
 EXAMPLE. An engine with a 52-in. stroke runs at a speed of 66 R. P. M. 
 What is the piston speed? 
 
 CO \/ Aft 
 
 SOLUTION. By the formula, 5 = - = 572 ft. per min. 
 
 The piston speeds used in modern practice are about as follows: 
 
 Small stationary engines .............................. 300 to 600 
 
 Large stationary engines ............................. 600 to 1,000 
 
 Corliss engines ...................................... 400 to 750 
 
 Marine engines ..................................... 200 to 1,200 
 
 Allowance for Area of Piston Rod. It is generally considered sufficiently 
 accurate to take the total area of one side of the piston as the area to be used 
 in calculating the horsepower of an engine. The effective area of one side of 
 the piston is, however, reduced by the sectional area of the piston rod, and 
 if it is important that the power be calculated with the greatest practical degree 
 of accuracy, an allowance for the area of the piston rod must be made. This 
 is done by taking as the piston area one-half the sum of the areas exposed to 
 steam pressure on the two sides of the piston. Thus, if a piston is 30 in. in 
 diameter with a 6-in. piston rod, the average area is 
 302 X. 7854 + (302 X. 7854- 62 X. 7854) 
 
 2 = o92.72 sq. in. 
 
 If the piston rod is continued past the piston so as to pass through the head- 
 end cylinder head; that is, if the piston has a tailrod, allowance must be made 
 for the tailrod. Thus, with a piston 30 in. in diameter, a piston rod 6 in. in 
 diameter, and a tailrod 5 in. in diameter, the average area is 
 (3Q2 X .7854 - 52 X .7854) + (3Q2 X .7854 - 62 X .7854) 
 2 
 
 Cylinder Ratios. The cylinders of compound and multiple-expansion 
 engines increase in diameter from the high-pressure to the low-pressure end, 
 and it is customary to refer to their relative sizes by means of cylinder ratios. 
 As all the cylinders have the same length of stroke, the volumes of the several 
 cylinders are in proportion to the areas of the cylinders, and therefore in pro- 
 portion to the squares of the diameters. The area of the high-pressure cylinder 
 is taken as unity, and the other areas are referred to it, and the ratios of these 
 areas, or the ratios of the squares of the diameters, are called the cylinder 
 ratios. For example, a triple-expansion engine having cylinders 12 in., 20 in., 
 and 34 in. in diameter will have the cylinder ratios of 12 2 : 20 2 : 34 2 , or 144 : 400. 
 1,156, which reduces to 1 : 2.78 : 8.03; that is, the intermediate cylinder is 
 2.78 times as large as the high-pressure cylinder and the low-pressure cylinder 
 is 8.03 times as large as the high-pressure cylinder. If there are two cylinders 
 to one stage of expansion, as, for example, two low-pressure cylinders, the sum 
 of their areas must be used in finding the cylinder ratios. Thus, if there had 
 been two 24-in. low-pressure cylinders instead of one 34-in. cylinder, in the 
 foregoing case, the cylinder ratios would have been 12* : 2Q2 : 2X242, or 144 : 
 400 : 1,152, which reduces to 1 : 2.78 : 8. 
 
STB AM ENGINES 459 
 
 CONDENSERS 
 
 There are two types of condensers in general use, namely, the surface con- 
 denser and the jet condenser. In the former, the exhaust steam comes in con- 
 tact with a large area of metallic surface that is kept cool by contact with cold 
 water. In the latter, the exhaust steam, on entering the condenser, comes in 
 contact with a jet of cold water. In either case, the entering steam is con- 
 densed to water, and in consequence a partial vacuum is formed. If enough 
 cold water were used, the steam on entering would instantly condense and a 
 practically perfect vacuum would be obtained were it not for the fact that the 
 feedwater of the boiler always contains a small quantity of air, which passes 
 with the exhaust steam into the condenser and therefore partly destroys the 
 vacuum. To get rid of this air, the condenser is fitted with an air pump, 
 which pumps out both the air and the water formed by condensation. 
 
 Surface Condensers. In the surface condenser, the exhaust steam and the 
 injection water are kept separate throughout their course through the con- 
 denser; and the condensed steam leaves the condenser as fresh water, free from 
 the impurities contained in the injection water. The water of condensation 
 from a surface condenser is therefore fit to be used as boiler feed, except that it 
 contains oil used for cylinder lubrication, which can b'e eliminated by means of 
 an oil separator. It is for this reason that the surface condenser, in spite of its 
 greater complication, cost, size, and weight, as compared with the jet con- 
 denser, is used instead of the latter where the supply of injection water is unfit 
 for use as boiler feed. Thus, the surface condenser is used altogether in 
 marine work, except for vessels navigating clean, fresh water like that of the 
 Great Lakes, in order to avoid the use of sea-water in the boilers. 
 
 In the surface condenser the steam may be outside and the water inside the 
 tubes, or the reverse. If the water is inside the tubes, it should enter at the 
 bottom of the condenser and be discharged at the top. This brings the coldest 
 water into contact with the partly condensed steam, and the warmest water 
 into contact with the hot entering steam. When the water is outside the tubes, 
 it is necessary to fit baffle plates on the water side to force the water into a 
 definite and regular circulation, and to prevent it from going directly from inlet 
 to outlet and also to prevent the water from arranging itself in layers according 
 to temperature, with the coldest water on the bottom and the hottest water 
 on top. The outlet should be well above the top row of tubes. A solid body 
 of water above the top row of tubes is thus assured, and the accumulation of a 
 stagnant body of hot water in the top of the condenser is prevented by its being 
 continually drawn off by the circulating pump and replaced by cooler water 
 from beneath. 
 
 Air tends to accumulate in the top of the water side of a surface condenser. 
 This is particularly inconvenient where the water is inside the tubes, as the 
 air fills the top rows of tubes and excludes the water, destroying their value as 
 cooling surfaces. To prevent this, an air valve must be provided, as high up 
 on the water side as possible, by which the air can be drawn off when it becomes 
 troublesome. Drain valves and pipes should be provided at the bottom. 
 
 As the condensed steam from the surface condenser is generally pumped 
 back into the boiler as feedwater, it is desirable to have it as hot as possible; 
 but it must be remembered that it is impossible to get the feedwater from the 
 condenser at a higher temperature than that of saturated steam at the absolute 
 pressure existing in the condenser. 
 
 It will be considerably cooler than this if, after being condensed, it is allowed 
 to lie in the bottom of the condenser and give up its heat to the circulating 
 water. The heat thus given up is a total loss, and should be avoided by con- 
 necting the air-pump suction to the lowest point of the condenser and by shaping 
 the bottom of the condenser so that the water will drain rapidly into the air- 
 pump suction. 
 
 Cooling Water for Surface Condenser. The amount of cooling water 
 required in the case of a surface condenser may be found by the formula 
 
 in which Q = number of pounds of cooling water required to condense 
 
 1 Ib. of steam; 
 
 H = total heat above 32 of 1 Ib. of steam at pressure at release; 
 t = temperature of condensed steam on leaving condenser; 
 t\ = temperature of cooling water on entering condenser; 
 to = temperature of cooling water on leaving condenser. 
 
460 STEAM ENGINES 
 
 EXAMPLE. Steam exhausts into a surface condenser from an engine cylinder 
 at a pressure of 6 lb., absolute; the temperature of the condensing water on 
 entering is 55 F., and en leaving it is 100 F. ; the temperature of the condensed 
 steam on leaving the condenser is 125 F. How many pounds of cooling water 
 are required per pound of steam? 
 
 SOLUTION. The total heat above 32 of 1 lb. of steam at 6 lb., absolute, 
 from the Steam Table, is 1,133.8 B. T. U. Then, substituting the values of 
 H,t,h, and fe> in the formula, 
 
 
 
 Injection Water for Jet Condenser. The quantity of injection water required 
 for a jet condenser may be found by the formula 
 fl-q-32) 
 
 t-h ' 
 in which Q = number of pounds of injection water required to condense 
 
 1 lb. of steam; 
 
 H = total heat above 32 of 1 lb. of steam at pressure at release; 
 t = temperature of mixture of injection water and condensed 
 
 steam on leaving the condenser; 
 
 h = temperature of injection water on entering the condenser. 
 EXAMPLE. Steam is exhausted into a jet condenser from an engine cylinder 
 at a pressure of 10 lb., absolute; the temperature of the injection water on 
 entering is 60 F., and on leaving 140 F. How much injection water is required 
 per pound of steam? 
 
 SOLUTION. The total heat above 32 of 1 lb. of steam at 10 lb. absolute, 
 from the Steam Table, is 1,140.9 B. T. U. Then, substituting the values of 
 H, t, and h in the formula. 
 
 ENGINE MANAGEMENT 
 
 STARTING AND STOPPING 
 
 Warming Up. About 15 or 20 min. before starting the engine, the stop- 
 valves should be raised just off their seats and a little steam should be allowed 
 to flow into the steam pipe. The drain cock on the steam pipe just above the 
 throttle should be opened. When the steam pipe is thoroughly warmed up 
 and steam blows through the drain pipe, the drain cock should be closed and the 
 throttle opened just enough to let a little steam flow into the valve chest and 
 cylinder; or if a by-pass around the throttle is fitted, it may be used. The 
 cylinder relief valves, or drain cocks, and also the drain cocks on the valve chest 
 and the exhaust pipe should be opened, if the engine is non-condensing. If the 
 cylinders are jacketed, steam should be turned into the jackets and the jacket 
 drain cocks should be opened. While the engine is warming up, the oil cups 
 and the sight-feed lubricator may be filled. A little oil may be put into all the 
 small joints and journals that are not fitted with oil cups. The guides should 
 be wiped off with oily waste and oiled. By this time the engine is getting 
 warm. If the cylinder is fitted with by-pass valves, they should be used to 
 admit steam to both ends of the cylinder. In general, all cylinders, especially 
 if they are large and intricate castings, should be warmed up slowly, as sudden 
 and violent heating of a cylinder of this character is very liable to crack the 
 casting by unequal expansion. 
 
 An excellent and economical plan for warming up the steam pipe and the 
 engine is to open the stop- valves and throttle valve at the time or soon after 
 the fires are lighted in the boilers, permitting the' heated air from the boilers 
 to circulate through the engine, thus warming it up gradually and avoiding the 
 accumulation of a large quantity of water of condensation in the steam pipe and 
 cylinder. When pressure shows on the boiler gauge or steam at the drain pipes 
 of the engine, the stop- valves and throttle may be closed temporarily, but not 
 hard down on their seats. When this method of warming up the engine is 
 adopted, the safety valves should not be opened while steam is being raised. 
 
 Stop-valves and throttle valves should never be opened quickly or suddenly 
 and thus permit a large volume of steam to flow into a cold steam pipe or cylin- 
 der. If this is done, the first steam that enters will be condensed and a partial 
 vacuum will be formed. This will be closely followed by another rush of steam 
 
STEAM ENGINES 461 
 
 with similar results, and so on until a mass of water will collect, which will rush 
 through the steam pipe and strike the first obstruction, generally the bend in 
 the steam pipe near the cylinder, with great force and in all probability will 
 carry it away and cause a disaster. This is called water hammer and has caused 
 many serious accidents. Before turning steam into any pipe line or into a 
 cylinder, all drain valves should be opened. 
 
 Another precaution that should be taken is the easing of the throttle valve 
 on its seat before steam is let into the main steam pipe; otherwise, the unequal 
 expansion of the valve casing may cause the valve to stick fast and thereby 
 give much trouble. Even if a by-pass pipe is fitted around the throttle, it is 
 better not to depend on it. As water is non-compressible, it is an easy matter 
 to blow off a cylinder head or break a piston if the engine is started when there 
 is a quantity of water in the cylinder. 
 
 Oil and Grease Cups. The last thing for the engineer to do before taking 
 his place at the throttle preparatory to starting the engine, provided he has no 
 oiler, is to start the oil and grease cups feeding. It is well to feed the oil liber- 
 ally at first, but not to the extent of wasting it; finer adjustment of the oiling 
 gear can be made after the engine has been running a short time and the 
 journals are well lubricated. 
 
 Starting and Stopping Non-Condensing Slide-Valve Engine. A non- 
 condensing slide-valve engine is started by simply opening the throttle; this 
 should be done quickly in order to jump the crank over the first dead center, 
 after which the momentum of the flywheel will carry it over the other centers. 
 The engine should be run slowly at first, gradually increasing the revolutions 
 to the normal speed. When the engine has reached full speed, the drain pipes 
 should be examined; if dry steam is blowing through them, the drain cocks 
 should be closed. If water is being delivered, the drain cocks should remain 
 open until steam blows through and should then be closed. 
 
 To stop a non-condensing slide-valve engine, it is only necessary to shut 
 off the supply of steam by closing the throttle, but care should be taken not to 
 let the engine stop on the dead center. After the engine is stopped, the oil 
 feed should be shut off and the main stop-valve clpsed. The valve should be 
 seated, but without being jammed hard down on its seat. The drain cocks on 
 the steam pipe and engine may or may not be opened, according to circum- 
 stances. It will do no harm to allow the steam to condense inside the engine, 
 as the engine will then cool down more gradually, which lessens the danger 
 of cracking the cylinder casting by unequal contraction. All the water of 
 condensation should be drained from the engine before steam is again admitted 
 to it. 
 
 Starting and Stopping Condensing Slide-Valve Engine. In the case of 
 condensing slide-valve engines, before the main engine is started, the air pump 
 and circulating pump should be put into operation and a vacuum formed in 
 the condenser; this will materially assist the main engine in starting promptly. 
 Prior to starting the air and circulating pumps, the injection valve should be 
 opened to admit the condensing water into the circulating pump; the delivery 
 valve should also be opened at this time. If an ordinary jet condenser is used, 
 no circulating pump is required, the water being forced into the condenser by 
 the pressure of the atmosphere. If the air pump is operated by the main engine 
 a vacuum will not be formed in the condenser until after the engine is started 
 and at least one upward stroke of the air pump is made. In this case the 
 injection valve must be opened at the same moment the engine is started; 
 otherwise, the condenser will get hot and a mixture of air and steam accumulate 
 in it and prevent the injection water from entering. When this occurs it is 
 necessary to pump cold water into the condenser by one of the auxiliary pumps 
 through a pipe usually fitted for that purpose; if such a pipe has not been pro- 
 vided, it may be found necessary to cool the condenser by playing cold water 
 on it through a hose. 
 
 The operation of stopping a slide-valve surface-condensing engine is pre- 
 cisely similar to that of stopping a non-condensing engine of the same type, 
 with the addition that after the main engine is stopped the air and circulating 
 pumps are also stopped, and in the same way, that is, by closing the throttle, 
 after which the injection valve and the discharge valve should be closed' and the 
 drain cocks opened. With a jet condenser, the operation of stopping the 
 engine is the same as the above, with the exception that the injection valve 
 should be closed at the same moment that the engine is stopped. 
 
 Starting and Stopping Simple Corliss Engine. In the Corliss engine the 
 eccentric rod is so constructed and arranged that it may be hooked on or 
 unhooked from the eccentric pin on the wrist-plate at the will of the engineer. 
 
462 STEAM ENGINES 
 
 After all the preliminary operations have been attended to, the starting bar is 
 shipped into its socket in the wristplate and the throttle ,is opened. The 
 starting bar is then vibrated back and forth by hand, by which the steam and 
 exhaust valves are operated through the wristplate and valve rods; as soon as 
 the cylinder takes steam, the engine will start. After working the starting 
 bar until the engine has made several revolutions and the flywheel has acquired 
 sufficient momentum to carry the crank over the dead centers, the hook of the 
 eccentric rod should be allowed to drop upon the pin on the wristplate. As 
 soon as the hook engages with the pin, the starting bar is unshipped and 
 placed in its socket in the floor. The way to determine in which direction 
 the starting bar should be first moved to start the engine ahead is to note the 
 position of the crank, from which the direction in which the piston is to move 
 may be learned. This will indicate which steam valve to open first; it will 
 then be an easy matter to determine in which direction the starting bar should 
 be moved. If the engine is of the condensing type, the same course of pro- 
 cedure in starting the air and circulating pumps should be followed as with the 
 simple condensing slide-valve engine. 
 
 A Corliss engine is stopped by closing the throttle and unhooking the 
 eccentric rod from the pin on the wristplate; this is done by means of the unhook- 
 ing gear provided for the purpose. As soon as the ecentric rod is unhooked 
 from the pin, the starting bar is shipped into its socket in the wristplate and the 
 engine is worked by hand to any point in the revolution of the crank at which 
 it is desired to stop the engine. The procedure is then the same as for the 
 simple slide-valve engine. After stopping a Corliss condensing engine the same 
 course should be followed as with a slide-valve condensing engine in regard to 
 draining cylinders, closing stop-valves, etc. 
 
 Starting and Stopping Compound Slide-Valve Engine. Before starting a 
 compound engine, the high-pressure cylinder is warmed up in the same manner 
 as a simple engine. To get the steam into the low-pressure cylinder is, however, 
 an operation that will depend on circumstances. If the cylinders are provided 
 with pass-over valves, it will be necessary only to open them to admit steam 
 into the receiver and thence into the low-pressure cylinder. If the cylinders 
 are not fitted with pass-over valves the steam can usually be worked into the 
 receiver and low-pressure cylinder by operating the high-pressure valves by 
 hand. Sometimes compound engines are fitted with starting valves, which 
 greatly facilitate the operations of warming up and starting. Usually a 
 compound engine will start upon opening the throttle. 
 
 If the high-pressure crank of a cross-compound engine is on its center and 
 the low-pressure engine will not pull it off, it must be jacked off. If the pressure 
 of steam in the receiver is too high, causing too much back pressure in the high 
 pressure cylinder, the excess of pressure must be blown off through the receiver 
 safety valve; if the pressure in the receiver is too low to start the low-pressure 
 piston, more steam must be admitted into the receiver. If the engine is stuck 
 fast from gummy oil or rusty cylinders, all wearing surfaces must be well oiled 
 and the engine jacked over at least one entire revolution. If the cut-offs are 
 run up, they should be run down, full open. If there is water in the cylinders, 
 it should be blown out through the cylinder relief or drain valves, and if there 
 is any obstruction to the engine turning, it should be removed. 
 
 If the crank of a tandem compound engine is on the center, it must be pulled 
 or jacked off. If the high-pressure crank of a cross-compound engine is on 
 the center, r^may or may not be possible to start the engine by the aid of the 
 low-pressure cylinder, depending on the yalve gear and the crank arrangement. 
 When the cranks are 180 apart, which is a very rare arrangement, the crank 
 must be pulled or jacked off the center. When the cranks are 90 apart and a 
 pass-over valve is fitted, live steam may be admitted into the receiver and 
 thence into the low-pressure cylinder, in order to start the engine. When 
 no pass-over is fitted, but the engine has a link motion, sufficient steam to 
 pull the high-pressure crank off the center can generally be worked into the 
 low-pressure cylinder by working the links back and forth. When no pass- 
 over is fitted, but the high-pressure engine can have its valve or valves worked . 
 by hand, steam can be got into the low-pressure engine by working the high- 
 pressure valve or valves back and forth by hand. If no way exists of getting 
 steam into the low-pressure cylinder while the high-pressure crank is on a 
 dead center, it must be pulled or jacked off. 
 
 If the air and circulating pumps are attached to and operated by the main 
 engine, a vacuum cannot be generated in the condenser until after the main 
 engine has been started. Consequently, in this case, there is no vacuum to 
 help start the engine; therefore, if it is tardy or refuses to start, it will be 
 
STEAM ENGINES 463 
 
 necessary to resort to the jacking gear and jack the engine into a position from 
 which it will start. A vacuum having been generated in the condenser before- 
 hand, the pressure in the receiver acting on the low-pressure piston causes the 
 engine to start promptly, even though the high-pressure crank may be on its 
 center. 
 
 Compound slide-valve engines, whether condensing or non-condensing, are 
 stopped by closing the throttle, and, if a reversing engine, throwing the valve 
 gear into mid-position. If the stop is a permanent one, the usual practice 
 of draining the engine, steam chests, and receiver, closing stop- valves, stopping 
 the oil feed, etc. should be followed. If the engine is intended to run in both 
 directions in answer to signals, as in the cases of hoisting, rolling-mill, and 
 marine engines, the operator, after stopping the engine on signal, should imme- 
 diately open the throttle very slightly, in order to keep the engine warm, and 
 stand by for the next signal. If the engine is fitted with an independent or 
 adjustable cut-off gear, it should be thrown off; that is, set for the greatest 
 cut-off, for the reason that the engine may have stopped in a position in which 
 the cut-off valves in their early cut-off positions would permit little or no steam 
 to enter the cylinders, in which case the engine will not start promptly, and 
 perhaps not at all. While waiting for the signal, the cylinder drain valves 
 should be opened and any water that may be in the cylinders should be blown 
 out. When dry steam blows through the drains, the cylinders are clear of 
 water. 
 
 When the signal to start the engine is received, it is only necessary to throw 
 the valve gear into the go-ahead or backing position, as the signal requires, 
 and to operate the throttle according to the necessities of the case, for which 
 no rule can be laid down beforehand, as the position of the throttle will depend 
 on the load on the engine at the time. 
 
 Starting and Stopping Compound Corliss Engine. The operation of starting 
 and stopping a compound Corliss engine is precisely similar to that of starting 
 and stopping a simple Corliss engine. The high-pressure valve gear only 
 is worked by hand in starting, the low-pressure eccentric hook having been 
 hooked on previously. The low-pressure valve gear is worked by hand 
 only while Warming up the low-pressure cylinder." The directions given for 
 operating the simple condensing engine apply to the condensing Corliss 
 engine, so far as the treatment of the air pump, circulating pump, and 
 condenser is concerned. 
 
 POUNDING OF ENGINES 
 
 Faulty Bearings. Loose journal brasses are the most frequent cause of 
 pounding in engines. The remedy for pounding of this nature is obvious. 
 The engine should be stopped and the brasses set up gradually until the pound- 
 ing ceases. In the case of shaft journals, they may be set up without stopping 
 the engine, provided the engineer can reach them without danger of being caught 
 in the machinery. 
 
 It may so happen that the boxes or brasses are worn down until the edges 
 of the upper half and those of the lower half are in contact and cannot be set 
 up on thejjournal any farther; they are then said to be brass and brass, or brass- 
 bound. In a case of this kind, the journal must be stripped, as it is called, when 
 the cap and brasses are removed from a journal. The edges of the brasses are 
 then chipped or filed off, in order to allow them to be closed in. 
 
 It is a most excellent plan in practice to reduce the halves of the brasses so 
 that they will stand off from each other when in place for a distance of J to ^ in. 
 and to fill this space with hard sheet-brass liners fro,m No. 20 to No. 22 
 Birmingham wire gauge in thickness, or even thinner. Should the journal 
 become brass-bound, the cap may be slacked off and a pair of the liners slipped 
 out without the necessity of stripping the journal. 
 
 In some instances journal-boxes are fitted with keepers, or chipping pieces, 
 as they are sometimes called. These usually consist of cast-brass liners from 
 1 to 5 in. in thickness, having ribs or ridges cast on one side, for convenience of 
 chipping and filing. These keepers are sometimes made of hardwood and are 
 capable of being compressed slightly by the pressure exerted upon them during 
 the setting-up process. When the boxes are babbitted, the body of the box is 
 occasionally made of cast iron, in which case iron liners and keepers are used 
 instead of brass ones. 
 
 In engines fitted with some types of friction couplings, there is a thrust 
 exerted upon the shaft in the direction of its length. This will necessitate having 
 a thrust bearing, or thrust block, as it is sometimes called. There are a number 
 of types of thrust bearings, but the most common is the collar thrust, which 
 
464 STEAM ENGINES 
 
 consists of a series of collars on the shaft that fit in corresponding depressions 
 in the bearing. If these collars do not fit in the depressions rather snugly 
 the shaft will have end play and there probably will be more or less ppunding 
 or backlash at every change of load on the engine. This can be remedied only 
 by putting in a new thrust bearing and making a better fit with the shaft 
 collars, unless the rings in the bearing are adjustable, in which case the end play 
 may be taken up by adjusting the rings. 
 
 Pounding in Cylinders. Pounding in the cylinders is frequently caused by 
 water due to condensation or to that carried over from the boilers. This may 
 be a warning that priming is likely to occur in the boilers 9r has already com- 
 menced. If the cylinders are not fitted with automatic relief valves, the drain 
 cocks should be opened as quickly as possible and the throttle closed a little 
 to check the priming. 
 
 Another source of pounding in the cylinder is a piston loose on the rod; this 
 will result if the piston-rod nut or key backs off or the riveting becomes loose, 
 permitting the piston to play back and forth on the piston rod. If due to 
 backing off of the nut, the engine should be shut down instantly. There is 
 generally very little room to spare between the piston-rod nut and the cylinder 
 head; therefore, it cannot back off. very far before it will strike and break 
 the cylinder head. After the engine is stopped and the main stop-valve is 
 closed, the cylinder head should be taken off and the piston nut set up as tightly 
 as possible. As a measure of safety, a taper split pin should in all cases be fitted 
 through the piston rod behind the nut or a setscrew should be fitted through 
 the nut. 
 
 A slack follower plate or junk ring will cause pounding in the cylinder. 
 It seldom happens that all the follower bolts back out at one time, but not 
 infrequently one of them works itself out altogether. This is a very danger- 
 ous condition of affairs, especially in a horizontal engine: If the bolts should 
 get end on between the piston and cylinder head, either the piston or the cylin- 
 der head is bound to be broken. Therefore, if there is any intimation that a 
 follower bolt is adrift in the cylinder, the engine should be shut down instantly, 
 the cylinder head taken off, the old bolt removed, and one having a tighter 
 fit put in. 
 
 Broken packing rings and broken piston springs will cause noise in the 
 cylinder, but it is more of a rattling than a pounding, and the sound will easily 
 be recognized by the practiced ear. There is not so much danger of a break- 
 down from these causes as may be supposed, from the fact that the broken 
 pieces are confined within the space between the follower plate and the piston 
 flange. 
 
 Pounding in the cylinders of old engines is often produced by the striking 
 of the piston against one or the other cylinder heads, due to the wearing away 
 of the connecting-rod brasses. Keying up the brasses from time to time has 
 the effect of lengthening or shortening the connecting-rod, depending on the 
 design, and this. change in length destroys the clearance at one end of the 
 cylinder by an equal amount. The remedy is to restore the rod to its original 
 length by placing sheet-metal liners behind the brasses; this obviously will 
 move the piston back or ahead and restore the clearance. A rather rare case 
 of the piston striking the cylinder head is due to the unscrewing of the piston 
 rod from the crosshead, in case it is fastened by a thread and check-nut. To 
 obviate any danger, the check-nut should be tried frequently. 
 
 Improper Valve Setting. The primary cause of another source of pound- 
 ing is the improper setting of the steam valve, or possibly its improper 
 design. In the case of improper setting of the valve, insufficient compression, 
 insufficient lead, cut-off 'too early, and late release may all cause pounding on 
 
 the centers. 
 
 .-^ ""-x Reversal of Pressure. The effect of a reversal of 
 \ x pressure is clearly shown in the accompanying illustra- 
 \ tion. With the crankpin at a and the engine running 
 , in the direction indicated by the arrow, the connecting- 
 j rod is subjected to a pull, but after the crankpin has 
 , passed the dead center c, the connecting-rod is subjected 
 f to a push, in which case the rear brass, as shown at b, 
 / bears against the crankpin, while in the former case, 
 ,'' as shown at a, the front brass bears against the crank- 
 pin. By giving a sufficient amount of compression, the 
 
 lost motion in the pins and journals is transferred gently from one side to the 
 other before the crankpin reaches the dead center. If the compression is 
 insufficient, there will be pounding. 
 
STEAM ENGINES 465 
 
 Insufficient Lead. Insufficient lead causes an engine to pound because the 
 piston has then little or no cushion to impinge on as it approaches the end of 
 its stroke, and it is brought to rest with a jerk. A similar effect will be pro- 
 duced by a late release; the pressure is retained too long on the driving side of 
 the piston. The ideal condition is that the pressures shall be equal on both 
 sides of the piston at a point in its travel just in advance of the opening of the 
 steam port. The position of this point varies with the speed of the piston and 
 other conditions that only the indicator card can reveal. 
 
 Pounding at Crosshead. The crosshead is a source of pounding from 
 various causes, of which the loosening of the piston rod is one of the most 
 common. There are several methods of attaching the piston rod to the cross- 
 head. The rod may pass through the crosshead with a shoulder or a taper, or 
 both, on one side of the crosshead and a nut on the other; or the rod may be 
 secured to the crosshead by a cotter, instead of the nut; or the end of the rod 
 may be threaded and screwed into the crosshead, having a check-nut to hold 
 the rod in place. In the case first mentioned, the nut may work loose, which 
 will cause the crosshead to receive a violent blow, first, by the nut on one side 
 and then by the shoulder or taper on the other, at each change of motion of the 
 piston; the remedy is to set up the nut. A similar effect will be produced if 
 the cotter should work loose and back out. In case the'piston rod is screwed 
 into the crosshead and the rod slacks back, the danger is that the piston will 
 strike the rear cylinder head. The check-nut should be closely watched. 
 Pounding at the crosshead may be due to loose wristpin brasses, in which case 
 they should be set up, but not too tightly. In case a crosshead works between 
 parallel guides, pounding may be caused if the crosshead is too loose between 
 the guides, and the crosshead shoes should therefore be set out. 
 
 If pounding results from the wearing down of the shoe of a slipper crosshead, 
 a liner should be put between the shoe and the foot of the crosshead or the shoe 
 should be set put by the adjustment provided. 
 
 Pounding in Air Pump. Pounding in the air pump is generally produced 
 by the slamming of the valves, caused by an undue amount of water in the 
 pump, which will usually relieve itself after a few strokes. The pump piston, 
 however, may be loose on the piston rod or the piston rod may be loose in the 
 crosshead. A broken valve may also cause pounding in the air pump, all of 
 which must be repaired as soon as detected. 
 
 Pounding in Circulating Pump. In a circulating pump of the reciprocating 
 type, pounding may be caused by admitting top little injection water, and the 
 pounding may be stopped by adjusting the injection valve to admit just the 
 right quantity. It may so happen, however, that the injection water is very 
 cold, and to admit enough of it to stop the pounding in the circulating pump 
 will make the feed water too cold. To meet this contingency, an air check- valve 
 is often fitted to the circulating pump to admit air into the barrel of the pump 
 as a cushion for the piston; this check- valve may be kept closed when not 
 needed to admit air. A broken valve, a piston loose on its piston rod, and a 
 piston rod loose in the crosshead will all cause pounding in the circulating 
 pump; they should be treated in the same manner as was specified for similar 
 troubles in the air pump. 
 
 HOT BEARINGS 
 
 _ Should any of the bearings show an inclination to heat to an uncomfortable 
 point when felt by the hand, the oil feed should be increased. If the bearing 
 continues to get hotter, some flake graphite should be mixed with the oil and 
 the mixture should be fed into the bearing through the oil holes, between the 
 brasses, or wherever else it can be forced in. 
 
 If, after trying the remedies just mentioned, the bearing continues to grow 
 hotter, to the extent, for instance, of scorching the hand or burning the oil, it 
 indicates that the brasses have been expanded by the heat and that they are 
 gripping the journal harder and harder the hotter they get. At this stage, if 
 the engine is not stopped or if the heating is not checked, the condition of the 
 bearing will continue to grow worse, and may become so bad as to slow down 
 and eventually stop the engine by excessive friction. By this time the brasses 
 and journal will be badly cut and in bad condition generally, and the engine 
 must be laid up for repairs. 
 
 After the simple remedies previously given have been tried and failed to 
 produce the desired results, the engine should be stopped and the cap or key 
 of the hot bearing should be slacked back and the engine allowed to stand 
 until the bearing has cooled off. If necessary, the cooling may be hastened 
 by pouring ; cold water on the bearing, though this is objectionable, as it may 
 
466 STEAM ENGINES 
 
 cause the brasses to warp or crack. Putting water on a very hot bearing 
 should be resorted to only in an emergency, that is, when an engine must be 
 kept running. Water may be used on a moderately hot bearing without doing 
 very much harm. It is quite common in practice, when sprinklers are fitted 
 to an engine, to run a light spray of water on the crankpins when they show a 
 tendency to heat, with very beneficial results. 
 
 Dangerous Heating. Should a bearing become so hot as to scorch the hand 
 or to burn the oil before it is discovered it is imperative that the engine should 
 be stopped, at least long enough to loosen up the brasses, even though it is 
 necessary to start up again immediately; otherwise the brasses will be damaged 
 beyond repair and deep grooves will be cut into the journals. If the brasses 
 are babbitted, the white metal will melt out of the bearing at this stage. The 
 engine will then be disabled, and if there is not a spare set of brasses on hand, 
 it will be inoperative until the old brasses are rebabbitted or until a new set 
 is made and fitted. 
 
 If it is absolutely necessary in an emergency to keep the engine running 
 while a bearing is very hot, the engineer must exercise his best judgment as 
 to how he shall proceed. After slacking off the brasses, about the best he can 
 do is deluge the inside of the bearing with a mixture of oil and graphite, sulphur, 
 soapstone, etc., and the outside with cold water from buckets, sprinklers, or 
 hose, taking the chances of ruining the brasses and cutting the journal. 
 
 Refitting Cut Bearing. The wearing surfaces of the brasses and journal 
 must be smoothed off as well as circumstances will permit; but if the grooves 
 are very deeply cut, it will be useless to attempt to work them out entirely, and 
 if the brasses are very much warped or badly cracked, it will be best to put 
 in spare ones, if any are on hand. If not, the old ones must be refitted and used 
 until a new set can be procured. As for the J9urnal, it is permanently damaged. 
 Temporary repairs can be made by smoothing down the journal and brasses; 
 but at the first opportunity the journal should be turned in a lathe and the 
 brasses properly refitted or replaced with new ones. 
 
 Newly Fitted Bearings. The bearings of new engines are particularly 
 liable to heat, as the wearing surfaces of the brasses and journal have just been 
 machined and hence are comparatively rough. The conditions just mentioned 
 also exist with new brasses and the journals of an old engine. If a new engine, 
 or one with new brasses is run moderately, in regard to both speed and load, 
 and with rather loose brasses, there will be little danger of hot bearings, pro- 
 vided proper attention is given to adjustment and lubrication. This is what 
 is familiarly termed wearing down the bearings. 
 
 Faulty Brasses. When the brasses of an engine bearing are set up too tight, 
 heating is inevitable. Often, an attempt is made to stop a pound in an engine 
 by setting up the brasses when the thump should be stopped in some other 
 way. The brasses should be slacked off as soon as possible. As a matter of 
 fact, hot bearings should never occur from this cause. 
 
 Bearings may heat because the brasses are too loose. The heating is caused 
 by the hammering of the journal against the brasses when the crankpin is 
 passing the dead centers. The derangement is easily remedied, however, 
 by setting up the cap nuts or the key. Most engineers have their own views 
 regarding the setting up of bearings. One method is to set up the cap nuts 
 or key nearly solid and then slack them back half way; if the brasses are still 
 too loose, they are set up again and slacked back less than before, repeating 
 this operation until there is neither thumping nor heating. 
 
 Another method of setting up journal brasses is to fill up the spaces between 
 the brasses with thin metal liners, from No. 18 to No. 22 Birmingham wire 
 gauge in thickness, and a few paper liners for fine adjustment. Enough of 
 these should be put in to cause the brasses to set rather loosely on the journal 
 when the cap nuts or keys are set up solid. The engine should be run for a 
 while m that condition; then a pair of the liners should be removed and the 
 brasses set up solid again. This operation should be repeated until there is 
 neither thumping nor heating. It may require a week or more, and with a 
 large engine longer, to reach the desired point. If this system is carefully 
 earned out, there will be very little danger of heating. In removing the liners, 
 great care should be exercised not to disturb the brasses any more than is 
 absolutely necessary. 
 
 Warped and cracked brasses will cause heating, because they do not bear 
 evenly on the journal, and hence the friction is not distributed evenly over 
 " 
 
 l^j 1 " 6 l urf . ace - the distortion is not too great, the brasses may be 
 refitted to the journal by chipping, filing, and scraping; but if they are twisted 
 so much that they cannot be refitted, nothing will do but new brasses 
 
STEAM ENGINES 467 
 
 Brasses and journals that have been hot enough to be cut and grooved are 
 liable to heat up again any time on account of the roughness of the wearing 
 surfaces. As long as the grooves in the journal are parallel and match the 
 grooves in the brasses, the friction is not greatly increased; but if a smooth 
 journal is placed between brasses that are grooved and pressure is applied, the 
 journal crushes the grooves in the brasses and becomes brazed or coated with 
 brass, and then heating results. The way to prevent heating from this cause 
 is to work the grooves out of the journal and brasses by filing and scraping as 
 soon as possible after they occur. 
 
 Faulty workmanship is a common cause of the heating of crankpins, wrist- 
 pins, and bearings. The brasses in that case do not bear fairly and squarely, 
 even though they appear all right to the eye. A crankpin brass must fit squarely 
 on the end of the connecting-rod and the rod itself must be square. If the 
 key, when driven, forces the brasses to one side or the other and twists the strap 
 on the rod, it will draw the brasses slantwise on the pin and make them bear 
 harder on one side than on the other, thus reducing the area of the bearing 
 surfaces. The same is true of the shaft bearings. If the brasses do not bed 
 fairly on the bottom of the pillow-block casting or do not go down evenly, 
 without springing in any way, heating will result 
 
 If the brasses are too long and bear against the collars of the journal when 
 cold, they will most surely heat after the engine has been running a while. It 
 is hardly possible to run bearings stone cold. They will warm up a little and 
 the brasses will be expanded thereby, which will cause them to bear still harder 
 against the collars. This, in turn, will induce greater friction and more expan- 
 sion of the brasses. The evil may be obviated by chipping or filing a little 
 off each end of the brasses until they cease to bear against the collars while 
 running. A little side play is a good thing because it also promotes a better 
 distribution of the oil and prevents the journal and brasses from wearing into 
 concentric parallel grooves. 
 
 Edges of Brasses Pinching Journal. Brasses, when first heated by abnormal 
 nd along the surface in contact with the journal ; this would 
 
 friction, tend to expand , 
 
 open the brass and make the bore of larger diameter were it not prevented by 
 the cooler part near the outside and by the bedplate itself. If the brass has 
 become hot quickly and excessively, the resistance to expansion produces a 
 permanent set on the layers of metal near the journal, so that on cooling, 
 the brass closes and grips the journal. This is why 
 some bearings always run a trifle warm and will not 
 work cool. A continuance of heating and cooling 
 will set up a bending action at the middle of the 
 brass, which must eventually end in cracking it. Heat- 
 ing produced in this way may be prevented by chip- 
 ping off the brasses at their edges parallel to the jour- 
 nal, as shown at a in the accompanying illustration, 
 in which b is a section of the journal and c and d repre- 
 sent the top and bottom brasses, respectively. 
 
 Hot Bearings Due to Faulty Oiling. It does not 
 take long for a bearing to get very hot if it is deprived 
 of oil. The two principal causes of dry bearings 
 are an oil cup that has stopped feeding, either by 
 reason of being empty or by being clogged up from dirt in the oil, and oil holes 
 and oil grooves stopped up with dirt and gum. 
 
 The effect produced upon a bearing by an insufficient oil supply is similar 
 to that of no oil, but in a less degree. Of course, it will take longer for a 
 bearing to heat with insufficient oil than with none at all, and the engineer 
 has more time in which to discover and remedy the difficulty. 
 
 Oils that contain dirt and grit are prolific sources of hot bearings. There 
 is a great deal of dirt in lubricating oils of the average quality ; therefore, all oil 
 should be strained through a cloth or filtered, no matter how clear it looks. 
 All oil cups, oil cans, and oil tubes and channels should be cleaned out fre- 
 quently. Oil may be removed from the cups by means of an oil syringe, and 
 all oil removed from the cups and cans should be strained or filtered before 
 being used. 
 
 There are on the market many lubricating oils whose quality cannot be 
 definitely decided on without an actual trial, and it is difficult to avoid getting 
 a bad lot of oil sometimes. About the only safe way to meet this trouble is 
 to pay a fair price to a reputable dealer for oil that is known to be of good 
 quality, unless the purchaser is expert in judging oils or is able to pay a 
 competent chemist to test them. 
 
468 STEAM ENGINES 
 
 Bearings carrying very heavy shafts sometimes refuse to take the oil; or, 
 if they do, it is squeezed out at the ends of the brasses or through the oil holes, 
 and then the journal will run dry and heat. Large journals require oil of a 
 high degree of viscosity, or heavy oil, as it is popularly called. Oil of this 
 character has more difficulty in working 'its way under a heavy shaft than a 
 thin oil has, but thin oil has not the body necessary to lubricate a large journal. 
 
 This difficulty may be met by chipping oil grooves or channels in the brasses. 
 A round-nosed cape chisel, slightly curved, is generally used for this purpose; 
 care should be taken to smooth off the burrs made by the chisel, which may 
 be done with a steel scraper or the point of a flat file. The grooves are usually 
 cut into the brass in the form of a V if the engine is required to run in only one 
 direction; if it is to run in both directions the grooves should form an X. In 
 the first instance, care must be taken that the V opens in the direction of 
 rotation of the shaft; that is, the grooves should spread out from their junction 
 in the same direction as that in which the journal turns. The oil grooves may 
 be about i in. wide and f in. deep, and semicircular in cross-section. 
 
 Grit in Bearings. Grit is an ever-present source of heating of bearings, 
 and only by persistent effort can the engineer keep machinery running cool 
 in a dirty atmosphere. The machinery of coal breakers, stone crushers, and 
 kindred industries is especially liable to be affected in this way. Work done 
 on a floor over an engine shakes dirt down upon it at some time or other; 
 hence, all floors over engines should be made dust-proof by laying paper between 
 the planks. If the engine room and firerooms communicate, and piles of red- 
 hot clinkers and ashes are deluged with buckets of water, the water is instantly 
 converted into a large volume of steam, carrying with it small particles of ashes 
 and grit that penetrate into every nook and cranny, and these will find their 
 way into the bearings sooner or later. Hot clinkers and ashes should be 
 sprinkled, and the fireroom door should be closed while the ashes and clinkers 
 are being hauled or wet down or while the fires are being cleaned or hauled. 
 As an additional precaution, all open oil holes should- be plugged with wooden 
 plugs or bits of clean cotton waste as soon as possible after the engine is stopped, 
 and should be kept closed until ready to oil the engine again preparatory to 
 starting up. Plaited hemp or cotton gaskets should also be laid over the 
 crevices between the ends of the brasses and the collars of the journals of every 
 bearing on the engine and kept there while the engine is standing still. 
 
 Overloading of Engine. The effects produced by overloading an engine 
 are: The pressure on the brasses is increased to a point beyond that for which 
 they were designed, the friction exceeds the practical limit, and the bearing 
 heats. In case an engine is run at or near its limit of endurance, or if the 
 journals are too small, it is wise and economical to have a complete set of spare 
 brasses on hand ready to slip in when the necessity arises. 
 
 Engine Out of Line. If the engine is not in line, the brasses do not bear 
 fairly upon the journals. This will reduce the area of the bearing surfaces in 
 contact to such an extent as to cause heating. If the engine is not very much 
 out of line, matters may be considerably improved by refitting the brasses by 
 filing and scraping down the parts of those that bear most heavily on the 
 journal. If this does not answer, the heating will continue until the engine is 
 lined up. 
 
 The crosshead guides of an engine out of line are apt to heat. The guides 
 may also heat from other causes; for instance, the gibs may be set up too 
 much. The danger of hot guides may be very much lessened by chipping 
 zigzag oil grooves in their wearing surfaces and by attaching to the crosshead 
 oil wipers made of cotton lamp wicking arranged so as to dip into oil reser- 
 voirs at each end of the guides if they are horizontal, and at the lower end 
 if they are vertical. These wipers will spread a film of oil over the guides at 
 every stroke of the crosshead. 
 
 Effect of External Heat on Bearings. Bearings may get hot by the appli- 
 cation of external heat. This may be the case if the engine is placed too near 
 furnaces or an uncovered boiler, or in an atmosphere heated by uncovered 
 steam pipes or other means. The excessive heat of the atmosphere will then 
 expand the brasses until they nip the journals, which will generate additional 
 heat and cause further expansion of the brasses, and so on until a hot bearing 
 is the result. The remedy obviously depends upon the conditions of each case. 
 
 Springing of Bedplate. If the bedplate of an engine is not rigid enough to 
 resist the vibration of the moving parts, or if it is sprung by uneven settling 
 or the instability of the foundation, the engine will be thrown out of line inter- 
 mittently or permanently, and the bearings will heat. But it will do no good to 
 refit the brasses unless the engine bed is stiffened in some way and leveled up. 
 
STEAM ENGINES 469 
 
 Springing or Shifting of Pillow-Blqck. The effect of the springing or shift- 
 ing of the pedestal or pillow-block is similar to the springing of the engine bed; 
 that is, the bearing will be thrown out of line, with the consequent danger of 
 heating. As the pedestal is usually adjustable, it is an easy matter to readjust 
 it, after which the holding-down bolts should be screwed down hard. If a 
 pedestal is not stiff enough to resist the strains upon it and it springs, measures 
 should be taken to stiffen it. 
 
 STEAM TURBINES 
 
 The turbine is a machine by which the energy of a moving fluid, as steam 
 or water, is transformed, producing a rotary motion. The rotating part of the 
 turbine is cylindrical in form, comprising a shaft carrying a wheel, to which 
 are fastened blades, also called vanes or buckets, against which the moving fluid 
 impinges. This wheel, known as a turbine wheel, is enclosed in a casing. This 
 form of motor is growing in popularity particularly in electrical work, the motor 
 and generator being keyed on the same shaft, and for the following reasons: 
 
 1. The ability to use highly superheated steam, resulting in greater 
 economy. 
 
 2. Reduced cost per unit capacity of the electrical generator, because of 
 increased speed and less weight per horsepower. 
 
 3. Reduced floor space, resulting in less cost for land and power-station 
 building. 
 
 4. Reduced cost of lubrication, as no cylinder oil is required and less oil 
 is needed for bearings. 
 
 5. Saving in labor; engine oilers are not required, and one engineer can 
 attend to more output than on reciprocating engines. 
 
 6. Reduced cost of foundations, as the turbine is balanced and has no 
 reciprocating parts. 
 
 7. The turbine gives good steam economy over a wider range of load than 
 the reciprocating engine; this is an important advantage in favor of the tur- 
 bine, particularly for electric power stations where the load is variable. If it 
 becomes necessary to operate a turbine unit at a comparatively light load, say, 
 one-fourth or one-half load, the increase in steam consumption per horsepower 
 per hour is not so great as it would be with a reciprocating engine under the 
 same conditions. Also, a turbine unit will work more efficiently on overloads. 
 The forces acting on the turbine wheels are continuous; hence, a uniform rotary 
 motion is secured without the necessity of heavy flywheels. 
 
 Types of Turbines. Steam turbines are of two general types, velocity 
 turbines and pressure turbines. In the velocity, or impulse, turbine the rotation 
 is produced by the direct impact or blow upon the blades of the turbine of 
 steam issuing from a nozzle at high velocity, the action being the same as 
 that of water in impulse water-wheels. Leading examples of this type of 
 turbine are the De Laval, which is a single-stage, expansion, velocity turbine, in 
 which all the expansion of the steam takes place in a single stage in one set 
 of nozzles; the Curtis turbine, which is a few-stage, expansion, velocity turbine, 
 in which the steam is expanded in two, three, four, or five stages; the Rateau 
 turbine, which is a multistage, expansion, velocity turbine, in which the steam is 
 expanded in many stages. 
 
 In the pressure, or reaction, turbine, the steam enters the central space and 
 flows out through a series of guide vanes and then through the vanes of the 
 moving wheel. In this type of wheel, the blades run full of steam, and there 
 is a continual fall of pressure from the entrance of the steam until it leaves the 
 turbine. The pressure turbine is always a multistage expansion turbine, 
 the number of stages reaching 50 or 100. The leading American example 
 is the Westinghouse-Parsons turbine. 
 
 When referring to the various stages of expansion in a turbine, it is cus- 
 tomary to omit the term expansion and speak of the single-stage velocity 
 turbine (instead of the single-stage expansion velocity turbine) ; the few-stage 
 velocity turbine; the multistage velocity turbine. 
 
 In the turbines named, the Curtis turbine has a vertical shaft around which 
 the blades rotate in a horizontal plane. In all the others the axis is horizontal 
 and the blades rotate in vertical planes. 
 
 Steam Consumption. The relation between the brake horsepower of the 
 steam turbine at full load and the steam consumption is shown in the follow- 
 ing table. The values in this table are taken from published tests of steam 
 turbines that have attained the greatest commercial success. The turbines used 
 saturated steam at from 115 to 140 Ib. per sq. in., gauge pressure, and exhausted 
 
470 
 
 STEAM ENGINES 
 
 into a vacuum of from 26 to 28.5 in. of mercury. Better results than those 
 noted in the table can be obtained by the use of highly superheated steam. 
 
 The better the vacuum, the greater is the economy in the use of steam, both 
 in the steam engine and in the steam turbine. A high vacuum is of greater 
 value to the turbine, however, because the turbine can take advantage of a 
 greater range of expansion. The degree of vacuum to be carried is a matter 
 of dollars and cents; that is, it may cost more to create and maintain a high 
 vacuum than may be saved in steam consumption. In a comparative test of a 
 turbine and a triple-expansion engine under like conditions, it was found that, 
 in the case of the reciprocating engine, little or nothing was to be gained by 
 carrying a greater vacuum than about 26 in.; but the economy of the turbine 
 in the use of steam increased rapidly as the vacuum was increased above 26 in. 
 The conclusion is that high degrees of vacuum are more desirable for turbines 
 than for engines. 
 
 Comparison of Turbines and Engines. If the matter of steam consump- 
 tion alone is considered, the average condensing turbine of less than about 
 700 H. P. is not so economical as the average compound or triple-expansion 
 condensing engine, although the turbine may be preferred to the engine 
 for other reasons. In larger sizes, however, and particularly in very large 
 units, the economy of the turbine is very noticeable. The turbine possesses 
 the ability to expand the steam to the lowest available condenser pressure 
 without difficulty; but to do this in a reciprocating engine would require very 
 
 STEAM CONSUMPTION PER HOUR OF TURBINES 
 
 Brake 
 Horsepower 
 
 Pounds of 
 Steam Used 
 
 Brake 
 Horsepower 
 
 Pounds of 
 Steam Used 
 
 100 
 200 
 300 
 400 
 500 
 
 18.2 
 17.5 : v> 
 16.9 
 16.3 
 15.8 
 
 600 
 700 
 800 
 900 
 1,000 
 
 15.3 
 14.8 
 14.3 
 13.7 
 13.2 
 
 large valves, and ports and heavy pistons, because of the great volume of steam 
 to be handled at very low pressures. 
 
 Finding Horsepower of Turbines. There is no way of finding the indicated 
 horsepower of a steam turbine, because no form of indicator applicable to 
 the turbine has been invented. Nor is any such instrument likely to be 
 developed, owing to the very great difficulty of determining the energy given 
 up to the blades of a turbine from a jet of steam. The usual way of finding 
 the power of a steam turbine is to use a brake or a dynamometer and thus to 
 determine the brake horsepower, or else to connect an electric generator to 
 the turbine and measure the electrical output at the switchboard. In case the 
 latter method is used, the efficiency of the generator and the turbine together 
 is involved. 
 
 Turbine Troubles.; To obtain free running, it is necessary to allow clear- 
 ance between the stationary and the moving rows of blades, as well as between 
 the ends of the blades and the casing or the rotor. In impulse turbines, such 
 as the Curtis and the Rateau, the clearance between the rows of blades is 
 important; however, if it is made no greater than is necessary for mechanical 
 reasons, the efficiency will not be affected seriously. In the reaction turbine, 
 such as the Parsons, the clearance between the rows is of small consequence 
 as compared with the clearance between the ends of the stationary blades and 
 the rotor and between the ends of the moving blades and the casing. The 
 former may vary from | to 1 in. or more from the high-pressure to the low- 
 pressure stage; but the tip clearance must be kept between a few hundredths 
 and a few thousandths of an inch. 
 
 The stripping of the blades is one of the troubles to which turbines are 
 subject. It may be due to the interference of the stationary and the movable 
 blades, or to the rubbing of the blades against the shell or the rotor. In either 
 of these cases the existing clearances are reduced by wear of the parts, shifting 
 of the rotor, or unequal expansion of the rotor and the casing, until the blades 
 touch and tear one another loose. The same result will occur if some foreign 
 solid, as a stray nut or bolt, is carried along with the steam into the turbine. 
 If a turbine is started too quickly, without being properly warmed up, the 
 
STEAM ENGINES 471 
 
 sudden unequal expansion set up in the heavy casing arid the lighter rotor may 
 cause the blades to come in contact and be stripped. Stripping is claimed by 
 some engineers to be more common in turbines in which the blades are not 
 supported at their outer ends. To prevent it, some manufacturers apply 
 shroud rings and metal lacings to the outer ends of the blades. 
 
 As there are no valves, pistons, or piston rings in the turbine to be main- 
 tained free from leakage, about the only thing that can affect the steam con- 
 sumption is the condition of the blades. The blades of steam turbines are 
 subjected to the cutting action of steam flowing at high velocities, and often 
 carrying water particles with it. This cutting, or erosion, wears away the 
 edges and surfaces of the blades. From the data available, it appears that 
 the erosion is very slight if the steam is dry or superheated, no matter what 
 velocities are used; but if the steam is wet, erosion will take place, and it will 
 be greatly increased if the velocity of the steam is high. The horsepower is 
 not affected to any great extent by blade erosion, according to the results of 
 experience. In the case of a 100-H. P. De Laval turbine, the steam inlet edges 
 of the blades were worn away about ^ in., yet the steam consumption was 
 only about 5% above that with new blades. 
 
 If the boiler supplying steam to a reciprocating engine primes badly, a 
 slug of water may be carried over into the cylinder, resulting in a cracked piston 
 or cylinder, a buckled piston rod or connecting-rod, or a wrecked frame. In 
 case a steam turbine is used, however, the danger is greatly lessened. In tur- 
 bines in which the blades are not supported at their outer ends, the water may 
 cause stripping of the blades; but this is not very likely, as the blades at the high- 
 pressure end of the turbine are short. A rush of water from the boiler has been 
 known to bring a turbine almost to a stop without damaging the blades. 
 
 On account of the high speeds attained in turbine practice, the rotors are 
 balanced accurately, so as to reduce vibration. But in spite of this careful 
 balancing, vibration may manifest itself during ordinary running. It may be 
 caused in any one of several ways, but the fundamental cause is lack of balance. 
 If the rotor is warmed up too rapidly, the shaft or the wheels may be warped 
 by unequal expansion, producing an unbalanced effect. The stripping of a 
 blade or two will affect the balance of the wheel and tend to produce vibration. 
 Even water carried into the turbine with the steam will bring about an unbal- 
 anced condition and will lead to vibration. When vibration is observed, it 
 is well to reduce the speed a little, and to note whether this causes the vibration 
 to cease. If it does, but comes back again as soon as the speed is increased, 
 the source of the trouble should at once be determined. 
 
 Operation of Turbines. If the steam turbine is a new one, or if it has been 
 standing idle for a long period, it should not be started until it, together with 
 its auxiliary apparatus, has been thoroughly inspected. The bearings should 
 be properly adjusted and freed from dirt, and the entire lubricating system 
 should be clean and filled with clean oil. The steam pipe from the boilers 
 should be blown through, so as to clear it of any foreign matter that could be 
 carried into the turbine by the steam. The governor mechanism should be 
 examined, to see that it is in good order; the oil pump shpuld be looked after, 
 to ascertain whether it is in condition to maintain a continuous supply of oil; 
 and, finally, before the turbine is started, the shaft should be turned over by 
 hand, to insure that the rotor will turn freely in the casing. 
 
 A steam turbine should be started slowly, and before it is allowed to turn 
 over under steam it should be warmed up. This is accomplished by opening the 
 throttle valve just enough to let steam flow into the turbine. The drains should 
 be kept open until the turbine is well started. The length of time required 
 for warming up depends on the size of the turbine, a large unit requiring more 
 time than a small one. As the warming up proceeds, the throttle may grad- 
 ually be opened and the auxiliary machinery may be started. Once it has been 
 started, the turbine should be brought up to speed slowly. If it is speeded 
 up too rapidly, vibration will result. After the normal running speed has been 
 reached, the load may be thrown on; but this, also, should be done gradually, 
 to prevent a rush of water from the boiler with the steam. 
 
 If superheated steam is used, extra caution must be employed in starting, 
 for during the warming up, with the throttle valve only slightly opened, the 
 passing steam will be cooled considerably. But when the valve is opened 
 wider, the greater volume passing will not lose so much of its superheat, and if 
 care is not exercised the turbine will be subjected to sudden expansion because 
 of the higher temperature of the steam. The main point in starting is to 
 avoid any sudden changes of temperature in the turbine. If a turbine must 
 be ready to be put in operation at short notice, steam may be allowed to flow 
 
472 STEAM ENGINES 
 
 through it continually, by means of a by-pass around the throttle valve. It will 
 always be warmed up, then, and can be brought up to speed with less danger and 
 
 The shaft or spindle of a turbine rotates at high speed, and therefore the 
 bearings should be kept well lubricated; for if the oil supply fails, or if a bearing 
 begins to heat because of grit carried into it, the resulting trouble will come 
 very quickly. The presence of a hot bearing will usually be evidenced by the 
 smell of burning oil or by the appearance of white smoke. When these signs 
 are observed the oil supply should immediately be increased to the greatest 
 possible amount. If this does not reduce the temperature of the bearing or 
 prevent its further heating, the turbine should be shut down. To continue 
 will result in burning out the bearing, and it is better to stop before this happens. 
 The high speed of the shaft renders it impossible to nurse a hot turbine bearing 
 as is done frequently in the running of reciprocating engines. 
 
 When shutting down a steam turbine, the throttle valve should be closed 
 partly before the load is reduced, so as to prevent any possibility of racing 
 when the load is finally taken off. The load may then be used as a brake to 
 bring the rotor to a stop. When the throttle valve has been closed and the 
 steam supply has been shut off completely, the auxiliary machinery may be 
 stopped. If the load is taken off before the throttle is wholly closed _ the 
 turbine may continue to rotate for $ hr., as the rotor is then running in a 
 vacuum and under no load. The speed may be reduced by opening the drains 
 and allowing air to enter the casing. The oil supply to the bearings must be 
 continued until the turbine has come to rest, and the oil pump should be the last 
 auxiliary to be stopped. 
 
 Economy of Turbine. As there are no internal rubbing surfaces in the 
 steam turbine, superheated steam may be employed without causing any of 
 the lubrication troubles attending its use in reciprocating engines. Because 
 of the greater amount of heat contained in 1 Ib. of superheated steam, the 
 economy of a turbine working with superheated steam is greater than that of 
 one working with saturated steam; also, the efficiency is increased because the 
 ' superheated steam causes less frictional resistance to the motion of the blades. 
 To show the value of superheated steam in turbine work, it may be stated 
 that 50 F. of superheat reduces the steam consumption about 6% ; 100 F. of 
 superheat reduces it about 10% ; and 150 F. of superheat reduces it about 13%. 
 The use of high superheat, however, produces expansion of the rotor and the 
 casing and may cause the blades to interfere; as a result, the usual degree of 
 superheat in steam-turbine practice is 100 F., and seldom exceeds 150 F. 
 
 The steam turbine shows better economy than the steam engine when work- 
 ing with low-pressure steam in connection with a high vacuum; but when work- 
 ing with high-pressure steam and a vacuum of about 26 in., the engine is the 
 more economical. As a consequence, a combination of the steam engine and 
 the steam turbine has been adopted. The engine uses the high-pressure steam 
 from the boilers and expands it to about atmospheric pressure. This exhaust 
 steam then passes into the turbine, which exhausts into a condenser carrying 
 a high degree of vacuum, and the expansion is carried to the extreme practicable 
 limit. The turbine thus used in connection with an engine is termed an 
 exhaust-steam turbine, 
 
 As the economy of the steam turbine is dependent so largely on the degree 
 of vacuum carried, it is necessary for the engineer to watch the vacuum gauge 
 closely. With reciprocating engines, the loss of 1 or 2 in. of vacuum may not 
 be of much consequence; but in a turbine plant, where the vacuum is from 27 to 
 28 in., a loss of 1 or 2 in. will result in a considerable increase in the steam 
 consumption. Because of the high vacuum employed, the difficulty of keeping ' 
 pipes, valves, and glands from leaking is greater in turbine practice than in 
 engine practice, but the greater economy obtained by keeping everything 
 tight overbalances the increased care and labor. 
 
 Care of Gears in De Laval Turbines. The De Laval Steam Turbine 
 Company in their directions for operating their turbines state that in order to 
 keep the gears in good condition the teeth should be cleaned occasionally when 
 the turbine is not in service. They recommend that a wire brush and kerosene 
 be employed for this purpose. At the same time the gear-case should also be 
 thoroughly cleaned, and after the cleaning the gears should be well lubricated. 
 
 Should an engineer for any reason desire to take the gears out of the case, it 
 is recommended that he secure special directions relating to their removal 
 from the manufacturers. The same statement also applies to the adjustment of 
 the gears, which need to be kept in perfect adjustment. 
 
STEAM ENGINES 473 
 
 RULES FOR STATIONARY ENGINEERS 
 
 If a gauge glass breaks turn off the water first and then the steam, to 
 avoid scalding yourself. 
 
 Don't buy oil or waste simply because it is very cheap; it will cost more 
 than a good article in the end. 
 
 When cutting rubber for gaskets, etc., have a dish of water handy, and keep 
 wetting the knife blade; it makes the work much easier. 
 
 Don't forget that there is no economy in employing a poor fireman; he 
 can, and probably will, waste more coal than would pay the wages of a first- 
 class man. 
 
 An ordinary steam engine having two cylinders connected at right angles 
 on the same shaft consumes one-third more steam than a single-cylinder 
 engine, while developing only the same amount of power. 
 
 A fusible plug ought to be renewed every 3 mo., by removing the old 
 metal and refilling the case; and it should be scraped clean and bright on both 
 ends every time that the boiler is washed out, to keep it in good working order. 
 
 When trying a gauge-cock, don't jerk it open suddenly, for if the water 
 happens to be a trifle below the cock, the sudden relief from pressure at that 
 point may cause it to lift and flow out, thus showing a wrong height. Whereas, 
 if it is opened quietly, no lift will occur, and it will show whether there is water 
 or steam at that level. 
 
 Always open steam stop-valves between boilers very gently, that they 
 may heat and expand gradually; by suddenly turning on steam a stop- valve 
 chest was burst, due to the expansive power of heat unequally applied. The 
 same care must be exercised when shutting off stop- valves; explosions have been 
 caused by shutting a communicating stop- valve too suddenly due to the recoil. 
 
 In order to obtain the driest possible steam from a boiler, there should be an 
 internal perforated pipe (dry pipe, so called) fixed near the top of the boiler, 
 and suitably connected to the steam pipe. The perforations in this pipe should 
 be from one-quarter to one-half greater in area than that of the steam pipe. 
 
 If a glass gauge tube is too long, wet a triangular file with turpentine, then 
 holding the tube in the left hand, with the thumb and forefinger at the place 
 where it is to be cut, saw it quickly and lightly two or three times with the 
 edge of the file. Take the tube in both hands, both thumbs being on the side 
 opposite the mark, and 1 in. or so apart, and then try to bend the glass, using the 
 thumbs as fulcrums, and it will break at the mark, which has weakened the tube. 
 
 A stiff charge of coal all over a furnace will lower the temperature 200 
 or 300 in a very short time. After the coal is well ignited the temperature 
 will rise about 500, and as it burns will gradually drop about 200, until the 
 fireman puts in another charge, when the sudden fall again takes place. 
 This sudden contraction and expansion frequently causes the bursting of a 
 boiler, and it is for this reason that light and frequent charges of coal, or 
 else firing only one-half of the furnace at a time, should be always insisted on. 
 
 Be careful when using a wrench on hexagonal nuts that it fits snugly, or 
 the edges of the nut will soon become rounded. 
 
 If a monkey-wrench is not placed on the nut properly, the strain will often 
 bend or fracture the wrench. 
 
 The area of grate for a boiler should never be less than sq. ft. per I. H. P. 
 of the engine, and it is seldom advisable to increase this allowance beyond 
 i sq. ft. per I. H. P. 
 
 The area of tube surface for a boiler should not be less than 2| sq. ft. per 
 I. H. P. of the engine. 
 
 The ratio of heating surface to grate area in a boiler should be 30 to 1 as a 
 minimum, and may often be increased to 40 to 1, or even more, with advantage. 
 
 Lap- welded pipe of the same fated size has always the same outside diameter, 
 whether common, extra, or double extra, but the internal diameter is of course 
 decreased with the increased thickness. 
 
 A good cement for steam and water joints is made by taking 10 parts, by 
 weight, of white lead, 3 parts of black oxide of manganese, 1 part of litharge, 
 and mixing them to the proper consistency with boiled linseed oil. 
 
 To harden a cutting tool, heat it in a coke fire to a blood-red heat and 
 plunge it into a solution of salt and water (1 Ib. of salt to 1 gal. of water), 
 then polish the tool, heat it over gas, or otherwise, until a dark straw and 
 purple mixed color shows on the polish, and cool it in the salt water. 
 
 Small articles can be plated with brass by dipping them in a solution of 
 9\ gr. each of sulphate of copper and chloride of tin, in If pt. of water. 
 
474 COMPRESSED AIR 
 
 Don't be eternally tinkering about an engine, but let well enough alone. 
 Don't forget that it is possible to drive a key with a copper hammer just as 
 well as with a steel one, and that it doesn't leave any marks. 
 
 Keep on hand slips of thin sheet copper, brass, and tin, to use as liners, 
 and if these are shaped properly, much time will be saved when they are needed. 
 
 A few wooden skewer pins, such as butchers use, are very useful for many 
 purposes in an engine room. 
 
 In running a line of steam pipe where there are certain rigid points, make 
 arrangements for expansion on the line between those points. 
 
 Arrange the usual work of the engine and firerooms systematically, and 
 adhere to it. 
 
 Don't forget that cleanliness is next to godliness. 
 
 Rubber cloth kept on hand for joints should be rolled up and laid away 
 by itself, as any oil or grease coming in contact with it will cause it to soften 
 and give out when put to use. 
 
 When using a jet condenser, let the engine make three or four revolutions 
 before opening the injection valve, and then open it gradually, letting the 
 engine make several more revolutions before it is opened to the full amount. 
 
 Open the main stop- valve before the fires are started under the boilers. 
 
 When starting fires, don't forget to close the gauge-cocks and safety valve 
 as soon as steam begins to form. 
 
 An old Turkish towel, cut in two lengthwise, is better than cotton waste 
 for cleaning brass work. 
 
 Always connect the steam valves in such a manner that the valve closes 
 against the constant steam pressure. 
 
 Turpentine well mixed with black varnish makes a good coating for iron 
 smoke pipes. 
 
 Ordinary lubricating oils are not suitable for use in preventing rust. 
 
 It is possible to make a hole through glass by covering it with a thin coating 
 of wax, warming the glass and spreading the wax on it; then scrape off the wax 
 where the hole is wanted, drop a little fluoric acid on the spot with a wire. 
 The acid will cut a hole through the glass, and it can be shaped with a copper 
 wire covered with oil and rottenstone. 
 
 A mixture of 1 oz. of sulphate of copper, J oz. of alum, teaspoonful of 
 powdered salt, 1 gill of vinegar and 20 drops of nitric acid will make a hole 
 in steel that is too hard to cut or file easily. Also, if applied to steel and 
 washed off quickly, it will give the metal a beautiful frosted appearance. 
 
 COMPRESSED AIR 
 
 CLASSIFICATION AND CONSTRUCTION OF 
 COMPRESSORS 
 
 An air compressor consists essentially of a cylinder in which atmospheric 
 air is compressed by a piston, the driving power being steam, water, oil, gas, 
 or electricity. Steam-driven compressors in ordinary use may be classed as 
 follows: 
 
 1. _ Straight-line type, in which a single horizontal air cylinder is set tandem 
 with its steam cylinder, and provided with two flywheels; this pattern is 
 generally adapted for compressors of small size. 
 
 2. Duplex type, in which there are two steam cylinders, each driving an 
 air cylinder, and coupled at 90 to a crank-shaft carrying a flywheel. 
 
 3. Horizontal, cross-compound engines, each steam cylinder set tandem 
 with an air cylinder, as in 2. 
 
 4. Vertical, simple, or compound engines, with the air cylinders set above 
 the steam cylinders. 
 
 5. Compound or stage compressors, in which the air cylinders themselves 
 are compounded; the compression is carried to a certain point in one cylinder 
 and successively raised and finally completed to the desired pressure in the 
 others. They may be either of the straight-line or duplex form, with simple 
 or compound steam cylinders. The principle of compound, or two-stage,air 
 compression is recognized as applicable for even the moderate pressures 
 required in mining. Compressors of class 5 are frequently employed, as well 
 as classes 1, 2, and 3. 
 
COMPRESSED AIR 475 
 
 Theory of Air Compression. The useful effect or efficiency of a compressor 
 is the ratio of the force stored in the compressed air to the work that has been 
 expended in compressing it; this probably never reaches 80% and often falls 
 below 60%. 
 
 Free Air is air at ordinary atmospheric pressure as taken into the com- 
 pressor cylinder; as commonly used, this means air at sea-level pressure 
 (14.7 Ib. per sq. in.) at 60 F. The absolute pressure of air is measured from 
 zero, and is equal to the assumed atmospheric pressure plus gauge pressure. 
 Air-compression calculations depend on the two well-known laws: 
 
 1. Boyle's Law. The temperature being constant, the volume varies 
 inversely as the pressure; or PV = P'V' = a constant; in which F equals the 
 volume of a given weight of air at the freezing point, and the pressure P; 
 V equals the volume of the same weight of air at the same temperature and 
 under the pressure P'. 
 
 2 Cay-Lussac's Law. The volume of a gas under constant pressure, when 
 heated, expands, for each degree of rise in temperature, by a constant pro- 
 portional part of the volume that it occupied at the freezing point; or, 
 V'= V (1 +at), in which a equals 2 fo for centigrade degrees, or *th: for Fahren- 
 heit degrees. 
 
 Theoretically, air may be compressed in two ways, as follows: 
 
 1. I sothermally , when the temperature is kept constant during compres- 
 sion, and in this case, the formula PF = P'F' is true. 
 
 2. A diabolically, when the temperature is allowed to rise without check 
 during the compression. 
 
 As the pressure rises faster than the volume diminishes, the equation 
 
 PV = P'V no longer holds, and p = (T?) W . * n which n equals 1.406. The 
 
 specific heat of air at constant pressure is .2375, and at constant volume 
 .1689. and n = . 2375 -h. 1689 = 1.406. 
 
 In practice, compression is neither isothermal nor adiabatic, but inter- 
 mediate between the two. The values of n for different conditions in prac- 
 tice as determined from a 2,000-H. P. stage compressor at Quai de la Gare, 
 Paris, are as follows: For purely adiabatic compression, with no cooling 
 arrangements, n= 1.406; in ordinary single-cylinder dry compressors, provided 
 with a water-jacket, n is roughly 1.3; while in the best wet compressors (with 
 spray injection) , n becomes 1.2 to 1.25. In the poorest forms of compressor, the 
 value n = 1.4 is closely approached. For large, well-designed compressors 
 with compound air cylinders, the exponent n may be as small as 1.15. 
 
 Construction of Compressors. Compressors are usually built with a short 
 stroke, as this is conducive to economy in compression as well as the attain- 
 ment of a proper rotative speed. In ordinary single-stage compressors, the 
 usual ratio of length of stroke to diameter of steam cylinders is H to 1 or 1J 
 to 1. In some makes, such as the Rand, the ratio is considerably greater, 
 varying from 1 to If to 1, as in several large plants built for the Calumet 
 & Hecla Mining Co. Many compressors have length and diameter of steam 
 cylinders equal. The relative diameters of the air and steam cylinders depend 
 on the steam pressure carried, and the air pressure to be produced. In mining 
 operations, there is usually but little variation in these conditions. For rock- 
 drill work, the air pressure is generally from 60 to 80 Ib. 
 
 In using water-power, a compressor is driven most conveniently by a bucket 
 impact wheel, such as the Pelton or Knight. The waterwheel is generally 
 mounted directly on the crank-shaft, without the use of gearing. As the power 
 developed is uniform throughout the revolution of the wheel, the compressor 
 should be of duplex form, in order to equalize the resistance so far as possible. 
 The rim of the wheel is made extra heavy, to supply the place of a flywheel. 
 When direct-connected, the wheel is of relatively large diameter, as its speed 
 of rotation must of necessity be slow. With small high-speed wheels, the 
 compressor cylinders may be operated through belting or gearing. In most 
 cases, however, the waterwheel may be large enough to render gearing unneces- 
 sary. Impact wheels may be employed with quite small heads of water, by 
 introducing multiple nozzles. To prevent the water from splashing over the 
 compressor, the wheel is enclosed in a tight iron or wooden casing. The force 
 of the water is regulated usually by an ordinary gate valve. If the head is 
 great, it may be necessary to introduce means for deflecting the nozzle, so that, 
 when the compressor is to be stopped suddenly, danger of rupturing the water 
 main will be avoided. 
 
 Rating of Compressors. Compressors are rated as follows: (1) In terms 
 of the horsepower developed by the steam end of the compressor, as shown by 
 
476 
 
 COMPRESSED AIR 
 
 indicator cards taken when running at full speed and when the usual volume 
 of air is being consumed; (2) compressors for mines are often rated roughly 
 as furnishing sufficient air to operate a certain number of rock drills; a 3-in. 
 drill requires a volume of air at 60 Ib. pressure, equal to 100 or 110 cu. ft. of 
 free atmospheric air per minute; (3) in terms of cubic feet of free air com- 
 pressed per minute to a given pressure. 
 
 As the actual capacity of a compressor depends on the density of the 
 intake air, it will be reduced when working at an altitude above sea level, 
 because of the diminished density of the atmosphere. The accompanying 
 table gives the percentages of output at different elevations. 
 
 EFFICIENCIES OF AIR COMPRESSORS AT DIFFERENT ALTITUDES 
 
 
 Barometer Pressure 
 
 Volumetric 
 
 
 Decreased 
 
 Altitude 
 
 
 Efficiency of 
 
 Loss of 
 
 Power 
 
 Feet 
 
 Inches 
 Mercury 
 
 Pounds per 
 Square Inch 
 
 Compressor 
 Per Cent. 
 
 Capacity 
 Per Cent. 
 
 Required 
 Per Cent. 
 
 
 
 30.00 
 
 14.75 
 
 100 
 
 
 
 
 
 1.000 
 
 28.88 
 
 14.20 
 
 97 
 
 3 
 
 1.8 
 
 2,000 
 
 27.80 
 
 13.67 
 
 93 
 
 7 
 
 3.5 
 
 3,000 
 
 26.76 
 
 13.16 
 
 90 
 
 10 
 
 5.2 
 
 4,000 
 
 25.76 12.67 
 
 87 
 
 13 
 
 6.9 
 
 5,000 
 
 24.79 
 
 12.20 
 
 84 
 
 16 
 
 8.5 
 
 6,000 
 
 23.86 
 
 11.73 
 
 81 
 
 19 
 
 10.1 
 
 7,000 
 
 22.97 
 
 11.30 
 
 78 
 
 22 
 
 11.6 
 
 8,000 
 
 22.11 
 
 10.87 
 
 76 
 
 24 
 
 13.1 
 
 9,000 
 
 21.29 
 
 10.46 
 
 73 
 
 27 
 
 14.6 
 
 10,000 
 
 20.49 
 
 10.07 
 
 70 
 
 30 
 
 16.1 
 
 11,000 
 
 19.72 
 
 9.70 
 
 68 
 
 32 
 
 17.6 
 
 12,000 
 
 18.98 
 
 9.34 
 
 65 
 
 35 
 
 19.1 
 
 13,000 
 
 18.27 
 
 8.98 
 
 63 
 
 37 
 
 20.6 
 
 14,000 
 
 17.59 
 
 8.65 
 
 60 
 
 40 
 
 22.1 
 
 15,000 
 
 16.93 
 
 8.32 
 
 58 
 
 42 
 
 23.5 ' 
 
 EXAMPLE. Calculate the volume of air furnished by an 18"X24" com- 
 pressor working at an elevation of 5,000 ft. above sea level, making 95 rev. per 
 min., and having a piston speed of 380 ft. per min. 
 
 SOLUTION. 9 2 X 3.14 = 254.3 sq. in. = piston area. rrjX 380 = 668.8 
 cu. ft. = volume displaced per minute by the piston; deducting 10% for loss 
 gives 602 cu. ft. At sea level at 80 Ib. gauge pressure, this equals 
 
 X 602 = 95 cu. ft. At an elevation of 5,000 ft., the output of a compressor 
 would be 95X84% = 79.8 cu. ft. per min. 
 
 Cooling. Compressor cylinders may be cooled by injecting water into the 
 cylinder, in which case they are known as wet compressors; or by jacketing the 
 cylinder in water, when they are known as dry compressors. 
 
 TRANSMISSION OF AIR IN PIPES 
 
 The actual discharge capacity of piping is not proportional to the cross- 
 sectional area alone, that is, to the square of the diameter. Although the 
 periphery is directly proportional to the diameter, the interior surface resis- 
 tance is much greater in a small pipe than in a large one, because, as the pipe 
 becomes smaller, the ratio of perimeter to area increases. 
 
 To pass a given volume of compressed air, a 1-in. pipe of given length 
 requires over three times as much head as a 2-in. pipe of the same length. 
 The character of the pipe, also, and the condition of its inner surface, have 
 much to do with the friction developed by the flow of air. Besides imper- 
 fections in the surface of the metal, the irregularities incident on coupling 
 together the lengths of pipe must increase friction. There are so few reliable 
 
COMPRESSED AIR 477 
 
 data that the influences by which the values of some of the factors may be 
 modified are not fully understood; and, owing to these uncertain conditions, 
 the results obtained from formulas are only approximately correct. 
 
 Among the formulas in common use, perhaps the most satisfactory is that 
 of D'Arcy. As adopted for compressed-air transmission, it takes the form: 
 
 in which D = volume of compressed air discharged at final pressure in cubic feet 
 
 per minute; 
 c = coefficient varying with diameter of pipe, as determined by 
 
 experiment; 
 
 d = diameter of pipe in inches (actual diameters of 1 J- and Ij-in. pipe 
 are 1.38 in. and 1.61 in., respectively; nominal diameters of all 
 other sizes may be taken for calculations) ; 
 I = length of pipe, in feet; 
 
 pi = initial gauge pressure, in pounds per square inch; 
 pz = final gauge pressure, in pounds per square inch; 
 wi = density of air, or its weight at initial pressure pi, in pounds per 
 
 cubic foot. 
 The values of the coefficients c for sizes of piping up to 12 in. are: 
 
 1 in ........... 45.3 5 in ........... 59.0 9 in ........... 61.0 
 
 2 in ........... 52.6 6 in ........... 59.8 10 in ........... 61.2 
 
 3 in ........... 56.5 7 in ........... 60.3 11 in ........... 61.8 
 
 4 in .......... .58.0 8 in.. ...... ...60.7 12 in ........... 62.0 
 
 Some apparent discrepancies exist for sizes larger than 9 in., but they cause 
 
 no very material differences in the results. 
 
 Another formula, published by Mr. Prank Richards, is as follows: 
 
 10,000 D*a 
 in which H =head or difference of pressure required to overcome friction and 
 
 maintain flow of air; 
 
 V = volume of compressed air delivered, in cubic feet per minute; 
 L = length of pipe, in feet; 
 D = diameter of pipe, in inches; 
 a = coefficient, depending on size of pipe. 
 Values of a for nominal diameters of wrought-iron pipe: 
 
 lin .......... 350 3 in ........... 730 Sin .......... 1.125 
 
 IJin ......... 500 3i .......... 787 10 in .......... 1.200 
 
 Hin ......... 662 4 in ........... 840 12 in ..... ...... 1.260 
 
 2 in .......... 565 5 in ........... 934 
 
 2in ......... 650 6 in.... ____ ..1.000 
 
 The values of a for 1 and l|-in. pipe are not consistent with those for 
 other sizes, for the reason already stated. When using this formula with its 
 constants, the calculated losses of pressure are found to be smaller, and, con- 
 versely, the volumes of air discharged are larger, under the same conditions 
 than those obtained from D'Arcy's formula. 
 
 It must be remembered that, within certain limits, the loss of head or 
 pressure increases with the square of the velocity. To obtain the best results, 
 it has been found that the velocity of flow in the main air pipes should not 
 exceed 20 or 25 ft. per sec. When the initial velocity much exceeds 50 ft. 
 per sec., the percentage loss becomes very large; and, conversely, by using 
 piping large enough to keep down the velocity, the friction loss may be almost 
 eliminated. For example, at the Hoosac tunnel, in transmitting 875 cu. ft. 
 per min. of free air at an initial pressure of 60 lb., through an 8-in. pipe, 7,150 ft. 
 long, the average loss including leakage was only 2 lb. A volume of 500 cu. ft. 
 per min. of free air, at 75 lb., can be transmitted through 1,000 ft. of 3-in. pipe 
 with a loss of 4.1 lb., while if a 5-in. pipe is used the loss will be reduced to 
 .24 lb. The velocity of flow in the latter case is only 10 ft. per sec. 
 
 When driving the Jeddo mining tunnel, at Ebervale, Pa., two 3j-in. drills 
 were used in each heading, with a 6-in. main, the maximum transmission dis- 
 tance being 10,800 ft. This pipe was so large in proportion to the volume of air 
 required for the drills (230 cu. ft. per min. of free air) that the loss was reduced 
 to an extremely small quantity. A calculation shows a los's of .002 lb., and 
 the gauges at each end of the main were found to record practically the same 
 pressure. 
 
 A due regard for economy in installation, however, must limit the use of 
 very large piping, the cost of which should be considered in relation to the 
 
478 COMPRESSED AIR 
 
 cost of air compression in any given case. Diameters of from 4 to 6 in. for 
 the mains are large enough for any ordinary mining practice. Up to a length 
 of 3,000 ft., a 4-in. pipe will carry 480 cu. ft. per min. of free air compressed 
 to 82 lb., with a loss of 2 Ib. pressure. This volume of air will run fpur 3-in. 
 drills. Under the same conditions, a 6-in. pipe, 5,000 ft. long, will carry 
 1,100 cu. ft. per min. of free air, or enough for 10 drills. 
 
 A mistake is often made by putting in branch pipes of too small a diam- 
 eter. For a distance of, say, 100 ft., a Ij-in. pipe is small enough for a single 
 drill, though a 1-in. pipe is frequently used. While it is, of course, admissible 
 to increase the velocity of flow in short branches considerably beyond 20 ft. 
 per sec., extremes should be avoided. To run a 3-in. drill from a 1-in. pipe 100 
 ft. long, will require a velocity of flow of about 55 ft. per sec., causing a loss 
 of 10 lb. pressure. 
 
 The piping for conveying compressed air may be of cast or wrought iron. 
 If of wrought iron, as is customary, the lengths are connected either by sleeve 
 couplings or by cast-iron flanees into which the ends of the pipe are screwed 
 or expanded. Sleeve couplings are used for all except the large sizes. The 
 smaller sizes, up to lj in., are butt-welded, while all from 1? in. up are lap- 
 welded, to insure the necessary strength. Wrought-iron, spiral-seam, riveted, 
 or spiral- weld steel tubing is sometimes used. It is made in lengths of 20 ft. 
 or less. For convenience of transport in remote regions, rolled sheets in short 
 lengths may be had. They are punched around the edges, ready for riveting, 
 and are packed closely four, six, or more sheets in a bundle. 
 
 All joints in air mains and branches should be carefully made. Air leaks 
 are more expensive than steam leaks because of the losses suffered when com- 
 pressing the air. The pipe may be tested from time to time by allowing the 
 air at full pressure to remain in the pipe long enough to observe the gauge. 
 A leak should be traced and stopped immediately. When putting together 
 screw joints, care should be taken that none of the white lead or other cement- 
 ing material is forced into the pipe; this would cause obstruction and increase 
 the friction loss. Also, each length as put in place should be cleaned thor- 
 oughly of all foieign substances that may have lodged inside. To render the 
 piping readily accessible for inspection and stoppage of leaks, it should, if 
 buried, be carried in boxes sunk just below the surface of the ground; or, if 
 underground, it should be supported upon brackets along the sides of the mine 
 workings. Low points in pipe lines, which would form pockets for the accu- 
 mulation of entrained water, should be avoided, as- they obstruct the passage 
 of the air. In long pipe lines, where a uniform grade is impracticable, pro- 
 vision may be made near the end for blowing out the water at intervals, when 
 the air is to be used for pumps, hoists, or other stationary engines. 
 
 For long lengths of piping, expansion joints are required, particularly 
 when on the surface. They are not often necessary underground, as the 
 temperature is usually nearly constant, except in shafts, or where there may be 
 considerable variations of temperature between summer and winter. 
 
 LOSSES IN THE TRANSMISSION OF COMPRESSED AIR 
 
 To obtain compressed air, an engine drives a compressor, which forces air 
 into a reservoir; the air under pressure is led through pipes to the air engine, 
 and is there used after the manner of steam. The resulting power is frequently 
 a small percentage of the power expended. In a large number of cases the 
 losses are due to poor designing, and are not chargeable as faults of the system 
 or even to poor workmanship. 
 
 The losses are chargeable, first, to friction of the compressor. This will 
 amount ordinarily to 15% or 20%, and can be helped by good workmanship, 
 but cannot probably be reduced below 10%. Second, a loss is occasioned by 
 pumping the air of the engine room, rather than air drawn from a cooler place; 
 this loss varies with the season, and amounts to from 3% to 10% and can all 
 be saved. The third loss, or series of losses, is caused by insufficient supply, 
 difficult discharge, defective cooling arrangements, poor lubrication, and a 
 host of other causes, in the compression cylinder. The fourth loss is found in 
 the pipe, it varies with every different situation, and is subject to somewhat 
 complex influences. The fifth loss is chargeable to a fall of temperature in 
 the cylinder of the air engine. Losses arising from leaks are often serious, 
 but the remedy is too evident to require demonstration; no leak can be so 
 small as not to require immediate attention. An attendant who is careless 
 about packings and hose couplings will permit losses for which no amount of 
 engineering skill can compensate. 
 
COMPRESSED AIR 479 
 
 It is possible to realize 100% efficiency in the air engine, leaving friction 
 out of our consideration, only when the expansion of the air and the changes 
 of its temperature in the expanding or air-engine cylinder are precisely the 
 reverse of the changes that have taken place during the compression of the 
 air in the compressing cylinder; but these conditions can never be realized. 
 The air during compression becomes heated, and during expansion it becomes 
 cold. If the air immediately after compression, before the loss of any heat, 
 was used in an air engine and there perfectly expanded back to atmospheric 
 pressure, it would, on being exhausted, have the same temperature it had 
 before compression, and its efficiency would be 100%. 
 
 But the loss of heat after compression and before use cannot be prevented, 
 as the air is exposed to such very large radiating surfaces in the reservoir and 
 pipes, on its passage to the air engine. The heat that escapes in this way, 
 did, while in the compressing cylinder, add much to the resistance of the air 
 to compression, and as it is sure to escape, at some time, either in reservoir 
 or pipes, the best plan is to remove it as fast as possible from the cylinder and 
 thus remove one element of resistance. Hence, compressors are almost uni- 
 versally provided with cooling attachments more or less perfect in their action, 
 the aim being to secure isothermal compression, or compression having equal 
 temperature throughout. 
 
 If air compressed isothermally is used with perfect expansion and the fall 
 of temperature during expansion is prevented, 100% efficiency will be obtained. 
 But air will grow cold when expanded in an engine, hence warming attach- 
 ments have the same economic place on an air engine that cooling attachments 
 have on an air compressor. In fact, attachments of this kind are found in 
 large and permanently located engines, but their use on most of the engines 
 for mine work is dispensed with, and the engines expand the air adiabatically, 
 or without receiving heat. 
 
 The practical engineer, therefore, has to deal with nearly isothermal com- 
 pression, and nearly adiabatic expansion, and must also consider that the air 
 in reservoirs and pipes becomes of the same temperature as surrounding objects. 
 Consideration must also be had for the friction of the compressor and the air 
 engine. For the pressure of 60 lb., which is that most commonly used, the 
 decrease in resistance to compression secured by the cooling attachments 
 is almost exactly equaled by the friction of the compressor. Hence it is safe, 
 when calculating the efficiency of the air engine, to consider the compressor 
 as being without cooling attachments, and also as working without friction. 
 The results of such calculations will be too high efficiencies for light pressures, 
 which are little used; about correct for medium pressures, which are com- 
 monly employed; and too low for higher pressures, and will thus have the 
 advantage of not being overestimated. This result is occasioned by the fact 
 that, owing to the slight heat in compressing low pressures of air, the saying 
 of power by the cooling attachments is not equal to the friction of the machine, 
 but at high pressures, on account of the great heat, the cooling attachments 
 are of great value and save very much more power than friction consumes. 
 
 In 'expanding engines, the expansion never falls as low as the adiabatic 
 law would indicate, owing to a number of reasons, but if the expansion is con- 
 sidered as adiabatic, an error in calculations caused thereby will be on the safe 
 side and the actual power will exceed the calculated power. Therefore, the 
 compressor and engine may be considered as following the adiabatic law of 
 compression and expansion, and as working without friction. 
 
 With this view of the case, the efficiency of an air engine, working with 
 perfect expansion, stated in percentages of the power required to operate 
 the compressor, can be placed as here shown for the various pressures above the 
 atmosphere. As the efficiencies for the lower pressures are very much greater 
 than for the high pressures, the conclusion is almost irresistible that to secure 
 economical results air engines should be designed to run with light pressures. 
 
 Pressure Above T? # 
 
 Atmosphere Efficiency 
 
 Pounds PerCent - 
 
 2.9 94.85 
 
 14.7 81.79 
 
 29.4 72.72 
 
 44.1 66.90 
 .58.8 62.70 
 
 73.5 59.48 
 
 88.2 56.88 
 
480 COMPRESSED AIR 
 
 In the foregoing the pipe friction has been entirely neglected. A pressure 
 of 2.9 Ib. is credited with an efficiency of 94.85%; but, if the air were con- 
 veyed through a pipe, and the length of the pipe and the velocity of flow 
 were such that 2.9 Ib. pressure was lost in friction, the efficiency of the air, 
 instead of being 94.85%, would be absolutely zero. It is the power that can be 
 obtained from the air, after it has passed the pipe and lost a part of its pressure 
 by friction, that must be considered when the efficiency of an apparatus is given. 
 
 The foregoing table of efficiencies with a loss of 2.9 Ib. in the pipe, now gives 
 different values for the efficiencies at the various pressures. 
 
 Pressure Above Efficiency 
 
 2.9 00.00 
 
 14.7 70.44 
 
 29.4 68.81 
 
 44.1 64.87 
 
 58.8 61.48 
 
 73.5 58.62 
 
 88.2 56.23 
 
 It will be noticed that the light pressures have lost most by the pipe fric- 
 tion, 2.9 Ib. having lost 100%; 14.7 Ib. 11%, and 88.2 Ib. only a trifle over one- 
 half of 1%. It is also seen now 14.7 Ib. is apparently the economical pressure to 
 use. But a further careful analysis of the subject shows, that when the loss in 
 the pipe is 2.9 Ib., then 20.5 Ib. is the most economical pressure to use, and that 
 the efficiency is 71%. But 2.9 Ib. is a very small loss between compressor and 
 air engine, and cases are extremely exceptional where the friction of valves, 
 pipes, elbows, ports, etc. does not far exceed this. Yet, with these conditions, 
 which are very difficult to fill, 20.5 Ib. is the lightest pressure that should prob- 
 ably ever be used for conveying power, and 71% is an efficiency scarcely to be 
 obtained. 
 
 Continuing the investigation and taking examples where the pipe friction 
 amounts to 5.8 Ib., it is found that the following efficiencies correspond to the 
 stated pressure: 
 
 Pressure Above 77 ,-,,. 
 
 Atmosphere Efficiency 
 
 Pounds PerCenL 
 
 14.7 57.14 
 
 29.4 64.49 
 
 44.1 62.71 
 
 58.8 60.12 
 
 73.5 57.73 
 
 88.2 55.59 
 
 As friction increases, or, in other words, when more air is used and greater 
 demands are made on the carrying capacity of the pipe, the pressure "must be 
 greatly increased to attain the most economical results. If the demands are 
 such as to increase the friction and loss in pipe to 14.7 Ib., the air of 14.7 Ib. 
 pressure at the compressor is entirely useless at the air engine. The table will 
 therefore stand thus : 
 
 Pressure Above 77 ./r - 
 
 Atmosphere Efficiency 
 
 Pounds Per Cent ' 
 
 14.7 00.00 
 
 29.4 48.53 
 
 44.1 55.13 
 
 58.8 55.64 
 
 73.5 54.74 
 
 88.2 53.44 
 
 It is to be noticed that 88.2 Ib. pressure has lost only about 3?% of its 
 efficiency by reason of as high a friction as 14.7 Ib., while the efficiency of the 
 lower pressures has been greatly affected. As the friction increases the most 
 efficient, and consequently, most economical, pressure increases. In fact, for 
 any given friction in a pipe, the pressure at the compressor must not be carried 
 below a certain limit. The following table gives the lowest pressures that should 
 be used at the compressor, with varying amounts of friction in the pipe: 
 
COMPRESSED AIR 481 
 
 ** 
 
 Pounds Per Cent ' 
 
 2.9 20.5 70.92 
 
 5.8 29.4 64.49 
 
 8.8 38.2 60.64 
 
 11.7 47.0 57.87 
 
 14.7 52.8 55.73 
 
 17.6 61.7 53.98 
 
 20.5 70.5 52.52 
 
 23.5 76.4 51.26 
 
 26.4 82.3 50.17 
 
 29.4 88.2 49.19 
 
 So long as the friction of the pipe equals the amounts there given, an 
 efficiency greater than the corresponding sums stated in the table cannot be 
 expected. In a case that corresponds to any of those cited in the table, the 
 efficiency can be increased only by reducing the friction. An increase in the 
 size of pipe will reduce friction by reason of the lower velocity of flow required 
 for the same amount of air. But many situations will not admit of large pipes 
 being employed, owing to considerations of economy outside of the question 
 of fuel or prime motor capacity. 
 
 An increase of pressure will decrease the bulk of air passing in the pipe, and 
 in that proportion will decrease its velocity. This will decrease the loss by 
 friction, and, as far as that goes, a gain is obtained, but there is a new loss, 
 and that is the diminishing efficiencies of increasing pressures. Yet as each 
 cubic foot of air is at a higher pressure, and, therefore, carries more power, 
 as many cubic feet will not be needed for the same work. It is obvious that 
 with so many sources of gain or loss the question of selecting the proper pres- 
 sure is not to be decided hastily. 
 
 As an illustration of the combined effect of these different elements, a very 
 common case will be taken. ^ The compressor makes 102 rev. per min., pres- 
 sure is 52.8 lb., loss in pipe is 14.7 lb., machine in mine running at 38.2 lb., 
 efficiency is 55.73%. As long as the friction of the pipe amounts to 14.7 lb., 
 52.8 lb. is the best pressure and 55.73% the greatest efficiency, but friction 
 may be reduced by reducing the bulk of air passing through the pipe and if 
 the cylinder of the air engine is reduced until it requires 47 lb. pressure to do 
 the same work as before; the friction of pipe will then drop to 11.7 lb. The 
 pressure on the compressor will rise to 58.8 lb., its number of revolutions will 
 fall to 100, and the resulting efficiency will be 57.22%. 
 
 Another change of pressure on compressor to 64.7 lb. will decrease its revo- 
 lutions to 93, friction to 8.8 lb., and its efficiency will rise to 57.94%. If the 
 pressure is increased to 73.5 lb., there will be only 84 revolutions of compressor, 
 5.8 lb. loss in pipe, and an efficiency of 57.73%. In this last case the efficiency 
 begins to fall off a little, and higher pressures will show less efficiency; but, in 
 comparison with the first example, the same work will be done with a trifle less 
 power and with a decrease of nearly 20% in the speed of the compressor. 
 
 Other common examples can be shown where an increase of pressure would 
 result in wonderful increase in efficiency and economy. There are many cases 
 where light pressures and high velocity in the pipe will convey a given power 
 with greater economy than higher air pressures and lower speed of flow through 
 the pipe. But these cases arise mostly when the higher air pressures become 
 very much greater than are at present in common use. Therefore, when esti- 
 mating the efficiency of the complete outfit, it is found that the pipe and the 
 pressure are very important elements, and must be determined with care and 
 skill to secure the most satisfactory results. As the volume and power of air 
 vary with its pressure, the size and consequent cost of compressor for a certain 
 work will also be affected by the pressure. To plan an outfit for a mine, due 
 regard must be had to the cost of fuel or prime motor power, and also to the 
 cost of compressor, pipes, and machinery, as the saving in one is often secured 
 by a sacrifice in the other. 
 
 Next to determining the size of pipe, the skilful engineer has need of fur- 
 ther care in the proper position of reservoirs, branches, drains, and other 
 attachments, as only by the exercise of good judgment in this can satisfactory 
 working be secured. The fact that, on account of the diminished density of 
 the atmosphere at high altitudes, air compressors do not give the same results 
 as at sea level, should also be taken into consideration when a compressor is to 
 be installed in a mountainous region. 
 31 
 
482 COMPRESSED AIR 
 
 LOSS OF PRESSURE, IN POUNDS PER SQUARE INCH, BY 
 FLOW OF AIR IN PIPES 1,000 FT. LONG 
 
 Velocity 
 
 J 
 
 
 
 of Air at 
 Entrance 
 
 1-In. Pipe 
 
 2-In. Pipe 
 
 2^-In. Pipe 
 
 to Pipe 
 
 
 
 
 
 
 
 Is 
 
 */? ^ 
 
 
 1| 
 
 li 
 
 
 li 
 
 li 
 
 d 
 
 | 
 
 M 
 
 rt rt 
 
 Ij 
 
 S 
 
 32 
 
 Si! 
 
 | 
 
 .*! 
 
 .b 
 
 g 
 
 1 
 
 fl 
 
 |i 
 
 4) 
 
 |8 
 
 A| 
 
 |g 
 
 11 
 
 11 
 
 1 
 
 l! 
 
 o. 
 
 3 
 
 0, 
 
 
 O .... 
 
 2 
 
 
 
 
 s; 
 
 vti 
 
 vw rt 
 O ... 
 
 "8 J 
 
 
 -p 
 
 
 >$ 
 
 *% 
 
 (0 
 
 +* + 
 
 -% 
 
 W 
 
 **$ 
 
 
 1 
 
 1 
 
 
 II 
 
 8 I 
 
 J3 
 
 i. 
 
 
 1 
 
 II 
 
 | 3 
 
 
 
 
 Is 
 
 |? 
 
 
 I*? 
 
 |? 
 
 
 Ife 
 
 1 
 
 
 
 
 O a 
 
 o 
 
 
 a ft 
 
 o ft 
 
 
 O ft 
 
 (5ft 
 
 1 
 
 3.28 
 
 .1435 
 
 6 
 
 7 
 
 .0794 
 
 23 
 
 29 
 
 .0574 
 
 32 
 
 41 
 
 2 
 
 6.56 
 
 .6405 
 
 12 
 
 15 
 
 .3050 
 
 46 
 
 59 
 
 .2562 
 
 65 
 
 82 
 
 3 
 
 9.84 
 
 1.4545 
 
 18 
 
 22 
 
 .7216 
 
 69 
 
 88 
 
 .5818 
 
 97 
 
 124 
 
 4 
 
 13.12 
 
 2.5620 
 
 24 
 
 29 
 
 1.2566 
 
 93 
 
 117 
 
 1.0248 
 
 130 
 
 165 
 
 5 
 
 16.40 
 
 3.9345 
 
 29 
 
 37 
 
 1.9642 
 
 116 
 
 146 
 
 1.5738 
 
 163 
 
 207 
 
 6 
 
 19.68 
 
 5.4225 
 
 35 
 
 44 
 
 2.7120 
 
 139 
 
 175 
 
 2.1690 
 
 195 
 
 247 
 
 8 
 
 26.24 
 
 10.2480 
 
 47 
 
 59 
 
 5.0264 
 
 185 
 
 234 
 
 4.0992 
 
 260 
 
 330 
 
 10 
 
 32.80 
 
 15.7380 
 
 59 
 
 74 
 
 7.8568 
 
 232 
 
 294 
 
 6.2952 
 
 326 
 
 413 
 
 
 
 l 
 
 
 
 
 
 
 
 
 3-In. Pipe 
 
 4-In. Pipe 
 
 5-In. Pipe 
 
 1 
 
 3.28 
 
 .0463 
 
 48 
 
 60 
 
 .0347 
 
 86 
 
 109 
 
 .0287 
 
 134 
 
 169 
 
 2 
 
 6.56 
 
 .2092 
 
 96 
 
 121 
 
 .1525 
 
 172 
 
 217 
 
 .1281 
 
 268 
 
 239 
 
 3 
 
 9.84 
 
 .4880 
 
 144 
 
 182 
 
 .3608 
 
 258 
 
 326 
 
 .2909 
 
 402 
 
 509 
 
 4 
 
 13.12 
 
 .8381 
 
 193 
 
 243 
 
 .6283 
 
 343 
 
 436 
 
 .5124 
 
 537 
 
 678 
 
 5 
 
 16.40 
 
 1.3176 
 
 241 
 
 304 
 
 .9821 
 
 429 
 
 544 
 
 .7869 
 
 671 
 
 844 
 
 6 
 
 19.68 
 
 1.8080 
 
 289 
 
 364 
 
 1.3560 
 
 515 
 
 653 
 
 1.0845 
 
 805 
 
 1,017 
 
 8 
 
 26.24 
 
 3.3525 
 
 386 
 
 486 
 
 2.5132 
 
 687 
 
 871 
 
 2.0496 
 
 1,073 
 
 1,357 
 
 10 
 
 32.80 
 
 5.2704 
 
 480 
 
 607 
 
 3.9284 
 
 859 
 
 1,088 
 
 3.1476 
 
 1,342 
 
 1,696 
 
 
 
 6-In. Pipe 
 
 8-In. Pipe 
 
 10-In. Pipe 
 
 1 
 
 3.28 
 
 .0232 
 
 193 
 
 244 
 
 .0173 
 
 343 
 
 434 
 
 .0143 
 
 537 
 
 680 
 
 2 
 
 6.56 
 
 .1046 
 
 386 
 
 488 
 
 .0762 
 
 687 
 
 864 
 
 .0640 
 
 1,073 
 
 1,359 
 
 3 
 
 9.84 
 
 .2440 
 
 579 
 
 633 
 
 .1805 
 
 1,030 
 
 1,303 
 
 .1455 
 
 1,610 
 
 2,039 
 
 4 
 
 13.12 
 
 .4190 
 
 772 
 
 977 
 
 .3141 
 
 1,373 
 
 1,736 
 
 .2562 
 
 2,146 
 
 2,719 
 
 5 
 
 16.40 
 
 .6588 
 
 965 
 
 1,221 
 
 .4910 
 
 1,717 
 
 2,171 
 
 .3934 
 
 2,683 
 
 3,399 
 
 6 
 
 19.68 
 
 .9040 
 
 1,158 
 
 1,466 
 
 .6780 
 
 2,060 
 
 2,605 
 
 .5423 
 
 3,220 
 
 4,079 
 
 8 
 
 26.24 
 
 1.6762 
 
 1,544 
 
 1,954 
 
 1.2556 
 
 2,747 
 
 3,473 
 
 1.0248 
 
 4,293 
 
 5,438 
 
 10 
 
 32.80 
 
 2.6352 
 
 1,931 
 
 2,443 
 
 1.9642 
 
 3,434 
 
 4,342 
 
 1.5738 
 
 5,367 
 
 6,798 
 
 Friction of Air in Pipes. Air in its passage through pipes is subject to 
 friction in the same manner as water or any other fluid; therefore, the pressure 
 at the compressor must be greater than at the point of consumption, m order 
 to overcome this resistance. The power that is needed to produce the extra 
 
COMPRESSED AIR 483 
 
 pressure representing the friction of the pipe is lost, as there can be no useful 
 return for it. The friction is affected by very many circumstances; it is 
 increased in direct proportion to the length of the pipe and also in the square 
 of the velocity of the flow of air. The pressure of the air does not affect it. 
 
 The losses by friction may be quite serious if the piping system is poorly 
 designed, and, on the other hand, extravagant expenditure in pipe may result 
 from a timid overrating of the evils of friction. A thorough knowledge of the 
 laws governing the whole matter, as well as a ripe experience, is necessary to 
 secure true economy and mechanical success. The loss of power in pipe 
 friction is not always the most serious result. When a number of machines 
 are in use in a mine, and the pipes are so small as to cause considerable loss of 
 pressure by friction, there will be sudden and violent fluctuations in pressure 
 whenever a machine is started or stopped. Breakages will be common occur- 
 rences, as the changes are too quick to be entirely guarded against by the 
 attendant; perfectly even pressure at the compressor is no safeguard against 
 this class of accidents. The trouble arises in the pipe, and the remedy must 
 be applied there. A system of reservoirs and governing valves will regulate 
 these matters and allow successful work to be done with pipes that would 
 otherwise be entirely inadmissible. 
 
 The ordinary formulas for calculating the volume of air transmitted through 
 a pipe do not take into account the increase of volume due to reduction of 
 pressure, i. e., loss of head. To transmit a given volume of air at a uniform 
 velocity and loss of pressure, it is necessary to construct the pipe with a gradu- 
 ally increasing area. This, of course, is impracticable, and in a pipe of uniform 
 section both volume and velocity must increase as the pressure is reduced by 
 friction. The loss of head in properly proportioned pipes is so small, how- 
 ever, that in practice the increase in volume is usually neglected. The table 
 on page 482 gives the loss of pressure by flow of air in pipes calculated for 
 pipes 1,000 ft. long; for other lengths, the loss varies directly as the length. 
 
 The resistance is not varied by the pressure, only so far as changes in pres- 
 sure vary the velocity. It increases about as the square of the velocity, and 
 directly as the length. Elbows, short turns, and leaks in pipes all tend to 
 reduce the pressure in addition to the losses given in the table. An elbow 
 with a radius of one-half the diameter of the pipe is as short as can be made. 
 
 LOSS BY FRICTION IN ELBOWS 
 
 Radius of Elbow Equivalent Length of Straight Pipe 
 
 Diameters Diameters 
 
 5 7.85 
 
 3 8.24 
 
 2 9.03 
 
 1* 10.36 
 
 H 12.72 
 
 17.51 
 
 a 35.09 
 
 121.20 
 
 DESIGN, OPERATION, AND INSTALLATION OF AIR 
 COMPRESSORS 
 
 With regard to the design, installation, and operation of air compressors, 
 the following suggestions made by Mr. Alex. M. Gow, Mechanical Engineer, 
 Oliver Iron Mining Co., and slightly enlarged, will be of interest. 
 
 Design for Avoiding Explosions. Clearance space should be reduced to a 
 minimum. Ingoing air should traverse as small a surface of hot metal as 
 possible. Discharge valves and passageways should contain no pockets or 
 recesses for the accumulation of oil. Cylinders and heads should be water- 
 jacketed; in some cases piston water-cooling may be resorted to. Stage com- 
 pression, with adequate intercooling should be employed wherever final 
 pressure and first cost of installation will warrant. Discharge valves must be 
 easy of access for cleaning and examination. There must be no excuse for 
 dirty or leaky valves. 
 
 Installation of Compressor. Air should be drawn from the coolest and 
 cleanest place possible, and never from the engine room. _ Engine-room air is 
 never cool nor clean and an open intake is a constant invitation to squirt oil 
 in from a can. Around collieries, it is well to consider the washing of the air. 
 Coal dust drawn in with the air, mixes with the oil and forms a substance that, 
 
484 ELECTRICITY 
 
 on heating, cakes and may take fire. The discharge pipe should be of ample 
 size and have as few bends as possible. A thermometer, preferably recording, 
 should be placed on the discharge pipe. Provision for aftercooling should be 
 made, a water spray will answer, to be used when the thermometer indicates 
 the necessity. The receiver should be provided with a manhole for cleaning, 
 and a drain easy of access and ample in size. Automatic sight-feed lubricators 
 should be depended on f9r regular lubrication, but in addition an oil pump 
 may be installed for the introduction of soap and water in case of necessity. 
 
 Operation of Compressors. High flash-test cylinder oil of the best obtain- 
 able grade should be used for regular lubrication of the air cylinders. Mr. 
 L. A. Christian advises that the flash point be 625 F., and that the oil should 
 be comparatively free from unnecessary volatile carbon compounds. Volatile 
 hydrocarbons tend to reduce the flash point, and, mixing with the dust from the 
 air, form combustible deposits in the receiver and outlet passages. Further, 
 oil of low-flash test, on reaching the interior of the heated air cylinder will be 
 vaporized and will pass out with the air into the receiver without affording any 
 lubrication to the wearing surfaces. If the oil is too dense or is compounded 
 with animal or vegetable oils, as is the case with many steam-cylinder oils, it 
 will have a tendency to adhere to the discharge valves and passages, and, 
 being subjected to the dry heat of the compressed air, will gradually change to 
 a hard, brittle crust, which in time will completely choke up the air passages 
 or will prevent the valves seating. The amount of oil to be fed into the air 
 cylinder should be, if the machine makes less than 120 rev. per min., about 
 1 drop every 3 min. Kerosene should never be used to cut or eat away deposits 
 of carbon, as is sometimes done, as its flash point is about 120 F. If the 
 cylinders or air passages need cleaning, soapsuds made of 1 part of soft soap and 
 15 parts of pure water should be fed into the cylinder and the machine worked 
 with a liberal solution instead of oil for a few hours or a day ; then the blow-off 
 valve of the receiver should be opened and the accumulation of oil and water 
 drained off. After this treatment and before the machine is shut down, oil 
 should be fed into the cylinder for an hour or so, in order that the valves and the 
 parts connected with the cylinder may be coated with oil and thus prevent rust. 
 
 Discharge valves must be kept tight; to this end the use of the steam 
 engine indicator is advised. The cards may not tell much about the conditions 
 of the valves, but one of the greatest values of the indicator is the moral effect 
 upon the engineer. The valves should be cleaned from dust and oil and fre- 
 quently examined. 
 
 Accumulations of water and oil must be blown from the receiver and an 
 internal examination made at stated intervals. 
 
 The thermometer on the discharge pipe should be watched like the steam 
 gauge. Before it reaches 400 F., the after cooling spray should be put on, and 
 all the water-supply pipes and the discharge valves examined. 
 
 The engineer in charge should be thoroughly instructed as to the possibility 
 of an explosion, the dangers attendant upon the use of any but the prescribed 
 oil, and the effect of leaky discharge valves. He should be instructed in the 
 use of the steam-engine indicator and required to submit cards at stated 
 intervals. He should record in the engine-room log the daily conditions of the 
 machines under his charge. He should be given a wholesome respect for an 
 air compressor, with imperative instructions to keep it clean, inside as well 
 as out. 
 
 ELECTRICITY 
 
 PRACTICAL UNITS 
 
 In electric work, it is necessary to have units in terms of which to express 
 the different quantities entering into calculations. The unit quantity of elec- 
 tricity ftowing through a circuit is called a coulomb. A coulomb is the quantity 
 of electricity that will deposit from a solution of silver nitrate through which 
 it flows .U01118 gram of silver. 
 
 Strength of Current. The strength of current flowing in a wire may be 
 measured in several ways. If a compass needle is held under or over a wire 
 it will be deflected and will tend to stand at right angles to the wire. The 
 stronger the current, the greater is the deflection of the needle. If the wire 
 carrying the current is cut and the end dipped into a solution of silver nitrate, 
 
ELECTRICITY 485 
 
 silver will be deposited on the end of the wire toward which the current is 
 flowing, and the amount of silver deposited in a given time will be directly 
 proportional to the average strength of current flowing during that time. 
 When the current flowing in a wire is spoken of, the strength of the current is 
 meant. 
 
 The unit used to express the strength of a current is called the ampere. 
 If a current of 1 amp. be sent through a bath of silver nitrate, .001118 g. per sec. 
 of silver will be deposited. The expression of the flow of current through a wire 
 as so many amperes is analogous to the expression of the flow of water through 
 a pipe as so many gallons per second. If 1 amp. flows through a circuit for 
 1 sec., the quantity of electricity that has passed through the circuit during 
 the 1 sec. is 1 coulomb; that is, 1 coulomb is equal to 1 amp. for 1 sec. 
 
 Electromotive Force. In order that a current may flow through a wire, 
 there must be an electric pressure of some kind to cause the flow. In hydraulics, 
 there must always be a head or pressure before water can be made to flow 
 through a pipe. It is also evident that there may be a pressure or head without 
 there being any flow of water, because the opening in the pipe might be closed; 
 the pressure will, however, exist, and, as soon as the valve closing the pipe is 
 opened, the current will flow. In the same way, an electric pressure or electro- 
 motive force (often written E. M. F.) may exist in a circuit, but no current 
 can flow until the circuit is closed or until the wire is connected so that there 
 will be a path for the current. 
 
 The practical unit of electromotive force is the volt. It is the unit of elec- 
 tric pressure, and fulfils somewhat the same purpose as head of water and steam 
 pressure in hydraulic and steam engineering. The electromotive force fur- 
 nished by an ordinary cell of a battery usually varies from .7 to 2 volts. A 
 Daniell cell gives an electromotive force of 1.072 volts. A pressure of 500 volts 
 is generally used for street-railway work, and, for incandescent lighting, 110 
 volts is common. 
 
 Resistance All conductors offer more or less resistance to the flow of a 
 current of electricity, just as water encounters friction in passing through a 
 pipe. The amount of this resistance depends on the length of the wire, the 
 diameter of the wire, and the material of which the wire is composed. The 
 resistance of all metals also increases with the temperature. 
 
 The practical unit of resistance is the ohm. A conductor has a resistance 
 of 1 ohm when the pressure required to set up 1 amp. through it is 1 volt. In 
 other words, the drop, or fall, in pressure through a resistance of 1 ohm, when 
 a current of 1 ampere is flowing, is 1 volt. 1,000 ft. of copper wire .1 in. in 
 diameter has a resistance of nearly 1 ohm at ordinary temperatures. 
 
 Ohm's Law. The law governing the flow of current in an electric circuit 
 was first stated by Dr. G. S. Ohm, and is known as Ohm's law. It may be 
 briefly stated as follows: The strength of the current in any circuit is equal to 
 the electromotive force divided by the resistance of the circuit. 
 
 Let E = electromotive force, in volts; 
 
 R = resistance, in ohms; 
 / = current, in amperes. 
 
 Then, / = ! R = j E = IR 
 
 EXAMPLE 1. A dynamo D generating 110 volts, is connected to a coil of 
 wire C that has a resistance of 20 ohms; what .current will flow, supposing the 
 resistance of the rest of the circuit to be negligible? 
 
 SOLUTION. As = 110 volts and R = 20 ohms, 
 by Ohm's law 7 = 110-:- 20 = 5.5 amp. 
 
 EXAMPLE 2. If the resistance of the coil C is 
 6 ohms, what electromotive force must the dynamo ( j) )E=110 Volts 
 
 generate in order to set up a current of 15 amp. V J C 
 
 through it? ' 
 
 SOLUTION. In this case the third formula will 
 be used; that is, = 15X6 = 90 volts. 
 
 In case the current and electromotive force are known, the resistance of 
 the circuit may be calculated by using the second formula. 
 
 EXAMPLE 3. If the current in the previous examples were 8 amp. and the 
 electromotive force of the dynamo 110 volts, what is the resistance of the 
 circuit? 
 
 SOLUTION. 1? = 110-;- 8 = 13.75 ohms. 
 
 Electric Power. The electric power expended in any circuit is found by 
 multiplying the current flowing in the circuit by the pressure required to force 
 
486 
 
 ELECTRICITY 
 
 the current through the circuit. In other words, W = EI, where W is the 
 power expended, E is the electromotive force and / is the current. When E 
 is expressed in volts and / in amperes, then W is expressed in watts. The 
 watt is the unit of electric power, and is equal to the power developed when 
 1 amp. flows under a pressure of 1 volt. The watt is equal to 7 j^ H. P. 
 Let E = electronwtive force, in volts; 
 
 / = current, in amperes; 
 R = resistance, in ohms; 
 W= power, in watts;' 
 H. P. = horsepower. 
 
 Then, W=EI = PR = ^ 
 
 The energy used in forcing a current through the wire reappears in the form 
 of heat; the heating effect of a current flowing in a conductor being proportional 
 to the square of the current. Furthermore, 
 
 H ' P ' = 746 = 746 
 
 This relation is very useful for calculating power in terms of electric units. 
 The watt is too small a unit for convenient use in^ many cases, so that the 
 kilowatt or 1,000 watts, is frequently used. This is sometimes abbreviated 
 to K. W. 
 
 The unit of work is the watt-hour, which is the total work done when 1 watt 
 is expended for 1 hr. For example, if a current of 1 amp. flows for 1 hr. through 
 a resistance of 1 ohm, the total amount of work done is 1 watt-hour. A kilo- 
 watt-hour is the total work done when 1 K. W. is expended for 1 hr. It is 
 about equivalent to If H. P. for 1 hr. The work done when 1 watt is expended 
 for 1 sec. is called the joule; or 1 joule is expended in a circuit when 1 volt causes 
 1 amp. to pass through the circuit for 1 sec. 
 
 ELECTRICAL EXPRESSIONS AND THEIR EQUIVALENTS 
 
 (Arranged for Convenient Reference by C. W. Hunt) 
 
 
 Rate of doing work 
 1. amp. per sec. at 
 
 
 Quantity of work 
 2,654.28 ft.-lb. 
 
 
 1 volt 
 
 1TTT- J.J. 
 
 .503 mi.-lb. 
 
 
 .7373 ft.-lb. per sec. 
 
 Watt- 
 
 T-Tnnp 
 
 1. amp. hr.Xl 
 
 1 Watt. 
 
 44.238 ft.-lb. per min. 
 
 riou.r 
 
 volt 
 
 
 2,654.28 ft.-lb. per hr. 
 
 >:/!" v ,- 
 
 .00134 H. P.-hr. 
 
 
 .5027 mi.-lb. per hr. 
 
 
 T& H. P.-hr. 
 
 
 .00134 H. P. 
 
 
 [Quantity of work 
 
 I Tig 1. r. 
 
 {Rate of doing work 
 737.3 ft.-lb. per sec. 
 44,238. ft.-lb. per min. 
 502.7 mi.-lb. per hr. 
 1.34 H. P. 
 IRate of doing work 
 550. ft.-lb. per sec. 
 33,000. ft.-lb. per min. 
 
 1 Ampere- 
 Hour ' 
 
 1,980,000. ft.-lb. 
 375. mi.-lb. 
 746. watt-hr. 
 .746 K. W.-hr. 
 [Quantity of current 
 1 amp. flowing for 1 hr., 
 irrespective of voltage 
 Watt-hour -j- volts 
 
 375. mi.-lb. per hr. 
 
 ( Force moving in a circle 
 
 746. watts 
 
 Torque < 
 
 Force of 1 Ib. at a radius 
 
 .746 K. W. 
 
 I of 1 ft. 
 
 CIRCUITS 
 
 The path through which a current flows is generally spoken of as an elec- 
 tric circuit; this path may be made up of a number of different parts. For 
 example, the line wires may constitute part of the circuit, and the remainder 
 may be composed of lamps, motors, resistances, etc. In practice, the two 
 kinds of circuits most commonly met with are those in which the different 
 parts of the circuit are connected in series and those in which they are connected 
 in multiple or parallel. 
 
 Series Circuits. In a series circuit, all the component parts are connected 
 in tandem, so that the current flowing through one part also flows through 
 the other parts; view (a) represents such a circuit made up of a different number 
 
ELECTRICITY 
 
 487 
 
 of parts. The current leaves the dynamo D at the + side and flows through 
 the arc lamps a, thence through the incandescent lamps I, thence through the 
 motor m and resistance r, back to the dynamo, thus making a complete cir- 
 cuit. All these parts are here connected in series, so that the current flowing 
 through each of the parts must be the same unless leakage takes place across 
 from one side of the circuit to the other, and this is not appreciable if the lines 
 are properly insulated. The pressure furnished by the dynamo must evi- 
 dently be the sum of the pressures required to force the current through the 
 different parts. 
 
 The most common use of this system is in connection with arc lamps, 
 which are usually connected in series, as shown in (fc). The objections to 
 
 Trolley Wire 
 
 ] this system of distribution 
 
 for general work are that 
 6i the breaking of the circuit 
 at any point cuts off the 
 Ol current from all parts of 
 the circuit; also, the pres- 
 1 sure generated by the dy- 
 namo must be very high 
 
 (e) if many pieces of appa- 
 
 ratus are connected in 
 
 series. In such a system, the dynamo is provided with an automatic regulator 
 that increases or decreases the voltage of the machine, so that the current in 
 the circuit is kept constant, no' matter how many lamps or other devices are 
 in operation. For this reason, such circuits are often spoken of as constant- 
 current circuits. 
 
 Parallel Circuits. In a parallel circuit, the different pieces of apparatus 
 are connected side by side, or in parallel, across the main wires from the dynamo 
 as shown in (c). In this case, the dynamo D supplies current through the mains 
 to the arc lamps a, incandescent lamps I, and motor m. This system is more 
 widely used, as the breaking of the circuit through any one piece of apparatus 
 will not prevent the current from flowing through the other parts. Incan- 
 descent lamps are connected in this way almost exclusively. The lamps are 
 connected directly across the mains, as shown in (d). Street cars and mining 
 locomotives are operated in the same way, the trolley wire constituting one 
 main and the track the other, as shown in (e). By adopting this system, any 
 car can move independently of the others, and the current in each device 
 may be turned off and on at will without affecting devices in other parallel 
 circuits. In all these systems of parallel distribution, the pressure generated 
 by the dynamo is maintained as constant as practicable, no matter what cur- 
 rent the dynamo may be delivering. For example, in the lamp system, view (d) , 
 the dynamo will maintain a constant electromotive force of 110 volts. Each 
 lamp has a fixed resistance, and will take a certain current (110 + R amperes) 
 when connected across the mains. As the lamps are turned on, the current 
 delivered by the dynamo increases, the pressure remaining constant. In 
 street-railway work, the pressure between trolley and track is kept in the 
 neighborhood of 500 volts, the current varying with the number of cars in 
 operation. In mine-haulage plants, the pressure is usually 250 or 500 volts, 
 the former being generally preferred as being less dangerous. Lamps may also 
 be connected in series multiple, as shown in (e). Here the two 125- volt lamps / 
 
488 ELECTRICITY 
 
 are connected in series across the 250-volt circuit. Such an arrangement is 
 frequently used in mines when lamps are operated from the haulage circuit. 
 
 Such circuits as those just described are called constant-potential or con- 
 stant-pressure circuits, to distinguish them from the constant-current circuit 
 mentioned previously. _ 
 
 RESISTANCES IN SERIES AND MULTIPLE 
 
 Resistance in Lines. If two or more resistances are connected in series, 
 as in Fig. 1, their total combined resistance is equal to the sum of their sepa- 
 
 rate resistances. If R equals 
 
 tances connected in series, then, 
 p IG . 1 R = Ri+R 2 +R 3 . 
 
 For example, if the separate 
 
 resistances are Ri = 10 ohms, Rz=l ohm, andJ? 3 = 30 ohms, the three combined 
 will be equivalent to a single resistance of 10 + 1+30 = 41 ohms. 
 
 Resistances in Parallel. If a number of resistances are connected in parallel, 
 the reciprocal of their combined resistance is equal to the sum of the reciprocals 
 of the separate resistances. In Fig. 2, three resis- 
 tances are shown connected in parallel; therefore, the 
 total resistance of such a combination must be lower 
 than that of the lowest resistance entering into the 
 combination. If the resistances in this case were all 
 equal, the resistance of the three combined would 
 be one-third the resistance of one of them, because 
 
 a current passing through the three combined 
 
 could split up equally between three equal paths, instead of having only 
 one path to pass through. If R represents the combined, resistance, 
 and Ri, Rz, Rs, and Jfa, the separate resistances, the following relation 
 
 is true for any number of resistances in parallel: -^ = -?r + ^ h^r+^r+etc. 
 
 K Ki K.2 Ks Kt 
 
 from which R = ~^ - ; - ; - ; - If three resistances in parallel are 
 
 E+S+S+J&+*'- 
 13 #1 
 
 ^ == ^' orR= ^- 
 
 EXAMPLE. Three resistances of 3, 10, and 5 ohms are connected in par- 
 allel; what is their combined resistance? 
 
 SOLUTION.- = ++ or, K = - = = 1.58 ohms. 
 
 If resistances in parallel are all equal, the current will divide equally 
 
 through them; if not equal, the current in each path will be inversely pro- 
 
 _ X _ >O _- N portional to the resistance of the path. In any 
 
 r ^0000 - 1 case - the current through any path is equal to 
 
 A the difference of potential across the path divided 
 
 I ^TWwWr^ * by its resistance. 
 
 UUWUU Shunt. When one circuit B, Fig. 3, is con- 
 
 nected across another A, so as to form, as it 
 
 ^ IG - " were, a by-pass, or side track, for the current, 
 
 such a circuit is called a shunt, or it is said to be in shunt with the other circuit 
 
 ELECTRIC WIRING (CONDUCTORS) 
 
 Materials. Practically all conductors used in electric lighting or power 
 work are of copper, this metal being used on account of its low resistance. 
 Iron wire is used to some extent for conductors in telegraph lines, and steel 
 is largely used as the return conductor in electric-railway or haulage plants 
 where the current is led back to the power station through the rails. The 
 resistance of iron or steel varies from six to seven times that of copper, depend- 
 ing on the quality of the metal. Aluminum is coming into use in electric 
 transmission. It is so much lighter than copper that it is able to compete 
 with-it as a conductor, even though its cost per pound is higher and its con- 
 ductivity only about 60% that of copper. 
 
ELECTRICITY 
 
 489 
 
 PROPERTIES OF ANNEALED COPPER WIRE; AMERICAN, OR 
 BROWN & SHARPE, GAUGE 
 
 
 
 * 
 
 
 ^ 
 
 Current 
 
 
 * 
 
 a 
 
 
 
 Capacity 
 
 <u 
 
 
 m 
 
 Weight 
 
 
 National 
 
 f 
 
 S 
 
 a ^ 
 
 
 o 
 
 Board Fire 
 
 Jo 
 
 c 
 
 3 1? 
 
 oun 
 
 T! 1 * pc,' 
 
 Underwriters 
 
 N 
 
 
 
 O 
 
 
 P, O o 
 
 Amperes 
 
 <& 
 
 
 
 S o 
 
 
 
 C 
 
 , 
 
 
 PQ 
 
 5 
 
 1 
 
 g| 
 
 fc.-S 
 
 
 ll 
 
 11 
 
 
 
 
 
 *! 
 
 *E 
 
 1~ 
 
 !# 
 
 &8 
 
 0000 
 
 460.00 
 
 211,600.00 
 
 641.0000 
 
 3,380.000 
 
 .0500 
 
 312 
 
 210 
 
 000 
 
 409.60 
 
 167,805.00 
 
 508.0000 
 
 2,680.000 
 
 .0630 
 
 262 
 
 177 
 
 00 
 
 364.80 
 
 133,075.00 
 
 403.0000 
 
 2,130.000 
 
 .0795 
 
 220 
 
 150 
 
 
 
 324.90 
 
 105,534.00 
 
 319.0000 
 
 1,690.000 
 
 .1000 
 
 185 
 
 127 
 
 1 
 
 289.30 
 
 83,694.00 
 
 253.0000 
 
 1,340.000 
 
 .1260 
 
 156 
 
 107 
 
 2 
 
 257.60 
 
 66,373.00 
 
 201.0000 
 
 1,060.000 
 
 .1590 
 
 131 
 
 90 
 
 3 
 
 229.40 
 
 52,634.00 
 
 159.0000 
 
 841.000 
 
 .2010 
 
 110 
 
 76 
 
 4 
 
 204.30 
 
 41,742.00 
 
 126.0000 
 
 667.000 
 
 .2530 
 
 92 
 
 65 
 
 5 
 
 181.90 
 
 33,102.00 
 
 100.0000 
 
 529.000 
 
 .3200 
 
 77 
 
 54 
 
 6 
 
 162.00 
 
 26,251.00 
 
 79.5000 
 
 420.000 
 
 .4030 
 
 65 
 
 46 
 
 7 
 
 144.30 
 
 20,816.00 
 
 63.0000 
 
 333.000 
 
 .5080 
 
 
 
 8 
 
 128.50 
 
 16,509.00 
 
 50.0000 
 
 264.000 
 
 .6410 
 
 46 
 
 33 
 
 9 
 
 114.40 
 
 13,094.00 
 
 39.6000 
 
 209.000 
 
 .8080 
 
 
 
 10 
 
 101.80 
 
 10,381.00 
 
 31.4000 
 
 166.000 
 
 1.0200 
 
 32 
 
 24 
 
 11 
 
 90.70 
 
 8,234.00 
 
 24.9000 
 
 132.000 
 
 1.2800 
 
 
 
 12 
 
 80.80 
 
 6,529.90 
 
 19.8000 
 
 104.000 
 
 1.6200 
 
 23 
 
 17 
 
 13 
 
 71.90 
 
 5,178.40 
 
 15.7000 
 
 82.800 
 
 2.0400 
 
 
 
 14 
 
 64.10 
 
 4,106.80 
 
 12.4000 
 
 76.200 
 
 2.5800 
 
 16 
 
 12 
 
 15 
 
 57.10 
 
 3,256.70 
 
 9.8600 
 
 52.000 
 
 3.2500 
 
 
 
 16 
 
 50.80 
 
 2,582.90 
 
 7.8200 
 
 41.300 
 
 4.0900 
 
 8 
 
 6 
 
 17 
 
 45.20 
 
 2,048.20 
 
 6.2000 
 
 32.700 
 
 5.1600 
 
 
 
 18 
 
 40.30 
 
 1,624.30 
 
 4.9200 
 
 25.900 
 
 6.5100 
 
 5 
 
 3 
 
 19 
 
 35.90 
 
 1,288.10 
 
 3.9000 
 
 20.600 
 
 8.2100 
 
 
 
 20 
 
 31.90 
 
 1,021.50 
 
 3.0900 
 
 16.300 
 
 10.4000 
 
 
 
 21 
 
 28.50 
 
 810.10 
 
 2.4500 
 
 12.900 
 
 13.1000 
 
 
 
 22 
 
 25.30 
 
 642.40 
 
 1.9400 
 
 10.300 
 
 16.5000 
 
 
 
 23 
 
 22.60 
 
 509.40 
 
 1.5400 
 
 8.100 
 
 20.8000 
 
 
 
 24 
 
 20.10 
 
 404.00 
 
 1.2200 
 
 6.400 
 
 26.2000 
 
 
 
 25 
 
 17.90 
 
 . 320.40 
 
 .9700 
 
 5.100 
 
 33.0000 
 
 
 
 26 
 
 15.90 
 
 254.10 
 
 .7690 
 
 4.000 
 
 41.6000 
 
 
 
 27 
 
 14.20 
 
 201.50 
 
 .6100 
 
 3.200 
 
 52.5000 
 
 
 
 28 
 
 12.60 
 
 159.70 
 
 .4840 
 
 2.500 
 
 66.2000 
 
 
 
 29 
 
 11.20 
 
 126.70 
 
 .3840 
 
 2.000 
 
 83.5000 
 
 
 
 30 
 
 10.00 
 
 100.50 
 
 .3040 
 
 1.600 
 
 105.0000 
 
 
 
 31 
 
 8.93 
 
 79.70 
 
 .2410 
 
 1.270 
 
 133.0000 
 
 
 
 32 
 
 7.95 
 
 63.21 
 
 .1910 
 
 1.010 
 
 167.0000 
 
 
 
 33 
 
 7.08 
 
 50.13 
 
 .1520 
 
 .801 
 
 211.0000 
 
 
 
 34 
 
 6.30 
 
 39.75 
 
 .1200 
 
 .635 
 
 266.0000 
 
 
 
 35 
 
 5.61 
 
 31.52 
 
 .0954 
 
 .504 
 
 336.0000 
 
 
 
 36 
 
 5.00 
 
 25.00 
 
 .0757 
 
 .400 
 
 423.0000 
 
 
 
 37 
 
 4.45 
 
 19.83 
 
 .0600 
 
 .317 
 
 533.0000 
 
 
 
 38 
 
 3.96 
 
 15.72 
 
 .0476 
 
 .251 
 
 673.0000 
 
 
 
 39 
 
 3.53 
 
 12.47 
 
 .0377 
 
 .199 
 
 848.0000 
 
 
 
 40 
 
 3.14 
 
 9.89 
 
 .0299 
 
 .158 
 
 1,070.0000 
 
 i 
 
490 ELECTRICITY 
 
 Most of the conductors used are in the form of copper wire of circular 
 cross-section. Conductors of large cross-section are made up of a number 
 of strands of smaller wire twisted together. For electrolytic plants, copper- 
 refining plants, etc., copper bars of rectangular cross-section are frequently 
 used. On account of the method used in supporting the larger sizes, large 
 trolley wires are not always of circular cross-section. 
 
 Wire Gauge. The gauge most generally used in America to designate 
 the different sizes of copper wire is the American, or Brown & Sharpe (B. & S.). 
 The sizes as given by this gauge range from No. 0000, the largest, .460 in. 
 diameter, to No. 40, the finest, .003 in. diameter. Wire drawn to the sizes 
 given by this gauge is always more readily obtained than sizes according to 
 other gauges; hence, when selecting wire for any purpose it is always desirable, 
 if possible, to give the size required as a wire of the B. & S. gauge. A wire 
 can usually be selected from this gauge, which will be very nearly that required 
 for any specified case. 
 
 The diameter of round wires is usually given in the tables in decimals of 
 an inch and the so-called area of cross-section is given in terms of a unit called 
 a circular mil. This is done simply for convenience, as it makes calculations 
 involving the cross-section much simpler than if the square inch was used as 
 the unit area. A mil is ^Vs in., or .001 in. A circular mil is the square of 
 the diameter of a wire expressed in mils. A wire having a diameter of 1 in. 
 has a sectional area of .7854 XI 2 = .7854 sq. in., and is said to have a 
 sectional area of 1,000 2 = 1,000,000 circular mils. Hence, the area of cross- 
 section of a wire in circular mils is equal to the square of its diameter expressed 
 in mils. CM is frequently used as an abbreviation for circular mils. 
 
 EXAMPLE. A wire has a diameter of .101 in.; what is its area in circular mils? 
 
 SOLUTION. .101 in. = 101 mils. Hence, (101)2 = 10,201 CM. 
 
 CARRYING CAPACITY OF COPPER CABLES 
 
 Area 
 
 Current, in Amperes 
 
 Area 
 
 Current, in Amperes 
 
 Mils 
 
 Exposed 
 
 Concealed 
 
 Mils 
 
 Exposed 
 
 Concealed 
 
 200,000 
 
 299 
 
 200 
 
 1,200,000 
 
 1,147 
 
 715 
 
 300,000 
 
 405 
 
 272 
 
 1,300,000 
 
 1,217 
 
 756 
 
 400,000 
 
 503 
 
 336 
 
 1,400,000 
 
 1,287 
 
 796 
 
 500,000 
 
 595 
 
 393 
 
 1,500,000 
 
 1,356 
 
 835 
 
 600,000 
 
 682 
 
 445 
 
 1,600,000 
 
 1,423 
 
 873 
 
 700,000 
 
 765 
 
 494 
 
 1,700,000 
 
 1,489 
 
 910 
 
 800,000 
 
 846 
 
 541 
 
 1,800,000 
 
 1,554 
 
 946 
 
 900,000 
 
 924 
 
 586 
 
 1,900,000 
 
 1,618 
 
 981 
 
 1,000,000 
 
 1,000 
 
 630 
 
 2,000,000 
 
 1,681 
 
 1,015 
 
 1,100,000 
 
 1,075 
 
 673 
 
 
 
 
 COMPARISON OF PROPERTIES OF ALUMINUM AND COPPER 
 
 
 Aluminum 
 
 Copper 
 
 Conductivity, for equal sizes 
 
 .54 to .63 
 
 1 
 
 Weight, for equal sizes 
 
 33 
 
 1 
 
 Weight, for equal length and resistance . . 
 Price of bare wire, per pound, aluminum, 
 29 o.; copper, 16 c 
 Price, equal length and resistance, bare 
 line wire 
 
 .48 
 1.81 
 868 
 
 1 
 1 
 1 
 
 Temperature coefficient, per degree F. . . . 
 Resistance of mil-foot, at 20 C. 
 
 .002138 
 18 73 
 
 .002155 
 10.5 
 
 Specific gravity 
 
 2 5 to 2 68 
 
 8 89 to 8 93 
 
 Breaking strength, equal sizes 
 
 1 
 
 1 
 
 
 
 
ELECTRICITY 
 
 491 
 
 The table on page 489 gives the dimensions, weight, and resistance of 
 annealed copper wire. The weights given are, of course, for bare wire. The 
 first column gives the B. & S. gauge number, the second the diameter in mils. 
 The diameter in inches will be the number given in this column, divided by 
 1,000. The third column gives the area in circular mils, the numbers in this 
 column being equal to the squares of those in the second column. The safe 
 carrying capacity is also given. In case a conductor larger than that given in 
 the table is required, stranded cables are used; these are made in various sizes. 
 The first table on page 490 gives some of the more common sizes of stranded 
 copper cables, with their allowable current capacity, while a comparison of the 
 properties of aluminum and copper is given in the second table on page 490. 
 
 Estimation of Resistance. The resistance of any conductor is directly pro- 
 portional to its length, and inversely proportional to its area of cross-section, 
 
 or R = K , where K is a constant. If L is expressed in feet and A is expressed 
 
 A 
 in circular mils, the constant K must be the resistance of 1 ft. of the wire in 
 
 BREAKING STRENGTH OF COPPER AND ALUMINUM WIRES 
 AND CABLES 
 
 
 
 Breaking Strain, Pounds 
 
 Wire 
 Number 
 
 Area 
 Circular 
 
 Copper, Solid 
 
 Aluminum 
 
 B. &S. 
 
 Mils 
 
 
 
 Gauge 
 
 
 
 
 
 
 
 
 Annealed 
 
 Hard- 
 Drawn 
 
 Solid 
 
 Stranded 
 
 0000 
 
 211,600 
 
 5,650 
 
 8,310 
 
 4,320 
 
 6,830 
 
 000 
 
 167,805 
 
 4,475 
 
 6,580 
 
 3,430 
 
 5,420 
 
 00 
 
 133,079 
 
 3,550 
 
 5,226 
 
 2,720 
 
 4,290 
 
 
 
 105,592 
 
 2,800 
 
 4,558 
 
 2,150 
 
 3,410 
 
 1 
 
 83,695 
 
 2,225 
 
 3,746 
 
 1,710 
 
 2,700 
 
 2 
 
 66,373 
 
 1,775 
 
 3,127 
 
 1,355 
 
 2,143 
 
 3 
 
 52,634 
 
 1,400 
 
 2,480 
 
 1,075 
 
 1,700 
 
 4 
 
 41,743 
 
 1,115 
 
 1,967 
 
 852 
 
 1,350 
 
 5 
 
 33,102 
 
 885 
 
 1,519 
 
 657 
 
 1,070 
 
 6 
 
 26,251 
 
 700 
 
 1,237 
 
 536 
 
 850 
 
 7 
 
 20,817 
 
 550 
 
 980 
 
 426 
 
 
 8 
 
 16,510 
 
 440 
 
 778 
 
 337 
 
 
 9 
 
 13,094 
 
 350 
 
 617 
 
 267 
 
 
 10 
 
 10,382 
 
 275 
 
 489 
 
 212 
 
 
 11 
 
 8,234 
 
 220 
 
 388 
 
 167 
 
 
 12 
 
 6,230 
 
 175 
 
 307 
 
 133 
 
 
 13 
 
 5,178 
 
 135 
 
 244 
 
 105 
 
 
 14 
 
 4,107 
 
 110 
 
 193 
 
 84 
 
 
 question of 1 circular mil cross-section. The resistance of 1 mil-ft. of copper 
 
 wire at 75 P. is about 10.8 ohms. Hence, for copper wire, R = ~, in which d 
 
 a 2 
 
 is the diameter in mils. This formula is easily remembered, and is very con- 
 venient for estimating the resistance of any length of wire of given diameter 
 when a wire table is not at hand, 9r when the diameter of the given wire does 
 not correspond to anything given in the table. 
 
 EXAMPLE. Find the resistance of 1 mi. of copper wire .20 in. in diameter. 
 
 SOLUTION. 1 mi. = 5,280 ft.; .20 in. = 200 mils, or 40,000 C. M.; hence, 
 
 10.8XL 10.8X5.280 
 R = ^ 40,000 = L42ohms 
 
 The breaking strengths of copper and aluminum wires and cables are given 
 in the preceding table. The ultimate strength of annealed copper is taken 
 as 34,000 Ib. per sq. in.; of hard-drawn copper, as 60,000 Ib. per sq. in., except 
 that for Nos. 000 and 00 it is taken at 50,000 Ib., for No. at 55,000 Ib., 
 and for No. 1 as 57,000 Ib. The ultimate strength of aluminum is taken as 
 26,000 Ib. per sq. in. The table gives the actual breaking strains to which 
 a suitable factor of safety must be applied to give a safe working load. 
 
492 ELECTRICITY 
 
 CALCULATION OF WIRES FOR ELECTRIC 
 TRANSMISSION 
 
 Direct-Current Circuits. No matter how large a wire may be, some energy 
 must always be expended in forcing a current through it, because no con- 
 ductor can be entirely devoid of resistance. It is true that the loss may be 
 made as small as desired by using a very large conductor, but in practice this 
 will not pay, because the interest on the cost of the copper will more than 
 counterbalance the gain in the efficiency of transmission. In starting out, then, 
 to estimate the size of wire to transmit a given amount of power over a given 
 distance, one of the first things to be decided is the amount of power that may 
 be allowed for loss in the line, because the greater the power lost the higher 
 may be the line resistance, and hence the smaller the wire. The pressure 
 required to force a current I through a wire of a resistance R is IXR. This 
 pressure is generally spoken of as the drop, for the reason that the pressure 
 necessary to set up the current through the line is lost, and, consequently, the 
 pressure falls off or drops from the dynamo to the receiving end of the line. 
 In all cases, the pressure at the end of the line, or point where the power is 
 delivered, is equal to the pressure .at the dynamo less the drop in the line, and, 
 conversely, the pressure that must be maintained by the dynamo in order to 
 obtain a given pressure at the end of the line will be equal to the pressure at 
 the receiving end plus the drop in the line. 
 
 This is shown in the accompanying illustration, where a dynamo D sup- 
 plies current to a motor M situated 1 mi. distant. In order that the motor 
 may operate properly, the pressure at its terminals must be kept constant at, 
 say 500 volts; therefore, the pressure between a and b (the dynamo terminals) 
 must be more than 500 volts by the drop or pressure necessary to force the 
 current through the line. If the motor is taking very little current, that is, 
 if it is running on a very light load, the current will be small, and hence the 
 drop in the line will be small. In order, then, that the pressure at the motor 
 may remain constant, or nearly so, the pressure at the dynamo must auto- 
 matically increase as the load increases and the line must be designed with 
 regard to the maximum current it has to carry. It will be supposed that the 
 motor takes 50 amp. at full load and that the line wire has a resistance of 
 .2 ohm per mi. The current has to pass through 2 mi. of wire (because it has 
 to flow out through 1 mi. and back through 1 mi.), and hence encounters a 
 resistance of .4 ohm. The drop in the line will then be .4X50 = 20 volts, 
 and in order to obtain a pressure of 500 volts at the motor, the pressure at the 
 dynamo will have to be 520 volts. The loss of power in the line would be 
 current X drop = 50X20 = 1,000 watts, or about 1J H. P. The drop in an 
 electric-transmission line is analogous to the loss in pressure due to the fric- 
 tion encountered by water flowing through a pipe line. 
 
 If, in the illustration just 
 given, the wire had a resistance 
 of .1 ohm per mi.', the loss in 
 the line would be halved, but 
 the weight of copper required 
 doubled, because the wire would 
 have to be double the cross- 
 section. The question as to 
 whether it would pay better to 
 invest more money in the line 
 or to put up with the larger 
 
 loss is something that must be 
 
 determined in each case by 
 the relative cost of power and copper. 
 
 In many cases, the loss allowed in the line is about 10% of the power to be 
 delivered, though sometimes the loss may be allowed to run as high as 15% 
 or 25%. This applies only to transmission lines. For local electric-light or 
 power-distributing systems, the amount of drop allowed is usually about 2% 
 for the former and 5% for the latter. 
 
 The problem of calculating line wires usually presents itself in the follow- 
 ing form: Given, a certain amount of power to transmit over a known dis- 
 tance with a certain allowable loss, to determine the cross-section of the wire 
 required. 
 
 Let P = power to be delivered, expressed in watts; P will be equal to horse- 
 power delivered at end of line multiplied by 746; 
 
ELECTRICITY 493 
 
 % = allowable percentage of loss in line, that is, percentage of power 
 
 delivered that may be lost in transmission; 
 E = voltage at end of line where power is delivered ; 
 / = current at full load ; 
 
 L = length of wire through which current flows. 
 
 The cross-section of the copper conductor will then be given by the for- 
 mula: 
 
 The circular mils will be d 2 , and the corresponding size of wire may be found 
 by consulting the wire table. It should be noticed, particularly, that in this 
 formula, L is the average length of conductor through which the current / 
 flows. The application of distance of transmission in the formula is shown 
 in the following example: 
 
 EXAMPLE. A mine pump, driven by an electric motor, is situated 2 mi. 
 from the power station. The electric input of the motor at full load is 50 H. P., 
 and the voltage at its terminals is to be 500. Estimate the size of line wire 
 necessary to supply the motor, the allowable loss in the line being 15% of the 
 power delivered. 
 
 SOLUTION. The actual length of line through which the current will flow 
 will be 4 mi., because the current has to flow out to the motor and back again. 
 Then 
 
 _ watts 50X746 
 I = ~E ---- 500 
 
 Applying the formula, 
 
 A M 10-8X2X2X5,280X74.6X100 00 . C0ft n ., 
 A = d z = = 226,880 C. M., nearly 
 
 ouuxio 
 
 By consulting the wire table it is found that this calls for a wire a little 
 larger than No. 0000, which has a cross-section of 211,600 C. M.; No. 0000 
 wire would probably be used in this case, as it is near enough to the calculated 
 size for all practical purposes. In case the calculated size comes out larger 
 than any size given in the table, a number of wires may be used in multiple to 
 make up the required cross-section, or, what is better, a stranded cable may 
 be used. These heavy stranded cables may now be obtained in different sizes, 
 up to 2,000,000 C. M. cross-section. 
 
 If it were allowable to waste twice as much power in the line, or what is 
 equivalent to having a line drop of 150 volts instead of 75 volts, the cross- 
 section of wire required would be one-half of that just found. Such a large 
 amount of loss would, however, be objectionable unless power was very cheap. 
 A large drop in the line is in any case objectionable, because the voltage at the 
 receiving end of the circuit will fall off greatly unless the voltage at the gen- 
 erating station is raised as the load conies on in order to compensate for the 
 line drop. Most of the uses to which electricity is put, in mines or other places, 
 require that the pressure at the point where the power is utilized shall be 
 kept approximately constant. For example, in the case of incandescent 
 lights, the lamps will fall off greatly in brightness if the pressure decreases 
 even by a comparatively slight amount. Also, if motors are being operated, 
 the speed will vary considerably if the pressure is not kept constant, and it 
 may be stated, in general, that a large line loss tends to poor regulation at 
 the end of the circuit where power is delivered. 
 
 From these considerations, it is evident that the size of wire to be used 
 under given conditions is determined by the allowable amount of drop. In 
 some cases, however, especially if the current is to be used near at hand, the 
 size of wire so determined might not be large enough to carry .the current with- 
 out overheating. Of course, in such cases, the safe carrying capacity of the 
 wire determines the size to be used, and the drop will be correspondingly less. 
 The amount of current that a given wire can carry without overheating depends 
 very largely on the location of the wire. For example, a wire strung in the 
 open air will carry a greater current, with a given temperature rise, than the 
 same wire when boxed up in a molding or conduit. 
 
 In order to keep down the size of wire required to transmit a given amount 
 of power over a given distance, with a certain allowable loss, the current must 
 be kept as small as possible. Now, for a given amount of power, the current 
 can only be made small by increasing the pressure, because the number of 
 watts, or power delivered, is equal to the product of the current and the pressure. 
 As a matter of fact, if the pressure in any given case is doubled, the amount of 
 copper required will be only one-fourth as great; in other words, for a given 
 
494 
 
 ELECTRICITY 
 
 amount of power transmitted, the weight of copper required decreases as the 
 square of the voltage. It is at once seen, then, that if any considerable amount 
 of power is to be transmitted over long distances, a high line pressure must be 
 used or else the cost of copper becomes prohibitory. The use of high pressures 
 in power transmission will be taken up in connection with alternating currents. 
 Insulated Wires. For most overhead line work using modern voltages, 
 weather-proof insulated wire is used. This wire is covered with two or three 
 braids of cotton, and treated with insulating compound. For inside work, 
 and in places where a better quality of insulation is required, rubber-covered 
 wires are used. The accompanying table gives the approximate weight of 
 weather-proof line wire. The cost of the wire per pound varies considerably, 
 owing to variations in the price of copper. 
 
 WEATHER-PROOF LINE WIRE (ROEBLING'S) 
 
 
 Double Braid 
 
 Triple Braid 
 
 Number 
 B. &S. 
 
 Outside 
 
 Weight, in Pounds 
 
 Outside 
 
 Weight, in Pounds 
 
 (jctllgC 
 
 Diameter 
 
 
 
 Diameter 
 
 
 
 
 32ds In. 
 
 Per 
 
 Per 
 
 32ds In. 
 
 Per 
 
 Per 
 
 
 
 1,000 Ft. 
 
 Mile 
 
 
 1,000 Ft. 
 
 Mile 
 
 0000 
 
 20 
 
 716 
 
 3,781 
 
 24 
 
 775 
 
 4,092 
 
 000 
 
 18 
 
 575 
 
 3,036 
 
 22 
 
 630 
 
 3,326 
 
 00 
 
 17 
 
 465 
 
 2,455 
 
 18 
 
 490 
 
 2,587 
 
 
 
 16 
 
 375 
 
 1,980 
 
 17 
 
 400 
 
 2,112 
 
 1 
 
 15 
 
 285 
 
 1,505 
 
 16 
 
 306 
 
 1,616 
 
 2 
 
 14 
 
 245 
 
 1,294 
 
 15 
 
 268 
 
 1.415 
 
 3 
 
 13 
 
 190 
 
 1,003 
 
 14 
 
 210 
 
 1,109 
 
 4 
 
 11 
 
 152 
 
 803 
 
 12 
 
 164 
 
 866 
 
 5 
 
 10 
 
 120 
 
 634 
 
 11 
 
 145 
 
 766 
 
 6 
 
 9 
 
 98 
 
 518 
 
 10 
 
 112 
 
 591 
 
 8 
 
 8 
 
 66 
 
 349 
 
 9 
 
 78 
 
 412 
 
 10 
 
 7 
 
 45 
 
 238 
 
 8 
 
 55 
 
 290 
 
 12 
 
 6 
 
 30 
 
 158 
 
 7 
 
 35 
 
 185 
 
 14 
 
 5 
 
 20 
 
 106 
 
 6 
 
 26 
 
 137 
 
 16 
 
 4 
 
 14 
 
 74 
 
 5 
 
 20 
 
 106 
 
 18 
 
 3 
 
 10 
 
 53 
 
 4 
 
 16 
 
 85 
 
 For high-tension lines, it is customary to use bare wires and insulate them 
 thoroughly on special porcelain insulators. The ordinary weather-proof wire 
 insulation is of little or no use as a protection when these high pressures are 
 used, and it only makes the line more dangerous because of the false appear- 
 ance of security that it gives. In many cases, it is also better to use bare 
 feeders for mine : haulage plants, because the ordinary insulation soon becomes 
 defective in a mine, and a wire in this condition is really more dangerous than 
 a bare wire, because the latter is known to be dangerous and will be left alone. 
 
 CURRENT ESTIMATES 
 
 Rr | 1 at this will de 
 
 * O O O O 6 is to be used 
 ^< ]_ are usually c 
 
 FIG. 1 
 
 Incandescent Lamps. Before cal- 
 culating the size of wire required for 
 any given case, it is necessary to know 
 the current, and the method of getting 
 at this will depend on what the current 
 for. Incandescent lamps 
 operated on 110- volt cir- 
 cuits, as shown in Fig. 1, or on the 
 three-wire system, as shown in Fig. 2. 
 
 In the three-wire system, two 110- volt dynamos are connected in series so that 
 the voltage across the outside wires is 220. The neutral wire a connects at 
 
ELECTRICITY 495 
 
 the point b where the machines are connected together. The wire a merely 
 serves to carry the difference in the currents on the two sides of the system, 
 in case more lamps should be burning on one side than on the other. The 
 outside wires for such a system are calculated as if the lights were operated 
 two in series across 220 
 volts. The middle wire 
 is usually made equal in 
 size to the outer wires. 
 An ordinary 16-c. p. 
 incandescent carbon- 
 filament lamp requires 
 about 55 watts for its 
 operation; a 32-c. p. 
 lamp requires about 1 10 
 
 watts. Tungsten lamps ,, 
 
 are designated by the 
 watts required rather 
 
 than by the candlepower light they give. Thus, a 25-watt tungsten lamp 
 gives about 20 c. p. Hence, in the case of ordinary parallel distribution, as 
 shown in Fig. 1, the dynamo will deliver about 5 amp. for each 16-c. p. 
 carbon lamp operated, and 1 amp. for each 32-c. p. carbon lamp. In the 
 case of the three-wire system, each pair of 16-c. p. carbon lamps will take 
 J amp., and the total number of amperes in the outside wires will be one-fourth 
 the number of lamps operated. 
 
 EXAMPLE 1. A certain part of a mine is to be illuminated by fifty 16-c. p. 
 carbon lamps and ten 32-c. p. carbon lamps. This portion of the mine is 
 1,000 ft. from the dynamo room, and the allowable drop in pressure is 5%. 
 The lamps are to be run on a 110-volt system. Find the size of wire required. 
 SOLUTION. Fifty 16-c. p. carbon lamps require ....25 amperes 
 Ten 32-c. p. carbon lamps require 10 amperes 
 
 Total current 35 amperes 
 
 10.8X1.000X2X35X100 ,. *-, r AT 
 110X5 - = 137,454 C. M., 
 
 or about a No. 00 B. & S. wire. 
 
 EXAMPLE 2. Take the same case, but suppose the lights to be operated 
 on the three- wire system. 
 
 SOLUTION. There will then be twenty-five 16-c. p. carbon lamps and five 
 32-c. p. carbon lamps on each side of the circuit, and the total current in the 
 outside wires will be 17.5 amp. The voltage between the outside wires will 
 be 220, and 
 
 10.8X1.000X2X17.5X100 ft r . , 
 
 220X5 34,363 C.M., 
 
 or about a No. 5 B. & S. wire. 
 
 If the central wire is made also of this size, this system would require three- 
 eighths the amount of copper called for by the plain 110-volt system. There 
 is the disadvantage that two dynamos are needed. 
 
 NOTE. The length to be used in the wiring formula is the "average dis- 
 tance traversed by the current in the conductor. For example, if, as in Fig. 3 (a) , 
 the lamps were all grouped or bunched at the end of the line, the length 
 used in the formula would be twice that from G to A, because the whole cur- 
 rent has to flow out to A through one main and back through the other. In 
 other words, the whole current here passes through the whole length of the 
 line. In case the load is uniformly distributed all along the line, as shown in (b), 
 the current decreases step by step from the dynamo to the end. In such a 
 case, the length or distance to be used in the formula is one-half that used in 
 the former case, or simply the distance from the dynamo to the end, instead 
 of twice this distance. 
 
 Arc Lamps. Arc lamps are frequently run on constant-potential circuits, 
 and usually consume from 400 to 500 watts. There are so many types of 
 these lamps that it is difficult to give any current estimates that will be gen- 
 erally applicable. Enclosed arc lamps usually take from 3 to 5 amp. when 
 run on 110-volt circuits. 
 
 Motors. Practically all the motors used in mining work are run on the 
 constant-potential system, either at 250 or 500 volts. The efficiency of ordi- 
 nary motors will vary from 65% to 94%, depending on the size. The efficiency 
 is greater with the larger machines, and, for the ordinary run of motors, it will 
 
496 
 
 probably lie between 
 
 ELECTRICITY 
 
 3% and 90%. By efficiency is here meant the ratio 
 
 of the useful output at the pulley or pinion of the motor to the total input. 
 The following table gives the efficiency of motors of ordinary size: 
 
 Approximate Motor Efficiency 
 
 | to li H. P., inclusive = 70-75% efficiency 
 
 3 to 5 H. P., inclusive = 75-80% efficiency 
 
 1\ to 10 H. P., inclusive = 80-85% efficiency 
 
 15 H. P. and upwards = 85-90% efficiency 
 
 If the required output, in horsepower, of a direct-current motor is known, 
 the input, in watts, will be W = ' '. - , and the current required at full 
 
 W 
 load will be 1 = r, where E is the voltage between the mains at the motor. 
 
 CURRENT REQUIRED FOR DIRECT-CURRENT MOTORS 
 
 Horse- 
 
 ' Effi- 
 
 
 Amperes 
 
 
 
 Watts 
 
 
 of 
 
 ciency* 
 Per Cent. 
 
 Input 
 
 110 
 
 220 
 
 250 
 
 500 
 
 550 
 
 
 
 
 Volts 
 
 Volts 
 
 Volts 
 
 Volts 
 
 Volts 
 
 1 
 
 65 
 
 1,148 
 
 10.4 
 
 5.2 
 
 4.58 
 
 2.29 
 
 2.08 
 
 2 
 
 65 
 
 2,295 
 
 20.8 
 
 10.4 
 
 9.16 
 
 4.58 
 
 4.16 
 
 2i 
 
 65 
 
 2,870 
 
 26.0 
 
 13.0 
 
 11.45 
 
 5.72 
 
 5.21 
 
 31 
 
 75 
 
 3,481 
 
 31.6 
 
 15.8 
 
 13.90 
 
 6.90 
 
 6.32 
 
 5 
 
 75 
 
 4,973 
 
 45.1 
 
 22.6 
 
 19.90 
 
 9.95 
 
 9.04 
 
 7* 
 
 80 
 
 6,994 
 
 63.5 
 
 31.7 
 
 27.90 
 
 13.95 
 
 12.70 
 
 10 
 
 80 
 
 9,325 
 
 84.6 
 
 42.3 
 
 37.20 
 
 18.60 
 
 16.90 
 
 15 
 
 85 
 
 13,165 
 
 119.8 
 
 59.9 
 
 52.70 
 
 26.40 
 
 23.90 
 
 20 
 
 85 
 
 17,553 
 
 159.6 
 
 79.8 
 
 70.20 
 
 35.10 
 
 31.90 
 
 25 
 
 90 
 
 20,770 
 
 189.0 
 
 94.5 
 
 83.10 
 
 41.60 
 
 37.80 
 
 30 
 
 90 
 
 24,864 
 
 225.8 
 
 112.9 
 
 99.40 
 
 49.70 
 
 45.20 
 
 40 
 
 90 
 
 33,232 
 
 302.6 
 
 151.3 
 
 133.00 
 
 66.50 
 
 60.50 
 
 50 
 
 90 
 
 41,540 
 
 378.0 
 
 189.0 
 
 166.20 
 
 83.10 
 
 75.60 
 
 75 
 
 90 
 
 62,310 
 
 567.0 
 
 283.5 
 
 249.30 
 
 124.80 
 
 113.40 
 
 100 
 
 93 
 
 80,215 
 
 729.0 
 
 364.5 
 
 320.50 
 
 160.30 
 
 145.70 
 
 125 
 
 93 
 
 100,269 
 
 912.0 
 
 456.0 
 
 401.00 
 
 200.50 
 
 182.30 
 
 150 
 
 93 
 
 120,322 
 
 1,094.0 
 
 547.0 
 
 481.00 
 
 240.70 
 
 219.00 
 
 200 
 
 94 
 
 158,510 
 
 1,442.0 
 
 721.0 
 
 634.00 
 
 317.00 
 
 288.00 
 
 FIG. 3 
 
 Conductors for Electric-Haulage Plants. In electric-haulage plants, the 
 rails take the place of one of the conductors, so that, in calculating the size of 
 feeders required, only the overhead conductors are taken into account. It 
 
 *Efficiencies are taken arbitrarily; a variation in these percentages will 
 make proportionate changes in watts and amperes. 
 
ELECTRICITY 497 
 
 is a difficult matter to assign any definite value to the resistance of the track 
 circuit, as it depends very largely on the quality of the rail bonding at the 
 joints. If this bonding is well done, the resistance of the return circuit should 
 be very low, because the cross-section of the rails is comparatively large. For 
 calculating the supply feeders, the following approximate formula may be used : 
 ., 14XLX/X100 
 
 circular mils = ^..^ , 
 
 X% drop 
 
 In this case, L is the average length of feeder over which the power is to be 
 transmitted. It will be noticed that the constant 10.8 appearing in the previous 
 formulas has here been increased to 14. This has been done to allow, approxi- 
 mately, for the track resistance, but this constant might vary considerably 
 depending on the quality of the rail bonding. If the load is all bunched at 
 the end of the feeder, L is the actual length of the feeder in feet. If the load 
 is uniformly distributed, as it would be if a number of locomotives were 
 continually moving along the line, the distance L in the formula will be taken 
 as one-half that used in the case where the load is bunched at the end. In 
 other words, the whole current / will only flow through an average of one-half 
 the length of the line. 
 
 1200 4 1 400O- 
 
 FIG. 4 
 
 EXAMPLE. In Fig. 4, ab represents a section of track 4,000 ft. long. From 
 the dynamo c to the beginning of the section, the distance is 1,200 ft. The 
 trolley wire is No. 00 B. & S., and is fed from the feeder at regular intervals. 
 Two mining locomotives are operated, each of which takes an average cur- 
 rent of 75 amperes. The total allowable drop to the end of the line is to be 
 5% of the terminal voltage, which is 500 volts. Calculate the size of feeder 
 required, assuming that the constant 14, in the formula, takes account of the 
 resistance of the return circuit. 
 
 SOLUTION. Since the locomotives are moving from place to place, the 
 center of distribution for the load may be taken at the center of the 4,000 ft. 
 The distance L will then be 1,200+2,000 = 3,200 ft. The total current will 
 be 150 amperes; hence, we have 
 
 14X3,200X150X100 
 
 circular mils = = 268,800. 
 
 oOUX 5 
 
 This would require either a stranded cable or the use of two No. 00 wires 
 in parallel from c to a. From a to & we have the No. 00 trolley wire in parallel 
 with the feeder; hence, the section of feeder ab may be a single No. 00 wire. 
 In many cases, the drop is allowed to run as high as 10%, because the loads 
 are usually heavier, and the distances longer, than in the example given above. 
 
 DYNAMOS AND MOTORS 
 
 DIRECT-CURRENT DYNAMOS 
 
 A dynamo, or generator, is a machine for converting mechanical energy into 
 electrical energy by moving conductors relatively to a magnetic field. An 
 electric motor is a machine for converting electrical energy into mechanical 
 energy by the relative motion between conductors carrying a current and a 
 magnetic field. In the case of a dynamo a number of conductors are made to 
 move across a magnetic field by means of a steam engine or other prime 
 mover, and the result is that an electromotive force is set up in the conductors, 
 and this electromotive force will set up a current if the circuit is closed. 
 
 In the case of a motor, a number of conductors are arranged so that they 
 are free to move across a magnetic field, and a current is sent through these 
 conductors from some source of electric current. The current flowing through 
 these conductors reacts on the magnetic field and causes the conductors to move, 
 thus converting the electrical energy delivered to the motor into mechanical 
 
ELECTRICITY 
 
 energy. As far as mechanical construction goes, dynamos and motors are 
 
 almost identical, and the operation of the motor is about the reverse of that of 
 
 the dynamo. 
 
 Dynamos and motors may be divided into two general classes: Dynamos 
 
 and motors for direct current; dynamos and motors for alternating current. 
 
 Direct-current dynamos are those that 
 furnish a current that always flows in the 
 same direction. This kind of dynamo is 
 largely used for incandescent lighting, and 
 also for the operation of street railways. 
 A dynamo generates an electromotive 
 force by the motion of conductors across 
 a magnetic field; hence, there must be a 
 magnet of some kind to set up a magnetic 
 field, known as the field magnet, or simply 
 as the field; and a series of conductors 
 arranged so that they may be moved or 
 revolved in the magnetic field, known as 
 the armature. The field is supplied by 
 means of a powerful electromagnet which 
 is magnetized by the current in the field 
 coils. Fig. 1 shows a typical six-pole 
 magnet of this kind; B are the magnetizing 
 coils, which, when a current is sent through 
 * them, form powerful magnetic poles at N 
 
 and 5. The framework A is usually made of cast iron or cast steel. These 
 
 field mapnets may have any number of poles, but machines of ordinary size 
 
 are usually provided with from two to eight poles. 
 
 The armature usually consists of a number of turns of insulated copper 
 
 wire, arranged around the periphery of a ring or drum built up of soft iron 
 
 sheets. Pig. 2 shows the construction of a typical armature of the ring type. 
 
 The winding is divided into a number of sections, and the terminals connected 
 
 to the commutator. 
 
 This commutator, consists of a number of copper bars, insulated from each 
 
 other by means of mica, the bundle of bars being clamped firmly into place 
 
 COMPLETCARMATWC. 
 
 nsulation,. 
 
 Binding- wires? 
 
 FlG. 2 
 
 and turned up to form a true cylindrical surface. The sections in the commu- 
 tator correspond with those in the armature, and the use and operation of the 
 commutator will be described later. The winding on the ring is endless, that 
 is, it consists of a number of coils or sections c, Pig. 3, the end of one section 
 
ELECTRICITY 
 
 499 
 
 being joined to the beginning of the next, thus forming an endless coil. The 
 construction of such a ring armature would be as shown in Fig. 2. 
 
 Suppose that the ring shown in Fig. 3 with its endless winding is rotated 
 between the poles of a two-pole field magnet. Magnetic lines will flow from 
 the N pole of the field magnet 
 across through the iron core of 
 the armature and enter the 5 
 pole on the other side. As 
 all the conductors on the right- 
 hand face of the ring are mov- 
 ing upwards, they will have an 
 electromotive force generated 
 in them in one direction, while 
 the conductors on the left side 
 will have an electromotive 
 force in the opposite direction, 
 because all the conductors on 
 this side are moving down- 
 wards, or in the opposite direc- 
 tion, to those on the other side. 
 These two opposing electro- 
 motive forces may be said to 
 start at a' and to meet at a, as 
 shown by the arrowheads on 
 the conductors, and will neu- 
 tralize each other so that no current will flow through the windings of the 
 armature. Suppose, however, that taps are connected at the points a 
 and a', as shown by the dotted lines, and these taps connected to two con- 
 ducting metal rings r and r', mounted so as to revolve with the armature. 
 By allowing brushes b and b' to press on these rings, connection can be made 
 with an outside circuit d, which may consist of a number of lamps or any 
 other device through which it is desired to send a current. By putting in the 
 taps at a and a', the two opposing electromotive forces may set up a current 
 through the common connections to the rings, and thence through the outside 
 circuit. Current now flows in each half of the armature winding, unites at a, 
 flows out by means of ring r' and brush b', thence through the outside circuit d 
 to brush b and ring r, from whence it passes to a', and thus completes the 
 circuit. When the ring makes a half revolution from the position in the 
 figure, the current in the outside circuit will flow in the opposite direction. 
 In fact, an arrangement of this kind will deliver a current that will be periodi- 
 cally reversing in the outside circuit; it will be what is known as an alternating 
 current. 
 
 Instead of simply bringing out two terminals to rings, suppose the winding 
 to be tapped at a fairly large number of points, and connections brought down 
 
 to a number of metal bars insu- 
 lated from one another, as shown 
 in Fig. 4. When the armature is 
 revolved the brushes will come in 
 contact with successive bars and 
 keep the outside circuit in such 
 relation to the armature winding 
 that the current will always flow 
 through it in the same direction. 
 Moreover, if the number of divis- 
 ions in the armature is large, the 
 current will fluctuate very little, 
 being nearly as steady as that 
 obtained from a battery. The 
 arrangement made up of insulated 
 bars is called the commutator, 
 because it commutes or changes 
 th3 relation of the outside circuit 
 to the armature winding so that 
 the current in the outside circuit 
 always flows in the same direction. All practical machines used for the gener- 
 ation of direct current must be provided with such a commutator. When 
 alternating currents are used it is only necessary to use plain collector rings, 
 as shown in Fig. 3. 
 
500 
 
 ELECTRICITY 
 
 Factors Determining Electromotive Force Generated. A dynamo should 
 be looked upon as a machine for maintaining an electric pressure rather than 
 as a machine for generating a current. A pump does not manufacture water 
 it merely maintains a head or pressure that causes water to flow wherever an 
 outlet is provided for it to flow through. In the same way, a dynamo main- 
 tains a pressure, and this pressure will set up a current whenever the circuit is 
 closed, so that the current can flow. The important thing to consider, there- 
 fore, is the electromotive force that the dynamo is capable of generating. 
 
 The electromotive force generated by an armature depends on the total 
 number of magnetic lines cut through per second by the armature conductors. 
 This means that (1) the faster the armature runs, the higher will be the electro- 
 motive force; (2) the greater number of conductors or turns there are on the 
 armature, the higher will be the electromotive force: and (3) the stronger the 
 magnetic field, the higher will be the electromotive force. The electromotive 
 force in terms of these quantities may be written 
 
 nCN 
 
 ' 100,000,000 
 in which n = speed, in revolutions per second; 
 
 C = number of conductors on face of armature; 
 
 N = number of magnetic lines flowing from one pole. 
 
 The constant 100,000,000 is necessary to reduce the result to volts. This 
 makes it possible to make calculations relating to any two-pole dynamo, and 
 with slight modification it is applicable to machines with field magnets having 
 a number of poles. 
 
 Field Excitation of Dynamos. In the earliest form of dynamo, the magnetic 
 field in which the armature rotated was set up by means of permanent magnets. 
 Permanent magnets are, however, very weak compared with electromagnets, 
 which are excited by means of current flowing around coils of wire wound on a 
 soft-iron core. As soon as the current ceases flowing around the coils of an 
 electromagnet, the magnetism almost wholly disappears, but a small amount, 
 known as the residual magnetism, remains. It is to this residual magnetism 
 that the dynamo owes its ability to start up of its own accord and excite its 
 own field magnets. When the armature is first started to revolve, a very feeble 
 electromotive force is generated in it, but the armature is connected to the field 
 coils in such a way that this small electromotive force is able to force a small 
 current through the field coils, and thus set up a larger amount of magnetism 
 in the field. This in turn increases the electromotive force in the armature, and 
 the building-up process goes on rapidly until the dynamo generates its full 
 pressure. There are three methods in use for supplying the field coils with 
 current, and continuous-current dynamos are divided into three classes, accord- 
 ing to the method used for exciting their fields. These three classes are: 
 Series-wound dynamos, shunt-wound dynamos, and compound-wound dynamos. 
 
 FIG. 5 
 
 FIG. 6 
 
 In series-wound dynamos the field coils are connected in series with the 
 armature, and all the current that passes through the armature also passes 
 through the field and the outside circuit. This arrangement is shown in 
 Fig. 5, where N and ^represent the poles of the magnet, +B and B the 
 brushes, and Re the outside circuit, which may consist of lamps, motors, or 
 any other device in which it is desired to utilize the current. With an arrange- 
 ment of this kind, and as long as the speed does not change, the electromotive 
 force will increase as the current increases, because the field will become 
 stronger. This will be true up to the point where the field carries all the 
 
ELECTRICITY 
 
 501 
 
 magnetism it is capable of, or, in other words, until it becomes saturated. 
 After this point is reached, the electromotive force will increase very little 
 with increase of current. In most of the work connected with lighting or 
 power transmission, it is desirable to have the voltage remain nearly constant. 
 For this reason, therefore, the series method of excitation has not been very 
 largely used for dynamos. The only style of generator to which it has been 
 applied at all generally is the arc-light dynamo, and these machines are pro- 
 vided with an automatic regulator of some kind to vary the voltage as desired. 
 The series field winding has, however, been largely used in connection with the 
 motors operated on constant-pressure circuits. 
 
 Shunt-wound dynamos have not been used largely of late years, although 
 they were formerly very common. In this method of excitation, the field is 
 connected as a shunt or by-pass to the armature; that is, the field winding is 
 connected in parallel with the armature. This winding consists of a large 
 number of turns of fine wire, so that its resistance is high and only a small part 
 of the total current flows through it. Fig. 6 shows the connections for this 
 kind of field excitation. An adjustable resistance r is usually inserted in the 
 field circuit, and by cutting this resistance in or out, the field may be weakened 
 or strengthened and the voltage varied accordingly. With this type of machine, 
 the current through the field does not vary greatly from no load to full load, 
 and if the dynamo is well designed, the pressure at the brushes will keep 
 approximately constant. The pressure will, however, always fall off more or 
 less as the amount of current produced increases on account of the drop in the 
 armature, due to its resistance, and also because of the tendency that the cur- 
 rent in the armature has of weakening the field. The shunt winding is used 
 quite largely for motors. 
 
 The compound-wound dynamo is the one most largely used for direct-current 
 power and light distribution, and it is so called because the winding used for 
 exciting the field is a combination of the series and 
 shunt windings. The series winding serves to keep 
 up the field strength while the load is increased, 
 and thus keeps the pressure constant, or even makes 
 it rise with increased load, if so desired. When the 
 series winding is so adjusted that the pressure rises 
 as the load is increased, the machine is said to be 
 over compounded. Fig. 7 shows the connections for 
 such a machine. It will be seen that the shunt 
 winding is connected as before, a field resistance 
 or rheostat, not shown in the figure, being inserted 
 for the purpose of adjusting the voltage. One brush 
 connects directly to one terminal of the machine 
 + T, while the other brush connects to one end of 
 the series winding on the field. The other end of 
 the series winding forms the other terminal T, to 
 
 FIG. 7 
 
 which the outside circuit Re is connected. By this arrangement, the shunt coil 
 supplies a certain amount of initial magnetization that is augmented by the 
 magnetism supplied by the series coils. Care must be taken to see that the 
 current in the series coils circulates around the field in the same direction as 
 that in the shunt coils, otherwise the electromotive force will fall off with an 
 increasing load instead of keeping it up. 
 
 DIRECT-CURRENT MOTORS 
 
 Direct-current motors, so far as their fundamental construction goes, are 
 almost identical with direct-current dynamos. But as . motors are often 
 required to operate under very trying conditions, as in mine haulage or pump- 
 ing plants or on the ordinary street car, the mechanical construction must be 
 so designed as to enclose the working parts as completely as possible, and thus 
 protect them from dirt and injury. The two kinds of motors most commonly 
 used are the series and shunt varieties; compound -wound motors are only used 
 for a few special kinds of work. Practically all the motors in use are operated 
 from constant-pressure mains; that is, the pressure at the terminals of the 
 motor is practically constant, no matter what load it may be carrying. Only 
 constant-potential motors will be considered here. 
 
 Principles of Operation. If the fields of an ordinary constant-potential 
 dynamo are excited and a current supplied to the armature from some outside 
 source, such as another dynamo D, Fig. 1, so that the current enters at -\-B, 
 and passing through the winding in the direction indicated by the arrowheads, 
 leaves at brush B, all the conductors under the 5 pole face, b, c, d, e, f, and g, 
 
502 
 
 ELECTRICITY 
 
 will tend to move downwards, and all those under the N pole face, j, k, I, m, n, 
 and o, will tend to move upwards, as indicated by the small arrows. 
 
 These forces combine to produce a tendency of the armature to rotate about 
 its axis as indicated by the large arrows, which tendency is called the torque of 
 the motor. 
 
 The amount of this torque which is usually expressed in pound-feet; that 
 is, a certain number of pounds acting at a radius of a certain number (usually 1) 
 of feet depends on the strength of the field, the number of conductors, their 
 mean distance from the axis of the armature, and the amperes in each con- 
 ductor. In any given machine, the second and third conditions are constant, so 
 that the torque depends on the strength of the field and the current. 
 
 If the armature is stationary, the electromotive force required to send the 
 current through the winding is only that necessary to overcome the drop, 
 which is due to the resistance of the winding. If the torque exerted by this 
 current is greater than the opposition to motion, so that it causes the armature 
 to revolve, the motion of the conductors through the field generates in them 
 an electromotive force that is opposed to the electromotive force that is sending 
 the current through the armature. This opposing electromotive force or 
 counter electromotive force as it is called, then diminishes the effect of the applied 
 electromotive force, so that the current is reduced, thereby reducing the torque. 
 Should the torque still be greater than the opposition to motion, the speed of 
 the armature will continue to increase, increasing the counter electromotive 
 force, and thereby further reducing the current and the corresponding torque 
 until the torque just balances the opposition to the motion, when the speed 
 will remain constant. 
 
 At all times, the drop of potential through the armature is equal to the 
 difference between the counter and the applied electromotive forces, and as the 
 product of this drop and the current represents energy wasted, it is desirable 
 
 to make it as low 
 as possible. In good 
 motors of about 
 10 H. P. output, the 
 drop in the arma- 
 ture is seldom more 
 than about 5% of 
 the applied electro- 
 motive force, and is 
 less in larger ma- 
 chines. This being 
 the case, it is evident 
 that if the arma- 
 ture is at rest, so 
 that it has no coun- 
 ter electromotive 
 force, and is con- 
 nected directly to 
 the mains, a very 
 large current will 
 flow through it, 
 which would be 
 liable to damage the 
 armature. On this 
 account an external 
 
 FIG. 1 
 
 resistance, called a starting resistance, is connected in series with the armature 
 when it is to be started. This resistance is made great enough to prevent 
 more than about the normal current from flowing through the armature when 
 it is at rest; as the armature speeds up and develops some counter electromotive 
 force, this resistance is gradually cut out, until the armature is connected 
 directly to the mains, and is running at normal speed. 
 
 The energy represented by the product of drop in the armature and the 
 current is wasted; that represented by the product of the current and the rest 
 of the electromotive force, that is, the counter electromotive force, is the energy 
 required to keep the armature in motion. 
 
 Aside from the comparatively small amount of current required to furnish 
 the torque necessary for overcoming the frictional losses in the motor itself, 
 which are practically constant, the amount of current taken from the mains 
 is directly proportional to, and varies automatically with, the amount of the 
 external load; for, if this external load is increased, the current that has been 
 
ELECTRICITY 503 
 
 flowing in the armature cannot furnish sufficient torque for this increased 
 load, so that the machine slows down. This decreases the counter electromotive 
 force, which immediately allows more current to flow through the armature, 
 increasing the torque to the proper amount. If the external load is decreased, 
 the current flowing furnishes an excess of torque, which causes the speed to 
 increase, increasing the counter electromotive force, and decreasing the current 
 until it again furnishes only the required amount of torque. 
 
 As the counter electromotive force is very nearly equal to the applied, it is 
 only necessary for it to vary a small amount to vary the current within wide 
 limits. For example, if the resistance of a certain armature is 1 ohm, and it 
 is supplied with current at a constant potential of 250 volts, then, when a 
 current of 10 amp. is flowing through it, the drop is 10X1 = 10 volts, and the 
 counter electromotive force is 25010 = 240 volts. Now, if the current is 
 reduced to 1 amp., the drop is 1 X 1 = 1 volt, and the counter electromotive force 
 
 g 
 is 250 1 = 249 volts; that is, the counter electromotive force only varies -^r~ 
 
 or 3.75%, while the current varies , or 90%. 
 
 As stated before, the field magnets of constant-potential motors are usually 
 either shunt-wound or series-wound. If shunt-wound and supplied from a 
 constant-potential circuit, the magnetizing force of the field coils is constant, 
 giving a practically constant field. This being the case, the counter electro- 
 motive force is directly proportional to the speed, so that variations of the 
 load make only slight variation in the speed. A shunt- wound motor is then 
 (practically) a constant-speed motor. 
 
 With series- wound motors, the strength of the field varies with the current; 
 if the load on such_a motor is reduced, the excess of torque makes the armature 
 speed up, but the increasing counter electromotive force produces a decreasing 
 current, thereby decreasing the field strength, and, consequently, the armature 
 must speed up to a much greater extent, in order to increase the counter 
 electromotive force to the right degree, than would be necessary if the field 
 were constant. If the load is increased, the increase in the current so increases 
 the field strength that the speed must decrease considerably, in order to decrease 
 the counter electromotive force by the right amount. The speed of a series- 
 wound motor, then, varies largely with variations in the load. 
 
 An advantage of the series motor is that if a torque greater than the normal 
 is required, it can be obtained with less current than with a shunt motor, since 
 the increased current increases the field strength, which remains practically 
 constant in a shunt motor, and the torque is proportional to both these factors. 
 
 It is not practicable to make the field strength of a shunt motor as great as is 
 possible to get with a series motor, because it would require a very large magnet- 
 izing force, and with the shunt winding, this extra magnetizing force would 
 have to be expended all the time, whether the strong field was required or not, 
 which would be very wasteful; in the series-motor, however, this extra magnet- 
 izing force is only expended while it is needed. 
 
 A disadvantage of the series winding is that if all the load is taken off, 
 the current required to drive the motor is very small, making a weak field, 
 which requires such a high speed to generate the proper counter electromotive 
 force that the armature is liable to be damaged. In other words, the motor 
 will race, or run away, if the load is all removed. This cannot occur with the 
 shunt motor as long as the field circuit remains unbroken. 
 
 On account of the foregoing features, shunt motors are used to drive 
 machinery that requires a nearly constant speed with varying loads, or which 
 would be damaged if the speed should become excessive, such as ordinary 
 machinery in shops and _ factories, pumps, etc. Series motors are used on 
 street cars, to operate hoists, etc., where, on account of the gearing used, the 
 load cannot be entirely thrown off, except by opening the motor circuit, and the 
 torque required at starting and getting quickly up to speed is much greater 
 than the torque required when the car is running at ordinary speed. 
 
 Speed Regulation of Motors. The speed of a motor may be varied by 
 varying the applied electromotive force or the strength of the field. The 
 simplest way to vary the applied electromotive force is to insert a resistance, in 
 series with the armature, similar to the starting resistance. By varying this 
 resistance, the applied electromotive force at the terminals of the motor is also 
 varied, although the electromotive force of the supply circuit remains constant. 
 It is evident that the energy represented by the product of the current and 
 the drop through the resistance is converted into heat, and is thereby wasted; 
 therefore, for great variations in speed, this method is not economical, though 
 
504 
 
 ELECTRICITY 
 
 often very convenient. The applied electromotive force may also be varied 
 by varying the electromotive force of the generator supplying the current, 
 but this can only be done where a single generator is supplying a single motor, 
 or several motors, whose speed must all be varied at the same time; so that 
 
 this method is 
 only used in 
 , special cases. 
 
 -250 Volt + 250 Volts >\ Varying the 
 
 -500 Volts *4 strength of the 
 
 p IG 2 field gives a con- 
 
 venient method 
 
 of varying the speed. If the strength of the field is lessened, the speed will in- 
 crease, and if the field is strengthened, the speed will decrease. With shunt motors, 
 the field may be weakened by inserting a suitable resistance in the field circuit, 
 as in shunt dynamos; with series motors the same result may be obtained by 
 cutting out some of the turns of the field coils or by placing a suitable resistance 
 in parallel with the field coils. This method of regulation is also of limited 
 range, as it is not economical to maintain the strength of the field much above 
 or below a certain density. The resistance method described, being rather 
 more simple, it is generally used. The regulating field resistance must be so 
 constructed as to remain in the circuit all the time the motor is running without 
 getting hot enough to be thereby damaged. 
 
 For special cases, such as street-railroad work, various special combinations 
 of the foregoing methods of regulation are used. One of the most common 
 of these is known as the series-parallel method, and is the method of regulation 
 generally used at present for operating street cars. This method is equivalent 
 to the method of cutting down the _^^_<^ ^f~~\ 
 
 speed by reducing the electromotive t 0000 ""T L** 
 
 force applied to the motor, and is __^_ 
 
 only applicable where at least two Trolley] _ | Ground 
 
 motors are used. It is also used, to 
 
 some extent, in haulage plants. 
 
 When a low speed is desired, or 
 
 when the car is to be started up, the 
 
 motors are thrown in series, as shown 
 
 in Fig. 2, thus making the voltage across each motor equal to one-half the voltage 
 
 between the lines, and cutting down the speed accordingly. When a high speed 
 
 is desired, the motors are thrown in multiple, as shown in Fig. 3, and each 
 
 motor runs at full speed because it gets the full line pressure. In practice, 
 
 starting resistances are used in connection with the foregoing to make the 
 
 starting smooth, but the two running positions are as shown, the motors being 
 
 connected in series in the one case, and in parallel in the other. 
 
 Connections for Continuous-Current Motors. Fig. 4 shows the manner in 
 which a shunt motor is connected to the terminals + and of the circuit. 
 The current through the shunt field does not pass through the resistance R 
 
 FIG. 4 
 
 FIG. 5 
 
 which is connected in the armature circuit, as to keep the field strength con- 
 stant, the full difference of potential of the supply circuit should be maintained 
 between the terminals of the field coil. This would not be the case if the 
 rheostat were included in the field circuit, for then the difference of potential 
 
ELECTRICITY 
 
 505 
 
 would be only that existing between the brushes +B and B. As on starting 
 the motor this difference of potential is small, only a small current will flow 
 through the field coils, which will generate such a weak field that an excessive 
 current will be required to furnish the necessary torque for starting the motor. 
 When connected as shown, the field is brought up to its full strength before 
 arfy appreciable current passes through the armature; so this difficulty does 
 not arise. The current through the armature is gradually increased as the 
 speed increases by gradually cutting out the resistance in the starting box. 
 
 As in a series motor the same current flows through 
 both armature and field coils, the starting resistance 
 may be placed in any part of the circuit. The diagram 
 in Pig. 5 illustrates one method of connecting a series 
 motor to the line terminals + and ; here the start- 
 ing or regulating resistance R is placed between the 
 line terminal and the b-ush B of the motor. To 
 reverse the direction of rotation of a motor it is neces- 
 sary to reverse either the direction of the field or the 
 direction of the current through the armature. It is 
 usual to reverse the direction of the current in the 
 armature, a switch being used to make the necessary 
 changes in the connections. 
 
 Fig. 6 shows the connections of one form of reversing switch. Two metal 
 bars B and Bi are pivoted at the points T and Ti\ one is extended and supplied 
 with a handle H, and the two bars are joined together by a link L of some 
 insulating material, such as fiber. Three contact pieces a, b, and c are arranged 
 on the base of the switch so that the free ends of the bars B and B\ may rest 
 either on a and b, as shown by the full lines, or on b and c, as shown by the 
 dotted lines. The line is connected to the terminals T and T\, and the motor 
 armature between a and b, or vice versa, a and c being connected together. 
 
 When the switch is in the position shown by the full lines, T is connected 
 to a by the bar B, and Ti to b by the bar B\. If the switch is thrown by means 
 of the handle H into the position indicated by the dotted lines, T is connected 
 to b by the bar B, and T\ to a by the bar B\ and the connection between c and a. 
 The direction of the current through the motor armature, or whatever circuit 
 is connected between a and b, is thus reversed. 
 
 In order to reverse only the current in the armature, the reversing switch 
 must be placed in the armature circuit only. Fig. 7 represents the connection for 
 a rever sing-shunt motor (a) and a rever sing-series motor (&); + and are the 
 
 line terminals; 
 R, the starting 
 resistance; B 
 and Bi. the 
 brushes of the 
 motor, and F, 
 the field coil of 
 the motor. 
 Some manufac- 
 turers combine 
 
 *> FIG- 7 th e starting re- 
 
 sistance and reversing switch in one piece of apparatus. When connecting 
 up motors, some form of main switch is used to entirely disconnect the motor 
 from the line when it is not in use. 
 
 To prevent an excessive current from flowing through the motor circuit 
 from any cause, short strips of an easily melted metal, known as fuses, mounted 
 on suitable terminals, known as fuse boxes, are placed in the circuit. These 
 fuses are made of such a sectional area that a current greater than the normal 
 heats them to such an extent that they melt, thereby breaking the circuit and 
 preventing damage to the motor from an excessive current. The length of 
 fuse should be proportioned to the voltage of the circuit, a high voltage requir- 
 ing longer fuses than a low voltage, in order to prevent an arc being maintained 
 across the terminals when the fuse melts. 
 
 If desired, measuring instruments (ammeter and voltmeter) may be con- 
 nected in the motor circuit, so that the condition of the load on the motor may 
 be observed while it is in operation. All these appliances, regulating resistance, 
 reversing switch, fuses, instruments, etc., are placed inside the main switch; 
 that is, the current must pass through the main switch before coming to any 
 of these appliances, so that opening the main switch entirely disconnects them 
 from the circuit, when they may be handled without fear of shocks. 
 
506 ELECTRICITY 
 
 ALTERNATING-CURRENT DYNAMOS 
 
 An alternating-current dynamo is one that generates a current that periodi- 
 cally reverses its direction of flow; as when an armature is provided simply 
 with collector rings. This current may be represented by a curve such as that 
 shown in Fig. 1. The complete set of values 
 that the current, or electromotive force, 
 passes through repeatedly is known as a 
 cycle. For example, the values passed 
 through during the interval of time repre- 
 - sented by the distance ac will constitute 
 FIG. 1 a cycle. The set of values passed through 
 
 during the interval ab is known as an alternation. An alternation is, there- 
 fore, half a cycle. The number of cycles passed through per second is known 
 as the frequency of the current, or electromotive force. 
 
 Alternating-current dynamos are now largely used both for lighting and 
 power transmission, especially when the transmission is over long distances. 
 The reason that the alternating current is specially suitable for long-distance 
 work is that it may be readily transformed from one pressure to another, and 
 in order to keep down the amount of copper in the line, a high line pressure 
 must be used. Pressures much over 500 or 600 volts cannot be readily gener- 
 ated with direct-current machines, owing to the troubles that are likely to 
 arise due to sparking at the commutator. On the other hand, an alternator 
 requires no commutator or even collecting rings, if the armature is made 
 stationary and the field revolving, as is frequently done. Alternators are now 
 built that generate as high as 11,000 volts directly. If a still higher pressure 
 is required on the line, it can be easily obtained by the use of transformers. 
 Alternating-current dynamos, like direct-current machines, consist of two 
 main parts, the field and armature. Either of these parts may be the revolving 
 member, and in many modern machines the armature, or the part in which the 
 current is induced, is the 
 revolving member. Fig. 2 
 shows a typical alternator 
 of the belt-driven type, 
 having a revolving arma- 
 ture. It is not unlike a 
 direct-current machine as 
 regards its general appear- 
 ance. The number of poles 
 is usually large, in order to 
 secure the required fre- 
 quency without running the 
 machine at a high rate of 
 speed. The frequencies met 
 with in practice vary all 
 the way from 25 to 150. 
 The higher frequencies are, 
 however, passing out of use, 
 and at present a frequency 
 of 60 is very common. This 
 frequency is well adapted 
 
 both for power and light- F 
 
 ing purposes. When ma- 
 chines are used almost entirely for lighting work, frequencies of 125 or higher 
 may be used. The frequency of any machine may be readily determined when 
 the number of poles and the speed is known, as follows: 
 
 _, number of poles rev. per min. 
 
 Frequency = - X ^ 
 
 & ou 
 
 For example, if an eight-pole alternator runs at a speed of 900 rev. per min., 
 the frequency will be 
 
 /=. 1X^ = 60 cycles per sec. 
 
 Alternators may be divided into single-phase alternators and multiphase 
 alternators. 
 
 Single-phase alternators are so called because they generate a single alter- 
 nating current (as represented by the curve shown in Fig. 1). The armature 
 is provided with a single winding and the two terminals are brought out to 
 collector rings. Single-phase machines have been largely used for lighting 
 work, but they are gradually being replaced by multiphase machines, because 
 
ELECTRICITY 
 
 507 
 
 the single-phase machines are not well suited for the operation of alternating- 
 current motors. 
 
 Multiphase alternators are so called because they deliver two or more 
 alternating currents that differ in phase; that is, when one current is, say, at 
 its maximum value, the other currents are at some other value. This is 
 accomplished by providing the armature with two or more distinct windings 
 which are displaced relatively to each other on the armature. One set of 
 windings, therefore, comes under the poles at a later instant than the winding 
 ahead of it, and the current in this winding comes to its maximum value at a 
 later instant than the current in the first winding. In practice, the two types 
 of multiphase alternators most commonly used are two-phase alternators, and 
 three-phase alternators. 
 
 Two-phase alternators deliver two alternating currents that differ in phase 
 by one-quarter of a complete cycle; that is, when the current in one circuit 
 is at its maximum value, the current in the other circuit is passing through its 
 zero value. By tapping four equidistant points of a regular ring armature, 
 as shown in Pig. 3, and connecting these points to four collector rings, a simple 
 two-pole two-phase alternator is obtained. One circuit connects to rings 1 
 and 1', the other circuit connects to rings 2 and 2'. When the part of the 
 winding connected to one pair of rings is in its position of maximum action, the 
 electromotive force in the other coils is zero, thus giving two currents in the 
 
 FIG. 3 
 
 FIG. 4 
 
 two different circuits that differ in phase by one-quarter of a cycle or one-half 
 an alternation. 
 
 Three-phase alternators deliver three currents that differ in phase by one- 
 third of a complete cycle; that is, when one current is flowing in one direction 
 in one circuit, the currents in the other two circuits are one-half as great, and 
 are flowing in the opposite direction. By tapping three equidistant points of 
 a ring winding, as shown in Fig. 4, a simple three-phase two-pole alternator 
 is obtained. Three mains lead from the collecting rings. 
 
 In order to have three distinct circuits, it would ordinarily be necessary 
 to have six collecting rings and six circuits; but this is not necessary in a three- 
 phase machine if the load is balanced in the three different circuits, because 
 one wire can be made to act alternately for the return of the other two. 
 
 Uses of Multiphase Alternators. Multiphase alternators are extensively 
 used because alternating-current motors can be readily operated from two- 
 phase and three-phase circuits. By using multiphase machines, motors can 
 be operated that will start from rest under load, whereas with single-phase 
 machines most motors have to be brought up to speed from some outside 
 source of power before they can be made to run. For this reason, such machines 
 are used for the operation of modern power-transmission plants. As far as 
 the general appearance of three-phase machines goes, they are similar to 
 ordinary single-phase alternators, the only difference being in the armature 
 winding and the larger number of collector rings. The multiphase alternator 
 is also adapted for the operation of lights, so that by using these machines both 
 lights and motors may be operated from the same plant. They are well adapted 
 for power-transmission purposes in mines, especially for the operation of 
 pumping and hoisting machinery, because the motors operated by them are 
 very simple in construction and therefore not liable to get out of order. 
 
508 ELECTRICITY 
 
 ALTERNATING-CURRENT MOTORS 
 
 Alternating-current motors may be divided into synchronous motors and 
 induction motors. 
 
 Synchronous motors are almost identical, so far as construction goes, with 
 the corresponding alternator. For example, a two-phase synchronous motor 
 
 will be constructed in the same way as 
 a two-phase alternator. They are called 
 synchronous motors because they al- 
 ways run in synchronism, or in step, 
 with the alternator driving them. 
 This means that the motor runs at 
 the same frequency as the alternator, 
 and if the motor had the same num- 
 ber of poles as the alternator, it would 
 run at the same speed, no matter what 
 load it might be carrying. This type 
 of motor has many good points, and 
 is especially well suited to cases where 
 the amounts of power to be transmitted 
 are comparatively large and where the 
 motor does not have to be started and 
 stopped frequently. Multiphase syn- 
 chronous motors will start up from 
 rest and will run up to synchronous 
 speed without aid from any outside 
 source. Most multiphase synchron- 
 
 p IG ous motors will not, however, start 
 
 with a strong starting torque or effort, 
 
 and will not, therefore, start up underload, and cannot be used in places 
 where a strong starting effort is required . For this reason most synchronous 
 motors are not suitable for intermittent work. Some special multiphase syn- 
 chronous motors are so designed, however, that they may be used where a 
 fairly strong starting effort is required. 
 
 Induction motors are so called because the current is induced in the arma- 
 ture instead of being led into it from some outside source. Fig. 1 shows a 
 typical induction motor. There are two essential parts in these machines, 
 viz., the field, into which multiphase currents are led from the line, and the 
 armature, in which currents are induced by the magnetism set up by the field. 
 Either of these parts may be the stationary or revolving member, but in most 
 cases the field, or part that is 
 connected to the line, is sta- 
 tionary. The stationary part 
 of an alternating-current motor 
 is called the stator and the rota- 
 ting part, the rotor. Fig. 2 
 shows the construction of the 
 stationary member or field. 
 This consists of a v number of 
 iron laminations, built up to 
 form a core and provided with 
 slots around the inner periph- 
 ery. Form-wound coils con- 
 stituting the field winding are 
 placed in these slots and con- 
 nected to the mains. This wind- 
 ing is arranged in the same way 
 as the armature winding of a 
 multiphase alternator. When 
 alternating currents differing in 
 phase are sent through the wind- 
 ing, magnetic poles are formed 
 at equidistant points abound 
 the periphery of the field, and 
 
 the constant changing of the FIG 
 
 currents causes these poles to 
 shift around the ring, thus setting up what is known as a revolving 
 magnetic field. The armature, Fig. 3, consists of a laminated iron core 
 provided with a number of slots, in each of which is placed a heavy copper 
 
ELECTRICITY 
 
 509 
 
 bar b. The ends of these bars are all connected together by two heavy short- 
 circuiting rings r running around each end of the armature. The bars and 
 end rings thus form a number of closed circuits. When such an armature is 
 placed in the revolving field, the magnetism will cut across the armature con- 
 ductors, inducing electromotive forces in them, and as the conductors are 
 joined up into closed circuits, currents will flow in them. These currents will 
 react on the field and the armature will be forced to revolve. Such an armature 
 will not run exactly in synchronism, because if it did, it would revolve just as 
 fast as the magnetic field, and there would be no cutting of lines of force. 
 The speed drops slightly from no load to full load, but if the motor is well 
 designed, this falling off in speed is slight. 
 
 The name squirrel cage is applied to a rotor of the type shown in Fig. 3. 
 Another type of rotor used in induction motors is provided with a coil winding 
 with ends brought out to three collector rings mounted on the shaft. By 
 means of stationary brushes resting on these rings, the resistance in the circuit 
 of such a rotor can be varied. Motors having such rotors are called wound- 
 rotor motors, or slip-ring motors. Induction motors possess many advantages 
 for mine work. Squirrel-cage mo- 
 tors having no sliding contacts 
 operate with absolutely no spark- 
 ing a desirable feature for mine 
 work. Such motors are also very 
 simple in construction, and are 
 therefore not liable to get out of 
 order. They have the additional 
 advantage over the synchronous 
 motor in that they exert a strong 
 starting effort, and, in fact, behave 
 in most respects like any good shunt- 
 wound direct-current motor. They 
 are used quite successfully for all 
 kinds of stationary work, such as 
 pumping, hoisting, etc., but are not 
 adapted for haulage purposes. 
 Wound-rotor (slip-ring) motors are 
 used where especially strong starting 
 effort or variable speed is required. 
 
 FIG. 3 
 
 At no load the speed of an induction motor is practically the quotient 
 obtained by dividing the number of alternations of the current by the number 
 of magnetic poles for which the motor field winding is connected. Thus with 
 a 60-cycle current, or 7,200 alternations, a two-pole motor runs at 3,600 rev. 
 per min., a four-pole motor at 1,800 rev., a six-pole motor at 1,200 rev., an 
 eight-pole motor at 900 rev., a ten-pole motor at 720 rev., a twelve-pole motor 
 at 600 rev., and a fourteen-pole motor at 514 rev. With a 25-cycle current, 
 or 3,000 alternations, the corresponding speeds are 1,500, 750, 500, 375, 300, 
 250, and 214 rev. per min. 
 
 The full-load speed is less than the no-load, or synchronous, speed, and 
 the decrease from no-load to full-load speed is called the slip. The slip depends 
 on the resistance of the rotor circuit and on the load, and, the higher the slip 
 with a given load, the lower the efficiency of the motor. In commercial motors, 
 slip ranges in value from 2 to 10% of the no-load speed, depending on the 
 size of the motor, large motors having low slip. 
 
 Selection of Induction Motors for Mine Use. Induction motors are made 
 for operating on single-phase, two-phase, and three-phase circuits. Single- 
 phase motors can be used advantageously in small capacities up to, say, 
 10 H. P., for many purposes. They start with fairly strong effort and operate 
 with efficiency and power factor approximately the same as two-phase and 
 three-phase motors. They require but two line wires and one transformer 
 to increase or decrease the voltage. 
 
 In cost and reliability of operation there is little choice between two-phase 
 and three-phase motors, but because the latter require but three line wires as 
 opposed to the four required by the former the resulting savinp in copper has 
 led to the more extensive use of the three-phase type. It should be noted, 
 however, that two-phase systems require but two transformers where the 
 voltage has to be changed as against three transformers for the three-phase 
 system. 
 
 By the use of static transformers the voltage for induction motors can be 
 made independent of the line voltage. For long-distance transmission lines 
 
510 ELECTRICITY 
 
 the generator voltage is usually stepped-up for transmission through the line, 
 and the line voltage stepped-down for use in the motors at the end of the line. 
 Large motors can be advantageously operated directly on the line if the voltage 
 does not exceed 6,600, but great care must be taken to keep them dry. High- 
 voltage motors cannot be used successfully in damp places; and low- voltage 
 motors for use in such places should have waterproof insulation on the windings. 
 The choice of frequency generally lies between the two prevailing standards 
 of 25 cycles and 60 cycles per sec. For railroad work the 25-cycle transmission 
 system is preferred because a better regulation is obtainable and the rotary 
 (synchronous) converters Used in connection therewith cost less. For general 
 lighting purposes, both arc and incandescent lamps operate better on 60-cycle 
 circuits. When the voltage does not exceed 110, incandescent lamps may be 
 used without flickering on 25-cycle circuits; but when the voltage is high, 
 frequency-changers should be employed to raise the frequency of that portion 
 of the current used for lighting from 25 to 60 cycles. For the operation of 
 stationary motors about mines, the 60-cycle system is generally preferred 
 because the transformers are less costly, because the choice of motor speeds is 
 much greater, and because this frequency is as well adapted to lighting as to 
 power purposes. 
 
 The full-load torque of a motor is the turning effort it must develop when 
 revolving at its rated speed in order to produce its rated horsepower; that is, 
 p = 2*TXRPM 
 ' 33,000 ' 
 in which ir = 3.1416; 
 
 T = torque, in foot-pounds; 
 RPM = ihe number of revolutions per minute. 
 
 , 33.000 HP 5,250 HP _, 
 
 By transformation, T= n ..,,,, = --,--. . Thus, the full-load torque 
 
 KJrM 
 
 of a 10-H. P. motor at 1,700 rev. per min. is 5>25 ^ 10 
 
 The starting torque of an induction motor is that developed at starting from 
 a state of rest and is commonly considerably greater than the full-load torque. 
 The pull-out torque is the maximum turning effort the motor can exert without 
 stopping and is usually from 1.5 to 3 times the full-load torque. An induction 
 motor cannot operate at more than full-load torque, except for short periods, 
 without overheating. 
 
 Squirrel-cage induction motors have no wearing parts except the bearings, 
 and these can be made dust-proof, so that these motors rarely need to be 
 enclosed unless they are to be used in extremely dusty places. A free circu- 
 lation of air through the interior of the motor is necessary to keep it cool. 
 Ordinarily, the necessary circulation is secured by arranging the casing as 
 shown in Fig. 1, where the openings are covered with gratings to prevent 
 objects falling into and injuring the motor. "Where the air is only moderately 
 dusty, a supply of clean air may be drawn through a special pipe from outside 
 the motor room and, after circulating through the motor, is discharged through 
 another pipe. For use in very dusty or damp places, the openings in the 
 casing (shown covered by gratings in Fig. 1) are closed with tight-fitting 
 plates; these should be fitted with gaskets to keep out dampness. It must be 
 remembered that this enclosing reduces the capacity of the motor for con- 
 tinuous operation owing to the heating through lack of interior ventilation; 
 in fact, an enclosed motor can operate at full rating only intermittently. 
 
 Squirrel-cage motors are generally preferred to wound-rotor motors for 
 driving machinery, such as mine fans, where the speed is constant. By pro- 
 viding a motor of this type with a high resistance rotor, its starting and pull- 
 out torque with a given input of current can be made high, although its 
 efficiency, when running under load, is correspondingly low. For intermittent 
 service where a high torque is necessary for starting or while in operation, 
 squirrel-cage motors with high-resistance rotors are sometimes desirable, as in 
 driving elevators, conveyers, etc. 
 
 Wound-rotor motors are preferred for driving machinery such as hoisting 
 engines, which must be frequently started and stopped with a high torque 
 and where ability to change the speed is important. By means of a controller 
 connected with the collector rings, the resistance in the rotor circuit can be 
 varied at will, thus limiting the starting current and giving any desired speed. 
 When driving machines other than hoisting engines where the engineer is con- 
 stantly on duty, it should be noted that when a motor of this type is operated 
 with external resistance in its rotor circuit, any change in the amount of the 
 
ELECTRICITY 511 
 
 load thrown upon it causes an inverse change in its speed so that, in these 
 cases, also, the presence of an attendant may be necessary to keep the speed 
 adjusted. 
 
 Induction motors are usually purchased under guaranteed heating limits 
 and performance characteristics, such as efficiency, power factor, starting and 
 pull-out torque, and, sometimes, slip. The heating limits, or rise in temper- 
 ature of the windings, etc., of the motor when in operation are at present 
 commonly guaranteed not to exceed 40 C. to 75 C. above the normal temper- 
 ature; the amount of rise guaranteed depending on the style of motor, whether 
 open, semi -enclosed, or enclosed, and on the nature of the service, whether . 
 under continuous or intermittent operation. High efficiency is desirable in a 
 motor that is to be run continuously under a steady load, and the efficiency 
 should be high at this load; the importance of high efficiency in such a motor 
 increases with the cost of electricity. Efficiency is not of importance in a motor 
 that opei ates intermittently, or where the cost of electricity is very low. 
 
 Low power factor indicates that some of the current in the generator and 
 transmission line is useless or idle, in that the energy supplied the motors 
 is less than is indicated by the line current. The actual energy that can be 
 delivered by a generator within its guaranteed heating limits decreases with the 
 power factor. Thus, a generator rated at 1,000 K. W. at 100% power factor 
 would have an output of 900 K. W. at 90% power factor; and similarly, the 
 carrying capacity of transmission lines is reduced in the same way. The power 
 factor 9f a system depends on the power factors of the motors operating 
 on the lines. A small number of motors operating at low power factors may not 
 affect the general capacity appreciably, but as the number of motors is increased, 
 the importance of operating them at high power factor increases, as the genera- 
 tor and lines may be overloaded with the current. 
 
 Installation and Care of Induction Motors. When ordering a motor, the 
 manufacturer should be advised whether it is to be placed on a side wall, 
 suspended in a reversed position overhead, or used on the ordinary horizontal 
 floor, or pedestal, mounting, as the arrangement of the housings, oil cups, etc., 
 will be different in the several cases. The machine should be mounted in the 
 driest, cleanest, and best-ventilated place possible, where it is in plain sight 
 and within easy reach. The foundations should be solid enough to prevent 
 vibration, masonry or concrete construction being preferred. The rails upon 
 which the motor slides in being adjusted to position should be supported 
 upon an absolutely even surface, so that the machine may rest properly upon 
 them. When the motor is belt-connected to the driven machine, the axles 
 of the two should be absolutely parallel, and the centers of the faces of the 
 driving and driven pulleys should be exactly in line, so that the rotor will not 
 be forced from its central position. If the motor is geared to the driven 
 machine, the axles of the two must be parallel, the centers of the faces of the 
 - gear-wheels must be in the same line, and the distance between the centers of 
 the gear-wheels must be exactly that demanded by the designs, that the pinion 
 may mesh properly with the gear. If a thin piece of paper is passed through 
 the gears while slowly turning the rotor, it should show by its crushing or 
 marking, an even pressure across the full width of the tooth. 
 
 Before starting a motor for the first time, care must be taken that all 
 circuits, connections, etc., are in accordance with the diagram furnished by the 
 manufacturer. With small motors, enclosed type fuses are used in connection 
 with the starter, but with larger motors circuit-breakers are used. Fuses that 
 are not out during starting should have a current capacity at least 2^ times 
 that of the motor. Very small motors require no starting apparatus and may 
 be put in operation by closing the line circuit. In motors of 5 H. P. and 
 upwards, the sudden throwing on of the entire current will cause fluctuations 
 in the line current, which -may interfere with the working of other motors on 
 the same circuit and may even damage the motor windings. 
 
 To permit the application of low voltage at starting, which may be increased 
 to full voltage after the motor has been brought up to speed, squirrel-cage 
 induction motors are provided with auto or compensating starters. These 
 starters differ in details of design, but in all cases they comprise the essential 
 elements of two or three single-coil transformers for reducing the voltage, and 
 a switch for changing the connections between the line, the transformers, and 
 the motor. The transformers are provided with taps, and by adjusting the 
 tapping-in point the voltage at starting may be varied. In the starting posi- 
 tion, the switch conrects the transformers to the line and the motor to the 
 transformers. In the running position, the motor is connected directly to the 
 line, no current passing through the transformers. Starters commonly have 
 
512 ELECTRICITY 
 
 but one starting position and open the circuit when passing from the starting 
 to the running position. They are designed so that it is impossible to move 
 from the off to the running position without passing through the starting 
 position, or to introduce the starting connection in passing back from the 
 running to the off position. The handles of most starters are moved clockwise 
 to start and stop the motor, and can be turned in the reversed position only 
 to return from the starting to the off position. 
 
 The power should not be thrown on in one rapid operation as such action 
 will cause excessive starting current; rather, the handle should be left at the 
 starting position for a short time, and then moved quickly either to the second 
 starting position (if there is one) or to running. 
 
 When setting up a motor, the oil wells should be examined and if dirty 
 should be blown out or cleaned with gasoline if they are badly clogged. After 
 cleaning, they should be filled with a high grade of mineral oil, preferably 
 dynamo oil, which flows easily and is readily carried up by the oil rings. Graph- 
 ite and similar lubricants are not satisfactory for use in motors as they clog 
 the oil ducts and interfere with the operation of the oil rings. When starting 
 the motor (which may be turned by hand for testing purposes) care must be 
 taken that the rings revolve and carry up the oil. At all times enough oil 
 must be kept in the bearings that the rings may dip well below its surface. 
 Bearings using oil and waste should be packed with a high-grade wool waste, 
 which should fit closely against the shaft. Cotton or the poorer grades of wool 
 waste become soggy and drop away from the shaft. The waste should be 
 thoroughly saturated with oil, preferably by immersing it for 48 hr., and then 
 letting it drip for 10 to 12 hr. Too much free oil will result in an overflow 
 and the possible introduction of oil within the motor. Dirty oil should never 
 be used; it should be replaced at once with clean oil, and to this end an oil 
 filter is an excellent investment. Bearings using grease should be filled with a 
 good quality of grease free from dirt or grit. 
 
 The distance between the centers of the driving and driven pulleys should 
 be great enough to allow some sag in the belt. Kent gives the following 
 general rules for belting. With narrow belts and small pulleys, the distance 
 between centers should be 15 ft., with a sag in the loose side of the belt of 1 ^ to 
 2 in. With belts of medium width and larger pulleys, the center distance 
 of the pulleys should be 20 to 25 ft., and the sag, 2| to 4 in. With main belts on 
 very large pulleys, the center distance should be 25 to 30 ft., and the sag from 
 4 to 5 in. If the distance between pulley centers is too great, the belt will flap 
 unsteadily resulting in unnecessary wear of the belt and bearings; if the distance 
 is too short, the severe tension required to prevent slipping will cause rapid 
 'wear and possible overheating of the bearings. The rules given represent good 
 practice for long life of belt and bearings. Shorter distances must sometimes 
 be used, in which cases the belt may be tighter, the belt and pulleys wider, or 
 the pulleys larger and the belt speed greater. Very short belts will work satis- 
 factorily if idler pulleys are used to increase the arc of contact between the 
 belt and pulleys. Belts should not be run at a greater angle with the horizontal 
 than 45 if this is possible, and never vertically. The belt should be just tight 
 enough to avoid slipping or flapping; the slack side should have a gently undu- 
 lating motion; the joints should be as smooth as possible, and a lapped joint 
 should always trail, never lead over a pulley. A sidewise movement of the 
 belt indicates poor alinement of the pulleys or unequal stretching of the edges 
 of the belt. 
 
 When a bearing becomes hot, the cause of the trouble should be looked for 
 at once. Some of the common causes of hot bearings are: Poor grades of oil, 
 grit and dust in the oil well and bearings, stopping of the circulation through 
 foreign particles in the oil grooves, an empty oil well, too tight or too heavy a 
 belt, too much end thrust on the rotor due to poor alining or leveling, a sprung 
 shaft, or worn or cut Babbitt metal in the bearings. The bearings of induction 
 motors should be inspected daily, because the air gap between the rotor and 
 stator being small, any excessive wear on the bearings may cause these parts 
 to rub. Some of the larger sizes of induction motors are provided with adjust- 
 able bearings so that the rotor may be shifted to secure a uniform air gap, 
 but in the smaller sizes the effects of wear can be overcome only by renewing 
 the linings. 
 
 Dust and grit should not be allowed to accumulate around the windings 
 and bearings. __ The motor should be regularly and thoroughly wiped and the 
 dust blown from all its parts. The projecting portions of the stator coils of 
 motors running in damp places should receive an occasional coating of water- 
 proof insulating varnish. 
 
ELECTRICITY 
 
 513 
 
 The temperature of all induction motors will rise above that of the atmos- 
 phere while running under load. As long as the hand can be held continuously 
 on the machine there is no danger, but as soon as the heat can be borne but 
 for a few seconds, and particularly if the odor of burning oil is noticeable, the 
 danger point has been reached. It will seldom be necessary to do more than 
 supply the bearings with an abundance of fresh clean lubricant, care being 
 taken that the oil or grease reaches the bearing surface; sometimes it may be 
 necessary to remove excessive belt tension. If relief is not afforded in this 
 way, a heavy oil should be poured directly on the journal if possible. If 
 necessary, part or all of the load should be removed but the rotor should be kept 
 in motion enough to prevent the bearing from becoming set or frozen. 
 
 When an induction motor is overloaded beyond its limit, it will stop or 
 pull-out. Should a motor stop when it is not overloaded, and an examination 
 of the bearings and air gap shows that the motor and stator are not rubbing, 
 the stoppage may be due to abnormally low voltage in the supply circuit. 
 The torque exerted by induction motors decreases as the square of the voltage; 
 hence, a comparatively small drop in the voltage produces a large decrease in 
 torque and the motor may come to a standstill if it happens to be carrying a 
 heavy load at the time the voltage drops. To secure the best results from an 
 induction motor, full voltage should be maintained and it is better to have the 
 voltage too high than too low provided excessive heating does not result 
 therefrom. 
 
 TRANSFORMERS 
 
 Transformers used for raising the voltage are known as step-up transformers; 
 those used for lowering the pressure are known as step-down transformers. 
 
 The transformer consists 9f a laminated iron core upon which two coils 
 of wire are wound; these coils are entirely distinct, haying no connection 
 with each other. One of these coils, called the primary, is connected to the 
 mains; the other coil, called the secondary, is connected to the circuit to which 
 . , current is delivered. Fig. 1 shows the arrangement of 
 
 coils and core for a common 
 
 type- of transformer. The 
 
 secondary coil is wound in 
 
 two parts 5 and S', and 
 
 the primary coil, also in two 
 
 parts P and P f , is placed 
 
 over the secondary. C is 
 
 the core, built up of thin 
 
 iron plates. Fig. 2 shows a 
 
 weather-proof cast-iron case 
 
 for this transformer. "When 
 
 a current is sent through 
 
 the primary it sets up a 
 
 magnetism in the core which 
 
 rapidly alternates with the 
 
 changes in the current. 
 
 This changing magnetism 
 
 FIG. 1 
 
 FIG. 2 
 
 sets up in the secondary an alternating electromotive force, which depends 
 on the number of turns in the secondary coil. If the secondary turns are 
 greater than the primary, the secondary electromotive force will be higher 
 than that of the primary. The relation between the primary electromotive 
 force and secondary electromotive force is given by the following: 
 
 Second E. M. P.-prfn^ E. M. 
 
 
 
 secondary E . M . P . 
 
 secondary turns 
 
 The ratio pnmary tun l!L j s known as the ratio of transformation of the 
 
 secondary turns 
 
 transformer. For example, if a transformer had 1,200 primary turns and 
 60 secondary turns, its ratio of transformation would be 20 to 1, and the secon- 
 dary voltage would be one-twentieth that of the primary. Transformers are 
 made for a number of different ratios of transformation, the more common ones 
 being 10 to 1 or 20 to 1. Of course, a transformer never gives out quite as much 
 
 33 
 
514 
 
 ELECTRICITY 
 
 power from the secondary as it takes in from the primary mains because there 
 is always some loss in the iron core and in the wire making up the coils. The 
 
 l--iooo t r T 
 
 l^oooooTdW-J 
 
 FIG. 4 
 
 efficiency of trans- 
 formers is, however, 
 high, reaching as 
 high as 97% or 98% 
 in the larger sizes. 
 Transformers are 
 connected in paral- 
 lel across the 
 mains, and if they 
 are well designed, 
 will furnish a very 
 nearly constant sec- 
 ondary pressure at 
 
 FIG. 5 
 
 all loads, when furnished with a constant primary pressure. Fig. 3 shows 
 transformers connected on a single-phase circuit, Fig. 4 shows the con- 
 nection for a two-phase circuit, and Fig. 5 shows one method of connection 
 for a three-phase circuit. 
 
 ELECTRIC SIGNALING 
 
 BATTERIES 
 
 Batteries are used for various purposes in connection with mining work, 
 principally for the operation of bells and signals. The Leclanche cell is one 
 that is widely used for bell and telephone work. It is made in two or three 
 different forms, one of the most common being shown in (a) of the accompany- 
 ing illustration. The zinc element of this battery is in the form of a rod Z, 
 and weighs about 3 oz. The other electrode is a carbon plate placed in a 
 porous cup and surrounded with black oxide of manganese, mixed with crushed 
 
 coke or carbon. The electro- 
 lyte used in the battery is a 
 saturated solution of sal am- 
 moniac. The electromotive 
 force of this cell is about 1.48 
 volts when the cell is in good 
 condition. In another form of 
 the cell, known as the Gonda 
 type, black oxide of manganese 
 is pressed into the form of 
 bricks and clamped against each 
 side of a carbon plate by 
 means of rubber bands. The 
 Leclanch6 type of cell will do 
 good work if it is only used 
 
 , j fft intermittently in circuits where 
 
 the insulation is good and where 
 
 there is no leakage causing the cell to give out current continuously. If cur- 
 rent is taken from it for any length of time, it soon runs down, but will recu- 
 perate if allowed to stand. 
 
 Dry cells are essentially the same as a Leclanch6 liquid cell, but the electro- 
 lyte is limited to the amount that can be retained in some absorbent material, 
 such as paper, that is placed inside a zinc can which forms one electrode. The 
 other electrode is a carbon rod in the center. The space between is filled with 
 crushed coke and peroxide of manganese and the whole interior is saturated 
 
ELECTRICITY 
 
 513 
 
 23 5 
 
 c<i o> 
 
 foil 
 
 ^ OS - 
 
 -sS-S 
 ' S g . & 
 
 CX ^ a3 
 ^ ^ 
 
 I 88 !* 
 
 M 
 
 ^ w ^ 
 
 si I 
 
 I I 
 
 O O 
 
 
 H 
 
 ft" 
 
 ll 
 
 1 bl 
 
 (B K RQ 
 
 II 
 
 < ' O . 
 
 I 
 
 m 
 ted 
 
 e-a p p 
 
 N < 
 
 1 I 
 
 l-l 
 
 s a 
 
516 
 
 ELECTRICITY 
 
 with the solution and the top sealed to prevent its evaporation. Dry cells are 
 extensively used in place of wet Leclanch6 cells because they are as good and 
 so much cheaper that it is economical to throw them away when exhausted and 
 buy new ones instead of spending the time and money required to replenish 
 the wet Leclanch6 cells. The internal resistance of cells not over 1 yr. old 
 nor entirely exhausted varies from .1 to .8 ohm and the electromotive force 
 from 1.3 to 1.5 volts. 
 
 In cases where the insulation is apt to be poor, as it often is in mines, it is 
 best to use a battery that will stand a continuous delivery of current and that 
 will at the same time operate all right on intermittent work or on work where 
 the circuit is open most of the time. For work of this kind, cells of the Edison 
 or Gordon type are excellent. View (b) shows the Edison cell. The elements 
 consist of two zinc plates Z hung on each side of a plate of compressed cupric 
 oxide C. The electrolyte is a saturated solution of caustic potash, which is 
 kept covered with a layer of heavy paraffin oil, to prevent the action of the 
 air on the solution. The voltage .of the cell is only .7 volt, but its internal 
 resistance is very low and its current capacity correspondingly large. The 
 electrolyte used in the Gordon cell is also caustic-potash solution, and the two 
 cells are much the same, so far as their general characteristics are concerned. 
 The preceding table gives data relating to a number of different types of cell. 
 
 BELL WIRING 
 
 The simple bell circuit is shown in Pig. 1, where p is the push button, b the 
 bell, and c the cells of the battery connected up in series. When two or more 
 
 88 
 
 PW.I 
 
 FiG - 2 
 
 bells are to be rung from one push button, they may be connected in series, 
 as shown in Fig. 2, or arranged in parallel across the battery wires, as at a and b, 
 Fig. 3. The battery B is indicated in each diagram by short parallel lines, this 
 being the conventional method. In the parallel arrangement, the bells are 
 independent of each other, and the failure of one to ring will not affect the 
 others; but in the series grouping, all but one bell must be changed to a single- 
 stroke action, so that each impulse of current will produce only one move- 
 ment of the hammer. The current is then interrupted by the vibrator in 
 the remaining bell, the result being that each 
 bell will ring with full power. The only change 
 
 FIG. 3 
 
 FIG. 4 
 
 necessary to produce this effect is to cut out the circuit-breaker on all but one 
 bell by connecting the ends of the magnet wires directly to the bell terminals. 
 When it is desired to ring a bell from one of two places some distance apart, 
 the wires may be run as shown in Fig. 4. The pushes p and p' are located at 
 the required points, and the battery and bell are put in series with each other. 
 
ELECTRICITY 
 
 517 
 
 A single wire may be used to ring signal bells at each end of a line, the 
 connections being given in Fig. 5. Two batteries are required, B and B', and 
 
 FIG. 5 
 
 a key and bell at each station. The keys k and k f are of the double-contact 
 type, making connections normally between bell b or b' and line wire L When 
 one key k is depressed, a current from one battery B flows along the wire 
 through the upper contact of the other key k' to a bell b' and back through the 
 ground plates G' and G. 
 
 When a bell is intended for use as an alarm apparatus, a constant-ringing 
 attachment may be introduced, which closes the bell circuit through an extra 
 
 wire as soon as the trip at a door or 
 window is disturbed. In the diagram, 
 Fig. 6, the main circuit, when the 
 push p is depressed, is through the auto- 
 matic drop d by way of the terminals 
 a and b to the bell and battery. This 
 current releases a pivoted arm which, 
 on falling, completes the circuit be- 
 tween b and c, establishing a new path 
 for the current by way of e, indepen- 
 dent of the push p. The bell will then 
 ring until the drop d is restored 
 by some one or the battery becomes 
 
 FIG. 6 
 
 exhausted. For operating electric bells, any good type of open-circuit battery 
 may be used; dry and Leclanche cells are largely used for this purpose. 
 
 Annunciator System. The wiring diagram for a single annunciator system 
 is shown in Fig. 7. The pushes 1, 2, 8, etc., are located in various places, one 
 side being connected to the battery wire b, and the other to the leading wire I 
 in communication with the annunciator drop corresponding to that place. A 
 battery B of two or three Leclanch6 cells is placed in any convenient location. 
 The size of wire used throughout 
 may be No. 18 annunciator wire. 
 
 Telephones are also used for 
 signaling and communicating pur- 
 poses. The mine telephone system 
 performs two functions: It expe- 
 dites the work, thereby lowering the 
 cost of production, and it enhances 
 the safety of the mine workers and 
 mine property. Its value was 
 realized first by some of the leading 
 mining companies and several states 
 have enacted mine laws requiring 
 its use. The principles involved 
 in a mine telephone system are 
 identical with ordinary telephone 
 practice, with such changes in de- 
 tails as are necessary to meet con- 
 ditions existing in mines. 
 
 The telephone case in mine work 
 must be damp-proof and dust-proof, 
 and wiring must be of such a nature 
 as to resist both dampness and the 
 corroding influence of drops of acid- p IG 7 
 
 ulated mine water. It must also be 
 
 suspended so as to be protected from injury due to falls of roof, cars, or the 
 carelessness of employes. 
 
 It has been found that a first-class, long-distance, bridging telephone is 
 the best type to use; bridging telephones are so called because they are bridged 
 
 Be// 
 
 -+H- 
 
518 
 
 ELECTRICITY 
 
ELECTRICITY 
 
 519 
 
 Arrester 
 
 Residence 
 
 fl 
 
 ngtrre House 
 
 l r 
 
 Ti'pp/e 
 
 first Left Enfry 
 
 eft Entry 
 
 Physician's 
 Office 
 
 f 
 
 FIG. 9 
 
ELECTRICITY 
 
ELECTRICITY 
 
 521 
 
 
 
 
 
 FOOT BELl O 
 J>-S\ 
 
 
 
 
 
 
 U 
 
 FBOM EUGIlfE ROOJf(j 1 
 
 
 
 
 
 ( 
 
 
 TO EfGlJft: ROOM & J 
 
 
 
 
 ? ^ ^ 
 
 
 
 
 1 FOOT UKLl.^ 
 
 ^7 
 
 3 
 
 
 
 
 
 
 
 
 ^ 
 
 O 
 
 !< 
 
 
 
 
 
 
 
 HMMIH- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ "' 
 
 r 
 
 
 
 
 
 i 
 
 zr 
 
 =TTT 
 
 fOOT 
 
 J TELEPUOUE 
 
 
 >^L 
 
 
 
 
 
 
 
 
 or connected in parallel 
 
 across the line, and are 
 
 
 
 
 not connected in series. 
 
 If one telephone should 
 
 
 
 
 get o 
 
 ut 
 
 of order, tl 
 
 ie o 
 
 thers 
 
 are n< 
 
 3t likely to 
 
 
 
 
 be disabled. Figs. 
 
 8 and 9 show the system of 
 
 
 
 
 wiring and installation used by the Stromberg- 
 Carlson Telephone Manufacturing Company. 
 It will be noted that there is a metallic circuit 
 
 *" 
 
 8 
 
 1ST. LEVKL 
 
 for the 
 
 telephones separate and distinct from 
 
 
 
 
 that used for either lighting or emergency bells. 
 
 
 
 
 Fi 
 
 0. 
 
 10 shows tl 
 
 ie c 
 
 ombm 
 
 ed tel 
 
 jphone and 
 
 ^-o- 
 
 $ 
 
 fcyZX LKFKT 
 
 emergency (alarm) system of bells employed by 
 the Western Electric Company, in which three 
 
 
 
 
 wires are used. As in the case shown in Fig. 8, 
 
 
 
 
 a separate generator is employed to ring the 
 alarm bells. One of these is installed at some 
 
 
 g 
 
 yttD. LEFISL 
 
 ** 
 
 central 
 
 ooint on the surface 
 
 where some one 
 
 
 
 
 is always on duty 
 
 to receive telephone calls 
 
 
 
 
 from 
 
 DO 
 
 ints inside t 
 
 he 1 
 
 -nine 
 
 md, if 
 
 necessary, 
 
 
 
 
 to sound the alarm bells 
 
 Other generators may 
 
 
 
 
 be installed at other points, say, at 
 
 the foot of 
 
 
 
 
 the shaft or at the inside parting, from which 
 it may be desirable to be able to send warn- 
 ing signals in event of accident. 
 Fig. 11 shows a complete bell annunciator 
 
 
 g 
 
 '\ *TH. L& 
 
 1 
 
 and telephone outfit as 
 anthracite mines of the 
 
 installed in 
 D.. L. & W 
 
 one of the 
 . R. R. Co. 
 
 
 
 
 Bridging instruments are used and each bell in 
 the shaft is provided with a return-call button. 
 
 0- 
 
 i 
 
 era. usrsi, 
 
 This 
 
 b 
 
 11 wiring sr 
 
 oul 
 
 3 be 
 
 put u 
 
 p in a sub- 
 
 
 
 
 stant 
 
 al 
 
 manner, an 
 
 d it 
 
 is be 
 
 3t. if 
 
 aossible, to 
 
 
 
 
 rur all the wires down the shaft in the shape of 
 
 
 
 
 aleac 
 
 l-c 
 
 overed cable 
 
 
 Anoth 
 
 er sha 
 
 ft-signaling 
 
 
 
 
 apparatus is shown in Fig. 12, as used at the 
 West Vulcan mines, Mich. Fig. 13 shows a 
 form of waterproof push button used at the 
 
 
 8 
 
 T" 
 
 same mine. Fig. 14 shows the arrangement 
 of flash signals as used in Montana. This con- 
 
 
 
 
 sists of 
 
 a switch cut into a lighting circuit at 
 
 
 
 
 each 
 
 Ie' 
 
 /el of the n 
 
 line 
 
 3. By 
 
 pulli 
 
 ng out the 
 
 
 
 
 hand 
 
 e 
 
 bar of the s 
 
 witc 
 
 h, all 
 
 the li 
 
 *hts on this v * 
 
 V ^=5L 
 
 circu 
 
 t 
 
 can be flash 
 
 ed 
 
 at one 
 
 e, anc 
 
 by a prop- 
 
 erly arranged code of flash signals 
 
 the system L 
 
 can 1 
 
 >e 
 
 used for co 
 
 mm 
 
 unicat 
 
 ing b 
 
 etween the 
 
 surface to any part of the mine, and between FlG. 11 
 different portions of the mine. 
 
522 
 
 ELECTRICITY 
 
 Hoisting Engine House. 
 
 ///// North Cable Be II. 
 --i '/// South Cab/e Bell, r- 1 .- - 
 
 PIG. 12 
 
ELECTRICITY 523 
 
 A system of signaling by which signals can be sent to the engine room from 
 any point along the haulage road is shown in Fig. 15. The bare conductors a 
 and b leading from the battery are sup- 
 ported on insulators parallel to each other 
 along the roadside, and about 6 in. apart. 
 A short iron rod, placed across the wires 
 a, signals to the engineer, or by simply 
 bringing the two wires together a signal 
 
 may be sent. When the engineer hauls 
 
 FIG. 15 
 
 from different roads, the signaling system 
 should be supplemented with indicators, so that when the bell rings the indi- 
 cator will show from which point the signal came, and in case several signals 
 were given at the same time, the engineer should not heed any until the indi- 
 cator shows that a complete signal came from one place. 
 
 A system of signaling for showing whether or not a section of track is 
 occupied by another motor is shown in Fig. 16. White lights indicate a clear 
 
 track and darkness an occupied 
 section. A single-center hinge, 
 double-handle switch at each 
 signal station is used and a 
 touch of the handle throws 
 the switch in the desired di- 
 p IG< IQ rection. The switches are 
 
 placed in the roof, 4 ft. 
 
 above the rails within easy reach of the motorman. Each switch is provided 
 with a spring (not shown in the figure) which, drawing across the center hinge 
 when the handles are in their central position, insures a perfect contact when 
 the switch is inclined toward either the trolley or rail-terminal plug. 
 
 LT/I 
 
 W i 
 
 DYNAMO AND MOTOR TROUBLES 
 
 SPARKING AT BRUSHES 
 
 Faults in dynamos and motors may be classed as follows: Sparking at 
 the brushes; heating of armature, field coils, and bearings; noise; too high or 
 too low speed. Besides, a motor may stop, fail to start, or may run backwards 
 or against the brushes and a dynamo may fail to generate electricity. 
 
 Brush Faults. Sparking at brushes may be due to some fault with the 
 brushes. 
 
 1. The brushes may not have been set diametrically opposite one another 
 because they were not set properly while at rest by counting the bars, by 
 measurement, or by the use of reference marks on the commutator. Brushes 
 can be set properly, if necessary, in an emergency while the machine is running 
 by bringing the brushes on one side to the least sparking point by moving 
 the rocker-arm, and then adjusting the brushes on the other side to the least 
 sparking point by moving in or out the brush holder and clamping in new 
 positions. 
 
 2. The brushes may not have been set at a neutral point. In this case, 
 move the rocker-arm slowly back and forth until the sparking is stopped or 
 reduced to a minimum. 
 
 3. The brushes may not have been properly trimmed. If sparking begins 
 from this cause and the dynamo cannot be shut down, bend back and cut off 
 the loose and ragged wires; retrim as soon as possible after the machine is shut 
 down. If there are two or more brushes in each set they may be changed one 
 at a time on a low-voltage machine while it is running. If there is a singing 
 or hissing at the brushes apply a little mineral oil or better yet vaseline, or hold 
 a piece of stearic-acid candle on the commutator a moment and then wipe off, 
 leaving just a faint trace of oil or grease. To eliminate noise, it may be neces- 
 sary to lengthen or shorten the brushes in the holders until a firm but gentle 
 pressure is maintained free from vibration. Use only a cloth, never waste, 
 to wipe off commutator. 
 
 4. The brushes may not be'in line. In this case, adjust each brush until 
 the brushes rest on the same line and square with the commutator bar, bearing 
 evenly throughout their width, unless purposely staggered. In case of a broken 
 circuit in an armature winding, it is sometimes necessary to bridge the break 
 temporarily by staggering the brushes until the machine can be shut down, 
 
624 ELECTRICITY 
 
 when it should be repaired; this is only a temporary makeshift to reduce spark- 
 ing during a run when the machine cannot be stopped for repairs. 
 
 5. The brushes may not make good contact. In this case, clean the 
 commutator of oil, dirt, or grit so that the brushes will bear properly on it and 
 adjust by the proper tension screws and springs until a light but firm and even 
 contact is secured. 
 
 Commutator Faults. Sparking at the brushes may also be due to some 
 fault with the commutator. 
 
 1. The commutator may be rough, worn in grooves and ridges or out of 
 round. In any case, the commutator should be ground down with fine sand- 
 paper (never emery in any form) laid in a piece of wood curved to fit the 
 commutator, or a curved suitable stone, and finally polished with soft, clean 
 cloth. If the commutator is too bad to grind down, it may be turned down with 
 a special tool and rest while the commutator is turning slowly in its own bear- 
 ings or the armature may be removed from the machine, placed in a lathe, and 
 the commutator turned off with light cuts. An armature should have from & 
 to i in. end motion so as to distribute the wear of the brushes evenly and to 
 prevent their wearing ruts in the commutator. Brushes may be shifted side- 
 wise occasionally to assist in the distribution of wear. If there is no end motion, 
 the shoulders should be turned off of the shaft or filed or turned off of bearings 
 until the armature has some free end play while in motion. 
 
 2. One or more commutator bars may be too high. A high bar should be 
 forced down carefully with a wooden mallet or block of wood, care being taken 
 not to bend, bruise, or injure the bar, and then tighten the clamping rings; 
 if this does not remedy the fault, the high bar should be filed or trimmed 
 down to the level of the other bars, or the commutator ground or turned down 
 a little. High bars may cause the brush to jump or vibrate so as to sing. 
 
 3. One or more commutator bars may be too low. In this case, the 
 commutator may be ground or turned down until no bearings are below a true 
 cylindrical surface. 
 
 HEATING OF ARMATURE, FIELD COIL, AND BEARINGS 
 
 Heating of Armature. The heating of an armature may be due to the 
 machine being overloaded, to a short circuit, a broken circuit, or a cross- 
 connection; the causes and remedies for such conditions are given under the 
 head of Miscellaneous Troubles. Moisture in the armature coils should be 
 removed by drying out the coils with a slow heat secured by sending through 
 the armature current that is regulated so as not to exceed the proper amount. 
 If the moisture is so bad as to cause a short circuit or a cross-connection or to 
 heat the armature too much, it may be dried out by the heat produced by 
 its under current while running. 
 
 The heating of an armature may also be due to eddy currents in the arma- 
 ture coil. If the iron of the armature is hotter than the coils after a short 
 run, the faulty armature core should have been more laminated and the lami- 
 nations should have been better insulated from one another. There is no 
 remedy but to rebuild the armature. 
 
 Heating of Field Coils. The heating of field coils may be due to excessive 
 current in the field circuit, eddy currents in the pole pieces, or moisture in the 
 field coils. Excessive currents in the field circuit of a shunt machine may be 
 reduced by decreasing the voltage at the terminals by reducing the speed or 
 increasing the resistance of the field coils by winding on more wire, by rewinding 
 with finer wire, or by putting a resistance in series with the field. Excessive 
 current in the field circuit of a series machine may be reduced by shunting 
 a portion or otherwise decreasing the current in the field coils or by taking 
 off one or more layers of wire or rewinding the field coils with closer wire. 
 Excessive current in a shunt or series machine may of course be due to a short 
 circuit or from moisture in the coils acting as a short circuit. 
 
 Eddy currents in pole pieces may cause the pole pieces to become hotter 
 than the coils after a short run. This is due to faulty construction or to 
 fluctuating current; if due to the latter, the current should be regulated. 
 
 Moisture in the field coils may cause the coils to be lower in resistance than 
 normal or it may cause a short circuit or a contact between the coils and the 
 iron of the machine. The coil should be c^ried out, as already explained. 
 Excessive current may be due to a short circuit or to moisture in the coils 
 acting as a short circuit. 
 
 Heating of Bearings. Heating of bearings may be due to not enough or a 
 poor quality of oil. The remedy is to use plenty of oil and see that it is fed 
 properly. Only the best quality of mineral oil, filtered clean and free from 
 
ELECTRICITY 525 
 
 grit should be used, and care must be taken not to flood the bearings so as to 
 force the oil upon the commutator or into the insulation of the brush holders, 
 as it will then gradually char and gather copper dust and form a short circuit. 
 Vaseline, cylinder oil, or other heavy lubricant may be used if the ordinary 
 oil fails to remedy the hot boxes; such lubricant should be used until the run is 
 over, when the bearings should be cleaned and adjusted. 
 
 When ice is used to cool the bearings, care must be exercised not to let it 
 get into the commutator or armature, which it may ruin unless they are water- 
 . proof as in the case of street-car and some other motors. A machine must 
 never be shut down because of a hot bearing until all the remedies given there- 
 for have been tried and proved of no avail. If it is absolutely necessary to 
 shut down a machine, take the belt off as soon as possible, do not allow the shaft 
 to stick in stopping, get the bearings out and cool off as soon as possible, but 
 not in water, as this may ruin them. Then scrape, fit, clean, and polish the 
 bearings and shaft and see if it can be turned freely by hand before putting on 
 the belt and starting again. Use none but the best of mineral lubricating 
 oil. New oil and oil from self-oiling bearings should be filtered before being 
 used. 
 
 Heating of bearings may be due to dirt, grit, or other matter in bearings. 
 In this case wash out the grit by flooding with clean oil until the run is over; 
 then clean out the bearings, being careful, however, not to flood the commu- 
 tator or brush holders. When the run is over, remove the cap of the bearing 
 and clean the journals and bearings very carefully, then replace caps and 
 lubricate well. Allow bearings to cool off naturally. It may be necessary to 
 entirely remove the bearings and clean the grit away, polish all parts, and set 
 up again. 
 
 Should rough journals or bearings cause hot bearinps, polish the bearings 
 in a lathe, remove cuts, scratches, and marks; then fit new bearings of Babbitt 
 or other metal. 
 
 If journals are too tight in bearings, loosen the bolts in the cap of the bearing, 
 put in very thin pieces of packing or sheet metal between the caps and the base, 
 retighten the bolts until the run is over; then make the journal bearing smooth 
 and so it can be rotated by hand. If necessary, turn down, smooth, and 
 repolish the journal or scrape the bearings to a proper fit. 
 
 In the case of a bent or sprung shaft, bend it by carefully springing the 
 shaft or turning it in a lathe. 
 
 If a bearing is out of line, loosen the foot of the bearing until the armature 
 can be turned freely by hand with the belt off, being careful to keep the arma- 
 ture in the center of the polar space. Ream out the bolt in dowel-pin holes 
 and fit new dowels to allow the new position to be retained when the bolts are 
 drawn up tight. If the shaft must be raised or lowered, pack up or trim down 
 the feet of the bearing to allow the proper setting. 
 
 Heating of bearings may be caused by end pressure of the pulley hub or shaft 
 collars against bearings. The foundation should be level and the armature 
 should have a free end motion. If there is no end motion, turn or trim off the 
 ends of the bearings or hub on the shaft until the proper end motion is secured. 
 Line up the shaft pulley and belt so that no end thrust is maintained on the 
 shaft by a sidewise pull of the belt. The armature should have free end 
 play while in motion. 
 
 If the heating of the bearings is caused by too great a load or strain on the 
 belt, reduce the load so that the belt may be slackened and yet not slip; avoid 
 vertical belts if possible. Use larger pulleys, wider and longer belts, run slack 
 on top to increase adhesion and pull of belt without excessive tightening, so that 
 a full load may be carried. Belts should be tightened just enough to drive a 
 full load smoothly without that vibrating or flapping which may cause the 
 lamps to flicker. 
 
 An armature out of center in polar space may cause hot bearings. The 
 bearings may be worn out, thereby allowing the armature to move out of the 
 center and to need replacing. Center the armature in the polar space and 
 adjust the bearings to a new position, as already explained. File out the polar 
 space to give equal clearance all around or spring the pole pieces away from the 
 armature and secure it in place; this will be a difficult, if not an impossible, 
 job in large machines. 
 
 NOISE 
 
 If the armature strikes or rubs against the pole pieces, bend or press down 
 the projecting wires and secure strongly in place with tie-bands or wire. File 
 out the pole pieces where the armature strikes. The bearings may be worn 
 
526 ELECTRICITY 
 
 out, thus allowing the armature to move out of the center and may need 
 readjustment. It is sometimes, though seldom, necessary to file out the polar 
 space to give equal clearance all around, or to spring the pole pieces away 
 from the armature and to secure it in place. This is a difficult, if not an 
 impossible, job on large and rigid machines. 
 
 Collars or shoulders on the shaft or the hub or web of the pulley may 
 strike or rattle against the bearings, because the bearings are worn out and too 
 loose New .bearings may be required if the remedies given for bearings out 
 of line and for loose screws, bolts, or connections do not remove the trouble. 
 
 If the noise is caused by loose screws, bolts, or connections, tighten them all 
 to a firm bearing and keep them so by daily attention. The jar and move- 
 ment of the machine tends to work screwed connections loose when they are 
 not held by check-nuts, cotter pins, or some other device designed for that 
 
 ""^Singing or hissing of the brushes may be stopped by the remedies described 
 for brushes not properly trimmed. Sometimes, it may be necessary to apply 
 a little mineral oil, preferably vaseline, or a piece of stearic-acid candle against 
 the commutator and then wipe it off; just a faint trace of oil or grease is all that 
 is necessary. The brushes may be adjusted in the holders until a firm, but 
 gentle pressure free from any vibration is secured. The trouble may be due 
 to a faulty commutator, the remedies for which have already been given. 
 
 Flapping or pounding of belt joints will be remedied if the ends of the belt 
 are properly laced or joined together, or an endless belt used. 
 
 If belts slip from overload, use larger pulleys, wider and longer belts, 
 and run with the slack side of the belt on top. 
 
 To stop the humming of armature lugs, or teeth as they pass the pole 
 pieces, slope the ends of the pole pieces, in order that the armature teeth shall 
 not pass the edges all at once. Decrease the magnetism of the field or increase 
 the magnetic capacity of the teeth. 
 
 REGULATION 
 
 Speed Too High. Too high a speed may cause the engine to fail to regulate 
 with a varying load, in which case adjust the governor or other means of regu- 
 lation. If this cannot be accomplished, get a better engine. The engine 
 should regulate closely with proper steam supply from no load to full load. 
 
 A series motor may run too fast on account of receiving too much current 
 for the load that it carries, and hence the motor runs away. In the case of a 
 series motor on a constant-potential circuit, insert a resistance in series with 
 the motor in order to cut down the current; or use a proper regulator or con- 
 trolling switch, or change to automatic speed regulating motor. 
 
 The regulator may not be properly set, the proper amount of current may 
 not be used, or the motor may not be properly proportioned and, therefore, 
 may fail to regulate properly. The regulator should be adjusted to control 
 the speed, the proper current, voltage, and rheostat should be used or get a 
 motor properly designed for the work. 
 
 Speed Too Low. It may be necessary to drive the dynamo with a better 
 engine that .will regulate better with proper steam supply from no load to full 
 load. The motor may be overloaded, the causes and remedies for which have 
 been previously given. There may be a short circuit in the armature, a striking 
 or rubbing of the armature against the pole pieces, or an unusual amount of 
 friction, all of which have been explained. 
 
 MOTOR STOPS, FAILS TO START, OR RUNS BACKWARDS OR 
 AGAINST THE BRUSHES 
 
 The stopping of a motor or its failure to start may be due to no load. The 
 stopping may also be due to the motor's being greatly overloaded. In this 
 case reduce the load to the proper amount that the motor is rated to carry. 
 
 Sometimes the stopping is caused by excessive friction, due to the heating 
 of the bearings, the cause and remedies for which have been given. Open 
 the switch and keep it open and the arm of the rheostat on the off-position 
 while locating and eliminating the trouble; then close the switch and shift the 
 arm gradually to the on-position to see if everything is correct. With a series 
 motor no great harm will result from the motor stopping or failing to start: 
 .with a shunt motor on a constant-potential circuit the armature may and 
 probably will burn out or the fuse will blow. 
 
 The stopping of the motor may be due to the circuit being open on account 
 of the safety fuse being melted, a broken wire, a broken connection, the brushes 
 not being in contact with the commutator or brush holder, or an open switch. 
 
ELECTRICITY 527 
 
 In any case, see that the switch is in good order and makes its connections 
 properly. Then, if necessary, open the switch, locate and repair the trouble, 
 and replace. A melted fuse should not be replaced until the fault is corrected, 
 for otherwise the fuse will melt again when the motor is started up. If the 
 open circuit is caused by a fault in the armature or with the brushes, the 
 remedy has already been given. If the current should fail or be shunted off 
 from the machine, open the switch, return the starting lever to its off-position, 
 and wait until the current is again supplied to the line, testing from time to 
 time by closing the switch and moving the starting lever to close the circuit. 
 
 When the trouble is due to a short circuit of the field, armature, or switch, 
 test for and repair the trouble if possible, carefully looking over the insulation 
 of binding posts and brush holders for poor insulation, oil, dirt, or copper dust. 
 Such causes and remedies are given more fully under Armature Faults due to 
 short-circuited coil. 
 
 When the trouble is due to wrong connections through the motor, connect 
 up the motor properly, referring to a correct diagram of connections; if same 
 is not to be had, try reversing the connections to brush holders or make other 
 changes until the correct connections are secured for the direction of rotation 
 desired; then connect up permanently. 
 
 FAILURE OF DYNAMO TO GENERATE 
 
 Reversed Residual Magnetism. The dynamo may fail to generate because 
 the residual magnetism is reversed, owing to reversed current through field 
 coils due to earth's magnetism, proximity of another dynamo, or too weak 
 residual magnetism. In this case, a current should be sent from another 
 dynamo or from a storage or primary battery through the field coils in the 
 proper direction to correct the fault. The polarity may be tested by holding 
 a compass needle as near as convenient to the center of each pole piece and the 
 connections of any or all of the field coils may be changed until the proper 
 polarity is obtained. 
 
 When the reversed residual magnetism is caused by reversed connections, 
 connect properly for the direction of rotation desired, referring to proper 
 diagram of connections if obtainable. See that connections for series coils 
 (in compound dynamo) are properly made as well as those for the shunt coil. 
 Make such changes in connection as may be necessary to give the desired and 
 correct rotation. 
 
 If the brushes are not in their right position, shift them until evidence of 
 improvement is secured. The position of the brushes for the best generation 
 of energy should be clearly understood and is generally at or near the neutral 
 point, as has already been stated. 
 
 Short Circuit in Machine. When the failure of the dynamo is due to a short 
 circuit in the machine, the procedure is the same as when a similar fault occurs 
 in the motor. 
 
 Short Circuit in External Circuits. If a lamp circuit or other device or part 
 of a line is short-circuited or grounded, it may prevent the building up of the 
 shunt, or compound, field of the dynamo. In this case, look for and remedy 
 the short circuit before closing the switch. This fault, also, should be treated 
 the same as similar faults in motors. 
 
 Field Coils Opposed to One Another. If some of the field coils should be 
 opposed to one another, reverse the connections of one or more of them and 
 test the pole pieces with a compass. Alternate poles should show opposite 
 polarity. If the pole pieces are found to be of proper polarity or are so con- 
 nected as to give the proper polarity, and if the dynamo does not build up, 
 try the remedies given under reversed residual magnetism due to a reversed 
 current through the field coils, earth's magnetism, proximity of another dynamo 
 or to too weakened residual magnetism. If current is not then produced in 
 the proper direction, reverse field connections or recharge in proper direction. 
 
 Open Circuit. When the failure of the dynamo to operate is due to an 
 open circuit, it may be that the brushes are not in contact. The remedy for 
 this fault has already been given. 
 
 In the case of a broken or melted safety fuse, open the switch, look for and 
 repair the trouble and replace the fuse. A dead short circuit should blow the 
 fuse and a new fuse should not be put in until this fault is removed, as it will 
 simply blow the fuse -again when the switch is closed. The remedy for this 
 trouble is obvious. 
 
 If the external circuit is open or not properly connected, locate the trouble 
 and repair it while the dynamo switch is open. The remedy for an open 
 circuit in the armature has already been given. 
 
528 ELECTRICITY 
 
 Overloaded Dynamo. If the dynamo fails to generate because of an over- 
 load, reduce the load. After the dynamo comes up to full voltage, as shown by 
 lamp or voltmeter, close external circuits in succession, watching and regulat- 
 ing the voltage. If the load consists entirely, or partly, of incandescent 
 lamps, shut off some of the lamps. If the insufficient voltage generated is due 
 to too weak a field, gradually turn the regulating switch to cut resistance 
 out of the field rheostat until the proper voltage is secured. 
 
 MISCELLANEOUS TROUBLES 
 
 Weak Magnetic Field. A weak magnetic field may be due to a broken 
 circuit in the field, or to a short circuit of one or more coils, or to a dynamo 
 not being properly wound, or without having the proper amount of iron. If 
 a broken circuit is outside of the field coils where it is possible to get at it, it 
 should be repaired. If the break is inside of a winding, that winding will have 
 to be rewound. If the machine is not properly wound or does not contain 
 the proper amount of iron there is no remedy except to rebuild the machine. 
 
 Excessive Current in Armature Due to an Overload. An overload in a 
 dynamo may be due to there being too many incandescent lamps on the circuit; 
 or to a ground and leak from a short circuit on the line. In a motor, an over- 
 load may be due to excessive voltage on a constant-potential circuit, or excessive 
 amperage on a constant-current circuit; it may also be due to friction or to too 
 great a load on the pulley. The load should be reduced by degrees by cutting 
 out a number of incandescent lamps on the circuit, or by removing a dead 
 short circuit. A dead short circuit should blow the safety fuses or operate the 
 circuit-breakers. The machine should be shut down, the fault located and 
 repaired, and a new fuse put in or the circuit-breaker restored before starting 
 again; fuse should not be inserted until the fault is corrected, as it is very 
 likely to blow again on starting up the machine. A motor should be operated 
 with the proper amount of current and no more, and a rheostat or controlling 
 switch should be used for starting it. Trouble due to friction should be 
 remedied by eliminating the excessive friction. 
 
 Armature Faults. In the case of a short-circuited coil in the armature, 
 look for copper dust, solder, or other metallic particles between the commu- 
 tator bars. See that the clamping rings are perfectly insulated from the com- 
 mutator bars and that carbonized oil, copper dust, or dirt is not causing the 
 short circuit. In the case of a short circuit inside the armature, remove the 
 armature from the machine and remove and rewind the defective coil; this 
 may require rewinding the entire armature. Examine the insulation of the 
 brush holders for the fault; dirt, oil, and copper dust may make a short circuit 
 from the brush holders to the rocker-arm and thus short-circuit the machine. 
 
 In the case of a broken circuit in the armature, bridge the break temporarily 
 by staggering the brushes until the machine can be shut down; then test out and 
 repair. This is only a temporary makeshift in an endeavor to stop bad start- 
 ing before the dynamo can be shut down. If the dynamo can be shut down, 
 look for and repair the broken or loose connection on a commutator bar. If 
 a coil is broken inside, rewinding of the armature is the only sure remedy, 
 although the break may be temporarily bridged by hammering the disconnected 
 bar until it makes contact across the insulating material with the next bar; 
 this remedy is of doubtful value, and if done the bars must be repaired again 
 when the fault is permanently remedied. Commutator lugs may be tempo- 
 rarily soldered together with or without a piece of heavy copper wire soldered 
 to both bars, thus cutting out the broken coil. Care should be taken not to 
 short-circuit a good coil, and thus cause sparking. 
 
 A cross-connection in the armature may have the same effect as a short 
 circuit and is to be treated as such. Each coil should show a complete circuit 
 without being crossed with any other coil. 
 
 GENERAL PRECAUTIONS 
 
 Cleanliness about a dynamo-electric machine is imperative; dirt, oil, or 
 copper dust may prove sources of great annoyance or damage. Small tubes, 
 bolts, or pieces of iron must be kept away from the dynamo, as the magnetism 
 may draw them into or cause them to fall upon the rotating armature and 
 ruin it. Hence, loose articles of any kind must never be placed upon any 
 portion of a dynamo-electric machine. It is preferable to use brass or copper 
 oil cans, as they are non-magnetic. All connections should be clean and 
 firm. All screws and bolts should be looked over daily and, if necessary, 
 tightened. The brushes should not rest on the commutator when a dynamo 
 is idle. 
 
ELECTRICITY 529 
 
 GENERAL RULES FOR HANDLING ELECTRICITY 
 
 In coal-mining practice, the pressure, voltage, or difference of potential 
 in or on any circuit, machine, or other piece of equipment, is frequently made 
 a basis for classification . Low-pressure circuits are those in which the difference 
 of potential at no -time exceeds 250 to 300 volts; in medium-pressure circuits, 
 the voltage does not rise above 550 to 650; and in high-pressure circuits, the 
 voltage while above 650 is commonly less than 3,000. Long-distance trans- 
 mission lines operate under voltages as high as 100,000 and installations at 
 150,000 volts are contemplated. However, pressures such as these are trans- 
 formed in a special transformer house outside the mine into low or medium 
 voltage before being conveyed underground, and, so, are not reckoned with 
 in ordinary mine practice. 
 
 No voltage higher than medium (say, 550 volts) should be used anywhere 
 in any mine for the actual operation of electrical machinery, and nothing 
 above low voltage (say, 250 volts) should be employed at the face for operating 
 coal- or rock-cutting machinery. 
 
 All high-voltage currents should be carried in properly insulated cables, 
 either through bore holes drilled from the surface or along passageways upon 
 which men do not travel, to a transforming station where they should be 
 converted to low- or medium-pressure currents for farther conveyance to the 
 point of application. In gaseous mines, high-voltage cables should be installed 
 in the intake airway only, and high-voltage motors and transformers should be 
 installed only in suitable chambers ventilated by a current of intake air that 
 has not passed through or by a gaseous district. High-voltage transformers 
 should have a normal capacity of not less than 5 K. W., and high-voltage 
 motors should have a normal capacity of more than 15-brake H. P. 
 
 All metallic coverings and armoring of cables (except trailing cables) and 
 the frames and bedplates of generators, transformers, and motors other than 
 low-voltage portable motors, should be properly grounded, as should be the 
 neutral wire of three- wire continuous-current systems. 
 
 When handling live wires or when making repairs to the live parts of 
 machines, a person should wear rubber gloves or should stand upon a mat 
 of rubber or other insulating material. Every mine should have a special 
 map of the workings, made upon a sufficiently large scale (not less than 200 ft. 
 to the inch) to show clearly the position of all wires, cables, conductors, trans- 
 formers, trolley lines, switches, lights, and all fixed machines such as pumps, 
 fans, etc. The plan should indicate the size, voltage, etc., of all motors and 
 other apparatus, and the duty performed by each. In addition, the map should 
 show the location of all signal and telephone wires, bells, telephones, and the 
 like. In the event of a breakdown or in event of any portion of the equipment 
 becoming alive, the current should be shut off, the trouble located, and repairs 
 made at once. 
 
 All single switches, circuit-breakers, and other electric instruments should 
 be mounted upon insulating bases of some suitable material. Switchboards 
 should be set at least 3 ft. from the rib if the current is medium voltage, and 
 4 ft. if the current is high voltage; they should be accessible on all sides and 
 combustible material should not be used near them. Insulating floors or 
 mats should be provided. All high-potential feeder circuits with a capacity 
 of 25 K. W. or over, should have, above ground, a switch on each pole, and 
 an automatic circuit-breaker on one pole of direct-current systems, and on 
 two poles of polyphase, alternate-current systems. Ground-return direct- 
 current circuits should have a switch and circuit-breaker on the ungrounded 
 side, and fuses may be substituted for circuit-breakers where the capacity of 
 the line is 25 K. W. or less. High-potential, alternating, feeder circuits should 
 have, at the surface, on each pole an oil-break switch provided with an auto- 
 matic overload trip. All circuits should have an ammeter. Transformer 
 rooms should be fireproof, should be provided with buckets of clean dry sand 
 for use in case of fire, and no unauthorized person should be allowed to enter 
 them. Where circuits enter or leave a transformer, they should be protected 
 by circuit-breakers, etc., as on the surface. 
 
 While medium- or low-pressure wires leading into the mine may be bare, 
 except in gaseous sections thereof, high-pressure wires should be enclosed 
 in lead or other armored covers. Underground cables, except trailing cables, 
 should be supported on insulators unless provided with a grounded metallic 
 covering. The conductors connecting lamp and power supply should always 
 be insulated. Lightning arresters should be provided at the generating 
 
 34 
 
530 ELECTRICITY 
 
 station, at the mine mouth if this is 500 ft. from the station, and at intervals 
 of not more than 1,000 ft. if this distance is exceeded. In gaseous mines 
 or through gaseous portions of a mine, the potential should not be above 
 medium and the currents should be brought in through the intake. Each 
 pole at the junction of a branch and main circuit should have a switch of 
 not less than 100 amp. capacity. One side of grounded circuits should be 
 carefully insulated from the earth. Trolley lines should be placed as far to 
 one side of the entry as possible and should be supported so that the sag between 
 points of support does not exceed 3 in., except where the clear height of the 
 wire above the rail is 5 ft. or more and where, the increased sag thus permissible, 
 does not cause the trolley in passing to force the wire upon the roof. All 
 wires, except telephone, shot-firing, and signal wires should be on the same 
 side of the entry as the trolley wire. Where men are constantly compelled 
 to work or pass under bare power wires less than 6 ft. above the top of the 
 rail, the wires should be set in channels cut in the roof or in inverted wooden 
 troughs, the sides of which are not less than 5 in. deep. Branch trolley lines 
 should be provided with some device by which the current may be shut off 
 from them. Track rails should be of sufficient size to provide ample capacity 
 for the return circuit, should be bonded rail to rail, and cross-bonded at intervals 
 of not less than 200 ft., and should be frequently bonded to any air or water 
 pipes where such exist, in order to eliminate difference of potential between 
 the rails and pipes and to prevent electrolysis. Lighting wires should not be 
 wrapped, or tied about the stems or studs of trolley hangers, but should 
 be inserted in holes drilled therein, held in place by a setscrew, and should be 
 grounded into the track circuit. Lighting wires should be strung on porcelain 
 or glass insulators and, unless protected with some insulating covering, should 
 be strung at least 3 in. apart. All joints in conductors should be soldered, if 
 at all possible, and joints in insulated wire should be carefully reinsulated. 
 The exposed ends of cables, where they enter fittings, should be protected, so 
 that moisture cannot enter the cable or the insulating material leak. All 
 holes through which bare wires pass through metal frames or into boxes or 
 motor casings, should be bushed with insulating material, which should be gas- 
 proof where necessary. Extra precautions should be taken to see that power 
 cables in shafts are highly insulated and very substantially secured in place. 
 If a cable cannot sustain its own weight, it should be supported at intervals 
 of not over 25 ft. by suitable grips. Hanging cables should be boxed in, but 
 if that is not possible, they should be hung clear of the walls so that they may 
 give and not break under a blow from falling materials. Cables and feed- 
 wires should be strung so as to clear passing cars or motors by at least 12 in. 
 and, if this is not possible, should be protected by guards. Further, unless 
 metal-covered, they should not be fixed to the ribs or timbers with uninsulated 
 fastenings; and while repairs are being made in the entry or while blasting is 
 going on, they should be protected from injury in some manner. Trailing 
 cables should be protected with extra strong insulating material, should be 
 frequently examined for defects, and if these are found, should be rejected 
 until the proper repairs are made. Where such cables are divided at the 
 motor, the split should be as short as possible, and they should be securely 
 clamped to the frame of the motor, so they may not pull out from the con- 
 nections. In gaseous portions of the mine, fixed, flame-proof, terminal boxes 
 with a switch and fuse on each pole of the circuit should be provided where 
 trailing cables are attached to the power lines. The switch should be oper- 
 atable only from outside the box when it is closed, and should be so arranged 
 that the trailing cables cannot be detached or removed when the switch is 
 closed. 
 
 All switches, circuit-breakers, and fuses should have incombustible bases. 
 Open-type fuses with terminals are permissible in non-gaseous parts of a 
 mine, but where gas is generated they, and switches and circuit-breakers, must 
 be inclosed in explosion-proof casings or must break under oil. Puses should 
 be marked with the maximum current they are allowed to carry and should be 
 adjusted and replaced only by a competent person. Circuit-breakers should 
 trip at from 50 to 150% of their rated capacity, and should be provided with 
 an indicator showing at what current they are set to trip. On feeder lines, the 
 circuit breaker should trip at the end of 10 sec. under an overload of 50%. 
 Except on signal lines, all making or breaking of circuits should be done by 
 means of switches, which should be so arranged that they cannot be closed by 
 gravity; except that connections between gathering locomotives and mining 
 machines and the trolley line may be made by means of hooks or similar 
 devices. 
 
ELECTRICITY 531 
 
 Stationary motors and their starting resistance should have a fuse on one 
 pole or circuit-breaking device where direct current is used, and on both poles 
 where alternating current is employed, and should be provided with switches 
 to cut off the power entirely. In gaseous parts of the mine, motors should be 
 placed in a room ventilated by a separate split of intake air, or, if this is not 
 possible, all current-carrying parts, starters, connections, terminals, and the 
 like, should be enclosed in non-inflammable explosion-proof casings, which 
 should be opened only by authorized persons when the power is off. Under- 
 ground fan motors, not provided with a regular attendant, should be totally 
 enclosed unless installed in a special room lined with incombustible material. 
 In gaseous mines, a safety lamp should be provided with each machine and, 
 on the first indication of gas, the machine should be stopped and the current 
 cut off at the nearest switch and should not be turned on until the place has 
 been made safe. Enclosed equipment should be regularly inspected and cleaned , 
 motors once a week and switches once a month. In gaseous mines, a coal- 
 cutting machine should not be operated unless the absence of gas has been 
 proved by the use of a safety lamp, the operator should not leave the machine 
 while it is in use, and tests for gas should be repeated at least every | hr. If 
 gas is found, the machine either should not be taken to the face, or if at the 
 face the current should be at once cut off and the trailing cable disconnected 
 from the power wires. A machine should never be left at the face unattended 
 unless the power is cut off from the trailing cable. If arcing outside the 
 machine is noticed or any defect is discovered in it, the trailing cables, etc., 
 the power should be cut off at once and the machine put out of commission. 
 
 Electric haulage locomotives should not have a higher voltage than medium 
 and should not be used in gaseous mines except upon an intake air-current fresh 
 from the outside. Storage-battery locomotives are permissible in gaseous 
 mines if the cells and other electric parts are enclosed in non-combustible 
 explosion-proof casings. 
 
 Arc lamps should be of the enclosed type and are permissible in gaseous 
 mines under the same conditions as electric haulage motors. The sockets of 
 incandescent lamps should be of the weather-proof type, the exterior of which 
 should be entirely non-metallic. Flexible lamp-cord connections should not 
 be used except in the case of portable lamps and. then only when the lamp 
 and socket are enclosed in a heavy wire cage, which is attached to a handle 
 through which the leading-in wires are carried. As a general rule, portable 
 incandescent lamps of the ordinary type should not be used in gaseous portions 
 of the mine, and in other parts thereof only for the inspection and repair of 
 the machinery. Portable incandescent lamps, of the battery type, that have 
 passed the requirements of the Bureau of Mines are permissible in any part 
 of any mine. Standard incandescent lamps should be placed so that they 
 cannot come in contact with combustible material, should be replaced by 
 competent persons after having tested for the absence of gas, and in gaseous 
 portions of the mine, unless ventilated by fresh intake air, should be protected 
 by gas-tight fittings of strong glass. If the lamps are of 220 volts or higher, 
 not over 8 c. p., and without tips, the gas-tight fittings are not necessary. 
 
 Electricity from grounded circuits should not be used for firing shots. Only 
 trained men should be allowed to handle electric shot-firing apparatus. Shot- 
 firing wires or cables should not be allowed to come in contact with light or 
 power wires. Electric detonators and their leads should be of an approved 
 type, should be kept in a dry place and should not be stored with other explo- 
 sives. Shot-firing machines should be enclosed in a tight case inside of which 
 all contacts, with the exception of the binding posts, should be made. The 
 shot-firer alone should connect the leads to the battery and then only after the 
 shot is actually and completely ready for firing, and all persons have sought 
 a place of safety. After firing a shot, the leads should be at once disconnected 
 from the current. If the shot has missed fire, the firing leads should likewise 
 be disconnected, and no one should be allowed to approach the face until at 
 least 5 min. thereafter. 
 
 Care should be taken to prevent signal and telephone wires from coming 
 in contact with power or other wires, whether the same are insulated or not. 
 The potential used for signal purposes in the gaseous parts of a mine should 
 not exceed 24 volts, and bare wires should not be used except on haulage roads. 
 
 The electric relighting of safety lamps should be done in a special room not 
 on the main return and where there is not likely to be an accumulation of gas. 
 The relighting apparatus should be locked so that it cannot be handled by 
 unauthorized persons, and all lamps should be carefully examined for defects 
 before being reissued. 
 
532 INTERNAL-COMBUSTION ENGINES 
 
 INTERNAL-COMBUSTION ENGINES 
 
 DEFINITIONS AND PRINCIPLES 
 
 Internal-Combustion Engines. An internal-combustion engine is an engine 
 in which power is generated by burning within the cylinder a mixture of air 
 and gas or air and alcohol, kerosene, gasoline, or other liquid fuel. The burning 
 of the fuel results in the production of gases of high temperature and pressure, 
 which act directly on a piston that moves back and forth in a cylinder into 
 which the air and fuel are admitted and from which the burned gases are 
 discharged through suitable valves. 
 
 Single- and Double-Acting Engines. Internal-combustion engines may be 
 single or double acting. Engines in which gas is admitted to only one side of 
 the piston are single acting, while those in which gas is admitted to each end 
 of the cylinder alternately and is, consequently, burned first on one side of the 
 piston and then on the other, are double acting. All haulage-motor engines 
 and most stationary engines in which gasoline is the fuel are of the single- 
 acting type; double-acting engines are sometimes used where gaseous fuel is 
 available. 
 
 Gasoline-Engine Cycles. As applied to a gasoline engine, the term cycle 
 refers to the operations, or events, that take place within the cylinder from 
 one explosion to the next, and by means of which the fresh charge is drawn into 
 the combustion chamber and exploded and the exhaust gases expelled. These 
 events always occur in the same order and are repeated after each explosion. 
 The cycle on which an internal-combustion engine operates is one of the 
 distinguishing features of different types. 
 
 In the first successful gas engine, the charge drawn into the cylinder under 
 atmospheric pressure during part of the outward -stroke was ignited when the 
 piston had traversed about four-tenths of its stroke; the sudden rise in pressure 
 due to the explosion of the gas was utilized to drive the piston to the end of 
 its stroke and work was performed during the expansion of the hot gases. 
 During the return stroke, the burned gases were driven from one end of the 
 cylinder while a fresh charge was drawn in and ignited at the other end, the 
 engine being of the double-acting type. Because of the extreme wastefulness 
 of this engine, which was of the two-cycle type, a French scientist, Beau de 
 Rochas, in 1870, proposed a new cycle of operations. This cycle was adopted 
 and put into practical use by Otto, a German, who built his first compression 
 engine in 1876; this engine is known by his name. 
 
 The Otto cycle, in its broad and strictly scientific meaning, is not concerned 
 with the method of getting the combustible mixture into the cylinder nor that 
 of expelling the hot burned gases. The steps of the cycle are as follows: 
 Assume that, at the beginning of operations, the valves are closed, that the 
 piston is at the position farthest out toward the crank-shaft, and that the 
 cylinder is filled with a combustible mixture at atmospheric pressure. By 
 forcing the piston inwards to the completion of the inward stroke, the charge 
 will be compressed into the compression space, or combustion space. Now by 
 igniting the compressed charge, the pressure will be increased still more by the 
 heat of combustion. The pressure tends to drive the piston outwards, and as 
 soon as the rotating crank-shaft has made the angle between the connecting- 
 rod and crank sufficiently great, the pressure of the hot gases against the piston 
 face will drive the crank-shaft. The burned gases expand to fill the increasing 
 volume of the cylinder as the piston moves outwards and the pressure decreases. 
 At the completion of the outward stroke, the exhaust valve is opened and the 
 hot burned gases escape by expansion until the pressure falls to that of the 
 atmosphere. This completes the Otto heat cycle. 
 
 The expulsion of the burned gases that remain in the cylinder at atmo- 
 spheric pressure and the taking in a fresh charge of combustible mixture is 
 accomplished in two distinct ways, which are the foundation for the com- 
 mercial names, four cycle and two cycle, as applied to gasoline engines. 
 le Engines. .' 
 
 Four-Cycle Engines. A four-cycle engine is one in which four complete 
 strokes of the piston are required to complete the cycle. In this engine the 
 burned gases remaining in the cylinder after the exhaust valve has been opened 
 and part of the hot gases removed by expansion are expelled in part by a 
 
INTERNAL-COMBUSTION ENGINES 
 
 533 
 
 separate inward stroke of the piston, and a fresh charge is drawn into the 
 cylinder through the inlet port by a separate outward stroke. Generally 
 speaking, one event occurs during each of the four strokes of this cycle; that is, 
 considering the stroke by which the charge is drawn into the cylinder as the 
 first stroke, the mixture is compressed during the second stroke, burned during 
 the third stroke, and the exhaust gases are expelled during the fourth stroke, 
 after which the conditions are the same as at first and the cycle is complete. 
 This type is sometimes known as the four-stroke Otto-cycle engine, and is in 
 more general use than the two-cycle engine as it is much more economical 
 in fuel. 
 
 Two-Cycle Engines. A two-cycle engine is one in which only two strokes 
 of the piston, corresponding to one revolution of the crank-shaft, are required 
 to complete the cycle. In this cycle an explosion occurs on each downward 
 stroke of the piston, the fresh charge being admitted and the exhaust gases 
 expelled at or near the end of this stroke. Hence, for the same number of 
 revolutions of the crank-shaft, there are twice as many explosions in the 
 cylinder of a two-cycle engine as in that of a four-cycle engine. However, this 
 does not mean that the power developed by a two-cycle engine 1 is twice as great 
 as that produced by a four-cycle engine of the same size and speed, for, on 
 account of the inefficient scavenging, or cleaning, of the cylinder after the 
 explosion and the lower compression pressure in the two-cycle engine, the 
 
 explosions are not so powerful as in the four-cycle engine. It is generally 
 estimated that a two-cycle engine of a certain size and speed will develop 
 about 1.65 times as much power as a four-cycle engine of the same size and 
 speed. This type is sometimes known as the two-stroke Otto-cycle engine. 
 
 Application of Four-Cycle Principle. In the four-cycle engine, the first 
 outward stroke is the suction stroke, the gas being driven into the cylinder by 
 the pressure of the atmosphere or other pressure, because of the partial vacuum 
 produced by the movement of the piston. This stroke fills the cylinder with a 
 mixture of fuel and air at very nearly the pressure of the atmosphere. On the 
 return stroke of the piston, all the openings leading from the cylinder are closed 
 and the mixture is compressed. As the piston nears the end of this second 
 stroke, which is known as the compression stroke, the igniter, or device by 
 means of which the charge is fired, is operated in time to produce full ignition 
 of the mixture at the end of the stroke. The pressure rises to three or four 
 times that due to compression, and drives the piston forwards on its next 
 outward stroke, which is known as the power, or expansion, stroke. Just before 
 this stroke is completed, or as it is, the exhaust valve is opened, permitting the 
 burned gas and uncombined air to escape to the atmosphere, and during the 
 following inward stroke practically all of this waste material is expelled; this 
 last is known as the exhaust stroke. 
 
 Graphic Representation of Four-Stroke "Cycle. The four strokes of the 
 engine and the corresponding indicator diagram are shown in Fig. 1. Here, 
 
534 INTERNAL-COMBUSTION ENGINES 
 
 p denotes the piston; r is the connecting-rod; k. the crankpin; q, the crank- 
 shaft. In the indicator diagram, the ordinates or vertical distances represent 
 pressures, and the abscissas or horizontal distances denote the distance the 
 piston has proceeded on its stroke. The pressures are measured from the 
 line 0V, which represents the pressure of the atmosphere. The line Ovbz is the 
 suction line, and the line bzcz is the compression line. At cz, the charge is 
 ignited, czdz is the explosion line; dzez, the expansion line; czfz, combined expan- 
 sion and exhaust; and fzwO is the exhaust line. The pressures represented by 
 the two lines and w are slightly exaggerated, in order that the lines may be 
 distinguished from the atmospheric line 0V, which they follow very closely. 
 
 In the suction stroke, the crank-shaft turns in the direction of the arrow 
 and the piston moves from the line ai to the position shown. The space 
 between the end of the cylinder, when at the line ai, and the cylinder head is 
 called the clearance space or the combustion chamber. In this stroke, the inlet 
 valve is open and the mixed air and gas is being drawn into the cylinder. The 
 pressure within the cylinder drops slightly below the atmosphere, as shown 
 by the line . The valve remains open until the piston gets to the right-hand 
 end of its stroke. The numbers at the left of the diagram represent the pres- 
 sures, and those at the bottom the volumes, corresponding to the cross-lines 
 opposite which they are written. 
 
 When the piston starts on its return stroke, the inlet valve is closed and the 
 mixture is trapped within the cylinder and compressed. The rise of pressure 
 during compression is shown in the indicator diagram by the line bzcz. When 
 the compression has proceeded to cz, a spark is produced by the igniter and 
 combustion begins. The rise of pressure from cz to dz is therefore due to the 
 compression and the combustion of the gas, but the maximum pressure is 
 lessened somewhat by expansion. The flame spreads rapidly, and during the 
 short time at the end of the stroke when the piston is practically at rest the 
 pressure rises to dz. This stroke is called the compression stroke. 
 
 It has been found that by compressing the charge before igniting it, a 
 greater amount of power can be obtained from a given quantity of fuel than by 
 simply burning it at atmospheric pressure. In other words, the efficiency of 
 the internal-combustion engine is increased by compressing the charge before 
 igniting it. Compressing the charge heats it; hence, on account of the danger 
 of preigniting the charge the compression pressure is limited to from 60 to 75 Ib. 
 per sq. in., as shown by a pressure gauge. 
 
 . In the expansion stroke, during which the pressure of the heated gases drives 
 the piston toward the right, the pressure falls as the piston moves forwards, 
 as shown by the drop in the line dzez. When the expansion stroke has been 
 nearly completed, the exhaust valve is opened and from ei to V the drop of 
 pressure is due both to expansion and to the escape of the gas through the 
 exhaust valve. By the time the end of the stroke is reached, the pressure has 
 fallen very nearly to that of the atmosphere, and the expanding gas has done 
 its work. 
 
 During the next stroke, the piston is returning, the exhaust valve is open, 
 and the gases are driven from the cylinder to prepare it for the reception of a 
 new charge. There is a small rise of pressure during this stroke, due to the 
 driving of the gas from the cylinder, indicated by the line w . At the end of 
 the exhaust stroke, the exhaust valve closes, and the succeeding outward 
 stroke begins a new cycle with the suction of a fresh charge of gas and air. 
 
 The series of operations that take place during the four-stroke cycle is as 
 follows: 
 
 FIRST REVOLUTION 
 
 First Stroke. Outwards; suction; inlet valve open; pressure falls below 
 atmosphere. 
 
 Second Stroke. Inwards; compression; both valves closed; pressure rises; 
 ignition before end of stroke, followed by explosion and rapid rise of pressure. 
 SECOND REVOLUTION 
 
 Third Stroke. Outwards; expansion; both valves closed; pressure falls; 
 exhaust valve opens near end of stroke. 
 
 Fourth Stroke. Inwards; exhaust; exhaust valve open; pressure rises very 
 little above that of the atmosphere. 
 
 Application of Two-Cycle Principle. Fig. 2 (a) illustrates the operation 
 of a typical two-cycle engine, in which p is the piston; q, the crank-shaft; 
 a, the crank; k, the crankpin; r, the connecting-rod; e, the exhaust port; o, the 
 inlet, or transfer, port; b, the passage leading from the crank-chamber to the 
 cylinder; s, the inlet valve; d, a deflector on the end of the piston; and i, the part 
 of the igniting device at which the spark is produced. The diagram of 
 
INTERNAL-COMBUSTION ENGINES 
 
 535 
 
 pressures in the cylinder is shown in (b), while the diagram for the pressures in 
 the crank-case is shown in (c). 
 
 The difference between the diagrams of this engine and that of the four- 
 cycle engine should be carefully noted. When the piston is moving toward 
 the cylinder head, it is compressing the mixture of gas and air, while at the 
 same time it is drawing a new charge into the crank-case through the valve s. 
 That portion of the diagrams given during this stroke is shown by full lines. 
 In reality, the first part of the cycle must always be the suction into the crank- 
 case before any mixture is taken into the cylinder. The line Vfgh is identical 
 with the compression and explosion line of the four-stroke cycle and covers 
 the same series of operations; namely, compression to /, where ignition takes 
 place, increase of the rate at which the pressure rises from / to g, and the 
 explosion line gh. While the piston is compressing the charge in the cylinder, 
 the crank-case is drawing more fuel through the valve s, the pressure in the 
 crank-case falling below the atmosphere, as shown by the line v below O'V. 
 
 360 
 320 
 28O 
 24O 
 200 
 160 
 120 
 80 
 4O 
 O 
 
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 X 
 
 
 
 
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 N 
 
 J! 
 
 123456789\K 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
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 V 
 
 It should be noted that the diagram for the pressures in the crank-case have a 
 different scale of pressures from the scale of the diagram for the pressures in 
 the cylinder. 
 
 The next stroke moves the piston away from the head end, making the 
 expansion stroke for the cylinder and the compression stroke for the crank- 
 case, the inlet valve 5 being closed. Before the exhaust port e is uncovered, 
 the portion of the indicator diagram from h to j for the cylinder and from o' 
 to c' for the crank-case is drawn. 
 
 When the piston is very near the end of the outward stroke, both the inlet 
 and the exhaust ports o and e are open; the exhaust gases escape from the 
 exhaust port e and the fresh charge enters through the by-pass b and port o, 
 and is thrown by means of the deflecting plate d toward the cylinder head. 
 The momentum of the column of exhaust gas as it leaves the cylinder is so 
 
536 INTERNAL-COMBUSTION ENGINES 
 
 great that, unless there is considerable resistance in the exhaust passage, the 
 pressure falls below that of the atmosphere, as shown by the small loop w, 
 and is raised slightly, as shown by the loop y, when the fresh charge enters from 
 the crank-case. If the engine is properly proportioned, none of the new mixture 
 will escape at the exhaust port e, as it will be closed before the fresh charge has 
 reached it. During this part of the stroke, the pressure in the crank-case 
 rises from c' to c and then drops to V, when the transfer port is opened. The 
 following inward stroke compresses the new mixture in the cylinder and draws 
 a new charge into the crank-case, thus beginning a new cycle. 
 
 The series of operations taking place during the two-stroke cycle are as 
 follows: 
 
 CYLINDER CRANK-CASE 
 
 FIRST STROKE, INWARDS 
 
 Compression: pressure rises; igni- Suction: inlet valve open; pressure 
 
 tion near end of stroke, followed by falls below atmosphere, 
 explosion and rapid rise of pressure. 
 
 SECOND STROKE, OUTWARDS 
 
 Expansion: pressure falls; exhaust Compression: pressure rises to 
 
 followed by entrance of fresh mixture from 4 to 8 lb.; charging cylinder; 
 from crank-case. pressure falls to atmospheric pressure. 
 
 GAS-ENGINE FUELS 
 
 Gaseous Fuels. Of the gases described on page 308 and the following 
 pages, those generally employed for power purposes are: Natural gas, used at 
 and within piping distance (150 to 200 mi.) of the wells where it is produced; 
 water, or illuminating, gas, used in those cities having gas plants, although its 
 application is limited by reason of its relatively high pYice; producer, or fuel, 
 gas, used generally at iron andsteel works; by-product gas, used at by-product 
 coke ovens, which are usually built in connection with steel works or in some 
 large city where there is a market for the coke as well as the gas. Gaseous fuels 
 are suitable for use in stationary engines but not in haulage motors. They are 
 rarely used in internal-combustion engines at coal mines, although natural gas, 
 if the price is low by reason of the wells being in the coal fields, is sometimes 
 used instead of coal under the boilers. 
 
 Alcohol. Of the two kinds of alcohol, methyl, or wood, alcohol, CH t O, and 
 grain, or ethyl, alcohol, CzHeO, the former is not suited for use in internal- 
 combustion engines as it apparently liberates acetic acid, which corrodes the 
 cylinders or valves. 
 
 Grain alcohol has a specific gravity of .795, or 64 Baume. It is obtained 
 by distillation from vegetable substances containing sugar or starch, such as 
 corn, wheat, rye, or other grains, potatoes, molasses, etc. When pure, it 
 absorbs water more rapidly than it loses its own substance by evaporation. 
 When diluted with 15% of water, it evaporates as if a single liquid and not a 
 mixture. 
 
 The revenue laws of most countries require that grain alcohol must be 
 denatured or rendered unfit for the manufacture of liquors before being sold 
 as a fuel, by the addition of some poisonous or harmful ingredient such as 
 wood alcohol, petroleum distillates, cotoring matter, or the like. In France, 
 the denaturing is accomplished by adding to 26 gal. of grain alcohol, 17 oz. 
 ot heavy benzine, and 10% of wood alcohol. The alcohols used are each of 
 strength or purity. To reduce the cost of the mixture below 38c., it is 
 generally mixed with an equal volume of benzol containing 85% of benzine. 
 In Germany a fuel costing from 15 to 17|c. a gallon is made Jay adding to the 
 grain alcohol 15% of benzol, no wood alcohol being used 
 
 Gasoline. Gasoline is produced by the distillation of petroleum, being 
 among the first of the hydrocarbons to be given off in the manufacture of kero- 
 sene or illuminating oil. Its boiling point varies from 158 to 176 F., its 
 f? e m SO^to^ <66 t0 ' 67 ' and itS density accordin g to the Baume scale 
 
 Commercial gasoline is not a simple substance but a mixture of lighter 
 and heavier products. It is rated according to its density by the Baum6 
 scale. Owing to evaporation and other causes, the density of the gasoline as 
 actually purchased is likely to be somewhat greater than its nominal rating 
 and may test as low as 68. The vapor of gasoline that forms over the liquid 
 
INTERNAL-COMBUSTION ENGINES 537 
 
 consists chiefly of pentane, C&Hu, having a specific gravity of .628; but the liquid 
 gasoline consists of a mixture of hexane and heptane, the composition varying 
 with the specific gravity of the gasoline. 
 
 A gasoline with a specific gravity of .683 and a boiling point of 154 F. has 
 shown the following composition by analysis: hexane, 80%; heptane, 18%; 
 pentane, 2%. The chemical composition is 83.8% carbon and 16.2% hydrogen ; 
 and the chemical formula is 41.86C 6 #i4 + 6.48C7#i6+C 6 fl]2. This formula will 
 aid in the calculation of the fuel value. 
 
 Commercial gasoline evaporates very readily at ordinary temperatures, but 
 quite slowly in cold weather, and leaves small percentages of a heavier oil, 
 which evaporates slowly or not at all. The vapor tension varies considerably 
 with the temperature, but at 60 F. the vapor of commercial gasoline repre- 
 sents about 130 volumes of the liquid and sustains a water pressure of from 6 
 to 8 in. An explosive mixture of gasoline vapor and air is composed of the 
 vapor of 1 part of liquid gasoline to from 8,000 to 10,000 parts of air by volume. 
 The volume of the vapor will vary, but an average proportion will be 2.15 of 
 gasoline vapor to 100 parts of air. 
 
 Kerosene. Kerosene, or illuminating oil, the principal product of the 
 distillation of petroleum and sometimes used in internal-combustion engines, 
 boils at 302 to 572 F., has a specific gravity of .753 to .964, and a density 
 of 56 to 32 Baume. 
 
 Commercial kerosene varies in specific gravity (at 59 F.) from .760 to .820. 
 Exceptionally light kerosene, such as the Pennsylvania light oil, has a specific 
 gravity below .760. The boiling point of kerosene of .760 specific gravity is 
 302 F. and of kerosene of .820 specific gravity 536 F. Kerosene begins to 
 give off vapor at from 100 to 120 F., and this vapor is mainly nonane, 
 
 Liquid kerosene is a mixture of decane, CioH&, with a little hexadecane, 
 The boiling points of these three liquids are as follows: nonane, CgHw, 277 F.; 
 decane CioHis, 316 F; hexadecane, C\sHu, 536 F. Average kerosene con- 
 sists chiefly of decane. For the chemical action that takes place when kerosene 
 is burned, that corresponding to the combustion of decane may be taken with- 
 out appreciable error. 
 
 Fuel, or Compound, Oils. Oils that are lighter than about 70 Baum6 
 evaporate so rapidly that a large part is often lost before they reach the con- 
 sumer. To reduce this loss on the part of the light oils and to make a market 
 for the less salable heavy oils, the two are sometimes mixed and offered as fuel, 
 or compound, oil or by some trade name. These mixtures are not to be con- 
 fused with the fuel oil produced directly from wells and described on 395 and 
 the following pages, which is crude petroleum. As the demand for the diffi- 
 cultly salable heavy oils varies, so will vary the composition of the artificial 
 fuel oils into which they enter. 
 
 Rating of Oil and Gasoline. In selecting gasoline, it is usually sufficient 
 to know its density by Baum6's scale, this being the rating at which it is sold 
 in the general market. For instance, "Gasoline 72 Baum6" means that the 
 density of the gasoline is 72 of Baum6's hydrometer. Kerosene is generally 
 rated by its flashing point. This point is the number of degrees of 
 temperature to which it must be heated before the vapors given off 
 from the surface of the oil will take fire from a flame held over the 
 containing vessel. Thus, oil of 150 test is oil that will flash or take 
 fire when heated to a temperature of 150 F. Kerosene, at ordinary 
 temperatures, should extinguish a lighted taper when the taper is 
 plunged into it. 
 
 Baume Hydrometer. The Bauml hydrometer shown in the 
 figure consists of a glass tube, near the bottom of which are two 
 bulbs. The lower and smaller bulb is loaded with mercury or shot, 
 so as to cause the instrument to remain in a vertical position when 
 placed in the liquid in the vessel a. The upper bulb b is filled with 
 .air, and its volume is such that the whole instrument is lighter than 
 an equal volume of water. 
 
 The point to which the hydrometer sinks when placed in water 
 is usually marked, the tube being graduated above and below in 
 such a manner that the specific gravity of the liquid can be read 
 directly. It is customary to have two instruments: one. with the 
 zero point near the top of the stem, for use in liquids heavier than 
 water; and the other with the zero point near the bulb, for use in liquids 
 lighter than water. 
 
 Comparative Value of Liquid Fuels. So far as their heating value per 
 pound goes, there is not mucn to choose between kerosene and gasoline, each 
 
538 
 
 INTERNAL-COMBUSTION ENGINES 
 
 READINGS 
 
 QPQ 
 
 QPQ 
 
 20 
 22 
 24 
 2(3 
 28 
 30 
 32 
 34 
 30 
 
 .9333 
 .9210 
 .9090 
 .8974 
 
 .8750 
 .8641 
 .8536 
 .8433 
 
 .8333 
 .8235 
 .8139 
 .8045 
 .7954 
 .7865 
 .7777 
 .7692 
 .7608 
 
 .7526 
 .7446 
 .7368 
 .7290 
 .7216 
 .7142 
 .7106 
 .7070 
 .7035 
 
 70 
 71 
 72 
 73 
 74 
 75 
 
 n 
 
 77 
 78 
 
 .7000 
 .6965 
 .6931 
 .6896 
 .6863 
 .6829 
 .6796 
 .6763 
 .6730 
 
 79 
 80 
 81 
 82 
 83 
 84 
 86 
 88 
 90 
 
 .6666 
 .6635 
 .6604 
 .6573 
 .6542 
 .6481 
 .6422 
 .6363 
 
 developing about 19,800 B. T. U. per Ib. Kerosene, however, is about 10% 
 heavier, so that 1 gal. of kerosene has more fuel value than 1 gal. of gasoline. 
 
 As compared with gasoline as a fuel for internal-combustion motors, alcohol 
 exhibits several striking peculiarities. First, the combustion is much more 
 likely to be complete. A mixture of 90-alcohol vapor and air will burn com- 
 pletely when the proportion varies from 1 of the vapor with 10 of air to 1 of 
 the vapor with 25 of air, thus exhibiting a much wider range of proportions for 
 combustibility than is the case with gasoline. As the combustion is complete, 
 the exhaust is practically odorless, consisting only of water vapor and carbon 
 dioxide. Second, the inflammability of an alcohol mixture is much lower. 
 This is due partly to the presence of water in the alcohol, which is vaporized 
 with the alcohol in the engine and must be converted into steam at the expense 
 of the combustion. For these reasons, the compression of an alcohol mixture 
 is carried far above that permissible with a gasoline mixture, without danger 
 of spontaneous ignition. The rapidity of combustion of alcohol in an engine 
 is considerably less than that of a gasoline mixture, and for this reason the 
 speed of alcohol engines must be somewhat slow. 
 
 With an engine of equal size, practically the same horsepower can be 
 obtained when adapted to burning alcohol as when adapted to burning gaso- 
 line. This is true in spite of the fact that 1 Ib. of alcohol contains considerably 
 less heat energy than 1 Ib. of gasoline, and it is explained by the fact that 1 Ib. 
 of alcohol requires much less air for its complete combustion than 1 Ib. of 
 gasoline. In other words, a larger quantity of alcohol than of gasoline is 
 required to make 1 cu. ft. of explosive mixture. Approximately speaking, if 
 there is no surplus air in either case, 1 Ib. of gasoline will make 210 cu. ft. of 
 explosive mixture, and 1 Ib. of alcohol will make 120 cu. ft. As a matter of 
 fact, a certain percentage of additional air is required, both for the most rapid 
 combustion, and for the necessary economy of fuel. So far as can be judged, 
 a somewhat greater proportion of air is advantageous with alcohol; but it 
 seems to be clear that from 50 to 60% more alcohol than gasoline by weight 
 is required to obtain the same power. On the other hand, alcohol is about 
 25% heavier than gasoline, so that 1 Ib. of gasoline has 1 \ times the volume 
 of 1 Ib. of alcohol. Consequently, if the weight of alcohol needed for a given 
 amount of work is 50% greater than the weight of gasoline, the volume of 
 alcohol required will be only one-fifth greater, or in the proportion of 1.5 to 1.25. 
 
 TYPES OF INTERNAL-COMBUSTION ENGINES 
 
 Internal-Combustion Engines at Mines. Internal-combustion engines, so 
 far as their use at mines is concerned, may be placed in one of three general 
 classes or groups; stationary, portable, or haulage-motor engines. 
 
 Those of the first class are permanently attached to their foundations and 
 comprise hoisting and dynamo engines, engines used for operating station 
 pumps, etc. They may be horizontal or vertical, may have one or more 
 cylinders, and usually run at a speed of 300 to 400 rev. per min.; they are, 
 
539 
 
540 
 
 INTERNAL-COMBUSTION ENGINES 
 
 therefore, relatively large and heavy for the amount of power developed. These 
 engines are rarely found at coal mines where fuel is always cheap and water 
 for boilers usually plentiful, but in the arid regions, where both fuel and water 
 are scarce, they are in extensive and satisfactory use. 
 
 Portable engines, which may be moved from place to place, are quite 
 commonly used in and around coal mines for operating concrete mixers, small 
 pumps used in any one place only temporarily, etc. These engines are hori- 
 zontal or vertical and usually have four cylinders. They are generally designed 
 so that their speed may be varied, but they are rated at the maximum power 
 they can produce at their highest speed of from 1,000 to 1,800 rev. per min. 
 They are, therefore, lighter than stationary engines of the same power. 
 
 Haulage-motor, or, as 
 they are commonly called, 
 gasoline-motor, or gasoline 
 locomotive, engines, may 
 be horizontal or vertical. 
 They are usually of the 
 four-cylinder, vertical type, 
 and differ but slightly from 
 those used on automobiles. 
 Stationary Gas Engines. 
 A section of a stationary 
 gas engine is shown in 
 Fig. 1. The valves are in 
 the cylinder head, which 
 is bolted to the cylinder 
 at the flange a. The inlet 
 valve is shown at b and the 
 exhaust valve at c. When 
 the pressure is very great, 
 the temperature due to 
 compression in the space d 
 may be sufficient to ignite 
 the mixture of gas and air. 
 In order that a high com- 
 pression pressure may be 
 used without igniting the 
 gas, the cylinder head is 
 cooled by water introduced 
 at e through the pipe /. 
 The water-cooled projec- 
 tion g extends into the 
 combustion chamber and 
 cools the explosive mixture 
 of air and gas. The water 
 passes from the cylinder 
 head to the water-jacket 
 around the cylinder through 
 the pipe h and flows to 
 waste through the pipe . 
 
 Haulage-Motor Gaso- 
 line Engines. One of the 
 four cylinders, as well as 
 the necessary mechanism 
 of a gasoline engine suit- 
 able for use on haulage 
 motors, is shown in Fig. 2. 
 The cylinder is a and the cylinder head is b. The piston c takes the place 
 of the crosshead and therefore carries the wrist-pin d. The crank-shaft, 
 crank, crankpin, and connecting-rod, are lettered e,f,fi, and g, respect- 
 ively. The charge enters the cylinder through the passages h and *, which 
 are closed by the conical inlet valve j on the yalve seat ji. The valve 
 stem k is pressed downwards through the guide ci, so that the valve is 
 held closed by the spring I, except when the valve stem is pushed up by 
 the push rod m. This push rod is lifted by the cam n on the half-speed, or lay 
 shaft o, and -is held in position by the guide 61. The letters from p to w mark 
 the parts on the exhaust side of the engine corresponding to those marked by 
 the letters h to o on the inlet side. The cup shown at x serves the double 
 
 FIG. 2 
 
INTERNAL-COMBUSTION ENGINES 
 
 541 
 
 purpose of priming cup and 
 compression relief valve. The 
 spark plug is shown at y and 
 the water-jacket for cooling the 
 various parts of the engine is 
 at z. In some cases, both 
 valves are placed on one side 
 of the engine and are operated 
 by cams on the same lay shaft. 
 The four-cylinder opposed 
 engine differs from the vertical 
 engine only in the arrangement 
 of the cylinders. The shaft a, 
 Fig. 3, has four cranks b. A 
 
 cylinder c with a piston d and connecting-rod e is placed opposite each crank. 
 The valves and operating mechanism, which are placed above the cylinders, 
 are not shown. 
 
 CARBURETION AND IGNITION 
 
 Carbureters for Constant-Speed Engines. When liquid fuel is used in 
 internal-combustion engines, it must be reduced to a vapor or fine spray before 
 it is introduced into the engine cylinder. The device by which this is done 
 is called a carbureter, or vaporizer, one form of which, suitable for use in con- 
 nection with stationary engines running at very nearly constant speed, is 
 shown in Fig. 1. 
 
 The carbureter a is attached to the side of the inlet pipe &. The fuel is 
 pumped to the carbureter through the pipe c into 'the reservoir d from the 
 side of which the nozzle e is led into the inlet pipe in such a way that the sur- 
 face of the fuel is just below the top of the nozzle. The surplus fuel overflows 
 from d and returns to the fuel-supply tank through the pipe /. The supply 
 of fuel may be regulated by the needle valve g and may be shut off by the valve h. 
 
 When the piston is moving out on the 
 suction stroke, the inlet valve i is 
 opened and air is drawn in through 
 the pipe j into the combustion cham- 
 ber k. The pipe b is contracted at the 
 level of the nozzle so that the velocity 
 of the passing air is increased, with 
 the result that some of the oil is sucked 
 up from the, nozzle and enters the 
 cylinder as a fine spray or vapor 
 mixed with the proper amount of air 
 to secure its complete combustion. 
 
 Carbureters for Variable - Speed 
 Engines. A carbureter suitable for 
 use with a variable-speed engine is 
 shown in Fig. 2. In it, the spray 
 nozzle a and the tube b are similar to 
 the corresponding parts of the car- 
 bureter just described. The gasoline 
 chamber c contains a cork float that 
 controls a small needle valve at the 
 right through which the gasoline enters 
 and which serves to maintain the fuel 
 at a constant level. The flow of gaso- 
 line through the spray nozzle a is 
 regulated by the needle valve d and 
 the handle e. When set, this valve 
 may be locked in position by the 
 screw m. The main air inlet is at / 
 through the horn g and the pipe lead- 
 ing to the engine is connected just 
 above the throttle valve j. 
 
 As the speed of the engine is in- 
 creased, the proportion of gasoline in the fuel mixture should be decreased. 
 On the other hand, increased speed causes the air to flow more rapidly around 
 
 p IG 
 
542 
 
 INTERNAL-COMBUSTION ENGINES 
 
 the nozzle a, thus taking up more gasoline and enriching the fuel mixture. 
 To reduce the proportion of gasoline to the requirements of increased speed, 
 the mixture is diluted by admitting air above the nozzle through auxiliary 
 inlets closed by bronze balls *. When a certain degree of suction has been 
 reached, one or more of these balls are lifted and air is admitted above the 
 nozzle a, thus diluting the mixture. The balls are held in place by cages k 
 that are screwed into the body of the carbureter. The gasoline chamber 
 
 may be drained by the cock I. 
 
 Make-and-Break Ignition. If 
 the ends of two wires forming part 
 of an electric circuit are brought in 
 contact, thereby closing the circuit, 
 and then quickly separated, a bright 
 spark will be produced as the con- 
 tact is broken. This phenomenon 
 underlies the operative principle 
 of what is known as the make-and- 
 break system of ignition, with which 
 it is necessary first to complete the 
 electric circuit through the spark- 
 producing mechanism, or igniter, 
 and then break the circuit to obtain 
 a spark for igniting the charge. In 
 stationary gas-engine practice, the 
 simplest kind of igniter uses city 
 lighting current, with an incandes- 
 cent lamp in series, in order to pre- 
 vent the current from being too 
 strong, and consists simply of a 
 mechanical device for making and 
 breaking the circuit in the combus- 
 tion chamber at the proper moment. 
 Batteries may be used with the 
 make-and-break system of ignition 
 by using a spark coil. 
 
 With a low-voltage current, 
 such as that derived from a primary 
 battery, a spark coil must be em- 
 ployed to produce the necessary 
 electric tension or voltage for the 
 spark. When a battery and spark 
 coil are employed, the abruptness 
 of the break between the contact 
 point serves to increase the inten- 
 sity of the spark, it being largely 
 proportional to the sharpness of 
 the circuit rupture. Fig. 3 shows 
 an elementary wiring diagram for a 
 primary ignition circuit, with the 
 direction of the current indicated by 
 an arrow. When the timing cam a 
 brings the points b and c into con- 
 tact, the current flows from the 
 battery d through the switch e 
 (when closed)-spark coil /-insulated 
 electrode g-rocking contact finger h- 
 grounded contacts *, back to the 
 battery. The grounded connec- 
 tions i may be made to the frame 
 of the machine, or any other convenient metallic return may be used. 
 ^ Jump-Spark Ignition. The mechanism of the make-and-break system of 
 ignition requires a considerable number of moving parts that may be more 
 or less objectionable. What is known as the jump-spark system of ignition, 
 in which the primary current is converted by an induction coil into a secondary 
 current of sufficiently high tension to cause a spark to jump an air gap may 
 therefore be used. With this system, a revolving contact timer is employed 
 in place of the snap cam. As there are no other moving parts, the whole 
 apparatus is extremely simple. 
 
INTERNAL-COMBUSTION ENGINES 
 
 543 
 
 In Fig. 4 are shown the essential elements of a jump-spark system of 
 ignition. Here c is the battery ; b, a switch for opening the primary circuit when 
 it is not in use; and c, a revolving timer turning at one-half the speed of the 
 crank-shaft, if the engine is of the four- 
 cycle type. The timer in the elemen- 
 tary apparatus shown consists of an 
 insulating ring d, mounted on the shaft 
 into which is dovetailed a copper or 
 brass segment e that is in electric con- 
 nection, by a screw or otherwise, with 
 the shaft/. A plate g is mounted loosely ^s~i 
 on the shaft, so that it does not turn with -~- 
 it, but may be rocked about it through a in~ 
 suitable arc, say 45. Mounted on this | 
 plate, and insulated from it, is a brush h 
 that bears against the insulating ring 
 and makes contact with the metal 
 segment at each revolution of the lat- 
 ter. The primary winding of the spark f 
 coil is represented by i, andj is the 
 ground on the engine. A trembler k is FIG. 3 
 provided so that the current may be rapidly interrupted. The trembler is 
 for the purpose both of interrupting the current more rapidly than could be 
 done with the timer and to produce a series of sparks in rapid succession instead 
 of only a single spark. 
 
 The course of the current is from the positive pole of the battery to the 
 trembler-primary winding of spark coil-the engine frame ./-contact e-brush 
 of timer, when contact is made-switch fc-negative terminal of battery. The 
 negative terminal of the secondary winding of the coil is connected to the bat- 
 tery terminal of the primary winding, and the positive secondary terminal is 
 connected to the insulated member of the spark device, or spark plug, from 
 which, after jumping over the gap /, the current returns to the coil by way of 
 the engine frame j and primary winding. When the circuit is closed by the 
 timer, a stream of sparks passes between the spark points /. For use with 
 small, highspeed motors, the coil vibrator is frequently omitted, and a snap or 
 vibrating form of timer is used that gives a quick break but only one spark. 
 
 FIG. 4 
 
 The primary winding is provided with a condenser m, which serves the 
 double purpose of increasing the abruptness of the circuit rupture, thereby 
 increasing the intensity of the secondary spark, and of absorbing the current 
 that otherwise would produce a hot spark at the trembler contacts, and soon 
 
544 INTERNAL-COMBUSTION ENGINES 
 
 burn them out. The function of a condenser is to absorb the extra current 
 induced in the primary coil at the moment of rupture. Under the primary 
 system of ignition, it is precisely this extra current that produces the useful 
 spark in the engine; but in the secondary system, this extra current is objection- 
 able, because it dies down so slowly that it fails to induce a sufficiently intense 
 spark in the secondary coil. 
 
 The change of the time of ignition is accomplished for different speeds by 
 rocking the plate g to the right or left by means of the rod n, so that contact 
 is made by the timer early or late in the revolution of the shaft. 
 
 To run an engine at varying speeds, it is necessary, in order to obtain the 
 best results, to modify the time of ignition to suit the speed, making the time 
 earlier for high than for low speed. It is also necessary to modify the time of 
 ignition, according to the load the engine is carrying, if the engine is regulated 
 by throttling. In other words, with a given speed, a charge will burn faster 
 if highly compressed, as when a full charge is taken, than if only slightly com- 
 pressed, as it may be if the charge has been much throttled. For these reasons, 
 a great many engines are provided with means for varying the time of ignition. 
 
 Requirements of Spark Plugs. The spark plugs on the market are of a 
 variety of designs, each with some special features of advantage that may or 
 may not be possessed by others. The chief requirements of a good spark plug 
 are the following: 
 
 1. Where exposed to burning gas and oil vapors, the insulating material 
 of porcelain or mica between the central electrode or stem, which is connected 
 to the positive terminal of the coil, must not be too easily coated with carbon 
 deposit. The electric resistance of any gas increases considerably as the gas 
 is compressed, so that, although the current may jump between the proper 
 spark points when the plug is in the open air, the resistance between these 
 points may become so great when the plug is in the cylinder and the charge 
 compressed, that the current will take an easier path through the carbon coat- 
 ing on the porcelain. Practically the same thing will happen if the porcelain 
 is cracked, for the current will then take the direct route through the crack 
 rather than the route from spark point to spark point through the compressed 
 gas. The leakage through the carbon deposit must, therefore, be made as 
 difficult as possible by giving the leaking current a considerable distance to 
 travel; besides, special devices are sometimes employed to prevent; the collec- 
 tion of carbon. 
 
 2. The plug must be easily cleaned of whatever carbon may be deposited 
 on it. It must, therefore, be taken apart, reassembled, and made gas-tight 
 easily; besides, the packing process must not endanger the porcelain more than 
 necessary. 
 
 3. The plug must fit the standard sizes of threaded spark-plug holes and 
 must not be unduly expensive to replace. Among the sizes most used is the 
 so-called metric size, the proportions of which are based on the metric system 
 of measurement. Most of the imported spark plugs are of this size, which is 
 approximately the size of a -in. pipe tap, but they are not tapered. American 
 spark plugs are either of the i-in. or the f-in. pipe sizes. The pipe sizes are 
 tapered and depend for tightness on the plug being screwed in tightly. This 
 methpd is not altogether satisfactory, as the thread in the engine wears and 
 permits leakage, which causes the plug to heat. Both the engine and plug 
 tapers are liable to variations that may make one plug screw well into its hole 
 while another catches only a few threads, and consequently is not so well placed 
 for prompt communication of flame to the compressed charge. Plugs that are 
 not provided with tapered threads are made gas-tight by gaskets of asbestos 
 covered with thin copper sheathing. 
 
 It is desirable, though not essential, that the spark points should be of 
 platinum, because they do not then burn away to any appreciable extent. 
 When not made of platinum, they are often made of a special alloy of steel 
 and nickel, which resists oxidation nearly as well as platinum. The air gap 
 between the spark-plug points should not exceed 3 V in. nor be less than ^ in. ; 
 the best size is about midway between these dimensions. In case a battery 
 gives out and there is no other at hand, the engine may be kept going for a 
 short time by pinching the spark-plug points a little closer together, to reduce 
 the resistance offered by the gap. 
 
INTERNAL-COMBUSTION ENGINES 645 
 
 OPERATION OF INTERNAL-COMBUSTION ENGINES 
 
 Engine Starters. Engines of less than 40 H. P. are usually started by 
 turning over by hand, but larger engines are usually provided with some form 
 of starting mechanism. The use of compressed air to start the engine is prob- 
 ably the most convenient. Its only disadvantage is the possibility of the air 
 supply becoming exhausted by leaks in the tank or connections or through 
 repeated failures to start the engine. This disadvantage is of course increased 
 if the air compressor is operated from the engine itself or from a line shaft 
 operated by the engine. It is of less consequence if the compressor is driven 
 from a small auxiliary engine, the only difficulty in that case being the delay 
 caused by the time required for charging the air tank. 
 
 The operation of compressed-air starters is much simplified if the engine 
 is equipped with a mechanically driven and timed valve that admits the air 
 to the cylinder during what is usually the expansion stroke of the engine, 
 and allows it to escape during the regular exhaust stroke. In this case, all the 
 operator has to do is to open the cock in the air pipe between the tank and the 
 engine, and keep it open until the engine has attained a fair speed, when the 
 air connection is shut off and the fuel supply is turned on. If no mechanically 
 operated timing valve for compressed air is provided, the cock between the air 
 tank and the engine must be opened and closed by hand, at proper intervals; 
 this requires skill and watchfulness on the part of the attendant, since the cock 
 must be closed except during the working stroke of the piston. 
 
 A very effective method, employed on large engines especially, is to admit 
 air during every forward stroke of the piston and expel it during both the 
 compression and the exhaust strokes. This is done by providing auxiliary 
 cams that, when thrown in gear, will open the inlet valve during the suction 
 and expansion strokes and the exhaust valve during the compression and 
 exhaust strokes. After the engine is under way, the cams are disengaged and 
 the engine is run in the regular manner. 
 
 In order that the engine may always be started promptly, the attendant 
 must keep the air compressor and storage tank in good working order. The 
 compressor requires lubrication at regular intervals, and the air valves must 
 be kept tight to insure efficient service. The pressure in the tank should show 
 no perceptible loss over night; and if it should fall to any great extent, the 
 cause of the leak should be determined and the proper remedies applied. If 
 the leak is located in the seams or rivets of the tank, they must be calked in 
 the usual manner. In case the pipes or fittings between the tank and the 
 engine are not tight, they must be screwed up or defective fittings replaced 
 with perfect ones. 
 
 Starting the Engine. The following rules for starting and stopping gasoline 
 engines should be followed: 
 
 1. Attend to all lubricators and oil holes, always following the same order. 
 
 2. Apply a few drops of kerosene to the valve stems. 
 
 3. Open the gas-cock back of the rubber bag or regulator, or, when using 
 gasoline, open the cock near the tank, and work the gasoline pump by hand 
 until the liquid appears in the valve or overflow cup 
 
 4. See that the electric igniter is properly connected, turn on the switch, 
 and see that the spark is of proper intensity. 
 
 5. Turn the flywheel until the engine is at the beginning of the working 
 stroke. 
 
 6. Open the fuel cock to the point that has been found most reliable for 
 starting. 
 
 7. Throw the relief cam in gear or open the relief cock. 
 
 8. If a compressed-air or some other self-starter is employed, operate the 
 device. If no starting devices are used, turn the flywheels rapidly until the 
 engine starts. 
 
 9. Close the relief valve or disengage the relief cam and open the fuel cock 
 to its full extent, gradually, as the speed of the engine increases. 
 
 10. Turn on the cooling water, if running water is used, or see that the 
 tank is full and the cocks open if the tank system of cooling is employed. 
 
 11. Throw in the friction clutch or shift the belt to the tight pulley on the 
 line shaft. 
 
 Stopping the Engine. 1. Disengage the friction clutch or shift the belt 
 to the loose pulley on the line shaft. 
 
 2. Close the gas-cock near the rubber bag or regulator or the gasoline cock 
 near the storage tank. 
 35 
 
546 INTERNAL-COMBUSTION ENGINES 
 
 3. Close the gas or gasoline cock on the engine. 
 
 4. Throw off the switch between the battery and the engine, or turn off 
 the burner that heats the tube. 
 
 5. Drain the water-jacket by closing the valve in the supply pipe and 
 opening the cock that connects the bottom of the cylinder to the drain pipe. 
 If water tanks are used, close the cocks in the water pipe and open the drain 
 cock. 
 
 6. Shut off all sight-feed lubricators. 
 
 7. Clean the engine thoroughly, wiping off any oil or dust that may have 
 accumulated on the engine. 
 
 8. See that the engine stops in a position where the exhaust and inlet 
 valves are closed. If necessary, turn the wheels by hand until this position is 
 reached ; it will protect the valve seats against corrosion. 
 
 Lubrication. There are three essential properties that a good gas-engine 
 cylinder oil must possess. 
 
 1. It must have as high a fire-test as possible; that is, the temperature at 
 which it gives off inflammable vapor .should be as high as possible. In the best 
 gas-engine cylinder oils, this temperature will be from 500 to 650 F., which 
 is none too great considering the temperatures to which the oil is subjected 
 when exposed to the burning charge in the cylinder. 
 
 2. As the oil is vaporized by the heat, it should leave as little residue as 
 possible. Any cylinder oil will leave some carbon deposit, which gradually 
 accumulates on the inner walls of the combustion chamber and on the piston 
 head and valves, but it is desirable that this accumulation should be prevented 
 as far as practicable. If it becomes thick, especially if the compression is high 
 or if the form of the combustion chamber is such that sharp corners are exposed 
 to the heat of the flame, particles of the unburned carbon clinging to the walls 
 or elsewhere may become heated to such a degree as to ignite the charge spon- 
 taneously before compression is complete. 
 
 3. The oil should have a fairly high viscosity; that is, it should be quite 
 thick, because the high temperature of the cylinder will cause any ordinary 
 oil t9 run on the piston much like water and lose practically all its lubricating 
 qualities. 
 
 It is often advisable to use a higher grade of oil in a high-speed engine than 
 is necessary in a low-speed engine, owing to the greater rapidity of the explo- 
 sions in the former and the consequently higher internal temperature. As 
 the cylinder head of a high-speed engine is frequently cast in one piece 
 with the cylinder, it is very hard to get at the combustion chamber to scrape 
 the carbon deposit from it, and consequently it is well to use an oil that 
 leaves as little deposit as possible. 
 
 For air-cooled cylinders, only the heaviest oil obtainable and with the 
 highest possible fire-test should be used, and the oil tank should be placed 
 near enough to the cylinder or exhaust pipe to insure that the oil will not refuse 
 to feed in cold weather. 
 
 For ordinary water-cooled engines, except in the largest sizes, the grade 
 of cylinder oil known as heavy is appropriate for summer use. In weather cold 
 enough to cause this oil to stiffen, the next lighter grade, or medium, may be 
 employed. In cold weather, if the medium oil does not feed freely, it is best 
 to use a special oil suitable for use at low temperatures, though it is possible 
 to thin the regular oil with kerosene or gasoline, to make it flow, and to increase 
 correspondingly the feed off the oil cup or mechanical lubricator. It is best in 
 every case to purchase oil that is known to be reliable. Besides, many manu- 
 facturers purchase and sell oils marked with their own labels, which they 
 recommend for use in their engines. These oils may always be used with 
 confidence in any engine of about the same character as that for which they are 
 put up. 
 
 Should it be found impossible to obtain oil that is known to be suitable, 
 the samples available may be tested for viscosity by putting a few drops of 
 each on an inclined sheet of clean metal or glass, and noting the relative rapidity 
 of their flow. The one that flows most rapidly has the least viscosity, and the 
 one that flows most slowly has the greatest viscosity. The oils may be tested 
 roughly for flashing point and for the carbon residue they leave by putting a 
 little on a sheet of iron or tin plate, and heating gradually over a flame, taking 
 care to move the plate over the flame so that all parts of it are evenly heated. 
 The oils will become less viscous and will run on the plate, and for this reason 
 two samples compared at the same time should not be placed too close together. 
 They will gradually vaporize, leaving only a brownish and somewhat thick 
 residue, which should be as small in amount as possible. A good, heavy oil 
 
INTERNAL-COMBUSTION ENGINES 547 
 
 will vaporize almost completely, but will retain considerable body even at 
 temperatures where an oil of low fire-test would be entirely burned away. 
 Oils, either heavy or light, that leave any considerable amount of black, tarry 
 residue should be avoided. 
 
 Although, strictly speaking, cylinder oil needs to be used only for cylinder 
 lubrication, it is the almost universal custom to use the same oil for all bearings 
 of the motor. This simplifies the lubrication and removes the danger of making 
 a mistake in oiling the pistons. Cylinder oil is an excellent lubricant for 
 bearings subjected to hard service, as those of the crankpins and crank-shaft. 
 The bearings do not require as much oil as the pistons, four or five drops a 
 minute usually being sufficient. 
 
 ENGINE TROUBLES AND REMEDIES 
 
 Hot Bearings. The causes of hot bearings and the remedies therefor are 
 the same in internal-combustion as in steam and other engines. 
 
 Misfiring. Either total or partial misfiring may be due to any of the 
 following causes: Circuit not closed; weak battery; ignition fouled with soot; 
 wet spark points; broken spark plug; grounded circuit, usually the secondary; 
 broken wire or loose connection; trembler out of adjustment; igniter spring 
 weakened or broken; rarely, a defective spark coil or condenser. 
 
 Back Firing. The cause of back firing is in most cases due to the delayed 
 combustion of a weak mixture containing an insufficient amount of fuel. The 
 result of such a mixture is a weak explosion and slow burning, so that, during 
 the entire exhaust stroke and even at the beginning of the sucti9n stroke, there 
 is a flame in the combustion chamber. The fresh charge will therefore be 
 ignited by the flame of the delayed combustion of the previous charge; and, as 
 the inlet valve is open at that time toward the air-supply pipe or passage, a 
 loud report will be heard in the air vessel or in the space under the engine bed 
 whence the air is taken. The remedy for this condition is to increase the fuel 
 supply until the explosions become of normal strength. 
 
 Another cause of back firing may be the presence of an incandescent body 
 in the combustion chamber, such as a sharp point or edge of metal, a projecting 
 piece of asbestos packing, soot, or carbonized oil, and similar impurities accumu- 
 lating in the cylinder. To stop back firing from these causes, any projections 
 of metal or other material should be removed with a suitable tool and the 
 walls of the combustion chamber made as smooth as possible, or the cylinder 
 should be cleared of any soot or carbonized oil that may have gathered there. 
 
 Failure of the igniter to fire all charges admitted to the cylinder, or improper 
 composition of the mixture resulting in the same way, will be indicated by heavy 
 reports at the end of the exhaust pipe. One or more charges may in this 
 manner be forced through the cylinder into the exhaust pipe, and the first hot 
 exhaust resulting from the combustion of a charge will fire the mixture that 
 has accumulated in the pipe. 
 
 On account of the shorter time between the opening of the exhaust port and 
 the admission of the new charge in a two-cycle engine, there is much greater 
 liability to back firing in an engine of that type than in a four-cycle engine. 
 In a four-cycle engine, back firing will occur only when the inlet valve is off 
 its seat; hence, back firing is more of an element of danger in four-cycle than 
 in two-cycle engines. If there is no check-valve in the carbureter or vaporizer, 
 and there is no direct opening to the atmosphere, the column of flame that would 
 be blown through a carbureter or auxiliary air supply on account of back 
 firing would be particularly dangerous because accumulations of gasoline 
 vapor might thereby become ignited. 
 
 To be absolutely safe, a four-cycle engine having a float-feed carbureter 
 not supplied with a check-valve should take its supply of air from some high 
 point rather than from a point near the base. As the use of a check-valve in 
 the carbureter would materially reduce the efficiency of the engine, it is rarely 
 used. If a float-feed carbureter is used, and indications point to imperfect 
 carburization, the carbureter should be examined carefully. If the float leaks, 
 so that the height of gasoline is constantly above the desired level, or if the 
 float does not cut off the supply where it should, it will be necessary to take 
 the carbureter apart to ascertain the trouble. 
 
 Explosions in the muffler and exhaust piping are usually caused by the 
 ignition of the gas accumulating from missed explosions due to weak mixtures 
 or faulty ignition. They are not usually dangerous unless the muffler is large 
 and is weakened by rusting inside or out. 
 
548 INTERNAL-COMBUSTION ENGINES 
 
 Explosions in the carbureter are sometimes caused by the inlet valve stick- 
 ing open and permitting the flame to communicate from the spark. More 
 often it is due to improper mixture, which burns so slowly that flame lingers 
 in the cylinder even after the exhaust stroke is completed and the inlet valve 
 begins to open. Either a weak or a rich mixture will produce this result, 
 though not always both in the same engine. Carbureter explosions are often 
 attributed to the exhaust valve closing after the inlet valve opens, or to simple 
 leakage of the inlet valve; but these are seldom the real causes. 
 
 Preignition. Premature ignition, or preignition, while somewhat similar to 
 back firing in its nature and origin, manifests itself in a different way and has 
 a different effect on the action of the engine. Premature ignition, as usually 
 understood, is the firing of the partly compressed mixture before the time 
 fixed by the igniting mechanism. Its causes are similar to those that result 
 in back firing, the effect being different in that the charge is ignited later than 
 when back firing takes place, but before the end of the compression stroke. 
 Preignition will cause the engine to lose power on account of the maximum 
 pressure being exerted on the crank before it reaches the inner dead center 
 and thus haying a tendency to turn it in the wrong direction. 
 
 Besides the causes cited in connection with back firing, preignition may be 
 due to any one of the following defects: ' Insufficient cooling of the cylinder, 
 due either to shortage of cooling water or to the fact that portions of the water- 
 jacket become filled with lime deposits or impurities contained in the water, 
 thus interfering with proper circulation; compression too high for the grade 
 of fuel used; imperfections in the surfaces of the piston end or valve heads 
 exposed to the combustion, such as sandholes or similar cavities in which a 
 small portion of the burning charge may be confined ; electrodes or other parts 
 of the engine exposed to the burning charge too light; or the piston head or 
 exhaust- valve poppet insufficiently cooled and becoming red hot while the 
 engine is running under a fairly heavy load. 
 
 Premature ignition manifests itself by a pounding in the cylinder, and, if 
 permitted to continue, a drop in speed, finally resulting in the stopping of the 
 engine. It will also put an excessive amount of pressure on the bearings, 
 especially the connecting-rod brasses, and cause them to run hot even when 
 properly lubricated. After a shut-down due to premature ignition and a short 
 period during which the overheated parts are allowed to cool, it is possible to 
 start again and run until the conditions of load will again cause the trouble. 
 
 The remedies to be applied, according to the source of the difficulty, are 
 as follows: Increase the water supply until the cooling water leaves the 
 cylinder at a reasonable temperature, which may vary with the fuel used, but 
 which should never be over 180 F. Clean the water space and ports of any 
 dirt or deposit so as to insure free circulation of the cooling water. Reduce 
 the compression by partly throttling the air and fuel supply. Plug any sand- 
 holes or blowholes in the piston or valve heads, and make these surfaces per- 
 fectly smooth. Replace electrodes or other light parts with some capable 
 of absorbing and carrying off the heat without becoming red hot. If necessary, 
 arrange for cooling the piston by blowing air into the open end of the cylinder. 
 
 If the head of the exhaust valve becomes too hot, it is a sign that it is not 
 heavy enough, and it should be replaced by one with a head of sufficient thick- 
 ness to carry off through the valve stem the heat imparted to it by the combus- 
 tion. If a small particle of dirt lodges in a remote portion of the combustion 
 chamber, the richer part of the charge may not reach it until the piston has 
 traveled over a considerable portion of the compression stroke, and the result- 
 ing self -ignition may properly be called preignition. Every part of the com- 
 bustion chamber should therefore be examined and all dirt removed. 
 
 Carbureter Troubles. An engine may work improperly because the car- 
 bureter delivers no gasoline, an insufficient amount of gasoline, or too much 
 gasoline to the cylinders. When little or no gasoline reaches the cylinders, 
 the difficulty may be caused by: A failure to turn on the supply of gasoline, a 
 clogged feedpipe, too light a float, failure of the needle valve to open wide 
 enough, and obstructed nozzle. Too much gasoline in the carbureter is caused 
 by too heavy a float or because the valve does not close tightly. In the latter 
 case, the valve may need grinding or there may be grit between it and its seat. 
 
 Compression Troubles. Either partial or total loss of compression may 
 be due to any of the following causes: The valve stem may stick in the guide, 
 in which case it should be washed with gasoline or kerosene and then well 
 oiled; the valve stem may be weak or broken; the cylinder may be cracked; the 
 piston ring may be broken or turned so that the slots are in line; the valve may 
 need regnndmg; water may leak into the cylinder through a bad joint. 
 
PROSPECTING 549 
 
 PROSPECTING 
 
 OUTFIT AND METHODS 
 
 The prospector should have a general knowledge of the mineral-bearing 
 strata, and should know from the nature of the rocks exposed whether to 
 expect to find coal or not. _ He should also possess such a knowledge of the 
 use of tools as will enable him to construct simple structures, and a sufficient 
 experience in blacksmithing to enable him to sharpen picks and drills, or to 
 set a horseshoe, if necessary. 
 
 Outfit Necessary. The character of the prospecting being carried on will 
 have considerable effect on the outfit necessary, which should always be as 
 simple as possible. In general, when operating in a settled country, the 
 outfit is as follows: A compass and clinometer for determining the dip and 
 strike of the various measures encountered; a pick and shovel for excavating, 
 and, where rock is liable to be encountered, a set of drills, hammer, spoon 
 for cleaning the holes, tamping stick, powder and fuse, or dynamite fuse and 
 cap; an aneroid barometer for determining elevations, and a small hand pick; 
 the latter should weigh about 1| lb., and should have a pick on one end and a 
 square-faced hammer on the other, the handle being from 12 to 14 in. long. 
 
 If the region under consideration has been settled for some time, there 
 will probably be geological, county, railroad, or other maps available. These 
 may not be accurate as to detail, but will be of great assistance in the work 
 on account of the fact that they give the course of the railroads, streams, etc. 
 
 When operating in a mountainous region, away from a settled country, 
 the following materials, in addition to those already mentioned, maybe required: 
 A donkey or a pony packed with a couple of heavy blankets, an A tent, cook- 
 ing utensils, etc.; a supply of flour, sugar, bacon, salt, baking powder, and coffee, 
 sufficient for at least a month. It is also well to take some fruit, but all fruit 
 containing stones or pits should be avoided, as they are only dead weight, and 
 every pound counts. For the same reason, canned goods should be avoided, 
 on account of the large amount of water they contain. A healthy man will 
 require about 3 lb. of solid food per day. Many prefer to vary the diet by 
 taking rice, corn meal, beans, etc., in place of a portion of the flour. 
 
 Where game is abundant, a shot-gun or rifle will be found useful for supply- 
 ing fresh meat. In regions abounding in swamps it becomes necessary to 
 operate from canoes, or to take men for porters or packers, who carry the outfit 
 on their backs or heads. These men will carry from 60 to 125 lb. 
 
 Plan of Operations. When the presence of coal is suspected in a tract 
 of land, a thorough examination of the surface and a study of the exposed 
 rocks, in place, may result in its immediate discovery, or in positive proof 
 of its absence; or it may result in still further increasing the doubt of, or the 
 belief that, it does exist. The first procedure in prospecting a tract of land 
 is to traverse it thoroughly, and note carefully any stains or traces of smut, 
 and all outcrops of every description; and, whenever possible, take the dip 
 and the course of the outcrop with a pocket compass. Any fossils should also 
 be carefully noted, to assist in determining the geological age of the region. 
 These outcrops are frequently more readily found along roads or streams than 
 any other place on the tract. In traveling along the streams, the prospector 
 should pay particular attention to its bed and banks, to see whether there are 
 any small particles of coal or roof slate in the bed of the stream, or any stains 
 or smut exposed along the washed banks. If small pieces of coal or roof slate 
 are found in the stream, a search up it and its tributaries will show where the 
 outcrop from which the find came is located. When the ravines and valleys 
 are so filled with wash that no exposures are visible, and nothing is gained by 
 a careful examination of them, the prospector must rely on topographical 
 features to guide him. 
 
 In cases where there are no outcrops or any other surface indications, it 
 would become necessary to sink shafts or test pits, or to proceed by drilling. 
 The absence of any indication of coal in the soil may not prove that there is 
 not an outcrop near at hand, for the soil is frequently brought from a distance, 
 and bears no relation to the material underlying it. In like manner, glacial 
 soil often contains debris transported from seams many miles away; but such 
 
550 PROSPECTING 
 
 occurrences can usually be distinguished by the general character of the asso- 
 ciated wash material. 
 
 Frequently, the weathered outcrop of a seam has been overturned or 
 dragged back upon itself, so as to indicate the presence of a very thick deposit. 
 For this reason, any openings made to determine the character of the material 
 should be continued until the coal is of a firm character, and both floor and 
 roof are well exposed. Sometimes, in the case of steeply pitching coal beds, 
 the surface may be overturned for a considerable depth, so that it is difficult 
 to tell which is the roof and which is the floor. Usually, if Stigmaria? are found 
 in the rocks of one wall, it is supposed that this wall is the floor of the seam, 
 while if Sigillariae, fern leaves, etc. are found in the wall rock, it is probably 
 the roof of the deposit. These indications are not positive proof, for both of 
 these fossils may occur in either the top or bottom wall of a coal deposit, though 
 they are usually found in the positions noted. Coal usually occurs in unaltered 
 deposits, i. e., in rocks that have not undergone metamorphism, while metals 
 and metallic ores usually occur in rocks that have undergone more or less 
 metamorphism. This change may have been accompanied by heat and 
 volcanic disturbances sufficient to render the rocks thoroughly crystalline, or 
 it may simply have been the converting of limestone into dolomite. The 
 prospector for coal usually avoids regions in which the rocks have been altered; 
 but it should be remembered that a basin of unaltered stratified rocks con- 
 taining coal seams may be found in the very midst of a high mountain range 
 and surrounded by granitic and volcanic rocks, as in the Rocky Mountains. 
 
 When a prospector is operating in any particular region, it is best to study 
 carefully the conditions of that region before proceeding, as such factors as 
 lack of rain, frozen ground, etc. may have played an important part in deter- 
 mining the character of the outcrop and surface appearance of coal deposits. 
 Experience obtained in one region is frequently very misleading when applied 
 in another. 
 
 COAL-BEARING FORMATIONS 
 
 Outcrops. The presence of the outcrop of any bed may often be located 
 by a terrace caused by the difference in the hardness of the strata; but as any 
 soft material overlying a hard material will form a terrace, it is necessary to 
 have some means of distinguishing a coal terrace from one caused by worth' 
 less material. Usually, the outcrop of a coal terrace will be accompanied by 
 springs carrying a greater or less amount of iron in solution, which is 
 deposited as ochery films upon the stones and vegetable matter over which 
 the water flows. The outcrops of beds of iron or other ores are very fre- 
 quently marked by mineral springs. Sometimes the outcrop of a bed will 
 be characterized by a marked difference in the vegetation, as, for instance, 
 the outcrop of a bed of phosphate rock by a luxuriant line of vegetation, the 
 outcrop of a mineral bed by a lack of vegetation, the outcrop of a coal bed 
 contained between very hard rocks by more luxuriant vegetation than the 
 surrounding country, etc. Some indication as to the dip and strike of the 
 material composing the bed may be obtained by examining the terrace and 
 noting the deflections from a straight line caused by the changes in contour 
 of the ground. If the variation occasioned by a depression is toward the foot 
 of the hill, the bed dips in the same direction with the slope of the ground; but 
 if the deflection is toward the top of the hill, the dip is the reverse from the slope 
 of the ground, or into the hill. After any terrace or indication of the outcrop 
 of a bed has been discovered, it will be necessary to examine the outcrop by 
 means of shafts, tunnels, or trenches. The position of such openings will 
 depend on the general character of the terrace. If the dip appears to be with 
 the hill, a trench should be started below the terrace and continued to and across 
 it; while if the dip appears to be into the hill, it may be best to sink a shallow 
 shaft above the terrace. 
 
 Formations Likely to Contain Coal. No coal beds of importance have as yet 
 been found below the Carboniferous period, but coal may be looked for in any 
 stratified or sedimentary rocks that were formed after this period, although 
 the bulk of the best coal has been found in the Carboniferous period. As a 
 rule, highly metamorphic regions and regions composed of volcanic or igneous 
 rocks contain no coal. An examination of the fossils contained in the rocks 
 of any locality will usually determine whether they belong to a period below or 
 above the Carboniferous, and hence whether there is a probability of the forma- 
 tions containing coal. On account of this fact, the prospector should familiar- 
 ize himself with the geological periods, and, by referring to any elementary 
 
PROSPECTING 
 
 551 
 
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552 
 
 PROSPECTING 
 
 Black shale 
 Limestone 
 Shales and sandstone (blue stone) 
 Black shale 
 Limestone 
 Cherty limestone 
 Crystalline limestone 
 Shaly sandstone 
 Shaly sandstone 
 Sandstone 
 
 I B 1 e IS 
 
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 Alternating series of sandstones, 
 conglomerates, and volcanic 
 rocks 
 Metamorphic and igneous 
 granites, gneiss, schists, 
 quartzites, marbles, limestones, 
 slates, phyllites, iron ores, and 
 jaspilites 
 
 Igneous and metamorphic only 
 Granite, gneiss, and other crys- % 
 talline rocks 
 
 
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PROSPECTING 553 
 
 geology, with the most common fossils of each. The rocks most common in 
 coal measures are sandstones, limestones, shale, conglomerates, fireclays, and, 
 in sonic localities, the coal deposits are frequently associated with beds of 
 iron ore. 
 
 The preceding table gives the names of the various geological eras, 
 periods, epochs, and stages as they occur in the United States, together with 
 the kinds of rocks characterizing each. 
 
 Faults. Frequently a seam becomes faulted or pinched out underground, 
 and it is necessary to continue the search by means of underground prospect- 
 ing. If a fault or dislocation is encountered, the manner of carrying on the 
 search will depend on the character of the fault. Where sand faults or wash- 
 outs are encountered, the drift or entry should be driven forwards at the 
 angle of the seam until the continuation of the formation is encountered, when 
 a little examination of the rocks will indicate whether they are the under- 
 lying or overlying measures. In the case of dislocations or throws, the con- 
 tinuation of the seam may be looked for by Schmidt's law of faults, which is 
 as follows: Always follow the direction of the greatest angle. It has been dis- 
 covered that, in the majority of cases, the 
 hanging- wall portion of the fault has moved 
 down, and on this account such faults are 
 commonly called normal faults. For in- 
 stance, if the bed ab, of the accompany- 
 ing figure, were being worked from a to- 
 ward the fault, work would be continued 
 down on the farther side of the fault to- 
 ward d, until the continuation of the bed 
 toward b was encountered. In like man- 
 ner, had the work been proceeding from 
 b, the exploration would have been carried 
 up in the direction of the greatest angle, 
 and the continuation toward a thus dis- 
 covered. A reverse fault is 'one in which 
 the movement has been in the opposite 
 direction to a normal fault. Especially in the case of those mines where the 
 material occurs as perpendicular or steeply pitching veins, faults are liable to 
 displace the seam both horizontally and vertically, in which case it may be 
 difficult to determine the direction of the continuation of the bed; but frequently 
 pieces of coal or slate are dragged into the fault, and these serve as a guide to 
 the miner, and indicate the proper direction for exploration. Where a bed or 
 seam is faulted, its continuation can frequently be found by breaking through 
 into the measures beyond, when an examination of the formation will indicate 
 whether the rocks are those that usually occur above or below the desired seam. 
 
 EXPLORATION BY DRILLING OR BORE HOLES 
 
 Earth Augers. When testing for coal seams that occur comparatively 
 near the surface, hand augers may be employed to great advantage. A good 
 form of hand auger consists of a piece of flat steel or iron, with a steel tip, 
 twisted into a spiral about 1 ft. long, and having four turns. The point is 
 split and the tips sharpened and turned in opposite directions and dressed to 
 a standard width, usually 2 in. The auger is attached to a short piece of 1-in. 
 pipe, and is operated by joints of 1-in. pipe, which are coupled together with 
 common pipe couplings. The auger is turned by means of a double-ended 
 handle having an eye in the center through which the rod passes. 
 
 The handle is secured by means of a setscrew. In addition to the auger 
 it is well to have a straight-edged chopping bit for use in comparatively hard 
 seams. This may be made from a piece of If-in. octagon steel, with a 2-in. 
 cutting edge. The upper end of the steel is welded on to a piece of pipe similar 
 to that carrying the auger. When the chopping bit is employed, it is neces- 
 sary to have a heavy sinking bar, which may be made from a piece of solid 
 IJ-in. iron bar, fitted with ordinary 1-in. pipe threads on the ends. Pros- 
 pecting can be carried on to a depth of from 50 to 60 ft. with this outfit. The 
 number of men necessary to operate the rods varies from two to four, depending 
 on the depth of the hole being drilled. When more than 30 ft. of rods are in 
 use, it is usually necessary to have a scaffold on which some of the men can 
 stand to assist in withdrawing the rods. When withdrawing the rods, to 
 remove the dirt, they are not uncoupled unless over 40 ft. of rods are in use 
 
554 PROSPECTING 
 
 at one time, and sometimes as many as 50 or 60 ft. are drawn without 
 uncoupling. 
 
 Percussion Drills. Percussion, or churn, drills are frequently employed in 
 drilling for oil, water, or gas, and were formerly much used in searching for 
 coal and ores, but, owing to the fact that they all reduce the material passed 
 through to small pieces or mud, and so do not produce a fair sample, and to 
 the fact that they can only drill perpendicular holes, they are at present little 
 
 used in prospecting for either ore or coal. 
 _ _ TT T The cost and rate of drilling by means of a 
 
 COST OF WELL DRILL- percussion or churn drill varies greatly, being 
 ING affected much more by the character of the 
 
 strata penetrated than is the case with the 
 diamond drill. In the case of highly inclined 
 
 Size of Well 
 Inches 
 
 Cost per beds of varying hardness, the holes frequently 
 Foot run out of line and become so crooked that the 
 
 tools wedge, and drilling has to be suspended. 
 
 For drilling through moderately hard forma- 
 $1.50 tions, usually encountered in searching for gas 
 
 or water, such as sandstones, limestones, slates, 
 
 etc., the accompanying costs, from the Ameri- 
 5 . 00 can Well Works, Aurora, 111., may be taken per 
 15 foot for wells from 500 to 3,000 ft. deep for the 
 central or eastern portion of the United States. 
 
 This cost includes the placing of the casing, but 
 
 not the casing itself. 
 
 When drilling wells for oil or gas to a depth of approximately 1,000 ft., 
 using the ordinary American rig with a cable, the cost is sometimes reduced 
 to as little as 65 c. per ft. for 6-in. or 8-in. wells; this is when operating in 
 rather soft and known formations. From 15 to 40 ft. per da. of 24 hr. is usually 
 considered a good rate of drilling, though in soft materials as much as 100 ft. 
 may be drilled in a single day, and at other times, when very hard rock is 
 encountered, it is impossible to make more than from 1 to 2 ft. per da. 
 
 Percussion Core Drill. In order to overcome the chief objection to the 
 use of percussion drills in coal prospecting work, an attachment is now provided 
 which can be used in connection with the ordinary oil-well drilling outfit and 
 by means of which a core of a coal seam may be recovered. A 6-in. hole is 
 sunk with the ordinary tools until the vicinity of the bed to be cored has been 
 reached. The tools are then withdrawn, the bit and stem are removed, leaving 
 the jars and rope socket attached to the cable, and the core drill is attached 
 to the jars. This drill is a steel pipe about 14 ft. long provided with chisel- 
 shaped cutting teeth, and within which is placed the core-barrel. The hole 
 is carefully cleaned with the sand pump and its exact depth measured and 
 recorded. This core-drilling attachment is lowered carefully into the hole 
 until it rests on the bottom and drilling is resumed in the ordinary way at 
 a moderate speed but with a stroke of from 15 to 18 in. After drilling 20 or 
 30 in. the tools are withdrawn; a slight jar is sometimes necessary to break the 
 core loose. At the t9p of the hole, the tools are swung to one side, the core 
 barrel with the contained core removed from the drill and another core barrel 
 attached if a longer core is needed. Drilling operations are resumed while 
 the core is being removed from the core barrel just brought up. The core 
 barrels are 9f two lengths, the shorter ones being designed for use in hard 
 formations like sand rock, limestone, etc. 
 
 Core Drills. What are known as core drills are the only forms that have 
 proved successful in drilling in any direction through hard, soft, or variable 
 material. Even with core drills, many difficulties present themselves and 
 demand careful study in adapting the form of apparatus to the work in hand, 
 and in rightly interpreting the results obtained from any set of observations. 
 Core drills are of two main types, the diamond drill and the calyx drill. 
 The two are essentially alike in consisting of a cutting bit attached to the 
 end of a series of connected rods to which a rotary motion is applied by a 
 steam, electric, compressed-air, or gasoline motor. In the diamond drill, the 
 cutting bit consists of a hard steel cylinder in the bottom rim (both inner and 
 outer edges) of which are set fragments of black diamond (bort, or carbonado) 
 the edges of which slightly project beyond the metal surface of the bit. Being 
 the hardest substance known, upon being rotated, the diamonds naturally 
 cut out a cylindrical core of any rock penetrated. 
 
 The bit of the calyx drill is of two forms. For drilling in comparatively 
 soft rock, it consists of a steel cylinder with chisel-shaped teeth that cut and 
 
PROSPECTING 555 
 
 scrape away the rock. For drilling in harder rock, the bit is without teeth, 
 being merely a ring of metal with a slot in the side through which chilled steel 
 shot fed into the bore hole above find their way so that they may be rolled 
 over the surface of the rock to be cut as the bit is" rotated in the hole. While 
 the following is intended primarily to guide in the selection, use, etc., of a 
 diamond drilling machine, it is also applicable to the calyx drill. 
 
 Selecting the Machine. It is not economy to employ a machine of large 
 capacity in shallow explorations, as the large machines are provided with 
 powerful motors, and hence do not work economically under light loads. 
 When a large machine is operating small rods on light work, the driller cannot 
 tell the condition of the bit, or properly regulate the feed. The machine 
 should possess a motor of sufficient capacity to carry the work to the required 
 depth, but where much drilling is to be done, it is usually best to have two or 
 more machines, and to employ the small ones for shallow holes, and the large 
 ones for deep holes. 
 
 All feed mechanisms employed in diamond drilling may be divided into 
 two classes: Those that are an inverse function of the hardness of the material; 
 this class includes friction, spring, and hydraulic feeds. Those in which the 
 feed is independent of the material being cut, as in the case of the positive 
 gear-feed. The first class is advantageous when drilling through variable 
 measures in search of fairly firm material, which does not occur in very thin 
 beds or seams. On account of the fact that this class of feed insures the 
 maximum amount of advance of which the bit is capable in the material being 
 cut, the danger is that the core from any thin soft seam may be ground up 
 and washed away, without any indication of its presence having been given. 
 The second class, or positive gear-feed, if properly operated, requires some- 
 what greater skill, but if used in connection with a thrust register, it gives 
 reliable information as to the material being cut, and is especially useful when 
 prospecting for soft deposits of very valuable material. 
 
 Size of Tools. The size of tools and rods, and consequently the size of the 
 core extracted, depends on the depth of the hole and the character of the 
 material being prospected. When operating in firm measures, such as anthra- 
 cite, hard rock, etc., it is best to employ a rather small bit, even when drilling 
 up to 700 ft., or more, in depth. For such work, a core of from H to l^g in. is 
 usually extracted. The rate of drilling with a small outfit is very much greater 
 than with a large one, owing to the fact that there is a small cutting surface 
 exposed, and the rate of rotation of the rods can be much greater. When 
 prospecting for soft materials, such as bituminous coal, valuable soft ores, or 
 for disseminated ores, such as lead, copper, gold, silver, etc., it is best to employ 
 a larger outfit and extract a core 2 or 3 in. in diameter, and sometimes larger, 
 even though a comparatively small machine is used to operate the rods. 
 
 Diamond-Drilling. Drift of diamond-drill holes, or the divergence from the 
 straight line, often becomes a serious matter. This trouble may be minimized 
 by keeping the tools about the bit as nearly up to gauge as possible. Core 
 barrels, with spiral water grooves about them, answer this purpose very well 
 if they are renewed before excessive wear has taken place. 
 
 Surveying of diamond-drill holes may be carried on by either one of two 
 methods, depending on the magnetic conditions of the district. Where there 
 is no magnetic disturbance, the system developed by Mr. E. F. MacGeorge, 
 of Australia, may be employed. This consists in introducing into the hole, at 
 various points, small tubes containing melted gelatine, in which are suspended 
 magnetic needles and small plummets. After the gelatine has hardened the 
 tubes are removed, and the angles between the center line of the tube, the 
 plummet, and the needle noted, thus furnishing the data from which the course 
 of the hole can be plotted. This method gives both the vertical and the 
 horizontal drift. 
 
 Where there is magnetic disturbance the needle cannot be used, but a system 
 brought out by Mr. G. Nolten, of Germany , has been quite extensively employed. 
 In this case, tubes partly filled with hydrofluoric acid are introduced into the 
 hole, at various points, and the acid allowed to etch a ring on the inside of the 
 tube. After the acid has spent itself the tubes are withdrawn, and by bringing 
 the liquid into such a position that it corresponds with the ring etched on the 
 inside of the tube, the angle of the hole at the point examined can be determined. 
 This method gives a record of the vertical drift of the hole only. 
 
 The value of the record furnished by the diamond drill depends largely on 
 the character of the material sought. The core extracted is always of very 
 small volume when compared with the large mass of the formation prospected, 
 and hence will give a fair average sample only in the case of very uniform 
 
556 PROSPECTING 
 
 deposits. The value of the diamond drill for prospecting may be stated as 
 follows: More dependence can be placed on the record furnished by the diamond 
 drill when prospecting for materials that occur in large bodies of uniform com- 
 position than when prospecting for materials that occur in small bunches or irregu- 
 lar seams. To the first class belong coal, iron ore, low-grade finely disseminated 
 gold and silver ores, many deposits of copper, lead, zmc, etc., as well as salt, 
 gypsum, building stone, etc. To the latter class belong small but rich bunches 
 of gold, silver mineral, or rich streaks of gold telluride. 
 
 The arrangement of holes has considerable effect upon the results furnished. 
 If the material sought lies in beds or seams (as coal), the dip of which is fairly 
 well known, it is best to drill a series of holes at right angles to the formation. 
 If the material sought occurs in irregular bunches, pockets, or lenses, it will 
 be necessary to drill holes at two or more angles, so as to divide the ground 
 into a series of rectangles, thus rendering it practically impossible for any vein 
 or seam of commercial importance to exist without being discovered. Where 
 the surface of the ground is covered with drift and wash material, it may be 
 best to sink a shaft or drill pit to bed rock, and locate the machine on bed rock. 
 After this, several series of fan holes may be drilled at various angles from the 
 bottom of the pit. Owing to the upward drift of diamond-drill holes, the 
 results furnished from a set of fan holes drilled from a single position would 
 make a flat bed appear as an inverted bowl, or the top of a hill. On this 
 account, it is best to drill sets of fan holes from two or more locations, so that 
 they will correct one another. If fan holes from different positions intersect 
 the same bed, a careful examination of them will usually furnish a check on the 
 vertical drift of the holes. 
 
 The speed and cost of drilling depend on the hardness and character of the 
 rock, the size of the hole, the depth of the hole, and the height of the derrick. 
 Sedimentary rocks, such as sandstones, slates, and limestones are generally 
 more rapidly drilled than the much harder and unstratified igneous rocks, and 
 firm rocks than those that cave and require that the hole be cased. Cores 
 of moderate size, say, up to 1 to 2 in. in diameter can be taken out more 
 rapidly and hence at less labor cost (the chief item in drilling) than larger ones, 
 and answer just as well for determining the nature and value of the rocks 
 passed through. The deeper the hole, the more costly and the less the progress 
 per shift, because of the time lost in pulling the drill rods and removing the 
 cores. With deep holes the labor cost is materially reduced if the derrick is 
 sufficiently high to permit unscrewing the drill rods at every fourth joint while 
 raising them for the purpose of extracting the core. 
 
 The actual rate of drilling, including pulling the rods, removing the cores, 
 etc., is dependent on the depth of the hole. In shallow holes, a rate of 2 ft. 
 per hr. is fair; in holes of moderate depth, say, up to 700 ft., a rate of 1 ft. per 
 hr. should be secured. 
 
 Prospecting with core drills is usually done under contract at an agreed 
 sum per foot, which is determined by the number of holes, their average depth, 
 size of core extracted, distance apart of the holes, etc. Contract prices for 
 diamond drilling in the bituminous coal regions range from $2 to $2.75 per foot 
 for extracting cores up to say, H in., where the holes range from 150 to 500 ft. 
 in depth (averaging, say, 250 ft.), where from 1,200 to 2,000 ft. of drilling is 
 required, and where the coal and water are furnished the contractor. 
 
 Where the drill is owned by an operating coal company, the cost of ordinary 
 drilling should be less than $1 per ft., including labor, diamonds, and ordinary 
 repairs. 
 
 Calyx Drilling. The calyx drill will do essentially the same work as the dia- 
 mond drill, except that it will rfot cut at angles of over 45 because the shot will 
 roll to and remain at the lower side of the hole, and even this pitch is too flat 
 for really satisfactory work. The gain in the use of the calyx over the diamond 
 drill consists in the saving in cost of the abrasive material used. Black 
 diamonds are now quoted as high as $90 a carat for the larger and better stones, 
 so that a single bit will often cost from $750 to $2,000, according to size. There 
 should be at least two bits in stock, so that one may always be in condition 
 for use. If drilling is carried on a long distance from the base of supplies, 
 three, four, or even more bits must be available, or else a diamond -setter must 
 be employed. Setting diamonds is highly skilled labor and is paid accordingly. 
 
 When the material is so soft that the shot wedge or press into it the bit with 
 teeth is to be preferred to the shot bit , the latter coming in use when the rock is 
 firm sandstone, limestone, and the like. The amount of shot used varies with 
 the hardness of the material being drilled. Shale, slate, limestone, and ordi- 
 nary sandstone may require from i to f Ib. of shot per foot of hole. Very 
 
PROSPECTING 557 
 
 hard sandstone, granite, quartz conglomerate, porphyry, taconite, and jasper 
 require from 1 to 4 Ib. per ft. Another material sometimes used is crushed 
 steel, variously sold under such names as "diamondite," "abrasite," etc. While 
 ordinarily inferior to chilled shot, and not giving such satisfactory results, for 
 comparatively soft formations it is sometimes better than shot. 
 
 The calyx drill, like the diamond drill, is manufactured to be operated by 
 hand or horsepower for use in boring shallow holes, and is also to be had mounted 
 on a wagon-luce frame with attached derrick for ease in transportation. 
 
 Prospecting for Petroleum, Natural Gas, and Bitumen. Among the surface 
 indications of petroleum and bitumen may be mentioned white leached shales 
 or sandstones, shales burned to redness, fumaroles, mineral springs, and 
 deposits from mineral springs. Also natural gas, springs of petroleum oil and 
 naphtha, porous rocks saturated with bitumen, cracks in shale, and other rock 
 partly filled with bitumen. Petroleum is never found in any quantity in 
 metamorphic rocks, but always in sedimentary deposits. Bitumen can be told 
 from coal, vegetable matter, iron, manganese, and other minerals, which it 
 sometimes closely resembles, by its odor and taste, also by the fact that it melts 
 in the flame of a match or candle, giving a bituminous odor. (Iron and man- 
 ganese do not fuse, and coal and vegetable matter burn without fusion.) Bitu- 
 men is also soluble in bisulphide of carbon, chloroform, and turpentine, usually 
 giving a dark, black, or brown solution. Frequently, springs or ponds have an 
 iridescent coating of oil upon the surface. Sometimes iron compounds give 
 practically the same appearance, but the iron coating can always be distin- 
 guished from the oil by agitating the surface of the water, when the iron coating 
 will break up like a crust of solid material, while the oil will behave as a fluid, 
 and tend to remain over the entire surface even when it is agitated. 
 
 Frequently, bubbles of gas are seen ascending from the bottoms of pools 
 or creeks. These may be composed of carbureted hydrogen or natural gas, 
 which is a good indication of the presence of petroleum or bitumen; they may 
 be composed of sulphureted hydrogen or carbonic-acid gas. Carbureted hydro- 
 gen can be distinguished by the fact that it burns with a yellow luminous 
 flame whereas sulphureted hydrogen burns with a bluish flame, and carbon 
 dioxide will not support combustion, but, on the contrary, is a product of 
 combustion. When carbureted hydrogen gas is discovered ascending from 
 water, the bottom of which is not covered with decaying vegetation, it is 
 almost a certain sign that there is petroleum or bitumen somewhere in the 
 underlying or adjacent formations. If natural gas or bitumen is found upon 
 the surface of shale, it is probable that the material ascended vertically through 
 cracks in these rocks from porous strata below; while if it is found in connection 
 with sandstones, it is probable that the material was derived from the porous 
 sandstone itself. This is especially liable to be true if the sandstone has a 
 steep pitch. 
 
 As a rule, deposits of bitumen or petroleum occur in porous formations 
 overlaid by impervious strata, such as shales, slates, etc. Anticlines are more 
 liable to contain such deposits, though they are not absolutely necessary to 
 retain them, as at times portions of the underlying porous strata have been 
 rendered impervious by deposits of calcium salts, silica, etc., and hence the 
 petroleum or bitumen will be confined to the porous portions. Natural gas 
 also occurs under similar conditions, but usually in anticlines only. 
 
 Construction of Geological Maps and Cross-Sections. After the surface 
 examination of a property is complete, the data should be entered on the best 
 map procurable, or a map constructed. The scale depends on the size of the 
 property, the complexity of the geological formation, the value of the property, 
 and the material to be mined from it. The amount of work that it will pay 
 to put on the survey will depend largely on the value of the property, more 
 detail being justified in the case of high-grade properties. If a property 1 ,200 ft. 
 X 3,000 ft. (the size of four U. S. metal mining claims) were to be surveyed 
 and mapped with a scale of 1 in. equal to 100 ft., the map would be 12 in, 
 X30 in. A stratum 10ft. wide on this map would appear as ^g in. wide, 
 which is about the smallest division that could be shown with its characteristic 
 symbol; for greater detail, a larger scale, or larger scaled sheets of the most 
 important portions of the deposit, will be necessary. If the geologist con- 
 structs the topographical contour map, he can take notes on the geology at 
 the same time. When the boundaries of the property are being surveyed, 
 certain points should be established, both vertically and horizontally, as 
 stations in future'topographical work. If the map is on government surveyed 
 fand, the government lines may be used for horizontal locations, but it will be 
 necessary to determine the elevation of the different points. If the property 
 
558 PROSPECTING 
 
 is much broken, it is well to run a few lines of levels across it, to establish 
 points from which to continue the work. This work is usually done with a 
 Y level and chain, the other details being subsequently filled in with a transit 
 and stadia; the levels of the other points are taken by using the transit as a 
 level, by vertical angles, by barometric 
 observations, or by means of a hand level. 
 Where lines of levels are run across the 
 property in various directions it is best to 
 run them so that they will cross the strike 
 of the strata as nearly at right angles as 
 possible, so that the profile thus deter- 
 mined may be used in constructing a 
 cross-section. Sometimes, for preliminary 
 work, simply a sketch map is all that may 
 be necessary. All of the outcrop and ex- 
 posures, together with their proper dip, 
 should be entered on the map. 
 
 To Obtain Dip and Strike From Bore- 
 Hole Records. Before the results obtained 
 from bore holes are available for use in 
 map construction, the dip and strike of 
 the various strata must be ascertained. 
 The process, in the case of stratified rock, 
 is as follows: If three holes were drilled, 
 
 FIG. 1 
 
 as at A, B, and C, Fig. 1, each intersecting a given bed, the strike and angle of 
 dip of the bed may be obtained by reducing the results from the three holes to a 
 plane passing through the highest point of intersection, which is at A. The 
 hole B intersected the bed at the distance Be, and C at the distance Cd below 
 the point A. By continuing the line CB indefinitely and erecting two lines Be 
 and Cd perpendicular to it, each representing the distance from the horizontal 
 plane through A to the intersection of the strata, two points in the line de are 
 obtained, which line intersects CB produced at /; / is one point in the line of 
 strike through A. In order to find the angle of dip, the perpendicular Cg is 
 dropped from the deepest hole C upon the line of strike A/. The distance Ch, 
 equal to Cd, is laid off at right angles to Cg, when the angle Cgh gives the 
 maximum dip. The results obtained from bore holes may thus be reduced 
 to such form that the dips can be projected on the surface to obtain the line of 
 outcrop for each stratum. Bore holes also furnish data for constructing 
 underground curves in cross-sections of stratified rocks. 
 
 Having recorded on the map all exposures, whether surface or those obtained 
 from underground work, draw the line of strike and the outcrops. Also con- 
 struct a cross-section. If the seam is perpendicular, the outcrop will be a 
 straight course across the map. If the bed is horizontal, the outcrop will 
 correspond with a contour line. For beds dipping at -any other angle, results 
 between these limits will be 
 obtained. % 
 
 If the property being ex- f- 
 amined is cut by synclines or 
 anticlines, the dips will not 
 all be in the same direction, 
 and if there is a dip along the 
 axis of the synclines or anti- 
 clines, the construction of the 
 map will be considerably com- ' 
 plicated. Fig. 2 represents a 
 plan or map on which there is 
 an axis xy toward which the 
 
 strata dip from both sides. \ / 
 
 Outcrops are indicated at 
 A, B, C, A' and B', each hav- 
 ing a dip in the direction of the V 
 arrow. The lines mn, op, and p IG 2 
 qr are contours. If the cross- 
 section were constructed on the line FG, perpendicular to the axis xy, the various 
 beds or deposits would be cut at such an angle as to show a thickness in the 
 cross-section greater than that which actually exists. In order to show 
 the actual- thickness for each seam, the cross-section must be taken along the 
 line perpeandictalar to the strike of the strata, which, in the present case, is 
 
PROSPECTING 
 
 559 
 
 along the line IHK. In other words, the cross-section must be constructed 
 in two parts. Where a general sketch is all that is necessary, a single cross- 
 section with notes correcting the thickness of the seams may answer. 
 
 In order to construct the cross-section IHK, the outcrops- A, B, C, A', 
 and B' must be projected to the points a, b, c, a', and b', this projection being 
 along their contours. If the points on the line of the intended cross-section 
 were not upon the contour, it would be necessary to project them on the plane 
 of the cross-section, as shown in the figure, and then from the dip of the strata 
 and the difference in elevation to obtain a corrected point along the line IHK. 
 The cross-section is constructed as 
 shown in Fig. 3, each seam having 
 its actual thickness as shown at the 
 outcrop. If the upper surface of 
 the cross-section is not a true profile 
 of the surface, and the points are not 
 projected in the plane on the cross- 
 section, on this cross-section, ac- 
 cording to their dips, there is con- 
 siderable danger of exaggerating 
 their thickness one way or the other. 
 
 On mine maps, the supposed 
 course of the beds should be sketched 
 in, subject to revision, as more 
 data are brought out by later 
 development work. Even in the 
 case of stratified rocks, it is diffi- 
 
 FIG. 3 
 
 cult to form a definite idea as to the underground conditions from surface 
 indications, and, in the case of metamorphic or crystalline rocks, it is abso- 
 lutely necessary to determine the underground conditions by drilling, or actual 
 development work. If the property being examined is liable to become a large 
 and valuable mining property, the original survey should be tied to monuments 
 or natural landmarks, so that it can be checked by future observations, and 
 these monuments or landmarks should become the basis of future and more 
 careful mining surveys. 
 
 Some of the advantages of a careful geological examination of a property 
 are that other materials of economic value would probably be discovered 
 if any should exist on the porperty: also, such an examination of the 
 property gives information as to the drainage system of the country that 
 nray be of great advantage in laying out the mine, and future exploration by 
 drilling or sinking can be done to better advantage after a careful surface 
 examination. 
 
 Sampling and Estimating the Amount of Mineral Available. In many 
 cases, it is necessary to do some development or exploration work before fair 
 average samples can be obtained. The samples as taken should fairly represent 
 the coal as it will be extracted. Such slate as would be sold with the coal 
 should be included in the sample. When sampling any property it is well to 
 divide the seam up into blocks, and sample each one separately. The samples 
 may then be analyzed and an average obtained later, or the different samples 
 may be mixed and an average analysis obtained. The amount of material 
 broken for sample may vary from a few pounds to several tons. Large samples 
 may be reduced by shoveling (that is, taking a proportionate number of shovel- 
 fuls for the sample, as every third or fourth shovelful). After the sample has 
 been partly reduced, the operation may be carried on by quartering, which 
 may be described as follows: 
 
 The coal is shoveled into a conical pile by throwing each shovelful on 
 to the apex of the cone. After this, the cone may be reduced by scraping it 
 down with a shovel, passing slowly around it. If the amount of material is 
 small, a flat plate may be introduced into the cone, and the pile flattened 
 by revolving the plate. The pile is then divided into quarters by drawing 
 lines across it. After this, two alternate quarters are scraped out and shoveled 
 away, and the other two quarters are left as the sample. The process may 
 be repeated until the block has been sufficiently reduced. In shoveling away 
 the discarded portions, care should be taken to see that the fine dust under 
 them is brushed away also, as it often contains much of the impurity in the 
 seams and its not being included might unduly increase the quality of the 
 resulting sample. If the property being examined is a mine in active opera- 
 tion, samples may be taken from the working faces, and also from cars, loading 
 chutes, etc. Usually, the samples from the face are kept separate from those 
 
560 PROSPECTING 
 
 from the cars and loading chutes, the latter being intended as a check on the 
 former. 
 
 The human factor always plays a large part in the value of a sample as 
 finally selected, and hence it should be taken by a man who has had con- 
 siderable experience in this class of work. For this reason, it is best to employ 
 a mining engineer. One not accustomed to sampling very rarely undervalues 
 a property, owing to the fact that it seems to be human nature to pick up a 
 pure piece of coal, rather than the worthless bone or slate. 
 
 If a seam is penetrated by a number oi bore holes, or by workings extended 
 over a considerable area, it is fair to estimate that the material will run prac- 
 tically as exposed for a considerable area; but especially in the case of bitu- 
 minous coal, it is a comparatively easy matter to form some estimate as to the 
 amount of material available. The tonnage of coal seams per 1 in. and 1 ft. 
 of thickness is given in the section upon weights of materials, etc. 
 
 1. SITUATION AND! 
 SURROUNDINGS | 
 
 2. TOPOGRAPHY 
 
 1. Name 
 
 DIAGRAM FOR REPORTING ON COAL LANDS 
 
 The following diagram will be useful as a guide in making out. .a report on 
 a coal mining property: 
 
 " 1. Location, if on surveyed land 
 
 2. Nearest town or village 
 
 3. Mineral district 
 
 . 4. County, state, or territory 
 
 (. 2. Distance and direction from one or more points 
 ' 1 . Hills or mountains 
 
 2. Character of surface, vegetation, and timber 
 
 3. Streams and water supply 
 
 4. Elevations 
 
 1. Stratified 
 
 Crystalline 
 . Igneous 
 Anticlines or synclines 
 
 1. Number 
 
 2. Strike 
 
 1. Structure 
 
 3. GEOLOGY- 
 
 1. Rocks 
 
 2. Axes 
 
 {I: 
 
 \3. 
 
 3. Faults 
 
 4. Dikes 
 
 Horses 
 
 2. Geological period 
 
 3. Dip 
 
 4. Throw 
 
 1. Number 
 
 2. Strike 
 
 ip 
 
 illi 
 
 Throw 
 
 Number and size 
 Location 
 Material 
 
 3. Di 
 
 4. Filng 
 
 3. Coal beds 
 
 (I: 
 
 | 1. Reported 
 
 4. Quality of coal, spec- 
 imens, appearance in 
 mine, in cars 
 
 Number I 2. Measured fl. Reported 
 Thickness I 3. Average < 2. According to 
 [ 4. Uniformity [ measurement 
 
 1. Color, external, powder 
 
 2. Luster 
 
 3. Clearness from clay or sand, shale 
 
 4. Sulphur 
 
 5. Resin 
 
 6. Firmness, size of lumps, air slaking 
 
 7. Cleavage or fiber 
 .8. Coking 
 
 9. Color of ashes 
 
 10. Use: Gas, steam, domestic, forge, 
 metallurgy, coking 
 
 11. Analyses 
 
PROSPECTING 
 DIAGRAM FOR REPORTING ON COAL LANDS (Continued) 
 
 561 
 
 4. MINING 
 
 1. History 
 
 2. Mine 
 
 1. Dates of opening, abandoning, reopening, num- 
 ber of mines and names 
 
 2. Ownership 
 
 3. Superintendence 
 
 1. Shaft, slope, or tunnel 
 
 {1. Total depth 
 2. Depth below water level 
 3. Number of levels 
 4. Extent of levels 
 
 3. Water pumps, size and kind, water cars, number 
 and size, natural drainage 
 
 4. Ventilation, natural, furnace, fan (force or 
 exhaust), sufficient or insufficient 
 
 o. Lighting, system used 
 
 6. Powder, kind and grade used 
 
 7. Explosive or noxious gases 
 
 8. Coal-cutting machines and power drills 
 
 '1. Room and pillar: (a) single entry, 
 (6) double entry, (c) three or more 
 
 9. Mode of I entries 
 
 working | 2. Longwall: (a) advancing, (b) re- 
 treating 
 3. Modifications of (1) and (2) 
 
 10. Rooms, p 
 
 lars, dimensions, and general plan 
 
 3. Sections 
 
 5. MAPS AND DRAWINGS 
 
 G. COKE OVENS < 
 
 11. Timbering 
 
 12. Roof, or hanging wall, strong or weak, air slakes 
 or not 
 
 13. Floor, or foot-wall, hard or soft, creeps or not 
 
 14. Roads, rails, and cars 
 
 II. Mules 
 2. Electricity 
 3. Compressed air 
 4. Wire rope 
 5. Chain 
 6. Locomotive 
 16. System of hoisting; Cage, skip, cars. 
 
 1. Of the whole region 
 
 2. Of the underground workings 
 
 '1. Cross 
 
 2. Longitudinal 
 
 fl. General 
 
 3. Columnar {2. Coal bed or other 
 
 I deposit 
 
 4. Buildings, works, or machinery 
 '1. Scale 
 2. North line, magnetic variation 
 
 o. Explanation <{ gate^ 
 
 5. Can buy, take, borrow, or have 
 copied 
 
 1. History, ownership, etc. 
 
 2. Number 
 
 3. Character of ovens 
 
 4. Dimensions 
 
 5. Construction, materials, etc. 
 
 f 1. Charge, quantity, etc. 
 
 6. Operations < 2. Working 
 
 13. 
 
 7. Repairs 
 
 8. Quality of product (analyses, if any) 
 
 9. Disposition of by-products 
 
 (1. Construction 
 2. Condition 
 3. Capacity 
 4. Water supply and consumption 
 5. Quality of product 
 
 Discharging, quenching 
 
 36 
 
562 PROSPECTING 
 
 DIAGRAM FOR REPORTING ON COAL LANDS (Continued) 
 
 7. DISPOSITION 
 OF PRODUCT 
 
 1. Shipped 
 
 t 
 
 K 
 
 As mined to 
 
 As coke | ; 
 
 Distance 
 Roads 
 
 jobber 
 
 Blast furnace 
 Trade or jobber 
 
 8. STATISTICS 
 
 2. Shipment, 3> Rail , oads 
 1.4. Navigation 
 f 1. Capacity, maximum and minimum 
 
 1. Productions fl. Daily.weekly, or monthly, in tons 
 
 1 2. ActuaK 2. Yearly, in tons 
 
 1 3. Average 
 1. Whole number of workers 
 
 2. Labor { 2. Number of workers in each class 
 
 3. Number of horses or mules 
 
 1. Timber 
 
 2. Tools 
 
 3. Fuel 
 
 4. Oil 
 
 5. Powder 
 
 i p Jfi T *fl. Day, different classes 
 
 Or l2. Contract or piece, yard or ton 
 
 7. Carriage 
 
 8. Local sales of product 
 
 (1. Machinery 
 2. Buildings 
 3. Roads, tracks, etc. 
 4. Rolling stock 
 5. Supplies 
 {1. Boilers 
 2. Waterwheels 
 3. Air compressors 
 4! Steam and gas engines 
 5. Electric plants 
 
 ( 1. Power for 
 1. Smith's 
 shop 
 
 9. SURFACE PLANT 
 
 2. Shops 
 
 3. Powder houses 
 
 4. Offices 
 
 5. Dry or change houses 
 
 6. Storehouses 
 
 2. Number of forges 
 
 3. Steam hammers 
 
 4. Other tools 
 
 {1. Power for 
 2. Saws 
 I! otSfmachines 
 5. Benches and vises 
 
 1. Power 
 
 2. Lathes 
 
 3. Planers 
 
 4. Shapers 
 
 5. Drill presses 
 
 6. Other tools 
 
 7. Benches and vises 
 
 3. Machine 
 shop 
 
 7. Boarding and dwelling houses 
 
 8. Stables 
 
 9. Shaft houses 
 
 10. Tipples 
 
 11. Pockets or slack bins 
 
 12. Company store 
 
 13. Timber yard and plant for preparing timber 
 
 14. Water 
 
 1. City or com- 
 mercial 
 
 2. Company 
 service 
 
 1. Quality of water 
 
 2. Sufficient or insufficient 
 
 3. Pressure 
 
 1. Quality of water 
 
 2. Sufficient or insufficient 
 
 3. Gravity system 
 
 fl. Direct 
 
 4. Pumping < 2. Reservoir 
 system I or stand pipe 
 
OPENING A MINE 
 DIAGRAM FOR REPORTING ON COAL LANDS (Co nlinued) 
 
 563 
 
 '15. Lighting 
 
 Character 
 
 Origin 
 
 f 1 . Commercial plant 
 \2. Company plant 
 
 I 3. Sufficient or insufficient 
 f 1. Steam engines 
 
 16. Hoisting or wind- 1 J ^1 oJgas^ne'engines 
 
 ing plant | ^ Electric motors 
 
 1 5. Water motors 
 
 
 1. Gauge 
 
 
 2. Total length 
 
 
 1. Railroad- 
 
 3. Size of cars 
 4. Number of cars 
 
 17. Surface trans- 
 
 
 5. Power used 
 6. Number of motors 
 
 portation 
 
 
 1. Character and sur- 
 
 
 2. Wagon 
 roads 
 
 face of 
 2. Length 
 3. Number of wagons 
 
 
 and teams 
 
 10. MISCELLANEOUS 
 
 11. CONCLUSIONS < 
 
 Gross 
 
 1. Yearly income, last year, or for any year-j ^ Net 
 
 2. Average cost per ton of material 
 
 f 1 . Quality of coal or coke 
 I 2. A 
 
 3. Merits of 
 property 
 
 4. Advice 
 
 
 5. Local considerations 
 
 Amount of coal/ 1. Gross 
 \ in sight 1 2. Net 
 
 1 3. Value of coal in sight 
 2. Value of plants and works 
 
 . Continue present system 
 
 Change system to 
 
 2. Disposition f 1. Ship as mined 
 Coke and ship 
 
 1. Troubles 
 
 2. Labor 
 
 3. Supplies 
 
 4. Climate 
 
 5. Shipment facilities 
 
 6. Markets 
 
 . 
 
 1 \/t- /! 
 
 1. Mining ( 2 . 
 
 2. Disposition fl. 
 of product \ 2. 
 
 OPENING A MINE 
 
 GENERAL AND FINANCIAL CONSIDERATIONS 
 
 Usually the kind of opening through which the coal underlying a tract of 
 land must be extracted is not a matter of choice but is fixed by the distance 
 of the seam above or below the surface at the point where the plant must of 
 necessity be built. If the seam outcrops near the selected site, the coal will be 
 opened by a drift if the measures are horizontal or nearly so, or by a slope 
 driven down the dip if the bed is inclined. If the coal does not outcrop, it 
 must be opened by a vertical shaft, although, if the distance to the seam does 
 not exceed, say, 50 to 100 ft., the mine may be opened by a rock slope; that 
 is, by an inclined passageway driven downwards through the rock to intersect 
 the seam. 
 
 In mountainous districts, the outcrop of a steeply pitching seam may be 
 inaccessible by reason of its great elevation above the valley. In such a case, 
 the mine may be opened by a rock tunnel driven from some point at the proper 
 elevation in the valley across the inclined measures until the seam is met. 
 In rare instances, the seam, while not outcropping within the limits of the 
 property, lies but a short distance beneath the surface, and may be worked 
 by stripping as explained under Methods of Working, 
 
564 OPENING A MINE 
 
 Relation Between Investment and Cost of Production. Where a choice is 
 possible, the relative cost of opening and equipping the mine by each type of 
 opening (drift, slope, and shaft) must be considered in connection with the 
 cost of operating through each before a selection can be made. If the capital 
 is to be had, an increased investment is often warranted by a lower cost of 
 production made possible through its use. The increased cost of driving and 
 equipping one kind of opening as compared with another can usually be deter- 
 mined within fairly close limits, but it requires the skill and judgment acquired 
 through long experience to be able to estimate, even approximately, in advance 
 of actual developments how much more it will cost per ton to extract coal under 
 one set of conditions than under another. The general method of making 
 these calculations is shown in the following: 
 
 EXAMPLE. --There are 2,000,000 T. of coal in a property that it is proposed 
 to extract in 10 yr. at the average rate of 200,000 T. per yr. A shaft costing 
 $50,000 to sink and equip will effect an estimated saving of 5.25 c. per T. in 
 the cost of production over a slope costing $20,000. If the money to open the 
 property must be repaid in ten annual instalments with interest at 6%, which 
 opening should be selected and what is the gain by so doing? 
 
 SOLUTION. In the case of the shaft, there will be due at the end of the first 
 year interest on the entire loan or $3,000 and one- tenth of the principal or 
 $5,000, a total of $8,000; at the end of the second year there will be due inter- 
 est on $45,000 or $2,700 and one-tenth of the remaining capital, a total of 
 $7,700; and similarly each year thereafter until the end of the tenth year 
 when the last payment of $5,300 for both principal and interest will be due. 
 During the life of the mine there will have been paid out for principal and 
 interest, the sum of $66,500, or an average of 66,500^2,000,000 = 3.325 c. per 
 T. of coal produced. 
 
 In the same way it may be shown that the total cost for principal and inter- 
 est for sinking and equipping a slope will be $26,600, or at the rate of 1.33 c. 
 per T. 
 
 So far as the investment alone is concerned, the slope is the cheaper to 
 the extent of 3.3251.33 = 1.995 c. per T., or very nearly $40,000 during the 
 life of the property. On the other hand, mining through a shaft means a reduc- 
 tion in the cost of production of 5.25 c. per T. Hence, a net saving of 5.25 
 -1.995 = 3.255 c. per T., or a total saving of .3255X2,000,000 = $65,100 will 
 be effected by sinking, equipping, and using a shaft. 
 
 Relative Cost of Different Types of Opening. As drifts and slopes are 
 driven through much softer material (coal), they are much less costly than 
 shafts, which are sunk through rock; and, further, the returns from the coal 
 extracted from them to some extent offset the cost of driving. Owing to the 
 greater difficulty of handling materials on a pitch, to the added cost of pump- 
 ing water, etc., slopes are more expensive to drive than drifts. Furthermore, 
 the cost of the massive head-frames, powerful pumps and hoisting engines, 
 etc., comnwnly required at shafts, and to but a slightly less extent at slopes, 
 adds materially to the capital invested in equipment over that necessary for 
 a drift. Therefore, from the standpoint of capital required, the choice of open- 
 ing will be in the order, drift, slope, shaft. 
 
 Cost of Production as Affected by Type of Opening. That type of opening 
 is to be preferred which permits of the lowest cost of production for the same 
 investment of capital. In the case of flat seams, the cost of production is 
 materially less in a mine opened by a drift than in one opened by a slope or a 
 shaft. This is largely due to the fact that in the latter cases, the delivery of 
 the coal to the tipple is made in two stages; first, hauling it to the foot of the 
 slope or shaft; second, hoisting it to the surface. In drift mines, the coal is 
 hauled directly to the tipple in one operation and hoisting costs are thus saved. 
 Furthermore, in drift mines the cost of pumping is usually negligible and that 
 of handling men and supplies is a minimum. Flat seams are sometimes opened 
 by a rock slope, but no reduction in operating costs is effected thereby unless 
 the slope is short and the pitch such that long trips can be hauled and the men 
 can walk to and from their work. 
 
 Whether a pitching seam is more cheaply operated through a slope driven 
 from the outcrop on the coal or through a vertical shaft intersecting the seam 
 at some depth below the crop cannot be determined without a careful study of 
 all the factors concerned in the particular case. If the slope is comparatively 
 flat it is to be preferred to a shaft, but if the pitch is so great that the mine cars 
 must be hoisted on a slope carriage or is so very steep that the coal must be 
 lumped at the foot of the slope into a gunboat or skip, a shaft is more cheaply 
 
OPENING A MINE 565 
 
 In general, the cost of production through the three types of opening is in 
 the same relative order as the cost of making openings; namely, drift, slope, 
 and shaft, although, in the case of highly inclined slopes, the order will be, 
 drift, shaft, and slope. 
 
 LOCATION OF SURFACE PLANT 
 
 While every endeavor should be made to locate the mine opening and 
 screening plant so that each may be operated with the greatest efficiency and 
 economy, this is not always possible. Usually, the surface plant must be 
 located to meet certain natural, business, or financial conditions, and the loca- 
 tion of the mine opening is subordinated to the absolute necessity of prepar- 
 ing the coal in such a way that it is marketable. When locating the surface 
 plant the following points have to be considered: 
 
 Grades. The track grade should be such that the railroad cars will drop 
 by gravity from one end of the siding to the other. Opinions differ as to 
 the most desirable grades, but 1.5 to 2% from the end of the tail-track to the 
 tipple is ample for the empties; and for loading under the tipple and thence to 
 the end of the loaded track, 1.25% gives excellent results. Sometimes grades 
 of 3% and more are met above a tipple, but such slopes are very dangerous, 
 owing to the liability of a string of empties running down into the cars being 
 loaded. When the grades are so flat that the cars will not run except when 
 pinch bars are used, it will prove profitable to install some kind of car haul 
 or car-spotting device operated by steam power. 
 
 Length and Number of Sidings. The length of the sidings necessary for 
 the storage of empty and loaded railroad cars will depend on the daily output 
 of the mine and the number of sizes of coal shipped. The output of the mine 
 depends on the ability of the company to sell the coal at a profit, and this, 
 in a great measure, hinges on the quality of the product. A high-grade fuel, 
 even at a high price, is more salable and is in steadier demand than a poor one. 
 
 There must be as much storage room for loaded cars below the tipple as 
 there is for the storage of empty cars above it. If the coal is loaded in steel 
 hoppers of 100,000 Ib. (50 T.) capacity, averaging 40 ft. in length there will 
 be required for each 1,000 T. of daily capacity (1 ,000 -i- 50) X 40 = 800 ft. of 
 siding. To allow for switches and for cars of less capacity, it is better to assume 
 1,000 ft. of siding for each 1,000 T. of daily output. For a single-track tipple, 
 that is, one under which there is but one loading track and hence shipping 
 mine-run coal only, there will thus be required 2,000 ft. of siding for each 
 1,000 T. of output. In the case of two- and three-track tipples (those load- 
 ing two or three sizes of coal) if there is 2,000 ft. from the point of switch on 
 the main line above the tipple to the corresponding point below it, there will 
 be car-storage room for more than 1,000 T. capacity. This is because the 
 second loading track will have, say, 1,500 ft., and the third, say, 1,000 ft. of 
 available storage room, half above and half below the tipple. Owing to 
 uncertainties and irregularities in train service, it is highly advisable to 
 provide storage room for 2 da. car supply. 
 
 The width of bottom land required for the siding depends on the number 
 of sizes of coal shipped. It is possible, but unusual, to ship but one size, that 
 is, mine run or the unscreened output as mined. If the supply train pushes 
 the empties above the tipple, they may be dropped down and loaded upon the 
 same track. This will require about 16 ft. in width^for the roadbed and ditches. 
 Commonly, the empties are placed by the switch'engine at the upper end of 
 the mine branch railroad (or are dropped on the main line if the mine is situated 
 thereon), and pass by gravity on to the mine siding or loading track, and down 
 it to the tipple. The two tracks are commonly laid with their center lines 13 ft. 
 apart, which requires a grade from 26 to 28 ft. wide, depending on the size of 
 the side ditches. At the tipple, and for a few hundred feet above and below 
 it where the cars are being handled during loading, the tracks should be laid 
 with not less than 15 ft. between center lines ; and if fast passenger traffic is 
 passing on the main line, this distance should be 18 to 20 ft., unless a high fence 
 is built between the mine and railroad tracks. This will require a bottom 
 width of from 28 to 35 ft. For each additional size of coal shipped one track 
 and 15 ft. of width should be allowed. Thus, if three sizes are made and the 
 supply and first loading track require 30 ft. of width, there will be needed a 
 total of 30+ 15+ 15 = 60 ft. for the three loading and one supply track. While 
 this width may be reduced in a tipple of steel construction, which spans the 
 tracks and does not require bents between them, it is not advisable to reduce 
 the distance between the supply and first loading tracks. 
 
566 OPENING A MINE 
 
 Mining Plant. The space required for the mining plant, including in that 
 term the tipple, boiler, and power house, car and repair shops, stable, sup- 
 ply house, fan, etc., will vary from a few hundred square feet at a small mine 
 to several acres at a large one. The tipple must be located with respect to the 
 tracks as explained. The fan is always and the car and repair shops and the 
 stable are commonly placed near the mine mouth. The supply house is better 
 placed near the tracks for ease in unloading supplies. If electric power is used 
 and the boiler and power plant are placed near the tipple, cheap slack may be 
 used for fuel, and the necessary power for running the fan, shop machinery, 
 haulage motors, etc., may be cheaply conveyed to the mine at any reasonable 
 distance. If compressed air is used for coal cutting and haulage, the air com- 
 pressor may be placed at the mine mouth and operated by electricity generated 
 at a distance. If room for the boiler and power plant is not to be had at the 
 tipple, they must be located near the mine mouth, must use mine-run coal for 
 fuel, and the power for operating the machinery must be transmitted to the 
 tipple. For ease in supervision, the various units of the plant should be near 
 to one another. 
 
 Mining Village. As it is easier to hold and secure men if their homes 
 are near their work, it is advisable to place the mining town (village, camp, or 
 settlement) near the mine mouth, as this location will suit practically all 
 the workers except, perhaps, the tipple hands. The space required for the 
 town varies according to the number of men required to produce the desired 
 tonnage, and this will depend on the thickness of the seam, its relative hard- 
 ness, use or non-use of coal-cutting machinery, etc. Probably it is a fair esti- 
 mate to assume that housing must be provided for from 150 to 200 families for 
 each 1,000 T. of daily output. In addition, space must be provided for a store, 
 a schoolhouse, several churches, a hall for assemblies, etc. It is now cus- 
 tomary to provide playgrounds for the children and baseball fields and swim- 
 ming pools, etc., for the men. Each house should be placed on a lot 50X 150 ft., 
 that there may be room for a kitchen garden in the rear. If i A. can be given 
 each house it is better, and the saving in insurance by having the houses farther 
 apart is an item of importance. Two hundred houses, each on a lot 50 X 150 ft., 
 can be built on 50 A., assuming the streets and alleys to take half as much 
 space as the building lots. To the 50 A. must be added from 10 to 25 A. for 
 stores, churches, schools, playgrounds, etc. Space for the village is easily 
 obtainable in level country, but in mountainous districts the houses are too 
 commonly perched along the hillsides in an unsightly fashion. In this case, 
 it is advisable to secure the services of a competent landscape architect to 
 secure the best and most artistic arrangement of the houses with respect to the 
 irregularities of the surface. It is greater economy to pump water, haul sup- 
 plies, etc., to a well-situated town, than to consider only the first cost and place 
 the town in an undesirable location near a stream or the railroad tracks. 
 
 Coke Ovens. If the coal, either as mine run or as slack, is coked on the 
 property, more room is required than if it is all shipped to market, except in 
 the unusual case where there are four or five loading tracks under the tipple. 
 The space required for the ovens will depend on the tonnage of coke desired, 
 whether the ovens are built in bank (single row) or in block (double row placed 
 back to back) , and on the width of yard required in front of the ovens to store 
 the coke before it is loaded into cars. A beehive oven may be counted upon 
 to yield an average of 2 to 2.5 T. of coke daily, depending on the size of the 
 oven, kind of coal charged, etc. An output of 500 T. per day will, therefore, 
 require 200 to 250 ovens. The distance apart, center to center, of the ovens 
 will be equal to the diameter of the oven plus twice the thickness of the lining 
 brick, or 2X9 = 18 in., plus from 4 to 6 in. between ovens in which clay is 
 tamped. The spacing for ovens 12 ft. 6 in. in inside diameter (a common size) 
 will thence be 12 ft. 6 in. + l ft. 6 in. + (say) 6 in. = 14 ft. 6 in. Allowing 5 ft. 
 for the two end walls, the 200 to 250 ovens required for an output of 500 T. 
 will be either 200X14.5+5 = 2,905 ft. or 250X14.5+5 = 3,625 ft. if built in 
 bank, and one-half these lengths if built in block. The capacity of the rail- 
 road cars into which coke is loaded varies greatly. It is difficult to get the full 
 30 T. into box cars of 60,000 Ib. capacity, but special coke racks, as they are 
 called, will hold 50 T. Thus it will require ten to twenty cars, depending on 
 their kind, to hold the assumed 500 T. of coke. If 750 ft. of clear trackage, 
 or, say, 1,000 ft. to allow for switches, clearance, etc., is allowed both above 
 and below the ovens, there will be ample room to hold the smallest cars used 
 in the coke business. Thus, including the storage tracks, a bank of 200 to 
 250 ovens will be, say, 4,900 to 5,600 ft. long. If built in block about 1,000 ft. 
 in total length will be saved. 
 
OPENING A MINE 567 
 
 The 12.5-ft. bank oven has a width of practically 16 ft. from the side hill 
 against which it is built to the front, or mortar wall. The width of the coke 
 yard in front of the ovens varies from as little as 10 ft., in cases where the coke 
 is loaded out promptly, to as much as 30 ft. where, owing to uncertain market 
 conditions, the coke must be piled on the yards pending sale. Further, there 
 must be added, say, 14 ft. for the track upon which the cars are loaded. Hence, 
 a row of bank ovens, exclusive of the space required for the supply track, will 
 have a width of from 16+10+14 = 40 ft. to 16+30+14 = 60 ft. 
 
 The same sized oven arranged in block will require a width of about 33 ft. 
 from the face of one front wall to the other. The two yards will vary between 
 2X10 = 20 ft. and 2X30 = 60 ft. in width, and the two loading tracks will 
 require 2 X 14 = 28 ft. Thus, a block of beehive ovens of standard size will be 
 81 to 121 ft. wide, exclusive of the supply track. 
 
 It is well to have the tipple or coal bins at the upper end of the ovens, 
 particularly if the grade is steep, so that the charging larry may run or may be 
 assisted in running by gravity. This is not so important if mechanical haulage 
 is used. 
 
 LOCATION OF MINE OPENING 
 
 In level countries, it is almost always possible to so locate the mine with 
 respect to the surface plant, that both mining and outside costs are a minimum. 
 In hilly countries, however, the site of the surface plant is determined by the 
 conditions just discussed, and the place for the mine opening may have to be 
 decided by striking a balance between an increased or decreased cost of pro- 
 duction on the one hand and a decreased or increased capital charge (interest 
 and sinking fund) on the other. 
 
 When locating the mine opening, the following points should be consid- 
 ered: The opening should be at the lowest point of the seam; that gravity 
 may assist both the underground haulage and drainage; haulage is almost 
 always cheaper underground than on the surface and particularly so where 
 the winters are severe and the fall and spring wet; the mine opening should be 
 as near as possible to the tipple, as the concentration of the plant at one point 
 tends to efficient management, and objectionable surface haulage is avoided. 
 
 Flat Seams. A flat seam is commonly understood to be one in which 
 the dip does not exceed 50 to 150 ft. to the mile, or, say, 1 to 3%; in all cases 
 such a seam should be opened at the tipple by the necessary drift or shaft. 
 It is desirable to have the dip of the seam in favor of the haulage, but if it is 
 not, the more advantageous location of the opening and the saving in surface 
 haulage more than offsets the small increased cost for power in hauling up such 
 slight grades. If the seam outcrops, an endeavor should be made to open it at 
 tipple height. By tipple height is meant the distance between the rail on which 
 the mine cars stand on the tipple and the rail on which the railroad cars are 
 loaded. This distance varies according to the number of sizes of coal shipped. 
 If mine-run coal only is loaded, this height need not exceed 16 to 18 ft. If 
 three, four, or more sizes are loaded the height will be 30 or 32 ft., or even more, 
 in order that the proper pitch may be given the screens over which the coal 
 is sized. For modern tipples, a fair height is 32 ft. It will be understood that 
 the outcrop of the seam is assumed to be at some elevation above the tipple 
 
 Klatform in order that gravity may assist the movement of the loaded mine cars 
 rom the drift mouth to the dump. This elevation will be at the rate of 1 to 
 1.5 ft. per 100 ft. of distance. Thus, a drift mouth 35 ft. above the railroad 
 and 300 ft. from the dump will afford a tipple height of 35 (300 X .01) =32 ft. 
 if the down-grade from the mine is 1%. If the coal is not shipped but is coked 
 at the plant, the mine cars may be run from an opening 60 to 75 ft. above the 
 valley directly to bins into which they are dumped, the coal being drawn out 
 below into larries and conveyed to the ovens. If the coal outcrops at more than 
 tipple height, say, at an elevation of 100 or 200 ft., or more, it is commonly 
 lowered on a self-acting or gravity incline. In other cases, the coal is dumped 
 at the mine mouth into a retarding conveyer and carried in a continuous stream 
 to the tipple, or the loaded cars are dropped to the tipple by a chain haul. In 
 the Pocahontas region of West Virginia, in order to provide storage room for 
 coal that the mine may be kept in operation while waiting for railroad cars to 
 load the output, as well as to secure height for the slack bins, which are built in 
 as an integral part of the tipple, it is customary to make the tipple height 60 ft. 
 or more, even in those cases where the mine cars are dropped down on a self- 
 acting incline. This permits of a very long chute in which may be stored 
 enough coal to fill three, four, or even more railroad cars. 
 
568 OPENING A MINE 
 
 Seams of Moderate Dip. Where the pitch of the seam does not exceed, 
 say 30 if the opening can be placed at the tipple, it is probably the better 
 plan to open the property by a slope driven directly down the dip. The seam 
 may then be developed by a series of levels driven both to the right and left 
 on grades favorable to haulage, and the mine cars may be run directly from 
 these levels to and up the slope. If a seam of this pitch is opened by a shaft, 
 it will be necessary to lower all the coal produced on each level to the mam level 
 driven from the shaft bottom. While this lowering is commonly done on self- 
 acting inclines at no expense for power, the machinery and track are costly to 
 maintain and there must be several attendants for each incline. If the seam 
 lays in the form of a syncline, whether it is better opened by one or more slopes 
 driven down from the outcrop or by a shaft tapping the basin at its lowest 
 point should be made the subject of a careful calculation by these methods. 
 
 Seams of High Dip. Where the dip of the seam is so great that the coal 
 must be dumped into gunboats, much fine coal is made through this extra 
 handling While this is not objectionable where the entire output is coked or 
 even in those cases where the slack alone is so treated, it is a source of loss at 
 those mines where a large percentage of lump coal is desirable. In the latter 
 case the cost of production is less and the coal will reach the surface in better 
 shape if the seam is opened from a vertical shaft by rock tunnels driven there- 
 from at regular intervals, as the underground haulage is less and the mine cars 
 are loaded directly on to the shaft cages. As before, the best method for open- 
 ing is to be decided after striking a balance between increased capital account 
 and decreased cost of production and higher selling price because of the larger 
 percentage of lump coal. 
 
 Method of Working. As the system ad9pted for actually extracting the 
 coal may have some effect upon the location and method of opening the 
 mine, the section entitled Method of Working should be consulted in connection 
 herewith. 
 
 DRIFTS 
 
 The size of a drift depends on the output desired, the size of the mine cars 
 to be used, the character of the haulage, the thickness and character of the 
 coal seam, and the character of the top and bottom rock. The height of the 
 drift should not exceed the thickness of the seam, unless absolutely necessary, 
 in order to avoid the expense of brushing (taking down) the roof or lifting 
 (taking up) the floor. There should be at least 6 ft., and better, 6 ft. 6 in., 
 from the top of the track tie to the roof or to the bottom of the timbers used 
 for supporting the roof, so that the men who are employed at the mine mouth 
 in handling the cars can walk without stooping. 
 
 The width of the drift depends on the purpose for which it is employed. If 
 used solely for a manway, a width of 6 ft. is ample. If used solely as an intake 
 airway, the drift should be as wide as economically possible, in order to reduce 
 the friction and the velocity of the air and the power required to move it. 
 Common widths for intake airways are 8 and 10 ft. When the drift is used for 
 haulage, about the least width that can be used when any allowance is made 
 for the safe passage of men is 8 ft., and 10 ft. is much better in view of the fact 
 that the average haulageway is also an airway in which the mine cars form a 
 serious obstruction to the ventilation, even if the opening is of good size. 
 
 When the drifts are used for haulage, it is a question whether the empty 
 and loaded trips should run upon parallel tracks or whether each should have its 
 separate opening. A two-track opening will have to be 16 to 20 ft. in width, 
 and if the roof is at all poor the cost of timbering will be excessive. For this 
 reason, and to prevent accidents to the employes from trips passing in opposite 
 directions, many operators prefer distinct openings for the in-going and out- 
 going traffic. In any case, posts (props) are to be avoided between tracks. 
 
 The grade of a drift is determined by the dip of the seam, but the perfect 
 grade is one on which the pull required to return the empty car to the face is 
 exactly equal to that needed to bring out the loaded car. A grade of from 1 to 
 1.5% in favor of the loads gives excellent results, but less will do if the track 
 is well kept up and the car wheels are provided with roller or ball bearings to 
 reduce friction. 
 
 A gutter or ditch is commonly dug along one rib, and is lined with tile or 
 concrete or has a wooden trough laid in it if the bottom is soft and apt to erode. 
 If the drift is being driven down hill, the water can be siphoned out for some 
 time, after which a small steam, compressed-air, or electric pump must be 
 used for the purpose. 
 
OPENING A MINE 
 
 569 
 
 In beginning a drift, an open cut is first started in the hillside. Its width 
 at the face should be somewhat wider than the drift itself, and the two wings, 
 or side walls, should diverge outwards so that the floor plan has somewhat the 
 shape of a truncated V. This open cut should be continued until rock firm 
 enough to be supported by timber is encountered, when a substantial set of 
 timbers should be placed. These may be replaced after the drift is sufficiently 
 
 advanced by steel beams or by masonry or concrete. When the coal is reached, 
 ordinary mining operations begin. 
 
 In order to prevent the hillside from washing into the cut and blocking the 
 tracks at the drift mouth, the loose material above the opening as well as that 
 forming the roof and sides is frequently held in place by masonry or concrete 
 walls, arches, etc. Some of the forms employed are shown in the accompany- 
 ing illustration. 
 
 TUNNELS 
 
 TUNNELS THROUGH LOOSE GROUND 
 
 Unless the outcrop of the seam is plainly exposed, it is well to put down a 
 number of churn-drill holes along the supposed place of outcrop and at an eleva- 
 tion above that of the roof of the coal. These holes will determine the char- 
 acter of the covering immediately over the seam. If the roof rock is found in 
 place but a short distance back of the toe of the crop, the drift.may be begun 
 by an open cut as just explained. If, however, the outcrop is covered with a 
 layer of wash or drift, 25 or 50 ft., or more, in thickness, it is not generally 
 possible (owing to the running of the sides, etc.) to proceed with an open cut. 
 Instead, some one of the methods for tunneling through loose ground must be 
 employed. These methods have been very completely developed in connec- 
 tion with railroad and underwater tunnels. Among the numerous processes 
 are forepoling, wedging, the pneumatic process, the freezing process, and the 
 use of metallic shields; the last three are described under the' heading Shafts. 
 
 Forepoling. Forepoling is used when driving through loose ground both 
 at the outcrop of the seam, and underground where the coal seam is replaced 
 by the clay, sand, and gravel of an old river bed. The process consists in 
 driving sharpened pieces of narrow plank, or lagging, into the roof at a very 
 slight pitch. The lagging rests on the collar of one timber set and is held 
 firmly by having its end underneath the next timber toward the outside. 
 
570 
 
 OPENING A MINE 
 
 In the cut, a are the posts of sets of timbers, b the caps, and e the top bridg- 
 ing. The front ends of the spiles g from any given set rest on the bridging of the 
 
 next advanced set, and the spiles 
 for advancing the work are driven 
 between the bridging and the set, 
 as shown. To force the spiles 
 into the ground, so as to provide 
 room for the placing of the next 
 set, tail-pieces * are placed behind 
 the back end of the spiles as they 
 are being driven. After the spiles 
 have been driven forwards the 
 desired amount, another set is 
 p]acedf the tail-pieces knocked 
 out, and the front end of the spiles allowed to settle against the bridging 
 of a new set. Where the face is composed of extremely bad material, it may 
 be necessary to hold it in place with breast boards k held in place by props I 
 that rest against the forward timber set. In a similar manner the side lagging h 
 is placed in position. When breast boards are used, it is generally necessary to 
 employ foot and collar braces between the sets, so as to transfer the pressure 
 of the breast back through several sets. 
 
 To start the forepoling at the mouth of the drift, several sets of timbers are 
 set up and long lagging driven over them into the earth beyond. By bal- 
 ancing the pressure of the earth on the points of the lagging with a weight of 
 stone or timber on the outside end, they are held up and enough earth removed 
 to allow another set being placed to support^the lagging nearer the tunnel face. 
 While practicable in rather loose ground, this method is not available in mate- 
 rial containing boulders, and is dangerous when used in quicksand. 
 
 Wedging. It has sometimes been possible to drive through quicksand 
 by using, in combination with forepoling, a number of wedges as shown in 
 the accompanying illustration. Here, a are the posts of regular timber sets; 
 b, the side planking; c, the spiling driven, as in forepoling, to support the top; 
 d, the wedges; e, the tailing pieces; /, the floor; g, the bridging pieces; and h, 
 the cap pieces. The set of timber shown below e is only placed temporarily, 
 and is removed after the spile c is driven forwards. 
 
 The wedges d are driven into the face by means of a ram made of a piece 
 of timber swung from the roof. They simply crowd the material away from 
 
 in front of the excavation; if the pressure becomes so great that they can be 
 driven no farther, a few auger holes are bored into the face to relieve the pres- 
 sure by allowing some of the material to flow into the drift. Wedges are 
 
OPENING A MINE 
 
 571 
 
 driven into the floor with a mallet as fast as those in the face advance, and are 
 ultimately covered with a plank floor. 
 
 TUNNELS THROUGH ROCK 
 
 Tunnels through rock, commonly called rock tunnels,- are used in coal- 
 mining operations to open a steeply pitching seam that extends upwards in 
 the hills a considerable distance above drainage, by driving across the measures 
 to the coal from some convenient elevation near the surface plant. They 
 are also much used in mines where the strata are contorted, as in the anthra- 
 cite regions of Pennsylvania, to connect two pitching and parallel seams, and 
 to drive through anticlines or synclines in those cases where following the con- 
 tour of the seam would result in the gangway being either too crooked or too 
 steep for successful haulage. 
 
 The conditions governing the location, size, etc., of rock tunnels used to 
 develop a property are the same as in the case of drifts. If the surface is firm , 
 the tunnel may be started by an open cut; if it is not, forepoling or wedging 
 must be resorted to. Underground tunnels, used to connect adjacent seams, 
 etc., are usually made as small as is consistent with safety as they are used 
 mainly for haulage. 
 
 Arrangement of Drill Holes. In driving rock tunnels, the chief item of 
 cost, under ordinary circumstances, is that of drilling. Where machine drills 
 
 are used, there will be more or less time consumed in shifting machines, for 
 which reason it is deemed advisable, wherever headings are large enough, to 
 use two machines and if possible on one column or bar. This is frequently 
 also the case in shaft sinking. The machines should be so placed that the holes 
 may be drilled methodically, so as to economize in powder and time. 
 
 In tunnel driving and in shaft sinking, there is always one free face, and in 
 order to obtain two free faces it is necessary to first take out a cone or wedge 
 of rock from the center or side of the heading. Holes put in for this purpose 
 are termed key holes, or cut holes, and are fired simultaneously, in order to obtain 
 the best effect of the powder and to save time. 
 
 In making key holes, the size of the heading and the hardness of the rock 
 are to be considered. In soft rock, key holes in the bottom may be the best. 
 In harder rock, the key holes may be arranged in circular form to take out a 
 cone. The outer holes are then arranged more or less concentrically with the 
 center cut holes, or more frequently the key holes are arranged in straight 
 lines from top to bottom of the face so as to take out a wedge-shaped center 
 cut. _ The enlarging holes are similarly arranged in straight lines parallel to 
 the lines of key holes. 
 
 American and European Practice. -It is customary in some European 
 countries to place the breaking-in holes so that they will not meet, in order 
 
572 
 
 OPENING A MINE 
 
 that there may be a wide end to the cavity broken out by them; American 
 practice however, is to make them meet so that the increased quantity of 
 powder that may be inserted will have more effect. European practice is gen- 
 erally to use short holes; that is, one-half the width of the heading, while Amer- 
 ican practice is to make the holes about as deep as the heading is high. While 
 the two systems call for about the same number of feet of drill hole, there must 
 necessarily be considerable saving in time where drills are not changed as often 
 as is required in European practice. 
 
 The American system is probably the better where labor is expensive, 
 since it permits of quicker advance and keeps the shifts up to their work in 
 better shape. It requires, however, more explosive, and is therefore best 
 adapted for countries where explosives are cheaper than labor. 
 
 Conical Center Cut. Fig. 1 (a) shows a rock heading 6 ft. by 7 ft. in 
 medium-hard homogeneous rock. The key holes 1 are put in at an angle so 
 that the bottom of the holes will meet at a depth of about 6 ft. from the face; 
 view (b) shows a section of (a). Where drill holes meet in this manner, they 
 form a chamber in which the powder can be placed in larger quantities and be 
 more effective than in single drill holes. The direction of the second rows of 
 holes is shown at 2, and the third row at 3. The holes are all drilled in one shift, 
 and the blasting done and the broken rock removed by the following shift, 
 It is customary to charge and blast the holes by rounds, 1 being first fired. 
 
 f\ y 
 
 
 3 3 
 
 3 
 
 9 2 
 
 
 :,3 1 
 
 3^, 
 
 jr ^o c _, J 
 
 
 y 
 
 
 ? J 2 
 
 3^ = 
 
 444 
 
 4 
 
 *? n fl 
 
 y 
 
 FIG. 2 
 
 and as soon as rock is cleared from this the enlarging holes & may be charged. 
 It is sometimes customary to fire holes 2 and 3 together, but it is better to 
 fire 2 and remove the dirt, and lastly S, as that gives a larger free surface to 
 work on. There must be a wait, after each round is fired, for the air to change, 
 but with an air hose the foul air can be driven out quickly, and while the rock 
 is being removed the next round may be charged. The number 8 round is 
 known as the squaring-up round, and while the holes are placed a short dis- 
 tance from the roof and floor they are kept, as nearly as is possible, parallel 
 with the side walls. That they are not put in exactly horizontal is due to the 
 inability of the drill runner to place the machine nearer the walls. The num- 
 ber and position of the drill holes for enlarging will depend on the size of the 
 heading and the explosive used. 
 
 In some cases, the bottom holes S are fired after the upper holes S, as by 
 that operation the debris is moved forwards making the work of the shovelers 
 easier. 
 
 Fig. 2 (a) and (6) shows another arrangement where the rock is hard. The 
 key holes 1 m this case are four in number and outside of them are four enlarg- 
 ing holes 2. It might be possible to load and fire holes S and 4 together, but 
 as the latter are in tension and the number S holes are assisted somewhat by- 
 gravity, better results will probably be obtained by firing number 4 holes last. 
 
OPENING A MINE 
 
 573 
 
 It is to be understood that what has 
 been stated is not always the proper 
 way to place holes; much depends on 
 the force of the explosive, the hard- 
 ness of the rock, and the evenness of 
 its texture. The miner must be 
 guided largely by experience and 
 common sense, in finding exactly the 
 best position. To drill extra hand 
 holes for squaring up a heading is 
 unsatisfactory and expensive, conse- 
 quently, the key holes that furnish 
 two free faces are the particular ones 
 to be watched. Key holes should be 
 placed as far apart as experiments 
 show it to be necessary to give the 
 best results, and when that distance 
 has been found, it should not be varied. 
 The Billy White Cut. Three holes 
 1, 2, and 3, Fig. 3, are drilled straight 
 into the breast, exactly in a line with 
 one another, at a distance of 5 in., 
 center to center, thus making the dis- 
 tance over all 12 in., assuming the | 
 holes are each 2 in. in diameter. An- ' _, 
 
 other hole 4 is drilled 7 in. to the right * IG - 8 
 
 of the first three holes and in a horizontal line with hole 2. Hole 5 is drilled 
 12 in. to the left of hole 2 and in the same line as hole 4. These five holes 
 
 complete the drilling of the cut. 
 5ust enough to hold water. 
 
 FIG. 4 (d) 
 
 All are put in horizontally or looking down 
 
574 
 
 OPENING A MINE 
 
 The success of this cut lies mainly in drilling the holes in planes with one 
 another and in shooting them in the proper rotation. Four of them are loaded 
 in the usual manner, care being taken to cut the several fuses of slightly vari- 
 able length so that the holes will go off in the following order; viz., 1, 3, 4, 
 and 5. Hole 2 is drilled merely to provide 
 space for hole 1 to break to, and is never loaded. 
 Each shot creates more clear face for the fol- 
 lowing shot. After holes 1 and 8 have gone, 
 the chamber is about 12 in. vertically by 5 in. 
 horizontally and somewhat oval in. section. 
 After all the holes have been shot, there is 
 produced a chamber about 12 in. by 21 in., as 
 shown in the illustration. 
 
 The cut breaks as big at the bottom as at the 
 collar, and to a depth of at least 6 ft. The full 
 bore of the tunnel is obtained by the usual 
 placing of holes that will break to this initial cut. 
 Square-Cut Drilling and Blasting. A center 
 cut is taken out the full height of the face and 
 all subsequent holes are drilled in lines parallel 
 T, _ with the side of the heading. Fig. 4 (a), (b), 
 
 (c), and (d) illustrates the square-cut method 
 
 driven according to the European practice in blasting; that is, the holes are 
 not more than one-half the width of the heading in depth. View (a) shows 
 the face of the heading; (b) and (c) are horizontal sections, and (d) is a 
 vertical section. 
 
 Two or four drills can be used to advantage in drilling the holes for the 
 square-cut system. With strong hard rock, the diameter of the holes will be 
 about If in. at the bottom, but the four holes 1, 2, 3, 4 will be somewhat shal- 
 lower than the others. It will also be noticed that there are only three upwardly 
 inclined or dry holes to be bored in this arrangement, as compared with four 
 in the center-cut systems, Figs. 1 and 2. As the drill holes are always slightly 
 conical (because each succeeding drill is of smaller diameter than the preceding) , 
 the four shallower holes will be nearly, if not quite, li in. in diameter at the 
 bottom. The entering wedge, Fig. 4 (b), is best removed in two stages: First, 
 the part e g h by the breaking-in shots 1, 2, 8, and 4, and then the part e f h 
 by the breaking-in shots 5, 6, 7, and 8. The order of firing the shots is as fol- 
 lows: First volley, 1, 2,8, and 4, simultaneously; second volley, 5, 6, 7, and 8, 
 simultaneously: third volley, 9, 10, 11, and 12, either simultaneously or 
 consecutively; fourth volley, 18 t 14, 15, and 16, either simultaneously or con- 
 secutively; fifth volley, 17, 18, 19, 20, 21, and 22, either simultaneously or 
 consecutively. The effect is practically the same whether the enlarging shot 
 holes are fired simultaneously or consecutively, on account of the fact that 
 they are top far apart to assist each other, but to save time simultaneous 
 firing is advisable. 
 
 Side Cut in 
 Heading. Some- 
 times there is a 
 natural parting at Y/ 
 one side of the head- ' 
 ing, as when the V 
 heading is following '/ 
 a vein of ore, or a '/ 
 slip in the rock. In y 
 such a case, the 
 side cut offers very '/ 
 important adyan y 
 tages and especially '/ 
 when only one rock 
 drill is employed ? 
 
 S'ofSMeS 
 to make an advance 
 of 3 ft. 6 in. in a 
 heading by means of a side cut. The order of firing would be as follows: 
 First volley, 1 and 2, simultaneously; second volley, 3, 4, and 5, consecu- 
 tively; third volley, 6, 7, and 8, consecutively; fourth volley, 9, 10, and 11, 
 consecutively. 
 
 40 
 
 OA 
 
 so 
 
 OB 
 
 CO 
 
 oc 
 
 DO 
 
 OD 
 
 
 
 o E 
 
 FIG. 6 
 
OPENING A MINE 575 
 
 Special Arrangement for Throwing Broken Rock from Face. Of course, 
 no general rules can be laid down for drilling holes under all circumstances, 
 as the rock may vary from point to point in the same drift or heading, and the 
 seams or joints will always have an effect on the results. Fig. 6 illustrates 
 a set of holes drilled in the face of a heading, which brings out another princi- 
 ple. In this case, the holes are fared in the order of their numbers, the holes E 
 being fired last. It will be noticed that there has been an extra hole placed 
 at the bottom, and these bottom holes are sometimes overcharged in order 
 that the last shot may have a tendency to throw the broken rock away from 
 the face. If the order had been reversed, and the upper shots fired last, the 
 broken rock would be piled against the face of the heading in the very place 
 where the drill would have to be set up for the next operation, and much valua- 
 ble time would be lost in throwing back the broken material before the 
 machine could be set up. 
 
 SLOPES 
 
 A slope resembles a tunnel, a drift, or a shaft, depending on its inclination. 
 A flat slope is treated, -as to its size, method of driving, timbering, etc., essen- 
 tially as a drift or tunnel, while a steep slope is treated like a shaft. Blasting 
 in a slope is more difficult than in either a shaft or a tunnel, as the rock is said 
 to bind, owing to the inclination of the strata; and, in general, it may be said 
 that more holes and more powder are required for a slope than for either a 
 tunnel or a shaft of equal size. The amount of increase in the width of the 
 slope pillars as the slope descends depends on the degree of pitch of the slope, 
 which determines the thickness of cover above the slope. 
 
 The removal of the material excavated from a slope is more difficult than 
 in drifting or tunneling, and this difficulty increases with the inclination of the 
 slope. When starting a steep slope, as when starting a shaft, the material is 
 removed by the use of a windlass for drawing the car up the slope, or a small 
 portable hoisting engine may be set up when the slope has been sunk but a few 
 yards. 
 
 The drainage of a slope is accomplished by pumps located at or near the 
 foot, small sinking pumps placed on trucks being generally used. In order 
 not to be obliged to move a large pump too often while sinking, inspirators, 
 which are easily moved as the work advances, are sometimes used at the slope 
 bottom to throw the water up to the pump station. 
 
 The timbering of a slope differs from that of a drift or tunnel in the man- 
 ner of setting the posts, which, in a slope, are underset or made to lean up the 
 pitch from the normal position in the seam, or from a position perpendicular 
 to the plane of stratification. The amount the post is underset and the man- 
 ner of undersetting vary with the inclination of the seam. 
 
 Safety Appliances. The necessity of safety appliances increases with the 
 inclination of the slope. Refuge, or shelter, holes for the safety of the men 
 engaged in the slope should be made in the sides; in some states, they are 
 required by law, owing to the liability to accident to men by being caught and 
 squeezed between the rib and a trip of cars, or by the breaking of the hoisting 
 rope or car couplings, or the possibility of cars descending the incline before 
 being attached to the rope. 
 
 Safety blocks are necessary at the knuckle or the head of all inclines, and in 
 some states are required by law. They consist of pieces of heavy timber so 
 arranged as to prevent cars descending the incline before all is ready and the 
 signal given. They may be operated at the knuckle, by the topman, or head- 
 man, or from the engine room. The block is- so arranged, by means of a spring 
 pole, weight, or spring, that the ascending cars will pass it without difficulty, 
 but it will automatically return to its place when the car has passed. At some 
 slopes, safety blocks are arranged at regular intervals along the incline, for 
 the purpose of preventing the descent of the car or cars if the hoisting rope 
 should break. 
 
 A derailing switch is sometimes employed either instead of or in conjunction 
 with a safety block. This is an automatic spring-pole switch similar to the 
 switch used for turnouts in mine haulage, and permits the ascending cars to 
 pass on the main track, but a descending car will be switched off on a side 
 track. The derailing switch, like the safety block, may be operated from the 
 knuckle or from the engine room, as desired. 
 
 The safety dog is a heavy trailing bar attached or coupled to the drawbar 
 at the rear of the ascending car or trip of cars, and allowed to drag along the 
 track as the car proceeds up the incline. The lower end, which drags on the 
 
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 I f or pipes 4' 8" X 2' 
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578 OPENING A MINE 
 
 ground may be either pointed or split. If the hoisting rope breaks, the weight 
 of the car on the incline forces the dog into the floor, and the cars are either 
 stopped or derailed. 
 
 SHAFTS 
 
 INTRODUCTION 
 
 Form of Shaft. A shaft may be circular, elliptic, polygonal, or rectangular. 
 The first three forms are better adapted to withstand pressure than the rect- 
 angular, but they are more difficult to timber, and there is always a consider- 
 able area of the cross-section that is not available for hoisting. Such shafts 
 are usually lined with brick, masonry, concrete, or metal instead of timber 
 and are preferred in many European countries. The practice of lining shafts 
 with concrete is growing rapidly and many of these have their sides and ends 
 made as arcs of circles, so as to present an arch to the side and end pressures; 
 the approximate section of the shaft is then elliptic. Rectangular shafts are 
 either oblong or square, the former being the usual form for a hoisting shaft, 
 while the latter is often used for a small prospect shaft, or for a second open- 
 ing to be used as an escape shaft or an air-shaft. Rectangular shafts are 
 usually not lined with masonry on account of the danger of the walls bulging 
 from the pressure of the strata behind them, although a number of rect- 
 angular shafts have been lined with concrete; timber of sufficient size is gen- 
 erally used for the lining in these shafts, and when bulging takes place, any of 
 these timbers can be taken out and replaced by others after the trouble has 
 been removed. 
 
 Compartments. A shaft is usually divided into two or more compartments, 
 either by buntons or cross-timbers placed one above another and spaced from 
 6 to 8 ft. apart, or by solid partitions formed of 3-in. or 4-in. planking. If 
 there are but two compartments, both of them may be hoistways or one may be 
 a hoistway and the other a pumpway and ladderway. If there are three com- 
 partments, two of them are hoistways, and the third, and smaller, compart- 
 ment, which is at the end of the shaft, is used for a manway and pumpway 
 and for carrying steam or compressed-air pipes or electric wires into the 
 mine. 
 
 Size of Shafts. The size of a shaft depends on the use for which it is 
 intended and is determined by the hoisting, drainage, and ventilating condi- 
 tions at the given mine. Nothing is saved in sinking a shaft of too small 
 dimensions, for the work of excavation is more easily accomplished in a large 
 shaft, while the serious annoyance and limitations of a small shaft, and the 
 great expense of enlarging a shaft already sunk, warrant a shaft of generous 
 size. A tight shaft is one in which there is but little space between the curb- 
 ing and the edge of the cage. In such a shaft, the cage acts like the piston of 
 an air pump, moving the doors in the mine, and causing a general disarrange- 
 ment of ventilation. In such a shaft, also, a very small amount of ice will 
 interfere with hoisting. Shafts for coal mines vary in size from 5 ft.XlO ft. 
 to 12 ft.X54 ft. inside the timbers. Shafts at metal mines vary in size 
 from 5 ft.X5 ft. to 15 ft.X25 ft. The table on page 576 gives interesting 
 data about some of the leading American shafts. The size of a hoisting shaft 
 is determined by the output of material required, the depth of the shaft, the 
 speed of hoisting, the size of the mine car, and the number of cars hoisted 
 at one time. 
 
 Width of Shaft. The width of the shaft depends on the size of the car to 
 be hoisted. The length of the box of a mine car is determined by the formula 
 
 in which /= inside length, in feet; 
 
 c = capacity, in cubic feet; 
 
 6 = average breadth, in feet; 
 
 d = depth, in feet, including the topping. 
 
 To the inside length of the car calculated by this formula, must be added 
 the thickness of the end planks, each end being from 1 to 2 in. thick, and the 
 length of the bumpers at each end of the car, from 4 to 10 in., according to the 
 style of car used, in order to obtain the length of car, out to out of bumpers. 
 To this must be added 6 to 8 in. for clearance between each end of the car and 
 
OPENING A MINE 
 
 579 
 
 the cage, and 6 to 9 in. more for clearance between each end of the cage and 
 the shaft timbers, to obtain the width of the shaft in the clear. 
 
 Cars, for use in coal mines, vary from 4 to 6 ft. in width, from 5 to 10 ft. 
 in length, and from 2 to 5 ft. in height. Their capacities vary from 1,000 to 
 8,000 Ib. and their weight from 500 to 4,000 Ib. 
 
 EXAMPLE. Find the width of a shaft required for hoisting an output of 
 1,200 T. of bituminous coal per day of 8 hr. from a depth of 500 ft.; the seam 
 is 5 ft. 6 in. thick, and has a good roof and floor; the specific gravity of the coal 
 is 1.3. 
 
 SOLUTION. Allowing 5% for delays, the net time of hoisting is .95 X (8X 60) 
 = 456 min. ; the output is 
 
 1 ' 200 4 ^ 2 ' 00 ^s> y . 5.263 Ib. per min. 
 
 The speed of hoisting in a shaft 500 ft. deep varies from 25 to 40 ft. per sec. 
 Assuming 25 ft. per sec., the time of hoisting one trip is 500^-25 = 20 sec. 
 Assuming 10 sec. for the time of caging and uncaging, the total time for each 
 hoist is 20+ 10 = 30 sec. Then 60 sec. -J- 30 = 2 hoists per min., and if one car is 
 hoisted at a time, the weight of material per hoist is 5,263-^-2 = 2,632 Ib. of coal. 
 
 The weight of bituminous coal having a specific gravity of 1.3 varies from 
 45 to 50 Ib. per cu. ft., when broken (loose). For the ordinary mine run, 
 assume 48 Ib. per cu. ft.; then the capacity of a car is 2, 632-7-48 = about 
 55 cu. ft. 
 
 Assuming that the depth of coal on the car, including topping, is 30 in. 
 (2J ft.) and the inside width 40 in. (3| ft.), then the inside length is 
 
 Adding, to the inside length, 4 in. for the ends of the car and 12 in. for bump- 
 ers, the total length of car will be 8 ft. Then adding 3 in. clearance, between 
 each end of the car, and the cage 
 and 9 in. at each end for shaft 
 clearance, the required width of 
 the shaft is 10 ft. in the clear. 
 
 Length of Shaft. The 
 length of the shaft must ordin- 
 arily be such as to provide for 
 two hoistways, and a pumpway 
 or man way. The width of 
 each hoisting compartment 
 should be such as to give at 
 least 6 in. of clearance between 
 the greatest width of the car, 
 out to out, and the guides. Al- 
 lowance must be made also for 
 the width 9f buntons separating 
 the two hoistways, the thickness 
 of the guides, and the width of 
 buntons separating the hoisting 
 compartment from the pump- 
 way. According to the size and 
 depth of the shaft and the char- 
 acter of the strata, the thickness 
 of the buntons will vary from 4 
 to 12 in. The size of the guides 
 often employed in hoisting shafts is 4 in.X4 in., and the guides are commonly 
 spiked to the buntons. 
 
 In Fig. 1, the width of the car is shown as 40 in., out to out, while the clear 
 width between the guides in each hoistway is 4' ft. 10 in., giving a clearance of 
 9 in. on each side of the car. The size of the guides is 4 in. X 4 in., making 
 the total width of each hoistway 5 ft. 6 in. The buntons shown in the figure 
 are 6 in. wide and the pumpway 5 ft. wide, making the total.length of the shaft, 
 in the clear, 17 ft. The width of the hoistway also depends on the number 
 and size of cars hoisted at one time, and whether two cars are placed side by 
 side on the cage, or one above the other on a double-deck cage. 
 
 Fig. 2 shows the cross-section of a shaft where two cars are hoisted side by 
 side on the cage. The entire length of the shaft in the clear, including hoist- 
 ways and pumpways, is 28 ft., giving two hoistways each 9 ft. 10 in. in the clear, 
 between guides, and a pumpway 5 ft. in the clear. The guides are each 4 in. 
 
580 
 
 OPENING A MINE 
 
 and the buntons 6 in. wide; the width of the cars is 46 in., giving a clearance 
 of 8 in. on each side, and 10 in. between the cars. This is a very large shaft, 
 
 FIG. 2 
 
 being capable of accommodating an output of between 3,000 and 4,000 T. 
 per da. 
 
 SINKING TOOLS AND APPLIANCES 
 
 Buckets. The buckets used for hoisting the material excavated in shaft 
 sinking are usually made of boiler iron or steel, weigh from 150 to 500 Ib. and 
 hold from 2.5 to 14 cu. ft. or more. The bucket C, Fig. 1, is commonly swung 
 between handles or bails b, which are attached to the hoisting rope by a 
 special hook provided with a clip or extra link and pin for securing the hook 
 fastening while the bucket is being dumped; or two hooks with the points 
 facing and closed by a drop link g passing over their necks may be used. In 
 the common form, the bail is attached to a point below the center of gravity 
 of the bucket so that the tendency of the bucket is to turn over and empty 
 itself. These buckets are easily dumped but have been the cause of many 
 fatal accidents through overturning while hoisting men and material. A 
 bucket is often made by sawing off an oil barrel just above the second hoop from 
 the top, and riveting to the lower part substantial eyes for securing the bail. 
 Buckets with drop bottoms are sometimes used instead of the form described, 
 
 and while a greater speed in re- 
 moving material is claimed for 
 them, they are dangerous on ac- 
 count of premature opening of the 
 bottom and sinkers should not be 
 allowed to ride on them. 
 
 Bucket Guides. When the 
 shaft is deep, the bucket has a ten- 
 dency to twist or spin. This may 
 be overcome by the use of guides 
 and some form of sinking yoke. 
 The guide ropes, which may be 
 made from old but unkinked 
 hoisting ropes c, Fig. 1, are either 
 coiled on a drum and lowered as the 
 sinking proceeds, or are hung from 
 timbers across the top of the shaft. 
 Large weights are attached to the 
 lower end to keep them steady. 
 The hoisting rope passes through a 
 hole in the center of the rider 
 (monkey, or jockey) d, which is an 
 iron frame consisting of two legs 
 joined together by a cross-bar, and 
 encircling the two rope guides 
 loosely at the four points d. At 
 the bottom of the shaft timbers stop-blocks hold the rider while the bucket 
 goes to the bottom of the shaft, thus keeping the rider and the guide ropes 
 out of the way of the sinkers. As the bucket is hoisted, the rope socket picks 
 up the rider when it is reached. 
 
OPENING A MINE 581 
 
 In some cases wooden, instead of rope, guides are used and the bucket is 
 provided with a yoke. This consists of two wooden uprights carrying the guide 
 shoes and two crosspieces holding the uprights together. In each crosspiece 
 is a ferrule through which the rope passes, the bottom one being conical to 
 receive the rope socket. At the bottom of the timbering, blocks are bolted 
 to each guide to prevent the yoke passing below the timbers, while the bucket 
 passes down to the bottom of the shaft. In using wooden guides and yokes 
 (crossheads), the former must be parallel and have smooth joints to prevent 
 the yokes from hanging while the bucket continues to descend. Should the 
 yoke stick and subsequently be jarred loose and fall upon the bucket a serious 
 accident may follow. 
 
 Dumping Buckets. The bucket may be dumped automatically by placing 
 a catch hook so that it engages one side of the bucket rim and tips it as the 
 hoisting is continued, dumping the material either into a car or chute. Dump- 
 ing the bucket while over the shaft is dangerous, as small stones may fall down 
 the shaft through the hole provided for the rope in the shaft covering. It also 
 throws a considerable strain on the head-frame, hoisting gear, and rope; and 
 if an accident occurs to the hoisting rope while dumping, the bucket and its 
 load may fall on the shaft cover with sufficient force to break through and fall 
 to the bottom. A better arrangement is to swing the bucket clear of the shaft 
 by means of a short snatch rope-that hangs from a point in the top of the head- 
 frame and at one side of the shaft opening. The hook is quickly put into 
 the bail of the bucket as it comes up, and when slack is given by the 
 engineer, the bucket is swung clear of the shaft and dumped or transferred 
 to a car. 
 
 Several buckets are often used for hoisting material, and as soon as the 
 bucket has passed through the shaft opening, a larry or truck running on a 
 broad track that spans the shaft opening is pushed underneath it, the bucket 
 is lowered on to the larry, the hooks are snapped, and an empty bucket attached 
 in its stead. The larry is then moved to one side and the empty bucket low- 
 ered into the shaft. 
 
 Engines and Boilers. When sinking small and shallow shafts, an ordi- 
 nary contractor's hoist is commonly used in which an upright boiler is mounted 
 on the same bedplate as a small hoisting engine. For larger and deeper shafts 
 the engine and boiler are in separate units. The former is usually placed on a 
 temporary foundation of heavy timbers and should be powerful enough to 
 pick up the bucket at the bottom at any time without getting stuck on the cen- 
 ter or having to run back for slack. The boiler is usually of the locomotive 
 type. In some cases the permanent boiler and hoisting-engine plant are 
 installed at the outset, and used to hoist the material while shaft sinking. 
 
 Sinking Head Frame. The sinking head-frame is generally designed for 
 temporary use only, though when an air-shaft or escape shaft is supplied with 
 cages or a bucket for hoisting, the sinking tower, or head-frame, may be left 
 in place after the shaft has been sunk. It is usually built of 8"X8" or 10" X 12" 
 pine timbers that are mortised and cross-braced, or tied, with heavy iron rods. 
 Fig. 2 shows an unusual form of frame that was used in sinking one of the largest 
 shafts ever sunk; it was 12 ft. X 54 ft. in cross-section. 
 
 Sinking frames are sometimes built of 2%"X2?" angle iron; in some cases, 
 these are cheaper than those made of timber, as they are put together with 
 bolts and rivets, which can be easily removed with less damage to the parts 
 than in the case of a timber frame put together with mortise and tenon. Rail- 
 road rails are laid across the shorter dimension of the shaft mouth midway 
 of its length for a larry track. 
 
 A single sheave from 6 to 8 ft. in diameter rests on the tower, usually at a 
 height of from 20 to 30 ft. above the ground, so that the bucket will hang in 
 the center of the shorter dimension of the shaft. Instead of using a head- 
 frame, a derrick is frequently used, at least until after the shaft has been sunk 
 through the surface wash. 
 
 In order that the work of sinking may not interfere with the progress of 
 the permanent work about and over the shaft, such as the erection of the main 
 tower, or head-frame, and the building of the foundations for the permanent 
 hoisting engine, buildings, etc., the temporary hoisting engine should be located 
 at one end of the shaft (at the end opposite the man way if possible) . The man- 
 way is divided from the hoisting compartments by a close partition of heavy 
 timber. The buntons separating the two hoistways are put in later, or when 
 the sinking is completed. The head-frame is set on the cross-sills, just inside 
 the main sills, so as not to interfere with the erection of the outer posts of the 
 permanent head-frame. By this arrangement, the hoisting of the excavated 
 
582 OPENING A MINE 
 
 material may continue uninterruptedly while the permanent head-frame and 
 buildings are being erected. 
 
 The waste material hoisted out of the shaft is dumped about the shaft 
 frame and about the foundations of the permanent machinery and a level sur- 
 face is thus gradually built up. If the ground slopes away rapidly from the 
 shaft, it may be necessary to build a trestle for the larry track. A smaller 
 car is sometimes placed on a larger truck and run out on a trestle at right angles 
 to the main dumping trestle. 
 
 Shaft Coverings. In order to prevent material falling into the shaft, the 
 top should be covered with 3-in. or 4-in. plank, excepting the portion that must 
 
 PIG. 2 
 
 be left open for the passage of the hoisting bucket. This opening may be simply 
 covered by the larry, but it is better to have a pair of doors meeting in the 
 middle and closing down flat, or as shown in Fig. 3. In the raised position , 
 they rest on a triangular boxing at each end and may be so arranged that the 
 ascending bucket will open the doors for its own passage, while they are closed 
 by means of weights not shown; or the doors may be opened and closed by the 
 levers shown in the figure. The balance weights should not hang inside the 
 shaft as is sometimes done, for if the ropes break they will drop to the bottom. 
 When the doors are closed, the hoisting rope passes through a small hole cut 
 in the two edges of the doors. 
 
OPENING A MINE 
 
 Ventilation and Lighting. An air-shaft of boards erected over the man- 
 way at the surface serves the double purpose of protecting the manway and 
 ventilating the shaft by means of a * 
 natural air-current. The partition | 
 separating the manway from the ' 
 hoistway should be kept close to 
 the bottom of the shaft. If this 
 does not produce a sufficient cur- 
 rent of air, a steam jet or small 
 blower, such as is used in a black- 
 smith's forge, may be employed. 
 Where rock drills driven by com- 
 pressed air are used in sinking, 
 their exhaust will commonly pro- 
 vide an ample supply of pure air. 
 fir 
 
 In some cases a fire of wood or 
 coal suspended in a bucket in 
 the shaft, and known as a fire- 
 basket, is used to produce the cir- 
 culation. 
 
 For general illumination at the 
 shaft bottom, incandescent electric 
 lamps protected by metal baskets, 
 are to be preferred. They do not 
 foul the air like oil lamps and may 
 be drawn up out of the way while 
 blasting. For individual use, portable electric or acetylene lamps are to be 
 preferred to those using oil. 
 
 SINKING THROUGH FIRM GROUND* 
 
 Preliminary Operations. Where the seam is flat, the long side of the shaft 
 should be made parallel to the loading tracks so that the chutes may be at 
 right angles thereto. If the seam is inclined, the long side of the shaft should 
 be, as nearly as possible, parallel to the line of dip of the coal; in which case 
 curved loading chutes will be necessary unless the lay of the ground permits 
 the tracks to be shifted into parallelism with the longer side of the shaft. 
 
 The shaft is staked out by driving eight stakes in line with the ends and 
 sides of the shaft and outside the area likely to be disturbed by the sinking 
 operations as shown in the cut. The lines formed by the side stakes are at a 
 distance apart equal to the \\idth of the shaft, and the distance between the 
 lines joining the end stakes-is equal to the length of the shaft. Cords stretched 
 between the stakes will, at their intersections, determine the four corners 1, 2, 
 S, 4, of the shaft. 
 
 Shallow trenches are dug on each end line and in them are laid the end- 
 or cross-sills, which extend 6 to 8 ft. outside the shaft line on each side. Similar 
 side or main sills are laid across the end sills and extend 4 or 5 ft. beyond 
 each end line. The sills are of carefully selected 12"X12" or 12"X16" oak. 
 They are fastened together where they cross one another by square boxings 
 \ in. to 2 in. deep, through which a heavy drift pin is passed. This framing is 
 called a shaft template and its inner sides define the dimensions of the shaft in 
 the clear. In order to prevent surface water 
 running into the shaft these sills are fre- 
 quently supported on blocking with clay 
 packed beneath and around them. 
 
 Sinking Through Earth and Loose Rock. 
 When the material overlying the coal 
 measures is composed of ordinary earth and 
 loose rock free from water, the excavation 
 
 iuuac lu^ft. iitc iiyuj wcitci, nic GA^CI v a tnjn ^ 
 
 to solid rock is carried on by means of Q t2 
 
 ordinary long-handled shovels. After a 
 depth of 8 or 10 ft. is reached, the earth 
 must be thrown upon a staging whence a i ^ f 
 
 second gang of shovelers throw it to the 
 
 surface. The excavation is made larger than the inside dimension by an 
 amount 2 or 3 in. more than the thickness of the lining. Thus, if the final 
 size of the shaft is, say, 10 ft. X 26 ft., and the lining is 1 ft. thick, the ex- 
 treme dimensions of the excavation will be, say, 12 ft. 4 in. X 28 ft. 4 in. 
 * See section on Timbering for methods of supporting excavations. 
 
584 
 
 OPENING A MINE 
 
 Plumb-lines are suspended in each corner of the shaft as a guide for the 
 sinkers. These may be hung from a triangular-shaped piece of plank nailed 
 in the corners of the template or from an iron plate screwed upon the surface 
 thereof. In either case the supporting device is perforated with a small hole 
 to receive the plumb-line, which hangs 4 to 6 in. from the face of the shaft 
 
 The lining is commonly built up from the bottom as sinking progresses, 
 the space behind being filled in with fine material to distribute the pressure 
 evenly over the lining. In wet ground, the space behind the lining is rammed 
 with clay to prevent the inflow of silt or fine sand between the timbers. The 
 work of sinking and placing the lining is carried on alternately, the lining, 
 except when sinking through rock, being kept close to the bottom, say, within 
 6 to 8 ft. at the most. 
 
 Sinking Through Rock. As soon as the strata become hard or firm enough 
 to hold the explosive charge, powder is employed and churn, hand, or machine 
 drills are used, the type of drill depending on the character of the rock. In 
 soft rock, a churn drill is used and a light lifting shot is employed to dislodge 
 the material from its bed. This material is afterwards broken by wedges and 
 hammers or sledges. For this class of work, a slow large-grained powder is 
 required. A quick powder exploded in soft material will find vent by a single 
 
 FIG. 1 
 
 FIG. 2 
 
 rupture of the strata without exerting the lifting force on a great mass of mate- 
 rial, as is done when a slower powder is used. If, however, the strata are full 
 of seams and cracks, a small charge of a quick powder is used, since such rock 
 will not confine the explosive force sufficiently to do effective work when a slow 
 powder is used. In hard rock, dynamite is used, and power drills, operated 
 by compressed air or steam and usually mounted on shaft bars, are employed. 
 The general position of the holes and their depth are about the same as 
 described under Tunneling. The first shots in a level floor should be inclined 
 at a fairly sharp angle with the floor, and are usually central in the shaft. These 
 holes are often called sumping hole.s; their purpose is to start the excavation 
 by blowing out a wedge-shaped piece of rock from the center of the floor. 
 The holes are generally arranged in series, or rows, on each side of the center 
 and across the width of the shaft, and- are spaced an equal distance from one 
 another. The general position of these holes is illustrated in Fig. 1, which 
 also shows the position of the shaft bar on which the drills were mounted. 
 The dimensions given are those that were employed in the sinking of a shaft 
 m a white crystalline limestone. In this shaft, at first, only 6-ft. cuts were 
 made, a single series of shots excavating the material to this depth. The depth 
 of cut, however, was afterwards greatly increased by boring the side holes 
 
OPENING A MINE 
 
 585 
 
 deeper, as shown in Fig. 2, until the cuts averaged 11 ft., six successive cuts 
 excavating the shaft a depth of 66 ft. 
 
 Fig. 3 illustrates the sinking of a 6'X 18' shaft in limestone of varying hard- 
 ness. The position of the shaft bar on which the drills were mounted is shown 
 at a, ci, at, b, b\, bt. The two center rows of 
 holes 1, or the sumping holes, were drilled 
 first, and each hole filled with from five to seven 
 f-lb. sticks of giant powder or dynamite, con- 
 taining 50% of nitroglycerine. The depth of 
 the holes varied from 3$ to 6 ft. Beginning 
 at the center, the successive rows of holes, 
 marked 1, 2, 3, and 4, respectively, on both 
 sides of the shaft, were drilled, charged, and 
 fired in pairs, the material being loaded and 
 hoisted between each operation. The end holes 
 required but 
 mite apiece; m- ^,. 
 used from 50 to 60 
 
 vated the material to a depth averaging from 
 3i to 6 ft. The average quantity of 40% and 
 50% dynamite used in this material was 12 Ib. 
 per ft. of depth, or 3 Ib. of dynamite per cubic 
 yard of excavation. The sinking was carried 
 on by three shifts of four men each, and the 
 record of the sinking showed a depth of 100 ft. 
 in 30 working da., or an average of 3? ft. per da. 
 
 Long-Hole, or Continuous-Hole, Method. 
 As in sinking in rock, much time is ordinarily 
 lost in drilling; and as machine drills cannot 
 work close to the sides, ends, or corners of the 
 shaft, the continuous-hole method is some- 
 times used. By this method, a number of 
 diamond-drill holes are put down at definite 
 distances apart, and from 100 to 300 ft. deep, 
 over the area where the shaft is to be sunk. 
 
 FIG. 3 
 
 They are arranged in rows, from 3 to 4 ft. apart, with the outside rows close 
 to the sides and ends of the shaft, so that they will nearly square it up and save 
 much digging and trimming. They are then filled with sand or water, pref- 
 erably the former. The sinkers prepare for the work of blasting by remov- 
 ing 3 to 4 ft. of sand from the holes and filling this space with explosives, 
 which are tamped and fired. 
 
 Fig. 4 shows how the holes are arranged. The holes marked a are first 
 cleaned and fired to give a loose end to the holes b on the outside, which are 
 next cleaned out and fired. This work is continued until the bottom of the 
 hole drilled by the diamond drill is reached, when another series of long holes 
 is drilled. 
 
 This method probably originated from one that is sometimes used in the 
 coal fields of the Central Basin. Shafts are sunk about the diamond-drill hole 
 that has been used in prospecting, and from which the casing has been with- 
 drawn, or is drawn as the sinking proceeds. The sinkers charge a section of 
 the hole, using a false bottom, and blow out a center cut. 
 
 , When shafts are sunk to workings al- 
 * ready opened, a diamond-drill or churn-drill 
 hole is sometimes put down into the open 
 works below, and this hole is kept open during 
 sinking, thereby avoiding all hoisting of water. 
 A long chain is used to clean out the hole 
 when it becomes stopped up. 
 
 Both this plan and the long-hole plan are 
 apt to cause crooked shafts, on account of the 
 
 [&__ .& & *__.?*. divergence of the drill hole from the vertical. 
 
 "FIG 4 The advantages of the long-hole system are 
 
 that sinkers need not wait while holes are 
 
 being drilled; and blasting can be done as soon as debris from shots is removed. 
 The method is said to be very much quicker than the ordinary practice of 
 using power drills driven by air or steam, but is more expensive. 
 
 Timbering is usually not required for securing the sides of the excavation 
 when sinking in hard rock. Cross-buntons to support the cage guides, pipes, 
 
 * * 
 
 <* a < 
 
586 OPENING A MINE 
 
 wires, etc., are set in hitches in the face of the rock, and are spaced 6 or 8 ft. 
 apart. They are carefully lined and placed vertically over each other and then 
 tightly wedged. When sinking through soft shale or loose crumbling rock, a 
 greater amount of timber is needed for securing the sides. The sides are 
 trimmed with the pick; and when the material is dry, a close-fitting lining of 
 3-in. or 4-in. planking is sufficient, the thickness of the planking increasing 
 with the depth of the excavation. In wet material, 4-in. timber should be 
 used at the surface, 6-in. at 100 ft., and 8-in. at 200 ft. 
 
 Sinking in Swelling Ground. Clay or marl that swells when brought in 
 contact with air and water is difficult to excavate and support. There is no 
 power that can prevent this swelling; it will burst any timber or break any 
 frame that can be put in. When sinking a shaft or a slope under such condi- 
 tions, the strata should be excavated for a certain depth back of the lining so 
 as to give a good clearance between the formation and the lining all around 
 the shaft. This space should be so arranged that a man can enter it and clear 
 it from time to time as may be required. Drainage should be provided by 
 cutting, in the hard pan or floor underlying such strata, a ditch connected by 
 a pipe with the sump at the foot of the shaft. A good circulation of air should 
 be made to travel around the space thus excavated so as to keep the clay as 
 dry as possible. 
 
 The method of sinking through such ground does _not differ materially 
 from that used in other loose ground or rock, but the timbering of the exca- 
 vation is of great importance. 
 
 SINKING THROUGH RUNNING GROUND* 
 
 Draining the Ground. Where beds of quicksand or loose water-bearing 
 sand or gravel are supposed to occur, the ground should be thoroughly drilled 
 before sinking operations are begun, and in localities where such deposits may 
 be expected there should be kept on hand an ample supply of the materials 
 required during sinking. Timber of different sizes should be framed and 
 ready for instant use, and pumps and piping of the proper kind and capacity 
 should be on hand. Eight or ten pointed pipes, with perforated ends, are 
 sometimes driven into the sand 6 or 8 ft. apart and connected at their upper 
 ends to a suitable pump. In some cases, a few hours' pumping draws off the 
 water and the boiling sand settles and solidifies so that it may be removed with 
 a shovel. Water can sometimes be drained from the soft ground within the 
 area of the shaft into wells or small temporary shafts sunk adjacent to the larger 
 shafts, thus leaving the sand within the shaft area compact and easily 
 removable by shoveling. 
 
 When the watery sand is thus drained, there is a considerable decrease in 
 volume of the material surrounding the sides of the shaft; the shaft lining is 
 thus frequently robbed of all supporting material for a considerable distance 
 up the shaft and begins to separate and sag, while the shaft may be swung 
 out of line. This decrease in volume, or displacement of the strata, due to the 
 draining off of the water, may be carried to such an extent that the surface 
 of the ground will sink several feet over a large area surrounding the shaft. 
 In removing the water, a large amount of sand is also removed; the effect of its 
 removal is often not appreciated until too late. The sand contained in the 
 water will often cut out the pump linings in a short time, and render the pump 
 useless; but if a layer of straw or other light material is thrown into the shaft, 
 it will form a mesh by which the sand will be largely filtered from the water. 
 
 The methods to be adopted when sinking through such material are par- 
 ticularly methods of timbering, or supporting, the sides of the excavation; 
 and the excavation must be kept timbered close to the bottom of the shaft. 
 There are, however, certain methods of sinking that are particularly applicable 
 to such ground, as follows: piling, forepoling, the use of shoes, the pneumatic 
 process, and the freezing process. 
 
 Piling. A bed of quicksand or other soft material lying near the surface 
 is often best treated by piling. If the bed is shallow, it may be sufficient to 
 drive a single set of piles all around the site of the proposed shaft. Where 
 thicker beds of quicksand occur, it may be necessary to drive several series of 
 piles, each successive series being driven inside the former after the material 
 has been excavated to a point near the bottom of the first piles driven. The 
 second set of piles having been driven, the material within these is excavated 
 to a point near the bottom of the piles, and, if necessary, a third set of piles 
 is driven within the second. This method is illustrated in Fig. 1. 
 
 *See section on Timbering for methods of supporting excavations. 
 
OPENING A MINE 
 
 587 
 
 After driving, the first set of piles a should be strengthened by timber frames 
 or timber sets at their top and half-way of their length, as the material is exca- 
 vated from the space they en- 
 close. It is important that 
 these frames should be set 
 promptly and braced by cross- 
 bun tons; they are supported 
 by punch blocks e. As will 
 appear from the figure, it will 
 be necessary to set the first 
 sets of piles back a sufficient 
 distance from the shaft to allow 
 for the decreased size of the 
 excavation when each series 
 of piles is driven. This dis- 
 tance is easily calculated when 
 the depth of the sand beds is 
 known (and this is given by 
 the bore or drill hole t made 
 beforehand). 
 
 In some cases, the soil at 
 the surface may be firm for a 
 considerable depth, but under- 
 laid by a flowing bed of quick- 
 sand. In this case, the excava- 
 
 tion of the overlying soil may 
 
 FIG. 1 
 
 be done in the usual manner, and after this is lined or curbed the piles may 
 be driven from the foot of the excavation in the same manner as from the sur- 
 face. In this system of sinking through watery strata, the permanent shaft 
 lining is built up as soon as the rock is reached. The space between the 
 shaft lining and the piles is then filled with clay, where this can be obtained, 
 or the timbers are backed with a sufficient thickness of cement, and this, in 
 turn, with the material excavated. 
 
 Forepoling. Fig. 2 shows a method of forepoling for sinking through 
 quicksand, very similar to the method of forepoling described under Tunneling. 
 Strong timber sets j are framed to the sides of the shaft. As each set is put in, 
 it is suspended from the timbers a above by the light strips, or lath, /, while 
 the punch blocks b are set between the frames to hold them apart. Two-inch 
 planks with the ends sharpened are used for the spiles k, and are driven down- 
 wards in an inclined position behind the lower timber set. Before driving 
 
 the spiles, the tail-pieces c are 
 spiked to the lining just above 
 the lower timber frame; the 
 spiles are then driven as the 
 excavation advances until their 
 tops reach this tail-piece. An- 
 other set of timbers is then 
 placed in position at the floor 
 and tied to the timbers above, 
 and the same operation re- 
 peated, driving the spiles and 
 excavating the material as 
 rapidly as possible. This proc- 
 ess of forepoling may be carried 
 on at any depth below the sur- 
 face where the strength of the 
 timbers will resist the pressure 
 of the sand. 
 
 Where the sand is thicker 
 and is found at a greater depth 
 below the surface, the spiles 
 are driven in at a flatter angle, 
 che timber frames are placed 
 p ir 2 somewhat closer and no tail- 
 
 piece is employed, the tops of 
 
 the spiles bearing against the timber above instead of against the tail-piece. 
 
 Fig. 3 illustrates the use of breast boards where the bottom has a tendency 
 
 to rise and fill the shaft and must be planked to keep it down. The material 
 
688 
 
 OPENING A MINE 
 
 is removed a little at a time. A sump is carried ahead of the regular exca- 
 vation by driving short piles and putting in a small frame. 
 
 Another method of forepoling requires the use of interlocking channel bars, 
 as in Fig. 4. The shaft is started 2 ft. larger each way than the size desired, 
 
 and sunk in the ordinary manner 
 v l ; to the sand; thus, an 8' XI 6' shaft 
 ;; must be started as 10 ft. X 18 ft. 
 "i The lining forming the sides is 
 i-: composed of alternate channels a 
 ;; and b. The channels a have Z 
 /. bars c riveted to them, which en- 
 Xy gage and interlock the edges of the 
 ';: channels. The channels b have 
 angle irons d riveted to them, thus 
 ;'s forming grooves in which the sides 
 V; of the channels a run. The cor- 
 ners of the shaft lining are made of 
 v three angles e riveted together, as 
 ;$ shown, which interlock with the 
 ,-f side and end channels a by means 
 : ' ; ' of the Z bar riveted to a. Heavier 
 sections can be used, which would 
 make the thickness of the metal 
 about \ in. When sand is reached, these channels are set plumb in a solid 
 frame inside of the shaft lining, and are driven vertically downwards 
 through the sand to the solid material, if possible, before any sand is 
 excavated. No one channel should be driven more than 2 ft. ahead of 
 the rest. A perfect fitting anvil, or clinker, is used to protect the head of 
 the channel bar while driving. Channels 12 ft. long are readily driven their 
 entire length into the sand. The sheathing can be driven to varying depths 
 by feeding in pieces from the top, thus driving the preceding one down, in the 
 same manner that a follower is used when driving piling. The individual 
 members, engaging and interlocking, slide on one another so that one can be 
 driven at a time, and thus afford an opportunity to drive channels all around a 
 boulder, should one be encountered. The channels interlock nearly water- 
 tight, and, by cementing above and below them, the water may practically 
 be shut off. The channels take up about 5 in., while 6 in. should be allowed 
 for timber. The price of this sheathing or lining is about $2.50 per sq. ft., 
 iin. ft. for an 8'X16' shaft. The channels are either left as a per- 
 
 FIG. 3 
 
 or $120 per lin 
 
 manent lining or they may be drawn after a timber lining has been laid. 
 
 are cheaper than steel shoes or drums. 
 
 They 
 
 FIG. 4 
 
 Shoes for Shaft Sinking. The shoe consists of a wooden or metal frame 
 of the same size and shape as the shaft. Attached to its bottom is a beveled 
 steel cutter that will sink easily through soft ground. While the shoe is 
 usually open at both top and bottom, the top is sometimes closed with heavy 
 
OPENING A MINE 
 
 589 
 
 $ Sheer iron Lap 
 
 Boiler P/ate a/larounct 
 
 steel plates in order to resist the pressure of the sand from the shaft bottom. 
 
 The upper part of the shoe is outside the shaft lining from 12 to 16 in., and 
 
 the lower part is usually divided into compartments by braces. 
 In principle, the plan 
 
 of sinking by a shoe is 
 
 similar to the method of 
 
 tunneling in soft ground 
 
 with the use of an advance 
 
 shield, except that shaft 
 
 shoes in America are 
 
 usually rectangular in 
 
 shape, while the shield in 
 
 tunnel driving is cylin- 
 
 drical. As the material 
 
 is excavated from beneath 
 
 the shoe, the shoe drops 
 
 by its own weight or on 
 
 account of pressure ap- 
 
 clied to its upper surface 
 
 by weights laid on it or 
 
 by means of jacks, gener- 
 ally the latter, thus wall- 
 ing back the sand, while 
 
 the lining is being put in 
 
 place. Only enough ma- 
 terial is excavated from 
 
 underneath the shoe and 
 
 it is moved just far enough 
 
 ahead to permit the plac- ,, _ 
 
 ing of one set of timbers 
 
 at a time; if planks are used for the shaft lining, they are put in flatwise. The 
 
 shoe should descend uniformly at all points, and should be carefully leveled 
 
 before the timber is placed. 
 
 The steel shoe shown in Fig. 5 is made of f-in. steel boiler plate braced as 
 
 shown, has a height of 30 in. under the shaft timbers, and a sheet-iron lap 
 _ a n ~ 18 in. deep extending outside 
 
 of the timbers. Fig. 6 shows 
 it in position at the bottom of 
 the shaft, as well as the manner 
 of supporting it and controlling 
 its descent. Four hooks, or 
 claws, are provided, which may 
 be screwed into the lower coup- 
 lings, Fig. 7. To each of these 
 hooks is fastened a strong chain 
 attached to the frame of the 
 shoe; by this means, the down- 
 '; ward progress of the shoe is con- 
 x trolled, and there is less liability 
 of its becoming wedged and 
 thrown out of line. 
 
 One of the disadvantages of 
 using the shoe is the fact that 
 it is apt to be stopped by boul- 
 ders, clay seams, or other ob- 
 structions, one part remaining 
 stationary while the other goes 
 down, thus throwing the shoe 
 out of level and wedging it so 
 tightly that it cannot be moved, 
 and causing the shaft to be 
 thrown out of line and perhaps 
 abandoned. By means of the 
 chains shown in Fig. 6, this 
 difficulty is partly overcome, 
 
 FIG. 6 
 
 as by their use the shoe can be held stationary until the obstruction is 
 removed. The chain may also be slacked at any time to allow the shoe to 
 move. 
 
590 OPENING A MINE 
 
 The cross-beams of the shoe frame furnish also a good support for the planks 
 that are used in the shaft lining. As the shoe is lowered 2 in., or the thickness 
 of a plank, the latter is slipped in place and spiked upwards from beneath, 
 40-penny nails being used for this purpose. 
 
 The shoe is sometimes forced downwards by the weight of the lining, if 
 this rests directly on top of the shoe instead of hanging from the top of the shaft. 
 The lining is then built from the surface by adding set on set, the increasing 
 weight gradually forcing the shoe through the soft material. 
 
 Owing to the flowing character of the material being sunk through there 
 is a tendency on the part of the shaft lining to settle and draw apart and for 
 the shaft itself to be thrown out of a vertical line. This is due to the running 
 into the bottom of the shaft of a large amount of the loose material from the 
 sides, or the removal of the water in the sand by pumping or drainage, as 
 explained. To remedy this, the lining is often hung from a strong frame at 
 the surface or at some point in the shaft where a firm foundation can be 
 
 Fig. 6 illustrates the hanging of the lining from a frame or built-up beam 
 at the surface, by steel rods coupled to each other in lengths of 10 ft., and sup- 
 porting at each coupling a cross-bunton on which rests the intervening lining. 
 The rods may be of any convenient length until the sand is reached, when 
 their length should be about 10 ft. The size of the rods may vary from 1J to 
 2i in according to the depth from the surface, the size decreasing as the depth 
 from the surface increases. The lower end of each section of the rods is passed 
 through a hole in a cross-bunton b, Fig. 7, and 
 an iron bearing plate, or washer, a is placed over 
 the end of the rod underneath the bunton. A 
 screw coupling c is then fitted to the end of the 
 rod and screwed in place. This coupling fur- 
 nishes the support for the next section of rod 
 below, which is not, however, put in position 
 until the excavation has reached the point where 
 another cross-bunton is required. Until this 
 time, the timbers of the shaft lining are sup- 
 ported by strips of lath nailed to their face, or 
 by being spiked together from underneath when 
 flat planks are used. 
 
 In some cases, instead of the built-up beam 
 shown in Fig. 6, the rods are supported from 
 ^ a wooden truss fashioned after the style of an 
 
 p. 7 ordinary highway bridge. In other cases, the 
 
 rods are supported from heavy railroad rails, 
 steel I beams, or girders. The supporting frame should extend outwards 
 beyond the shaft to solid ground so as not to be affected by shifting sands, 
 and should be strong enough to support the weight of the sinking head-frame 
 and sheaves, if necessary. These frames are commonly built of 12"X12" to 
 16"X16" white oak. 
 
 Pneumatic Process. The pneumatic process used for sinking shafts is 
 commonly known as the Triger method after its inventor, and is an adapta- 
 tion of the caisson method used in building bridge piers or driving tunnels 
 through mud, as beneath a river. In this method, a cylinder of cast iron, 
 made by successively adding one ring to another at the surface, is made to 
 gradually sink into the loose ground, either by its own weight, by weights piled 
 on top of the cylinder, or by means of pressure applied through jacks. In 
 order to keep out the water from surrounding strata, compressed air is led into 
 a closed chamber at the bottom of the iron cylinder, the pressure of the air 
 being kept just sufficient to prevent an inflow of water and loose sand. This 
 chamber forms the working space in which the material is excavated; above it, 
 and connected to it by suitable trap doors, is another closed space, known as 
 an air lock. This air lock, by means of trap doors above and below, gives 
 a means of communication between the working chamber and the surface. A 
 person enters it through the upper trap door; after closing this door he allows 
 the compressed air from the working chamber to enter, by means of suitable 
 valves, until the air has reached the same pressure as that in the working 
 chamber or caisson; the lower trap door, which leads to the caisson, is then 
 opened and he descends into the working chamber. In order to leave the 
 caisson, the opposite procedure is adopted. 
 
 The excavated material can either be removed through the air lock, or it 
 can be blown out through a pipe by means of air pressure after being mixed 
 
OPENING A MINE 591 
 
 with water. If only a few boulders are found during the sinking, they are car- 
 ried down in the caisson and are hoisted out after solid material has been 
 reached and the roof of the caisson cut away. If many boulders are encoun- 
 tered, they must be blasted and the pieces hoisted out through the air lock. 
 In some cases, the metal casing on top of the caisson forms a sufficient lining 
 for the shaft; in other cases, it is necessary to build a lining of timber or metal 
 in'side of this casing. 
 
 Freezing Processes. In the freezing process, a sufficient thickness of the 
 fluid material is frozen to form a substantial wall around the shaft so as to per- 
 mit the excavation of the material encased within its area. Surrounding the 
 shaft, a series of holes from 6 to 10 in. in diameter, is bored through the sand 
 bed and cased with ordinary well casing; or if the sand is very fluid the casing 
 may be driven through the sand. These holes if bored from the surface are 
 usually vertical, but if bored from a point in the shaft a few feet above the bed 
 of sand, they are inclined. They are not more than 3 or 4 ft. apart, in order 
 to insure the thorough freezing of the sand between them. Inside these casing 
 tubes, smaller ones, usually about 4 in. in diameter and closed at the bottom, 
 are let down to the solid stratum, and the outer temporary casings withdrawn. 
 The 4-in. tubes are closed at the top with metal cap pieces, and each contains 
 a 1-in. tube that extends almost to the bottom. The 1-in. and the 4-in. tubes 
 are connected at the surface to circular mains, each vertical tube being fitted 
 with a screw-down stop-valve so that it can be cut off from the main. 
 
 There are two freezing processes distinguished by the character of the 
 freezing medium. The Pcetsch system uses a brine composed of a solution of 
 calcium chloride (or magnesium chloride) passed through a cooling machine 
 on the surface, where its temperature is reduced to about 8 F. below zero. 
 The solution of chloride of calcium is pumped through the smaller tube to the 
 bottom of the hole, and then rises through the larger tube to the surface. 
 In this process, the material is frozen first and hardest at the bottom where the 
 greatest pressure is. Since this freezing mixture is much heavier than water, 
 the pressure inside the pipes is greater than that outside, so that there is a 
 tendency to burst the tube conveying the freezing solution, thus allowing it to 
 escape into the sand outside and rendering it incapable of being frozen. 
 
 In the Gobert system anhydrous ammonia is sent down the inner tube (which 
 is then usually made of copper) and allowed to vaporize in the tubes, thus freez- 
 ing the ground directly instead of allowing it to cool a mixture that freezes 
 the ground indirectly, as in the Pcetsch process. The ammonia gas is drawn 
 off by a pump and reliquefied by compression and used over again. As the 
 pressure is less inside than outside the tubes, if a leak occurs in the tube any 
 water entering will be immediately frozen and the leak thus stopped. 
 
 The pipes may be driven well outside of the intended shaft area and a wall 
 of earth frozen around the shaft, the central portion or shaft area being removed 
 before it is frozen. In most cases, however, the ground has to be frozen solid 
 and then blasted as though it were rock. 
 
 Cementation Process. Cement injection is now replacing the various 
 freezing processes for the sinking of shafts in water-bearing ground. The proc- 
 ess appears to have been developed in the chalky formation of Northwestern 
 France, but is suited for any fissured water-bearing rocks, although not for 
 soft running ground such as quicksand. It consists of a number of bore holes 
 sunk at equal intervals in the form of a ring surrounding the proposed site of 
 the shaft. Cement and water, injected through these bore holes by means of 
 a force pump, find their way into all the cavities and crevices of the ground sur- 
 rounding each hole, in which the cement sets. As the cement from one hole 
 penetrates the rocks surrounding it, that coming from the adjoining hole is 
 encountered and a cemented, water-tight wall is formed around the proposed 
 shaft. In France, the cost of sinking by this process is found to be about one- 
 third that of the Pcetsch system. 
 
 The sizes of the holes through which the cement is forced vary from as 
 much as 12 in. down to as low as 3 in. The larger holes are commonly sunk 
 with an ordinary oil-well drilling outfit, but the smaller ones are put down 
 with a diamond drill. The pressure under which the cement is forced into the 
 ground varies from 800 to 1,200 Ib. per sq. in. The holes are drilled to a depth 
 of from 10 to 20 ft., and the cement injected. After it has set about 30 hr. 
 the holes are drilled out, and sinking resumed. When solid non-water bear- 
 ing rock is reached, cementation is discontinued. While sinking, the various 
 drill holes are watched for signs of escaping water; if such is noted, cement solu- 
 tion is again injected into the holes. In some cases as an additional precau- 
 tion, holes are drilled horizontally as the various water-bearing horizons are 
 
OPENING A MINE 
 
 encountered, and cement injected. The open spaces behind the permanent 
 shaft lining are also filled with cement in the same way. 
 
 OTHER METHODS OF SHAFT SINKING 
 
 The Kind-Chaudron system is applicable only to the sinking of circular 
 shafts, and has been extensively used in Europe for sinking through strata 
 with heavy feeders of water that prevent the use of ordinary methods. The 
 excavation is carried down to water level by the ordinary methods ot sinking, 
 and the shaft is lined to this point with timber or masonry. Boring is then 
 commenced by means of a large trepan sus- 
 pended in the shaft. The diameter of the 
 excavation to water level must be suffi- 
 cient to allow for the thickness of the wall- 
 ing or timbering, so that the latter will not 
 interfere with the use of the trepan for 
 sinking below this level. The excavation 
 is effected in two or more successive opera- 
 tions. The first trepan used cuts a hole in 
 the center of the shaft from 4 to 5 ft. in 
 diameter; this is called the guide pit and is 
 kept at least 35 ft. in advance of the 
 second cut, which is made by enlarging 
 the guide pit by means of a special trepan. 
 During the entire boring, the water is allowed 
 to accumulate in the hole, which often 
 stands full, and the boring is done under- 
 neath the water. 
 
 The first trepan, or cutting tool, Fig. 1, 
 consists of a horizontal wrought-iron bar T 
 having steel teeth B attached below. The 
 action of the cutting tool is the same as 
 that of a churn drill. The trepan is sus- 
 pended in the shaft by means of heavy 
 iron rods attached to a large walking beam 
 at the surface, and the weight is partly 
 balanced by a counterpoise at the other 
 end of the beam. An engine operates the 
 beam, raising the rod a height varying from 
 10 to 20 in. and dropping it to the bottom. 
 To avoid the shock caused by a cutting 
 tool of such great weight, a slide bar similar 
 to the jars in the American rope method of 
 drilling is used. The trepan is turned by 
 men who stand on a platform built above 
 the level of the water in the shaft. When 
 making this first cut, the hole is cleared by 
 means of a sheet-iron sand pump about 
 6 ft. long, which is raised and lowered by 
 the trepan rods. 
 
 The second cut is an enlargement of 
 the first and is made with a trepan that 
 usually weighs from 36,000 to 50,000 Ib. 
 It is quite similar to the first trepan, being 
 formed of a wrought-iron bar having teeth 
 attached to that portion of its length that 
 exceeds the diameter of the guide pit. It 
 is guided by means of a cradle, or iron bar. 
 that fits closely within the excavation made 
 by the smaller trepan. The teeth on the 
 large trepan are "so set that they cut the 
 
 FIG. 1 
 
 bottom of the annular portion surrounding the guide-bore pit into a sloping 
 surface, so as to allow the fragments and cuttings to roll into the smaller shaft, 
 where they are caught in a sheet-iron bucket previously lowered to the bottom 
 of the guide-bore pit. Sometimes scrapers, which drag around after the trepan 
 and sweep the material down the incline and into the bucket, are provided. 
 The excavation having been made of the required size in two or more successive 
 operations, the shaft is lined with iron tubbing, which is built in sections 4$ or 
 5 ft. high and added at the top as the whole is lowered from the surface. 
 
OPENING A MINE 
 
 593 
 
 s bored the desired diameter at one operation by 
 
 To assist in lowering the great weight of the steel tubbing, it is provided 
 with a water-tight bottom in which is a nozzle having a stop-cock by which 
 a sufficient amount of water 
 can be let into the tubbing 
 to sink it gradually. The 
 tubbing is thus floated in 
 the shaft until it finally 
 rests on the solid bed leveled 
 to receiye it. A special 
 moss packing below the tub- 
 bing makes a watertight 
 joint when the water is 
 pumped out. 
 
 The Lippman system 
 differs from the Kind- 
 Chaudron in that the shaft 
 
 using the cutting tool shown in Fig. 2. The tools are made and the cutting 
 teeth secured in a manner similar to that employed in the Kind-Chaudron system. 
 
 ENLARGING AND DEEPENING SHAFTS 
 
 Enlarging Shafts. Shafts may be enlarged by extending one end or one 
 side of the shaft, for then timbering already in place is made use of, the aline- 
 ment of the shaft is maintained, excavating is done easily, and less readjust- 
 ment of hoisting sheaves, stops, etc., 
 is necessary. In order not to inter- 
 fere with the hoisting of coal, the 
 widening operations are commonly 
 carried on at night. 
 
 A method used for doing the work 
 is shown in Fig. 1. Cleats a are 
 nailed on the old lining and buntons 
 b placed on them across the shaft; 
 on these is laid a temporary platform 
 on which the men work. The enlarg- 
 ing is begun on the surface and car- 
 ried downwards, a section about 8 ft. 
 high being taken out from each plat- 
 form. The drillers work on the rock 
 bench cd and load the waste directly 
 
 into cars on the regular ostng 
 cage. The end ef is timbered and 
 
 ef is 
 inking 
 
 hoisti 
 red a 
 
 backed as in sinking a new shaft. 
 The timber joints at the corners g and 
 h are left undisturbed. Each alter- 
 nate side timber is taken out for part 
 of its length and a new timber dove- 
 tailed in between it and the timbers 
 above and below, the parts being 
 joined by a feather-edge joint. The 
 dotted lines show the original posi- 
 tion of the partitions and linings. 
 These cannot be moved if mining 
 operations are being carried on until 
 the widening is completed for the 
 depth of the shaft. 
 
 If both the length and breadth 
 of the shaft are to be increased, 
 mining operations must be suspended 
 as the shaft will .have to be entirely 
 relined. Shafts have been enlarged 
 and retimbered by filling them to the 
 surface with cinders and ashes. The 
 retimbering or enlarging begins at the 
 
 p IG -t surface, and the method, while 
 
 costly, is often cheaper in the end 
 
 than endeavoring to use one or more sides or ends of the old shaft. 
 
 Deepening Shafts. First Method. A false bottom of heavy timbers is 
 
 provided in the sump as a resting place for the cage, and sinking is begun on 
 38 
 
594 
 
 OPENING A MINE 
 
 the bottom of the sump. When the new seam is reached, a new sump is made, 
 new guides are extended from the bottom upwards to meet the old guides, 
 the false bottom is removed, and the cage ropes spliced, or new ones of sufficient 
 length to allow the cages to hoist from the lower seam substituted for the old 
 ropes. This method is often used where material is being hoisted during the 
 day and sinking done at night. A small sinking cage is slung under the regu- 
 lar cage or a bucket is used instead, the material being hoisted to the old shaft- 
 bottom level and there taken back into the old workings and gobbed. The 
 disadvantages of this method are that all the water from the old sump drains 
 through the false bottom and down on the sinkers at their work, and there is 
 always danger of materials falling down the shaft on the sinkers. 
 
 Second Method. At a short distance from the shaft bottom and on a pas- 
 sageway that is not much used, a steep slope ab, Fig. 2, or small shaft is sunk, 
 the depth of sinking depending on the amount of rock necessary to be left as a 
 support under the old sump while the deepening proceeds. At the foot of the 
 slope a level heading be is first driven to the opposite face of the shaft; the roof 
 of this heading is strongly timbered by setting the collars in hitches cut in the 
 sides, before the work of excavating the shaft below is commenced. When this 
 is done, the excavation is begun and carried down in exact line with the shaft 
 above, the material being removed by a hoisting bucket, operated by a wind- 
 lass or temporary hoisting engine lo- 
 cated at some point near the head of 
 the slope. The further operation of 
 sinking, timbering, etc., is the same 
 as that previously described. When 
 the sinking is complete and the shaft 
 timbered, the main sump s is drained 
 and the two shafts connected by dri- 
 ving downwards from the bottom of 
 the sump, or upwards from below 
 from a strong temporary staging 
 erected at c. 
 
 Third Method. Fig. 3 shows the 
 method of deepening a shaft while the 
 upper part is in use, by opening only 
 that portion of the shaft area not un- 
 der the hoistway for a distance of 12 
 to 15 ft., and then widening it out the 
 entire size of the main shaft. This 
 leaves a roof of rock (pentice) that 
 shields the men. When another lift 
 has been sunk, the pentice is cut away 
 and another started for the next drop. 
 The hoisting is done by an under- 
 ground engine or by a bucket and 
 windlass. 
 
 The main hoisting engine may be 
 used by setting out one of the cages and 
 
 FIG. 2 
 
 passing the hoisting rope through a hole drilled through the pentice and attach- 
 ing it to the sinking cage. 
 
 Upraising. Shafts are sometimes driven from the bottom upwards as 
 when two parallel seams are to be worked through the same opening. From 
 the labor standpoint the process is much cheaper, as there is no hoisting to do. 
 The material extracted is generally stowed in the old workings below, but some- 
 times when room is not available it is sent to the surface. Before commencing 
 to drive upwards, a careful survey is made : to establish the four corners of the 
 shaft in the mine immediately under the surface location. Four iron pins are 
 driven in the bottom to mark these corners. If necessary, posts or timber 
 cribs are set to secure the roof around the place before blasting is begun. When 
 the excavation has proceeded upwards 8 or 10 ft. in the roof, the bottom is 
 cleaned up, the pins located, and the shaft tested for alinement by hanging 
 plumb-bobs in each of the four corners. Timbering is then begun by first 
 setting a heavy square frame/, Fig. 4, in the roof, resting on substantial posts 
 ad sills, as shown in the figure. The inside measurements of the frame must 
 correspond to the size of the shaft in the clear when timbered. This frame is 
 exactly located by means of the plumb-bobs hanging over the four points pre- 
 viously established, and is then firmly wedged in place. The timbering of the 
 shaft is built up on this frame after the ordinary manner of shaft timbering. 
 
OPENING A MINE 
 
 595 
 
 The timbering is carried as close to the roof as practicable, and a partition is 
 carried up dividing the shaft into two compartments. This partition may later 
 be used in the opera- 
 tion of the shaft as one i 
 of the permanent par- 
 titions, and should be 
 located accordingly. 
 
 A heavy bulkhead 
 is now constructed at 
 the bottom of the shaft, 
 and a chute arranged 
 under the larger com- 
 partment h, by which 
 the loose material ex- 
 cavated above and 
 thrown into this com- 
 partment may be 
 drawn and loaded as 
 required. To control 
 the descent of the loose 
 material in this com- 
 partment, a door is 
 arranged at the foot 
 of the chute. The 
 compartment m serves 
 the .double purpose of 
 a manway and air 
 shaft, and for this pur- 
 pose it is divided by a 
 temporary partition. 
 A ladder is constructed 
 in the manway, by 
 which the workmen 
 travel up and down. 
 
 In the operation of 
 upraising, the workmen 
 ascend the manway by 
 
 the ladder and stand ""**' 
 on a temporary plat- 
 form, or on the loose material that is allowed to fill the compartment h. The 
 material is drawn from this compartment only as is required to furnish good 
 
 standing room at the face. In up- 
 raising, the ventilation of the shaft is 
 always more or less difficult, owing to 
 the tendency of the smoke and hot bad 
 air to remain at the top. The air com- 
 partment may be connected, by a box, 
 to the main air-course while the man- 
 way is open to the return, or vice 
 versa; by this means, a fair current of 
 air may be maintained at the top of the 
 shaft or upraise. At times, a small 
 blower is used to blow the air into the 
 face. When compressed air is used to 
 operate the drills, there will be air 
 sufficient for the ventilation of the up- 
 raise without making other provisions. 
 The timbers required must be taken up 
 the manway or the air compartment. 
 When blasting, the manway and air 
 compartments are covered with heavy 
 planks, to avoid the material loosened 
 by the blast falling down the shaft. 
 
 Of these methods of deepening 
 shafts, those shown in Figs. 2 and 3 
 are generally employed, because it is 
 
 FIG. 4 
 
 unusual to have a lower seam open in advance of development; a condition 
 that is assumed to exist when the method shown in Fig. 4 is used. 
 
596 
 
 OPENING A MINE 
 
 FIG. 1 
 
 SHAFT DRAINAGE AND PUMPING 
 
 Surface water is kept put of tho- shaft by banking around the shaft sills 
 the clay and other material taken out during sinking. The water pumped 
 or hoisted from the shaft is carried away in tight wooden troughs that lead in the 
 direction in which the surface dips, and extend far enough from the shaft to 
 prevent the water from returning. Water within a comparatively short dis- 
 tance from the surface can be drained from 
 the shaft by sinking a well or small shaft 
 adjacent to the main shaft. During the 
 sinking, a hole, or sump, is excavated at 
 one end or in the center of the shaft some- 
 what in advance of the general work. The 
 water is either bailed out of this hole and 
 hoisted in buckets, or a sinking pump of 
 special form is employed. These pumps 
 may be hung by hooks from the timbering, 
 at any point or simply hung by ropes, and 
 may be hoisted and lowered as desired. 
 Instead of a special sinking pump, a small horizontal pump of ordinary pattern 
 is often set up on a temporary staging, which is moved downwards as the 
 work advances. Either of these pumps is connected with the steam and 
 water pipes in the manway by short lengths of wire-wound rubber hose. 
 
 Water Rings. To draw away the water made by the shaft, a notch is cut 
 in the rock as shown in Fig. 1, or if the shaft is timbered water rings, or curb 
 rings, are built in the lining as shown in Fig. 2. These catch the water run- 
 ning down the lining and conduct it to the corner of the shaft, from whence^ 
 a pipe leads it to the sump at the bottom 9r to a lodgement or a coffer dam. 
 
 Coffer Dams. A coffer dam is a section of solid lining designed to dam 
 back water coming from a bed of water-bearing rock. Sufficient material is 
 excavated from the water-bearing bed to allow a good cement backing to be 
 inserted behind the shaft timbers. This excavation should be carried a short 
 distance into the overlying and underlying impervious rock so as to form a 
 water-tight joint. The space behind the timbers is filled with concrete either 
 at the time they are placed or later through an opening left in them. The 
 timber is often made much stronger and heavier at this point. 
 
 Lodgements, or Basins. Lodgements, or basins, are openings from 6 to 
 8 ft. high, equal in width to the shaft, and driven, usually, from the end thereof. 
 As they extend from 50 to 60 ft. back from the shaft they 
 hold large quantities of water, which may be pumped thence 
 to the surface instead of from the sump at the shaft bot- 
 tom, thus effecting a large saying in power. They are 
 commonly floored and lined with cement to prevent the 
 water reaching lower levels through cracks in the rock. 
 The mouth of the lodgement is closed with a timber, or 
 concrete, dam, in which an opening large enough to admit 
 a man is left. In the case of basins, no dam is necessary as 
 it is made by excavating the floor of the lodgement to a 
 sufficient depth to hold the water. 
 
 Sump. The shaft is carried far enough below the cage 
 landing at the bottom to provide a catch basin, or sump, 
 large enough to hold the water draining into it from the 
 shaft and workings during 24 hr. The depth of the sump 
 will be the height to which the suction end of the pump 
 can draw water, say, 25 ft. at sea level. Where the mine _ 
 
 makes much water, the area of the shaft is not sufficient to * IG - 
 
 afford the required capacity, and the sump must either be extended at one end 
 or a second sump, draining into the first, must be provided. 
 
 SLOPE AND SHAFT BOTTOMS 
 
 SLOPE BOTTOMS 
 
 At the foot of a slope, or at the landing at any lift, the entry is widened out 
 to accommodate at least two tracks one for the empty and the other for 
 loaded cars. The empty track should be on the upper side of the entry, or 
 that side nearer the floor of the seam, and the loaded track on that side of 
 the entry nearer the roof of the seam. 
 
OPENING A MINE 
 
 597 
 
 Fig. 1 shows an arrangement of tracks often used. At a distance of 40 or 
 
 50 ft. above the entry, the slope is widened out to accommodate the branch 
 
 leading into the entry loaded track. This branch descends with a gradually 
 
 lessening inclination un- 
 til nearly at the level of 
 
 the entry it turns into 
 
 the main loaded track. 
 
 A short distance above 
 
 the entry and below 
 
 the switch b a hinged 
 
 bridge d is placed, 
 
 which, when lowered, 
 
 forms a connecting 
 
 platform or bridge by 
 
 which the empty cars 
 
 are taken off the slope. 
 
 The empty track e is 
 
 about 6 ft. higher than 
 
 the loaded track /, and 
 
 is carried over it on a 
 
 trestle. 
 
 The figure shows the 
 
 plan A and profile B as 
 
 arranged for a single 
 
 slope, or one side only 
 
 of a slope taking coal from both sides. When coal is to be hoisted from 
 
 this landing, the bridge is closed, the empty cars lowered in the slope run off 
 
 over the bridge, the cars unhooked from the rope, and the hook and chain 
 
 thrown down to the track below on 
 which the loaded cars are standing; the 
 loaded cars are then attached to the 
 rope and hauled to the main track on 
 the slope and hoisted. This plan can 
 only be economically employed in a 
 seam of moderate thickness that will 
 not require the taking down of a large 
 amount of the top. The cars can be 
 handled on the landing by gravity. 
 
 Fig. 2 shows an excellent method 
 of laying switches in either thick or 
 thin seams where the pitch does not 
 exceed 20. When there is only one 
 track in the slope and coal is to be 
 
 B 
 
 FIG. 1 
 
 FIG. 2 
 
 hoisted from both sides, the same arrangement is used on each side; but to 
 avoid complications, such as crossings, etc., it is better to locate one of the 
 switches on the main track farther down the slope, as indicated by the dotted 
 lines. The empty track e joins 
 the loaded track / before it 
 reaches the slope track s. 
 
 Fig. 3 shows a plan A and 
 profile B ot a switch used at 
 the bottom of a slope. The 
 figure shows one side only of 
 the slope, the other side be- 
 ing similar. At the switch a 
 there is a pair of spring latches 
 set for the empty track e and 
 which causes the empty cars 
 coming down the slope to 
 take this track. The empty 
 cars pull the rope in to where 
 it can be attached to the loaded 
 cars, which are standing near 
 the slope on the road /. 
 
 Fig. 4 shows a cross-section 
 of the slope landing shown in 
 
 FIG. 3 
 
 Fig. 3 when the empty track e is higher than the loaded track /, so that both 
 the loaded and empty cars can be handled by gravity. 
 
598 
 
 OPENING A MINE 
 
 When the pitch of the slope is so steep that the coal or ore falls out of the 
 
 cars during hoisting, a gunboat is used or the cars are raised on a slope car- 
 riage in either case, the arrangement 
 of the tracks at lift landings is entirely 
 different. With either a gunboat or a 
 slope carriage, the arrangement of 
 tracks on the slope is the same; but, in 
 the former case, a connection between 
 the slope and empty tracks is often ad- 
 visable. When a gunboat is used, the 
 empty tracks run direct to the slope, 
 and a tipple, or dump, is placed on 
 each side to dump the mine cars over 
 the gunboat; but when the cars are 
 raised on a slope carriage, the gang- 
 way tracks run direct (at right angles) 
 to the slope, to carry the car to the 
 cage or carriage. The floor of the cage 
 is horizontal, and has a track on it 
 that fits on the end of the entry track 
 when the- carriage is at the bottom, 
 and this track is arranged with stops 
 similar to those on cages used in 
 shafts. 
 Another common arrangement ot tracks at the bottom of a slope is shown 
 
 in Fig. 5. A branch is made by widening the slope out near the bottom, and 
 
 this, being a few feet higher than the main track, is used to run off the empties 
 
 by gravity. The loaded cars run in by gravity around the curve to the foot 
 
 of the slope in position to be attached to the rope. 
 
 In ascending, the loaded car forces its way through the switch, or the switch 
 
 may be set by a lever located at the foot of the 
 
 slope. When the empty car descends, it runs in 
 
 on the branch, where the chain is unhooked and 
 
 thrown over in front of the loaded car, and runs 
 
 around the curve into the entry by gravity. 
 
 It will be observed that in this plan the loaded 
 
 car and, consequently, the bottom men, stand on 
 
 the track in line with the slope, and are in danger 
 
 from any objects falling down the slope, or from 
 
 the breakage of the rope or couplings; but this 
 
 can be obviated by making the bottom on the 
 
 curve. The illustration shows only one side of the 
 
 slope; the other side is, of course, similar. 
 
 FlG. 4 
 
 FIG. 5 
 
 pw MFBB MOU* WB la, Ul U0WUVU vMlliildl . 
 
 Ail these plans necessitate the location of that part of the entry near the 
 slope, in the upper benches of the coal or near the top rock. The gangway 
 is then curved gently around toward the floor, so that, when it has been driven 
 far enough to leave a sufficiently thick pillar, the bottom bench is reached 
 arid the entry is then driven along the bottom rock. 
 
 A very different bottom arrangement is shown by Fig. 6, which also rep- 
 resents a plan frequently adopted on surface planes. 
 The two slope tracks are merged into one a short dis- 
 tance from the bottom of the slope, and on the oppo- 
 site sides of the bottom two tracks curve around into 
 ) LATCH S7 the entry on opposite sides of the slope. As these 
 Br CAR branches curve into the main entry tracks, a switch 
 sends off a side track for the empty cars. The switch 
 on the slope is either set by the car and this can be 
 done because the next loaded goes up on the same side 
 on which the last empty descended or by a lever 
 located at the bottom. 
 
 It will at once be seen that in this plan np oppor- 
 
 . The 
 
 FIG. 
 
 tunity is afforded of handling the cars by gravity 
 curved branches are made nearly level, and the mo- 
 mentum of the descending car, if quickly detached, 
 is often sufficient to carry it partly or wholly around the curve, even against a 
 slight adverse grade. The disadvantage of having the bottom in direct line 
 with the slope (where there is danger from breakage and falling material) 
 also obtains in this plan. 
 
OPENING A MINE 
 
 599 
 
 In the plan shown by Fig. 7, the grades may be so arranged that the cars 
 can be entirely handled by gravity. The latches on the main-slope track may 
 be closed automatically by a spring or weight, the loaded car running through 
 them in its ascent on the slope, or both sets may be 
 operated by a single lever at the bottom. The switch 
 at the upper end of the central track (loaded) is 
 set by a hand lever. All three sets may be linked 
 together, so that they can all be properly set by a 
 single lever. Reference to Fig. 5 will show that 
 this is only a modification of that method. It 
 requires space at the bottom for only three tracks, 
 while Fig. 7 requires width to accommodate four 
 tracks, and is objectionable because it is more com- 
 plicated. The extra set of latches at the top of the 
 central track, and the curvature of both main tracks 
 into this central one, must inevitably cause much 
 trouble and delay from cars jumping the track at 
 this point. 
 
 The plan shown in Fig. 8 is open to many of the objections pertaining to 
 some of those already described, and which need not be reiterated here. It 
 can only be employed in thick seams, or in seams of moderate thickness lying 
 at a slight angle or dip. v 
 
 In planning the arrangement of tracks on a slope, it is advisable to place 
 as few switches as possible on the slope itself, to keep the main track unbroken, 
 to make the tracks as straight as possible, to have nothing standing at the 
 bottom in direct line with the slope tracks, and to arrange the tracks so that 
 cars are handled by gravity. 
 
 The arrangement of tracks near the top of the slope, and on the surface 
 is often very similar to the bottom arrangements, as already described; but 
 as all loaded cars (except rock and slate cars, which are run off on a separate 
 switch) are to be sent off on one track, and all the 
 empties come in on the same track to the head of 
 the slope, and as there is usually abundance of 
 room for tracks and sidings, these top arrangements 
 are, in a measure, much more easily designed. In 
 some instances, the two main-slope tracks run into 
 a single track near the head of the slope a plan 
 somewhat similar to the bottom arrangement shown 
 in Fig. 6 and the cars are then brought to the sur- 
 face on one track, which, after passing the knuckle, 
 bifurcates into a loaded and empty track. A similar 
 arrangement is frequently adopted at slopes on which 
 a carriage or gunboat is used. When the two main- 
 slope tracks are continued up over the knuckle to the 
 surface the most common and best plan the arrange- 
 ment of tracks and switches may be planned entirely 
 with a view to the quickest and most economical 
 method of handling the cars. 
 
 Vertical Curves. The vertical curves at the knuckle 
 and bottom of a slope or plane should have a suffi- 
 ciently large radius, so that when passing over them the car will rest on the 
 rail with both front and back wheels. The wheel base of the car must be 
 considered in adopting the radius for these curves, for if the curve is of too 
 short a radius, there is danger of the car jumping the track every time it 
 passes over the curve. 
 
 SHAFT BOTTOMS 
 
 When coal is received on one side of the shaft only, an arrangement of tracks 
 such as shown in Fig. 1 is often adopted, by which the empty car, when bumped 
 from the cage s by the loaded car, descends a short, sharp grade to b, and then 
 by its own momentum ascends a short grade c called a kick-back and return- 
 ing by gravity passes through a spring latch at b, by which it is automatically 
 switched and passes around the shaft by the track g that connects with the 
 empty track, which is from 2 to 3 ft. lower than the level of the loaded track. 
 At times, the track leading around the shaft passes through a cross-over to 
 an air-course or parallel entry occupied by the empty track, instead of return- 
 ing to the main shaft bottom where the loaded track is located. Sometimes, 
 the loaded track is in line with the center of the shaft, instead of as shown in 
 the figure, the switch allowing the cars to pass to either cage, as desired. 
 
 FIG. 8 
 
600 
 
 OPENING A MINE 
 
 Where there is not room back of the shaft for the length of track shown in 
 the cut and where power is available, the empty tracks are brought together 
 
 FIG. 1 
 
 as soon after leaving the cageway as possible. At the point of the spring latches 
 is the foot of a power-djriven chain haul, which hoists the empty cars to a suf- 
 ficient elevation for them to run back by gravity along the line bd to a con- 
 nection with the main entry track. The height through which the empties 
 
 are hoisted will vary from 4 to 
 8 ft. or more, and depends on 
 the length and grade of the sid- 
 ing bd. A profile, of the ar- 
 rangement is shown in Fig. 2. 
 in which s is the shaft, d the 
 switch connecting the empty 
 
 t 2 
 
 and loaded tracks on the main road, and b the switch back of the shaft between 
 the car haul track and empty car siding bd. 
 
 When loads are caged from both sides of the shaft, the bottom arrange- 
 ments are as shown in Fig. 3, or some modification thereof. The grades should 
 
 Air Shaf, 
 
 Air Course 
 
 Empty Trad 
 Level 
 
 IS. 
 
 Loaded 
 Track 
 
 ILoaaea trac 
 '*' G ' a 
 
 FIG. 3 
 
 be so arranged that from the inside latches of the crossings the empty track 
 has a slight down-grade from the shaft, and the loaded track a slight 
 
OPENING A MINE 601 
 
 down-grade toward it. The crossings and the short straight piece of road 
 close to the shaft should be level. 
 
 As it is often necessary to move cars from one side of the shaft to the other 
 without stopping the hoisting, a narrow branch road connecting the tracks 
 on opposite sides of the shaft should be cut through the shaft pillar, similar 
 to that shown in bgd. Fig. 1. 
 
 Other shaft-bottom arrangements will be found in the section on Timber- 
 
 GENERAL BOTTOM DETAILS 
 
 In arranging tracks for shaft bottoms, at tops and bottoms of slopes, on 
 coal bins, for mechanical-haulage landings, at foot of slopes or shafts, or in 
 the body of the mine, it is customary to provide double tracks of sufficient 
 length to hold the requisite number of cars for economically operating the 
 plant and with sufficient distance from center to center of tracks, and 
 from centers of tracks to sides of entries, to easily pass around the cars where 
 it may be necessary, either in handling them, or in lubricating the wheels. 
 For cars with a capacity of from 1$ to 2 T., it generally requires an entry to 
 be about 15 to 17 ft. wide in the clear for ordinary landings in the body of the 
 mine, while at shaft bottoms the necessary width may attain 17 to 18 ft. in 
 the clear, owing largely to location and local requirements. The curved cross : 
 overs connecting the tracks at shaft bottoms should be designed with radii 
 of as great length as can be introduced, thereby giving an easy running track. 
 They should not be less than from 20 to 50 ft. on center lines for ordinary 
 gauge of tracks, i. e., 36 to 44 in. 
 
 On landings constructed in the body of the mine for the reception of empty 
 and full cars handled by mechanical haulage from shaft or slope, and from this 
 point transported by animal power to the various working places in the mine, 
 a grade of about 1% in favor of the loaded cars to be handled by the stock 
 will be found quite an assistance in delivering the cars to the haulage. The 
 frogs and switches for these landings, as well as those required at the shaft or 
 slope, should be formed of regular track rails, and can generally be arranged 
 to be thrown by a spring or a conveniently located hand lever, as has been 
 described, instead of being kicked to position, as was the custom at one time. 
 
 Besides these usual arrangements of shaft-bottom landings, at many 
 plants the natural grades of the entries can be taken advantage of in design- 
 ing convenient and economical methods for handling the mine cars. For 
 instance, where the coal is to be hauled from the dip workings of a mine by 
 some form of mechanical haulage, and a summit can conveniently be arranged 
 for in the track on the same side of the hoisting shaft, at the proper distance 
 therefrom, to accommodate the requisite number of loaded cars to be hauled, 
 thus allowing them to run by gravity over, say, a 1% grade to the shaft, sev- 
 eral empty-track arrangements can be made. The most simple form is to have 
 the empty cars descend a short grade of from 4% to 5% when pushed from the 
 cage by the succeeding full one. The momentum thus secured is quite suf- 
 ficient to carry the car up an opposing grade of about 1.5%. It again descends 
 on the same track, and passing through an automatic switch, continues to the 
 empty-car siding. From this latter point it is handled by the regular haulage 
 machinery, and in its route passes around the shaft through an _entry especially 
 prepared for this arrangement. A shaft bottom so constructed is very economi- 
 cal to operate, requiring but few men to handle the cars. 
 
 Occasionally, it becomes more expedient to have a separate short haulage 
 to draw the empty cars to the main haulage when it cannot be easily arranged 
 to construct a complete gravity landing. Several other modifications of such 
 a general design can be made. All the different devices, however, depend 
 largely on the local requirements of the particular mine under consideration. 
 
 When endless-rope haulage is employed, it is generally found to be most 
 convenient to have the landings for full and empty cars in the body of the mine 
 reached by switches off of the main-haulage track, the cars coming on and 
 leaving the main track at slight knuckles introduced in the track, in order 
 to allow a place for the passing of the rope, which then moves along through 
 a short cut or channel through the switch rails. The flanges of the cars pass 
 over the rope in this manner without any injury to it. 
 
 Mine Stables. In the location of the mine stable, the following points 
 should be considered: The prompt rescue of the mules in case of accident; the 
 ventilation of the stable by a separate split of fresh air without contaminat- 
 ing the air-current passing into the mine; the handling of the daily stable refuse 
 and feed to and from the surface; water supply; distance from the stable to 
 the working face. The stable is generally located near the bottom of the shaft 
 
602 OPENING A MINE 
 
 especially during the early development of the mine; though sometimes later, 
 and after the workings have become extensive, the stable may be moved to 
 some convenient second opening or air-shaft where the mules will be closer 
 to the working face and can still be rescued promptly and fed and cared Tor 
 economically. One arrangement is shown in the accompanying figure. 
 
 Usually no door is required at the entrance to the stable, but a regulatpr 
 is placed at its rear end to control the supply of air entering from the main 
 
 As a protection from fire, the posts for supporting the roof, as well as the 
 partitions between the stalls, the doors, etc., are made of sheet iron. Very 
 frequently, the walls and floors are coated with cement, which material, but 
 with a wooden lining, is also often used in the construction of the feeding 
 troughs. Stalls are commonly built so that there will be a passageway 2 to 
 3 ft. wide between the heads of the mules and the ribs. Commonly a track 
 is laid back of the mules so that all manure, straw used for bedding, and. other 
 stable litter may be loaded into a mine car and sent to the surface each day. 
 Wherever possible, underground stables should be provided with incandescent 
 lights hung in metal wire baskets. 
 
 The question of water supply for the stables is sometimes a troublesome 
 one. Where the mules cannot drink the mine water, as is usually the case, 
 a supply of water must be piped to the stable from the surface. It is impor- 
 tant to maintain a bar or chain at the entrance of the stable to prevent mules 
 that get loose from wandering into other parts of the mine; the instinct of 
 the mule will almost invariably lead him to the sump where he may be drowned. 
 
 Pump Room. The pump room frequently is located near the foot of the 
 pump way of the main hoisting shaft. The use of a compartment of the hoist- 
 ing shaft for pumping, however, often proves a serious inconvenience in the 
 operation of the mine, owing to the exhaust steam filling the shaft and shaft 
 bottom so as to interfere with the work of hoisting. With the pump room 
 located in the shaft pillar between the downcast or air-shaft and the main hoist- 
 ing shaft, this trouble is avoided. 
 
 It frequently happens that owing to the varying grades in the seam it is 
 impracticable to drain all the mine workings to a sump at the shaft bottom. 
 In such cases, a sump is often located at some c9nvenient low point in the work- 
 ings, and the pump room is then located at this point, and the water pumped 
 to the surface through bore holes drilled for this purpose. The steam supply- 
 ing the pump is likewise conducted in pipes from the boilers at the surface 
 to the pump in the mine through a bore hole. 
 
 Engine Room. The engine for rope haulage is often located at some point 
 in the mine, and where steam is used for power it may be taken down the shaft 
 and along the entry to the engine room, or down a bore hole that opens into 
 the mine near the engine room. The engine may exhaust into a pipe leading 
 up the shaft, or bore holes for this purpose may be sunk from the surface at the 
 point where the engine is located. The engine room is an opening made in 
 the shaft pillar or, if away from the shaft, in the entry pillar, which is then 
 made larger to provide for the room. The roof over the engine room is well 
 secured by solid timbers, or by steel I beams supported on brick or concrete 
 walls at the sides of the room. The engine should be placed so that the pull 
 of the rope will be as direct as possible. 
 
 Lamp Stations. In a very gaseous mine where none but safety lamps are 
 used in the workings, the lamp room or lamp station is generally located at 
 the surface. In many gaseous mines, however, safety lamps are restricted 
 to a portion of the workings only and naked lights are used in the other 
 
OPENING A MINE 603 
 
 portions ot the mine. In such cases, lamp stations are frequently provided 
 at some point on the main intake of the mine near the mouth of the entries 
 or headings leading to these workings. Similar lamp stations, called relight- 
 ing stations, are likewise often provided at different points on the main intake 
 wherever safety lamps are used, where lights that have been extinguished 
 may be relighted. A lamp station is a simple opening made in rib or pillar 
 coal on the intake airway, where a strong current of pure air is passing, and 
 where safety lamps may be kept or relighted when extinguished. 
 
 Shanties. The various other shanties used in the operation of the mine, 
 such as the mine-boss shanty, tool shanty, oil house, etc., as well as the wash 
 rooms and hospital rooms, are simple openings made in the shaft or entry 
 pillar, the size and arrangement depending on their use. Many mines now have 
 wash rooms and hospital rooms at the shaft bottom, supplied with steam and 
 water pipes, for the convenience of the men and for the care of the injured. 
 The walls of these rooms, as also those of the mine-boss shanty, are often 
 cemented and whitewashed, and the floors are also cemented so that they can 
 be kept clean and comfortable. Tool shanties are often located at convenient 
 points for the distribution of the tools to the company men, and sometimes 
 there are blacksmith shops in the mine for the sharpening of the tools, though 
 this is generally done at the surface. 
 
 Manway About the Shaft. A small manway should encircle at least one 
 end of every hoisting shaft. This manway is sometimes made by enlarging 
 the shaft excavation by widening on the rib, but this is not a good plan. At 
 other times, a narrow heading or passageway is driven in the solid coal from 
 one side of the shaft to the other. A manway in the shaft pillar is objected to 
 by some as endangering the shaft pillar, but allowance can be made for it in 
 laying out the size of the shaft pillar, and it can be well timbered, if necessary, 
 so as to run no risk of weakening the strata near the shaft. No hoisting shaft 
 should be operated without such a manway, in order to avoid the risk to which 
 the eager is exposed if obliged to pass under the moving cages. 
 
 SURFACE TRACKS FOR SLOPES AND SHAFTS 
 
 The arrangement of the tracks on the surface naturally differs at every 
 mine, owing to the different existing conditions. All surface roads should be 
 so arranged that the loaded cars can be moved with the least possible power, 
 always looking out for the return of the empties with as little expenditure of 
 power as possible. To secure the running of the loaded cars from the mouth 
 of the shaft or slope by gravity, a slight grade is necessary, the amount of which 
 depends on the friction of the cars, which varies greatly. Care should be taken 
 that an excessive grade is not constructed, or there will be trouble in return- 
 ing the empties from the dump to the head of the shaft or slope. 
 
 The tracks connecting the top of the shaft and the tipple may be very 
 short, or of considerable length, depending on the conditions at each mine. 
 Usually from 20 to 60 ft. will be sufficient, although no definite rule can be 
 given for this. 
 
 There are two general arrangements of tracks about the head of a shaft: 
 First, where the loaded cars are removed from the cage and the empty cars 
 placed upon it from the same side of the shaft; second, where the loaded cars 
 are removed from one side of the shaft and the empty cars returned to the 
 cages from the opposite side of the shaft. 
 
 In either case there are usually several empty cars on the platform ready 
 to be put on the cages when the loaded cars have been removed. 
 
 Where the conditions are such that the loaded cars can be run by gravity 
 to the dump, a good plan is to have a short incline, equipped with an endless 
 chain, in the empty track. The empty cars can be run to the foot of this, 
 hoisted by machinery to the top, and thus gain height enough to run them 
 back to the shaft or slope by gravity. 
 
 At the Philadelphia and Reading Coal and Iron Co.'s Ellangowan colliery, 
 where the tipple at the head of the breaker is above the level of the head of 
 the shaft, the following plan is used: The loaded cars are taken off the east 
 side of the cages, and run by gravity to the foot of the incline where the axles 
 of the car are grasped by hooks on an endless chain and the car pulled up to 
 the tipple. After being dumped, the car is run back from the tipple to the 
 head of the incline, and is carried to the foot of the empty track of the incline 
 by an endless chain. The foot of the empty track is several feet higher than 
 that of the loaded track, and the cars are run by gravity around to the west 
 side of the cages, and are put on from that side. The empty cars, as they run 
 on the cage, have momentum enough to start the loaded car off the cage and 
 
604 METHODS OF WORKING 
 
 on toward the foot of the incline. There are a number of hooks attached to 
 both the empty and loaded chain on the incline, and there are often several 
 loaded and several empty cars on different parts of the plane at once. This 
 arrangement permits of the hoisting of from 700 to 800 cars per day out of a 
 shaft 110 yd. deep, with single-deck cages. 
 
 Another excellent arrangement for handling coal on the surface is the 
 invention of Mr. Robert Ramsey, and has been adopted by the H. C. Frick 
 Coke Co. and a number of other prominent operators. A description of 
 this arrangement as applied at the H. C. Frick Coke Cp.'s standard shaft 
 is as follows: The landing of the shaft is made slightly higher than the level 
 of the tipple, which is north of the shaft. South of the shaft is located a 
 double steam ram, one ram being directly in line with the track on each cage. 
 Directly in front of the rams is a transfer truck, worked east and west by 
 wire rope. The loaded car on the cage is run by gravity to the tipple, where 
 it is dumped by means of a nicely balanced dumping arrangement. As soon 
 as it is empty it rights itself and runs by gravity alongside the shaft to the trans- 
 fer truck, which carries it up a grade to a point directly in line with the cage 
 that is at the landing, and one of the steam rams pushes it on the cage, and at 
 the same time starts the loaded car off toward the tipple. This second loaded 
 car is then returned by the same means to the opposite cage. The whole 
 mechanism is operated by one man, by means of conveniently arranged levers, 
 each of which is automatically locked, except when the proper time to use it 
 arrives. It is therefore impossible for the topman to work the wrong lever 
 and put an empty car into the wrong compartment of the shaft. Besides 
 the one man at the levers, there is but one other man employed at the tipple, 
 and his work is solely to look after the cars when dumping. All switches are 
 worked automatically, and the average hoisting at this shaft is at the rate 
 of 3 cars per minute. The shaft is about 250 ft. deep, and single-deck cages are 
 used. 
 
 The Lehigh and Wilkes-Barre Coal Co. has a system in use at a number 
 of collieries that has also proved very effective. In this system the loaded 
 cars are run by gravity from the cage to the dump, and the empties are hauled 
 from the dump back to a transfer truck by a system of endless-rope haulage. 
 The transfer truck carries the car to a point opposite the back of the cage. 
 The empty car runs by gravity to the cage, and its momentum starts the loaded 
 car on the cage on its way to the dump. This system necessitates the employ- 
 ment of more topmen, but is a very good one. At the Nottingham shaft, 
 which is 475 ft. from landing to landing, from 140 to 150 cars per hour are 
 hoisted on single-deck cages. 
 
 METHODS OF OPEN WORK 
 
 No definite rules can be given for the selection of a method of mining that 
 will cover all the conditions that may exist at any given mine. The system 
 finally selected is that which will yield the maximum percentage of coal in the 
 best marketable condition at the minimum of cost and danger. 
 
 All methods of working may be grouped under one of two heads or classes, 
 viz., open work, or closed work. 
 
 Open work applies to the mining of those deposits that are either so thick 
 or lie so near the surface that the material overlying them may be removed 
 and the coal quarried out at a profit. 
 
 The advantages of this system are that all the coal may be extracted with- 
 out any loss in pillars or through squeezes, and in the lumpiest condition; 
 no timber is required; unprofitable underground workings do not have to be 
 kept open and in repair; when required, a simple hoisting plant is used; there 
 is less danger to the workmen from falls of roof and from blasting; there is 
 practically no danger from fire; artificial lights are not required; mining can 
 be done more economically, as larger faces are open, larger blasts can be used, 
 and the amount of work accomplished per miner is greater, and better super- 
 intendence can be had; the health of the men is usually much better when 
 working in the open; and, under proper conditions, the output can be increased 
 almost indefinitely. 
 
 The chief disadvantage of open work is the possible reduction in output 
 during the winter months owing to snow, the exposure of the men to the 
 weather, etc. Further trouble may arise from flooding during the rainy 
 season, and, unless the seam lies parallel to the surface, the cost of remov- 
 ing the over-burden soon becomes excessive. 
 
METHODS OF WORKING 605 
 
 The removal of the overburden is known as stripping, and may be carried 
 on with or without the use of excavating machinery. When machinery is 
 not used, the covering is removed with pick and shovel when it is earth, and 
 by hand drilling and blasting when it is rock. This is the original method of 
 stripping, probably first applied in the United States to the thick deposits 
 of the anthracite region of Pennsylvania, and is limited in its application to 
 those seams that are either very near the surface or are abnormally thick. 
 Experience has shown that it will pay to remove, without the aid of machinery, 
 1 ft. in thickness of overburden for each foot in thickness ot the underlying 
 coal. Thus a seam 6 ft. thick will permit of the profitable removal of 6 ft. of 
 cover, and one 25 ft. thick of 25 ft., possibly 35 ft., of cover. Mines of this 
 class are known as strippings in Pennsylvania, and as strip-pits in the middle 
 West. 
 
 Steam-Shovel Mines. Steam-shovel mines are the result of the applica- 
 tion of the familiar railroad contractor's steam shovel to stripping. Under 
 favorable conditions, there is probably no cheaper method of mining. It is 
 extensively used in the neighborhood of Park City, Utah, in metal mining 
 and on the iron ranges of the Lake Superior region, where an output of 2,000 T. 
 of ore per da. for a steam shovel and one locomotive has been reached. 
 
 The cost of removing 97,854 yd. of material from over a seam of anthra- 
 cite (Pa.) was $1 a yd. of material stripped and $.516 per T. of coal obtained. 
 The average depth of the stripping was 75 ft., and about two- thirds of the 
 material removed was rock. Recent contracts in the same region have been 
 let for as low as 25 c. a yd. for rock and 5 c. a yd. for earth. Where conditions 
 are very favorable and a shovel of large size can be kept steadily employed, 
 even lower average costs per yard (shale rock and dirt combined) may be had. 
 The volume, in cubic yards, of overburden removed per long ton of coal 
 extracted in recent Pennsylvania practice is 3.3, 3.8, 3.5, 3.6, and 3.0 to 1. 
 In one extreme case, 5.4 cu. yd., and in another but 1.8 cu. yd. of overburden 
 were removed per long ton of coal extracted. 
 
 In the Kansas field, where the surface is level and the seams horizontal, 
 shovels of the largest size are employed to remove the covering to an average 
 depth of 17 ft. (6 ft. to 24 ft.) from a seam that is but little more than 36 in. 
 thick. The upper 6 ft. of cover is dirt, the second 6 ft. is soft shale or soapstone, 
 underlying which is blue shale to the top of the coal bed. Where the seam has 
 about 20 ft. of cover, the average steam shovel will, if employed pretty con- 
 stantly, strip 12 to 15 A. a yr. at a cost of from 5 to 6 c. per cu. yd. The wage 
 scale on an 8-hr, basis, is very close to $2.50, varying from $1.95 for water- 
 boys to $3.05 for blacksmiths. Most of the workers receive $2.52 to $2.62 
 per da. 
 
 Near Danville, Illinois, where the conditions are very similar to those in 
 Kansas, 38 to 40 ft. of overburden, of which 16 to 24 ft. is shale, is profitably 
 removed from a coal seam 8 ft. thick. This is a fair general average for the 
 district, although a ratio of 6 to 1 has been had. 
 
 The disposal of the overburden is frequently a matter of difficulty, par- 
 ticularly when it is thick. If it has to be transported to any great distance, 
 the cost thereof may be prohibitory. If much water or sand occurs in the cover 
 the cost of stripping is likewise increased. Strippings liable to overflow from 
 flooded rivers are costly to operate and the workings should be protected by 
 dams built of the overburden. 
 
 After the surface covering has been removed, a track is usually laid along 
 the face of the stripping on the bottom of the workings, and the coal, after 
 being blasted, is loaded into railroad cars by the steam shovel if it is shipped 
 as mine run or into smaller cars for transportation to the tipple if it must be 
 screened into sizes. 
 
METHODS OF WORKING 
 
 METHODS OF CLOSED WORK 
 
 INTRODUCTORY 
 
 By closed work is meant the mining and removal of the coal without the 
 previous removal of the overburden. In general, the word mine is used to 
 define a series of underground workings, and the words stripping, strip-pit, 
 open-cut, open-pit, and the like, to what are more properly coal quarries of 
 the nature just described. 
 
 No definite rules can be given for the selection of a method of mining that 
 will cover all the conditions that may exist at any given mine. The system 
 finally selected will be that which will result in the production of the maximum 
 amount of coal per acre in the best marketable condition and at the minimum 
 cost of extraction with the least danger to the workers. 
 
 General Considerations. Some of the items to be considered in selecting 
 a method of working are the thickness of the seam and the amount, location, 
 and nature of its impurities; the use to which the coal is to be put; the 
 character of the roof and floor; the amount of cover over the seam; the dip 
 of the coal; the nature and direction of the cleat or cleavage of the seam; the 
 character of the labor to be employed; the presence or absence of gas, etc. 
 
 1. Roof Pressure. Of these items, the roof pressure is the most impor- 
 tant, and a number of other causes are directly affected by it. The weight of 
 the overlying cover will give a maximum roof pressure, but this may be so 
 variously modified that the determination of the actual pressure is practically 
 impossible, and estimates of this pressure must be based largely on practical 
 experience; hence, rules for its calculation are of comparatively little value. 
 One very essential point, however, must be borne in mind, i. e., that the direc- 
 tion of pressure is perpendicular to the bedding plane. 
 
 2. Strength and Character of Roof and Floor. The strength of roof refers 
 to the power of being self-supporting over smaller or larger areas. A strong 
 roof permits larger openings, but increases the load on the pillars, thereby 
 necessitating larger pillars. A weak roof requires smaller openings, and per- 
 mits smaller pillars when the floor is good. A strong roof may yield and settle 
 gradually, giving good conditions for longwall work, or it may be hard and 
 brittle, and difficult to manage. 
 
 The character of floor influences largely the size of pillars. A soft bottom 
 requires large pillars and narrow openings, especially when the roof is strong. 
 
 3. Texture of Coal and Inclination and Thickness of Seam. Soft, friable 
 coal requires large pillars, while a hard, compact coal requires only small 
 pillars. The inclination and thickness of the deposit increase the size of pillars 
 required, and also influence the haulage, drainage, timbering, method of 
 working, arrangement of breasts, etc. 
 
 4. Presence of Gas. The presence of gas in the seam or in the enclosing 
 strata affects the system of working, as ample air passages must be provided, 
 and provision must frequently be -made for ventilating separately the different 
 sections of the mine. Where the gas pressure is strong, and outbursts are of 
 frequent occurrence, narrow openings are necessitated that render the working 
 safe until the gas has escaped. 
 
 5. Use to Which Coal is Put. If the coal is destined to be coked, a method 
 of mining is to be preferred which results in the production of the largest pos- 
 sible amount of slack; whereas, if the coal is screened into sizes in the ordinary 
 way, choice should be given to that system which results in the largest amount 
 of lump coal. 
 
 When the longwall method is used, it is particularly important to have a 
 constant market for the output, such as obtains if the mine is shipping fuel 
 coal to a railroad at a fixed tonnage per day, as a few days' idleness may cause 
 serious trouble at the face, even in temporarily closing it if the pressure is 
 great. 
 
 6. Character of Labor. While, in the room-and-pillar system of mining, the 
 temporary or even long-continued stoppage of work in a portion or all of the 
 working places, does not commonly have other effect than reducing the out- 
 put and, consequently, the profits, under the longwall system the shutting 
 down even for a few days of a comparatively few working places may cause 
 
METHODS OF WORKING 607 
 
 serious trouble in handling the pressure at the face. Hence the necessity, 
 under the longwall system, of having not only a steady car supply as explained, 
 but also steady men who will not lay off for one trivial excuse or another. 
 
 General Systems of Mining. For purposes of classification the various 
 systems of mining coal fall into one of two groups, as follows: 
 
 1. Systems in which the tract to be exploited is first penetrated by a series 
 of two or more relatively narrow (8 to 10 ft.) entries (headings or gangways) 
 from some of which entries are (usually) turned relatively wide (15 to 30 ft.) 
 rooms (breasts or chambers) which are separated the one from the other by 
 pillars of coal, and in which rooms the bulk of the output of the mine is obtained. 
 This group may be further subdivided into the room-and-pillar, pillar-and-stall, 
 and panel methods. 
 
 2. Systems in which entries are not driven, but in which all the coal is 
 extracted in one operation from a continuous face, the roof being allowed to 
 fall or cave as fast as the coal is removed, haulage roads being maintained 
 through the caved area by means of walls of stone built along their sides. The 
 longwall system, largely used abroad, and but to a slight extent in the United 
 States where the vast bulk of the coal is mined by the room-and-pillar method, 
 is the single example of this second group. 
 
 The consideration of any system of mining requires a discussion of the fol- 
 lowing subjects: The system of mining as a whole, including the direction of 
 driving the entries and rooms, the number and grade of the former, etc.; meth- 
 ods of supporting the roof and sides of excavations, see Timbering; methods 
 and appliances for removing water from the workings, see Hydraulics; methods 
 of bringing down the coal at the working face, see Explosives and Blasting; 
 methods of transporting the coal from the face to the tipple, see Haulage and 
 Hoisting; methods of supplying the working places with a current of fresh air 
 from the surface, see Ventilation. 
 
 ROOM-AND-PILLAR SYSTEMS OF MINING 
 
 PRELIMINARY CONSIDERATIONS 
 
 In the room-and-pillar system of mining, the tract to be worked is divided 
 into small districts, or blocks, by main entries and cross-entries intersecting 
 one another at right angles or nearly so. The coal in each block is mined by 
 turning off from the cross-entries a number of rooms. 
 
 That part of the coal which is left between the individual rooms and entries 
 is called a pillar, and the pillars are pierced at more or less regular intervals 
 by cross-cuts or break-throughs in part for the purposes of haulage, but most 
 largely to provide a passage for the air-currents that a better ventilation of the 
 working faces may be secured. The removal of the coal in driving the entries 
 and rooms is called the first working, or more rarely the advance working or 
 working on the advance. 
 
 Unless it is necessary to leave in the pillars to support the surface per- 
 manently they are commonly removed as soon as the rooms, either in part or 
 all those turned from a single cross-entry, have been driven their full length; 
 and unless the pillars can be removed the room-and-pillar system of mining 
 is very wasteful of coal, as from 30 to 50% of the total amount must be left 
 in the mine. The removal of the pillars is variously known as second working, 
 working on the retreat, robbing, drawing-back the pillars, pillar working, pillar 4 
 drawing, pulling pillars, etc. Fig. 1 shows a mine laid out on the double- 
 entry room-and-pillar system of mining. 
 
 Number of Entries. The haulageways in a bituminous mine are known 
 as entries or headings and in an anthracite mine as gangways. There are sev- 
 eral methods of arranging these passageways, known as single-entry, double- 
 entry, triple-entry, etc. 
 
 The multiple-entry systems are expensive to drive, and the greater the num- 
 ber of entries the greater the expense, and are only used by companies with 
 ample capital, large acreage of undeveloped coal, and a large and regular 
 market. 
 
 In the single-entry system, now used but very rarely if at all, a single entry 
 is driven ahead and rooms are turned from one or both sides of it. This entry, 
 which is also the main haulage road, acts as an intake, the air being conducted 
 along it to the last room, up which it passes to the break-through and back 
 along the working faces to the first room and thence by a small air-course to 
 the upcast. The circulation of air is liable, in this method, to be cut off at any 
 
60S METHODS OF WORKING 
 
 time by a fall of roof in the rooms, and the mine must be closed until the ven- 
 
 * fThe^double-entry system of mining, illustrated in Fig. 1, may be considered 
 the standard of American practice. The main entries are driven from the shaft 
 bottom or from the drift mouth, and from these the cross- or butt-entries are 
 driven usually at right angles. The rooms may be turned directly off these 
 
 FIG. 1 
 
 cross-entries, or other entries may be driven at right angles to the cross-entries, 
 and the rooms turned off them. 
 
 The advantages of the double-entry system are that in case of accident 
 on one entry the other is available for escape, a fall of roof in one of the rooms 
 does not obstruct the circulation in other portions of the mine, one or more 
 of the pairs of cross-entries may be closed for any reason without in any way 
 affecting other parts of the mine, and the entries may be driven ahead of room 
 turning, as far as desired, for the purpose of prospecting the seam or to pro- 
 vide for a large number of extra working places that the output may be increased 
 in event of a sudden demand. 
 
METHODS OF WORKING 
 
 In the triple-entry system, the center one of the three parallel entries is 
 usually made the intake and t% main haulage road for the mine, while the 
 two side entries are made the return air-courses for their respective sides of the 
 workings. Overcasts are usually built at the mouth of the center entry of 
 each set of cross-entries to conduct the return current over the haulage road. 
 Although this system requires a greater outlay because of the extra price paid 
 for narrow work, it is often absolutely necessary in the working of. a gaseous 
 seam, to which it is particularly adapted. It is also used where it is not pos- 
 sible to drive a single entry of sufficient width for a double-track haulage road 
 pr where single or double entries of sufficient area to give the required quantity 
 of air cannot be driven or economically maintained on account of poor roof or 
 creep. Sometimes this system is applied to the main entries only, the cross- 
 entries being driven double, as shown in Fig. 2. 
 
 In the four- or quadruple-entry system of mining, four parallel entries are 
 driven. In this case, each side of the mine usually has its own intake (one 
 of the center entries) and return (one of the outer entries) . The center entries 
 are the haulage roads, or one may be used for haulage and the other as a man- 
 way or traveling road for the men. Where high-speed endless-rope haulage 
 is employed, this system is well adapted, the loads coming from the mine along 
 one of the center entries and the empties entering it along the other. In some 
 cases the center entries 
 are not connected by 
 breakthroughs, the 
 right-hand and left- 
 hand pairs of entries 
 being used as the intake 
 and return, respective- 
 ly, of corresponding 
 sides of the mine. This 
 is equivalent to operat- 
 ing two distinct mines 
 through the same main 
 opening. 
 
 The five- or quin- 
 tuple-entry system is the 
 same as the preceding 
 with the addition of 
 one more entry, which 
 is used as a manway. 
 
 Size of Entries. 
 The size of an entry de- 
 pends on its use, as well 
 as on the thickness of 
 the seam and the na- 
 ture of the roof and 
 floor. The cost of main- 
 taining wide roadways under a bad roof or where the floor has a tendency to 
 heave or where the coal is frail, often prevents their use and necessitates nar- 
 rower openings. The thickness of the seam also affects the width of the road- 
 ways for a given output of coal, by reducing the height of .~~ l *-"..' thin seams, 
 and requiring a greater width of car, and consequently greater jdth of road- 
 way for the same capacity or output. The amount of the daily output of 
 coal is also a factor determining to a large extent the size of the haulage roads 
 required. In a coal seam 6 ft. thick, with a good roof, and when the coal is 
 clean and does not yield much gobbing material, the width of a single-track 
 entry is generally from 8 to 10 ft. As the amount of material to be gobbed 
 increases, the width is increased, if the roof will permit; but occasionally entries 
 are driven only 6 ft. wide owing to poor roof. The general practice is, however, 
 to drive entries as wide as the roof conditions will permit so as to avoid 
 yardage as much as possible. In thin seams, where the roof must be taken 
 down or the bottom lifted to provide headroom on the haulage roads, an entry 
 is often driven 12 or 14 ft. wide where the conditions with respect to the roof 
 and coal will permit. By this means, the cost of driving is paid by the coal 
 taken out, there is no charge for yardage, and room is provided for stowing 
 the waste material taken down from the roof. This waste is built along the 
 side of the road as a pack wall, or building, as it is called. Fig. 3 shows a 
 cross-section of an entry where the roof has been taken down to afford head- 
 room and the waste built up at the side of the road. 
 
 FIG. 2 
 
610 
 
 METHODS OF WORKING 
 
 A common, but bad, practice is to make the haulage road, which is the 
 intake, of a good height for passage of car by Dipping down the roof, but leaving 
 the return airway of the height of the seam. Thus, if both entries are driven 
 10 ft. wide, and the roof in the intake is taken down to give a height of 6 ft. 
 while the height of the return is that of the coal, or, say, 4 ft., the one entry 
 has an area of 60 sq. ft. and the other one of 40 sq. ft., the disadvantages of 
 which from the standpoint of proper ventilation are obvious. The return air- 
 way should have, at least, the same area as the intake. 
 
 Where practicable, the airways should be made in the form of a square 
 instead of a parallelogram of the same area. Thus a square entrv 10 ft. by 
 10 ft. in dimensions has an area of 100 sq. ft. and a perimeter of 40 ft.; whereas, 
 an entry 5 ft. by 20 ft. in size while having the same area has a perimeter of 
 100 ft., and the friction of the air in passing through and the power required 
 to produce ventilation is much greater than in the square entry. 
 
 Break-throughs between entries are usually made about the same width 
 as the entry and at a distance apart determined by law Or by the gaseous con- 
 dition of the coal. 
 
 Distance Between Entries. The distance between the center lines of the 
 main entries is commonly made from 30 to 60 ft., which provides for a pillar 
 from 20 to 50 ft. in thickness if the entries are 10 ft. wide as is usually the case. 
 While the pillars are made as thin as possible to reduce the cost of narrow work 
 in driving break-throughs, they must be sufficiently strong to withstand the 
 effects of the pressure brought upon them by drawing the room and entry 
 pillars on the cross-headings. Furthermore, as the main-entry pillars must 
 last through the lifetime of the mine, they must be larger and stronger than 
 those between the cross-entries, which are frequently pulled as soon as the rooms 
 on them are worked out. The cross-entry pillars, which do not have to stand 
 
 so long, are frequently made 20 ft. 
 thick, indicating a spacing of the 
 center lines of 30 ft. when the en- 
 tries are 10 ft. wide. 
 
 The distance between the cen- 
 ter lines of the room entry of one 
 pair of cross-entries and the return 
 air-course of the next parallel 
 pair of cross-entries is equal to 
 the width of one entry plus the 
 length of the room plus the thick- 
 ness of the pillar left between the 
 faces of the rooms driven from the 
 
 FIG. 3 
 
 one entry and the return air-course of the next entry. 
 
 Direction of Entries in Flat Seams. The direction of the main entries is 
 determined by the shape of the property, the direction of the cleavage of the 
 coal, etc. If the property is long and narrow, it effects an economy in haul- 
 age if the main entries are driven as near as possible and parallel to one of the 
 longer sides so that all the cross- or room-entries may be on the same side of 
 the haulage road. If the property is square, the main entries are commonly 
 driven to divide the tract into two as nearly equal parts as possible, with room 
 entries of the same length on each side of the main road. If the property is 
 short and wid?m order to avoid excessive length of the cross-entries, two sets 
 of main entries may be driven, which diverge toward opposite sides of the 
 mine at a point a short distance inbye the drift mouth or the foot of the shaft 
 or slope. 
 
 The influence of the direction of the cleavage of the coal upon that of the 
 workings is more particularly noted under the head of Laying off Rooms, 
 but it should be noted here that it is advisable to drive the headings parallel 
 to one of the vertical cleavages and usually to the face. It is not unusual to 
 demand an extra price per ton for mining coal in entries driven across the cleav- 
 age in those districts where this feature is pronounced. In such cases, it is a 
 question for_ calculation whether the saving in haulage, etc., by having the 
 headings divide the property on the lines just explained will offset the increased 
 cost of driving them across the cleavage; assuming that the cleavage and prop- 
 erty lines are not parallel. 
 
 So-called flat seams usually have a more or less decided dip, often rising 
 to 3%, in one direction or another. Where possible, the main roads are driven 
 either directly up or directly down the dip, so that the cross-entries on which 
 the coal is produced may be level, and the haulage on a pitch is confined to 
 that on the main entries. 
 
METHODS OP WORKING 611 
 
 If the property lies in a syncline, it is advisable to lay out the main roads 
 in the basin, rather than across it, that the coal from the rooms may run down 
 hill toward them. 
 
 Direction of Entries in Inclined Seams. In pitching seams, the main roads 
 are almost always driven either directly up or directly down hill, regardless of 
 the direction of cleavage, etc. If the dip is not very marked, the main roads 
 are frequently called dip headings or rise headings as may be, but when the dip 
 is pronounced they are commonly referred to as the slope, main slope, hoisting 
 slope, etc. 
 
 The cross-entries are driven to the right and left (either or both) of the 
 slope, approximately on the strike of the seam, but with an up-grade of 1 to 2% 
 to favor the haulage of the loaded cars, to insure drainage, etc. 
 
 If it is desired to drive the cross-entries on any given grade, the direction 
 of the cross-entry may be found from the formula 
 
 tan x z 
 
 sm A = - = , 
 
 tan y tan y 
 
 in which A = angle between cross-entry and strike of seam; 
 
 * = pitch of cross-entry, in degrees; 
 
 y = pitch of seam, in degrees; 
 
 2 = percentage of grade of cross-entry = tan x. 
 
 EXAMPLE. A slope pitches 15 in the direction N 25 30' E; what are 
 the bearings of the right and left cross-entries if driven with a rising grade of 1%? 
 
 SOLUTION. Substituting, sin A =.-? = ~^^ = .03732, whence A = 2 8'. 
 
 tan y tan 15 
 
 The strike has a bearing of S 64 30' E on the right of the slope and one of 
 N 64 30' W on the left. The bearing of the right-hand cross-entry will be 
 64 30'-2 8' = S 62 22' E, and of the left-hand entry, 64 30'+ 2 8' = N 66 
 38' W. 
 
 Alinement and Grade of Entries. As far as possible, the entries should 
 be straight and of uniform grade in order to reduce the friction and wear and 
 tear on the rolling stock, tracks, etc., to lessen the amount of coal shaken 
 from the cars, which is subsequently ground into explosive dust, to diminish 
 the number of accidents due to cars jumping the track, and to decrease the 
 amount of power required for haulage. 
 
 Natural conditions are usually such in American mines that it is easily 
 possible to secure straight tracks, although to produce a uniform grade it may 
 be necessary to fill in swamps and cut down hills by shooting down the roof in 
 the bottom of the dips and by taking up the floor at the top of a local rise. 
 This grading is commonly confined to the main haulage road, which must 
 usually last throughout the life of the mine, the cross-entries being allowed 
 to follow the convolutions of the seam but with a slight upward grade. 
 
 Sharp angles are to be avoided on all entries, whether used for haulage or 
 for air-courses, by substituting curves for angles or by means of diagonal roads 
 or cut-offs. 
 
 In flat seams, the grades depend on the slight inclination of the seam that 
 may exist. On the main haulage roads, the grade is the same as the pitch of 
 the seam; and on cross-entries it is just sufficient for haulage and drainage pur- 
 poses, say, with a rise toward the face of 1 to 1.5%. Uniform grades, on main 
 roads, are commonly secured by brushing the roof and lifting the floor as 
 explained; and on cross-entries, by following the strike of the seam, although 
 the alinement thus secured may not be the best. In inclined seams, any 
 desired grade can usually be obtained by altering the direction of the cross- 
 entry, as described before. 
 
 Rooms in General. Rooms are commonly turned off one side on an entry 
 at a predetermined distance apart, the distance between the center lines of 
 adjacent rooms being equal to the width of the room added to the thickness 
 of the pillar between the rooms. They are usually opened by driving a nar- 
 row neck of about the width of the entry for a distance of 10 to 30 ft., depend- 
 ing on the roof pressure, after which the place is -widened out more or less rap- 
 idly on one or both sides to full room width, which may be from 15 to 30 ft. 
 or more, probably - averaging 24 ft. in American mines. If the rooms are 
 inclined to the entry, the necks must be longer than if they are at right 'angles 
 to it, in order to furnish a sufficiently solid entry pillar. Room necks should 
 not be driven any wider than need be and the seam should be undercut or 
 sheared before blasting, that the minimum amount of powder may be required 
 to bring down the coal, thus preventing shattering and consequent weakening 
 of the entry pillar. 
 
612 METHODS OF WORKING 
 
 The tracks are generally laid along the straight rib (opposite to the gob 
 side, or that side on which the room is widened) and at such a distance from it 
 that there may be safe clearance for the miner between the side of a car and 
 the rib. Sometimes the track is laid up the center of the room, in order to 
 shorten the distance the coal has to be shoveled into the car at the face, in 
 which case the room is commonly widened on both sides. In the case of very 
 wide rooms, a track is sometimes laid up along each side. These tracks join 
 at the neck of the room, that there, may be but one room switch on the entry. 
 Unless the mouth of the room is very wide the corner of the pillar on the entry 
 and on the gob-side of the room is commonly rounded or beveled off to per- 
 mit of a less abrupt curve on the track entering the place. Where necessary, 
 the roof is supported over the track and at the face by props or props and caps 
 (cross-bars). Any roof rock that falls and refuse from the seam are stowed 
 on the wide side of the room; whence the term, gob side. The practice of 
 throwing the fine coal resulting from mining (slack or bug-dust) into the gob 
 cannot be too strongly condemned, as it will serve to furnish fuel for the propo- 
 gation of a dust explosion. 
 
 The distance between centers of parallel and adjacent rooms as well as 
 the width of the room and the thickness of the separating pillar, depend on the 
 character of the roof, coal, and floor, and on the thickness of the coal and the 
 amount of cover over it. No general rule for properly proportioning the width 
 of room to the thickness of the pillar can be given, but points for consideration 
 are given under the head of Timbering. The distances between the centers 
 vary from 33 ft. to 80 ft. under different conditions. With 40-ft. centers, 
 the pillars are usually 12 to 16 ft. wide, and the rooms 28 to 24 ft. wide. When 
 the centers are farther apart than 40 ft., the pillars are often 20 to 30 ft. wide. 
 Narrow rooms, about 12 ft. wide, are often driven and wide pillars of 60 to 
 70 ft. left between. The greater part of the coal is then got out by drawing 
 _ m ^^^^^^^^^^^^^ back these wide pillars, as explained later. When 
 HHH^I the room centers are 40 ft. or more apart, if the 
 1,1 I coal is soft the pillars are wide and the rooms 
 
 ^H narrow, but if the coal is hard the rooms are wide 
 
 and the pillars narrow, provided that the roof 
 
 ^ ^ ^1 and door conditions will permit. The ratio be- 
 
 tween the width of the room and width of pillar 
 _ _ m.^^^m.^m^^m^'^f m general decreases with an increase in depth 
 
 below the surface. When an undue proportion 
 
 |l,J^HHH^^Hj^HI| f coal is mined in the first working, creeps are 
 brought on, with all [the accompanying evils of 
 II | crushed coal, dilapidation of roadways and air- 
 
 ways, extra cost for labor and material in repair- 
 * IG> 4 ing damages, and diminished production. 
 
 The length of the rooms is governed by the distance decided on between 
 entries. It is usual to make them from 150 to 300 ft. long, the former being 
 preferable in thin beds and the latter in thick and steep pitching beds in order 
 to avoid the expense of narrow work and cross-entry rails. The length of the 
 rooms is also somewhat governed by the distance to whioh the coal can be 
 economically hauled from the face to the entry, and by the gas present in the 
 coal. 
 
 The distance apart of break-throughs depends on the amount of gas given 
 off by the coal, on local practice, and on the mine laws of the state. Owing to 
 the tendency of heated air, gas, etc., to accumulate at the face, rooms driven 
 to the rise require the distance between break-throughs to be less than if the 
 rooms are flat, while rooms driven to the dip require break-throughs at less 
 frequent intervals than flat ones. Break-throughs should have the same cross- 
 section as the other airways in the mine and should be turned and driven with 
 as much care. Break-throughs between adjoining rooms should be driven 
 in line so that the series of openings through the pillars formed by them can be 
 used for haulage purposes when necessary. 
 
 Double Rooms. When it is necessary to have a greater length of face than 
 is afforded by a single room, double rooms, as illustrated in Fig. 4, may be 
 driven. These rooms are connected to the entry by two necks and have two 
 straight ribs with a track along each. Refuse is stored between the tracks, 
 and where enough material is to be had, pack walls are built along the track 
 so as to form two roadways leading to the face. The pillars are also wider 
 than in the case of single rooms. 
 
 For the purposes of ventilation in gaseous seams, or as a protection against 
 squeeze, to which a bed of coal may be especially liable, or for the purpose of 
 
METHODS OF WORKING 
 
 613 
 
 starting a long face for machine working, rooms are sometimes turned off of 
 an entry as already described, but are opened into each other by the removal 
 of the pillar in the 
 first working, thus 
 forming a contin- 
 uous breast, as 
 shown in Fig. 5. 
 
 Rooms With 
 Extra Entry Pillars. 
 Where there is ex- 
 cessive weight on 
 the entry pillars, it 
 is necessary , in order 
 to keep open the 
 entries, that these 
 pillars be very large, 
 or that a special pil- 
 lar be left to protect 
 the entry used as a 
 haulage road, while FIG. 5 
 
 the rooms are 
 opened out from a parallel entry or cross-cut. 
 
 Fig. 6 shows a method used at Danville, Illinois, where the coal is under- 
 laid by a soft bottom, but has a strong cover. The weight of the coyer would 
 tend to force the pillars into the bottom and thus close up the entries. This 
 is prevented by leaving the extra pillar e. The main entries a are driven and 
 timbered for a double track; the cross-entries b are driven 10 ft. wide and the 
 first room neck c is turned 10 ft. wide and driven up 15 ft. and then widened 
 out on one side to a full width of 30 ft. A cross-cut d is driven 20 ft. wide and 
 two more rooms are turned off this cross-cut, as shown; the fourth room is 
 turned directly off the cross-entry, widened out on the right, and a cross-cut 
 turned to the right as before and two more rooms are turned off this cross- 
 cut, etc. The large entry coal pillars e, 40 ft. X 125 ft. in size, keep the weight 
 off the cross-entries; and by making a rather thin pillar between the rooms, 
 
 the weight is thrown 
 on the face and made 
 to assist in the mining. 
 In the second work- 
 ing, these large pillars 
 can be taken out, as 
 well as the stumps /, 
 the room pillars g, and 
 the pillars h between 
 the entries. 
 
 Fig. 7 shows an- 
 other method of turn- 
 ing off the rooms in 
 order to give additional 
 support to the entries. 
 
 ^^_^_^^^^_ ^^^^^^^^^^^ ^^ Large pillars a are left 
 ^^^VJY^^^I ^^^^^HHi I aDOVe t ne entry b, and 
 ^BHHBHH !' from each neck c 
 
 a , t ^| turned off the entry b 
 
 mm mmm two roads are driven, 
 
 ^Bl ^BB ^Hl ^Bfl ^pj one along each side of 
 B li V I ^ ^B ^ the room Pillars e. 
 
 v -.-- B B I / I This plan has been 
 2 _ ~ S^ I successfully used in a 
 B I B B B B I bed of hard coal with 
 
 B| B| V I a strong bottom and a 
 
 ^ thick, strong roof. 
 
 Inclination of 
 Rooms to the Entry. 
 The direction in which 
 rooms are driven with respect to the entries off which they are turned depends on 
 the inclination of the bed, the cleat of the coal, and the nature of the overlying 
 rock. When possible, the rooms are usually driven at a right angle to the entry. 
 If the bed is flat, the rooms may be turned both to the right and to the left of 
 
614 
 
 METHODS OF WORKING 
 
 the cross-entries, and in such a seam, and where the entries are driven in pairs, 
 a series of rooms is often driven off each entry of the pair. If the bed is inclined 
 to any extent, the rooms are turned only to the rise of the higher entry, the 
 other entry of the pair being used as an air-course. Rooms are usually not 
 
 turned to the dip if much water will 
 accumulate at the face. Where there 
 is not much water to collect at the face, 
 the rooms may be turned to the dip 
 on a pitch as high as 6, although, if 
 the loaded car must be hauled out by a 
 mule, the dip of the room toward the face 
 should preferably not exceed 3 to 4. 
 If the loaded cars are pushed out of the 
 rooms by hand, the road should dip 
 from the face toward the entry, or should 
 at least be level. A car can be con- 
 trolled by spragging when pushed by 
 hand until the inclination of the track 
 is about 6; that is, until the grade is 
 about 10%. 
 
 As it is not usually practicable to 
 haul empty cars up a grade of more than 
 6 to 8, if the pitch of the bed is greater 
 than this but less than about 12, a 
 suitable grade for haulage may be secured 
 in the rooms by driving the rooms at an 
 
 p, r angle to the entry, as shown in Fig. 8. 
 
 The method of working an inclined room 
 
 does not differ from that used where the room is at right angles to the 
 entry. The angle that the room makes with the entry should not be less 
 than 30 or the entry pillar will not have the required strength, unless it is 
 left very large. Where rooms are driven at an angle to the entry, the coal 
 between the first room and the slope or main entry, as the case may be, is 
 worked out by means of cross-rooms b 
 driven off from the first room a as 
 shown. When the inclination of the 
 bed is above 10 to 12, the rooms are 
 usually turned at right angles to the 
 entry and the coal conveyed from the 
 face to the entry and there emptied 
 into the mine car. 
 
 Rooms driven to the dip are also 
 sometimes driven at an angle to the 
 entry where the inclination of the seam 
 exceeds 3 and where mule haulage is 
 used in the rooms. 
 
 The angle that a room should make 
 with the entry in order to obtain a 
 given grade of track in a seam having 
 a given inclination is found by the method described under Direction of 
 Entries in Inclined Seams, but placing A = angle between room and cross-entry. 
 Direction of Rooms as Determined by Cleat. In most coal seams there 
 are vertical cleavages, called cleats, which cross the seam in two directions 
 
 about at right angles to each other. 
 The face cleats are the longer and usually 
 the more pronounced, while the end 
 or butt cleats are the shorter and more 
 irregular. The cleat of the coal some- 
 times determines the direction in which 
 the room should be driven, since the 
 coal may break more easily on one 
 cleat than another and thus produce a 
 larger amount of coal for a given 
 amount of undercutting. Fig. 9 shows 
 rooms driven at various angles to the 
 cleat and the name by which each is designated. 
 
 In driving face on, the room is driven so that the face is parallel to the face 
 cleats, which are represented by the longer white lines, while the end cleats 
 
 FIG. 8 
 
 FIG. 9 
 
METHODS OF WORKING 
 
 615 
 
 DISTANCE FROM CENTER TO CENTER OF ROOMS OR BREASTS 
 MEASURED ON ENTRY OR GANGWAY 
 
 &: 
 
 Width of Room + Thickness of Pillar, in Feet 
 
 Q) M H. 
 
 20 
 
 25 
 
 30 
 
 35 
 
 40 
 
 45 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 ** 
 
 Distance Measured on Entry, in Feet 
 
 90 
 
 20.0 
 
 25.0 
 
 30.0 
 
 35.0 
 
 40.0 
 
 45.0 
 
 50.0 
 
 55.0 
 
 60.0 
 
 65.0 
 
 70.0 
 
 75.0 
 
 85 
 
 20.0 
 
 25.1 
 
 30.1 
 
 35.1 
 
 40.2 
 
 45.2 
 
 50.1 
 
 55.2 
 
 60.2 
 
 65.3 
 
 70.3 
 
 75.3 
 
 80 
 
 20.3 
 
 25.4 
 
 30.5 
 
 35.5 
 
 40.6 
 
 45.7 
 
 50.8 
 
 55.8 
 
 60.9 
 
 66.0 
 
 71.1 
 
 76.2 
 
 75 
 
 20.7 
 
 25.9 
 
 31.1 
 
 36.2 
 
 41.4 
 
 46.6 
 
 51.8 
 
 56.9 
 
 62.1 
 
 67.3 
 
 72.5 
 
 77.7 
 
 70 
 
 21.3 
 
 26.6 
 
 31.9 
 
 37.2 
 
 42.6 
 
 47.9 
 
 53.2 
 
 58.5 
 
 63.9 
 
 69.2 
 
 74.5 
 
 79.8 
 
 65 
 
 22.1 
 
 27.6 
 
 33.1 
 
 38.6 
 
 44.1 
 
 49.6 
 
 55.2 
 
 60.7 
 
 66.2 
 
 71.7 
 
 77.2 
 
 82.8 
 
 60 
 
 23.1 
 
 28.9 
 
 34.6 
 
 40.4 
 
 46.2 
 
 52.0 
 
 57.7 
 
 63.5 
 
 69.3 
 
 75.1 
 
 80.8 
 
 86.6 
 
 55 
 
 24.4 
 
 30.5 
 
 36.6 
 
 42.7 
 
 48.8 
 
 54.9 
 
 61.0 
 
 67.1 
 
 73.3 
 
 79.4 
 
 85.5 
 
 91.6 
 
 50 
 
 26.1 
 
 32.6 
 
 39.2 
 
 45.7 
 
 52.2 
 
 58.7 
 
 65.3 
 
 71.8 
 
 78.3 
 
 84.9 
 
 91.4 
 
 97.9 
 
 45 
 
 28.3 
 
 35.4 
 
 *42.4 
 
 49.5 
 
 56.6 
 
 63.6 
 
 70.7 
 
 77.8 
 
 84.9 
 
 91.9 
 
 99,0 
 
 106.1 
 
 40 
 
 31.1 
 
 38.9 
 
 46.7 
 
 54.5 
 
 62.2 
 
 70.0 
 
 77.8 
 
 85.6 
 
 93.3 
 
 101.1 
 
 109.0 
 
 116.7 
 
 35 
 
 34.9 
 
 43.6 
 
 52.3 
 
 61.0 
 
 69.7 
 
 78.5 
 
 87.2 
 
 95.9 
 
 104.6 
 
 113.4 
 
 122.1 
 
 130.8 
 
 30 
 
 40.0 
 
 50.0 
 
 60.0 
 
 70.0 
 
 80.0 
 
 90.0 
 
 100.0 
 
 110.0 
 
 120.0 
 
 130.0 
 
 140.0 
 
 150.0 
 
 25 
 
 47.3 
 
 59.2 
 
 71.0 
 
 82.8 
 
 94.6 
 
 106.5 
 
 118.3 
 
 130.1 
 
 142.0 
 
 153.8 
 
 165.6 
 
 177.5 
 
 20 
 
 58.5 
 
 73.1 
 
 87.7 
 
 102.3 
 
 117.0 
 
 131.6 
 
 146.2 
 
 160.8 
 
 175.5 
 
 190.1 
 
 204.7 
 
 219.3 
 
 15 
 
 77.3 
 
 96.6 
 
 115.9 
 
 135.2 
 
 154.5 
 
 173.9 
 
 193.2 
 
 212.5 
 
 231.9 
 
 251.2 
 
 270.5 
 
 289.8 
 
 10 
 
 115.2 
 
 144.0 
 
 172.8 
 
 201.6 
 
 230.4 
 
 259.2 
 
 287.9 
 
 316.7 
 
 345.5 
 
 374.3 
 
 403.1 
 
 432.0 
 
 5 
 
 229.5 
 
 286.9 
 
 344.2 
 
 401.6 
 
 459.0 
 
 516.3 
 
 573.7 
 
 631.1 
 
 688.4 
 
 745.8 
 
 803.2 
 
 860.5 
 
 are shown by the shorter ones. This is the general direction of driving rqotns 
 and is adopted where conditions permit. Fig. 1 shows that in the prevailing 
 American practice the rooms are parallel to the main entries; hence main 
 entries are face entries and cross-entries are driven parallel to the ends of the 
 coal and are end-entries, although far more commonly called butt-entries. 
 Face on is adopted where the face cleats are not as free or as numerous as the 
 end cleats. Coal worked in this way breaks well, and the yield is perhaps 
 larger for the same amount of undercutting than by any of the other methods, 
 producing also a greater proportion of lump coal. 
 
 In working long horn, the opening is driven so that the face makes an 
 angle less than 45 with the face cleats of the coal; the coal breaks in long slabs 
 or wedge-shaped masses, giving rise to the name long horn. A face driven this 
 way does not require the same amount of cutting; and if slightly inclined grip 
 shots are used, good-sized lump coal is produced. If the coal works too freely 
 face on, by this method support is given the ends of the coal while being 
 undercut. 
 
 In working half on, the rooms are driven at an angle of 45 with the cleats 
 of the coal. The method is adapted to coals that break about equally well on 
 the face and the end cleats. 
 
 In working short horn, the face of the room makes an angle between 45 
 and with the face cleats. The method is adapted to the working of coal 
 where the end cleats are so pronounced as to require the additional support 
 given to the coal by this method when mining or undercutting. It bears the 
 same relation to end-on work that long horn bears to face-on. 
 
 In working end on, the face of the room is at right angles to the face cleats, 
 and, consequently, parallel to the end or butt cleats. This method, and short 
 horn, are adapted to the working of coals under strong roof pressure. In gen- 
 eral, the size of the coal and the yield are not as great as in face on or long horn. 
 
 As the face cleats are quite pronounced when rooms are driven end on, 
 wide pillars are generally used. 
 
 Where there is much occluded gas at high pressure, the direction of the work- 
 ing face with respect to the face cleats of the coal is important, as a breast 
 driven face on affords little or no opportunity for the escape of this gas, except 
 
616 METHODS OF WORKING 
 
 as it finds vent in violent outbursts. On the other hand, if this coal is worked 
 end on, the face cleats are cut across and exposed and the gas escapes gradually 
 and quietly. The method by short horn or half on, may be found to give good 
 results in such a case, as the pressure of the gas is then made to do effective 
 work in assisting to break down the coal. 
 
 Direction of Rooms as Determined by Slips in the Roof. A roof slip is a 
 line of weakness that was at some time a line of fracture in the rock and 
 which may or may not have been filled subsequently, by infiltration, with 
 clay or other matter. Roof slips frequently occur in parallel lines in the 
 rocks overlying coal seams; if this is the case, there is great danger from 
 roof falls if the room face is parallel to the direction of the slips, for the 
 miner cannot see the slip until too late to prevent accident by the falling of 
 the slate or the sudden breaking down of the coal. By driving the room at 
 an angle across the slips, not only is sufficient support given to the roof to 
 prevent its breaking suddenly, but the presence of the slip is readily observed. 
 
 When the face is at right angles to the direction of the slips, there is not 
 the same danger at the face as when the face is parallel to the slip, because the 
 roof is better supported by the coal. The chief danger occurs when drawing 
 back the pillars, for as the slips are parallel to the line of the pillars, a large 
 fall may occur suddenly at any time by an unexpected cross-break. In any 
 case, when driving under such roof, a larger amount of good timber is required. 
 
 WORKING FLAT SEAMS 
 
 The general arrangement of a mine worked on thedouble-entry system 
 according to the common American practice is shown in Fig. 1. The reasons 
 for the direction, dimensions, etc., of the entries and rooms have been given 
 in previous paragraphs. The general method is, of course, slightly changed 
 locally to meet prevailing conditions, some of the modifications being given 
 here under the names of the mining districts in which they are used. 
 
 Pittsburg Region. The coal is worked with double entries, with cut- 
 throughs between for air, and on face and butt entries are about 9 ft. wide, 
 and the rooms 21 ft. wide and about 250 ft. long; narrow (or neck) part of room, 
 21 ft. long by 9 ft. wide; room pillars, 15 to 20 ft. wide, depending on depth 
 of strata over the coal, which is from a few feet to several hundred feet. The 
 mining is done largely by machines of various types. Coal is hard, of course, 
 and, in many places, the roof immediately over the coal is also quite hard. 
 There are about 4 ft. of alternate layers of hard slate and coal above the coal 
 seam. Rooms are mined from lower end of butt as fast as butt is driven, 
 the ribs being drawn as mining progresses. As the coal is harder than in the 
 Connellsville region, thickness of coal pillar between parallel entries is some- 
 what less. 
 
 Clearfield Region. The butt and face are not strongly marked in the B 
 or Miller seam, the one chiefly worked in this region. Where possible, these 
 cleavages are followed in laying out the workings, but the rule is to drive to 
 the greatest rise or dip and run headings at right angles to the right and left, 
 regardless of anything else. The main dip or rise heading is usually driven 
 straight, and is raised out of swamps or cut down through rolls very com- 
 mon here unless they are too pronounced, when the heading is curved around 
 them. The same is true of room headings, except that they are more usually 
 crooked, not being graded except over very minor disturbances. 
 
 As the B seam rarely runs over 4 ft. in thickness, and is worked as low as 
 2 ft. 8 in., in the haulage headings the roof is taken down to give 5 ft. to 5 ft. 
 2 in. above the rail, or 5 ft. 8 in. to 5 ft. 10 in. in the clear. Where the result- 
 ing rock is taken outside, the headings are driven 10 ft. wide with 24 ft. of 
 pillar, roof taken down in haulage heading but not in the air-course. Where 
 the rock is gobbed underground, the haulage heading is 18 to 24 ft. wide, air- 
 course 10 ft., pillar 24 ft., and roof taken down in haulage heading only. The 
 thinner the coal, the wider the heading. It is more economical to haul the rock 
 to daylight. The bottom generally consists of 3 ft. to 5 ft. of hard fireclay, 
 frequently carrying sulphur balls. 
 
 In numerous places, the sand rock is immediately over the coal, but in 
 most cases there is from 3 to 5 ft. of slate before the sand rock is reached. 
 Room headings are driven 280 ft. apart, haul rock to daylight, heading 10 ft. 
 wide with > 24 ft. pillar to 10 ft. air-course, in which roof is left up. A 15 ft. to 
 25 ft. chain pillar is left between air-course and faces of rooms from the lower 
 heading, every fourth to eighth of which is driven through to the air-course 
 to shorten the travel of the air. The rooms are therefore 180 to 200 ft. long, 
 and the men push the cars to the face, an important item in this thin coal. 
 
METHODS OF WORKING 617 
 
 Rooms are 21 ft. wide with a 15 ft. pillar, and a 15 ft. chain pillar is left 
 between the first room on any room heading and the main heading, and roof 
 is not taken down in rooms. Main-heading track is usually 30-lb. iron, room 
 heading, 12 lb., and 2"X 1" strap iron set on edge is used in the rooms in low 
 coal. Mine cars hold from 600 to 800 lb. in low seams, and 1,500 to 2,000 lb. 
 in the so-called thick seams; i. e., 3 ft. 8 in. to 4 ft. thick. 
 
 Reynoldsville Region. The measures are very regular, and the method 
 employed is the typical one shown in Fig. 1. The average thickness of the prin- 
 cipal seam is 6$ ft. and the pitch is 3 to 4. The coal is hard and firm, and 
 contains no gas; the cover is light, and on top of the coal there are 3 or 4 ft. 
 of bony coal; the bottom is fireclay. Drift openings and the double-entry 
 system are used. Both main and cross-entries are 10 ft. wide, with a 24-ft. 
 pillar between. The cross-entries are 600 ft. apart, and a 24-ft. chain pillar 
 is left along the main headings. The rooms are about 24 ft. wide and open 
 inbye, the necks being 9 ft. wide and 18 ft. long. The pillars are from 18 to 
 30 ft. thick. 
 
 West Virginia Region. The general plan of working the Pittsburg coal 
 in the northern part of West Virginia is as follows: The coal measures vary 
 from 7 to 8 ft. in thickness, and have a covering varying from 50 to 500 ft. 
 The coal does not dip at any place over 5%. In most places the coal is prac- 
 tically level, or has just sufficient dip to afford drainage. The usual method 
 of exploitation is to advance two parallel headings, 30 ft. apart, on the face of 
 the coal. At intervals of 500 to 600 ft., cross-headings are turned to right and 
 left, and from these headings rooms are turned off. These cross-headings are 
 driven in pairs about 20 or 30 ft. apart. Between the main headings and the 
 first room is left a block of coal about 100 ft. wide, and on the cross-headings 
 there is often left a barrier pillar of 100 ft. after every tenth room. 
 
 The headings are driven from 8 to 12 ft. wide, and the rooms are made 
 24 ft. wide and 250 to 300 ft. long. A pillar is left between the rooms about 
 15 to 20 ft. wide. These pillars are withdrawn as soon as the panel of rooms 
 has been finished. The rooms are driven in from the entry about 10 ft. wide 
 for a distance of 20 ft., and then the room is increased in width on one side. 
 The track usually follows near the rib of the room. Cross-cuts on the mam 
 and cross-headings are made every 75 to 100 ft., and in rooms about' every 
 100 ft. for ventilation. 
 
 The double-heading system of mining and ventilation is in vogue. Over- 
 casts are largely used, but a great many doors are used in some of the mines. 
 Rooms are worked in both directions. This is the general practice when the 
 grades are slight. When the coal dips over 1%, the rooms are driven in one 
 direction only. In this case, the rooms are made longer, as much as 350 ft. 
 It is the custom then to break about every third room into the cross-heading 
 above (a practice ill advised). The floor of this bed of coal, being composed 
 of shale and fireclay, often heaves, especially when it is made wet. Some trouble 
 is at times experienced by having the floor heave by reason of the pillars being 
 too small for the weight they support. 
 
 The dimensions of rooms and pillars given are for a mine (with covering 
 300 to 500 ft. thick) having a fairly good and strong roof. Where roof, bot- 
 tom, and thickness of cover change, these dimensions are altered to suit the 
 requirements. The main-heading pillars may be reduced to 30 or 40 ft.; 
 the rooms may be made 15 ft. wide with 12 ft. pillars, and no barrier pillars 
 may be left on the cross-headings. 
 
 The foregoing plan is very much followed in other parts of the state; at 
 least an attempt is made to do so, but local disturbances often require changes 
 in the plan. This plan is followed on some parts of New River, and also in 
 the Flat Top field. 
 
 George's Creek District, Md. Fig. 10 shows the method used in the 
 George's Creek field, Maryland. The coal shows no indication of cleats, and 
 the butts and headings can be driven in any direction. The main heading is 
 driven to secure a light grade for hauling toward the mouth. Cross-headings 
 making an angle of 35 to 40 are usually driven directly to the rise, and of the 
 dimensions shown. Pillars are drawn as soon as the rooms are completed, 
 being attacked on the ends and from the rooms on either side, the coal being 
 shoveled to the mine car on a track in the room. Very wide pillars are split. 
 No effort is made to hold up the overlying strata, and the entire bed is removed 
 as rapidly as possible. An extraction of 85% of the bed is considered good 
 work. A section of the seam is as follows: Roof coal, 10 in.; coal, 7 ft.; 
 slate, i in.; coal, 10 in.; slate, \ in.; coal, 10 in.; fireclay; slate. The top bench 
 is bony and frequently left in place to prevent disintegration of the roof by the 
 
618 
 
 METHODS OF WORKING 
 
 air Above this coal is from 8 to 10 ft. of rashings, consisting of alternating 
 thin beds of coal and shale, that is very brittle, and requires considerable 
 timber to keep it in place. 
 
 Blossburg Coal Region, Pa. Coal is generally mined trom emits, but in a 
 few cases by slopes. Fig. 11 shows the general method adopted; the breasts 
 are run at right angles to the slips; the breast pillars are split by a center head- 
 ing and taken out as soon as the breasts are finished. The gangway pillars 
 
 FIG. 10 
 
 are taken out retreating from the crop or boundaries of the property. The 
 general average of the coal seams is not over 3^ ft., accompanied by fireclay 
 and some iron ore. The dip of the veins is about 3%. 
 
 Indiana Coal Mining. Fig. 12 shows the double-entry room-and-pillar 
 methods as used in Indiana. The entries are generally 6 ft. high, 8 ft. broad, 
 the minimum height required by law being 4 ft. 6 in. The rooms are from 
 21 to 40 ft. in width. The mines are generally shallow. The rooms are shown 
 as widened on both ribs, but a more usual method in this locality is to widen 
 the room on the inbye rib, leaving one straight rib for the protection of the 
 road in the room. 
 
 Iowa Coal Mining. The coal lies at a depth of 200 ft. below the surface, and 
 is geologically similar to that of the Missouri and Illinois fields. It lies in 
 lenticular basins extending northwest and southeast and outcropping in the 
 larger river beds. The seams are practically level, non-gaseous, and gen- 
 erally underlaid by fireclay and overlaid by a succession of shales, sandstones, 
 
 FIG. 11 
 
 Mouth N3 Drift 
 
 and limestones, which are generally of a yielding nature, giving a strong, 
 good roof for mining. There are three distinct seams, the lower one, which 
 varies from 4 to 7 ft. in thickness, being the only one worked. The coal is a 
 hard, brittle, bituminous that shoots with difficulty, but is excellent for steam 
 and domestic uses. About Centerville, the coal has a distinct cleat, but else- 
 where in the state this is lacking. 
 
 The entry pillars along the main roads are 6 to 8 yd. thick, for the cross- 
 entries 5 to 6 yd., and for the rooms 3 to 5 yd. Room pillars are drawn in 
 when approaching a cross-cut. Both room-and-pillar and longwall methods 
 
METHODS OF WORKING 619 
 
 are in use, with modifications of each. In the room-and-pillar method, the 
 double-entry system is almost invariably used in the larger mines. Rooms are 
 driven off each entry of each pair of cross-entries at distances of 30 to 40 ft., 
 center to center; the rooms are 8 to 10 yd. in width, and pillars 3 to 4 yd. The 
 rooms are narrow for a distance of 3 yd., and then widened inbye at an angle 
 of 45 to their full width. They vary from 50 to 100 yd. in length, and the 
 road is carried along the straight rib. 
 
 When double rooms are driven, the mouths of the rooms are 40 to 50 ft. 
 apart, and they are driven narrow from the entry a distance of 4 or 5 yd. A 
 cross-cut is then made connecting them, and a breast 16 yd. wide is driven 
 up 50 to 60 yd. The pillar between each pair of rooms is 12 to 15 yd. 
 
 In pillar-and-stall work, the stalls are usually turned off narrow and widened 
 inside, the pillar varying from 5 to 8 yd. The stalls are 30 to 40 yd. in length, 
 and the pillars are drawn back. When the stalls are driven in pairs, the 
 pillar 8 to 10 yd. in width is carried between them. 
 
 Steep Rooms. Where the pitch is so great that mules cannot haul the car 
 to the face for loading, a windlass may be used for the purpose, the handle 
 of which is turned by the miner. If electric haulage is used, the motor may 
 be blocked on the rails near the mouth of the room, and its cable reel or a special 
 drum used to wind up a rope running over the necessary sheaves (pulleys) 
 at the mouth and face of the room, which rope, attached to the end of the car, 
 
 FIG. 12 
 
 hauls it up to the face. In other cases, self-acting inclines are used, in which 
 the weight of the descending loaded car pulls the empty car to the face. This 
 arrangement requires a double track in the room. Where roof conditions 
 permit of only a single track, another pair of lighter rails may be laid between 
 those of the regular room track and upon these a carriage with a counterweight 
 will run. This counterweight is so adjusted that while the loaded car in descend- 
 ing will raise it to the face, its weight in descending will pull the empty car 
 to the face. 
 
 Usually, a grade at which mules may pull the cars to the face is secured 
 by inclining the rooms to the entry, the direction being determined by the 
 formula given before. If the rooms are inclined and equipped with some 
 one of the mechanical appliances just described, coal may be loaded at the 
 face on much steeper pitches than would otherwise be the case. 
 
 WORKING PITCHING SEAMS 
 
 Difficulties in Mining on a Pitch. A soft friable coal when mined on a 
 steep pitch has a tendency to run; that is, without any mining, it breaks freely 
 from the face of the breast and then slides down the pitch. Sometimes little 
 or no work need be done in the breast after the chute has been widened out 
 to form the breast, as sufficient coal thus breaks from the face from time to 
 time to keep the breast full as the coal is drawn out through the loading chute; 
 the coal continues to run until the breast breaks through into the upper gang- 
 way. The uncertainty that necessarily exists in regard to the flow of the coal 
 
620 METHODS OF WORKING 
 
 renders this method unreliable, although it is often adopted from neces- 
 sity. One objection to this method is that the running of the coal cannot be 
 controlled, and the widths of the breast and pillars cannot be maintained; 
 the breast is often increased in width and much or all of the pillar coal runs 
 out at the chutes, while at other times the width of the breast gradually 
 decreases and ultimately the coal stops running. The miner must then go 
 up into the breast and start the coal to running again by widening out the 
 breast, or by placing one or more small shots in the coal; this is a dangerous 
 operation, as the coal may come with a rush. 
 
 The coal on a steep pitch may not run sufficiently to do away with mining, 
 but it may be so free as to require particular support at the face to prevent the 
 coal from running sufficiently to injure the miners. The working of free coal 
 on a heavy pitch requires skilled labor; and as gas usually issues from such coal 
 in large quantities, safety lamps must often be used, thus increasing the danger 
 from falls on account of insufficient light. The props used under these con- 
 ditions should not be less than 6 in. in diameter and should be very firmly set. 
 If the roof is strong and firm, these props may be taken out and moved for- 
 wards as required, thus saving labor and material. 
 
 In working coal by the battery method, the coal will sometimes become 
 clogged and form an arch, which supports all the coal above the arch and allows 
 the breast below to become empty as the coal is gradually drawn out through 
 the loading chute. This condition is dangerous to the men working on top 
 of the coal near the face, for if the arch suddenly gives away they may be car- 
 ried down and buried in the coal. Such a slide is also apt to be very disastrous 
 to the battery and the sides of the chute. To break down such an arch, an 
 opening may be made in the side of the chute and the coal started to running 
 by means of bars. Occasionally a small stick of dynamite is put under the 
 coal and the arch loosened in this way. When this is done, an opening should 
 be made from the side, and the miner should not, as he sometimes does, climb 
 up the chute and after setting off his fuse trust to getting out before the coal 
 begins to slide, as this is extremely dangerous. 
 
 After the face has been blasted down, lumps'of coal will sometimes lodge 
 in the manways alongside the chute and these must be similarly dislodged by 
 means of bars or with dynamite. In returning to the face after a blast has 
 been fired, the miner and his laborer should be exceedingly careful that the 
 loose coal does not roll down the manway on them, and should also use great 
 care to see that all loose coal in the face is barred down before they again 
 begin work. 
 
 Working Thick and Gaseous Seams That Run. In large seams, when the 
 coal is soft and shelly or slippery, lies at an angle of more than 50, and 
 generates large quantities of firedamp, a source of danger is the sudden lib- 
 eration of gas should a breast run. To meet these conditions, the air-eourse 
 may be driven above the entry or gangway and used as a return, the fan being 
 attached as an exhaust, and the working rooms or breasts ventilated in pairs. 
 The inside manway of one of a pair of breasts is connected with the gangway for 
 the intake, and the outside manway of the other breast with the return airway, 
 giving each pair of breasts a separate split of the current. In collieries where 
 this system of working is followed, the coal is soft. A new breast is worked up 
 a few yards, but as soon as it is opened out, the coal runs freely and the man- 
 ways are pushed up on each side as rapidly as possible, to keep up with the 
 face. Two miners, one on either side, sometimes finish a breast without being 
 able to cross to each other. The work is done exclusively with safety lamps, 
 and when a breast runs the gas is liberated in such quantities that it fre- 
 quently fills breasts from the top to the airway before the men can get down 
 the manway on the return side. When the gas reaches the cross-hole, it 
 passes into the return airway without reaching any part where men are work- 
 ing. Should a run of coal block a breast by closing the manway, it affects the 
 current of one pair of breasts alone. As the gangway is the intake, leakage at 
 the batteries passes into the breasts, as the cross-holes are above their level 
 and the gas is thus kept above the starter when at the draw-hole. The gang- 
 way, chutes, and airway are supplied by wooden pipes, which connect with a 
 door behind the inside chute. If a breast runs up to the surface, it does not 
 affect the return airway, as it is in the solid. 
 
 Among the disadvantages urged against this system of working are the 
 following: 
 
 It increases the friction, as the air must pass in the airway all the distance 
 from the breast to the fan, the area of the airway being small in comparison 
 to the gangway or intake. 
 
METHODS OF WORKING 621 
 
 As the faces of the breasts are so much higher than the return airway, the 
 lighter gas must be forced down into the return against the buoyant power of 
 its smaller specific gravity. 
 
 The reduction of friction obtained by splitting is neutralized by each split 
 running up one small man way and down another; the advantage of running 
 through several pillar headings and thus securing a shorter course being lost. 
 This can be partly obviated by ventilating the breasts in groups, but the dangers 
 avoided in splitting are increased. 
 
 Blackdamp, which accumulates in the empty or partly empty breasts, 
 works its way down and mixes with the intake current, as there is no return 
 current in the breast strong enough to carry it away, the return being closed 
 in the airway. 
 
 All things considered, when the seam is soft and has a pitch of 40 and 
 upwards, and emits large quantities of gas in sudden outbursts, as in running 
 breasts, this system is the best that can be adopted. 
 
 Working Thick Non-Gaseous Seams. The reverse of the system just 
 described is followed at some collieries where the coal is hard and but little gas 
 is encountered. The airway is driven over the gangway or against the top, 
 the fan being used to force the air inward to the end of the airway. The air is 
 distributed as it returns, being held up at intervals by distributing doors placed 
 along the gangway. 
 
 Among the advantages claimed for this plan are the following: 
 
 As the pressure is outwards, it forces smoke and gas out at any openings 
 that may exist from crop-hole falls or other causes. 
 
 The warm air from the interior of the mine returning up the hoisting slope 
 or shaft prevents it from freezing. 
 
 As the current is carried from the fan to the end of each lift without passing 
 through working places, the opening of doors as cars are passing, etc. does not 
 interfere with the current. 
 
 If a locomotive is used, the smoke and gases generated by it are carried 
 away from the men toward the bottom. Locomotives are generally used only 
 from the main turnout to the bottom. 
 
 An objection to this system is that the gangway, as the return, is apt to be 
 smoky. Starters and loaders are forced to work in more or less smoke, and 
 even the mules work to disadvantage, while if gas is given off, it is passed out 
 over the lights of those working in the gangway. 
 
 However, in places where there is but little gas, and airways of large area 
 can be driven, this plan works very satisfactorily, and some of the best ven- 
 tilated collieries are worked upon it. 
 
 An objection advanced by some against forcing fans is that they increase 
 the pressure, thus damming the gas back in the strata. In case the speed of 
 the fan is slacked off, the accumulated gas may respond to the lessened pres- 
 sure and spring out in large volumes from its pent-up state. This argument, 
 however, works both ways. An exhaust fan running at a given speed is taking 
 off pressure, and if anything occurs to block the intake, the pressure is dimin- 
 ished, and the gas responds to the decrease on the same principle. 
 
 Working Small Seams Laying From Horizontal to 10. Two gangways 
 may be driven, the lower or main gangway being the intake. Branch gang- 
 ways should then be driven diagonally or at a slant, with a panel or group of 
 working places on each slant gangway. Large headings should connect the 
 panels. In this system, the air is carried directly to the face of the gangway 
 and up into the breasts, returning back through the working places. The intake 
 and return are separated by a solid pillar, the only openings being the slant 
 gangways on which are the panels. The advantages of this plan are: 
 
 The main gangway is solid, with the exception of the small cross-holes 
 connecting with the gangway above; these furnish air to the gangway and 
 are small and easily kept tight. These stoppings should be built of brick, 
 and made strong enough to withstand concussion. 
 
 A full trip of wagons can be loaded and coupled in each panel or section 
 without interfering with, or detaining the traffic on, the main road; one trip 
 can be loaded while another is run out to the main gangway for transporta- 
 tion to the bottom. 
 
 The only break in the intake current is when a trip is taken out from, or 
 returns to, a panel; this can be partly provided against by double doors, set 
 far enough apart to permit one to close after the trip before the other is opened. 
 This distance can be secured by opening the first three breasts on a back 
 switch above the road through the gangway pillar, or by running each branch 
 over the other far enough to obtain the distance for the double doors. 
 
622 
 
 METHODS OF WORKING 
 
 If it is not desired to carry the whole volume of air to the end of the air- 
 way, a split can be made at each branch road. These will act as unequal 
 splits in reducing friction, and, although not theoretically correct, are prefer- 
 able to dragging the whole current the full length of the workings. 
 
 The objections urged to this plan are that it involves too much expense 
 in the large amount of narrow work at high prices necessary to open out a 
 colliery, that it necessitates a double track the whole length of the lift, and 
 that the grade ascends into each panel or section. But the latter criticism 
 falls, because the loss of power hauling the empty wagons up a slight grade 
 is more than made up by the loaded wagons running down while the mules 
 are away pulling a trip into another panel or section. 
 
 For a large colliery this is without doubt the best and cheapest system. 
 Working Small Seams Laying at More Than 10. In small seams lying 
 at an angle of more than 10, and too small to permit an airway over the chutes, 
 it is more difficult to maintain ventilation. If air holes are put through every 
 few breasts, and a fresh start obtained by closing the back holes, or if an open- 
 ing can be gotten through to the last lift as often as the current becomes weak, 
 an adequate amount of air can be maintained, because the lift worked can be 
 
 used as the intake, 
 and the abandoned 
 lift above as the re- 
 turn. To ventilate 
 fresh ground, the 
 filling of the chutes 
 with coal will have 
 to be depended on, 
 or a brattice must 
 be carried along the 
 gangway. This can 
 be done for a lim- 
 ited distance only, 
 as a brattice leaks 
 too much air. As 
 a rule, collieries 
 worked on this plan 
 are run along until 
 the smoke accumu- 
 lates and the venti- 
 lation becomes 
 poor; then a new 
 hole is run through 
 and the brattice re- 
 moved and used as 
 before for the next 
 section. This oper- 
 ation is repeated 
 
 13 
 
 until the lift is worked out. Sometimes, to make the chutes tight, canvas 
 covers are put on the draw holes, but as they are usually left to the loaders to 
 adjust, they are often very imperfectly applied. Then, as the coal is fre- 
 quently very large, the air will leak through the batteries. 
 
 This plan works very satisfactorily if the openings are made at short inter- 
 vals, say, as frequent as every fifth breast, but the distance is usually much 
 greater to save expense. As the power of the current decreases as the distance 
 between the air holes is increased, good ventilation is entirely a question of how 
 often a cut-off is obtained. 
 
 An effective ventilation could be maintained in a small seam at a heavy 
 angle by working with short lifts, say two lifts of 50 yd. instead of one of 100 yd., 
 as at present. The gangways should be frequently connected, and one used 
 as an intake and the other as a return. This would necessitate driving two 
 gangways where one is now made to do, but the additional expense would be 
 made up in the greater proportion of coal won. 
 
 Buggy Breasts. For inclinations between 10and 18, that is,' after mule 
 haulage becomes impossible and until the coal will slide in chutes, buggies 
 are often used. Fig. 13 shows a buggy breast m plan (a) and section (&). Coal 
 is loaded into a small car or buggy c, which runs to the lower end of the breast 
 and there delivers the coal upon a platform I, from which it is loaded into the 
 mine car. The refuse from the seam is used in building up the track, and if 
 there is not sufficient refuse for this, a timber trestle is used. 
 
METHODS OF WORKING 
 
 623 
 
 Another form of buggy breast is shown in Fig. 14. Here the coal is 
 dumped directly into the mine car from the buggy. If the breast pitches 
 less than 6, the buggy can be pushed to the face by hand, but in rooms of 
 a greater pitch, a windlass is permanently fastened to timbers at the bottom 
 of the breast, while the pulleys at the face are temporarily attached to the 
 props by chains, so that they can be advanced as the face advances. The 
 rope used is from in. to f in. in diameter, and any form of ordinary hori- 
 zontal windlass can be used. With the windlass properly geared, one man 
 can easily haul a buggy to the face of a breast in a few minutes' time. The 
 buggy runs upon 20-lb. T rails spiked with 2\"Xl" spikes upon 2"X4" hem- 
 lock studding sawed into lengths of 14 ft. 
 
 Chutes. A chute is a narrow inclined passage down which the coal slides 
 by gravity, or is pushed. When the pitch of the chute is between 15 and 30, 
 sheet iron is laid in it to furnish a good sliding surface for the coal. When the 
 inclination is less than 20, it is generally necessary to push the coal down the 
 chute, as it does not then slide readily even on sheet iron. When the inclina- 
 tion of the chute exceeds 30, coal will slide readily on a rock bottom without 
 
 FIG. 14 
 
 the use of sheet iron. The use of chutes is therefore limited to seams whose 
 inclination is greater than 15, that is, to what are generally called steep seams. 
 
 When the inclination of the seam is less than 30 to -35, a single chute is 
 usually placed in the center of the room. The chute ends in a platform pro- 
 jecting into the entry, and from this platform the coal can be readily loaded into 
 the mine car. The refuse made in mining is thrown on either side of the chute; 
 and, if the pillars are to be robbed, this refuse should be kept as near to the 
 center of the room as possible. Two chutes are sometimes employed, one along 
 each rib, but as the cost of the second chute is considerable, it is not generally 
 used unless it is required for purposes of ventilation. 
 
 Fig. 15 shows an inclined room with a sheet-iron chute a in the center. 
 As the coal is mined at the face b, it is shoveled into the chute and slides by 
 gravity to the platform c, from which it is shoveled into the mine cars on the 
 track d. Rows of props e are frequently stood alongside the chute to keep up 
 
624 
 
 METHODS OF WORKING 
 
 the roof above it, and the gob is stored between the posts and the rib in the 
 spaces /. The chute also acts as a manway, and by means of the props the 
 
 FIG. 15 
 
 miners are able to work their way up and down the room. The top coal g 
 is left up to help keep up the roof and may be taken down after the room has 
 been driven to its full length or it may be left in 
 place. 
 
 When the bed inclines at a greater angle than 
 about 35, it is necessary to provide a staging or 
 platform of some kind on which the workmen can 
 stand in mining the coal. A staging of timbers 
 may be built and advanced as the face advances, 
 but this is an expensive method, and it is gener- 
 ally better to allow the room to fill up with the 
 broken coal, keeping the level of this broken coal 
 just near enough to the face to provide a stand- 
 ing place for the workmen. The coal is supported 
 at the bottom of the room by a bulkhead of heavy 
 timber known as a battery, and the method of 
 working is known as working on battery. Only 
 enough coal is taken out through a chute at the 
 bottom of the room to take off the excess of coal 
 that cannot be thus stored in the room owing to 
 the fact that the broken coal occupies about 75% 
 more space than the same coal in the solid. 
 
 Single-Chute Rooms. Fig. 16 illustrates the 
 general form of a single-chute room. The coal a 
 is stored in the center and a manway b is con- 
 structed up each side with props and planking for 
 the purpose of ventilation and to afford access to 
 the face for the workmen. Cross-cuts c are made 
 by driving through the pillar separating adjacent 
 rooms. At the point where the room neck widens 
 to full room width, a battery is constructed to hold 
 FIG. 16 back the coal in the chute. This is composed of 
 
METHODS OF WORKING 
 
 625 
 
 FIG. 17 
 
 FIG. 18 
 
 strong posts d set in the roof and floor of the seam as a support for the cross- 
 timbers e\ a small opening /, known as the loading chute, is left at the center 
 of the battery and through this the coal is drawn as required. The man- 
 ways b are connected with the room neck by a small opening in the battery, 
 through which workmen 
 pass in going to and from 
 work. This opening as 
 covered by a curtain so is 
 to maintain the air-current 
 along the face. 
 
 When the coal is drawn 
 put through a central load- 
 ing chute, the movement 
 takes, place principally in 
 the coal lying near the cen- 
 ter of the breast. If the 
 roof is poor, the movement 
 of the coal will not in this _ 
 way cause it to fall and mix with the coal; and if the floor is soft the props 
 protecting the chute, and which are stepped into the floor, are not so liable 
 to be unseated, closing the manway and blocking the ventilation. The sur- 
 plus coal is sometimes thrown down the manways, instead of being drawn out 
 at the bottom of the breast through a loading chute, leaving the loose coal 
 in the center of the breast undisturbed until the limit is reached. 
 
 Double Chute Rooms. Fig. 17 shows the arrangement of an inclined 
 room in which the weight of the loose coal is supported mainly by a pillar of 
 coal left along the entry. The coal is drawn out of the room by two loading 
 chutes, one at each side of this pillar, and the workmen gain access to the man- 
 ways along the room ribs through short manways driven through the entry 
 pillars. Fig. 18 shows a similar arrangement to that shown in Fig. 17 except 
 that the sides of the loading chutes are in line with the sides of the chute in the 
 room, the manways are straight, and the loading chute and manway are in 
 the same opening in the coal. This method has an advantage over that shown 
 in Fig. 17, as it requires less cutting of the entry pillars. 
 
 An advantage of supporting the coal by a pillar at the bottom of the room, 
 as shown in Fig. 24, is that there is less likelihood of a break occurring in the 
 batteries, which would throw all of the coal on the gangway or airway, and thus 
 close off these passages and interfere both with haulage and ventilation. 
 
 If the coal seam is mixed with rock that can be readily separated from the coal 
 underground, this separation may be made on the platform /, Fig. 19 (a), 
 the rock being left in the center of the room instead of the coal, as was illus- 
 
 () * (*) 
 
 FIG. 19 
 
 trated in Figs. 16, 17, and 18. The coal is then thrown down the chutes c 
 and loaded into cars on the entry g. Fig. 19 (b) is a section through the room 
 shown in (a) on the line bdeh. This method is also used where the coal is very 
 gaseous and where it is not well, therefore, to keep broken coal stored in the 
 40 
 
626 
 
 METHODS OF WORKING 
 
 room. The air-current passes through the airway a and up the chute c to the 
 face. This method is not adapted to very thick seams, as it is impracticable 
 to build the necessary platforms in such seams. 
 
 The accompanying table gives approximate inclinations of the seam when 
 the several methods just described are employed. These inclinations may be 
 varied by local conditions. 
 
 METHOD SUITABLE FOR USE IN INCLINED SEAMS 
 
 Method 
 
 Cars lowered by hand, or drawn by mule or motor, 
 rooms on full pitch < 
 
 Cars lowered by hand, or drawn by mule or motor, 
 rooms at angle with pitch 
 
 Cars lowered by windlass, rooms on full pitch 
 
 Self-acting incline or jig road .' ^v^; 
 
 Buggy system, thick seams -..?.. 
 
 Sheet-iron chutes 
 
 Natural chutes with battery 
 
 Inclination of Seam 
 Degrees 
 
 0-6 
 
 5-12 
 
 5-10 
 
 5-30 
 10-18 
 15-30 
 30 upwards 
 
 The manways in steeply inclined rooms are constructed in two general 
 ways. In a seam that is not over 6 to 8 ft. thick, the method shown in Fig. 20 
 may be used. The posts a are set as shown and lined with plank; this par- 
 tition forms the sides of the chute b and leaves a manway c between the chute 
 and the rib. 
 
 In thick seams, inclined posts called jugulars a, Fig. 21, are used. These 
 are set in hitches cut in the floor and the rib, so as to form a triangular pas- 
 sageway or manway b. The jugulars are lined with plank to form the sides 
 of the center chute c, which is filled with loose coal or refuse. 
 
 As a general rule, in inclined seams as in flat seams, the rooms are driven 
 up to within a short distance of the entry above, a chain pillar being left 
 between the ends of the rooms and this entry; the width of this pillar varies 
 with the character of the roof, floor, and coal, depth of cover, and inclination 
 of the seam. To secure better ventilation, an occasional room is often holed 
 through this pillar into the entry above; and where the coal has been worked 
 
 FIG. 20 
 
 FIG. 21 
 
 out from the chambers above, and there is no water to interfere with the lower 
 workings, many or all of the rooms are thus driven through to the upper entry. 
 The chain pillar is sometimes drawn back with the other pillars. The distance 
 between the successive lifts or entries varies with the conditions, but is usually 
 about the same or slightly less than the distance between entries in flat work- 
 ings under the same conditions. 
 
 Battery Breasts. The methods of working by single and double chutes 
 and batteries are adaptations of similar methods originally applied in connec- 
 tion with anthracite mining. Many modifications of these simple methods are 
 used in order to meet the requirements of different pitches and different thick- 
 nesses of coal. The following are the most important of these modifications: 
 
 Fig. 22 shows an elevation (a) and cross-section (fc) of a breast in a thick 
 seam pitching about 60. The seam is 16 ft. thick with several thin slate part- 
 ings; the roof and floor are good, and the coal hard and firm. The gangway g is 
 driven on the strike of the seam, near the bottom of the coal and with sufficient 
 
METHODS OF WORKING 
 
 627 
 
 grade to insure drainage. A small airway h is driven just below the top 
 bench of coal, and is connected with the gangway by occasional openings not 
 shown. This airway is often called a monkey gangway, or simply a monkey. 
 
 FIG. 22 
 
 (&) 
 
 A narrow opening, called a chute, is opened off the gangway and driven up 
 on the floor of the seam a distance of about 5 yd., and at this point it is widened 
 out gradually on both ribs, until the full width of the breast, 5 to 8 yd., is 
 reached. A timbered chute c conveys the coal into the car on the gangway g. 
 A battery of timber b is constructed at the point where the breast is widened 
 out by setting double posts on each side of the center and close to the ribs; 
 
 
 these posts are firmly set in holes cut in the floor and the roof, and cross-tim- 
 bers are then placed behind them, leaving only a small opening for the coal 
 to pass through. A manway w is constructed up each side of the chute, by 
 
628 
 
 METHODS Of WORKING 
 
 placing about 30 in. from each rib a line of posts which are firmly set in holes 
 cut in the roof and floor and lined with plank to form the sides of the chute. 
 An opening r in the battery connects each manway with the chute c and also 
 affords access to the face of the breast. Cross-cuts a are driven between 
 adjoining breasts at points up the pitch. The breast is kept full of loose coal, 
 on which the miner stands as he works at the face. 
 
 Fig. 23 represents in elevation (a) and cross-section (6) breasts driven to 
 the full pitch of a thick seam whose inclination is about 60. The gangway g 
 is driven on the strike and in the top of the seam while the airway c is above 
 the gangway and in the top coal. 
 
 The breasts are opened by a narrow opening 9 ft.X6 ft. driven up the pitch 
 for a distance of 18 to 24 ft., this neck being gradually widened out to the proper 
 breast width, as shown. The section is taken on the lines Ik and ij, and the 
 elevation is made on the line pq, and does not show, therefore, the headings c 
 and d shown in (b). In the middle of the pillar between the loading chutes, 
 a small manway m is driven up a few yards, and then branches s are turned 
 off in both directions until intersection is made with the breasts on each side. 
 From these points the manways w are carried up on each side of the breast along 
 the rib as shown. A narrow manway n is usually made by planking off a por- 
 
 (ft) 
 
 FIG. 24 
 
 tion^of the opening so that the loaders may have free access to the battery at 
 all times. 
 
 A small airway d is driven from airway c to the manway m, but cross-cuts 
 between the airway and gangway are also necessary where much gas is given 
 off during the working. The air-current passes along the gangway g and returns 
 along the faces of the breasts. The small airways d and c are not used when 
 the breast is working, but if any accident in a breast manway ID blocks the ven- 
 tilation, the air can be conveyed around the breast, through the airways d 
 and c by simply removing stoppings. This plan is especially adapted to 
 working thick steeply inclined seams of soft gaseous coal. 
 
 _ When the pitch of the bed is less than about 50, the gangway g is usually 
 m the bottom coal, but for a greater inclination it is in the top coal, so that 
 the flpw-of the coal may be more easily controlled. 
 
 Fig. 24 shows a method in which a loading chute c is arranged on each side 
 of the breast and a supporting pillar of solid coal is left in the mouth of each 
 breast; the batteries b are built near the upper side of this pillar. The gang- 
 way g and the airway h above it are driven in the top coal. The loading chutes c 
 are driven up from the gangway and across the full width of the seam at such 
 an angle that the coal can be easily controlled in the chute. When the chutes c 
 reach the floor of the seam, they are widened out to breast width and at the 
 same time the coal face is opened up to the top of the seam in a more or less 
 vertical line, as shown in the cross-section (6). The manways m are driven 
 
METHODS OF WORKING 
 
 629 
 
 through the gangway pillar between the breasts and are divided into two parts, 
 as was described in connection with Fig. 23, a manway n extending up each 
 side of the breast. The advantage of the method illustrated in Figs. 23 and 24 
 over that shown in Fig. 22 is that the man ways and 
 the coal chutes are kept apart and there is therefore 
 usually free access to the face at all times, even 
 should there be a break in the coal chute. 
 
 By driving the gangway near the roof, as shown 
 in Fig. 24, where the pitch is heavy the loading chute 
 c is more easily controlled, and the gangway is also 
 less likely to be injured by a squeeze. The disad- 
 vantage of the method is the extra expense incurred 
 in driving long chutes. 
 
 Fig. 25 is a sectional view of a thick seam of coal 
 standing vertically and mined by room and pillar. 
 The gangway or level g is connected with the air- 
 way h by the passages c, d, and e. The battery b 
 is at the inner end of the chute c and near the foot 
 of the vertical manway m, in which a ladder is placed. 
 The passages d and e are for the purpose of ventila- 
 tion; they also serve as man ways to connect the gang- 
 way g with the foot of the vertical manway m. 
 
 Fig. 26 is a section through what is called a back 
 breast p in thick anthracite seams. The regular 
 breast b having been mined out, the coal over the 
 main gangway g and monkey gangway k is worked '__ 
 
 by opening a breast p off the monkey gangway or 
 
 off another gangway driven especially for the purpose of getting out this coal, 
 and driven so that the coal may slide through chutes to the cars. Such a 
 mode of working may enable a large proportion of the gangway stumps to be 
 removed, which would be entirely lost otherwise. 
 
 Working Contiguous Seams. Coal seams that are approximately parallel 
 and are close together are said to be contiguous. The following points must be 
 carefully considered in the working of contiguous seams: Thickness and char- 
 acter of the rock separating them; thickness of the seams; nature of the roof, 
 floor, and coal of each seam; inclination of the strata; and general depth below 
 the surface. The thickness of strata separating contiguous seams varies from 
 a fraction of an inch to several feet. When this thickness does not exceed 2 or 
 
 3 ft., the separating rock is 
 called a parting and all the 
 coal and rock are then usually 
 taken out at the same time 
 as one face of coal, or the face 
 in the lower seam is kept a 
 few yards in advance of that 
 above. The waste material 
 forming the parting is not 
 removed in either case, but 
 simply left where it falls, 
 except on the roads, as the 
 handling of so large an 
 amount of waste would ren- 
 der the econ9mical working 
 of the coal impossible. At 
 other times, the openings are 
 first driven in the' lower 
 seam, and when these reach 
 the limit of the workings the 
 tracks in the rooms are taken 
 up and the rock or slate 
 parting is allowed to fall or 
 is blasted down. The upper 
 coal is then taken down. 
 When the thickness of the 
 
 FIG. 26 
 
 intervening rocks is greater, contiguous seams may be worked either by what 
 are called rock chutes or by cross-tunnels. Fig. 27 shows a section of two seams, 
 separated by a few yards of rock. Chutes from 4Jto 7 ft. high and 7 to 12 ft. 
 wide are driven in the rock from the gangway or level g to the level / in the seam 
 
630 
 
 METHODS OF WORKING 
 
 above, at such an angle that the coal will gravitate from the upper seam into 
 
 the gangway g. The working, otherwise, is similar to that previously described. 
 
 Rock-chute mining contemplates the following sequence of operation: 
 
 1. The opening of all gangways 
 and airways in the lower seam, to 
 develop coal as yet untouched in a 
 thick seam lying a few feet above it. 
 
 2. Developing the thick bed by 
 a regular series of rock chutes driven 
 from the gangway below; workings 
 being opened out from the chutes as 
 in ordinary pillar-and-breast work- 
 ing the panel system or some other 
 plan may be found better than pillar- 
 and-breast workings. 
 
 3. Driving the breast to the 
 limit of the lift and robbing out the 
 pillars from a group of breasts as soon 
 as possible, even if a localized crush 
 is induced. 
 
 4. After one group of breasts is 
 taken out and the roof has settled, 
 
 p IG> 27 opening a second series of chutes for 
 
 the recovery of coal from any large 
 pillars that were not taken out when the crush closed the workings. 
 
 5. While the work of recovering the pillar coal is in progress, a second 
 group of breasts may be worked, and the process continued until all the area 
 to be worked from that gangway has been exhausted. The same process is 
 employed in opening lower lifts. 
 
 6. When all the upper bed of coal has been exhausted, the lower seam 
 may be worked by the ordinary method. Workings in this seam may be 
 carried on simultaneously with the upper bed, but to avoid the possibility 
 of a squeeze destroying these workings, very large pillars must be left. After 
 exhausting the upper seam, these pillars may be advantageously worked by 
 opening one or two breasts in the center of each, and when these are worked 
 to the upper limit, attacking the thin rib on each side, commencing at the top 
 and drawing back. 
 
 When the roof of the lower bed is good, the cost of timbering and keeping 
 open the gangways and airways will ^^ 
 be considerably less than if these were 
 driven in the upper seam, and this dif- 
 ference, in some cases, may be sufficient 
 to pay for driving all the rock chutes. 
 
 There are three undetermined 
 points in this connection, viz.: (1) 
 The maximum distance between the 
 two beds, or the length of rock chute 
 that can be driven with satisfactory 
 financial results. (2) The maximum 
 dip on which such workings can be suc- 
 cessfully opened. (3) The maximum 
 thickness of the upper and also of the 
 lower seam, which will yield results 
 warranting the additional outlay when 
 rock chutes are of considerable length. 
 
 Fig. 28 shows how one or more 
 seams are worked by connecting them 
 by a stone drift, or tunnel, driven hori- 
 zontally across the measures, through 
 which the coal from the adjacent seams 
 is taken to the haulagewa'y leading to 
 the landing at the foot of the slope or 
 shaft. Tunnels are sometimes driven 
 horizontally through the measures from 
 
 FIG. 28 
 
 the surface, so as to cut one or more seams above water level. 
 
 The lower seam of coal is worked from a gangway or level I, connected 
 by a tunnel, or stone drift /, to the level or gangway g, in the thick seam. The 
 stone drift may be extended right and left to open seams above and below the 
 
METHODS OF WORKING 631 
 
 thick seam. This tunnel, or stone drift, is never driven under a breast in the 
 upper seam, but directly under the middle of the pillar. 
 
 In the upper and thicker seam, when the coal is very hard, a breast b is 
 worked to the limit and the loose coal nearly all run out through the chute s 
 into the gangway g. The monkey gangway m is driven near the top as a 
 return airway, and is connected to the upper end of the chute s by a level 
 heading , and to the main gangway g by a heading v. These headings are 
 driven for the purpose of ventilation and to provide access to the battery in 
 case the chute 5 should be closed. In the lower seam, the breast is still being 
 worked upwards in the ordinary way. 
 
 New Castle, Colorado, Method. The following method is used at New 
 Castle, Colorado, for highly inclined bituminous seams. The coals mined are 
 only fairly hard, contain considerable gas, and make much waste in mining. 
 Fig. 29 shows the method used for extracting the thicker vein to its full width 
 of 45 ft., and the E seam 18 ft. thick, excepting that left for pillars. Rooms 
 and pillars are laid out under each other in the two seams whenever practi- 
 cable. Entries are along the foot-wall; 30 ft. up the pitch is an air-course. 
 Rooms and breasts are laid out as shown in Figs. 17 and 18. In the thick vein, 
 the manways go through the entry pillars to the air-course and thence along the 
 
 FIG. 29 
 
 ribs each side of the room, one manway to tne main entry serving for two 
 double rooms. A lower bench of 6 ft. is first mined the full length of the rooms, 
 120 ft., side manways being protected by vertical or leaning props, bordered 
 with 3-in. planks outside, and the chute or battery is then put in. At the top 
 the rooms are connected by cross-cuts, and, occasionally, intermediate cross- 
 cuts are required. The room is kept full of loose coal, only sufficient being 
 drawn to keep the working floor at the proper height for the mining. When 
 driven to the limit and with cross-cuts connected, the coal is all drawn out at 
 the chutes, which have receptacles for rock and waste at their sides, to be 
 picked out by the loaders. The next operation is to drive across the seam at 
 the air-course until the hanging wall is reached, manways, called back man- 
 ways, being maintained as before. A triangular section of coal is mined off, 
 as shown in Fig. 17, and the room filled with loose coal. The full thickness 
 of the seam is now taken off, shots being first placed at SS, coal being drawn 
 out at the bottom as required. In robbing a pillar, the manways are moved 
 back into the pillar each side 10 ft. or so, by mining on the lower bench as before, 
 and holes are drilled into the roof with long drills, which bring down as much of 
 the overhanging part as can be reached. 
 
 Alabama Methods. Fig. 30 shows the common methods used in working 
 the Alabama coals. The seams now working vary from .2 to 6 ft. thick, and 
 
632 METHODS OF WORKING 
 
 they pitch from 2 to 40. Where the seams are thin, the coal is hard, and 
 pillars of about 20 to 30 ft. are used to support the roof. The thick seams are 
 soft and easily broken, and much larger pillars are left. The character of bot- 
 tom and top varies; fireclay bottom and slate roof are usually found with the 
 thick seams, and hard bottom and sandstone roof with the thin seams. The 
 general plan of laying out the mine is to drive the slope straight with the pitch 
 of the seam; this is usually on the butts of the coal. A single-track slope is 
 8 ft. wide, and a double-track slope 16 ft. Cross-headings are driven or turned 
 from the slope water level every 300 ft.; air-courses are driven parallel on either 
 side of the slope. Where an 8 ft. slope is driven, 30 ft. of pillar is left between 
 the slope and airway, and for a 16 ft. slope, 40 ft. of pillar. The size of pillar, 
 however, depends largely on the character of the roof and thickness and 
 strength of coal. On the lower side of the heading, pillars from 20 to 60 ft. 
 are left on the entry before turning the first room. The rooms are worked 
 across the pitch on an angle of about 5 on the rail, as shown in A , when the 
 coal does not pitch greater than 20; where the pitch is greater, chutes are 
 
 PIG. 30 
 
 worked and the rooms are driven straight up the pitch B. In a few cases 
 where the pitch is not greater than 15, double rooms are worked with two 
 roadways in each room, as shown in C. A rope with two pulleys is used, and 
 each track keeps the rib side of the room, the loaded car pulling up the empty 
 on the opposite side of the room; distance between room centers, about 42 ft. 
 Where single rooms are worked, the room is driven narrow (8 ft. wide) for 
 j i j en connectlons are made with the room outside of it; the room is then 
 widened out to about 25 ft., sloping gradually until this width is attained; 
 pillars of from 10 to 20 ft. thick are left between the rooms, and cross-cuts for 
 ventilation are made about every 50 ft.; every third or fourth room is driven 
 through to the entry above; pillars are then drawn back to the entry stumps 
 or pillars. The average cover over the coal now working is from 100 to 600 ft 
 Air-courses usually have an area of 30 ft., and sufficient coal is taken out to 
 give this area, the roof and bottom being left. 
 
 Tesla, California, Method. The Tesla, California, method is shown in 
 *ig. 31. The coal seam averages 7 ft. of clear coal, and pitches 60. This 
 
METHODS OF WORKING 
 
 633 
 
 system was adopted in a portion of the mine to get coal rapidly; for, at this 
 point, a short-grained, slate cap rock came in over the coal, making it difficult 
 to keep props in place. The floor is a close blue slate and has a decided heaving 
 tendency. The roof is an excellent sandstone. There is a small but trouble- 
 some amount of gas. Two double chutes are driven up the pitch at a distance 
 of 36 ft. apart, connected every 40 ft. by cross-cuts. One side of each chute is 
 used for a coal chute and the other for a manway and air-course. At a distance 
 of 12 yd. apart small gangways are driven parallel with the main mine gang- 
 ways. These are continued from each chute a distance of 300 ft., if the con- 
 ditions warrant it. The top line is then attacked from the back end and the 
 coal is worked on the cleavage planes; the breast, or room, therefore consists 
 of a 12-yd. face, including the drift or gangway through which the coal is car- 
 ried to the chutes; a rib of coal (2 or 3 ft.) is left between the breasts to keep the 
 rock from falling on the breast below. Thus in each breast the miners have a 
 working face of about 15 or 16 yd., and as the coal is directed to the car by a light 
 chute, moved along as the face advances, the coal is delivered into the cars at 
 small cost, and but little loss results from the falling coal, as a minimum of 
 handling is thus obtained. Immediately above each gangway, and starting 
 from these main chutes, an angle chute is driven at about 45, connecting with 
 a part as the gangway chutes (30 ft) , at an angle of 35, and cross-cuts are driven 
 the breast gangway above it, and into these chutes the coal from that breast 
 
 Manway fc/f/r Course 
 
 FIG. 31 
 
 is delivered, runs into the main chute, and from it is loaded into the mine cars 
 in the main gangway. These angle chutes serve as a means of keeping the 
 main chute full, and at the same time give each breast an opportunity to 
 send out coal continuously. They also serve the purpose primarily intended, 
 of saving the coal from breakage, by giving it a more gradual descent into the 
 full chute. The breast gangways are driven 5 ft. wide. No timbers are needed 
 in these gangways, as they are driven in the coal, except on the foot-wall or floor 
 side, which, as before stated, is a firm sandstone. It is found safest to leave 
 a rib of coal on the top of the breast 2 or 3 ft. thick, until the working face 
 has passed on 12 or 15 ft., when this rib is cut out and thus all the coal extracted, 
 the roof caving behind and filling in the opening. As cross-cuts are driven 
 every 36 ft., ventilation is kept along the working faces, and a safe and effec- 
 tual means of securing all the coal in the seam is thus attained. 
 
 Fig. 32 shows another system used in No. 7 vein at the same place. The 
 seam averages 7 ft. of coal. The roof is shelly and breaks quickly, hence the 
 coal must be mined rapidly. 
 
 In this system the gangway chutes are driven at right angles with the strike 
 of the seam, 40 ft. up the pitch; a cross-cut 5 ft.X6 ft. is then driven parallel 
 with the gangway. From this cross-cut, chutes are driven at same distance 
 every 40 ft. between chutes, for ventilation. After a panel of five or more 
 chutes is driven up the required distance, work is commenced on the upper 
 
634 
 
 METHODS OF WORKING 
 
 outside pillar and the pillars on that line are drawn and the next line is attacked , 
 and this is continued until the panel or block is worked down to the cross- 
 cut over the gangway. About every 80 ft. in this level it is found advantageous 
 
 QSeam 
 
 
 
 anaway 
 
 -Fie. 32 
 
 to build a row of cogs parallel with the strike of the seam as the pillars are 
 drawn. This serves to save the crushing of the pillars, and prevents any acci- 
 dents from falls, qf rock. But few timbers are required by this system. 
 
 PILLAR-AND-STALL SYSTEMS OF MINING 
 
 The pillar-and-stall system, also known as post-and-stall, board-and-pillar, 
 or stoop-and-room, is a modification of the general room-and-pillar method in 
 
 which the openings, usually called 
 stalls or rooms in America, are narrow, 
 rarely exceeding 4 or 5 yd. in width. 
 The pillars are at least as wide and 
 usually wider than the stalls. In the 
 single-stall system, the stalls are turned 
 narrow off the entry as shown in Fig. 1 
 (a), and widened inside as described in 
 room-and-pillar work. In the double- 
 stall system, shown in (6), the openings 
 are wider, and are similar in every 
 respect to double rooms, except that 
 the pillars separating the double stalls 
 are generally wider in proportion to the 
 width of the stalls than are the pillars 
 separating rooms. In double-stall 
 work, the openings are often 12 or 15 yd. 
 , the roof being supported on 
 
 p 
 riG ' 
 
 in width 
 
 good pack walls in the center of the 
 
 stall; the pillars often reach a width of 30 yd. The pillar-and-stall system is 
 adapted to weak roof and floor, to strong roof and soft bottom, to soft, brittle 
 coal, and in general to conditions requiring ample support of the roof; the 
 system is particularly useful in deep seams where the roof pressure is great. 
 
METHODS OF WORKING 
 
 635 
 
 Connellsville Region. Fig. 2 shows the common method used in the Con- 
 nellsville, Pennsylvania, region. The average dip is about 5%. The face 
 and butt headings are driven, respectively, at right angles to each other on 
 the face and the butt of the coal. The face headings leave the main butts 
 about 1,000 ft. apart, while from these face headings, and 400 ft. apart, sec- 
 ondary butts are driven, and again from these butts on the face of the coal the 
 rooms or wide workings are excavated to a length of 300 ft., this having proved 
 the most convenient length for economical working. Room pillars have a 
 thickness of 30 to 40 ft., while the rooms are 12 ft. in width and are spaced 
 42 to 52 ft. between centers, depending on depth of strata over the coal. The 
 headings are 8 ft. wide, and in all main butts and faces the distance between 
 centers of parallel headings is 60 ft., leaving a solid rib of 52 ft. A solid rib 
 of 60 ft. is also left on the side of each main heading. The average thickness 
 
 FIG. 2 
 
 of cover at the Leith mine, which is here described and which may be con- 
 sidered as a type of the region, is 250 ft., the overlying measures being alter- 
 nate layers of soft shale and coal for 4 ft. The bottom is an 18-in. layer of hard 
 fireclay and slate. These floor and roof materials are soft, and are easily dis- 
 integrated by air and water. At some mines, cover will reach as much as 
 700 ft., and the dip of 5% (as at Leith) is much heavier at some points on east- 
 ern outcrop, and will run as high as 12%, flattening off as the synclinal line 
 of the basin is reached, until it is almost level. In some localities, the material 
 below coal is hard limestone, requiring blasting to remove it, and at other 
 places the roof slates are much more solid than at Leith, and not readily dis- 
 integrated. The method of drawing ribs is one of the advantages of the sys- 
 tem, since it is harder to do successfully in a soft coal like the Connellsville 
 than in hard coal. The coal itself is firm. When necessary to protect the 
 top or bottom, 4 to 6 in. of coal is left covering the soft material. 
 
636 METHODS OF WORKING 
 
 The method just given is often applied to a whole series of butts (4 or 5) 
 at once instead of to butt by butt, as shown in Fig. 2. In this case, work 
 is started at the upper end of the uppermost butt and progresses, as shown, 
 but, after cutting across the butt heading from which the rooms are driven, 
 the butt heading itself and the upper rooms from the second butt, or that 
 just before, are likewise drawn back by continuous slices being removed from 
 the rooms of the upper butt, and on across the next lower butt, etc., all on an 
 angle to the butts, and so continued as the operations progress, until another 
 butt is reached, etc., thus gradually making a longer and longer line of frac- 
 ture, which is only limited by the number of butts it is desired to include at 
 one time in the section thus mined. This works very nicely and makes long 
 
 Breasf to Surface Holes fo putdbwn Timber - 
 
 FIG. 3 
 
 even lines of fracture, the steps of the face of the workings (in the rib drawing) 
 being about 30 ft. ahead of one another. 
 
 J. L. Williams Method. The J. L. Williams method of working anthracite. 
 Fig. 3, was applied successfully by the originator at the Richards mine, 
 Mt. Camel, Pennsylvania, and by it 90% of the available coal is said to have 
 been obtained. The method is a pillar-and-stall method with the following dis- 
 tinguishing points: (1) Timbering the gob with props set not more than 6 ft. 
 apart, to keep up the roof during the extraction of the pillars. (2) Making 
 holes from the crop, for the delivery of timber into the workings. (3) Remov- 
 ing the pillars in shorter lifts than is possible when the roof is supported with 
 culm pillars. (4) Keeping the gob open with timber for dumping the fallen 
 rock, that would have to be sent to the surface if the breasts were flushed. 
 
 Both the floor and the roof of the mine were weak, so that it was not 
 possible to make either the breasts or the pillars wide. In some cases, the 
 floor consisted of 3 ft. of clod, and to prevent its lifting and sliding, every 
 
METHODS OF WORKING 
 
 637 
 
 alternate prop was put through the clod and its foot set in the slate beneath, 
 while the other props were set on pieces of 2-in. plank 2 ft. in length to keep 
 down the bottom. A small gangway X is driven to take out the chain pillar, 
 and Y is a small gangway for taking in timber. 
 
 PANEL SYSTEM OF MINING 
 
 In the panel system, the coal area is first blocked out by pairs of entries 
 driven at right angles to one another if possible. As soon as the panel has been 
 thus blocked out, the removal of the coal within the panel is begun by driving 
 openings a, Fig. 1, from the cross-entries. These openings are connected by 
 a cross-heading b, a suitable pillar being left between b and the cross-entry. 
 Rooms, or stalls c are then opened off the heading b and driven almost the full 
 length of the panel, only leaving suitable chain pillars d for the protection' of 
 the main and cross-headings enclosing the panel. After the rooms, or stalls, 
 have been driven their full length, the pillars separating the stalls are drawn 
 back, allowing the roof to fall as shown. The Connellsville method described 
 under the heading Pillar- 
 and-Stall Systems of Min- 
 ing, while closely resem- 
 bling the Scotch and En- 
 glish pillar-and-stall 
 method, may be considered 
 a modification of the panel 
 system. 
 
 When a panel is worked 
 out, in order to close off the 
 whole panel it is usually 
 necessary only to put stop- 
 pings in the mouths of the 
 openings a. A pipe is put 
 through each stopping with 
 a valve in the pipe on the 
 outside of the stopping. 
 As firedamp is often given 
 off in the panel after it is 
 worked out, these valves 
 should be opened at regu- 
 lar intervals and the issu- 
 ing air tested for firedamp 
 with a safety lamp held a 
 few inches from the mouth 
 of the pipe, so that any 
 escaping gas can mix with 
 the fresh air. If gas is 
 found, the valve is left open 
 and the gas allowed to escape and should be led into the return; it is 
 sometimes lighted at the pipe and allowed to burn off, but this is danger- 
 ous, for the flame may travel back through the pipe and explode the gas in the 
 panel. A second pipe on which is a pressure gauge is sometimes placed in the 
 stopping to test the pressure of gas behind the stopping, particularly when the 
 gob is on fire and generating gases. If there is much pressure of gas behind 
 the stoppings, the pipe through the stoppings should be left open when the men 
 are not in the mine. In some cases, the pipe through the stopping is con- 
 nected with a pipe laid along the entries and leading into the return air-current. 
 
 The term panel system is rather loosely applied in the United States to 
 any system of mining in which the mine is divided into a series of blocks in 
 which blocks the pillars are drawn and that section of the mine sealed off 
 while operations are being carried on in adjacent blocks. Thus, a tract devel- 
 oped by a series of parallel cross- or butt-entries, say, 350 to 500 ft. apart, is 
 often spoken of as being worked on the panel system when the respective butt 
 entries are not connected and the room workings from one pair of entries are 
 not driven through to the next parallel entry, the pillars being drawn as soon 
 as the rooms and the entries reach their limit of length, or the coal between 
 pairs of the parallel entries may even be worked by the longwall method. 
 
 Col. Brown's Method. Fig. 2 shows a panel system devised by Col. D. P. 
 Brown, of Lost Creek, Pennsylvania, which gives good results in thick seams 
 
 
 FIG. 1 
 
638 
 
 METHODS OF WORKING 
 
 pitching from 15 to 45, where the top is brittle, the coal free, and the mine 
 gaseous. Rooms or breasts are turned off the gangway in pairs, at intervals 
 of about 60 yd. The breasts are about 8 yd. wide, and the pillar between, 
 which is about 5 yd. wide, is drawn back as soon as the breasts reach the airway 
 near the level above. In the middle of each large pillar between the several 
 pairs of breasts, chutes about 4 yd. wide are driven from the gangway up to 
 the airway above. These are provided with a traveling way on one side, 
 giving the miners free access to -the workings. Small headings are driven in 
 the bottom bench of coal, at right angles to these chutes, and about 10 or 
 20 yd. apart. These headings are continued on either side of the chutes until 
 they intersect the breasts. When the chute and headings are finished, the work 
 of getting the coal in the panel is begun by going to the end of the upper- 
 most heading and widening it out on the rise side until the airway above is 
 reached and a working face oblique to the heading is formed. This face is 
 then drawn back to the chute in the middle of the panel. After the work- 
 ing face in the uppermost section has been drawn back some 10 or 12 yd., 
 work in the next section below is begun, and so on down to the gangway, 
 working the various sections in the descending order. Both sides of the pil- 
 lar are worked similarly and at the same time toward the chute. 
 
 Small cars, or buggies, are used to convey the coal from the working faces 
 along the headings to the chute, where it is run down to the gangway below 
 
 
 FIG. 2 
 
 and loaded into the regular mine cars. This system affords a great degree of 
 safety to the workmen, because whenever any signs of a fall of roof or coal 
 occur, the men can reach the heading in a very few seconds and be perfectly 
 safe. A great deal of narrow work must be done before any great quantity 
 of coal can be produced. The breasts are driven in pairs and at intervals, 
 to get a fair quantity of coal while the narrow work is being done, and they 
 are not an essential part of the system. It is claimed that the facility and 
 cheapness with which the coal can be mined, handled, and cleaned in the mine 
 more than counterbalance the extra expense for the narrow work. 
 
 The advantages of the panel system are: A more complete control of the 
 ventilating current is possible, and the ventilation in any panel may be altered 
 as circumstances may require; the powder smoke from each panel goes directly 
 into the return air-current and does not go throughout the mine; an explosion 
 or a fire occurring in one panel is usually confined to that panel; creeps or 
 squeezes are of rare occurrence, and are confined to the panel in which^they 
 occur; the output of coal is better regulated and more reliable. The dis- 
 advantage of the system is the expense of entry driving, and the delayed extrac- 
 tion of the coal within the panel until the driving of the main and cross-head- 
 ings has been completed. 
 
 MINING AND BLASTING COAL 
 
 SHOOTING OFF THE SOLID 
 
 Coal may be broken down at the working face by blasting from the solid; 
 by blasting after having undercut or sheared the seam; and by a combination 
 of the methods. 
 
 The term solid shooting, or shooting off the solid, is used to describe a method 
 of working in which the coal is blasted from a solid face without previous 
 
METHODS OF WORKING 
 
 639 
 
 shearing or undercutting. It is practically the only method used in mining 
 anthracite, and is also much used in bituminous mining. The chief labor in 
 the production of coal by this method is the drilling of the holes for the powder 
 and the loading of the coal into mine cars. The holes are drilled with a 
 churn drill or with a rotary drill worked either by hand or by electric or 
 compressed-air power. 
 
 The location of the holes, the d.epth to which they must be drilled, and 
 their direction depend on the nature of the coal. If the coal is compact and 
 without cleat, as is the case with anthracite, the holes are placed as they would 
 be for a rock face worked under similar conditions. If the coal has a cleat, 
 advantage must be taken of this to produce the maximum effect of the shot 
 and to prevent the shot seaming out. The best method of blasting a par- 
 ticular coal can only be learned by experience. 
 
 Drill holes must be so placed that the explosion of the charges will increase 
 the number of free faces (loose or open ends) exposed to the action of subse- 
 quent blasts and thus reduce the amount of powder otherwise necessary to 
 bring down the coal. 
 
 FIG. 1 
 
 Fig. 1 shows a common method of placing the shots in shooting off the solid 
 used both for rooms and wide entries, where the coal is 5 to 7 ft. thick and is 
 strong and close-grained and without cleats or partings which need be con- 
 sidered in the blasting. When firing with squib or fuse, the holes are exploded 
 singly or in the numbered order, except 1 and 2, which must be fired simul- 
 taneously. When firing with electric detonators, the shots are fired in pairs; 
 first 1 and 2\ then 3 and 4; and, lastly, 5 and 6, The mutual reinforcing 
 action of two charges when fired together is very noticeable in the case of 
 holes pitching toward one another as 1 and 2, which may be placed much 
 farther apart and will break down much more coal when fired together than 
 when fired singly. Shots 1 and 2 are sometimes called breaking, or busting, 
 shots, as they break out the center and thus give loose ends for the shots 3 and 
 4, which should take out the greater part of the coal. The shots 5 and 6 are 
 placed about 10 in. from the ribs and are intended mainly to straighten the 
 ribs; they are often inclined toward the rib. A cut from 4^ to 6 ft. deep 
 across the face should be taken out by such a round of holes. 
 
 If any shot does not blow out the entire face from top to bottom, it is neces- 
 sary to mine out the bottom or top coal that is left in order to square up the 
 face in preparation for the next round of shots. Occasionally, a short hole, 
 
640 
 
 METHODS OF WORKING 
 
 or plug shot, is used to do this, but such a shot results in small coal, and a pick 
 should preferably be used. The miner should aim to keep the center slightly 
 
 ahead of the 
 sides in order to 
 have free faces 
 for the side 
 shots. The only 
 difference in the 
 application of 
 this method of 
 placing the 
 shots for a room 
 or entry is that 
 the shots are 
 closer together 
 in the case of 
 an entry. 
 
 (a) 
 
 (c) 
 
 FIG. 2 
 
 When shooting fairly hard bituminous coals, especially where the coal breaks 
 in wedge-shaped pieces, the holes should be inclined at a small angle with the 
 face of the coal. Shots inclined to the face of the coal are called grip shots, 
 and the shot is said to be gripped more or less according as it makes a greater 
 or less angle with the face. _ When a shot is gripped 
 too strongly, and the charge is located too deep on the 
 solid, the force of the blast will be _ insufficient for the 
 strength of the coal and may result in a blown-out shot. 
 
 If the center of the coal seam is soft or if it contains 
 a parting, shots placed near the center, as shown in 
 Fig. 1, may only tear out a gap, leaving the top and 
 bottom intact. Under such conditions, it is necessary 
 to place the shots so as to blast off the top and bot- 
 tom alternately, as is shown in Fig. 2 (a), (b), and (c). 
 The holes are placed across the face about as shown in 
 Fig. 1, but are inclined at a much greater angle with 
 the horizontal. In Fig. 2 (a), the coal face is shown 
 vertical and the first round of drill holes is intended to 
 take off the lower part of the face; the holes are run 
 from a little below the center of the coal as shown at 1 , 
 and, excepting the buster and rib shots, the holes are 
 drilled diagonally across the face of the room and down- 
 wards, so that the charge of powder is placed across 
 the strong portion of the coal to be displaced. This 
 round of shots will throw out the bottom coal and 
 leave the coal face standing with the top overhanging 
 as shown in (b). The next round of holes 2 is run up- 
 wards and diagonally across the room to take off the 
 upper bench of coal. The third round 3, shown in (c) , 
 will be run downwards, and by thus alternately inclin- 
 ing the rounds upwards and downwards the face is 
 advanced. 
 
 If the face is kept straight and center or buster 
 shots must be used in connection with each round, an 
 excessive use of powder is necessary and a larger 
 amount of small coal is made than where an irregular 
 face is carried, with the center in advance of the sides, 
 or with either side in advance of the center. An ir- 
 regular face provides a free side for the shots and allows 
 the holes to be placed to greater advantage than where 
 the face is kept straight. Fig. 3 shows a method of 
 blasting off the solid that is applicable either to rooms 
 or to wide entries under conditions similar to those 
 given in connection with the method illustrated in 
 Fig. 1. The coal is assumed to be from 5 to 7 ft. 
 thick, strong, and close grained, and without partings >* 
 
 or cleats that interfere with or assist in the blasting, _, 
 
 and is under a strong roof. Fig. 3 (a) and (b) shows 
 
 the location of the holes in the first round. These holes are placed about midway 
 of the face vertically ; they are inclined to the face about as shown in (a) and to the 
 horizontal about as shown in view (b). Shot 1 is a buster shot, which takes 
 
METHODS OF WORKING 
 
 641 
 
 out a piece dbc\ shot 2 is placed about 10 in. from the rib to straighten the rib; 
 shot 3 takes out the greater part of the center coal, while 4 and 5 act simi- 
 larly to 1 and 2. After the straight face has thus been broken, the location 
 of the subsequent shots is largely a matter of judgment, as so much depends 
 on the conditions. No definite rules can be given, except that in solid coal the 
 direction of the hole should be parallel to a free face if possible, though even 
 this general rule will be greatly modified by cleats, partings, etc. 
 
 Fig. 4 shows approximately the appearance of the face after the shots 
 shown in Fig. 3 have been fired. If there was a cleavage to the coal, a shot 
 placed about as shown might blow out the piece of coal within the dotted line 
 and thus provide two free faces with respect to which side shots could then be 
 placed. If there was no cleavage and the coal was hard and solid, the shot 
 would be placed nearer the previous shot 4- 
 
 Precautions in Solid Shooting. Where a single center shot, which is also 
 known as the opening shot, such as is shown by the treble dotted line in Fig. 4, 
 is employed to make an additional free face, its angle of grip and its length 
 should bear such a relation to the strength of the coal that not to exceed 2 Ib. 
 of black powder (provided permissible powder is not used) will be required 
 to bring the coal. This is commonly accomplished in coals where there are 
 no marked cleats by limiting the angle between the straight face and the hole 
 to 35, in which case a 5-ft. hole, which is of the maximum allowable length, 
 would have a line of least resistance 2 ft. 10 in. 
 long to work against. Where the cleats are 
 favorable, the angle of grip may be as much as, 
 but -should never be greater than, 45. 
 
 Gripping shots (see under Explosives) 
 should not be permitted, as they are very apt 
 to blow out, or to blow off the heel, leaving the 
 toe in place, in which case a portion of the 
 powder may burn in the air. On the other 
 hand, holes should not be so pitched as to give 
 them too thin a toe as the shot may blow out 
 at the back leaving the heel standing. 
 
 Shots that are all dead (as would be 6 in 
 Fig. 3 if fired alone) or are partly dead, should 
 be prohibited. No shots should be drilled 
 directly into the face and no shot should be 
 drilled to such a depth that any portion of the 
 charge is beyond the point where a perpendicu- 
 lar dropped from the drill hole will not cut a 
 free face. 
 
 As a rule, shot holes should be parallel to 
 a free face, as shown in Fig. 4, and should 
 pitch a few degrees from the horizontal so as to 
 cut across the bedding planes. It is advisable -p, , 
 
 to incline the holes slightly in the direction of 
 
 the length of the room, so that they may cut across the vertical cleavage 
 planes. Shots should not be placed in soft streaks of coal, or shale, or mother 
 coal, as they may blow out along these lines of weakness. 
 
 Shots should be well balanced with toe and heel of equal width, which should 
 never be more than 5 ft. in any case and never greater than the thickness of the 
 seam when less than 5 ft. A hole 5 ft. long, working against a toe and heel 
 each 4 ft. wide, will give excellent results in seams 4 ft. thick and over. 
 
 Straight holes of uniform diameter give better results than crooked ones, 
 and generally short holes are to be preferred to long ones. To ensure the holes 
 being of a uniform size best adapted to the coal, the drills should be frequently 
 tested. 
 
 Shots that cannot do their work when fired separately but depend for their 
 successful action on the results accomplished by another shot or shots fired at 
 the same time, and which are, consequently, known as dependent (or follow) 
 shots, should not be permitted and are prohibited by law in some states. In 
 Fig. 1, while shots 1 and 2 are strictly dependent shots, since either one fired 
 alone would blow out, yet with proper judgment they may be safely used if 
 fired at the same instant with an electric battery. The holes S and 4 are in 
 every sense dependent as they are dead unless a free face has been made by 
 firing 1 and 2. Similarly, 5 and 6 are dependent on the successful" firing of S 
 and 4- If fuse or squibs are used, S and 4 may explode a few seconds before 
 the others, resulting in blown-out shots, to be followed by the detonation of 1 
 
 41 
 
642 METHODS OF WORKING 
 
 and 2 simultaneously which will do their work, the final explosion of 5 and 6 
 resulting in blown-out shots. The reason for the failure to explode at the same 
 instant is due to the impossibility of securing either squibs or fuse that will 
 burn at exactly the same rate. In electric firing with a blasting machine, holes 1 
 and 2 may be fired first, and then, after the smoke and dust have cleared away, 
 S and 4 and 5 and 6 in separate pairs. If delay-action detonators are used, 
 all the holes may be fired in sequence in pairs by a single application of the cur- 
 rent by using no-delay caps in 1 and 2, first-delay caps in 3 and 4, and second- 
 delay caps in 5 and 6. However, one of the strongest arguments against solid 
 shooting is that it is so entirely impossible to place the second of a series of drill 
 holes until the results accomplished by the detonation of the first hole have been 
 studied. Good practice, then, demands, that the center shot or shots (as 1 
 and 2, Fig. 1) be fired first, and that the other shots be placed where needed 
 after the face has been examined. 
 
 Objections to Solid Shooting. The objections to solid shooting are two- 
 fold: It increases the percentage of slack coal produced and is dangerous 
 to the men and mine, particularly where inexperienced or careless workers 
 using black powder, are allowed to drill, charge, and fire their own shots, when, 
 where, and how they please. 
 
 From an economic standpoint, the objection to solid shooting is that the 
 usual employment of excessive charges of powder in poorly placed holes always 
 leads to the production of an excessive amount of slack. While this may be 
 an advantage where the coal is coked, for ordinary commercial use the coal 
 must be lumpy and as free from slack as possible. 
 
 The same causes that tend to produce an excessive amount of fine coal, 
 also tend to the production of blown-out shots, and these, in turn, have been 
 the cause of many mine explosions. These dangers are largely reduced if per- 
 missible powders are used and particularly so if shot firers and electric blasting 
 are employed. They are reduced to the minimum if, in addition, the coal is 
 undercut before blasting. 
 
 If the duties of the shot firer are limited to firing the holes that have been 
 previously drilled, charged, and otherwise prepared by the miner, the pos- 
 sibility of damage to property is not reduced, and the danger to life is merely 
 transferred from the miner to the shot firer. Under these conditions the shot 
 firer is killed in event of accident and not all the underground workers. 
 
 A distinct advance toward safety is made if the shot firers charge as well 
 as blast the holes previously drilled by the miner, and are required to refuse 
 to fire any and all holes that are improperly placed. In theory, the method is 
 perfect, but leads to many accidents in practice, as the shot firers, through 
 mistaken friendship for the miner, often fire shots their better judgment must 
 condemn. 
 
 The highest degree of safety is attained by employing an inspector who 
 is independent of the miners to oversee the placing and drilling of all shot 
 holes. The inspector not only instructs the miner where to place the holes 
 but determines their pitch, depth, and the amount of charge as well. Before 
 the miner leaves his place, the inspector examines it, and compels the drilling of 
 other holes in place of those drilled contrary to his previously issued instructions. 
 The inspector commonly places a marker or flag (a piece of paper) in the mouth 
 of each hole to be fired, the charging and blasting being left to the shot firers. 
 
 Notwithstanding all precautions taken by inspecting the holes as described, 
 the fatality rate among shot firers is needlessly high by reason of the failure 
 of many of them to blast the holes properly. Having a certain number of holes 
 to charge and fire in order to complete their shift, the work is commonly done 
 in from one-half to one-third the time that should be devoted to it; and this 
 leads to carelessness in charging, in going back on delayed shots, and has led 
 to serious mine explosions through blown-out shots igniting the dust thrown 
 into suspension through rapid firing. To protect the shot firers against them- 
 selves has arisen the custom of firing all the shots at one time by means of a 
 current of electricity applied from some point outside the mine, and after all 
 the men have left the workings. This practice is not without danger to the 
 mine, through its possible wrecking by a dust explosion caused by the detona- 
 tion at a single instant of many hundred pounds of high explosives in an atmos- 
 phere charged with dust. 
 
 BLASTING AFTER UNDERCUTTING 
 
 The object of mining or undermining the seam of coal previous to blasting 
 is to secure the advantages of an additional free face. The mining may be 
 made in the bottom of the seam or in the fireclay underlying it (undercutting), 
 
METHODS OF WORKING 
 
 643 
 
 in a band or layer of shale or clay near the middle of the seam, or near the roof 
 (topcutting) and may be done by a pick or by machinery. The depth of the 
 undercut in seams up to 6 ft. or 8 ft. in thickness is commonly equal to the 
 thickness of the seam where machinery is used, but is not usually much over 
 4 J ft. where the work is done with a pick. Where the cut is made with a chain 
 machine, it has a uniform height from front to back of from 4 in. to 6 in. When 
 made with a punching machine or with a pick, the height of the cut decreases 
 from 14 in. to 18 in. at the front to 4 in. to 6 in. at the back. 
 
 The proper placing of the shot holes in a face that has been mined is a 
 simple matter compared to the same work in solid shooting. The precautions 
 previously given concerning the drilling of gripping, dead, and unbalanced 
 shots, and charging with the proper amount of explosive must be heeded. 
 As a rule, the depth of any hole should be about 6 in. less than the depth of the 
 mining, and to secure this relationship between depth of mining and length o, 
 shot hole, it is a common practice where the coal is undercut to a depth of, 
 say, 7 ft., to make the drills furnished the miner of a maximum length of 6 ft. 
 to 6 ft. 6 in. 
 
 In entries and in rooms not over 20 ft. wide where the coal is 6 ft. to 8 ft. 
 thick, three shots placed as 1, 2, and 3, in Fig. 1, should serve to bring down 
 the coal. Where the place is 
 
 FIG. 1 
 
 more than, say, 2 times as 
 wide as the coal is thick, in- 
 stead of a single center or burst- 
 ing shot 1, two may be used, as 
 A and B. The bursting shots, 
 where the seam has been un- 
 dercut to a depth of 6 or 7 ft 
 are commonly but from 4 to 
 5 ft. in length and are usually 
 given a pitch of from 5 to 10 
 downwards. In some cases, 1 
 may advantageously be placed nearer the roof in the same horizontal line 
 with 2 and S, but is usually placed about as shown at two-thirds the height 
 of the seam from the floor, and will break out a piece of coal with a cross- 
 section approximately GlH. When two holes A and B are used and the place 
 is not too wide, the coal broken will be about on the line EABF. The holes 2 
 and 8 are placed from 10 in. to 15 in. from the rib and so far below the roof 
 that when diilled with an upward pitch of from 5 to 10, their points will 
 just clear the roof slate. 
 
 In some tough, tenacious coals, when undercut by chain machines and 
 blasted with the comparatively slow-acting black powder, there is a tendency 
 on the part of the coal to sit down on the undercut because its height is so 
 small that, in falling, the coal does not gather 
 sufficient impetus to roll forwards away from the 
 face. In this case, the front part of the mining 
 must be snubbed to a height of 18 in. to 24 in. either 
 with a pick or by placing a series of snubbing, or 
 pop shots, as AB, Fig. 2, in a row along the face. 
 These shots require a very small amount of pow- 
 der, are not usually more than 2 ft. deep and 
 serve to break out a wedge-shaped piece of coal 
 appioximately along the lines A BCD. If the 
 r= coal thus brought down is loaded out of the way, 
 "~ there will be ample room provided for the free 
 fall of the rest of the seam. 
 
 When shots are fired by blasting machine or 
 battery, shot 1 is fired first and the coal loaded out into cars. When two 
 bursting shots A and B are necessary, they are fired simultaneously, and , as 
 before, the place cleaned up. Shots 2 and 3 may then be fired together. 
 Whet firing from a point on the surface is practised, the three shots are 
 detonated at the one time, but good practice seems to indicate that no-delay 
 caps should be used in 1 (or in A and E), and first-delay or even second-delay 
 caps in 2 and 3. 
 
 COMBINED UNDERCUTTING AND SOLID SHOOTING 
 
 A method sometimes followed, which reduces the amount of undercutting 
 in rooms, is shown in plan in the accompanying illustration. Here, the face be 
 with a width of from 8 ft. to 10 ft. is driven some 6 to 10 ft. in advance of the 
 
 FIG. 
 
644 METHODS OF WORKING 
 
 rest of the room. Only the narrow face be is undercut and is shot down with 
 the customary three holes. After the coal thus made is loaded out, two or 
 at the most three light shots serve to bring the coal bounded by the faces cd 
 and de. The method is adaptable to pick mining, but where machines are used 
 it would be much better to carry a straight face and undercut the room for the 
 _____ full width. 
 
 gMMMH^ A method of mining formerly employed to some 
 
 extent is known as following the crack, and consists in 
 
 ^^^^^^_ shearing to a depth of 2 ft., and firing a shot, called a 
 
 HHHB snubber, placed close to the side of the cut, the hole 
 
 <f I being drilled 3 ft. deep, thereby locating the charge 1 ft. 
 
 I on the solid. The firing of the snubber cracks or 
 
 H crevices the seam along the rib. After the firing of 
 
 / the snubber, successive back shots are fired between 
 
 these and the rib at the far side of the face, the coal 
 
 being removed after the firing of each shot. The next shear or side cut is 
 made at the place where the snubber, drilled 1 ft. on the solid, has cracked 
 the coal. The dangers incident to the use of this method are apparent. 
 
 UNDERCUTTING IN LONGWALL 
 
 In longwall work, the weight of the roof is made to act upon the face so as 
 to materially assist the breaking down of the coal. Usually a succession of 
 shallow cuts 6 or 8 in. deep is made across the entire face of the coal, thereby 
 giving the roof pressure time to act on the face of the cut, the coal at the back 
 being thus crushed and rendered more easy to mine. If, however, the roof 
 pressure is excessive or is allowed to act on the face for too long a time, the 
 crushed mining dirt is compacted and the undercutting made more difficult. 
 
 By machinery, the coal is undercut to the full depth in one cut. When 
 the old-style, chain-breast machines are employed, the cockermegs, or cockers, 
 are placed before the undercutting is started, and are removed and reset in 
 turn as the machine advances. With the present, self-propelling, longwall 
 machine, which can make a continuous cut of any length without resetting, 
 the sprags are placed immediately behind the machine as fast as it pulls itself 
 along the face. As these machines require 5 ft. or less of space between the 
 face and the gob, they do not interfere with the timbering, gob, pack walls, etc. 
 
 MACHINE MINING 
 
 The commercial use of coal-mining machines may be said to date from the 
 year 1891 when the 545 machines in use undercut 6,211,732 T. of coal, or 6.66% 
 of the entire output for the year, and at an annual rate of 11,398 T. per machine. 
 In 1910, 13,254 machines undercut 174,012,293 short T. of coal, or 41.7% of 
 the output, showing an annual capacity of 13,127 T. each. In 1910, the 
 machines in use comprised 6,716 of the pick or puncher type, 5,973 of the qjiain- 
 breast type, 518 longwall machines, and 47 of the shortwall type. It will be 
 noted that the puncher machines formed more than one-half of the entire num- 
 ber used. 
 
 A universal mining machine has not yet been brought out, and one of the 
 principal reasons for the failure of mining machines in a number of instances 
 has been the attempt to use a machine under conditions to which it was not 
 adapted. _ When a mining machine is designed and built to suit the conditions 
 under which it is to be operated, it is safe to say that there are but few mines 
 in which they cannot be successfully utilized. They are of particular advan- 
 tage where there is a long working face and where the coal is over 3 ft. in thick- 
 ness. Low seams require more undercutting for a given output than high 
 seams. As a rule it has not been found economical to use machines in seams 
 pitching over 12 to 15, though pick machines have been used in mines having 
 an inclination of 23, the difficulty being not so much in the cutting as in moving 
 the machine from place to place. 
 
 There are two general types of mining machines: Pick, or puncher, 
 machines in which a steel pick attached to the end of a piston rod is given a 
 reciprocating motion by means of compressed air; the action of the machine 
 simulating that of a miner with a hand pick. Cutter, or chain, machines in 
 which a series of teeth attached to a chain (usually) or to a disk or bar moved 
 by an electric or compressed-air motor, scrape away the coal. 
 
 Pick Machines. Pick machines may be divided into several classes accord- 
 ing to their mounting. The ordinary type is mounted upon low wheels and is 
 especially adapted for undercutting a straight face. For making a vertical 
 sheer, the machine is mounted upon much larger wheels and is provided with 
 
METHODS OF WORKING 645 
 
 longer bits. Pick machines mounted upon wheels are not adapted to under- 
 cutting seams where the pitch is more than 10 because of the difficulty of 
 keeping the machine up to the face. For pitches up to 40, the machine is 
 mounted on a post that is firmly wedged in the roof and floor, constituting 
 what is commonly known as a post puncher, although the various manufac- 
 turers have their distinctive names. While the post puncher is able to work 
 at practically any angle of pitch, in seams inclined at more than 40 shoot- 
 ing is generally done off the solid, the difficulty of moving weights of any 
 kind on such steep slopes prohibiting the use of machinery. The post puncher 
 is adapted for shearing or for undercutting in a horizontal line at any dis- 
 tance above the floor. One of the objections made to punchers, that they cut 
 put too much coal or the cut is too high, making an excessive amount of slack, 
 is overcome by the use of these machines, which will cut nearly as close to the 
 floor as a chain cutter. 
 
 Punching machines directly operated by electricity have not met with 
 success, but a punching machine in which the electric current operates a small 
 air compressor, which in turn supplies the power for operating the pick are 
 well and favorably known. In the Pneumelectric puncher, the motor and air- 
 compressing mechanism are all in the one machine, which may be mounted 
 upon wheels in the ordinary way or upon a post. In mines intending to use 
 electric motors for haulage or in mines already wired, this machine will save 
 the cost of special compressed-air piping. 
 
 The advantages claimed for pick machines are that they are able to cut 
 around sulphur balls or other obstructions in the seam and are particularly 
 suitable in places having rolls in the floor; that the exhaust air helps the 
 ventilation, particularly in tight places; that there is no danger of igniting 
 either gas or dust from short circuits of the electric arc; that they can be 
 pointed at any horizontal angle and so can cut around and between posts 
 which may be set close to the face; that they require less skilled labor than 
 chain machines; and that they may be used for working pillars on which there 
 is a squeeze, as they are light and can be easily handled and readily removed. 
 
 Chain Machines. Chain machines consist of a low metal bed frame upon 
 which is mounted a motor that rotates a chain to which suitable cutting teeth 
 are attached. To operate chain machines to the best advantage, the coal 
 should be comparatively free from pyrites. They also require more room than 
 pick machines, and a space from 12 to 15 ft. in width is necessary along the 
 face to work them to advantage. These machines have proved failures in some 
 mines on account of the incessant jarring of the roof by the rear jack. Chain- 
 cutter machines cannot be used to undercut coal when a squeeze is upon it. 
 Coal seams that are comparatively level and free from pyrites and have a com- 
 paratively good roof can undoubtedly be more satisfactorily and economically 
 cut with chain-cutter machines than with any other type. 
 
 The average height of cut is 4| to 5 in., and at this height, the chain-cutter 
 machine makes only about 60% as much small coal as a pick machine. This 
 is not always an advantage, as it does not always allow sufficient height for 
 the coal to fall down after the cut is made. In a 3^-ft. seam, three men are 
 required to handle the machine to advantage. 
 
 Chain machines may be operated either by compressed air or electric motor 
 and both are very extensively used. The original form of chain machine, after 
 making its undercut, has to be moyed across the face the width of a cut before 
 another cutting can be made. This takes considerable time and in low seams, 
 especially, involves much hard labor. To overcome these difficulties, what are 
 known as short-wall machines are extensively used. These machines are set 
 up in the same general way as the older type, but after making the first or 
 sumping cut at one side of the face, instead of withdrawing the cutter and jack- 
 ing the machine into a new position for another cut, the whole machine pulls 
 itself across the face by means of a chain or wire rope attached to the opposite 
 rib, cutting as it goes. 
 
 When a dirt or slate parting exists in the seam at such a distance above the 
 floor that the bed is divided into two more or less nearly equal parts, it often 
 is a material economy and leads to the production of clean coal if the cutting 
 is done in the parting. When post punchers are used, this is easily done by 
 raising or lowering the puncher on its supporting post, but cannot generally 
 be done with chain machines unless they were supported upon a cribbing of 
 logs, the building of which requires much time. The recently introduced 
 turret coal cutter permits the undercutting of the seam by a chain machine at 
 any height from 2 ft. to 5 ft. from the floor. The machine consists of a self- 
 propelling truck with the necessary cable-reel to attach to the power line in 
 
646 METHODS OF WORKING 
 
 the entry. The cutting machine is mounted on a turntable carrying lour 
 heavy standards on which the machine is moved up and down to the desired 
 height. After moving itself to the face of the working place, the machine is 
 anchored, the cutter raised to the proper height, and the machine turned on 
 the turret towards the right-hand rib and locked in position at an angle of about 
 15 with the track. After the cut is made on this setting, the cutter is swung 
 across the face, cutting as it moves, until its angle with the room is about 20 
 to the left. The cutter is withdrawn, completing the left-rib cut, is swung 
 parallel to the track, and is ready for moving to the next place. One advantage 
 of this machine is that the entire cut may be made without removing it from 
 the truck. 
 
 Capacity of Coal Cutting Machines. So much depends on local conditions 
 that it is almost impossible to give specific data or rates of working and costs 
 of operating cutting machines, but the following figures are fair working approxi- 
 mations. In the case of chain machines, the amount of undercutting that 
 can be done in a given time depends on the ability of the men running it, the 
 character of the coal, and the presence of faults and impurities and other 
 obstructions and hindrances to the work_ of cutting. Under favorable con- 
 ditions, one machine operated by two men is recorded as having made 104 cuts, 
 each 6 ft. deep, in 10 hr., these cuts being made in rooms and entries. This is 
 exceptional cutting and much higher than the average. It is fair to say that a 
 machine making from 36 to 45 cuts, 6 ft. deep, in 10 hr., is doing good work. 
 An average of 40 cuts, 42 in. wide, will represent 140 lin. ft. of face, which 
 for coal 6 ft. in height will make approximately 140 T. of coal per shift of 10 hr. 
 Under unfavorable conditions, the result will not run nearly so high. There 
 are cases where, with the chain breast machine, the undercutting of one room 
 per shift of 10 hr. is considered good work. The capacity of the machine or 
 the number of runs it will make differs in every locality and seam, and experi- 
 ence in the use of machines in a given locality is by far the best guide when the 
 capacity of the machine is to be considered. The time it takes for a machine 
 to make a cut is generally but a small part of the total time consumed in its 
 operation, unless unfavorable conditions exist, as the time for moving and reset- 
 ting the machines greatly exceeds the time of cutting. In cutting clean coal, 
 a machine should make a cut its full depth in 4 J min., and 1 min. more will be 
 required to withdraw the machine; the rest of the time is consumed in loading 
 and unloading, moving and setting the machine in place ready for another cut, 
 besides such delays as waiting to have rooms cleaned for operation, waiting 
 for driver, and many small accidents that are liable to occur at any time. 
 In the use of longwall machines, a record has been made of 500 lin. ft. of coal, 
 cut 6 ft. deep, in 10 hr. This is an unusual record, as a longwall machine 
 under ordinary conditions will not average more than 400 lin. ft. In a seam 
 4 ft. thick, a length of 400 ft., cut 6 ft. deep, makes approximately 280 T. of 
 coal, which would be the average output of a machine per shift of 10 hr.; 
 but under unfavorable conditions the output will, of course, be much less. 
 
 In the case of pick machines, a fair average of cutting for any one machine 
 working in rooms would be 100 lin. ft. per da. of 10 hr., making a cutting 6 ft. 
 deep. This in a seam 6 ft. thick makes about 100 T. of coal, which is the aver- 
 age output of a machine per day of 10 hr. The amount of coal that a loader 
 can shoot down and load in a day varies, of course, with the thickness of the 
 seam and the character of the coal, but an average for a day of 10 hr. is 12 to 
 15 T. In longwall work, as no changing of places is required, a fair average 
 is 150 lin. ft., 6 ft. deep, per da., making about 150 T. per machine per da. 
 The capacity of a pick machine for shearing depends largely on the height of 
 the coal sheared. Working in coal of average height, eight cuts, sheared 6 ft. 
 deep, in 10 hr. is considered fair work. 
 
 Longwall Machines. Longwall machines are of two main types: (1) Disk 
 and cutter-bar machines; (2) modified forms of chain machines. In the disk 
 machine, a series of bits or cutters are inserted in the periphery of a cutter 
 wheel or disk to which a horizontal rotary motion is imparted. The machine 
 impels itself across a longwall face by means of a rope fixed at any convenient 
 distance as in the shortwall machine. In the cutter-bar machine, the cutting 
 is d^ne by means of teeth set in a shaft about 2 in. in diameter set at right 
 angles to the machine. The teeth are arranged so that one-fourth of them 
 cut and three-fourths of them break the coal as the bar advances horizontally 
 along the face. Lateral motion is secured by the use of a pair of rails laid along 
 the face. One of these rails is notched and the other is plain. The machine 
 is propelled by means of a toothed wheel meshing into the notches of the 
 notched rail, 
 
METHODS OF WORKING 
 
 647 
 
 Longwall machines of the second class generally consist of a cutter arm of 
 any desired length, depending on the depth of undercut needed. Around 
 the necessary sprocket wheels on this arm is passed a chain bearing cutting 
 teeth, the chain being given motion by a compressed air or electric motor of 
 the type used for ordinary chain machines. 
 
 Heading Machines. In the Stanley header, shown in the accompanying 
 figure, the driving and the feeding mechanisms are placed on a massive frame a 
 that is mounted on wheels. When the machine is in place ready to commence 
 work, it is held fast by the top jacks b and the side jacks c. At the end of the 
 main shaft s, an auger drill e is placed for the purpose of steadying the cutter 
 frame while the machine is working.- The cutter frame consists of a large 
 revolving cross-head h carrying two arms / in the ends of which the cutters 
 or bits are set. The driving mechanism is so constructed that different rates 
 of speed of the cutter frame can be produced as desired for a given rate of feed 
 advance, on coals of varying hardness. As the main shaft rotates, it advances, 
 turning the cutter frame. The bits cut out an annular groove from 3 to 85 in. 
 wide, forming a C9mplete cylinder of coal as deep as the arms /. When this 
 is done, the machine is run back and the coal is taken down and loaded up. 
 The machine is again set in place and another cylinder is cut out. 
 
 The cuttings are forced to the front of the annular groove by the scrapers 
 on the arms /, and from here they are raked to one side of the machine by a 
 helper whenever the revolving arms are not in the way. Lumps of coal that 
 
 fall from the face are also drawn to the side by the helper, and finally loaded 
 into a car. In many of these machines, however, the cuttings and the coal 
 that falls while the machine is working are taken from the face by a friction 
 worm and loaded into a mine car by means of a conveyer or elevator. 
 
 The principal use of this machine is for entry driving, where the work must 
 be pushed rapidly. It is especially advantageous for prospecting a piece of 
 coal, as an entry can be driven a long distance as a single entry, and with no 
 other ventilation than that caused by the air used by the machine. 
 
 The Stanley header can cut out a cylinder of bituminous coal 4 ft. in diam- 
 eter and 5 ft. in length in 15 min., and after making the necessary allowance 
 for removals, a rate of advance equal to 75 ft. per shift of 10 hr. is accomplished. 
 Where it is necessary to drive wide entries, two machines may be worked side 
 by side, thus driving two parallel entries that nearly intersect each other. 
 The thin pillar left between them can easily be cut out with a pick. If the 
 coal could be removed as quickly as the cutting is done, the machine could 
 advance an entry 12 ft. wide 25 ft. in 10 hr. The entries thus cut can be 
 widened out to the desired height and width by the use of the pick. Impurities, 
 such as sulphur balls, existing in coal hamper the use of the Stanley header, 
 and when they are present its progress cannot be as rapid as in coal favorable 
 to mining. An average cost per linear foot of entry for a cylindrical cut alone 
 should not exceed 25 c. 
 
648 
 
 METHODS OF WORKING 
 
 Machine Mining in Anthracite Mines. Owing to the exhaustion of the 
 thicker seams and the rapidly increasing cost of mining the thinner seams, 
 the anthracite operators in northeastern Pennsylvania have begun to use 
 undercutting machines of the ordinary bituminous-coal mine type. The 
 method of using the machines differs in no way from that employed in the 
 soft-coal fields, although numerous ingenious expedients have been adopted 
 
 pitch and can be used on pitches of 
 these pitching places, after the sumping cut is made, an iron rail is placed back 
 of the machine and parallel to the face of the room. This rail, which is held 
 in place by jacks, holds the machine up to the face and along it the machine 
 slides to the end of the cut. The rail is, of course, moved up after each cut 
 is made and the coal shot down. The machine has the necessary power to pull 
 itself up to the face and to make the sumping cut at the same time. 
 
 DRAWING PILLARS 
 
 The work of drawing back, or robbing, that is, removing the pillars left in 
 the first working, should be commenced as soon as the rooms are worked up 
 their full length, whenever this is possible. If this is delayed, and the open- 
 ings left to stand for any length of time, the roof will settle heavily on the pil- 
 lars and there will be danger of crushing them and thus losing the coal. Fig. 1 
 shows the way of drawing the pillars in rooms turned off one side of a single pair 
 of entries where the drawing begins next to the main entries and progresses inbye. 
 
 The drawing of the pillars has been completed in rooms 1,2, 3, and 4, down 
 to the entry pillars a, which are left and these rooms are closed; the work on 
 pillars 5, 6, and 7 is in progress; rooms 8 and 9 have reached the limit, and the 
 
 FIG. 1 
 
 work on the pillar separating rooms 8 and 9 will now begin. The rooms inside 
 of number 9 have not been completed, and the last room on this pair of entries 
 has just been turned. After the cross-entries b and c have been completed 
 and all of the rooms off them completed and the pillars between the rooms 
 drawn, the pillars between the entries b and c and the stumps a will be drawn 
 back to the main entries d. It is advantageous to carry on the pillar drawing 
 systematically and to keep the ends of the pillars in a line to avoid excessive 
 pressure being brought on a single pillar by the drawing of the pillars on either 
 side of it. Unless the ends of the pillars are kept in line, there is also increased 
 danger from falls, and the work of drawing timber is made more difficult. 
 If rooms are driven toward each other from adjoining cross-entries, a pillar 
 should be left between the ends of the rooms and removed when the pillars 
 between the rooms are taken out. 
 
METHODS OF WORKING 
 
 649 
 
 Fig. 2, page 635, shows the reverse method of drawing the ribs, that is, 
 from the inby end of the entries or headings toward the haulage roads. The 
 cross-headings are driven in pairs off the main headings, and off of one of these 
 cross-headings other headings called butt headings, are driven. These butt 
 headings divide the mine into panels and they are driven their full length, 
 but so as to leave a chain pillar c between the end of the butt headings and the 
 next pair of cross-headings. The rooms are then started from the inbye end 
 of the butt headings, and as soon as the first or inbye room has been driven 
 up to its full length, leaving a chain pillar between it and the next pair of butt 
 headings, the pillars are drawn, as shown. As soon as the pillars have been 
 drawn back to the butt headings, the pillars between the butt headings, and the 
 
 
 lit 
 
 imi 
 
 
 ii 
 
 FIG. 2 
 
 chain pillar between the lower butt heading and the next lower tier of rooms 
 are drawn back as shown. The advantage of this method over that illustrated 
 in Fig. 1 is that both the room pillars and the entry pillars are drawn back 
 in one operation, instead of the room pillars being first drawn and the entry 
 pillars and stumps drawn subsequently. A greater portion of the total amount 
 " of coal is probably obtained in this manner when it is possible to carry it out. 
 The method of drawing back the pillars illustrated in Fig. 2 is similar to 
 that just described, but it is extended over a much larger area. The cross- 
 headings a are driven to the boundary of the property before the robbing is 
 begun; from these headings the butt headings b are driven, and off these 
 
650 
 
 METHODS OF WORKING 
 
 narrow rooms, as shown. The pillars over the entire length of the property 
 are then brought back at one time. 
 
 Work of Drawing. When the work of drawing the pillar is to begin, a 
 cut-through is driven from the face of each room to the face of the room adjoin- 
 ing so as to give a free face across the end of the pillar. There are a number 
 of ways of attacking the pillar, the choice of a method being determined by 
 
 local conditions and 
 custom. 
 
 Fig. 3 illustrates 
 one way of drawing 
 back pillars separ- 
 ating wide rooms 
 in which there is a 
 track along each rib 
 of the pillar. The 
 work of drawing 
 
 <-'CWA T ck the 5iUar? is 
 
 4$v&39r.j 
 
 FIG. 3 
 
 shown as having 
 just begun, the pil- 
 lars having been cut 
 through at the face, 
 
 and the first shots having removed the coal at each corner of the pillar. 
 The second holes a will remove the remainder of the first slice across 
 the pillar and the holes b the first cut of the second slice. The coal is thus 
 removed in steps. A row of props c keeps up the roof along the face of the pil- 
 lar. As the pillar is drawn back a sufficient distance, a second row of props 
 similar to that shown at c is stood across the face of the pillar, parallel to the 
 first row c, which is then withdrawn. In pillar drawing, the back timber 
 should be drawn only so fast as to throw a proper weight on the pillar. If this 
 weight is excessive, the end of the pillar is crushed. An excessive weight is 
 also thrown on the pillars by leaving too much timber standing. Just how 
 much timber to use can be determined only by experience. If the pillar is 
 very wide, a slice or skip may be taken off it from the entry to the face before 
 the pillar is cut across at the face. 
 
 When the pillars have been drawn back to the entry stump at the mouth of 
 the room, where the room begins to narrow toward the neck, care should be 
 taken to break the roof, if necessary, back 
 to the entry pillar or stump. With a hard 
 roof, it may be necessary to place one or 
 two shots in the roof at this point. By 
 this means the entry pillars are relieved 
 of excessive pressure due to the settlement 
 in the abandoned rooms, which have been 
 closed by the drawing of the pillars. 
 
 Fig. 4 shows other methods very com- 
 monly used for drawing pillars in both 
 flat and inclined seams, known as splitting 
 a pillar. In the method shown in (a) , the 
 opening b is driven up the center of the 
 pillar as wide as the strength of the roof 
 will permit without crushing the pillars 
 left between this opening and the rooms. 
 Each of these small side pillars is then 
 drawn back in slices by a method similar 
 to that shown in Fig. 3. In Fig. 4 (b), the 
 pillar is shown divided into a number of 
 small pillars by cross-cuts c. Each of 
 these small pillars is then divided lengthwise as shown at d. In (c), the 
 pillar is divided up its full length by a narrow place e. This narrow 
 place and the break-throughs / divide the original pillars into a number of 
 small pillars g. These small pillars are next broken up by other cross-cuts 
 h, leaving still smaller pillars, and these are then taken out by shots, as 
 shown. 
 
 Fig. 5 shows some of the methods used in robbing the pillars in steep pitch- 
 ing, thick beds of anthracite. To get the coal out of the pillar at the left of A , 
 a skip is taken off the side, as shown. Successive skips are thus taken off until 
 the whole is removed, the miner keeping the manway open to the heading 
 below as a means of retreat. The pillar between A and B is very similarly 
 
METHODS OF WORKING 651 
 
 worked. To remove that between B and C, a narrow chute or heading is 
 driven up the middle, and cross-cuts put to the right and left a few yards from 
 the upper end. Shots are placed in the four blocks of coal thus formed, as 
 shown, and they are fired simultaneously by battery. This operation is 
 repeated in each descending portion 
 unless the pillar begins to run. A 
 pillar from which the coal has started 
 to run is shown to the right of C. 
 
 Delayed Pillar Drawing. The 
 work of drawing pillars between the 
 rooms is sometimes preferably delayed 
 until the entries have been driven to 
 the boundary and the rooms also 
 worked up to that point, when the 
 work of drawing pillars will be com- 
 menced at the boundary and proceed 
 uniformly toward the mine opening. FIG. 5 
 
 This may be necessary in the working 
 
 of two beds separated by only a few feet of solid strata where a number of 
 overlying beds are worked; or in certain cases where the bed is overlaid by 
 water-bearing strata, and where the breaking of the_roof rock would result in 
 the flooding of the mine. 
 
 When this method is used, a constantly increasing extent of airways and 
 roadways must be kept open and in repair, until the robbing begins, while the 
 difficulties of ventilation are also increased. Again, the pillars first formed 
 are last removed and there may be a loss from depreciation of the pillar coal 
 due to weathering and also from the crushing of the pillars, unless much larger 
 pillars are left than are required when the pillars are drawn as soon as the rooms 
 are finished. With fairly thick and very soft coals, the rapid working up of 
 the rooms and equally quick drawing of the ribs as soon as the rooms are driven 
 their full distance, is essential to economical working; for delay in extracting 
 ribs and pillars in such circumstances results in their getting crushed and the 
 coal lost or largely ground to slack. 
 
 Precautions in Pillar Drawing. When two or more overlying seams are 
 worked simultaneously, the pillars in the lower seam should not be removed 
 until the upper seams have been worked out and the pillars drawn. 
 
 It is not generally advisable to attempt to draw the pillars in a limited area 
 surrounded by a district in which the pillars are not drawn, particularly under 
 a hard roof, as an excessive weight will then be thrown on the pillars left stand- 
 ing and a disturbance set up that may extend a long distance from the imme- 
 diate district from which the pillars are removed. 
 
 In very gaseous mines, the pillars are sometimes not taken put until the 
 workings have reached a considerable distance from the shaft, in order that 
 there may not be accumulations of gas in the gob and waste near the shaft, 
 since it is often more difficult to prevent gas accumulations in robbed workings 
 than when the pillars are left standing. If the coal is tender, the removal of 
 the pillars should be delayed if the roof will not fall readily, because if they are 
 taken out, excessive pressure may be brought on the entry pillars. In the case 
 of bad roof, the pillars should be taken out as soon as possible, not only for 
 economy, but also because, when the roof is bad and falls freely as the pillars 
 are drawn, the d6bris soon sustains the superincumbent pressure and relieves 
 the weight on the pillars next to the entries. Early drawing of pillars also con- 
 centrates the working district, and, excepting in a gaseous mine, reduces the 
 area to be ventilated. 
 
 With a strong roof that does not break readily when the pillars are removed, 
 great care must be taken that the removal of the room pillars does not bring 
 sufficient weight on the entry pillars to crush them. A weak roof falls freely 
 and soon fills up the gobs, thus partly sustaining the pressure from the roof 
 and relieving somewhat the weight on the pillars along the side and main 
 roads, due to the layers of rock immediately above the coal. 
 
 If the roof has fallen in the rooms before the work of drawing begins, the 
 strata above the pillar can usually be kept up comparatively easily by props 
 about the working face, without great danger to the miner, but where the roof 
 remains over the rooms, excessive pressure is often thereby thrown on the pil- 
 lars and the work of drawing is very dangerous and treacherous; under such 
 circumstances, the whole pillar can rarely be removed, as it will usually crush 
 before it can be taken out. 
 
 In drawing pillars, their ends should be kept in a straight line, for if they 
 
652 
 
 METHODS OF WORKING 
 
 are not, some pillars are subjected to greater pressure than others, valuable 
 coal is lost, and the work is materially interfered with. 
 
 Especial attention should be paid to the effect of the removal of the pillars 
 on the surface and the overlying strata, particularly if the latter are water- 
 bearing or contain running materials, such as quicksand. 
 
 The work of drawing pillars is particularly dangerous where faults or slips 
 are frequent in the roof, or top coal is to be taken down, or where pot bottoms, 
 sink holes, boulders, etc. are of frequent occurrence in the roof, or where the 
 workings underlie or approach buried valleys or extensive beds of quicksand. 
 
 Where the pillars are crushed and creviced, blown-out shots are liable to 
 occur in their working. Undermining, in pillar work, should be done with 
 caution. Pillar coal can sometimes be undermined with machines, but the 
 practice is not general and hand work is usually depended on. Small stumps, 
 or portions of pillars should not be left scattered through the gob, as they 
 interfere with the uniform breaking of the top. 
 
 The conditions at different mines are so varied that no general rule can be 
 laid down to suit all. There is probably no more dangerous work in mining 
 than pillar drawing and the method adopted depends largely on local conditions 
 and on the experience of the miner. 
 
 LONGWALL SYSTEM OF MINING 
 
 SYSTEMS OF LONGWALL 
 
 In the longwall system of mining, the coal is taken out in a single oper- 
 ation, the face of the workings advancing in an unbroken line or wall; no pil- 
 lars of coal are left to support the -roof which is allowed to fall and settle behind 
 the miners as the workings advance. The accompanying illustration shows 
 the general system of longwall followed in the United States. From the shaft, 
 or point from which the workings are opened out, a number of roads are kept 
 
 open for haulage pur- 
 poses to the working 
 face, as shown. Roads 
 a, d, e, h and * are 
 called main roads, or 
 main entries, as they are 
 kept open permanently. 
 The roads d and e are 
 sometimes called diag- 
 onal main roads, or 
 main diagonal roads, as 
 they cut diagonally ac- 
 ross the workings be- 
 tween the straight roads 
 a and h and a and i. 
 Each of the broken 
 straight lines represents 
 a temporary road from 
 the face to the nearest 
 haulage road. The dis- 
 tance between any two 
 of these broken lines 
 constitutes a working 
 place, or a room. The 
 crossroads b, c, f, g, j, k 
 are driven off the main 
 roads usually at an angle 
 of about 45, and their purpose is to cut of? the working rooms from time to 
 time so that haulage distances may be reduced. The distance between cross- 
 entries, or the limiting lengths, of the rooms is determined by the time it is 
 possible to keep the temporary roads from the face to the main or cross-roads 
 open. 
 
 The waste material from the seam, roof, or floor, is built in the form of 
 pack walls along each side of the roadways and in the spaces between, from 
 which the coal has been taken out. The pack walls, or packs, lining the road- 
 ways, are called road packs, and those between the roads gob packs. 
 
METHODS OF WORKING 653 
 
 There are two general systems of longwall: longwall advancing and long- 
 wall retreating. In longwall advancing, the face is started from the foot of the 
 shaft or from the inner side of the shaft pillar and advances toward the boun- 
 dary of the property. As the haulage roads under this system are maintained 
 by pack walls, it is often called the gob-road system. This is the method widely 
 favored in those parts of the United States where longwall is used, as by 
 means of it the mine is rapidly opened up and early returns are secured upon 
 the capital invested. There is no expense for narrow work, and a minimum 
 amount of timber is required. 
 
 In longwall retreating, narrow entries are driven through the solid coal to 
 the boundary of the property and the longwall face is started at that point, 
 the coal being taken out completely as the face is brought back toward the 
 shaft. This is probably the better system of the two, provided the demand 
 for coal and the capital available are such th<*t the time may be taken to drive 
 the entries. For fragile roof and soft coal, or a soft bottom, the method has 
 many advantages, particularly for working seams lying at a great depth, as 
 there is practically no expense for the maintenance of the haulage roads and 
 the mined-out area is abandoned as soon as the coal is removed. The ventila- 
 tion of the face is also more efficient and less expensive. 
 
 CONSIDERATIONS AFFECTING THE ADOPTION OF LONGWALL 
 
 The points that must be considered before adopting the longwall method 
 of mining coal, in preference to the room-and-pillar method, are as follows: 
 The roof strata overlying the seam; depth of cover; nature, thickness, and incli- 
 nation of the seam; nature of the floor or underlying strata; quantity of stow- 
 age or waste in the seam or contiguous strata; surface damage and the presence 
 of water or gas in the seam or contiguous strata; supply of timber; labor con- 
 ditions; and the transportation and marketing of the product. 
 
 Roof Pressure. Although the longwall method is most successfully 
 employed when the seam lies at a considerable depth below the surface, yet 
 it has been successfully adopted under favorable roof strata where the depth 
 of coyer did not exceed 80 ft. The ideal roof in longwall is composed of tough, 
 elastic, and pliable strata, that yield gradually by bending when the coal is 
 removed, thereby causing a uniform settlement over the area mined and throw- 
 ing a sufficient weight, or roof pressure, on the coal face to break the coal when 
 the same has been mined or undercut. 
 
 The roof pressure depends on the depth and character of the cover or mate- 
 rial overlying the seam. In the longwall method of mining, the weight of the 
 strata overlying the seam is made to settle on the waste material or the pack 
 walls that are built as the coal is removed, hence there is practically no limit 
 of depth beyond which it cannot be worked. 
 
 In the room-and-pillar system, there is a practical limit to the width of 
 opening that can be safely and economically kept open, and to the width 
 of pillar that can be left to support the increasing roof pressure without 
 crushing. These widths of opening and pillar determine the depth of the 
 workings that can be mined by this method. As the width of pillar increases, 
 the expense of driving the necessary cross-cuts increases, and the percentage of 
 coal obtained in the first working is decreased. The limiting depth is not 
 absolute, but will vary according to conditions, and as this depth is approached, 
 pillar mining becomes more and more difficult and expensive. On this account, 
 the longwall system is generally better adapted to the working of very deep 
 seams than the room-and-pillar method. 
 
 Nature of Coal Seam. Longwall is best adapted to a strong, tough coal 
 that can be undercut to a moderate depth without breaking, and to seams of 
 uniform and moderate thickness lying flat or nearly flat. Irregularities in the 
 seam, such as sudden thickenings or thinnings, the presence of large masses 
 of iron pyrites, black bat, etc., are unfavorable to the adoption of longwall, 
 but in the room-and-pillar system can usually be cut through or around. In 
 steep inclinations of the seam, longwall is not as successful as in flat seams, 
 owing to the weight being drawn from the working face. 
 
 Waste. In the longwall method, there is usually ample space for the 
 storage underground of all waste rock, so that the expense and delay due to the 
 haulage and hoisting of such rock is avoided. It is not always possible to 
 avoid this expense and delay in room-and-pillar work. .If there is not suf- 
 ficient waste as the result of mining the coal by longwall, this method cannot 
 be adopted to advantage unless it is practicable to bring material for the pack 
 walls into the mine from the surface. This objection to the method is very apt 
 
654 METHODS OF WORKING 
 
 to apply in the case of thick seams where a large quantity of waste or gob is 
 required for the packs. 
 
 For the working of a thin seam, on the other hand, longwall is particularly 
 advantageous; for it is often absolutely essential for the successful working 
 of a seam that all the coal be f ecovered, and that the expense for timber and 
 maintenance of roadways be reduced to a minimum. This can often best be 
 secured by the longwall method. Where plenty of waste material is present, 
 there is little probability of a creep or squeeze in longwall work, except with a 
 very soft bottom-. 
 
 Surface Damage, Water, Gas, Etc. In longwall W9rking, damage to the 
 surface is not as liable to occur, nor is it as great, as in the room-and-pillar 
 system of mining, the subsidence of the surface, owing to the removal of the 
 coal, being more gradual and uniform in longwall, and seldom producing the 
 large breaks and caving in of the surface that are so common in room-and-pillar 
 work. Consequently, the inflow of surface water is less in longwall work than 
 in the room-and-pillar system. 
 
 The presence of gas in a seam is unfavorable to longwall work, for while 
 the ventilation of the working face is as good, or better, in this system than in 
 room-and-pillar work, it is less easily controlled, and a large quantity of gas 
 liberated in one portion of the mine is not as easily confined to that portion 
 of the mine in extended longwall work as in some forms of room-and-pillar 
 work, unless some of the panel adaptations of longwall are used. In general, 
 in longwall work, gas issuing at one point of the face is carried along the_entire 
 working face. 
 
 Timber Supply. Where timber is scarce or expensive, longwall is par- 
 ticularly advantageous, owing to the small amount of timber required. In 
 longwall, much more of the timber can generally be used again and again than 
 in room-and-pillar work, the props being drawn and set forwards as the face 
 advances. On the other hand, in room-and-pillar work, a more abundant 
 supply of timber is usually necessary, as the timbers cannot generally be used 
 again. 
 
 Labor and Trade Conditions. The longwall miner is a more highly skilled 
 artisan than one who works in mines operated on the room-and-pillar system, 
 and must be a steady, regular worker. If absent a day his place falls behind, 
 making his work harder and his output less because of the excessive amount 
 of slack that is likely to result from excessive roof pressure where the face 
 falls behind. Longwall work is not adapted to conditions where regularity 
 of output is not certain, owing to the frequent occurrence of strikes, to the 
 scarcity of labor, or where market conditions are irregular or transportation 
 facilities uncertain and liable at any time to cause an enforced idleness of the 
 mine. Long seasons of idleness are not favorable to longwall work. 
 
 The chief advantages claimed for the longwall method of mining coal are 
 as follows: Complete removal of the coal at a minimum expense, requiring 
 a smaller capital; an earlier development on an extended scale is afforded than 
 by any other method of mining, bringing earlier returns on the capital invested ; 
 the output of the coal is more uniform and of a better marketable size, yield- 
 ing a better price; fewer roadways are required to be maintained for the same 
 face of coal; there is no yardage for entry driving; less timber is required on the 
 roadways and at the face; better ventilation of the working face is secured at 
 less expense, a minimum quantity of air being required, and fewer doors, stop- 
 pings, and overcasts are necessary; there is less liability to accident from falls 
 of roof, and there are no pillars to be drawn; less damage results to the sur- 
 face in this method; the amount of surface water in the workings is gener- 
 ally less. 
 
 The disadvantages of the longwall method are as follows: To obtain the 
 best results by this method, experienced longwall miners are required, or those 
 familiar with the work, and ordinary labor cannot be used to the same advan- 
 tage as is often done in room-and-pillar work ; where a large amount of gas is 
 present, the ventilation of a portion of the mine cannot be controlled or the 
 section sealed off as in room-and-pillar work, where a panel system of working 
 is adopted; a large amount of labor must be expended in the building of pack 
 walls; this, however, is accomplished by cheap labor; the method is not practi- 
 cable where periods of enforced idleness are liable to occur from any cause 
 whatsoever; when the coal field is disturbed by faults, it is difficult or impossible 
 to maintain a continuous tongwall face. When the seam is thick and the roof 
 hard, it is difficult to obtain sufficient packing material. 
 
METHODS OF WORKING 
 LONGWALL WORKING IN FLAT SEAMS 
 
 665 
 
 Scotch, pr Illinois, Plan. The system of longwall mining extensively used 
 in the interior coal basin of the United States is illustrated in Fig. 1, and is a 
 modification of the Scotch, or 45 system of longwall, in that the diagonal roads 
 make an angle of 60 instead of 45 with the main roads. A main entry a for 
 single track is driven from the hoisting shaft H through the shaft pillar, which 
 is left large enough to protect all buildings on the surface and to contain the 
 air-shaft or escapement shaft A and the stables, which are placed as shown. 
 At the edge of the shaft pillar, entries b are driven at right angles to the main 
 entries. Diagonal roads c are then driven at an angle of 60 with the main 
 road b and 300 ft. apart. After the work has progressed a certain distance, 
 every other cross-road is discontinued and coal is hauled out through the remain- 
 
 
 FIG. 1 
 
 ing roads; after the work has progressed still farther, the center cross-road 
 only is used for hauling the coal out of each quarter of the mine, the coal being 
 taken to this road through the rooms or along the face. The permanent haul- 
 age roads are shown in the plan with packs. 
 
 The main haulage roads are made 6 ft. high above the rails and 10 ft. wide; 
 the cross-roads c are 8 ft. wide. Pack walls not less than 4 ft. thick, and well 
 built of strong slate, are erected along all main roads. In the first brushing 
 along the roads, the miner takes down 18 in. to 2 ft. of slate for pack walls; 
 and in the second brushing, the company men secure the roof and take down 
 slate to make the roof 6 ft. above the rail. Heavy cross-bars and legs are used 
 to support the roof after the final brushing on the main entries. The legs are 
 given 1 ft. pitch in 6 ft. Permanent timbers or doors cannot be set until the 
 roof has settled and no permanent timbers can be put in for a distance of 200 
 to 300 ft. back from the face. When turning off the roads c from the main 
 roads, an angle crib of some soft wood is put in so that it will give to the weight. 
 Each room or working face is about 30 ft. wide, and as the circle of the working 
 
656 
 
 METHODS OF WORKING 
 
 face increases in size, the mine manager measures along the face and locates 
 a new room, giving each two men about 30 ft. of face to work in. When the 
 mine is first opened out, if water is present, a gutter is made in the entry around 
 the shaft pillar below the coal and covered with railroad ties. 
 
 The air is first split at the bottom of the downcast shaft H and again at the 
 face of the main road a on each side of the mine, thus giving each quarter of 
 the mine a fresh current of air, a canvas door being used in each ross-road c 
 to direct the air along the working faces. 
 
 Rectangular Longwall. Fig. 2 shows a rectangular, or square, longwall 
 method, which, in some sections, is taking the place of the diagonal method 
 just described. The entries and rooms are turned off at an angle of 90 
 instead of at 60, as in Pig. 1. A pillar is left about the shaft and work 
 begun in much the same way as in the Scotch plan. The room necks a are 
 made 10 ft. wide and are driven in from the haulageway 18 ft. The coal 
 pillars & are left in to protect the haulageways at the ends of the shaft pillar. 
 
 FIG. 2 
 
 The caging is done on one side of the shaft, empties are run to the bumping 
 post shown and mules or motors pass through the smail passages c called boll 
 holes to the empties. The distance between the cross-entries is 100 ft. The 
 main entry is single- tracked, and partings, or pass-bys, are made every 1,000 ft. 
 by going into the mouth of one of the entries, passing up the first room to the 
 next cross-entry, and then out to the main entry again. After the work has 
 been opened to a certain extent, each alternate cross-entry is abandoned and 
 later more of the cross-entries are abandoned, leaving only an occasional cross- 
 entry for haulage purposes, thus decreasing the expense for maintaining 
 haulageways. The last room on an entry is always kept open between cross- 
 entries as a means of bringing coal from one entry to another. 
 
 An objection to the square system is the longer haulage roads required than 
 in the diagonal system. 
 
METHODS OF WORKING 
 
 657 
 
 LONGWALL WORKING IN PITCHING SEAMS 
 
 True longwall in which the face advances in a more or less circular form 
 cannot be applied to pitching seams, as the face cannot be carried down hill 
 because the packs would fall upon the miner. The general method of open- 
 ing pitching seams is strikingly similar to that used in the room-and-pillar 
 method. A pair of slopes is carried to the dip and to the right and left of them 
 are turned pairs of levels. The coal between the pairs of levels is worked up 
 hill on the longwall advancing system, the pillars between the pair of upper 
 levels being taken out when the longwall face from the lower level reaches 
 them. A barrier pillar is left throughout the life of the mine on each side of the 
 slope, and these barrier pillars are extracted after the property is otherwise 
 worked out. 
 
 As the movement of the loose coal down steep pitches would probably 
 injure men working at a lower point on the same face, longwall faces in pitch- 
 ing seams are frequently laid out in steps. This step arrangement of the face 
 is not used unless the pitch is so steep as to render it necessary as it increases 
 the amount of small coal, does not permit of systematic regulation of the weight 
 
 FIG. 1 
 
 over the entire face, and makes it more difficult to insure regularity of working 
 and of advance in adjoining places. 
 
 A longwall face is usually advanced across the pitch in order to regulate 
 the roof pressure on the coal; to decrease the grade on the roads; lessen the 
 inclination of the face and thus reduce the danger in the work of mining while 
 making the coal more easily handled at the face. Breaks and slips in the roof 
 as well as the cleavage of the coal often require that the line of face should make 
 an angle with the strike of the seam in order to give a better support to the roof 
 at the face. . 
 
 One of the chief difficulties in working longwall in pitching seams is the 
 tendency of the roof to slip and sink back from the face, thus taking the pres- 
 suie from the coal. For flat working it is comparatively easy to control the 
 traveling weight on the coal; but as the inclination increases, there is consider- 
 able difficulty in preventing the broken roof masses from falling away from the 
 coal in the direction of the dip, and then either sinking in front of the line of 
 face, or, if they wedge and jam too tightly, they may bring an excessive pres- 
 sure on the coal face and crush it. In inclined seams, it is very much more diffi- 
 cult to maintain the roads than in level seams, owing to the tendency of 
 
 42 
 
658 
 
 METHODS OF WORKING 
 
 materials to slide down hill; for this reason, the principal level haulage roads 
 are frequently protected on one or both sides by pillars of solid coal. 
 
 Longwall on Low Inclination. In Fig. 1 is shown a longwall face on the 
 advancing system, in which the gob roads are built across the pitch on a suit- 
 able grade for handling the cars by mule or by hand. This method can be 
 employed in seams having an inclination varying from about 5 to 15, 
 
 FIG. 2 
 
 Fig. 2 shows a pair of levels, the upper for haulage and the lower for drain- 
 age purposes. The levels are driven on the strike of a seam, and the long-wall 
 face is arranged at a small angle with the line of strike. The coal is lowered 
 from the face to the levels by the self-acting inclines i, which are provided with 
 safety holes, or manholes, o near the face. A slant road a is driven from the 
 haulage road to the lower, or drainage, level on such an angle that the coal 
 may be drawn out of this level by a mule. 
 
 Longwall When Inclination is Less Than 40. Thin seams of coal having 
 an inclination of about 40, or less, are worked in Great Britain, France, and 
 Belgium, by driving levels or lifts on the strike of the seam in each direction 
 to .the right and left of a main slope or incline. Both the advancing and the 
 retreating methods are used. When the retreating method is used, the levels 
 are driven to their limit or boundary, and the longwall face started at this point. 
 In the advancing method, the longwall face is started at the slope, after leav- 
 ing a sufficient pillar of solid coal for its protection. In either case, the upper 
 rib of the level is marked off in sections, the length of which depends on the 
 conditions for getting the coal to the roads. This length varies from a few 
 
 yards, 15 or 20, up to 60 or 
 100. Fig. 3 represents the 
 general plan where the ad- 
 vancing method is used. 
 
 The coal is attacked by 
 the usual longwall methods 
 of undercutting and sprag- 
 ging the face in each sec- 
 tion. In this system, the 
 longwall face advances 
 directly up the pitch or on 
 the face cleats of the coal. 
 The face in each section 
 has one fast end that must 
 be sheared. Each section 
 is kept from 3 to 5 yd. in 
 The work in the first section started, a 
 
 FIG. 3 
 
 advance of the section next inby. 
 
 being the most advanced, has two fast ends and is the most difficult. The waste 
 of the seam is stowed in the space between the roads b maintained by solid 
 pack walls and placed in the center of each section, so as to provide a minimum 
 distance the coal must be handled at the face. The pack walls are started at 
 the level by building substantial cribs that are supported against slipping by 
 timbers set in foot-holes cut in the roof and floor. The road from the face to 
 the level is sometimes called a jig road. 
 
METHODS OF WORKING 
 
 659 
 
 The coal is lowered from the face to the level by buggies operated by a wind- 
 lass located either at the top or the bottom of the incline; when located at the 
 bottom of the incline, the position of the windlass is permanent. The rope 
 by which the buggy is raised and lowered passes over a block, or pulley, that 
 
 FIG. 4 
 
 s attached by a rope or chain to a timber at the head of the incline. Instead 
 of the windlass, a form of wheel is often used for lowering and raising the buggy 
 by hand. The rope is given a couple of turns around the wheel, the slack end 
 being held in one hand, while the brake band is applied with the other hand 
 by means of a lever to control the movement of the buggy or car down the 
 incline. The buggies are emptied into cars along the level and the coal carried 
 to the slope or shaft and hoisted to the surface. 
 
 It is possible to shorten the jig roads from the face to the main haulage 
 road from time to time. This may be done as slwwn in Fig. 4, by building 
 cqunterlevels a in the waste or gob parallel to the main level b either connecting 
 with one of the jig roads c, which is kept open and operated as a main jig, or 
 else these counterlevels may run to a landing on the main incline or slope. 
 
 Longwall When Inclination is 
 From 30 to 60. The method 
 shown in Fig. 5 may be used for a 
 seam pitching from 10 to 60, but 
 it is particularly adapted to seams 
 pitching from 30 to 60 and where the 
 roof and floor are good and the roof 
 pressure is moderate. In this method, 
 owing to the steeper inclination or to 
 the fact that the coal works better, 
 the working face is advanced on the 
 ends of the coal or parallel to the 
 strike of the seam. The working 
 face is broken into steps, or sections, 
 usually about 20 yd. long, each sec- 
 tion being kept from 5 to 8 yd. in ad- 
 vance of that above it to protect the 
 miner from the falling coal in the up- 
 per sections. In each section, there 
 are several miners, usually three or 
 four for a face 20 yd. long, and each 
 miner stands on a temporary plat- 
 form, or on planks laid on props 
 securely set in foot-holes cut in the 
 roof and floor of the seam, or else 
 stands on a gob built up from below. 
 The platforms also serve to protect the miners working in the lower portions of 
 each section, from the falling coal above them. Level roads are built in the 
 waste or gob at the foot of each section. The coal is sheared at the upper end 
 of each section and after being undercut it falls to the road at the bottom of the 
 section where it accumulates and is loaded in cars or buggies and transported 
 
 FIG. 5 
 
660 METHODS OF WORKING 
 
 directly to the slope or to a jig road, or main incline a, down which it is taken 
 to the level b, and then to the slope c. The lowest section of longwall face is 
 started on the inby rib of the level b, the face extending a short distance below 
 the level. A sufficient amount of coal is taken out on the lower side of the level 
 to bring the breaks in the roof over the gob packs below the roadway. In 
 deciding what breadth of coal should be worked on the lower side of the^ level, 
 it is necessary to be guided largely by the direction of the first breaks in the 
 roof, both on the rise side and the dip side of the opening-out places. It is 
 generally found that the direction of these first breaks varies considerably from 
 the direction of the main break. 
 
 When the first section has advanced over 5 or 8 yd., the next section above 
 is started, and a second level built in the gob. In this manner, the upper sec- 
 tions are started consecutively one after another. As the face advances, the 
 length of the level roads increases; so to avoid the unnecessary expense of main- 
 taining these roads, they are cut off, from time to time, by an incline driven 
 on the full pitch of the seam. It is often necessary to cut off these inclined 
 planes by a counterlevel driven on the strike of the seam between the main 
 
 FIG. 6 
 
 levels, or built in the waste or gob as the face advances. When the method is 
 used for comparatively flat seams, an inclined road is maintained at an angle 
 with the main level instead of perpendicular to it, as shown. 
 
 The nature of the roof, floor, and coal at times necessitates greater pro- 
 tection against squeeze or creep than is afforded in the method just described. 
 In this case, a pair of entries, a and b. Fig. 6, are driven on the strike of the seam 
 from the main slope or incline c and roads, or chutes, d turned off these levels 
 at regular intervals and on the full pitch of the seam. A pillar of coal from 10 
 to 15 yd. thick is left for the protection of the level a before opening out the 
 longwall face on these rise roads. As shown in the figure, the face is opened 
 to the right and left of each road d, cross-roads e being maintained in the gob. 
 The faces in each section, or lift, are advanced until they hole into each other, 
 when the lift is abandoned, the cross-road being often filled with waste from 
 other parts of the mine. 
 
 Where the roof is particularly frail or the bottom soft, especially with a 
 heavy roof pressure, the method just described may be modified as follows: 
 As before, the inclined roads, or chutes, d are driven at regular intervals on 
 
METHODS OF WORKING 
 
 661 
 
 the full pitch of the seam, Fig. 7, and cross-levels e are then driven to the right 
 and left of each chute until they hole into each other. At this point, the pil- 
 lars separating the cross-levels are holed through on the pitch of the seam 
 and the coal drawn back by longwall retreating. In both of the methods 
 shown in Figs. 6 and 7, the coal is lowered down jig roads or inclines from 
 the levels to the entry, whence it is taken to the main hoisting slope or shaft. 
 
 FIG. 7 
 
 Longwall in Steeply Inclined Seams. The work in steeply inclined seams, 
 as shown in Fig. 8, is similar to that described in connection with Figs. 5 and 6; 
 but the length of each section of the face is only about 6 ft.; one miner works 
 in each section. The coal is worked on end, the face being advanced in a direc- 
 tion parallel to the strike of the seam. Small shafts, or chutes, to carry the coal 
 to the entry are built in the waste on the full pitch of the seam, one chute being 
 built to three sections of the face. They are similar to the chute used in work- 
 ing steep seams by the room-and-pillar method, except that they are built in 
 the waste instead of being driven in the coal. These chutes are kept full of 
 coal, which is drawn as desired by opening a gate at the bottom. The miner 
 
 FIG. 8 
 
 stands on the gob, on planks, or on a temporary platform reaching from the 
 gob to the face of the coal. In the three methods illustrated in Figs. 6, 7, and 8, 
 the risk or danger from falling coal increases with the inclination of the seam. 
 
 SPECIAL FORMS OF LONGWALL WORKING 
 
 Longwall in Panels. With the ordinary longwall method, the mine can- 
 not be divided easily into separate districts, as it is often desirable to do in 
 working gaseous seams. In order to adapt longwall to the working of such 
 
METHODS OF WORKING 
 
 Beams, it is necessary to restrict the length of continuous working face by divid- 
 ing the mine into panels and carrying a longwall face in each panel, as shown 
 
 in Fig. 1. Several 
 rooms, or chambers, 
 are turned off of a 
 pair of entries and 
 are connected at 
 the inside of the 
 entry pillar by being 
 holed into each 
 other. They are 
 then driven up as a 
 single breast by 
 longwall advancing. 
 The breast, how- 
 ever, has two fast 
 ends, one on each 
 side of the panel, 
 p IG . i which must be 
 
 sheared as the face 
 
 is advanced. Each panel has a separate ventilating current and may be 
 stopped off in case of a fire or a squeeze without interfering with the rest 
 of the mine. The methods of working inclined seams previously described 
 are practically panel methods. 
 
 The modified longwall system followed at Vintondale, Pa,, is shown in 
 Fig. 2. The pitch of the seam is 8%, or about 4^, and the coal is about 
 3 ft. 8 in. thick, the roof being blue slate, and the floor a hard fireclay. The 
 cover is a fairly hard sandstone, 174 ft. thick. The main entry a, is driven 
 directly up the pitch and centrally in the coal field, bisecting itbetween the 
 outcrops. This main entry is paralleled by two airways b as shown, one on 
 each side for the purpose of ventilating each side independently. On the 
 right side of the figure, at c, is shown one method of laying out the faces par- 
 allel to the dip. At the end of the cross-entry d, an ordinary room is turned 
 up the pitch and driven practically parallel to the main heading to a connec- 
 tion with the next pair of cross-entries inby, as shown at e. The outby rib 
 of this wide room forms the longwall face, which is worked back toward the 
 main entry. Empty mine cars are taken to the faces on the lower road of the 
 
 FIG. 2 
 
 inner cross-headings / and hauled along the face c, where they are loaded and 
 hauled out on the upper road of the lower cross-headings d to the main heading. 
 
METHODS OF WORKING 
 
 663 
 
 On the left of the diagram at g, is shown the method of laying out faces so 
 that they are 90 with the line of pitch, so that the full influence of any roof 
 pressure due to the pitch is exerted fully on the gob. In this case, the empty 
 mine cars are taken into the lower road of the upper pair of cross-entries h, 
 dropped through the room i, which connects the pair of cross-entries, then to 
 the face g along which they are loaded, thence dropped through a gob road- 
 way j to the upper road of the lower pair of cross-entries k. The gob road- 
 way j has solid coal for one of its ribs, and is maintained by means of a sub- 
 stantial timber crib, built as the face progresses. On the left of the diagram, 
 the faces advance directly up hill. 
 
 Longwall in Thick Seams. A thick seam of coal is usually worked in sev- 
 eral benches of moderate thickness. The longwall method i variously modified 
 to suit the conditions, but the plan generally adopted, and which has given 
 the best results in France, Bohemia, and other countries where such seams are 
 worked, both with respect to the safety of the working and the percentage of 
 coal obtained from the seam, is that of close packing, or completely filling with 
 waste the space from which the coal is taken. Sufficient waste is not pro- 
 duced, ordinarily, in the working of the seam, and waste material is brought 
 from the surface to fill in this space. 
 
 In the working of flat seams by this method, a longwall face is carried for- 
 wards in each bench of the coal, the face in each bench being kept from 80 to 
 100 yd. in advance of that in the bench next above. Fig. 3 shows the general 
 plan and cross-section of the workings at the face of a thick flat seam, the seam 
 being divided, as shown, into three benches. The first mining is done in the 
 lowest bench, in which the parallel main roads ab and en are driven and con- 
 nected by the cross-roads c. The roads o that lead to the face are protected 
 by packs, and correspond to the temporary roads, or working places in the gen- 
 eral longwall method. Above the cross-roads c and from 80 to 100 yd. back 
 from their faces are the cross-roads c' in the second bench. Above the cross- 
 roads c' and from 80 to 100 yd. back from their^faces are the cross-roads c" 
 in the third bench. As the temporary roads o in the lower bench attain a 
 length equal to the advance between the cross-roads c, they are cut off by a 
 new cross-road in the lowest bench of the seam. At the same time, the corre- 
 sponding temporary roads o in each of the benches above and which are in the 
 
664 METHODS OF WORKING 
 
 same line with the roads o in the lowest bench reach their limits. The roof of 
 the cross-roads c in the lowest bench is then ripped or taken down and the road 
 is packed with waste on which a new cross-road c' is laid in the bench above. 
 In like manner, the roof of each cross-road c' in the second bench is taken down, 
 and the old road is packed with waste on which the new cross-road is laid in 
 the bench above, as before. The main roads on each side are treated in the 
 same manner, the road being graded from the cross-road in the lower bench 
 to the cross-road in the upper bench, as indicated in the cross-section by the 
 dotted line across the 'gob and marked road. This inclined road advances 
 with the work in each bench. 
 
 Longwall in Inclined Thick Seams. In the working of inclined thick 
 seams, when the inlination of the seam is moderate, the method just described 
 may be used for the removal of the coal. In steeper inclinations, a slope road 
 is driven in the lower bench of the coal on the floor of the seam, and gangways, 
 or levels, are driven to the right and left in the seam from this slope. Cross- 
 drifts are then driven from these gangways across the seam to the roof rock, 
 at intervals varying from 16 to 20 yd. At the roof, they are holed across from 
 one to the other, and the coal drawn back, on the retreating method, in hori- 
 zontal slices from 5 to 6 ft. in thickness. The face is also broken into steps 
 between the cross-drifts, and as each slice of coal is taken out, it is often neces- 
 sary to fill in the space with waste. 
 
 Longwall in Contiguous Seams. In the application of longwall to con- 
 tiguous seams, the methods of work at the face do not differ from those already 
 described. Seams have been worked in England as one seam when separated 
 by a slate parting 7 ft. in thickness. In this particular case, the lower seam 
 was 7 ft., and the upper seam 2 ft., in thickness. A general method for work- 
 
 PIG. 4 
 
 ing contiguous seams is shown in Fig. 4, which is a cross-section of the working 
 face. The lower seam a is worked first, the slate parting b being supported 
 on three rows of props c, d, e set parallel to the face. By the withdrawal of 
 the rear row of props e, the slate parting falls or is wedged down. The work 
 of taking down the upper seam / then follows. The slate parting, as it falls, 
 is broken up and leveled off, thus forming a convenient flat g at the top of the 
 incline *'. Thereof above the incline is supported by pack walls j. 
 
 When contiguous seams are worked separately by the longwall method, 
 either by driving cross-tunnels between the different seams, or by separate 
 slopes or inclines, the longwall face in an overlying seam should generally be 
 kept in advance of that in a lower one, as the working of an underlying seam 
 by longwall will usually result in the crushing and crevicing of overlying seams 
 to a certain extent. 
 
 DETAILS OF LONGWALL WORKING 
 
 T S.** 1 *? 118 kongwall. There are two methods of starting longwall workings, 
 in the first, the work of extraction begins at the shaft itself, the coal being 
 taken out all around and its place filled with solid packs, leaving only space 
 for the roadways. In the second method, a pillar of solid coal is left to sup- 
 tort the shaft, cut only by the roadways. The longwall work is then started 
 uniformly all around this pillar. Great care is needed in building the first pack 
 
METHODS OF WORKING 665 
 
 walls around the shaft pillar, to see that they are solidly built and well rammed, 
 in order to break the roof over the coal. The system will not work rightly, 
 however, until the breast has been advanced some distance from the pillar, 
 so as to secure the benefit from the weighting action of the roof upon the coal 
 face. The mining will be more difficult in the start, and in some exceptional 
 cases it may even be necessary to place some light shots; this, however, should 
 be avoided, if possible. 
 
 Roadways. The general plan of laying out the roads is shown on pages 652 , 
 655, and 656. The temporary roads connect the working places, or rooms, with 
 the cross-roads, but as they are cut off from time to time by other cross-roads 
 they are not protected by as substantial pack walls as the other roads. The 
 length of the temporary roads may be different for each section of the mine, 
 and must be determined in each case as the work progresses. A cross-road is 
 started off the main road whenever the temporary road gives signs of closing. 
 It will thus be seen that the distance between cross-roads, measured on the 
 main entries, may not be a uniform distance for the different sections of the 
 mine, and may even vary in the same section. Again, owing to a creep or 
 crush closing some rooms, it may be necessary to turn a short stub road directly 
 across the heads of such rooms or working places, the old roads in this case being 
 gobbed tightly to counteract the effect of the squeeze. The distance between 
 the temporary roads is decided mainly by the possibility of taking the cars 
 along the face, which, in turn, depends on the clear width it is possible to keep 
 open between the face of the coal and packs. When it can be done, roadways 
 are laid along the face and protected by timbers. At the junction of the track 
 along the face with the track running into the room, a turntable consisting 
 of an iron plate that allows the car to be turned is sometimes used. This track 
 may be made of oak mine rails spiked to cross-ties, or of light iron rails, held 
 together by spreaders of "X1" strap iron. 
 
 If the mine car cannot be taken along the face and there is a hard, smooth 
 bottom, the coal is often loaded on a sled, or buggy, which is dragged along 
 the face to the head of the temporary road, where it is loaded into a car. The 
 distance between the temporary roads will then depend on the distance to 
 which the coal can be thus conveniently carried, but is usually from 40 to 60 yd., 
 though it has reached 100 yd. in exceptional cases. 
 
 When it is necessary to shovel the coal to the road head where it is loaded 
 or to wheel it in barrows along the face, the roads are made from 15 to 20 yd 
 apart, center to center. 
 
 In some mines a motor-driven conveyer laid along the face is used to carry 
 the coal to one of the roads where it is loaded into mine cars. The conveyer 
 is usually of the trough type, is moved forwards bodily as the face is advanced, 
 and works well where the face is reasonably straight. 
 
 Control of Roof Pressure. The removal of the coal and the slow advance 
 of the working face is followed by a slow, but irresistible, downward move- 
 ment of the cover or overburden, known as settlement. The immediate effect 
 of this is to produce breaks in the roof strata over the area from which the coal 
 has been taken, more or less parallel to the working face, and, consequently 
 at right angles to the line of advance. The effect of removing the coal is to 
 divide the overburden into two portions: 
 
 1. An underweight of broken material from 10 to 40 ft. thick which may 
 be likened to heavy falls of the rocks immediately overlying the seam in room- 
 and-pillar work. The weight of this broken material is small, compared with 
 the overweight, and it may be temporarily supported by the timbers and by 
 the face of the coal and the packs. By the withdrawal of the timber next the 
 packs, the weight is thrown, or settles, forwards on the coal and breaks it. 
 The amount of the underweight thrown on the coal face is controlled, as far 
 as possible, by the posts set parallel to the face. The amount of timber, num- 
 ber of rows, and the distances apart of the rows and of the timbers in each row 
 depend on the conditions at the face. For given conditions of roof and floor, 
 more weight is thrown on the face of the coal by decreasing the amount of 
 timber, while increasing the timber decreases the weight on the coal. With 
 a hard roof and floor, the posts should be set on some soft material, or be pro- 
 vided with a thick soft cap that will yield and allow the post to take the weight 
 gradually, or the post is sometimes tapered at the end for the same purpose. 
 
 2. An overweight due to the weight of the rocks from the_ top of that por- 
 tion of them causing the underweight to the surface, and which is practically 
 equal to the weight of the entire overburden. It is irresistible and its effect 
 is to compress the pack walls and gob into spaces between the walls until the 
 resistance offered to the weight is practically equal to that of the coal that has 
 
666 METHODS OF WORKING 
 
 been removed. The amount of settlement due to this overweight is regulated 
 mainly by the proportion of pack walls to the entire area from which the coal 
 has been removed and by the manner of building these pack wails. 
 
 The aim in longwall work is to so control the roof pressure that it may be 
 just sufficient to break the coal from the face and yet not crush it. When this 
 pressure can be controlled, it is done by means of the number and size of the 
 pack walls, by rows of props placed parallel to the face, and by varying the open 
 space left along the face between the coal and the pack walls. Experience 
 under the given conditions alone determines in just what way and to what 
 extent this control may be secured. The pack walls provide for a gradual 
 and uniform settlement of the roof over the entire area from which the coal has 
 been removed. They relieve the timbers at the face of a great part of the weight 
 they would otherwise have to carry and permit the weight on the coal face to 
 be regulated largely by means of timbers so that the coal may be properly 
 broken and not crushed. 
 
 Excessive weight on the face of the coal is shown by increased hardness of 
 the under clay and the increased difficulty of undercutting in it, and also by 
 the crushing and nipping of the coal. This excessive weight may be due to too 
 small packs and too little timbering, or to the attempt to carry too wide an 
 area between the packs and the face. The remedy is to increase the amount 
 of timber and the size or number of packs, or to decrease the distance between 
 the face and the packs. 
 
 Too small a weight on the face of the coal is evidenced by the slow break- 
 ing of the coal. This may be due to too large a proportion of packs, to too many 
 timbers, or to too narrow a space between the face of the coal and the packs. 
 The remedy is to decrease the proportion of packs or the amount of timber, 
 or to increase the open width at the face. 
 
 Building Pack Walls and Stowing. Pack walls should be built , large 
 enough at first and kept well up to the face, to prevent the weight coming upon 
 the timber and also to permit the roof to settle rapidly when the timber is 
 taken out of the face. Often the roof will not stand this second movement 
 without breaking, and possibly closing in the entire face. The face should 
 therefore be kept in shape, and just as soon as there is room for a prop or chock, 
 it should be put in immediately, and the pack walls likewise should be extended 
 after each cut or web is loaded out. 
 
 As a general thing, the pack walls in the gob are not so wide as the road- 
 side ones, particularly when the seam produces enQugh waste material to stow 
 the marches, cundies, or gobs, between these pack walls. Usually about 50% 
 of the cubic contents of the solid seam taken out will stow the spaces between 
 the pack walls in thick pitching seams, where the entire gob must be completely 
 filled or nearly so. No waste material, except such as will hasten spontaneous 
 combustion, should be taken out of the mine to the surface. 
 
 Timbering a Longwall Face. The method of 
 timbering the working face depends on the nature 
 of the roof, floor, coal, etc. The action of the roof 
 on the coal face is regulated almost entirely by 
 timber; consequently, when the coal is of such a 
 nature as to require little weight to make it mine 
 easily, the roof must be timbered with rows of 
 chocks and, if necessary, a few props. 
 
 The ends of all stone packs nearest the face of 
 the coal should be in line, and the ends of these 
 pack walls should form a line parallel to the face of the coal. Timbers set at 
 equal distances and in line along a longwall face are much more efficient in sup- 
 porting the roof than irregularly set timbers. The accompanying figure shows 
 the proper way of locating the pack walls and the face timber. 
 
EXPLOSIVES AND BLASTING 
 
 667 
 
 EXPLOSIVES AND BLASTING 
 
 CLASSIFICATION OF EXPLOSIVES 
 
 The characteristics of a good blasting explosive are: (1) Sufficient stability 
 or difficulty of detonating by mechanical shock, and strength; (2) convenience 
 in form and safety in handling; (3) absence of injurious effects upon the user. 
 
 Explosives are of two general classes: low explosives, or those discharged 
 by fire, and high explosives, or those that require a detonator. 
 
 Low Explosives. Ordinary gunpowder and black, or blasting, powder 
 are low explosives. Blasting powder consists of 73 parts of Chili saltpeter 
 ([nitrate of soda, NaNOa), 16 parts of charcoal, and 11 parts of sulphur. Blast- 
 ing powder is graded according to the size of the grains passing through and 
 over various sizes of round holes in sieves. In low explosives, the force of 
 shattering effect is produced by the rapid combination of the oxygen of the 
 saltpeter with the carbon of the charcoal; the sulphur is added merely to make 
 the mixture more easily ignitable. 
 
 SIZES OF GRAINS OF BLACK BLASTING POWDER 
 
 Trade Name 
 
 Through 
 
 Over 
 
 CCC 
 CC 
 C 
 F 
 FF 
 FFF 
 FFFF 
 
 I 
 
 if 
 
 High Explosives. High explosives, which are very commonly called 
 dynamites regardless of their composition, usually consist of a base or absorbent 
 known as dope, which may or may not be an aid to the explosive, and an explo- 
 sive proper. If the active agent is a liquid, as it is in the case of true dynamites, 
 the dope is added to hold or absorb the explosive; if the active agent is a solid, 
 the base is added to reduce the temperature of the gaseous products of com- 
 bustion or to shorten the length of the flame produced by their burning, and, 
 in general, to render their use safer. The high explosives generally derive 
 their names from those of their active principle. 
 
 Nitroglycerin is prepared by slowly running glycerin into a mixture of con- 
 centrated nitric and sulphuric acids, the bath being stirred and kept cool dur- 
 ing the process of mixing. It is a dense, oily liquid, white when pure but of a 
 yellowish cast as found on the market. It is very poisonous, not only when 
 taken through the mouth but also through the inhalation of its fumes, pro- 
 ducing violent headaches which, however, tend to diminish in intensity after 
 repeated exposures. Nitroglycerin may freeze after some exposure to a tem- 
 perature of 52 F. It explodes when confined at 360 F. It takes fire at 
 306 F. and, if unconfined, usually burns harmlessly unless in large quantities, 
 so that a part of it, before coming in contact with the air, becomes heated to the 
 exploding point. 
 
 Picric acid, which forms the basis of many explosives, is made by treating 
 carbolic acid (derived from coal tar) with concentrated nitric acid. 
 
 Ammonium nitrate is a salt similar to sodium and potassium nitrate and is 
 largely used in the manufacture of a class of explosives known as ammonium 
 (or ammonia') nitrate powders, ammonia dynamite, etc. It has been used in 
 the United States for nearly 30 yr. in the manufacture of some dynamites, 
 taking the place of sodium nitrate over which it has the advantage that upon 
 exploding it goes completely into gases. It is also largely used here and abroad 
 in the making of the so-called permissible, or permitted, powder for use in gaseous 
 and dusty coal mines, for the reason that upon exploding it forms large amounts 
 of water, and this lowers the temperature of all the products of combustion. 
 
EXPLOSIVES AND BLASTING 
 
 EXPLOSIVES FOR ROCK WORK 
 
 Explosives for rock work in mining are all of the high-explosive type. The 
 original form is dynamite, which consists of a base, usually wood pulp, with 
 which the explosive or explosives are mixed. 
 
 Straight Nitroglycerin Dynamite. By a straight dynamite is meant one 
 that contains no other high explosive than nitroglycerin. Straight dynamites 
 are graded according to the percentage of nitroglycerin they contain and their 
 strength is made the basis of comparing the strengths of dynamites of other 
 types. Thus, a 40%-ammonia dynamite means a dynamite that has the same 
 strength as a 40% straight nitroglycerin dynamite. The Un ted States Bureau 
 of Mines has given the subject of explosives considerable study, and in this con- 
 nection the results of its investigations are freely used. The compositions 
 of straight nitroglycerin dynamites are given in the accompanying table. 
 
 COMPOSITIONS OF STRAIGHT NITROGLYCERIN DYNAMITES OF 
 VARIOUS STRENGTHS 
 
 Ingredients 
 
 15% 
 
 20% 
 
 25% 
 
 30% 
 
 35% 
 
 40% 
 
 45% 
 
 50% 
 
 55% 
 
 60% 
 
 Nitroglycerin . . 
 
 15 
 
 20 
 
 25 
 
 30 
 
 35 
 
 40 
 
 45 
 
 50 
 
 55 
 
 60 
 
 Combustible material* . . . 
 Sodium nitrate 
 
 20 
 64 
 
 19 
 60 
 
 18 
 56 
 
 17 
 52 
 
 16 
 
 48 
 
 15 
 
 44 
 
 14 
 40 
 
 14 
 35 
 
 15 
 
 29 
 
 16 
 23 
 
 Calcium or magnesium 
 carbonate 
 
 1 
 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 *Consisting of wood pulp, flour, and sulphur for grades below 40%; wood 
 pulp only for other grades. 
 
 The straight nitroglycerin dynamites, as a class, develop greater disruptive 
 or shattering force than any of the other commercial types of explosives, and for 
 this reason they should be used, whenever the conditions permit, for producing 
 shattering effects or for blasting very tough or hard materials. 
 
 Slow, or Low-Freezing, Dynamites. The accompanying table shows 
 typical compositions of low-freezing dynamites. The slow, or low-freezing, 
 dynamites have the advantage of not freezing until exposed for a considerable 
 time to a temperature of 35 F. or less, but, like all nitroglycerin explosives, 
 after they become frozen they must be thawed before used in order to insure 
 the most effective results. 
 
 COMPOSITIONS OF LOW-FREEZING DYNAMITES OF VARIOUS 
 STRENGTHS 
 
 
 A 
 
 4 
 
 fc?M 
 
 >4 
 
 of 
 
 4 
 
 4 
 
 Ingredients 
 
 o c 
 
 "3 g 
 
 O C 
 
 
 
 1C 
 
 |?c 
 
 
 CO (H 
 
 CO 
 
 ^ IH 
 
 
 
 
 o S 
 
 
 w 
 
 to 
 
 to 
 
 w 
 
 to 
 
 w 
 
 to 
 
 Nitroglycerin 
 
 23 
 
 26 
 
 30 
 
 34 
 
 38 
 
 41 
 
 45 
 
 Nitrosubstitution compounds .... 
 
 7 
 
 9 
 
 10 
 
 11 
 
 12 
 
 14 
 
 15 
 
 Combustible material* 
 
 17 
 
 16 
 
 15 
 
 14 
 
 14 
 
 15 
 
 16 
 
 Sodium nitrate" 
 
 52 
 
 48 
 
 44 
 
 40 
 
 35 
 
 29 
 
 23 
 
 Calcium or magnesium carbonate . 
 
 1 
 
 1 
 
 
 1 
 
 1 
 
 1 
 
 1 
 
 Composition similar to that in the straight nitroglycerin dynamites. 
 
 Ammonia Dynamites. The ammonia dynamites, compared with the other 
 dynamites, have the disadvantage of taking up moisture very readily, because 
 ammonium nitrate is deliquescent, and care should be observed when they are 
 stored or used m wet places. The following table shows typical compositions 
 of ammonia dynamites; 
 
EXPLOSIVES AND BLASTING 
 
 COMPOSITIONS OF AMMONIA DYNAMITES OF VARIOUS 
 STRENGTHS 
 
 669 
 
 Ingredients 
 
 30% 
 
 strength 
 
 35% 
 
 strength 
 
 40% 
 
 strength 
 
 50% 
 
 strength 
 
 60% 
 
 strength 
 
 Nitroglycerin 
 Ammonium nitrate .... 
 Sodium nitrate 
 Combustible material*. 
 Calcium carbonate or 
 zinc oxide 
 
 15 
 15 
 51 
 
 18 
 
 1 
 
 20 
 15 
 
 48 
 16 
 
 1 
 
 22 
 20 
 42 
 15 
 
 1 
 
 27 
 25 
 36 
 11 
 
 1 
 
 35 
 30 
 24 
 10 
 
 1 
 
 
 
 
 
 
 
 Composition similar to that in the straight nitroglycerin dynamites of the 
 grades below 40%. 
 
 Gelatin Dynamites. The gelatin dynamites have been used to a large 
 extent in wet blasting, as in the removal of obstacles to navigation and in deep 
 workings, and as a general rule are best suited for these purposes. In the 
 manufacture of these dynamites, the nitroglycerin is gelatinized by the addi- 
 tion of a small percentage of nitrocellulose. The jelly-like mass thus formed 
 
 COMPOSITIONS OF GELATIN DYNAMITES OF VARIOUS 
 STRENGTHS 
 
 Ingredients 
 
 og 
 
 CO (H 
 M 
 
 ^ 
 
 10 g 
 
 coj; 
 to 
 
 f"o 
 
 
 "w 
 
 ^1 
 
 
 V 
 
 ?& 
 
 s 
 
 In 
 
 4 
 l 
 
 4 
 g l 
 
 Nitroglycerin 
 
 23.0 
 
 28.0 
 
 33.0 
 
 42.0 
 
 46.0 
 
 50.0 
 
 60.0 
 
 Nitrocellulose 
 
 0.7 
 
 0.9 
 
 1.0 
 
 1.5 
 
 1.7 
 
 1 9 
 
 2 4 
 
 Sodium nitrate 
 
 62.3 
 
 58.1 
 
 52.0 
 
 45.5 
 
 42.3 
 
 38.1 
 
 29.6 
 
 Combustible material . . . 
 
 13.0 
 
 12.0 
 
 13.0 
 
 10.0 
 
 9.0 
 
 9 
 
 70 
 
 Calcium carbonate 
 
 1.0 
 
 1.0 
 
 1.0 
 
 1.0 
 
 1.0 
 
 1.0 
 
 1.0 
 
 is impervious to water and is of high density and plasticity. For these reasons, 
 it is generally preferred for tunneling in hard rock. By the addition of dif- 
 ferent percentages of suitable absorbents the various grades of these dynamites 
 are made. 
 
 The compositions of gelatin dynamites generally offered for sale in this 
 country are given in the accompanying table. The combustible material 
 
 ANALYSES OF HIGH EXPLOSIVES 
 
 Constituent 
 
 40% 
 Strength 
 Low- 
 Freezing 
 Dynamite 
 
 40% 
 Straight 
 Nitro- 
 glycerin 
 Dynamite 
 
 40% 
 Strength 
 Ammonia 
 Dynamite 
 
 40% 
 Strength 
 Gelatin 
 Dynamite 
 
 
 1 13 
 
 .97 
 
 .88 
 
 1.47 
 
 Nitroglycerin 
 Nitrocellulose 
 Ammonium nitrate 
 
 27.56 
 10.13 
 
 39.19 
 
 21.60 
 18.86 
 
 30.70 
 .88 
 
 Sodium nitrate 
 
 51.54 
 8.52 
 
 49.53 
 9.77 
 
 46.04 
 5.45 
 
 54.27 
 8.58 
 
 
 
 
 4.85 
 
 3.08 
 
 
 
 
 .88 
 
 1.02 
 
 Calcium carbonate 
 
 1.12 
 
 .54 
 
 1.44 
 
 
670 
 
 EXPLOSIVES AND BLASTING 
 
 
 6 &' 
 
 qqqqqqqqqqq 
 
 qqqqqqqqqqq 
 
 1C iO 1C O 
 
 8 & 3 ^ 
 
 in the 60 and 70% strength 
 gelatin dynamite is wood 
 pulp. Sulphur, flour, wood 
 pulp, and sometimes resin 
 are used in other grades. 
 Some manufacturers replace 
 a small percentage of the ni- 
 trpglycerin in these explosives 
 with an equal amount of am- 
 monium nitrate. Ammonia- 
 gelatin dynamites have some- 
 what the same advantages 
 over straight gelatin dyna- 
 mites that ammonia dyna- 
 mites have over straight dy- 
 namites, except that they 
 are no slower in velocity of 
 detonation, but in certain 
 classes of work the fumes are 
 less objectionable. 
 
 Comparative Analyses. 
 The analyses on page 669 
 show the composition of the 
 four classes of high explosives, 
 each being rated as a 40% 
 dynamite. It will be noted 
 that the only one of these 
 analyses showingan approxi- 
 mate content of 40% of nitro- 
 glycerin is the straight dyna- 
 mite in the second column, 
 which is the basis of com- 
 parison. 
 
 Products of Combustion. 
 The analyses of mine air taken 
 at West Winfield, Pa., while 
 blasting operations were be- 
 ing carried on in the usual 
 way are given in the accom- 
 panying table. They are of 
 interest in showing that where 
 the ventilation is good, the 
 contamination of mine air by 
 the products of combustion 
 of high explosives is very 
 slight, even in the case of 
 straight dynamites which 
 yield a large amount of CO. 
 
 Dynamite is frequently 
 condemned for producing in- 
 jurious fumes, when, as a 
 matter of fact, these fumes 
 were made by the partial 
 burning of the dynamite be- 
 fore its explosion, the dyna- 
 mite having been lighted by 
 the fuse before the fare reached 
 the cap. An experienced per- 
 son can readily distinguish 
 between the fumes produced 
 by burning dynamite, and 
 those produced by detonation. 
 Comparative Strength of 
 Explosives. The following 
 table gives the^ relative 
 strengths of the different high 
 explosives as determined from 
 an extended series of tests 
 
EXPLOSIVES AND BLASTING 
 
 671 
 
 by the Bureau of Mines. In all cases 40% straight nitroglycerin dyna- 
 mite has been taken as the standard with a value of 100%. The relative 
 disruptive and propulsive effects here tabulated are shown graphically in the 
 accompanying figure. Disruptive effect indicated represents averages of 
 energies developed in the Trauzl lead-block, small lead block, and rate-of- 
 detonation tests; propulsive effect indicated represents averages of ballistic- 
 pendulum and pressure-gage tests. _ The figures given in this table are fairly 
 consistent with general practice, and it is believed that the classification will serve 
 
 RESULTS OF TESTS TO DETERMINE POTENTIAL ENERGY AND 
 DISRUPTIVE AND PROPULSIVE EFFECTS OF EXPLOSIVES 
 
 Class and Grade 
 
 Percentage 
 Strength 
 Represent- 
 
 Average 
 Percentage 
 Strength 
 Represent- 
 
 Average 
 Percentage 
 Strength 
 Represent- 
 
 
 Potential 
 Energy 
 
 ing^ 
 Disruptive 
 Effect 
 
 Propulsive 
 Effect 
 
 30% straight nitroglycerin dynamite . . 
 40% straight nitroglycerin dynamite. . 
 50% straight nitroglycerin dynamite . . 
 60% straight nitroglycerin dynamite. . 
 60% strength low-freezing dynamite . . 
 
 93.1 
 100.0 
 111.0 
 104.0 
 60.2 
 
 84.1 
 100.0 
 109.2 
 119.8 
 93.5 
 
 96.8 
 100.0 
 107.4 
 114.9 
 91.2 
 
 40% strength ammonia dynamite 
 
 101.8 
 
 67.9 
 
 99.1 
 
 40% strength gelatin dynamite 
 
 105.7 
 
 78.4 
 
 95.8 
 
 5% granulated nitroglycerin powder. . . 
 
 67.6 
 
 21.6 
 
 53.3 
 
 Black blasting powder 
 
 71.6 
 
 6.8 
 
 58.6 
 
 as a useful guide for comparing the practical value of explosives. It is worthy 
 of note that the potential energy of 40% strength ammonia dynamite and of 
 40% strength gelatin dynamite (that is, the theoretical maximum work that 
 these explosives can accomplish) is higher than that of 40% straight nitro- 
 glycerin dynamite, but that the disruptive and propulsive effects, which 
 represent the useful work done as shown by actual tests, are less than those 
 of 40% dynamite. While it is true that straight dynamites possess greater 
 
 EXPLOSIVE 
 
 ENERGY 
 
 Disruptive Effect, 
 Per Cent. 
 
 Propulsive Effect, 
 Per Cent. 
 
 20 30 40 50 60 70 80 flOWOIlO 
 
 Black powder (FFF) 
 
 5% granulated powder. . . 
 40% ammonia dynamite . . 
 
 40% gelatin dynamite 
 
 30% nitroglycerin dynamite 
 60% low-freezing dynamite 
 40% nitroglycerin dynamite 
 50% nitroglycerin dynamite 
 60% nitroglycerin dynamite 
 
 shattering effect than other standard types of explosives they are being rapidly 
 displaced by the ammonia and gelatine explosives on account of the greater 
 safety in handling characteristic of the latter. In hard, brittle rock, especially 
 in chambered holes, the straight dynamites are more effective than the slower 
 acting ones, but in softer rocks like sandstone, calcite, marl, etc., explosives of 
 
672 EXPLOSIVES AND BLASTING 
 
 the gelatin and ammonia types are very much more effective. Ordinary black 
 blasting powder has only about one-third of the disruptive effect of granulated 
 nitroglycerin powder. 
 
 EXPLOSIVES FOR COAL MINES 
 
 As the object in practically all coal mines is to obtain as large a proportion 
 of lump coal as possible, the quick-acting, powerful, high explosives are not 
 well adapted to use. In their stead, the slower acting low explosives are greatly 
 to be preferred. These coal mine explosives are of two general kinds: Black 
 powder and the so-called permissible powders. 
 
 Black powder is an excellent explosive, but, unfortunately, is not always 
 safe for coal mine use. Unless skilfully handled, its long flame is practically 
 certain to ignite dust or methane when more than a small amount of these is 
 present in the workings. 
 
 Permissible, or permitted, explosives have come into use in the United States 
 within the past few years, although they have has been used in Europe for 
 a much longer time. The original terms, flameless explosive and safety explosive 
 have been dropped for the ones given, as none of them is absolutely flameless 
 or absolutely safe. 
 
 In the United States, it is a function of the Bureau of Mines to determine 
 by tests what explosives are relatively safe under the dangerous conditions of 
 gas and dust prevailing in coal mines. 
 
 In determining this, the following rules are observed: The charge of 
 explosive to be fired in tests 1 and 2 shall be equal in deflective power to $ Ib. 
 (227 grams) of 40% nitroglycerin dynamite of the composition given on 
 page 669. Each charge shall be fired with an electric detonator, which will 
 completely explode the charge, as recommended by the manufacturer. In 
 order that the dust used in tests 2 and 3 may be of the same quality, it is 
 always taken from the same mine, ground to the same fineness, and used while 
 still fresh. 
 
 If a powder passes the three following tests made in the explosion gallery 
 of the Bureau's testing station, at Pittsburg, Pa., it may be placed upon the 
 list of permissible explosives. 
 
 Test 1. Ten shots each with the charge described, in its original wrapper, 
 shall be fired, each tamped with 1 Ib.* of clay stemming, at a gallery temperature 
 of 77 F., into a' mixture of gas and air containing 8% of gas (methane and 
 ethane). An explosive is considered to have passed the test if no one of the 
 ten shots ignites this mixture. 
 
 Test 2. Ten shots each with the charge described, in its original wrapper, 
 shall be fired, each tamped with 1 Ib.* of clay stemming, at a gallery temperature 
 of 77 P., into 40 Ib. of bituminous-coal dust, 20 Ib. of which is to be distributed 
 uniformly on a wooden bench placed in front of the cannon and 20 Ib. placed 
 on side shelves in sections 4, 5, and 6. An explosive is considered to have 
 passed the test if no one of the ten shots ignites this mixture. 
 
 Test 3. Five shots each with 1$ Ib. charge, in its original wrapper, shall 
 be fired without stemming, at a gallery temperature of 77 F., into a mixture 
 of gas and air containing 4% of gas (methane and ethane) and 20 Ib. of bitumi- 
 nous-coal dust, 18 Ib. of which is to be placed on shelves along the sides of 
 the first 20 ft. of the gallery and 2 Ib. to be so placed that it will be stirred up 
 by an air-current in such manner that all or part of it will be suspended in the 
 first division of the gallery. An explosive is considered to have passed the test 
 if no one of the five shots ignites this mixture. 
 
 Classes of Permissible Explosives. The following is the classification 
 of permissible explosives made by the Bureau of Mines: 
 
 Class 1. Ammonium-Nitrate Explosives. To Class 1 belong all the explo- 
 sives in which the characteristic material is ammonium nitrate. The class is 
 divided into two subclasses. Subclass a includes every ammonium-nitrate 
 explosive that contains a sensitizer that is itself an explosive. _ _ Subclass b 
 includes every ammonium-nitrate explosive that contains a sensitizer that is 
 not in itself an explosive. When fresh, these explosives, if properly detonated, 
 have the advantage of producing only small quantities of poisonous and 
 inflammable gases, and are adapted for mines that are not unusually wet, and 
 also for mines and working places that are not well ventilated. 
 
 Class 2. Hydrated Explosives. To Class 2 belong all explosives in which 
 salts containing water of crystallization are the characteristic materials. The 
 
 *Two Ib. of clay stemming is used with slow-burning explosives. 
 
EXPLOSIVES AND BLASTING 673 
 
 explosives of this class are somewhat similar in composition to the ordinary 
 low-grade dynamites, except that one or more salts containing water of crystal- 
 lization are added to reduce the flame temperature. They are easily detonated, 
 produce only small quantities of poisonous gases, and most of them can be used 
 successfully in damp working places. 
 
 Class 3. Organic Nitrate Explosives. To Class 3 belong all the explosives 
 in which the characteristic material is an organic nitrate other than nitro- 
 glycerin. The permissible explosives listed under class 3 are nitrostarch 
 explosives. They produce small quantities of poisonous gases on detonation. 
 
 Class 4- Nitroglycerin Explosives. To Class 4 belong all the explosives 
 in which the characteristic material is nitroglycerin. These explosives contain 
 free water or an excess of carbon, which is added to reduce the flame tempera- 
 ture. A few explosives of this class contain salts that reduce the strength 
 and shattering effect of the explosives on detonation. The nitroglycerin explo- 
 sives have the advantages of detonating easily and of not being readily affected 
 by moisture. On detonation some of them produce poisonous and inflammable 
 gases equal in quantity to those produced by black blasting powder, and for 
 this reason they should not be used in mines or working places that are not 
 well ventilated. 
 
 CARE OF EXPLOSIVES 
 
 Storing Explosives. Dynamite cartridges should always be laid on the 
 side and not stood on end, for in the latter position the nitroglycerin may ooze 
 out from the dope and collect in the bottom of the cartridge. Dynamite should 
 never be kept for any length of time (as in storage magazines) at a temperature 
 greater than 75 F. It should be stored in a dry place having a reasonably 
 uniform temperature. Magazines should be heated by means of hot-water 
 or exhaust-steam pipes, never by a stove or live-steam pipes. There should, 
 preferably, be two powder houses or magazines at a mine. The main maga- 
 zine, holding the stock of explosive on hand, should be built sufficiently far from 
 the plant or with some natural obstruction (such as a hill) between it and the 
 plant that its accidental explosion may not injure the miners' village or the 
 surface equipment. This magazine is commonly under the direct supervision 
 of some one of the higher officials and is usually opened only to receive sup- 
 plies in carload lots direct from the manufacturer and to withdraw the daily 
 amount required by the men. Near the mine mouth is a smaller magazine, 
 commonly called the powder house, to which the day's supply is taken from 
 the main magazine, and where it is handed out to the men individually. All 
 main magazines should be proof against high-power rifle bullets fired at short 
 range. Storing explosives in large quantities in a mine is a bad and dangerous 
 practice and in most states is prohibited by law. 
 
 The effect of storing fuse for several days at temperatures much above or 
 below the normal is to greatly retard its rate of burning; commonly to the 
 extent of 50% or more. It follows that fuse should not be stored in too warm 
 a place as over boilers and steam pipes in winter, or in a tin box exposed to the 
 direct rays of the sun in summer, nor should it be left in an unheated tool 
 house when the temperature is much below the freezing point. Fuse is 
 extremely difficult to dry out after wetting, and, as a general rule, fuse that 
 has been stored in damp places or has in any way become wet should not be 
 used in mining. 
 
 Thawing Dynamite. Dynamite freezes at about 45 F., and when solidly 
 frozen it is exploded with difficulty, and if it is exploded the detonation is 
 only partial. It is dangerous to cut, break, or ram a frozen dynamite cart- 
 ridge, as the frozen nitroglycerin crystals may explode. No attempt should 
 be made to explode dynamite that has been frozen until it has been thoroughly 
 thawed and is soft and plastic ; many accidents occur through failure to observe 
 this precaution. If incomplete detonation occurs, unexploded powder is often 
 found in the holes or in the material blown down by the shot. 
 
 In cold weather, the cartridges should not be taken to the place where they 
 are to be used until all the holes are ready to be loaded, and all cartridges 
 should be soft and warm when charged into the holes. Dynamite that has been 
 chilled, but not frozen, looses a large part of its efficiency. Many instances 
 are on record in which some of the holes of a blast were loaded with warm, 
 and others with frozen, or partially frozen, dynamite; the dynamite that had 
 been warmed exploded and that which was frozen did not, and miners have 
 subsequently been killed or injured by drilling into these misshots. 
 
 43 
 
674 EXPLOSIVES AND BLASTING 
 
 When thawing dynamite, it is necessary to use caution to keep the tempera- 
 ture from rising very high, as each degree rise is that much nearer the danger 
 limit where extreme sensitiveness to shock prevails. The thawing of dynamite 
 by placing it in a tight box surrounded by manure is a good method if the 
 manure is fresh so that it is giving off heat. Dynamite should never be thawed 
 before an open fire, on a shovel, in a tin can, or in an oven, for, while dynamite 
 will very frequently burn in the open and when unconfined, it very often 
 explodes. Also, it should never be thawed by immersion in hot water as that 
 has a tendency to leach out the nitroglycerin and make it dangerous. The 
 common practice of thawing dynamite cartridges by passing them through 
 an oven or over a lighted candle is very dangerous. 
 
 When dynamite is being used on a large scale during the winter, it is well 
 to provide a special thawing room, in which 1 or 2 days' supply can be kept 
 ready for use. The room need not be of great size, say 12 ft.X16 ft. The 
 powder needed for the day's consumption can be carried in during the after- 
 noon and left over night, the boxes simply being opened or the explosive taken 
 out and put on shelves, the procedure depending on the time available. A 
 thermometer should be consulted to insure that the temperature does not rise 
 above 85 and is preferably kept between 75 and 80 F. If a brick or stone 
 vault is made below the surface and tightly roofed over and banked with earth, 
 dynamite may be kept in it all winter without freezing. 
 
 For handling smaller quantities of frozen dynamite, special thawing kettles 
 are used to advantage. One device consists of a metal can having tubes that 
 pass through it. The tubes are surrounded by water, and the whole so arranged 
 that a miner's lamp or candle may be placed underneath the can to keep the 
 water warm. When in use, the tubes are filled with sticks of dynamite, the 
 space surrounding them is filled with water, and the cover slipped over so 
 that the cartridges cannot fall out of the tubes. A lamp or candle placed 
 under the can will soon heat the water sufficiently to thaw out the cartridges. 
 These thawers, being portable, are very convenient and, filled with hot water, 
 will keep dynamite in good condition for some time without being artificially 
 heated. It is, however, of great importance that the water -receptacle should 
 always contain water, otherwise an explosion may occur. A double thawing 
 kettle commonly used consists of an outer kettle standing on legs and an 
 inner kettle, which is held up by a bead around the edge, in which the cartridges 
 are placed. 
 
 Handling Explosives. While the dangerous practice still prevails to some 
 extent of daily opening the main magazine and there handing out to the men 
 all the explosives they may demand, this method has been very largely super- 
 seded by the much safer plan of taking the estimated total daily mine con- 
 sumption to the small powder house near the opening where only enough for 
 the day's work is given each miner. The amount of explosive is charged to the 
 men either from entries made by the person in charge of the powder house 
 or from written orders or receipts given by the men themselves. At some 
 mines, the men purchase in advance several dollars' worth of so-called powder 
 checks, which are pieces of metal stamped with a number of value (12J c., 
 25 c., 50 c., etc.) and which may be exchanged at the powder house for explo- 
 sives and other blasting supplies. After the men have taken their require- 
 ments, the explosive remaining is commonly returned to the main magazine, 
 although this may not be done until late in the afternoon for fear it may be 
 needed. 
 
 The amount of explosive that a miner may have in his possession or carry 
 into the mine at one time is commonly regulated by law. In rare instances 
 there is no limit placed upon this amount, although a miner will seldom carry 
 in more than a single keg of 25 Ib. Where there is a limit, a keg is purchased, 
 but is kept in the magazine, and from it the miner draws his daily allowance of 
 from 5 to 10 Ib., which he carries to his working place in a metal canister, 
 preferably of copper. Where permissible powders are used, a day's supply 
 should not exceed 5 Ib., as this amount of powder exploded in properly placed 
 holes will, in a seam of average thickness and when undercut as it should 
 be, bring down all the coal a man can load out on one shift. 
 
 t It is a dangerous practice to carry large metal cans of black powder into the 
 mine upon the shoulder or in mine cars where electric wires charged with current 
 are strung along the roadway. Cars in which powder is being transported 
 should be hauled by mules when the current is shut off the wires. At the 
 working face, the powder can should be stored in a wooden box separate from 
 the caps and fuse. The box should be kept locked when not in use and should 
 be placed some 100 ft. from the face and 25 ft, from the track if this is possible. 
 
EXPLOSIVES AND BLASTING 675 
 
 Where shot-firers are employed who charge the holes, the mine is commonly 
 divided into a series of districts of a size that two men can charge and fire all 
 the holes therein in a reasonable time. The explosives estimated to be enough 
 for the various districts are placed in separate boxes at the main magazine, 
 conveyed to the nearest point to where they are to be used in a car hauled by a 
 mule, and are there unloaded by the district shot-firer and his helper. 
 
 Precautions When Handling Coal-Mining Explosives. The Bureau of 
 Mines suggests that the following precautions should be observed in handling 
 black powder: 
 
 Never open a metal keg of powder with a pick or metal object; use the 
 opening provided by the manufacturer of the keg. 
 
 Never make up charges or handle cartridges or powder with an open light 
 on the head; place the light at least 5 ft. away on the return-air side so that 
 sparks from it will not fall into the powder. 
 
 Never allow powder or other explosive to remain exposed; keep it in a well- 
 locked box at least 100 ft. from the working face and in an unfrequented place. 
 
 Never go nearer than 5 ft. to a powder box or powder when wearing an open 
 light or when smoking. 
 
 Never use coal slack or coal spalls for stemming; it is dangerous. Use 
 moistened clay, wet wood pulp, or other noninflammable material; even wet 
 coal slack may, under some circumstances, cause an explosion. 
 
 Never withdraw a shot that has missed fire; drill a fresh hole at least 2 ft. 
 from it but parallel to the old hole and fire this new hole. After the shot a 
 careful search should be made for the unexploded charge to prevent its being 
 struck by a pick and perhaps causing an explosion. 
 
 Never fire the hole the second time; if the first charge proves useless powder 
 and labor are wasted in loading the hole a second time. Moreover, the first 
 shot often cracks the coal so much that the second shot has a chance to blow 
 out of the cracks, and thus a blown-out shot may result. 
 
 Never use iron or steel tampers or needles; have at least 6 in. of hard-drawn 
 copper on the tamping end of the bar or, better still, use a hardwood tamping 
 stick. The needle should be made entirely of hard-drawn copper. 
 
 Never tamp shots with an iron or steel scraper and do not push a cartridge 
 into the drill hole with the scraper; the scraper rod should be tipped with at 
 least 6 in. of brass or copper on the scraping end. 
 
 Never allow the point of the coal auger to become dull or to become of less 
 than the standard gauge, so that a drill hole may be made with it into which 
 the cartridge may always be pushed freely. 
 
 Never drill a hole past the loose end, chance, or cutting in solid shooting; 
 if the coal has been undercut, do not drill beyond the undercutting. It is better 
 to stop at least 6 in. short of the solid coal. 
 
 Never bore gripping holes ; keep the holes parallel to the ribs or as nearly so 
 as possible. Use the side gear on the machine if you can when boring a hole. 
 
 Never guess at the quantity of powder to be used; always measure it. This 
 course is cheaper and better than guessing. Use cartridges rather than loose 
 powder and make them of cartridge paper. Don't use newspaper for cart- 
 ridge making. 
 
 Never place black blasting powder in the same drill hole with dynamite 
 or a permissible explosive. 
 
 Never use short fuse; always have the fuse long enough to stick out at 
 least 2 in. from the mouth of the drill hole. When the short fuse is lit any 
 gas in the hole may be ignited, and this may result in a premature blast. 
 
 Never bite a piece of the match off the squib, nor oil it to make it burn 
 faster. 
 
 Never use sulphur and gas squibs at the same working face. 
 
 Never light two or more shots at the same time. 
 
 Never fire shots in adjoining working faces at the same time. 
 
 Never return to a shot that has failed to explode until at least 10 min. after 
 lighting it, if squibs were used, or 12 hr. after lighting if fuse was used. When 
 shots are fired electrically be sure that all wires are disconnected from the 
 battery, and wait at least 5 min. before returning to the face. 
 
 Never fire a rib or butt shot before a center or busting shot is fired; the 
 opening shots should be fired first, in order to give the succeeding shots a chance 
 to do their work. 
 
 Never drill a hole near the remaining portion of a former shot, nor near 
 cracks and fissures made by previous shots, because there is great danger of 
 the powder gases on explosion flying out of the loose coal or the cracks and 
 igniting gas or dust in the mine air. 
 
676 EXPLOSIVES AND BLASTING 
 
 Never use squibs or any kind of fuse, except electric fuse, in mines that 
 make inflammable gases. 
 
 Never fire a shot without making sure that the coal dust near by is well 
 wet down. 
 
 Never light a dependent shot at the same time as another shot, and never 
 fire a dependent shot until the first shot has broken properly. 
 
 Never fire a split shot; that is, never fire a hole that has been drilled into a 
 mass of coal, cracked and shattered by a previous shot that failed to dislodge 
 the coal. 
 
 The following additional precautions are to be observed in handling per- 
 missible explosives: 
 
 Never take more than 1 da. supply of permissible explosives into the mine 
 at one time. 
 
 Never leave permissible explosives in the mine over night. 
 
 Never purchase permissible explosives not suited to the coal bed. 
 
 Never use weak detonators. 
 
 Never fire a charge until it has been completely and carefully tamped. 
 
 Never put black blasting powder and permissible explosives together in 
 the same drill hole. 
 
 Never break the covering of a cartridge of a permissible explosive until 
 ready to charge. 
 
 Never expect permissible explosives to yield entirely satisfactory results 
 when coal is blasted off the solid. 
 
 Never expect the first blast with permissible explosives in a newly opened 
 coal bed to be satisfactory. Several trials are often required before satis- 
 factory results are obtained. 
 
 Never forget that permissible explosives are different from dynamite and 
 entirely unlike black blasting powder. 
 
 Never use fuse to fire permissible explosives when it is possible to use 
 electric firing. 
 
 FIRING EXPLOSIVES 
 
 MEANS OF FIRING LOW EXPLOSIVES 
 
 Ordinary black blasting powder may be ignited by means of squibs, fuse, 
 and electric squibs. High explosives, including permissible powders, are fired 
 with fuse and caps, or, preferably, by means of electricity, and by means of an 
 electric detonator; in the latter case the current is derived either from a battery 
 or from a dynamo. Fuse and caps are commonly employed for firing single 
 holes, and electric firing is used where several holes are fired at once, or in a 
 volley, although portable electric blasting machines (formerly called batteries) 
 are to be preferred even for firing single holes. 
 
 Squibs. A squib (sometimes known as a match, reed, rush, spire, etc.) 
 consists of a small paper tube that is filled with quick-burning powder and 
 has a slow match attached at one end. The burning of the slow match gives 
 the miner time to get to a place of safety between the time that he lights the 
 match and the time that the flame reaches the quick powder. When the 
 quick powder is ignited by the burning match, the squib shoots like a rocket 
 through the hole that has been left in the tamping by the withdrawal of the 
 needle into the blasting powder. Two kinds of squibs are in general use, 
 gas squibs and sulphur squibs. In the gas squib, the match end is impregnated 
 with a composition that does not flame when burning but glows throughout 
 its length, and, for this reason, is supposed to be safe in an explosive mixture 
 of methane and air. In the sulphur squib, the match end is dipped in sulphur 
 and burns with a flame and somewhat faster than a gas squib. Since, in the 
 rocket-like action that is necessary to propel the squib into the charge, large 
 volumes of sparks are given off, neither type of squib can be safe in explosive 
 atmospheres. 
 
 Fuse. Fuse, sometimes called safely fuse or Bickford's fuse, from its 
 inventor, consists essentially of a central core of fine-grained gunpowder 
 wrapped about by threads of hemp, jute, or cotton. These threads are wound 
 in two sets, the inner being known as the spinning threads and the outer as 
 the counter-threads or, simply^ countering. In single-tape fuse, the threads 
 are wound with tape and then coated with tar and covered with fuller's earth 
 or powdered talp to prevent sticking. Double-tape fuse is single-tape fuse 
 wound with a second layer of tape, which is also tarred and powdered. Cotton 
 or hemp fuse, not tape wound, is made, but is only suitable for use in absolutely 
 
EXPLOSIVES AND BLASTING 677 
 
 dry places and in hot climates. In cold countries, fuse covered with tar is apt 
 to crack and thus become wet and misfire, while in hot countries it becomes 
 sticky and unfit for use. For these reasons special fuses are manufactured 
 for use in either arctic or tropical regions. For use under water, gutta-percha 
 covered fuse has been made. 
 
 According to the work in which it is intended to be used, fuse may be 
 divided into four classes. Fuse of the first class is suitable for dry work such 
 as stump blasting and quarrying; it is usually untaped hemp and cotton fuse. 
 Fuse of the second class is intended for damp work, as in coal mining, or. in 
 surface work where mud, rain, or dampness is encountered; it is commonly of 
 the single tape variety. Fuse of the third class is suitable for very wet work, 
 such as tunneling, shaft-sinking, etc. Fuse of the fourth class is designed for 
 submarine work; double- tape, triple-tape, gutta-percha, and taped double- 
 countered fuse belong to these classes. Owing to the large amount of car- 
 bonaceous material in the wrappings of fuse, the gases produced by its burning 
 contain a large proportion of carbon monoxide, CO. Where numerous coils 
 of fuse have caught fire and burned,. as has happened in magazines and in the 
 rooms of poorly ventilated mines, the gases evolved have been found to be 
 particularly suffocating and poisonous. 
 
 The rate of burning of the better grades of American fuse has been deter- 
 mined by the Bureau of Mines to be very nearly 30 sec, per ft. of length, with 
 a variation of some 10% either way. 
 
 Electric Squibs. F9r use with black blasting powder only, electric squibs 
 are made. They are similar to electric blasting caps in appearance, but the 
 cap is made of paper instead of copper and the charge does not detonate but 
 shoots out a small flame. They are made with iron wires 4, 5, 6, or 8 ft. long, 
 and with copper wires of the same lengths as well as 10 and 12 ft. The wires 
 are insulated and the space between them in the squib is bridged with fine 
 platinum .wire, which glows when the electric current is applied and furnishes 
 enough heat to ignite the powder. They are designed to ignite the powder at 
 the center of the charge, something that is obviously impossible with the 
 ordinary paper squib. 
 
 MEANS OF FIRING HIGH EXPLOSIVES 
 
 Fuse and Caps. Dynamite and other detonating explosives, including 
 permissible powders, may be fired by means of detonators or caps, but are best 
 exploded by means of electric detonators of the strength prescribed for each 
 one. Caps, blasting caps, detonators, or exploders, as they are variously called, 
 consist of copper capsules, about as thick as an ordinary lead pencil, that are 
 commonly charged with dry mercury fulminate or with a mixture of dry mer- 
 cury fulminate and potassium chlorate that is compressed in the bottom of 
 the capsule, filling it to about one-third its length. Several grades of these 
 detonators are on the market, and they are differently designated by different 
 manufacturers. A strong detonator is essential to securing the perfect explo- 
 sion of permissible powders, etc., and for this purpose those of No. 6 strength, 
 containing 15.4 gr. of charge, are recommended. Fulminate of mercury is 
 extremely sensitive to heat, friction, and blows, and for these reasons blasting 
 caps should be handled with as much care as dynamite, or a violent explosion 
 may result. 
 
 The following precautions are recommended in handling them: 
 
 Never attempt to pick out any of the composition. 
 
 Do not drop caps or strike them with anything hard. 
 
 Do not step upon caps or place them where they may be stepped upon. 
 
 When crimping caps on to the fuse, take care not to squeeze the fulminate, 
 and never crimp with the teeth. 
 
 Caps should be stored in a dry place and in a separate building from any 
 other explosives. 
 
 Caps should not be carried into the mine with other explosives, or placed 
 near other explosives except 
 in a bore hole. 
 
 Electric Detonators. 
 To overcome the dangers 
 incident to the use of fuse 
 and squibs, electric deto- 
 nators (also called electric blasting caps) have been devised. These are 
 simply ordinary detonators that have been fitted with the means of firing 
 them with the electric current. This is done, as shown in the accom- 
 panying figure, by inserting within the caps two copper wires d, joined 
 
678 EXPLOSIVES AND BLASTING 
 
 at the inner ends by an extremely fine platinum or other high-resistance 
 wire e, which becomes heated until it glows when an electric current is passed 
 through it. This wire, known as the bridge, is set within the fulminate b, 
 above which is placed a composition / designed to hold the wires more firmly 
 in place. The space above is filled and closed by means of a plug of sulphur 
 or other waterproof composition which is poured in while soft and which is 
 held in place by means of the corrugation a, in the shell of the cap. The copper 
 wires c beyond the cap are called legs or wires and are insulated, and come in 
 lengths of 4 ft. increasing by 2 ft. to 30 ft. For firing charges of permissible 
 powder or high explosives, the detonator used should be at least a No. 6 (double 
 strength) with 15.4 gr. of fulminate. The precautions to be used in handling 
 blasting caps apply with equal force to electric detonators. Heavy jars are 
 particularly to be avoided as they may break the delicate bridge wire; and 
 when this is broken the detonator is worthless. The wires must not be bent 
 sharply or forcibly separated at the point where they enter the copper cap, 
 as this may break or loosen the filling material and permit water to enter and 
 damage the charge. 
 
 Delay-Action Detonators. In some kinds of blasting, particularly in tunnel 
 work and shaft sinking, it is necessary to blast the holes in sets or rounds, and 
 it is a saving in time and adds to the safety of the operations if it will not be 
 necessary for the men to return to the face, after the first round has been fired, 
 in order to light the fuses in the second and subsequent rounds. This firing 
 of the holes in sequence, or rounds, when fuse is used is accomplished by cut- 
 ting the fuse to different lengths (assuming that it all has the same rate of 
 burning per foot) and lighting all the holes as nearly as may be at the same 
 time; the holes exploding in the order of the length of the fuse used. When 
 electric firing is employed, the same result is accomplished with one application 
 of the electric current by means of what are known as no-delay, first-delay, and 
 second-delay, electric blasting caps. No-delay caps detonate at the instant the 
 electric current passes through them. The first- and second-delay caps contain 
 a slow-burning substance, which is ignited by the electric spark and which, 
 after burning a short time, ignites the detonating composition below it. It is 
 impossible from a commercial standpoint, to make the rate of burning of this 
 slow-burning composition absolutely uniform and, consequently, delay-action 
 detonators in the same circuit may not all explode at exactly the same instant. 
 On the other hand, there is always a distinct time interval between the explo- 
 sion of the no-delay caps and the quickest of the first-delay, and between the 
 slowest of the first-delay and the quickest of the second-delay. These delay- 
 action detonators are commonly made in the No. 6, or double strength, grade 
 only. . : m . :[: 
 
 CHARGING AND FIRING EXPLOSIVES WITH SQUIBS OR WITH CAP 
 AND FUSE 
 
 Charging Black Powder and Firing With Squib. Black powder (blasting 
 powder) is used in paper cases or cartridges, which are made and filled by the 
 miner at the face and which are of slightly less diameter than the drill holes, 
 in the bottom of which they are placed. If the hole is dry, these cartridges 
 may be tamped hard enough to break the cartridge paper so that the powder 
 will pack closely and fill all spaces, for the closer the powder is packed in the 
 hole the greater will be the effect produced by the blast. In putting paper 
 cartridges into holes, care should be taken not to break the paper until the 
 bottom of the hole is reached. In case the hole is in seamy rock, a ball of clay 
 is first put in the hole and then a clay bar driven into it, to spread it out and 
 fill all crevices. If these crevices are not filled, the gases due to the explosion 
 escape through them and much of the force of the explosive is lost. The clay 
 bar is a good hickory or oak stick with a slightly pointed iron shoe at one end, 
 or is an iron bar pointed at one end with an eye at the other for removal from 
 the hole. To make the hole round, after using the clay bar, an auger may be 
 turned in the hole and the surplus clay removed. Should the hole be wet, 
 the same method of claying is followed, but the cartridges are well coated with 
 miners soap and not tamped so hard as to break them. 
 
 The needle, which is a copper rod about i in. in diameter pointed at one 
 end and provided with a handle at the other, is run into the cartridge, and about 
 it the tamping is rammed in by means of a tamping bar, which has a groove 
 through the head to accommodate the needle. The tamping bar is commonly 
 of iron with a copper head of a diameter a little less than that of the drill hole. 
 Where cartridges are not used and powder is charged in bulk, the tamping bar 
 is made entirely of copper, since if iron comes in contact with rock or pyrites 
 
EXPLOSIVES AND BLASTING 
 
 679 
 
 it is apt to strike a spark and cause a premature explosion if loose powder is 
 sticking to the sides of the hole. The danger from the use of metal tamping 
 bars has been recognized in some states and their employment wisely pro- 
 hibited by law. The tamping or stemming is put in and tamped little by 
 little, being rammed hard to keep the needle hole open when the needle is 
 removed. 
 
 In anthracite mines, the blasting barrel is often used instead of the needle, 
 as tamping fine enough to pack is not obtainable unless the miner pounds up 
 slate and coal. The blasting barrel is a steel or wrought-iron tube of about 
 \ in. inside diameter; one end is inserted in the cartridge ^and the squib is fired, 
 through it to the powder. The rammer fits over the blasting barrel in the same* 
 way as over the needle. The blasting barrel is valuable where the tamping 
 is damp or the hole slightly wet, but after each shot is fired it has to be recovered 
 and if used again must be straightened. 
 
 The squib is inserted in the needle hole or blasting barrel with the match 
 end outwards and after igniting the extreme end of the match with his lamp, 
 the miner hastens to a place of safety. The practice of biting or breaking off 
 the end of a squib, or unrolling it, or dipping it in oil in order to hasten its 
 burning is extremely dangerous and is almost sure to result in a premature 
 explosion. 
 
 Firing Black Powder With Fuse and Cap. After cutting off, with a sharp 
 knife, 1 or 2 in. of the fuse in order that the portion about to be used is dry and 
 in good condition, the detonator (cap) is slipped over the end and is crimped 
 tightly in place by a form of pliers or 
 pincers known as a crimper. The cap 
 should never be crimped on the fuse 
 with the teeth as an explosion may 
 result, and the cap contains enough 
 fulminate to blow off a man's head. 
 When placing the cap in the cartridge, 
 there is great diversity of opinion as to 
 which of the many ways used is the 
 best. Fig. 1 shows a very common 
 method in which the cap is placed in 
 the top of the cartridge and in the 
 center with only about two-thirds of 
 the cap embedded in the material of 
 
 the cartridge. This is done to avoid the danger of its igniting the explosive 
 and thus causing deflagration of the cartridge in place of detonation. An 
 objection to a cap placed in the center of the cartridge is that the fuse is 
 very apt to be bent and injured in the tamping, while it also interferes with 
 the tamping. 
 
 Instead of placing the cap in the center of 
 the end of the cartridge and tying the end of 
 the paper wrapper about the fuse, an inclined 
 hole is made in the end of the cartridge, as 
 shown in Fig. 2, and the cap placed deep down 
 in the charge. Instead of inserting the cap 
 through the end of the cartridge, many manu- 
 facturers of explosives strongly recommend 
 placing it in a hole in the side, as shown in 
 Fig. 3. The fuse is tied in two places, a half 
 hitch being taken around it. 
 
 A common, but bad, practice among miners 
 is to make a hole in the side of a cartridge, 
 place the cap and fuse in it, and bend back 
 the fuse, as shown in Fig. 4 in order to prevent 
 the cap being pulled out. The sharp bend in 
 the fuse is sometimes sufficient to cause a break 
 in the train of powder, resulting in a misfire. 
 
 If the length of the cap is greater than the 
 diameter of the cartridge and it is stuck through 
 FIG. 2 FIG. 3 FIG. 4 the side either diagonally -or straight across, 
 
 there is danger of its being jammed against the 
 
 side of the hole when tamping, and thus cause a premature explosion. Care 
 must be taken to insure that that portion of the cap which contains the fulmi- 
 nate is entirely within the charge; otherwise, the detonation of the explosive 
 will be imperfect. 
 
680 
 
 EXPLOSIVES AND BLASTING 
 
 When tamping holes to be fired with fuse, hard bits of rock or slate mixed 
 with the stemming may cut the fuse and cause a misfire, or the fuse may be 
 kinked by a hump in the hole and thus cause either a misfire or a delayed shot. 
 In order to use fuse with entire safety, it should be long enough and should 
 be run through a blasting barrel. In gaseous mines, it is extremely important 
 that the fuse extend beyond the end of the hole, for if it does not, when such a 
 fuse is lighted any gas in the untamped part of the drill hole is certain to be set 
 on fire at the same time and a premature explosion will follow. 
 
 If the work is wet, waterproof fuse should be used, the end of which should 
 be protected by applying bar soap, pitch, or tallow around the edge of the cap 
 where the fuse enters it. 
 
 Charging and Firing Dynamite With Cap and Fuse. Blasting powder is 
 commonly charged into the drill hole in one large cartridge, whereas dynamite 
 and other high explosives, including permissible powders, are charged as a num- 
 ber of single and much smaller cartridges. When loading a hole with explosives 
 of the latter type, the cartridges are placed in one after another and pressed, 
 not rammed, into place with a wooden bar. If the cartridges at hand are 
 less than the required size, the paper coverings may be split open with a knife 
 and the explosive forced to fill the hole with the aid of the tamping bar. It is 
 very important, if the full effect of the explosive is to be obtained, that the part 
 of the hole in which the charge is located is completely filled, and that no air 
 spaces are left between the charge and the walls of the hole. 
 
 The cartridge containing the cap is called the primer, and while it is usually 
 the last or next to the last cartridge to be placed in the hole, it may be placed 
 in the middle of, or even at the bottom of the charge, with the idea of insuring 
 a more thorough explosion. This is theoretically correct, as the explosion acts 
 equally in all directions, but while there may be some reason for firing a charge 
 with black powder in this manner, there is no good reason for such practice 
 when firing dynamite, except when firing holes consecutively, for the explosion 
 of dynamite is so quick that there is no appreciable difference in the result, 
 whether the cap is placed in the top or in the middle of the charge. There is, 
 however, a decided objection to placing the cap in the middle or bottom of the 
 charge when using common fuse, as there is a chance that the fuse will set fire 
 to the dynamite and cause not only a loss of dynamite, but a premature explo- 
 sion, which cannot be as thorough as if detonated by the cap. The primed 
 cartridge is pressed down until it rests on 
 those already placed, and, after the car- 
 tridges are all pressed into place, the 
 tamping is pressed lightly on the charge, 
 care being taken not to explode the primer. 
 Fig. 5 (a) shows a hole with the primer 
 placed in the center of the charge and in 
 which there is no bend in the fuse, a theo- 
 retical arrangement seldom found in prac- 
 tice. View (b) shows a common method 
 of placing a charge with the primer on top 
 and the cap placed in the side of the cart- 
 ridge as illustrated in Fig. 3. 
 
 Precautions When Tamping Explosives. 
 Before any shots are fired in a bituminous 
 coal mine, the dust made by the augers 
 should be scraped from the shot holes and, 
 with the bug dust made by mining ma- 
 chines, should be loaded into tight cars and 
 hauled outside. This is to prevent the pos- 
 sibility of a dust explosion either in the 
 hole or in the bug dust immediately at the 
 face. As the loading out of the dust throws 
 considerable of the finest, and consequently 
 most dangerous, particles into the air, some time, say hr., should elapse after 
 this loading out is done before shots are fired. In very dusty mines, the face 
 should be wet down with a hose or a liberal application of shale dust made 
 before shots are fired. The material used for tamping should be of fine and uni- 
 form grain that it may be packed tightly and should not contain any substances, 
 such as grains of quartz, pyrites, etc., that may strike fire while being rammed 
 home. The depth of the stemming should be at least one-half that of the .drill 
 hole, and it should completely fill the hole from the explosive to the mouth. 
 Under no circumstances whatsoever should slack or bug dust from bituminous 
 
 p IG 5 
 
EXPLOSIVES AND BLASTING 
 
 681 
 
 coal be used for tamping. Moist clay or brick dust sufficiently moistened to 
 make it adhere form the best of tamping materials. Suitable stemming 
 may be had by grinding and screening clay or shale rock, by digging it from ' 
 a bank on the surface, or from the fireclay floor of the seam. The stemming 
 is usually distributed in quantity by the company men after working hours, 
 being left in a pile at the mouth of each entry or, more rarely, at the mouth 
 of each room. For use, the miner makes the material into cartridges of the 
 same diameter as those containing powder but only about 10 in. long. Where 
 shot firers do the charging, the miner commonly makes and leaves at the face 
 beneath each shot hole a sufficient number of these dobe, or dummy, cartridges 
 to supply the tamping. Holes of large diameter require a proportionally greater 
 length of tamping than smaller holes. The tamping should be rammed solid, 
 in order to diminish the risk of a blown-out shot and to confine the powder 
 tightly, that it may do its full work. 
 
 High explosives of the nitroglycerin type, which develop their full power 
 instantaneously, usually require less tamping than powder, although the best 
 results from their use are obtained by thorough tamping. The experiments of 
 the Bureau of Mines prove that in the case of high explosives when the weight 
 of the tamping is about that of the charge, the efficiency or work done by 
 them is increased from 60 to nearly 80%, depending on the kind of stemming 
 and the way it is used. While in deep downward-pitching holes, water makes 
 a fair tamping, fine sand, clay, etc., are preferable and are generally used. 
 The first 5 or 6 in. above the charge is filled in carefully so as not to displace 
 the cap and primer; and then with a wooden rammer the balance of the 
 stemming is packed in as solidly as possible, ramming with the hand alone, 
 and not using any form of hammer. 
 
 FIRING EXPLOSIVES BY ELECTRICITY 
 
 Charging for Electric Firing. Figs. 1 and 2 illustrate the method of placing 
 an electric exploder, or cap, in a cartridge of dynamite. The cap a is placed 
 either in the bottom or at the side of the cartridge, the hole to receive it having 
 been made with a sharp stick or lead pencil. The best practice is to place 
 the detonator so that it points to the bulk of the charge. 
 After this is accomplished, the blasting wires b are tied 
 firmly to the cartridge, as illustrated at c. In firing 
 dynamite by means of electricity, there is no danger 
 of the wires setting fire to the powder, and hence the 
 exploder can be placed well down in the cartridge. 
 Sometimes, when a long charge in a very deep hole is 
 to be fired, two or more electric exploders are used in 
 the same charge, one cartridge containing an exploder 
 being placed near the bottom of the hole and another 
 at the top. The method of loading holes for firing by 
 electricity is the same as that described for firing with 
 fuses. As much care as possible should be taken to 
 prevent the leading wires from coming in contact with 
 the damp earth, also that in tamping the hole the wires 
 do not become broken, or the covering materially 
 injured, and that the wires are not brought into con- _^_ 
 tact with each other or with the damp ground. _ _ _, 
 
 Many miners have a bad practice of putting the cap * IG - * 
 of an electric exploder in obliquely and bending the wire over and securing the 
 cap by a half hitch of the wire, as shown in Fig. 3, or, to make it worse, by 
 two half hitches. So much force is used in making the half hitch that there 
 is danger of a short-circuit being formed, or the sulphur filling in the electric 
 cap may be broken, sometimes disarranging the wires in the cap and even 
 breaking the fine platinum wire or bridge. In any event, the cement is so broken 
 as to leave free passage into the cap of any water that may be contained in 
 the hole. The platinum bridge of an electric cap is very small and delicate 
 in order to be heated red hot by the very small current of electricity that is 
 used to fire the cap, and any unusual strain on the wires may break the bridge, 
 thus breaking the circuit and causing a failure of the shot. Furthermore, 
 sharp bending of the copper wires may damage the insulation, very likely 
 leaving bare wires touching, causing a short circuit and a failure of that par- 
 ticular cap. The bared wires, even if they do not touch, offer an opportunity 
 for a short circuit through any moisture present, which will rob that particu- 
 lar cap of part of the current of electricity, while the next cap might get the 
 full current. The result will be that the first cap will miss fire. 
 
682 
 
 EXPLOSIVES AND BLASTING 
 
 Shot Firing With the Electric Blasting Machine. <)ne method of electric 
 blasting, as used in America, depends on the generation of a current of elec- 
 tricity by means of a small electric machine, which 
 is really a small dynamo, the armature of which 
 is made to revolve rapidly between the poles of the 
 field magnets by means of a crank or by a ratchet. 
 The machine, commonly, but incorrectly, called a 
 battery, is shown in Fig. 4. It consists of a field 
 magnet a and an armature b that revolves between 
 the poles of the field magnet. The loose pinion 
 c (the teeth of which engage the rack bar d) is 
 arranged with a clutch, so that as the rack bar 
 descends the pinion causes the armature b to 
 rotate and generate a current. During the down- 
 ward stroke of the rack bar, the connections are 
 such that the current flows inside the machine 
 without affecting the outside circuit. The current 
 increases in strength until the rack bar strikes the 
 spring e, which changes the connections so as to 
 send the full strength of the current into the out- 
 side circuit and through the caps for firing the 
 blasts. When more than one shot is fired at a time 
 by means of a blasting machine the holes should 
 be connected in series. Blasting machines are also 
 called push-down machines and are rated by the 
 number of electric detonators they can explode, as 
 4-hole machines, 50-hole machines, etc. 
 
 Connecting Wires. To connect the ends of two 
 wires, scrape off the insulation for about 2 in. from 
 each end and scrape the wires clean and bright. 
 Then twist the ends together, as shown in Fig. 5. 
 
 FIG. 4 
 
 FIG. 5 
 
 It is very important, to prevent misfires, that all connections are clean and 
 well made, as one bad connection may cause all the holes to misfire. 
 
 Connecting Up and Firing the Blasts. After the holes have been loaded, 
 the fuse wires are left projecting from the holes, and are joined by connecting 
 wires in such a manner as to leave one free wire at each end of the series to be 
 fired, as at b, Fig. 6, the fuse wires a leading downwards to the charges to be fired. 
 After all is in readiness, the 
 leading wires are connected to 
 the loose ends b, and when 
 every one has left the vicinity 
 of the blast, the other ends of 
 the lead wires or cables are 
 attached to the blasting ma- 
 chine. Some blasting machines 
 are provided with three 
 screws on the outside, to which leading wires are attached. When only a 
 small number of blasts are to be fired, one of the lead wires is attached to the 
 middle screw and the other to the outside as illustrated in Fig. 6. When a 
 large number of blasts are to be fired the lead wires are arranged as shown 
 in Fig. 7, a being one series of charged holes, and b another. The wires on the 
 outside are attached to the ends of the entire series, as in the previous case, 
 
 while the wire from the central screw 
 is attached to the center of the series 
 of connecting wires as at c. By this 
 arrangement, a large number of blasts 
 can be fired with a single battery and 
 the size of the lead wires very much 
 reduced. The firing is accomplished 
 by lifting the handle of the machine to 
 its full height, and pushing it down- 
 wards with full force, until the rack 
 attached to the handle reaches' the 
 bottom of the box and sends the cur- 
 rent through the caps in the holes. When firing a hole by means of a blasting 
 machine, the handle, or rack bar, should never be churned up and down, but 
 should simply be given one vigorous stroke, as directed. Most blasting 
 machines are made to fire with a downward stroke, but some fire with an 
 
 FIG. 6 
 
EXPLOSIVES AND BLASTING 683 
 
 upward stroke of the handle. A machine should always be kept clean and never 
 abused and played with. Its strength should be tested from time to time by 
 means of a test lamp or rheostat. Test galvanometers are used to ascertain 
 if any breaks exist in the circuit and the caps. 
 
 In Europe, another form of electric blasting machine is used. These 
 magneto machines consist essentially of an armature revolving between the 
 poles of a set of permanent magnets, are not unlike the American blasting 
 machine in appearance, and are used in very much the same way. 
 
 FIG. 7 
 
 Firing With Dry Batteries. Firing charges of explosives by means of ordi- 
 nary dry cells has been prohibited in foreign countries, because premature 
 firing of detonators, and sometimes of the charge, has been caused by the 
 wires coming in contact with the poles of the batteries. Safety-contact dry- 
 cell batteries have lately been introduced in the United States and abroad. 
 They are made with a spring-key contact, or with two safety-spring contact 
 buttons, which are the poles of the battery. The two leading wires are laid 
 on the buttons, which are at the same time pushed downwards. When the 
 pressure of the thumbs is released the contact is broken. If the wires of a 
 detonator accidentally come into contact with the poles of the battery, the 
 current cannot be discharged unless both poles are pushed downwards. As 
 these dry-cell batteries are cheap and easily portable in comparison with the 
 blasting machine, they have become quite popular, but those without safety 
 contacts have been the means of numerous fatal accidents through premature 
 explosions due to the unintentional coming in contact of the wires with the 
 binding posts before the men had left the face, or when carried in sacks with 
 the explosives and detonators through a contact made between the battery 
 and the detonator wires resulting in an explosion. 
 
 Small devices such as these can be used to fire only a few shots in one circuit, 
 as those in a single room. The number of shots to be fired and the length of 
 the leading wires and other conductors must be known, so that a battery of 
 sufficient capacity may be selected. The strength of the battery may be tested 
 by passing the current through a small electric lamp of known capacity and 
 noting the brightness of the light given by the lamp. Or the battery current 
 may be passed through a testing circuit whose resistance is equal to that of the 
 circuit to be fired and which has in it one electric detonator, which must be put 
 in a safe place. If the battery fires this detonator, it is strong enough and is 
 in good condition. 
 
 Precautions When Firing With the Electric Blasting Machine. To insure 
 success when firing blasts by electricity, the following points should be observed: 
 
 1. The machine wires and primers should be suitable to each other; two 
 kinds of primers must not be used in the same blast. 
 
 2. The blasting machine should be of sufficient power to fire all the caps 
 or primers connected at one time; a blasting machine must not be loaded to 
 its full limit. 
 
 3. The electric caps or primers should be kept in a dry place, and every- 
 thing kept as clean as possible. 
 
 4. All the joints at connections and points of contact of the wires should 
 be well made so that the wires cannot separate, and the surfaces should be 
 clean; the joints in one wire must not touch those in another, and bare joints 
 must not touch the ground. 
 
 5. The wires must not be kinked or twisted^so as to cut the insulation 
 during the process of tamping. If the insulation is cut, the fuse is useless for 
 wet ground or a wet hole and should be laid to one side. 
 
 6. The operator's hands should not touch the terminals of the blasting 
 machine when firing. 
 
684 EXPLOSIVES AND BLASTING 
 
 7. The blasting machine should not be connected to the leading wire or 
 cable until every one is in safety. 
 
 8. The wire connections should be bound with insulating tape in damp 
 places to avoid leakage and short-circuiting of the current. 
 
 9. Before firing the blast, the circuit should be tested by a galvanometer 
 to insure that there is no break or short-circuit. 
 
 Firing From. Dynamo Instead of obtaining the necessary current to fire 
 the blasts from a blasting machine or a dry -cell battery, it is a very common 
 practice to derive it from the dynamo used in the power plant of the mine. 
 While, in most cases, the current is carried into the mine upon special wires 
 known as the firing circuit, the practice prevails to some extent of connecting 
 up to and firing the shots by the trolley, or haulage, wires. The latter practice 
 is extremely dangerous and is commonly prohibited by law because the power 
 on the trolley wires is always much more than is required to fire the shots. 
 There is, consequently, a certainty of arcing and a probable fusing of the lead 
 wire on account of its small size and high resistance. 
 
 In some cases the shots, either those in a single room or those in all the rooms 
 in a district, are exploded from a firing station or from a number of firing 
 stations within the mine; in other cases, the shots are fired as a whole from a 
 firing cabin on the surface after all the men have been withdrawn from the 
 
 Feed line from Sub 
 
 Pilot Lamp"! 1 
 Trolley from Sub Station-' 
 
 Wire to shot 
 
 fT^ A Hlot Lamp 
 
 
 ition-" J 
 
 Trolley and shot wire to mine) 
 
 workings. Fig. 8 shows the system in use at the mines of the Stag Canon Fuel 
 Company, Dawson, N. Mex. As the men enter the mine they are required 
 to deposit a metal check at the shot-firing house outside, near the entrance. 
 These checks are placed on a check-board and returned to the men as they 
 come from the mine. A record of the working place of each check number is 
 kept in the shot-firing house, and in case any check is uncalled for, the shot 
 firer makes a search for the man until he is found. No shots are fired until it 
 is known positively that no one is in the mine. The method of placing the 
 shots is shown in Fig. 8. To insure safety against accidental discharge of the 
 shots by electricity, there are two or more locked switch boxes in each mine, 
 with throw-off switches, one at the mouth of the mine and at one or more 
 stations inside the mine. After inspecting the inside connections with the shots 
 to be fired, the shot firer en route from the mine makes connection at each of 
 the switches mentioned. He then goes to the shot-firing cabin to turn on the 
 electric current, but before doing so he turns on an electric signal light in a 
 red globe, to warn all persons to remain away from the vicinity of the mouth 
 of the mine; so that should an explosion occur within the mine, no one outside 
 could be injured by flying debris. In connection with this system of shot 
 firing, the company's rules provide that the undercutting must extend at least 
 6 in. beyond the back of the shot holes; that all shot holes must be at 
 least 2$ ft. deep; that all dust must be removed from the shot holes before 
 they are charged; that no more than five sticks of powder (which, at some 
 mines, is in excess of the safe limit) shall be used in any one hole; that stand- 
 ing holes, or parts thereof, must not be recharged ;that holes in tight corners 
 must be at least 1 ft. from the rib at the back end of the hole; and that, in 
 solid faces, shot holes must not be more than 6 ft. apart horizontally, and that 
 not less than two such holes shall be fired. 
 
EXPLOSIVES AND BLASTING 685 
 
 All shot-firing wires should be well insulated. The size of wire used is 
 commonly No. 6 on the principal line along the main entry; from a No. 8 to a 
 No. 12 on the cross-, butt-, or side entries, depending on their length; and a 
 No. 14 for the room connections. The connections between the cross-entry 
 lines and the main line and between the rooms and cross-entry lines are made 
 in parallel so that the failure of the shots to explode on a cross-entry or in any 
 room or rooms on a cross-entry, will not prevent the detonation of any others. 
 When two or more shots are to be fired in the same room, they are connected 
 in series. The connecting up of the shots should proceed outwards from the 
 working faces to the mine mouth; that is, the detonator wires should first 
 be connected to the room wires; then the room wires to the cross-entry wires; 
 and, finally, the cross-entry wires to those on the main entry. The room 
 connections are usually permanent, unless it is desired to fire shots singly from 
 the room mouth, but the connections on the main entry with the cross-entry 
 circuits and at the foot of the shaft are made by switches. These switches 
 are contained in locked boxes, the head shot firer alone being trusted with 
 the keys. 
 
 When preparing for blasting, all the holes in all the rooms on No. 1 entry 
 are first connected to their respective room firing circuits, then all the holes 
 in all the rooms on No. 2 entry are connected, and so on until those on the 
 innermost entry are connected. On the way out from the last entry, the shot 
 firer opens the boxes and throws in the switches at the mouth of each room 
 entry. At the foot of the shaft, or at the drift mouth, the final switch con- 
 necting the mine and firing circuits is thrown in. The current from the dynamo 
 is then applied. After the shots have been fired, the shot firer returns to the 
 mine, opening the various switches and relocking the boxes on the way. At 
 the working places, an examination is made for fire, the room wires are placed 
 out of the way of the loaders, and are disconnected from any detonators that 
 may have failed to explode; the mine foreman being subsequently notified 
 of the location of any misfires. During the day the entire shot-firing system 
 is overhauled, defective insulations, etc., are repaired, and everything made 
 ready for the work of the following shift. 
 
 Firing Single Shots From the Surface From time to time various devices 
 have been introduced to reduce or overcome the danger of a coal-dust explosion 
 due to the detonation in a single blast of the very large amount of high explo- 
 sives (often over 1,000 Ib.) required in large mines. The logical procedure is 
 to have a separate circuit from each working place to the firing cabin, but the 
 cost of installing and maintaining the 400 or more wires necessary for this 
 purpose in a mine of even moderate size, is prohibitory. The mine may be 
 divided into two, three, or four, districts with the same number of firing circuits 
 and four, six, or eight sets of wires, but beyond this subdivision it is not 
 usually economically possible to go. In a recent device, what are known as 
 sparker boxes are introduced in the firing circuit at the mouth of each room. 
 The main-line wires A enter the box in the usual way but are separate from 
 the wires B connecting one box with another. The room wires C are also 
 distinct from either pair of wires A or B. By pushing a button, the room 
 wires C are placed in circuit with the entry wires A, the wires B to the next 
 box remaining dead. The application of the current at the surface detonates 
 the holes in the room and at the same time releases the button so that the 
 wires A and B become in circuit. A second application of the current fires 
 the shots in the second room and arranges the mechanism in the sparker box 
 at its mouth so that the current may pass to the third box, and similarly 
 throughout the mine. . The failure of the shots in any room to detonate does 
 not interfere with the current passing from one box to another. According 
 to the statements of a Western operator, this device has proved successful 
 at his mine. 
 
 SUBSTITUTES FOR BLASTING IN DRY AND DUSTY 
 MINES 
 
 Before the introduction of permissible powders and the adoption of the 
 various safety measures used in connection therewith, numerous substitutes 
 for powder and divers means of bringing down coal without blasting were 
 tried from time to time and with more or less success. 
 
 Wedging Down Coal The plan of wedging down coal has been employed 
 until quite recently and has its uses even at present. The seam is undercut 
 in the usual way, and a series of drill holes but a short distance apart are placed 
 
686 EXPLOSIVES AND BLASTING 
 
 in a horizontal row near the roof in thin seams or between the roof and the 
 floor in thick ones. If the seam has a pronounced, bedding plane, an inter- 
 stratified layer of slate, or another line of weakness along which it splits readily, 
 the holes should be drilled in it. Wedges, placed in the holes and driven 
 home by blows of a sledge will bring down the coal in large lumps. Other 
 things being equal, the nearer the drill holes to one another, the easier is the 
 coal brought down. If the coal is thin, hard, and blocky and adheres strongly 
 to the roof, wedges will not work well, as the coal will break off short and but 
 1 in. or so in depth of the face will be removed at each application of the wedges. 
 If the coal is soft, the wedge will be driven in flush with the face and will merely 
 enlarge the size of the drill hole without bringing down any part of the seam. 
 Seams having a tendency to split horizontally along a bedding, or other plane, 
 are best adapted to wedging. 
 
 The wedges used are of various types. The common form is, of course, 
 the ordinary single-piece wedge. The device known as plug and feathers, 
 familiar to quarry men, has been largely used. This consists of two narrow 
 triangular pieces of iron (the feathers) placed on opposite sides of the hole, 
 between which a long wedge (the plug) is driven by blows of a sledge. As both 
 the feathers and plug are tapered, the force of the blow is multiplied. To still 
 further increase the force of the blow, multiple wedges have been used. They 
 are essentially the same as the device just described, but there are four instead 
 of two tapering feathers between which the plug is driven as before. In a 
 special form of wedging machine, the plug and feathers are introduced in the 
 back of the hole, the plug being drawn forwards by a combination of a screw 
 and a lever. In a similar machine, in order to reduce the friction of two plane 
 wedges sliding upon one another, the plug is made to run upon roller bearings 
 between double feathers, and is drawn forwards from the back of the hole by 
 the action of a screw and nut, driven by a ratchet and pawl. 
 
 In a French device used in rock work, a series of holes are drilled in a group 
 in the face. The drill bit is replaced with a hammer head, which by compressed 
 air drives in the plugs inserted between the feathers in the holes, breaking 
 down and splitting up the rock. 
 
 Hydraulic Cartridge. The hydraulic cartridge has been in use in many 
 foreign mines for several years past, is absolutely safe in any atmosphere, and 
 is remarkable for the large proportion of lump coal produced in comparison 
 with blasting, but does not appear to be adaptable to breaking down all kinds 
 of coal. The cartridge itself is a forged-steel cylinder of varying length and 
 diameter, and having eight duplex rams or pistons arranged in a row, along 
 one side. The size most generally in use is 21 in. long and 3 in. in diameter, 
 and the expansion of the duplex piston is 2J in., giving a pressure of 60 T. 
 The larger sizes are used only in very narrow-entry work or in extremely 
 thick coal. The action of the pistons is simultaneous, the pressure being 
 applied through the longitudinal passage in the steel cylinder at the back of 
 the pistons. A liner of sheet iron, <fa in. to J in. thick, 1J in. wide, and 22 in. 
 long, is usually introduced in the lower side of the hole, to present a uniform 
 bearing surface for the pistons and to prevent their sinking into the coal. 
 
 In the original machine the pressure was produced by the operation of a 
 lever pump, but in the present type a powerful screw pump is used to compress 
 the water and expand the pistons. The coal having been undercut and the 
 holes drilled as near the roof as possible, and parallel to it, the cartridge, shown 
 
 FIG. 1 
 33*1 IM 
 
 in Fig. 1, is inserted in the hole, the pistons being telescoped and contained 
 within the body of the cartridge. The small handle attached to the pump 
 plunger is then slowly drawn in and out a few strokes until the cartridge is 
 filled with water from the small reservoir, which is connected by a reinforced- 
 rubber tube, and pressure is reached, the quantity of water thus used being 
 about 1 i pt. The valves then being closed , the screw is operated by the handles 
 and the compression rapidly increased. As the pistons are forced out the coal 
 
EXPLOSIVES AND BLASTING 687 
 
 begins to work and crack, and as the maximum expansion is approached, it 
 falls in large lumps rarely exceeding one-man size. The release valve is then 
 opened, the water returns to the reservoir, and the pistons are pushed back 
 ready for the next hole. The pipe connecting the pump and cartridge is made 
 in any required length suitable to the depth of the hole, which is usually about 
 6 in. less than that of the undercut. The number of holes necessary depends 
 on the thickness of the seam, the nature of the coal, the partings, if any, and the 
 adhesion of the roof rock; but in general it averages one hole for every 10 ft. of 
 face in room-and-pillar work, and one hole for every 30 ft. of face in longwall 
 work. The length of time necessary to bring down one hole varies with the 
 location, breaking-in shots requiring from 10 to 15 min., and free-end shots 
 from 3 to 5 min. In an English mine where 38,263 thrusts were made in 12 mo. , 
 the average cost of breaking down the coal was 2& mills per ton. A pressure 
 of 3 T. per sq. in. is usually required in seams up to 4 ft. thick, and this gives 
 a total pressure of 60, 90, and 150 T., respectively, on the three sizes of cart- 
 ridges made. 
 
 Lime Cartridges. The expansion of quicklime under the action 
 of water has been used to some extent abroad as a substitute for pow- 
 der in fiery mines. Ordinary limestone is calcined; that is, has the 
 carbon dioxide driven off by burning in kilns, and is ground to a fine 
 powder. The powder is compressed hydraulically into" a cartridge 
 having a groove running down its side. The cartridge is about 5 in. 
 long and 2$ in. in diameter, is wrapped in paper, and is kept in an air- 
 tight box. The seam is undercut and the holes drilled in the cus- 
 tomary way. A perforated iron tube, $ in. in diameter and having a 
 small external chan nelon the upper side, is inserted for the full length &- 
 of the hole. Several cartridges are placed in each hole, the grooves 
 in them fitting around the pipe, and the rest of the hole is tamped 
 with clay. Water is forced into the tube by means of a small hand 
 pump, and the water acting on the lime greatly expands its bulk, 
 forcing down the coal. The process can be used only for certain classes 
 of coal, and much care must be taken to keep the cartridges dry. 
 
 Water Cartridge. The water cartridge is not a substitute for ex- 
 plosives, but is a means of using them in a less dangerous manner 
 than as ordinarily employed. A cartridge of high explosive is placed 
 in a skeleton case, a, Fig. 2, having a number of thin metal diaphragms, 
 or wings b, which keep the cartridge in the center of the case c which FIG. 2 
 contains water. A detonator is inserted in the cartridge and its wires 
 connected up to the firing wires of a battery. After the detonator is placed, 
 the outer case is filled with water and its mouth tightly tied around the wires d. 
 There is, also, a guide wire e used to keep the cartridge lengthwise in the 
 center of the case. The apparatus is delicate, requires a large size hole, and 
 materially reduces the effect of the explosive. 
 
 GENERAL CONSIDERATIONS AFFECTING BLASTING 
 
 Definitions. A free face, or free end, is the exposed surface of a mass of rock, 
 or of coal. Thus, AB, BC, etc., are free faces in the room of a coal mine shown 
 in plan in Fig. 1, and represent parts of the coal detached from the main 
 body of the seam by blasting or undercutting. That part of the seam in which 
 the shot hole 6-7 is placed has but one free face CD, whereas those portions 
 of the seam in which the holes 11-14 and 1-2 are placed have two free faces 
 AB and BC, and DE and EF. In the latter cases, additional free faces could 
 be secured by shearing into the rib in the direction of the length of the room 
 at A and F, or at right angles to the room at C and D, or by undercutting the 
 seam. When a block of coal has the maximum number of free faces, six, it is, 
 of course, entirely detached from the rest of the seam. 
 
 The heel of a shot is the distance 1-E from the mouth of the drill hole to 
 the corner of the nearest free face ED; or is that portion 1-2 of the hole that is 
 filled with the tamping; or is that portion 1-2-5-E of the coal to be broken 
 that is entirely outside the powder. 
 
 The toe of a shot is the distance 3-4 from the inner end of the hole to the 
 adjacent free face measured at right angles to the direction of the hole; or is 
 that portion of the hole 2-3 that is filled with powder; or is that part 2-3-4-5 
 of the seam to be broken lying between the powder and a free face. 
 
 The line of least resistance is the distance from the charge of powder in a hole to 
 the nearest free face. In the case of the hole 11-14, the line of least resistance 
 
688 
 
 EXPLOSIVES AND BLASTING 
 
 is 1S-C. In the hole 6-7, the line of least resistance is not the line 7-8, but a 
 shorter line, a perpendicular from 7 to the face CD. 
 
 FIG. 1 
 
 A dead, hole is one that extends into the solid coal beyond that part that 
 can be broken by the maximum safe charge of explosive. Thus, the hole 11-14 
 is dead because the part 13-14 extends into the solid beyond the line of least 
 resistance 13-C. Sometimes such a hole is spoken of as being dead for 9 or 10 
 or any number of inches, depending on the length of the portion 13-14- A 
 definition taken from the mining laws of a Western state is: "A dead hole 
 is a shot hole so placed that its width at the point (toe), measured at right 
 angles to the drill hole, is so great that the heel is not strong enough to at 
 least balance the resistance at the point (toe)." The hole 1-3 would be dead 
 if the point 3 was so far to the right of its indicated position that the explosion 
 of the charge would fail to break the portion of the coal marked 1-3-4-E, and 
 would result in a blown-out shot, or in merely breaking off a part of the heel. 
 The hole 9-10 drilled directly into the solid is a dead hole. 
 
 A gripping hole is one whose direction is inclined 
 away from the adjacent free face, or may be denned 
 as one whose width at the toe is greater than at the 
 heel. In the figure, both 6-7 and 1-3 are gripping 
 shots. The degree of grip is indicated by the angle 
 between the hole and the face it is intended to break. 
 Thus, in the hole 6-7, the greater the angle 7-6-8, the 
 stronger or greater is the grip. Similarly, in the hole 
 1-3, the greater the angle between the lines 1-3 and 
 E-D, the stronger is the grip. By increasing the 
 angle mentioned, gripping holes become dead holes. 
 
 In a balanced shot, the width of the toe and heel are 
 equal and are less than the length of the drill hole. 
 The shot 1-3 would be balanced were its direction 
 parallel to the free 
 
 face E-D. Similar- .a a A 
 
 ly, the shot 11-14 
 would be balanced 
 did it not extend 
 beyond 13. A bal- 
 anced hole will do 
 the work expected 
 of it with the mini- 
 mum expenditure of 
 powder. 
 
 Note that the FlG> 3 
 
 definitions of the 
 
 FIG. 2 
 
 terms used in connection with drill holes are not uniform throughout the 
 country; the foregoing are believed to be in accord with general practice. 
 
 Effect of Free Faces in Mining. The form of cavity produced when a single 
 drill hole is fired in a mass of rock having one free face is usually that of a cone; 
 
FIG. 4 
 
 EXPLOSIVES AND BLASTING 689 
 
 thus, in Fig. 2, if ab represents a vertical drill hole, the rock broken will theo- 
 retically have the form cbd, the line cd being the diameter of the base of a cone. 
 If the strength of the explosive is not sufficient to overcome the tenacity of the 
 rock to so large an extent as represented, the cone might have the form ebf, 
 or igh. It is more than probable that a shot hole perpendicular to the face will 
 break no rock at all but will result in a blown-out shot, as it is in the worst 
 position to do effective work. This is because 
 any pressure exerted in the direction of m or n 
 is opposed by the resistance of an indefinite 
 thickness of rock and the line of least resis- 
 tance along which the force of the explosive 
 naturally will act will be the resultant of the 
 forces acting on m and n, or in the line of the " 
 drill hole. 
 
 When a hole is inclined to the face, as ab f 
 in Fig. 3, the line of least resistance eb is per- 
 pendicular to the face, and the cross-section of 
 the piece of rock broken out will be approxi- 
 mately of the form abc and rarely that of 
 dbc. Commonly, one edge will coincide with 
 the drill hole and the other will be between 
 the lines eb and cb. The angle eab is usually 
 about 35 for the best results, and 45 is its 
 limit. Less and less rock will be broken as the angle becomes less and when 
 the direction of the drill hole ab is the same as that of the free face aci that is, 
 when the powder is placed on top of the ground, no rock will be broken out. 
 Similarly, as the drill hole becomes more nearly perpendicular the less will 
 be the volume of the rock broken and when the hole is vertical as eb, it will, 
 in the very great majority of cases, result in a blown-out shot. 
 
 The more free faces there are, the greater 
 _ will be the ease with which an explosive will 
 accomplish its work. Fig. 4 is a cross-section 
 showing a hole ab placed in a rock having two 
 free faces C and D. If there were but the one 
 free face C, the force from the charge at b would 
 break out the cone or crater ebg', if the face D 
 were the only one exposed, the charge b would 
 break out the crater ebj. With the charge b 
 equally distant from the faces C and D, and of 
 just the right size, the bounding surface between 
 the two craters will coincide in the line be, but 
 as the force of the explosion at b is divided be- 
 tween the two craters and a portion of it is 
 reflected by the solid rock, the crater actually 
 broken out will be approximately hbi; that is, a crater that is not equal to the 
 sum of the two craters ebg and ebj. 
 
 If the charge b, Fig. 5, is located so that bf is greater than ba, the force 
 acting on each face separately will break the craters gbk and jbl, the wedge- 
 shaped piece ekbl not being included in either. With the charge b acting on 
 both faces C and D together, part of the force is used in breaking down the 
 mass ekbl and the crater 
 broken out is bounded 
 by the lines ,hbi, instead 
 of by the lines gbj. 
 
 Similar reasoning 
 may be applied to any 
 increase in the number 
 of free faces. The 
 greater the number of 
 free faces the larger 
 the amount of material 
 that can be broken 
 down with a single shot; or what amounts to the same thing, a smaller charge 
 will do the same amount of work, the greater the number of free faces, but 
 the increased amount of material loosened will not be proportional to the 
 increase in the number of free faces. 
 
 There is a general rule that the longest line of resistance should not exceed 
 three-halves of the shortest line of least resistance if the maximum effect of 
 44 
 
 D 
 
 FIG. 5 
 
 FIG. 6 
 
690 
 
 EXPLOSIVES AND BLASTING 
 
 the explosive is to be obtained. If possible, the shots should be placed so that 
 the shortest line of resistance is horizontal and the longest vertical so that the 
 weight of the rock may assist the breaking down. 
 
 It is evident, therefore, that in blasting it is advantageous to have as many 
 free faces exposed as possible, not only on account of the decrease in the amount 
 of powder required, but also because it is possible to obtain the material blasted 
 in larger lumps than when blasting is done with a single free face. This is 
 advantageous particularly in coal mining where the lump coal is more valuable 
 than the fine coal. 
 
 Fig. 6 represents two drill holes h, V drilled at a distance W from the free 
 faceA-B. If these holes are fired independently, each will break out approx- 
 imately the same amount of material, as mhn or nh'o. If they are fired together , 
 
 amount of 
 
 powder required to break the two masses mhn and nh'o. The distance D 
 between the holes must be varied according to the character of the rock. In 
 comparatively soft material it is less than in hard rock, though probably the 
 limit is twice the distance W. 
 
 Fig. 7 illustrates another case. Here three holes h, h', h" have been drilled 
 close together, and each one loaded with a charge the depth of which will be 
 represented by HE. Any one of the holes, 
 if fired separately, will not be able to break 
 through the distance W, but, by firing the 
 three together, the mass ehh"gg'GHe'e may 
 be removed at one shot. By this means, 
 greater masses of rock can be removed with 
 smaller drilled holes than is possible with- 
 out the combined effect of the several 
 charges. 
 
 The form of cavity and the amount of 
 material dislodged by a shot are largely 
 theoretical and no universal rules can be 
 given. Experience is the only safe guide 
 in choosing the location and size of the 
 holes and the amount of the charge of ex- 
 plosive, and an experienced miner will study 
 the character of the rock to be blasted so 
 as to place his holes at such an angle that 
 he may get the maximum effect from them 
 and avoid blown-out shots, and take advan- 
 tage of slip and cleavage in the rock. 
 
 Diameter of Shot Holes. When driv- 
 ing tunnels or sinking shafts, holes having 
 a diameter between J and 1$ in. at the bot- 
 tom give the most economical results in 
 
 FIG. 7 
 
 hard rock if they are charged with the strongest of the high explosives. 
 When the rock is weaker, the explosive should be of less strength, but the 
 diameter of the holes should be increased to 1$ to 2,\ in. All holes should be 
 of the same diameter, each should have an equal resistance of rock to work 
 against, and each should be so placed that it will receive the greatest benefit 
 from the free faces formed by blasting the holes previously fired. 
 
 Amount and Kind of Explosive. The maximum pressure or effect that an 
 explosive can develop is obtained when it entirely fills the space in which it is 
 exploded; hence, the greatest efficiency is obtained when the charge fills the 
 hole up to the tamping. There are no rules from which the amount of explosive 
 necessary to be used in charging a given hole or series of holes can be deter- 
 mined. If the right amount of explosive has been used in a properly placed 
 hole, upon detonation there will be a deep boom and the material will not be 
 thrown with great force from the solid. If the charge is too heavy, there will 
 be a sharp cracking report and the excess of explosive will throw the broken 
 material away from the solid and will shatter it badly. If insufficient explosive 
 is used or the hole has been badly placed, the rock will not be broken, but the 
 tamping will be blown from the hole, resulting in a blown-out shot. The depth 
 of the hole is to be considered when estimating the amount of powder to be 
 used as a shallow hole requires less powder than a deep one. In some parts 
 of the bituminous coal field, where the seam is of moderate hardness and 
 from 4 to 6 ft. thick, it is a common practice to make the holes from 2 to 2* in. 
 
EXPLOSIVES AND BLASTING 691 
 
 in diameter and to charge them with 2 to 6 Ib. of black powder. Two Ib. of 
 black powder is not an excessive amount in a well-balanced hole, but any 
 weight over this is dangerous, particularly if the mine is noticeably dusty or 
 gaseous. 
 
 The length of the charge of explosive for single holes should not exceed 
 from eight to twelve times the diameter of the hole; that is, a 1-in. hole should 
 never have a charge of more than 12 in. of explosive placed in it. Where 
 several holes are fired together this rule is sometimes slightly deviated from. 
 It is usually best to employ a length of charge between these two limits, as, for 
 instance, about ten times the diameter of the hole. After the proper relation 
 between the diameter of hole and the length of charge has been determined 
 by experiment for a certain diameter of hole under given conditions, it is safe 
 to conclude that the same ratio of length of charge to diameter may be taken 
 for other diameters. Thus, if it has been found that for a hole 2 in. in diameter 
 the best results are obtained from a charge 24 in. long (2X12), it may be 
 assumed that in a hole 2 in. in diameter the charge should be 25X12 = 30 in. 
 long. If the diameter of the hole ab, Fig. 4, remained the same and the length 
 of the line of least resistance was increased, a place would soon be reached 
 where the charge of explosive would fail to break out the rock. It is not good 
 practice to. have a powder charge occupy more than one-half the hole; hence, 
 in order to increase the effect of a charge the diameter ab of the hole should be 
 increased; that is, as the distance^ increases, the diameter of the hole ab must 
 be increased; or there must be a chamber formed at the lower end of the hole 
 in which the powder charge is to be contained, so as to increase the size of the 
 cone of throw toward any free face. This chamber is sometimes formed by 
 using some form of expansion bit or reamer, but the usual custom is to introduce 
 a small charge of high explosive that will enlarge the end of the hole. By 
 continuing this process, an opening of sufficient size to contain the desired 
 charge may be formed. This operation is called chambering or squibbing. 
 Where large masses of soft material are to be loosened, it is common practice 
 to use dynamite or nitroglycerine for chambering the hole and black powder 
 for the blasting. Holes are sometimes drilled as much as 20 ft. deep and 
 several kegs of powder introduced into the chamber formed by firing the high 
 explosive. This method of blasting is used in open-cut ore mines, milling, 
 and in steam-shovel mines; also in side cuts of earth works ; 
 
 When mining soft cleavable minerals, powerful explosives are not generally 
 used, their effect being to shatter; on the other 'hand, in tenacious minerals, 
 powerful explosives are used for their shattering properties. Less powerful 
 explosives, such as gunpowder, are used where a rending action is desired, such 
 as in mining coal, but they are not desirable in tough ore formations, because 
 they break down the mineral in large pieces that, to be handled, must be 
 block-holed and reblasted. 
 
 While the power of most explosives can be calculated, the theoretical power 
 can never be obtained in practice." The factors that enter into^ the problem 
 vary so widely and are so numerous that seldom can exactly similar results 
 be obtained from blasts fired apparently under similar conditions. _ The weight 
 of a mass of rock opposes the action of a blast, and this weight is assisted by 
 the atmosphere that presses on it with a weight of 14.7 Ib. per sq. in. at sea 
 level. If the hole is damp or wet or the rock cold, the heat produced by the 
 discharge and the power' of the explosive will be decreased. Slips, joints, and 
 cleavage planes affect the blast, as do also texture and structure of the rock 
 The shape and location of the drill hole and the method with which it is 
 charged and tamped are important factors. 
 
 Brittle rocks are easily fractured, while strong, compact rocks in which the 
 cohesive powers are great are much harder to break. Plastic materials, like 
 fireclay, which are neither brittle not tenacious, are very difficult to blast. 
 
 Fissures, or joints, and bedding planes, when open, have something the 
 effect of free faces, and as a consequence they influence _the best position for 
 placing a blast. When possible, the charge of explosive should never be 
 placed in contact with a fissure or bedding plane, but should be located in the 
 firm rock, in order to avoid the escape of the gases through the fissure, that 
 would thus reduce the effect of the blast. If it is possible to avoid it, a drill 
 hole should not cross crevices and slips. 
 
 In compact and brittle rocks the limit of elasticity is soon reached and they 
 rupture under the shock of exploding charges before there has been an appreci- 
 able enlargement of the drill hole. With porous rocks and sand, the blast 
 tends to solidify the rock and to fill empty spaces, thereby increasing the size 
 of the drill hole and decreasing the force of the explosion. 
 
692 SUPPORTING EXCAVATIONS 
 
 SUPPORTING EXCAVATIONS 
 
 INTRODUCTION 
 
 The various methods of supporting the surface overlying a seam from which 
 the coal has been or is being removed may be roughly divided into those that 
 use natural and those that use artificial materials for the purpose. The sole 
 example of the use of natural means is afforded by the familiar American 
 room-and-pillar system of mining in which natural pillars of coal are left, in 
 the course of working, either to support the overlying rock indefinitely or. 
 throughout the life of the mine. There are numerous examples of the second 
 method; the use of wood or steel posts or beams, called timbering; the use of 
 built-up packs, cribs, etc., of timber, stone, or timber and stone; and the 
 flushing of culm into the workings. 
 
 A distinction must be made between the methods and materials used for 
 supporting the surface lying several hundred or several thousand feet above the 
 coal bed, and those used to support the roof or that portion of overlying rocks 
 usually but 1 to 2 ft. thick or in rare cases as much as 40 ft. The use of wooden 
 or steel timbering is confined to supporting the comparatively thin roof rock, 
 whereas pillars of coal, built-up cribs, and flushing are resorted to to sustain 
 the weight of the many hundred feet of rock between the coal bed and the 
 surface. 
 
 COAL PILLARS 
 
 GENERAL CONSIDERATIONS AFFECTING SIZE OF PILLARS 
 
 Amount of Pillar Coal. The amount of coal left in the pillars for the 
 support of the workings is generally expressed as a percentage, or a certain 
 portion, of the total volume of the bed within the area included by the pillars. 
 The term pillar coal, therefore, includes not only the coal left in the room pillars, 
 but also that left in the pillars supporting the entries. The amount of coal 
 left in the pillars in the first working varies widely under different conditions, 
 but the best practice now counts on ample pillars in the first working so as to 
 minimize the danger from squeezes. Many of the collieries in the anthracite 
 region of Pennsylvania are now extracting but one-third of the coal in the first 
 working, leaving two-thirds of all the coal as pillars to be taken out later as 
 the different sections of the mine are worked up to the limit. In many of the 
 mines in the Connellsville region of Western Pennsylvania, the rooms are only 
 12 ft. wide and the pillars from 60 to 72 ft. wide, so that only one-fifth to one- 
 sixth of the coal is taken out in the first working, but the removal of the pillars 
 begins as soon as the rooms have been driven their full length. 
 
 The proportion of coal left in the pillars along the entries to the amount 
 of coal taken out in mining the entries is relatively larger than the percentage 
 of pillar coal between the rooms, as the entry pillar sxusually have to stand a 
 much longer time than the room pillars. 
 
 The amount of pillar coal left depends on the method of working the mine, 
 on the nature of the coal, the top and the bottom, on the thickness of the coal, 
 and the depth of cover, and on the time of drawing the pillars. 
 
 Practical Considerations Determining Size of Pillars. It is impossible 
 to give exact rules or formulas for determining proper size of pillars and rooms 
 that will be universal in their application. Each mine is a special problem, 
 and in laying out the rooms and pillars it is well to find out what is the success- 
 ful practice in the same field or in similar fields worked under the same condi- 
 tions. Similar practice should not be followed blindly, as a great deal of the 
 lack of progress in mining has been due to this copying of other methods. 
 Still it is always well to find out how others have succeeded and why they have 
 failed. 
 
 In general, the thicker the bed and the greater its depth below the surface, 
 the wider must be the pillars and the narrower the opening. This rule is not 
 invariable, however, for certain coals deteriorate very rapidly when exposed 
 to the atmosphere and the pillars must be much larger than with hard, compact 
 coals under similar conditions. 
 
SUPPORTING EXCAVATION'S 693 
 
 The length of time that a pillar must stand before it is to be drawn should 
 be considered in determining the width of the pillar required. If a pillar is 
 to be drawn in a short time, it need not be as large as one that is to be more 
 permanent, as it is not subject to the disintegration due to pressure and to 
 atmospheric effects. 
 
 Extremely large pillars are usually left to protect surface buildings, and 
 also under swamps or large bodies of water, to avoid any possibility of a break 
 in the roof through which the water can enter the mine. 
 
 Some coals are of such a nature that the sides and corners of pillars chip 
 or split off when the coal is opened up, due to the disintegrating effect of the 
 atmosphere, to the pressure of gas in the coal, or to the pressure of the roof. 
 When this chipping or splitting off of pillar coal occurs, pillars of greater area 
 are required. 
 
 Strong heavy strata, such as limestone or sandstone above the coal, that 
 do not break and fall easily, act as a lever to crush the edge of the coal pillar 
 and require larger pillars to prevent creep and squeeze than where the pres- 
 sure is distributed over the pillar and not so much along the edge; under a 
 friable roof, such as black shale or slate, that breaks and falls easily, and thus 
 relieves the pressure on the edge of the pillar, a smaller pillar can often be used 
 than under a strong compact roof, which brings the weight on the edge and 
 constantly chips off the pillar. With a strong roof that does not break, there 
 is danger from a movement of the strata over the pillar when robbing begins. 
 A soft bottom requires a large pillar to prevent the heaving of the bottom. 
 Faults, slips, and similar geological disturbances in the roof generally increase 
 the size of the pillars, and also the difficulty and danger of drawing them. 
 
 If the floor is soft and the roof hard, a creep is likely to occur, and in such a 
 case small pillars are so squeezed down into the floor as to be both trouble- 
 some and expensive to remove. If the floor is hard and the roof brittle, the 
 latter will fall more or less in spite of all efforts, and the expense of cleaning up 
 and timbering is heavy. If top and bottom are both strong, the weaker sub- 
 stance the coal if left too long or in too small an amount is crushed, and its 
 value decreased or lost. 
 
 If the seam of coal is gaseous, the length of the pillar is decreased on account 
 of the length of the cross-cuts or breakthroughs required to ventilate the rooms, 
 thus necessitating a wider pillar than would otherwise be required. 
 
 While it is desired to have a certairr excess of strength in the mine pillars, 
 the expense of driving long cross-cuts through them for ventilating the open- 
 ings, as well as the necessity for realizing as large a percentage as possible of 
 coal in the first working, makes it desirable in many cases to use the minimum 
 width of pillar required for the safe support of any given roof pressure. 
 
 When the room-and-pillar system is used, the best results as regards the 
 percentage of coal won from a coal bed are undoubtedly obtained where narrow 
 rooms are driven in the first working with ample pillars left between, and when 
 the pillars are withdrawn as quickly as possible after the rooms are worked up 
 their full length. 
 
 When two or more beds are worked at the same time, the width of pillar 
 required in the lowest bed will, in most cases, determine the maximum width 
 for all the overlying beds, for the pillars should be placed with their center lines 
 vertically one above the other, and if any difference is made in the size of pillars 
 in overlying beds the lower of the pillars should be the larger. This is the more 
 important the closer the seams are together. 
 
 The inclination of the seam, although decreasing the normal pressure or 
 the pressure perpendicular to the roof and floor, gives rise to a tendency of the 
 roof to slide on the pillars when the coal is removed. This tendency greatly 
 increases when the work of drawing the pillars is begun, especially if the roof 
 is hard and fails to break. Although the decreased pressure in an inclined seam 
 will call for a narrower pillar than for a flat bed, the tendency of the roof to 
 slip necessitates an increased width over what will be required in a flat bed 
 with the other conditions similar. 
 
 Depth of Cover. The depth of cover, or the thickness of the rocks lying 
 between the seam and the surface, is the prime factor, other things being the 
 same, in determining the size of coal pillars. The table on page 694 gives 
 the weight, in pounds per cubic foot, of the coal-measure rocks of the United 
 States. For practical purposes, the weight of the overlying cover may be taken 
 as 160 Ib. per cu. ft. Thus, every 12f ft. in depth of cover causes a weight of 
 1 T. on each square foot of pillar. The pressure at a depth of 100 ft. will be 
 8 T. per squ. ft.; at 500 ft., 40 T.; at 1,000 ft., 80 T., and similarly for other 
 thicknesses of cover. 
 
694 
 
 SUPPORTING EXCAVATION'S 
 
 WEIGHT OF ROCKS Crushing Strength of Anthracite. 
 
 The following table gives the 
 crushing strength of anthracite as 
 determined by experiments made under 
 the auspices of the Engineers' Club, of 
 Scran ton, Pa. The results are averages 
 of a large number of tests made on 
 samples from a number of different beds 
 and from different parts of the anthra- 
 cite field. The test pieces were right 
 prisms with a 2 in. square base, and 
 of heights of 1, 2, and 4 in., respec- 
 tively, corresponding to a, b, and c in 
 the headings in the table. These tests 
 suggest the following conclusions in 
 regard to the samples tested : 
 
 Although the area of the base, or the 
 area pressed, is the same in each case, 
 the total crushing load and the crushing 
 load per square inch are not the same 
 
 in the different samples, but vary, approximately, inversely as the square root 
 of the height of the sample; that is to say, sample c having four times the 
 height of sample a has approximately but one-half the crushing strength of the 
 former. Other experients indicate that similar samples (samples whose heights 
 and bases are proportional) have the same unit crushing load, or require the 
 same crushing load per square inch of the area of the base, and the total crush- 
 ing load in this case is proportional to the area of the base. For example, a 
 cube measuring 2 in. on a side requires four times the total crushing load 
 required by a cube measuring 1 in. on a side, but the unit crushing load or load 
 per square inch of the area of the base is the same in each. If this can be con- 
 clusively proved for small test samples, it is fair to reason by analogy that the 
 same rule holds for mine pillars, so that if the strength of the pillar or the unit load 
 supported is constant for similar pillars, a pillar 40 ft. wide in a seam 20 ft. thick 
 has the same strength as a 10-ft. pillar in a 5 ft. seam; or a 60-ft. pillar in a 
 
 AVERAGE COMPRESSIVE STRENGTH OF ANTHRACITE 
 
 Rock 
 
 Weight per 
 Cubic Foot 
 Pounds 
 
 Clay 
 
 115 
 
 Earth 
 
 100 
 
 Gravel 
 Limestone . . 
 
 117 
 165 
 
 Sand 
 Sand full of water . . 
 Sandstone 
 
 117 
 120 
 150 
 
 Shale 
 
 162 
 
 Slate 
 
 175 
 
 
 Sample a 
 
 Sample b 
 
 Sample c 
 
 Total crushing load, in pounds 
 Crushing load per square inch, in 
 pounds 
 
 23,000 
 5 750 
 
 16,348.000 
 4087 000 
 
 11,416.0 
 2 854 
 
 Load producing first crack in sample 
 in pounds 
 
 3 022 
 
 2025000 
 
 1 8750 
 
 Height h 
 
 1 
 
 2 000 
 
 4 
 
 V* 
 
 1 
 
 1 414 
 
 2 
 
 Approximate relative crushing 
 
 strength, = 
 V/t 
 
 Mi|. --t 
 
 .707 
 
 .5 
 
 15-ft. seam has the same strength as a 40-ft. pillar in a 10-ft. seam; the unit 
 load supported, or the load per square foot of pillar, being the same in each case. 
 Also, if this be so, the crushing strength of any coal pillar, per square inch, 
 can be found by multiplying the crushing strength of a unit cube 1 in. on a side 
 by the square root of the ratio of the area of the base to the height of the pillar. 
 The crushing strength of the unit cube as given by these experiments is 4,000 Ib. 
 The unit loads producing the first crack; that is, when the coal begins to scale 
 off on the outside of the block, are approximately one-half of the unit crushing 
 loads in each case, except in sample c, where the height of the sample is four 
 times the width of the base. This form, however, need not be considered in 
 the study of the crushing strength of mine pillars, which usually have a broad 
 base as compared to the height of the pillar, and are represented more closely 
 by samples a and b. Hence, the unit load producing the first crack in mine 
 pillars may be assumed as one-half of that obtained, or 2,000 Ib. 
 
SUPPORTING EXCAVATIONS 695 
 
 Crushing Strength of Bituminous Coal. There are no figures for bituminous 
 coal similar to those given for anthracite, and owing to the great variation in 
 the character of different bituminous coals, an average value cannot be given. 
 In order to make similar calculations for bituminous coal, tests of the coal from 
 the particular mine in question must be made. 
 
 ROOM, ENTRY, AND SLOPE PILLARS 
 
 Load on Pillars. As the removal of the coal throws the total load on the 
 pillars, the roof pressure per square foot on the pillars is increased in the ratio 
 of the total area of the opening and pillars to the area of the pillars. In the 
 accompanying illustration, o represents the width of an opening separated 
 from other similar openings by pillars, the width of each pillar being w. A 
 weight of cover equal to w-+-o then rests on each pillar w, and if L represents 
 the roof pressure or load per square foot on each pillar, 
 
 EXAMPLE. Find the roof pressure at a depth of 900 ft. below the surface, 
 
 when the rooms are driven 
 
 on 70-ft. centers with pillars {feffiffiffl A ''. ' / T "^_ Vj r : : i ~~~r ' ~ 
 50 ft. wide between them 
 and the width of the rooms 
 is 20 ft. 
 
 SOLUTION. -In this case, 
 d = 900, >+o = 70, and w 
 = 50. Substituting these 
 values in the formula, 
 L = 160X900Xi8 = 201,6001b. per sq. ft.; 201, 600 * 144-1, 400 Ib. per sq. in.; 
 201,600-7-2,000 = 100.8 T. per sq. ft. This roof pressure must be below the 
 safe crushing strength of the coal if the pillars are to stand and not be immedi- 
 ately ground to powder. 
 
 Strength of Pillars. The safe strength of pillars may be estimated as 
 one-half or one-third of the squeezing strength that is, the point at which 
 the first cracks appear-^-or one-fourth to one-sixth of the crushing strength, 
 according to the conditions of mining; that is, using the values given in the 
 table on page 694, the safe load for anthracite should not be estimated as 
 greater than 2,000-f-3, say, 700 Ib. per sq. in. under adverse conditions; or, 
 under more favorable conditions, 2, 000 -f- 2 = 1,000 Ib. per sq. in. Expressed 
 in tons per square foot, these values will vary from 50 to 70 T. 
 
 If the conclusions deduced from the experiments made on anthracite are 
 verified by other experiments, the allowable unit load on a pillar of anthracite 
 may be expressed by a formula as follows: 
 
 in which S = unit load that can be supported, in tons per square foot; 
 C = constant expressing safe crushing strength of a unit sample of 
 
 anthracite, in tons per square foot; 
 w = width of pillar, in feet; 
 t = thickness of seam, in feet. 
 
 EXAMPLE. Find the safe load that can be put on anthracite pillars having 
 a width of 20 ft. in a seam 5 ft. thick. 
 
 Solution. Substituting the given values in the formula, the safe load on 
 these pillars is 5 = 50 X V^ = 100 T. per sq. ft. Ans. 
 
 Width of Room Pillars. The strength of mine pillars, or the safe unit load 
 they will support, must be at least equal to the roof pressure or load per square 
 foot resting upon them; hence, to sustain the roof, L = S. Calling the percent- 
 
 age of room-pillar coal to be left in the mine J (expressed decimally), J ; ; 
 
 w-\-o 
 
 multiplying the right-hand side of the equation for S by 2,000 to reduce tons 
 to pounds; and equating L and S, and solving for w, 
 f 160 d \2 
 
 in which w = width of pillar, in feet; 
 
 J percentage of coal in room pillars; 
 d = depth of cover, in feet; 
 
 C constant for safe unit crushing strength of coal; 
 / = thickness of coal seam, in feet. 
 
696 SUPPORTING EXCAVATIONS 
 
 The percentage of pillar coal to be left between the rooms is often assumed, 
 and it depends, of course, on the relative size of pillar and room openings. 
 The safe width of opening is best determined by practical experience and 
 
 In the 'foregoing equations there are two variable quantities, w and o, which 
 may have any values. Hence, if the width of the room o is assumed, the value 
 for w selected must satisfy the equations for both J and w. This can only be 
 accomplished by trial, as appears from the following example. 
 
 EXAMPLE. Assume that a 16-ft. seam of anthracite lying 600 ft. below the 
 surface is overlaid with alternate layers of shale and sand rock. Find the 
 width of pillar that should be left between the rooms if the rooms are made 20 ft. 
 
 SOLUTION. Assume a width of pillar w = 40 ft. Substituting this and 
 o = 20 ft. in the formula for J, J = 66|%. Substituting this value of J in the 
 second formula, w = 23+ft.; very much less than the assumed value of 40 ft. 
 
 For a second trial, assume w = 35 ft., whence / = 63 + %, and a; = 36.4 ft. 
 This second value is close enough for practical purposes, but another may be 
 made by placing w = 36 ft., whence J = 64 + % and w = 35.7 ft. 
 
 From this, the pillars should be 36 ft. wide, and the rooms are driven on 
 20+36 = 56 ft. centers. 
 
 For bituminous coal of medium hardness and good roof and floor, a rule 
 often used is to make the thickness of room pillars, equal to 1% of the depth 
 of cover for each foot of thickness of the seam, according to the expression 
 
 t 
 
 in which Wp = pillar width; 
 
 t = thickness of seam; 
 D = depth of cover. 
 Then make the width of breast or opening equal to the depth of cover 
 
 divided by the width of pillar thus found, according to the expression Wo = ^-, 
 
 Wp 
 where Wo = width of room. 
 
 Frail coal and coal that disintegrates readily when exposed to the air, and 
 a soft bottom, may increase the width of pillar required as much as 50% of 
 the amount just found; also, a hard roof may increase the same as much 
 as 25%; while on the other hand, a frail roof or a hard coal or floor may reduce 
 the width of pillar required 25%. The hardness of the roof affects both the 
 width of pillar and width of opening alike, which is not the case with any of 
 the other factors. 
 
 In the accompanying table, the weight thrown upon pillars at different depths 
 by the removal of different proportions of coal is given: 
 
 WEIGHT ON PILLARS AT VARIOUS DEPTHS 
 
 
 Percentage of Coal Left in Pillars 
 
 Depth 
 
 
 
 
 
 
 
 
 
 
 Seam 
 
 90 
 
 80 
 
 70 
 
 60 
 
 50 
 
 40 
 
 30 
 
 20 
 
 10 
 
 Feet 
 
 
 
 
 
 
 
 
 
 
 
 Weight on Pillars in Pounds per Square Inch 
 
 100 
 
 111 
 
 125 
 
 142 
 
 166 
 
 200 
 
 250 
 
 333 
 
 500 
 
 1,000 
 
 500 
 
 555 
 
 625 
 
 710 
 
 830 
 
 1,000 
 
 1,250 
 
 1,665 
 
 2,500 
 
 5.000 
 
 1,000 
 
 1,111 
 
 1,250 
 
 1,428 
 
 1,666 
 
 2,000 
 
 2,500 
 
 3,333 
 
 5,000 
 
 10,000 
 
 1,500 
 
 1,666 
 
 1,875 
 
 2,138 
 
 2,496 
 
 3,000 
 
 3,750 
 
 4,998 
 
 7,500 
 
 15,000 
 
 2,000 
 
 2,222 
 
 2,500 
 
 2,956 
 
 3,333 
 
 4,000 
 
 5,000 
 
 6,666 
 
 
 
 3,000 
 
 3,333 
 
 3,750 
 
 4,384 
 
 4,999 
 
 6,000 
 
 7,500 
 
 
 
 
 4,000 
 
 4,444 
 
 5,000 
 
 5,912 
 
 6,666 
 
 8,000 
 
 
 
 
 
 5,000 
 
 5,555 
 
 6,250 
 
 7,340 
 
 
 
 
 
 
 
 10,000 
 
 11,110 
 
 12,500 
 
 
 
 
 
 
 
 
 Slope Pillars. A slope should have a pillar along its full length and theoreti- 
 cally the pillar should gradually increase in width from top to bottom as the 
 
SUPPORTING EXCAVATIONS 697 
 
 thickness of cover increases, but in practice this is seldom done and the slope 
 pillar is the same width throughout. The frequency of squeezes on slopes 
 indicates that this is faulty practice. The width of the slope pillar is some- 
 times prescribed by law. 
 
 There is not much danger of the draw destroying a slope sunk in the coal, 
 except that due to mining in an underlying seam, because the line of the 
 slope is in the same plane as the bed in which the mining is done and nearly at 
 right angles to the plane of fracture, whereas in a shaft, the lines of fracture 
 may reach or cross the line of the shaft, and in a pitching seam this danger is 
 even greater than in a flat seam. 
 
 Entry Pillars. Much that has been said with reference to room and slope 
 
 The chief factors determin- 
 thickness, and character 
 
 opening. The size of entry pillars, as of room 
 pillars, is determined almost entirely by practical experience. The best 
 practice advises leaving large pillars about the entries and all airways so as to 
 avoid all possibility of a squeeze. 
 
 SHAFT PILLARS 
 
 Great diversity of opinion exists among mining authorities as to the size 
 of shaft pillars and the matter must be decided largely by local considerations 
 and practical experience in the district in which the shaft is sunk. The shaft 
 pillar should be large enough so that the effect of the draw cannot reach the 
 shaft or the buildings on the surface about the shaft and thus interfere with 
 its alinement. The same general rules apply to shaft pillars as to other pil- 
 lars; namely, in general, the deeper the shaft and the thicker the seam the 
 larger must the pillar be, while the harder the coal the smaller the pillar. 
 
 Pillars in Flat Seams. In flat seams, the size of the shaft pillar required 
 depends chiefly on the depth of the seam below the surface, that is, the depth 
 of cover, and to a less extent on the thickness of the seam. The rules given for 
 determining the size of the shaft pillar afford widely varying results, owing 
 to the varying conditions under which each rule was formulated, and for this 
 reason that rule should be employed that seems best suited to the particular 
 conditions of the case. These rules are given as formulas and the results 
 obtained by applying them to determine the shaft pillars required at depths 
 of 300 feet and 600 feet, respectively, are tabulated later. 
 Let D = diameter of round pillar, or side of square pillar, in yards; 
 d = depth of cover, in yards; 
 t = thickness of seam, in yards. 
 
 Merivale's Rule. Diameter of circular pillar, or side of square pillar, in 
 yards, is equal to twenty-two times the square root of the depth of the shaft, in 
 fathoms, divided by 50. 
 
 * \2X50 
 
 Andre's Rule. Minimum diameter of circular pillar, or side of square pillar, 
 35 yd. to a depth of 150 yd.; add 5 yd. for each 25 yd. of additional depth. 
 
 (2) 
 
 Wardle's Rule. Minimum diameter of circular pillar, or side of square 
 pillar, 40 yd. to a depth of 60 falh.; add 10 yd. for each 20 fath. of additional depth. 
 
 (3, 
 
 Pamely's Rule. Minimum diameter of circular pillar, or side of square pil- 
 lar, 40 yd. to a depth of 100 yd., add 5 yd. for each 20 yd. of additional depth. 
 
 (4) 
 
 Mining Engineering (London) Rule. Radius of circular pillar, or half side 
 of square pillar, in yards, is equal to SO yd. plus one-tenth of the product obtained 
 by multiplying the depth of shaft, in yards, by the square root of the thickness of 
 the seam, in yards. 
 
 Z, = 40+ (5) 
 
 Foster's Rule. Radius of circular pillar, or half side of square pillar, in 
 feet, is equal to three times the square root of the product of the depth of cover, in 
 feet, and the thickness of the seam, in feet. _ 
 
 (6) 
 
698 SUPPORTING EXCAVATIONS 
 
 Dron's Rule. Draw a line enclosing all surface buildings that should be pro- 
 tected by the shaft pillar. Make the pillar of such size that solid coal will be left 
 in all around this line for a distance equal to one-third of the depth of the shaft. 
 
 D = s+j (7) 
 
 in which 5 = diameter of circle, or side of square, in yards, at the surface. 
 
 Hughes's Rule. For the diameter of a circular pillar, or the side of a square 
 pillar, allow 1 yd. for each yard in depth. 
 
 D = d (8) 
 
 Central Coal Basin Rule. In the Central Coal Basin of the United States, 
 for shaft mines worked on the room-and-pillar method, the rule is: Leave 
 100 sq.ft. of coal for each foot that the shaft is deep, it being understood that a main 
 entry of average width is driven through this pillar. If the bottom is soft, the result 
 given by this rule is increased by one-half. 
 
 SIZE OF SHAFT PILLAR OBTAINED BY USE OF SEVERAL FORMULAS 
 
 Authority 
 
 Diameter of Side of Pillar 
 Yards 
 
 Shaft 100 Yd. 
 Deep 
 
 Shaft 200 Yd. 
 Deep 
 
 Merivale 
 
 22.0 
 35.0 
 40.0 
 40.0 
 68.3 
 84.8 
 100.0 
 100.0 
 100.0 
 
 31.00 
 45.00 
 60.00 
 65.00 
 96.50 
 120.00 
 166.66 
 200.00 
 142.00 
 
 Andre ; . . 
 
 Wardle 
 
 Pamely 
 
 Mining Engineering (London) * 
 
 Foster* 
 
 Dronf 
 
 Hughes 
 
 Central basin 
 
 
 *The seam is assumed to be 2 yd. (6 ft.) in thickness. 
 
 fAn allowance of 100 ft. has been made for the diameter of the circle, or side 
 of the square, enclosing the buildings on the surface. 
 
 When using formulas 2, 3, and 4, negative results in the fractional part must 
 be rejected, as the diameter of pillar cannot be less than the minimum diameter 
 or side allowed by the rule. For example, it is useless to apply Andre's rule to 
 depths less than 150 yd., Wardle's rule to depths less than 60 fath. (120 yd.), 
 or Pamely's rule to depths less than 100 yd. 
 
 The foregoing table shows clearly that no hard-and-fast rule can be 
 given for determining the size of shaft pillar required in any particular case. 
 The rules stated, however, determine the size of pillar required within certain 
 practical limits, and suited to different conditions of roof strata, and are, there- 
 fore, useful and desirable. The presence of faults or slips in the roof makes 
 larger pillars necessary. 
 
 Pillars in Inclined Seams. The inclination of the seam increases the 
 uncertainty in respect to the draw in the strata overlying the seam, making it 
 more difficult to give any rule of universal application. The general practice 
 in regard to the size of pillar required when the seam is inclined, is to increase 
 the pillar on the rise side of the shaft, while that on the dip side of the shaft is 
 often made the same as for a flat seam. To what extent it is necessary to 
 increase the pillar on the rise side is largely a matter of experience and judgment 
 in particular localities, and this is always the most reliable guide. 
 
 One method is to calculate the extent of the pillar on the dip side of the 
 shaft by the rules given for flat seams, choosing for this purpose the rule that 
 seems best suited to the conditions with respect to the character of the seam 
 and overlying strata. The diameter of the circular pillar, or the side of a square 
 pillar, thus obtained, will give the width of the pillar measured on the strike 
 
SUPPORTING EXCAVATIONS 699 
 
 of the seam, and half of this width will give the extent of the pillar measured 
 below the shaft on the dip of the seam. Then, calling the width of the pil- 
 lar D, the depth of the shaft d, and the inclination of the seam a, the extent of 
 
 the pillar measured on the pitch of the seam may be taken as + j d sin a. 
 
 This rule is arbitrary, but approximates to a certain extent the condition rela- 
 tive to the inclination of the seam. All the rules and formulas given for deter- 
 mining the sizes of pillars, both in flat and inclined seams, are only suggestive 
 of what is required, and must always be modified according to the experience 
 and judgment of the person in charge of the work. 
 
 PILLARS FOR MISCELLANEOUS PURPOSES 
 
 Pillars for Supporting Buildings, Etc. Dron's rule for shaft pillars is 
 probably the most practicable, as it provides for a given pillar of coal all around 
 the buildings, etc., to be supported. 
 
 Reserve Pillars. Extra large pillars of coal are often left at regular inter- 
 vals in the workings; their purpose is to divide the mine into sections or districts 
 so as to localize the effect of any squeeze that may start in one of these districts 
 by breaking the roof at the reserve pillar. These pillars are usually equal to 
 the width of one room and two pillars, and are formed by not driving one room 
 as called for by the plan of the mine. They are taken out before the entry or 
 gangway is abandoned. 
 
 Chain Pillar. A chain pillar is usually left across the ends of a group of 
 rooms to protect the gangway, or entry, toward which the rooms are being 
 driven. The miners frequently drive their rooms too far and hole through into 
 the next gangway in spite of the precautions that are taken to prevent this 
 occurrence. To avoid the possibility of rooms being driven too far and holing 
 through the chain pillar, a cut-off room is sometimes driven parallel to the 
 entries or gangways. This place is driven wide enough to avoid the expense 
 of yardage, and rooms driven from the next gangway are allowed to hole into 
 it, thus avoiding the necessity of accurately measuring the length of the rooms 
 and of carefully watching the miners to see that they do not exceed the limit 
 allowed. The method also possesses the advantage of giving a regular width 
 to the entry pillar and thereby avoiding the loss of a considerable amount of 
 pillar coal when these entries are abandoned and their pillars drawn. When 
 drawing back an ordinary chain pillar, any irregularity in the -width of the pil- 
 lar may cause a loss of some of the coal, which cannot occur when a cut-off 
 room is driven as described. 
 
 Barrier Pillars. The laws of some states require a pillar of coal to be left 
 in each bed of coal worked along the line of adjoining properties, of such width, 
 that, taken in connection with the pillar to be left by the adjacent property 
 owner, it will be a sufficient barrier for the safety of the employes of_mines on 
 either property in case one should be abandoned and allowed to fill with water. 
 These pillars are known as barrier pillars. The width of such pillars is deter- 
 mined by the engineers of the adjoining property owners and the mine inspec- 
 tor in whose district the properties are located. 
 
 An arbitrary rule for the width of barrier pillars, adopted by a number of 
 coal companies and by the state mine inspectors of the anthracite districts 
 of eastern Pennsylvania, is as follows: 
 
 Rule. Multiply the thickness of the deposit, in feet, by 1% of the depth below 
 drainage level, and add to this five times the thickness of the bed. 
 
 Thus, for a bed of coal 6 ft. thick and 400 ft. below drainage level, the bar- 
 rier pillar will, according to this rule, be (6 X 400 X. 01) + (6X5) = 54 ft. wide. 
 
 The Bituminous Mine Law of Pennsylvania requires a thickness of 1 ft. of 
 pillar for each 1J ft. of water head if, in the judgment of the engineer of the 
 property and of the district mine inspector, this thickness is necessary for the 
 safety of the persons working in the mine. The same law makes it lawful for 
 any operator whose mine is endangered by an accumulation of water in aband- 
 oned workings located on an adjoining property, to drive a drift or entry pro- 
 tected by bore holes, across the barrier line, for the purpose of tapping and 
 draining such water, and makes it unlawful for any person to attempt to, or in 
 any way to obstruct the flow of such water to a point of drainage. The law 
 also provides that no coal shall be mined within 50 ft. of any abandoned work- 
 ings containing a dangerous accumulation of water, until such danger has been 
 removed as described above. 
 
700 SUPPORTING EXCAVATIONS 
 
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SUPPORTING EXCAVATIONS 701 
 
 SQUEEZE AND CREEP 
 
 When the roof and floor are strong and unyielding and the pillars are insuf- 
 ficient to withstand the pressure thrown on them, they are filled with breaks 
 and cracks, large pieces split off, and the pillars are finally crushed into small 
 coal and the roof comes down. This is known as a squeeze, thrust, or crush. 
 
 When the material composing the floor or roof, or both, is soft and weak 
 and the pillars left are too small, the weight on them causes the roof to sag or 
 the floor to bulge upwards, or both. This result is known as a creep. The 
 soft character of the floor or roof permits the pillars under the enormous roof 
 pressure either to sink into the floor or to be forced into the roof, pressing out 
 the softer material, which fills the openings. Fireclay is particularly suscepti- 
 ble to creep, and many of the fireclays that are hard when dry become extremely 
 soft and plastic when moist; it is important to keep such a clay bottom dry. 
 
 The terms squeeze, thrust, crush, and creep are often incorrectly used 
 synonymously. A squeeze and a creep may be going on at the same time. A 
 squeeze or a creep does not generally come suddenly, but the pillars and tim- 
 bers usually give evidence of the too great roof pressure by cracking and by 
 pieces flaking off at the sides. The chipping or nicking of the pillar coal, indi- 
 cating that the pillars are too small, should not be mistaken for the gradual 
 spalling or chipping due to weathering alone. When pillars or timbers thus 
 give evidence of increased pressure, they are sometimes said to be taking the 
 weight. The coming of a squeeze is often first told by the departure of the 
 rats from the affected area, as their sense of hearing is more acute than man's; 
 next the coal begins to crack; and then the timbers split and crush. 
 
 Stopping a Squeeze. When any sign of a squeeze appears, the pillars 
 should be reenforced as much as possible by wooden chocks, or cribs, as here 
 shown, and by supports of any kind that can be put up just outside of the part 
 affected. If the action of the squeeze 
 is slow, some of the pillars may be 
 removed rapidly, which will allow the 
 top to break and thus relieve the stand- 
 ing pillars of part of the weight. 
 
 The treatment of a squeeze should 
 be determined by the inspection of an 
 accurate and complete map of the 
 workings. If the disturbed region can- 
 not be isolated by timbering and build- 
 ing strong stoppings in all the roads 
 round about it, the trouble may often 
 be stopped with little expense by draw- 
 ing out some of the timber already in place, and throwing the weight on some 
 small outlying patches of coal that can, with advantage, be sacrificed to save the 
 roads and pillars of the district affected. In many cases, such trouble can more 
 quickly be arrested by helping it than by trying to prevent it. When once the 
 roof becomes unsteady and the timbers are breaking and the floor is lifting, 
 a force is operating that cannot be stopped by artificial means; it can. however, 
 be directed by assisting it to find relief where the least damage will be done. 
 If the roof does not break readily, dynamite should be used at different points 
 to start the fall. By this means, the power of the squeeze may be broken and 
 the danger of its spreading to adjacent workings lessened. The building of 
 large cribs to avoid the disastrous results of squeeze often acts to increase the 
 evil rather than to diminish it, especially if the cribs are placed at points where 
 complete settlement is desired. The cribs are not easily removed, and serve 
 as fulcrums by which the weight is carried forwards to other points. As per- 
 manent supports for the roof, cribs are of great advantage, but care should be 
 taken to break the roof back of them when the weight comes on, in the same 
 manner as over entry pillars, by the use of shots placed in the roof near them. 
 Confining a squeeze to a certain limit is a difficult, expensive, and dangerous 
 operation, requiring the utmost skill and care in every individual engaged in 
 the work. 
 
 The creep will continue until the excavations are filled, and the whole 
 becomes compact enough to resist the weight. This sometimes takes many 
 months, but it is a sure result, whether the action is fast or slow. A creep can- 
 not be resisted unless the space from which the coal has been removed is filled 
 with other material like culm. 
 
 Reopening a District Closed by Squeeze. Time should be given for the 
 complete settlement of the roof before any attempt is made to reopen a dis- 
 trict closed by a squeeze, for if work is begun before the action of the squeeze 
 
702 . SUPPORTING EXCAVATIONS 
 
 has wholly ceased, the movement will begin again and may extend to other 
 parts of the mine. The work of reopening is expensive and seldom pays in thin 
 seams unless the coal is very valuable. Where the entries are wholly closed, 
 it is often possible to drive a new entry in the old pillars, or even across the 
 pillars. 
 
 It is not usually economical to attempt to reopen old entries closed, or par- 
 tially closed, by squeeze, as a larger amount of material must be handled, and 
 more timber will be required than when a new opening is driven. 
 
 In the treatment of creep, it is usually better to excavate in the roof and 
 leave the bottom undisturbed as the bottom often keeps working and fills up 
 about as rapidly as it can be taken out. 
 
 Whenever practicable, the work of reopening can be done to better advan- 
 tage by driving a pair of entries beyond the affected district, and coming back 
 on the coal. By this means, the least affected portion of the district will be 
 reached first and as much of the coal recovered as is found desirable; the demand 
 for coal, however, will not always permit the adoption of this method. 
 
 FLUSHING OF CULM 
 
 In the anthracite regions of Pennsylvania, in Europe, and in South Africa, 
 worked-out portions of the mine are now commonly filled with refuse mate- 
 rial brought in on streams of water. This is done not only to support the roof 
 over the workings but also to permit the recovery of the coal or the ore which 
 would otherwise have to be left in the pillars. 
 
 Abroad, the material used for filling is very generally sand, but in Pennsyl- 
 vania, the culm, or fine refuse from the breakers, washeries, etc., is commonly 
 employed. In addition to culm, ashes from the boiler house, crushed slate, 
 and the like are employed, either alone or, preferably, mixed with culm. 
 
 The plants for handling culm are more or less elaborate. The Dodson 
 
 S'ant cost $7,473.42 with a capacity of flushing 119 T. a da. and the Black 
 iamond plant, with a daily capacity of 287 T., cost $6,280.12. They usually 
 consist of crushers (where needed), troughs, conveyers, settling or mixing 
 tanks, and in some instances storage tanks. Where culm alone is employed, 
 it is usually brought from the breaker or culm bank by means of a scraper 
 conveyer to a mixing tank, which may be anything from a simple oil barrel 
 at a small operation to extensive wooden and concrete tanks at the larger ones, 
 If a number of openings are being flushed at the same colliery, the mixing tank 
 is generally set on a hill and is made of large size, pipes radiating from it to the 
 various bore holes through which flushing is going on. Where coal is wet 
 screened, the screenings from the breaker are generally caught in settling tanks 
 so that the excess water flows away, the dewatered culm alone being elevated 
 to the central mixing or distributing tank. At the Shenandoah City colliery, 
 Shenandoah, Pa., all the waste material from the breaker is sent through the 
 mine. The slate and screenings are brought out on separate conveyers. The 
 screenings are dumped directly into the first of two flights of conveyers, which 
 carry them to a distributing tower where enough water is added to flush them 
 into the mine. The slate is carried first to a No. 3 Williams crusher where 
 everything over 2f in. is broken and then conveyed back to be mixed with 
 the breaker screenings. The ashes from the boiler house are run into the slate 
 conveyer so that the lumps of clinker may be broken by the crusher and are 
 thus mixed intimately with the culm and slate. When the breaker is not run- 
 ning the ashes pass to a concrete storage bin holding 1 wk.'s supply, from 
 which they may subsequently be flushed when the breaker is running. The 
 composition of the slush or sludge, the material used for flushing, is 50% screen- 
 ings or culm, 44% slate, and 6% ashes. 
 
 The amount of water required for flushing depends on the material being 
 flushed, the pitch of the seam and that of the pipe, and the distance to which 
 the sludge has to be carried. At West Shenandoah, the proportion between 
 water and screenings is made as nearly 2 to 1 as can be estimated. At this 
 mine, the seam pitches 45 and less water is required than if the seam was 
 flatter. At the Kohinoor colliery, 565 cu. yd. of culm were flushed daily with 
 an expenditure of water of from 67 to 334 gal. per cu. yd. of culm; an average 
 of 200 gal. of water per yd. of dry material. Experience has shown that from 
 1$ to If Ib. of water is required to flush 1 Ib. of culm to level and down-hill 
 places; 3 to 6 Ib. of water to 1 Ib. of culm to flush up-hill for heights varying 
 from 10 to 100 ft. above the level of the shaft bottom. Any elevation of the 
 pipe very materially increases the amount of water necessary. Mr. James B. 
 
SUPPORTING EXCAVATIONS 703 
 
 Davis, when superintendent of the Dodson and Black Diamond mines, ascer- 
 tained by experiment that 1 cu. ft. of anthracite ground to culm can be flushed 
 into a space of nearly l cu. ft., and it is therefore impossible to compress the 
 culm more than one-third. In addition to acting as a filling and a support, 
 to prevent squeezes and crushing, flushing has been advantageously used for 
 fighting and sealing off mine fires. No instance has been recorded where 
 spontaneous combustion has taken place in the flushed culm. 
 
 On the surface, the culm is generally conducted to the y a ri u s openings 
 through which it enters the mine in wooden troughs lined with sheet iron or 
 terra-cotta, the latter being preferred. For handling culm, wooden pipe is 
 preferred to iron, although the latter is, of course, largely used. The life of 
 the pipe is dependent on the kind of material passing through it and the grade 
 on which it is laid. Breaker screenings and culm will not wear a pipe as quickly 
 as ashes and broken slate. A 6-in. iron pipe laid at West Shenandoah colliery, 
 which carried crushed slate for a distance of 1,500 ft. on a considerable grade 
 was worn out after passing 16,000 cu. yd., whereas wooden pipes carrying 
 breaker screenings have lasted 1, 2, and 3 yr. Wrought-iron pipe is often 
 used where ashes are being flushed separately. Wooden pipes should be turned 
 after being in one position for a certain length of time. On very light grades, 
 it may be necessary to turn them every 6 mo. On steep slopes, they had better 
 be turned every few weeks to distribute the wear evenly over the interior and 
 thus lengthen the life of the pipe. The life of wrought-irqn pipe depends on 
 the nature of the water used and the material flushed. With fresh water and 
 small culm from the_ buckwheat screen, it lasts 18 mo.; when carrying culm 
 from the bank, ranging from dust to pea coal and some chestnut, 9 mo.; and 
 when mixed with ashes, 6 mo. The smaller the material the better. 
 
 The sludge is usually let into the mine through bore holes sunk with a rope 
 drill and from 6 in. to 8 in. in diameter, although the opening to a room driven 
 to the crop, an old slope, or even an abandoned shaft have been used for the 
 purpose. No rules can be given as conditions vary at each mine. 
 
 The handling of the culm underground will also vary from place to place. 
 Basicly, the methods are the same in that brattices or dams are built at the 
 mouths of the rooms or headings, the sludge let into the excavations through 
 pipes and the water allowed to drain off through a pipe in the dam, leaving 
 the solid material behind. If the sludge can be let in at the tops of pitching 
 breasts it is naturally the best way, as they then fill by gravity. At several 
 mines, gangways have been driven along the faces of a series of pitching breasts 
 and along these gangways the sludge is conveyed in pipes, which are tapped 
 at the face of each room. The mouths of the rooms on the main gangways 
 are blocked with heavy bulkheads, so that the material is retained in the desired 
 place. These bulkheads, or batteries, are built of material of a size and strength 
 to suit the pitch of the seam. The steeper the pitch, the larger the props and 
 the closer together are they placed. On pitches of 20 to 30 and upwards, 
 12-in. to 14-in. and larger props are used, set 2 ft. apart with braces between 
 them. Care must be taken to place the props with their inside faces in line, 
 so that the lining planks can be securely fastened. The lining or facing con- 
 sists of a double layer of 1^-in. plank securely hitched into the coal and all 
 cracks stopped with hay. The tops and bottoms of the main posts are hitched 
 into the roof and floor to a depth proportionate to the weight they will have to 
 sustain. 
 
 The surplus water may be drained off in various ways. At some mines, 
 small iron pipes are inserted in the bulkheads; in others, it merely drains off 
 through the cracks. At Indian Ridge colliery and some others, the water 
 drains off in wooden pipes placed in the brattices. These pipes are made of 
 1-in. boards and are 4 in. square inside. On their sides, saw cuts about 1 ft. 
 long are made, four series of slots being made in each board. These slots allow 
 the water to pass while holding the culm. Three, four, or six pipes may be 
 placed in a battery as desired. Where the seam has not much pitch, a couple 
 of square-board pipes are run up the breast. These are provided at the upper 
 end with an upright branch pipe. When the dewatered material reaches the 
 top of the upright, the pipe is closed with a board. Where the seam is flat, the 
 flushing pipes are fastened along the roof for the full length of the chamber. 
 Then as the chamber fills and the slush rises up to the pipe, a length of pipe is 
 taken off and the flushing continued. In this case the seam cannot be filled 
 completely, a little space always being left between the flush and the roof. 
 After flowing for 1 or 2 hr. into one room, the slush is commonly turned into 
 an adjacent room for the same length of time, during which interval the first 
 place drains. The slush is then turned back to the first place while the second 
 
704 
 
 SUPPORTING EXCAVATIONS 
 
 one drains. A room having a pitch of 5 or more can be filled with slush if it 
 is poured in at the high end. If ashes are used alone, a pitch of 10 or more is 
 needed, as ashes, being porous, allow the water to drain away quickly and will 
 not flow in a stream as readily as breaker screenings. In caved areas, slush 
 makes an excellent filling as it completely fills the spaces between the broken 
 
 The pipes used to convey the sludge underground are 6 in. in size and will 
 carry any material coming to them, as the sludge has to pass through a 2 J-in. 
 screen placed over the mouth of the bore hole. A common trouble in flush- 
 ing is to have the pipe become blocked. This will happen if the pipe is not full 
 of clear water without solids before flushing is begun, and if the pipe is not 
 cleaned out with clear water after flushing is stopped. Water must be turned 
 into the pipe and be flowing before the slush enters and must be kept flowing 
 after the slush is stopped. The slush should be so mixed that there is a con- 
 stant uniform flow. Sudden rushes of slush are likely to block the pipe. To 
 quickly locate a block, holes are bored in wooden pipes and closed with plugs. 
 The pipe is likely to clean itself out below any block, and by knocking the plugs 
 out the blocks can be located and the pipes need be taken apart only at the 
 
 When roadways are cut through slush the sides will stand without tim- 
 bering unless they become water soaked. When drawing pillars after flushing, 
 regular systems are followed as much as possible. One method is to take out 
 every third pillar, and it is mined from the gangway advancing, ventilation 
 being maintained by means of a door on the gangway and a brattice up to the 
 working face, as no breakthroughs can be maintained. The coal pillars of the 
 original working are now the rooms. As soon as one is drawn, a battery is built 
 at its mouth, and the empty space is flushed. When one pillar is drawn the 
 next one is mined, care being taken that the pillars on which work is being done 
 are three apart and that all rooms in between are flushed. When the pillars 
 are irregular, no system can be followed. Pillars in underlying seams can be 
 taken out without disturbing those in seams above, but it is better to take them 
 but simultaneously and have the rooms flushed in sections one over the other. 
 When removing the pillars certain precautions have to be followed. In doing 
 this the face of the pillar along the gangway is attacked, and a road driven 
 up through the pillar, splitting it, as shown at 
 z in the accompanying illustration. This road 
 may be the full width of the pillar, but in 
 general it is necessary to leave a narrow stump 
 of coal on either side to keep up the fine flushed 
 material in the adjoining breasts. The thick- 
 ness of this supporting coal depends entirely on 
 the condition of the flushed material behind it. 
 If that is fine, it will set firmly and form a 
 compact mass that will not run. In such a 
 case, the pillar may be entirely taken out, 
 leaving a vertical wall of solidly packed flushed 
 culm. When the flushed material is of a size 
 larger than buckwheat, it will not set com- 
 pactly, but will run when it is opened up, and 
 when such material fills the adjoining breasts, 
 the thin pillar of coal must be left to keep 
 back the culm. Timbers are placed flush up 
 against the culm or the coal stumps, as the 
 case may be, and if there is a tendency for 
 the culm to run, lagging is placed behind the 
 timbers. In some cases, as much as 700 ft. of 
 timber have been used per 100 ft. of pillar taken out. As the pillar is removed, 
 the top settles until it finally rests upon the flushed culm, and as the weight 
 from the top and the pressure from the sides comes upon these props, they are 
 broken, while the coal that has been left will also be crushed. At the Black 
 Diamond colliery, the props used are 16 ft. long, and at this colliery the top 
 settles about 4 ft. if the flushed material is packed tightly before the roof pres- 
 sure comes on it. After this settling, new props 12 ft. in length are put in close 
 up against the culm and the broken stump of the original pillar, and they serve 
 to keep the road open up to the working face. 
 
 The Mammoth seam, ranging from 40 to 60 ft. thick, at the Kqhinoor 
 colliery is being mined by a flushing and slicing system. A room is driven in 
 the bottom bench and as soon as finished is flushed solidly full. With the top 
 
SUPPORTING EXCAVATIONS 705 
 
 of the flushing as a floor, about 10 ft. more of coal is mined out, and this second 
 space again filled with culm. In a similar manner the rest of the seam is 
 sliced out and the openings flushed until the roof is reached. In working the 
 first or bottom bench, the track is laid on the regular floor of the seam, but in 
 working the remaining slices, a buggy or small car pushed by hand is used to 
 carry the coal to a chute through which it is dumped into the regular mine car 
 standing on the gangway. _ 
 
 The saving from flushing of culm over depositing it on the surface varies 
 for the ordinary anthracite colliery from $5 to $15 per da. The average cost 
 of putting in stoppings in a 9 ft. seam is given by Mr. James B. Davis as $9.50, 
 including the material. 
 
 BUILT-UP PACKS AND CRIBS 
 
 While the term pack is sometimes applied to any built-up structure of stone 
 used to support the roof where the coal has been removed from a wide area, 
 the word should be restricted in its meaning to the walls built up of roof slate, 
 etc., used in longwall mining as a support for the roadways. In this system 
 of mining, the packs must be carefully built, the larger and flatter stones used 
 for facing, and all of them bedded in fine material so that the rock pressure may 
 compact the pack into a solid mass. The face stones should be well bonded, 
 and a number of them should extend back into the center of the pack so as to 
 bind the face walls and prevent their bulging out when the weight comes on 
 them. 
 
 Cribs, or chocks, consist of a square building of round logs built in log-cabin 
 style and either notched into each other or pinned together at the ends. The 
 interior is closely packed with loose slate, rock, spalls, etc., and when well built 
 cribs offer substantial support to the roof. They are quite commonly employed 
 to strengthen the corners of pillars that have been left too small; as permanent 
 supports where the pillars have been entirely removed ; and to cause a break to 
 the surface and thus stop a squeeze. Cribs are of almost universal employ- 
 ment in longwall mines, and especially in those where there is a scarcity of mate- 
 rial from which to build the necessary packs. Cribs are not adapted as per- 
 manent supports if the seam is more than a short distance beneath the surface, 
 as they crush and may even be ground to powder under the enormous pressure 
 at great depths. 
 
 Strength of Packs and Cribs. In 1911, Prof. Frank P. McKibben made at 
 the Fritz Engineering Laboratory of the Lehigh University, South Bethlehem, 
 Pa., a series of important tests upon the crushing strength of various kinds and 
 forms of artificial mine supports. These investigations were undertaken on 
 behalf of Messrs. William Griffith and Eli T. Connor, appointed by the city of 
 Scranton, Pa., to investigate mining conditions under that municipality and to 
 suggest methods by which the surface might be supported over extended areas 
 while, at the same time, mining and removal of coal was going on beneath. 
 
 The results of these investigations are summarized in the table on page 706, 
 and while, naturally, made upon structures much smaller than those used in 
 actual mining operations, give an excellent idea as to the relative value of the 
 various types of support in common use. It will be noted that, in a general 
 way, the tests were made upon two types of support. In the one, the sup- 
 ports consisted of cribs or piers of rock, or of rock and timber, or of piles 
 of stone which were free to expand laterally. That is, they represented on a 
 small scale the larger structures frequently built in open places in the mine 
 upon the approach of a squeeze. The other type represented the various 
 methods of filling in which the material used as a support is contained within 
 the confines of a room in the mine and is not free to expand laterally, being 
 held in place by the coal in the ribs and face. 
 
 Supports of the first class, whether artificial structures or piles of loose 
 material, are not as strong as those of the second class except for small amounts 
 of compression. Under heavy pressure and a consequent high percentage of 
 compression, they are not to be recommended except for temporary use. It 
 will be noted that circular piers, particularly if the interstices are filled with fine 
 shovel stuff so that the voids are reduced to a minimum, are much stronger 
 than the usual square or rectangular pier. Timber cogs, while stronger than 
 square gob piers, are of short life owing to the decay of the wood, which is par- 
 ticularly rapid in warm, humid mine atmospheres. Concrete piers, as in 
 test 14, give most excellent results up to a pressure sufficient to produce about 
 3% of compression and cracking, beyond which very little increased weight 
 will grind them to powder. Test 6' was made upon slabs of sandstone, such 
 
 45 
 
706 
 
 SUPPORTING EXCAVATIONS 
 
 
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SUPPORTING EXCAVATIONS 707 
 
 as would result from shooting down the roof over a wide area. The material 
 was not packed, stowed, or built up artificially but was used as it fell and proved 
 as good a support, practically, as the built-up circular gob pier used in test 2. 
 
 Tests 7, 8, and 9 represent unstowed material resulting from shooting down 
 the roof in a room; this gives much greater support when the voids are filled 
 with fine material; in fact, is as strong as the best sand flushing under the 
 maximum pressure. It will be noted that the sand flushing, so largely used 
 abroad, affords a better support in the ratio of about 4 to 1 than the culm flush- 
 ing commonly employed in the United States. 
 
 TIMBERING WITH WOOD 
 
 GENERAL REMARKS 
 
 Nature of Rock Pressure. The weight of the rocks overlying a coal seam 
 exerts both a major and a minor pressure on the timbering. The major, or 
 greater, pressure is practically irresistible and is due to the weight of all the 
 overlying rocks from the coal seam to the surface, and at a depth of 1,000 ft. 
 is equal to about 80 T. per sq. ft. It cannot be supported by timbering and 
 cannot be entirely resisted by flushing culm into the workings. Solid masonry 
 or concrete will alone withstand the major pressure. The minor pressure is 
 caused primarily by the weight of the draw slate, which may vary from a few 
 inches to several feet in thickness, producing a pressure of as much as, say, 
 500 Ib. per sq. ft. In some places, to the weight of the draw slate must be 
 added that of from 5 to 40 ft. of so-called soapstone, which crumbles on expo- 
 sure to the weather and gradually falls until some solid stratum is reached. 
 If as much as 40 ft. thick, this will cause an additional pressure of some 3 T. 
 per sq. ft. It follows that mine timber is ordinarily designed to withstand a 
 pressure of from, say, 50 Ib. to 3 T. per sq. ft. 
 
 Choice of Timber. Timber should be long grained and elastic, strong 
 but not too heavy for easy handling in thick seams and in pitching places. 
 Elasticity combined with the proper strength is of prime importance. The 
 timber must be strong enough to resist the minor pressure for which it is 
 designed and at the same time elastic so that, while resisting the minor pres- 
 sure, it will bend without breaking and give warning of the approach of a 
 major pressure caused, say, by a squeeze. Oak, beech, and similar hardwoods 
 while very strong are heavy, and, being short grained, are not elastic, com- 
 monly breaking with but slight bending. The softer coniferous woods, such 
 as pine, fir, and spruce, possess considerable strength and great elasticity and 
 make the most desirable mine timbers. Very elastic timbers, such as cypress 
 and willow, are not satisfactory for props because they bend like a bow without 
 offering the resistance necessary to keep the draw slate in place even for a short 
 time. 
 
 When selecting props, the principal points to be observed are: Straight- 
 ness, slowness of growth as indicated by narrow annular rings, freedom from 
 knots, indents, resin, gum, and sap. 
 
 ROOM TIMBERING IN FLAT SEAMS 
 
 Props. Single props are set to support the draw slate during the process 
 of removing the coal. They are generally made of natural logs, cut and sea- 
 soned in the woods, with a diameter of from 6 to 18 in., depending on the weight 
 of the roof and the thickness of the seam, and of a length some 2 in. less than 
 the height of the coal. Where the seam varies in thickness in different por- 
 tions of the mine, props of proportionate lengths are kept on hand. 
 
 If it is necessary to reduce the size of an individual stick, it is usually better 
 to split than to saw it (thus forming a split prop}, especially in the case of wood 
 from coniferous trees, as splitting does not destroy the sap wood, or unduly 
 injure the grain or fiber of the stick. If a prop must be shortened, the ends 
 should be sawed off square and parallel, and not cut with an ax. 
 
 Props should be straight, have square ends, rest fully and firmly on the 
 floor, have a cap piece between them and the roof, and" be set perpendicularly. 
 
 The stronger the roof is, the stronger must be the props required, because 
 the roof, if broken, is in much larger pieces; conversely, where the roof is broken 
 and tender, the props set must be more numerous, and if these must be set so 
 thick as to interfere with the carrying on of the work, or the ventilation, cross- 
 bar sets with lattice-work lagging must be substituted. 
 
708 SUPPORTING EXCAVATIONS 
 
 Where there is a strong roof and bottom, the props should be set so as to 
 permit the roof to ease, or gradually settle down, or the bottom to heave, and 
 thus prevent the breaking of the prop or prolong its usefulness as such. Under 
 such conditions, they should not be driven very tight and caps of soft timber 
 should be used, otherwise the prop will be bent and later on broken. To accom- 
 plish and extend the same purpose, tapered props have been introduced, which 
 have given great satisfaction, both from a safe and economic standpoint. The 
 face of the tapered end is usually about 3 in. in diameter and is about one- 
 fourth of the area or section of the body of the prop. 
 
 In some localities, the butt end of the prop is placed toward the roof in 
 order to afford more surface for the cap to rest on. This position is unstable 
 and the stick is also harder to handle, but the butt end up gives greater bear- 
 ing surface at the point where the prop is wedged and driven. 
 
 Whether posts should be set with their butt ends up or down is largely a 
 matter of opinion, as practice differs in different localities. Some timbermen 
 set the thick end down, while others set the larger end against the weaker 
 stratum, whether it is top or bottom. The splitting or furring of the post is 
 more apt to take place at the small end, and many prefer that this should occur 
 at the bottom rather than at the top where the cap or other timbers are resting 
 on the post. 
 
 Other things being equal, the strength of a prop varies directly as the 
 square of the diameter and inversely as the length. The ratio of the diameter 
 to the length of the prop, in order to have equal power of resisting compres- 
 sion and deflection, is 1 to 12. However, if by reason of physical defects, such 
 as knots, splits, worm holes, or disease, the wood is weaker, the diameter of 
 the post should be increased. 
 
 The crushing strengths of various American timbers are given in the sec- 
 tion entitled Strength of Materials. For illustration, taking chestnut with an 
 average strength of 5,300 Ib. per sq. in., and allowing 75% of the material to 
 be sound and straight in fiber, a prop with a cross-section of Ifrsq. in. will sup- 
 port .75X16X5,300 = 63,600 Ib. If the prop is 8 ft. long, the weight required 
 to crush it will be 63,600-5-8 = 8,000 Ib., about. This represents the weight 
 of approximately 50 cu. ft. of draw slate, equivalent to that of a piece a little 
 more than 7 ft. square and 1 ft. thick, or of a piece 3 ft. X 4 ft. and a trifle 
 more than 2 ft. thick. 
 
 If the draw slate is not more than 3 in. thick, the best plan is to take it 
 down and stow it in the gob, making no attempt to hold it by propping. When 
 the slate is from 3 in. to 6 in. thick, a row of props is placed along the gob side 
 at a sufficient distance from the track to allow cars to pass. Where the roof 
 is poor, the arrangement shown in Fig. 1 is employed. This consists of an 
 extra long cap set on the post at one end and set in a hitch cut in the coal at the 
 other. Over the cap is driven lagging b, which extends from one set to another. 
 The cross-bar is not usually jointed to the post, but is merely laid on top of it. 
 The sticks used for this purpose are about 6 in. thick; sometimes split props 
 are used, as the timbering is temporary and is needed only until the room is 
 worked out. 
 
 Systematic Timbering. In systematic 
 timbering, props are placed at regular dis- 
 tances apart, both in the direction of the 
 length and in that of the width of the 
 room, and are placed whether the appear- 
 ance of the top does or does not indicate 
 the necessity for support at the particular 
 point where the prop is placed. The idea 
 involved is that a much greater number of 
 roof falls will be prevented if the props are 
 placed systematically and symmetrically, 
 than if their placing is left to the judg- 
 ment of the miner. The H. C. Frick 
 p IG< i Coke Co., working the 8-ft. Pittsburg seam 
 
 in the Connellsville region of Pennsylvania, 
 
 in connection with rooms 10 ft. to 12 ft. wide and separated by pillars from 
 40 ft. to 80 ft. thick, have adopted a center-to-center spacing of the posts 
 of 4 ft. 6 in. Where rooms are of the usual width of 20 to 25 ft., there 
 will be several series of posts set in parallel rows from 4 ft. 6 in. to 6 ft. apart 
 as local experience dictates. Alternate parallel rows are set in such a way that 
 a plan of the room timbering suggests the arrangement of the spots on the five 
 of a suite of playing cards. Along the roadway, the props are commonly pro- 
 
SUPPORTING EXCAVATIONS 
 
 709 
 
 The 
 
 vided with a long cap, and sometimes with lagging as shown in Fig. 1. 
 printed rules of this company in regard to systematic timbering are: 
 
 " In rooms exceeding 10 ft. in width, posts must be set as near the center 
 of the room as practicable, and the distance between centers must not exceed 
 4 ft. 6 in. In rooms where coal is mined by hand, the distance between the 
 last post and the face must not exceed 6 ft. In rooms undercut by machine, 
 the distance between the last post and the face shall be such as, in the opinion 
 of the mine foreman and the mine inspector, affords the best protection for the 
 workmen. 
 
 " In all rib or pillar drawing, where the coal can be reached without additional 
 track, a line of posts not exceeding 4 ft. 6 in. between centers must be set in the 
 working places, and when widening out, other posts not exceeding 4 ft. 6 in. 
 between centers must be set parallel, and at right angles, to the first line. In 
 rib or pillar drawing, where additional track must be laid when cutting over 
 near the end of the rib or pillar, posts not exceeding 4 ft. 6 in. between centers 
 must be set in line on both sides of the opening; and in the following named 
 mines, cross-bars or collars must be set over them. The idea of setting these 
 cross-bars across the track, where the roof is comparatively good, is that they 
 may give warning, by their condition, of any unusual condition in the roof, 
 as the presence of smooth slips or great weight; therefore, where the roof is 
 usually of good character, they may be of lighter weight than where bad or 
 dangerous conditions are known to exist. 
 
 " In all mines, when the gob is reached, a line of posts shall be set around its 
 edge; the distance between such posts, or between the post and coal, must not 
 exceed 4 ft. 6 in. between centers." 
 
 Timbering Bad Roofs. Slips are vertical or inclined cracks reaching 
 through the draw slate to a sound stratum above. Where the roof is known 
 to contain slips, the props should be close together and kept as close to the face 
 as possible. When the slip is vertical, a post is set immediately under it; 
 if inclined, the post is set back from the crack a short distance so as to be more 
 nearly under the 
 place of greatest 
 weight. The cap 
 is usually larger 
 and thicker than in 
 ordinary prop tim- 
 bering under a uni- 
 form roof, and is 
 usually placed at 
 right angles to the 
 crack. Where the 
 roof is very bad, 
 the arrangement 
 shown in Fig. 1 
 may be used, the 
 
 FIG. 2 
 
 slate being allowed to fall in the gob, or the form of timbering illustrated 
 in Fig. 2 may be employed. The caps a are placed on the props b, 
 but are not notched, being secured by the wedges c. In all cases, they 
 should have a regular arrangement through the room. Props for tim- 
 bering under a cracked roof should be about 8 in. in diameter and the caps 
 about 6 in. thick. The props should be about 8 ft. apart, but the cross-bars 
 can project 18 in. over their ends. After the room is completed and the track 
 removed, such timbering may be drawn and saved for future use, the roof 
 then being allowed to fall. It may be necessary, in some extreme cases where 
 the cross-joints occur, to have two sets of cross-bars, one across the room and 
 the other parallel to the ribs. 
 
 Where the slips are not visible, but are known to be present, some form of 
 systematic timbering should be employed. 
 
 Timbering is varied to meet the conditions of the roof at each mine; there- 
 fore, at mines with good roofs, but little is needed, but it is always safe prac- 
 tice to timber under sags in the roof, as these suggest the bed of a stream of 
 water in the past and an opportunity for its accumulation in the present;* in 
 fact, in flat beds, water is nearly always encountered in depressions of this 
 kind. If the roof and bottom are both hard, the props are driven in as solidly 
 as possible, the number of props used and their arrangement depending on the 
 width of the opening and the nature of the roof, whether it is firm or shaly. 
 In long wall work, where the roof is allowed to settle gradually, the props may 
 be set on mounds of dirt. Where the roof of the bottom is soft, extra large cap 
 
710 
 
 SUPPORTING EXCAVATIONS 
 
 pieces or foot pieces are used, so as to give 
 as great a bearing surface as possible be- 
 tween the top or bottom and the props. 
 
 Supporting the Face While Undercut- 
 ting. As the coal is being undercut, it is 
 usually necessary to support the web of 
 coal over the miner's head to prevent its 
 falling on him. The simplest method of 
 doing this is by means of a sprag a, Fig. 3, 
 which may be placed either at the opening 
 of the undercut, or may be placed within 
 the undercut. 
 
 The combination of timbers be used for 
 supporting the face is termed a cockermeg. 
 It consists of two braces b between which 
 a horizontal stick of timber c is placed along the face. If the angle that the 
 braces b make with the vertical is less than 20, they will not slip and they may 
 be driven tightly against the roof and floor so as to bear against the stick c. 
 If the braces b are placed at a greater angle than 20, the ends should be put 
 in hitches as shown. 
 
 ENTRY TIMBERING IN FLAT SEAMS 
 
 Two-Stick Sets. A two-stick set of timber, sometimes used for timbering 
 entries, consists of two round or sawed sticks, wedged, but not framed, together 
 
 FIG. 3 
 
 FIG. 1 
 
 FIG. 2 
 
 The post-and-bar or post-and-cap arrangement is shown in Fig. 1. A hitch a 
 12 or 15 in. deep and only high enough to receive the cap is cut in the coal. 
 The post c is then set close to the rib and the cap b placed in position. After 
 tightening the post by driving the wedge e, the wedge / is fitted in place. Where 
 the coal is soft, it is advisable to make the hitch a wide enough to receive a piece 
 of heavy planking. By driving wedges between the cap and plank, a much 
 better bearing surface is secured and the pressure thrown upon a greater area 
 of coal. 
 
 Where the roof re- 
 quires lagging, the ar- 
 rangement shown in 
 Fig. 2 is quite frequent- 
 ly employed, but is to 
 be severely condemned. 
 The ribs should be ver- 
 tical as the overhanging 
 coal will weather and 
 fall into the entry, and 
 the shoulder of coal b 
 is so small that very 
 little roof pressure will 
 break it oft, causing the set to fall. Further, it is not usually good practice 
 to gouge out the roof slate to receive the lagging, as it weakens the roof and may 
 open a seam of water. The leg / has too much batter to withstand heavy 
 pressure and should be set vertically. 
 
 > Instead of having the post the full height of the opening, a method some- 
 times used is to have short posts set on a ledge in the coal, Fig. 3, or on top of 
 the coal when the top rock is taken down, as shown in Fig. 4. 
 
 FIG. 3 
 
 FIG. 4 
 
SUPPORTING EXCAVATIONS 
 
 711 
 
 FIG. 5 
 
 Three-Stick Sets. A set composed of two legs and a cap is the standard 
 
 form of entry timbering in both wood and steel; such a set, used in a seam of 
 
 gentle pitch, is shown in Fig. 4, page 714. 
 
 The lagging is only necessary when the 
 
 roof is weak and the coal at the sides of 
 
 such a nature as to readily weather and 
 
 fall into the roadway. Also, in flat seams 
 
 where the pressure is almost entirely in a 
 
 vertical direction, the legs are made 
 
 plumb, or with a batter of about 1 in. to 
 
 the foot. In Fig. 1, if the hitch a is 
 
 omitted and a second leg placed under the 
 
 cap, the ordinary form of entry timbering 
 
 will be illustrated. 
 
 A variant of the three-stick set, used 
 
 extensively abroad for timbering wide en- 
 tries, turnouts, etc., is shown in Fig. 5. 
 
 The regular three-stick set is first put in 
 
 place and is then reinforced with the tim- 
 bers, c, d, and e. The system is costly 
 
 and interferes to some extent with the 
 
 ventilating currents, but is serviceable in timbering underground stables, 
 
 engine rooms, and the like. 
 
 Certain materials composing the floor, such as fireclay, while giving little 
 
 trouble as the entries are being driven , frequently soon afterwards soften under 
 
 the action of the damp mine air and swell. The trouble is greater where it is 
 necessary to lift the bottom or brush the top 
 to get height for haulage. In ground of this 
 character various modifications of the three- 
 stick set are used, one of which is shown in 
 Fig. 6. The timbers a and b running length- 
 wise of the heading are commonly 10 ft. long 
 and extend over several sets, holding them 
 together. These timbers are temporarily held 
 in place while the struts c and d and the cap 
 piece e are driven into position. The lower 
 ends of the struts are inclined away from the 
 legs to further strengthen the latter against 
 pressure from the sides. 
 
 In timbering in such swelling ground, the 
 best results appear to be obtained by using 
 fairly strong timbers and excavating some of 
 p ir fi the material behind them whenever the swell- 
 
 m ing begins to exert too great a pressure. The 
 
 lagging is usually light, sometimes 1-in. plank, is open in construction, and by 
 
 its bending and breaking, gives warning that the sets are in danger of being 
 
 crushed. In some cases skin-to-skin timbering is used; that is, heavy logs 
 
 set in close contact, or any of the forms shown on pages 710 and 715 may be 
 
 used when placed close together and closely 
 
 lagged. 
 Fou 
 
 four-Stick Sets. A four-stick set of tim- 
 bering is the same as a three-stick set, with the 
 addition of a sill laid across the floor, which 
 serves as a support for the ends of the legs and 
 is designed to resist the upward pressure of the 
 floor. A method of framing such sets is shown 
 in Fig. 7. In some instances, the legs are ten- 
 oned to fit into a mortise in the sill, but this is 
 unnecessary if the angle the leg makes with the 
 vertical does not exceed 15. 
 
 When the ground is so heavy that this 
 method of timbering is demanded, modern 
 practice suggests the use of concrete or con- 
 
 FIG. 7 
 
 crete-and-steel construction, particularly on main haulage roads designed 
 to be open during the life of the mine, at shaft and slope bottoms, main 
 partings, andother important places in the haulage system. Sets composed 
 of structural steel shapes have been advantageously used in such places. 
 
712 
 
 SUPPORTING EXCAVATIONS 
 
 ROOM TIMBERING IN PITCHING SEAMS 
 
 The general arrangement of the timbering at the mouths of rooms or breasts 
 worked on a pitch, and which is designed primarily to keep the loose coal from 
 rushing into the roadway rather than as 
 a support for the roof, is shown under the 
 title Working Pitching Seams. 
 
 In room timbering in pitching seams, 
 the posts are not set quite at right angles 
 to the roof, but are given a slight pitch, 
 known as underset, up hill as shown in an 
 exaggerated degree in b, Fig. 1. Any 
 movement of the roof will cause the top of 
 the prop a to move in the direction of the 
 arc shown by the dotted lines and thus to 
 fall down. The top of the prop b, moving 
 in a similar arc will, however, be bound 
 more tightly against the roof. 
 
 The following table, from "Sawyer's 
 Accidents in Mines," gives the maximum 
 and minimum angles at which props should 
 be set for varying inclinations. This table 
 can be taken as a general guide, but it 
 does not take account of the length of prop 
 
 nor the varying amounts of movement of the top rock under different con- 
 ditions. 
 
 UNDERSETTING OF PROPS 
 
 FIG. 1 
 
 Rate of Inclination of 
 Seam 
 Degrees 
 
 Angle of Underset of Props 
 
 Minimum 
 Degrees 
 
 Maximum 
 Degrees 
 
 6 
 12 
 
 18 
 24 
 30 
 36 
 42 
 48 
 54 and upwards 
 
 
 
 1 
 1 
 2 
 2 
 2 
 3 
 3 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 To prevent the coal from falling on the roadway, it is also often necessary 
 to place a series of props as shown in Fig. 2. The prop a is underset, its foot 
 being placed in a hitch in the floor. 
 Part of the draw slate b is taken 
 down to prevent its falling and the 
 remainder is held up by the prop a 
 and cap c. To prevent the coal 
 from falling into the gangway, the 
 props are placed short distances 
 apart and covered with stout lag- 
 ging d. It is necessary to wedge 
 the foot of the prop and drive the 
 cap c in tightly; then, any move- 
 ment of the roof will tighten the 
 joint between the prop and the cap. 
 
 If the seam is very steeply in- 
 clined, so that there is danger of the 
 cap between the roof and the prop 
 
 slipping out, a hitch is cut in the F, r 2 
 
 roof rock so that the prop may 
 
 have rock rests at each end. The pressure that the prop then has to sus- 
 tain is from the coal, and the prop is in the position of a beam uniformly loaded 
 
SUPPORTING EXCAVATIONS 
 
 713 
 
 along its length. This system, shown in Fig. 3, is the better method in highly 
 inclined beds, but the hitches cut in the roof must be at least 12 in. deep and 
 the prop thoroughly wedged at both ends. The object of wedging timbers 
 when placed in such positions is to give them stiffness, for if they bend they 
 
 FIG. 3 
 
 FIG. 4 
 
 will eventually break; by wedging the ends, the bending is, in a great measure, 
 prevented. 
 
 Fig. 4 shows the method of timbering a wide coal bed at one mine in Penn- 
 sylvania. The logs a were about 20 ft. long and 18 in. in diameter at the top. 
 They were placed 8 ft. apart and lagged with 8-in. round sticks. Handling 
 these sticks and placing them were laborious operations and the method is not 
 recommended. 
 
 The use of single props for timbering deposits exceeding 12 to 15 ft. in thick- 
 ness is limited, as large, heavy timbers must be handled in such cases, making 
 the system an expensive one; furthermore, the resistance of a' prop to bending 
 is not great when the length is more than twelve to fifteen times its diameter. 
 
 ENTRY TIMBERING IN PITCHING SEAMS 
 
 Two-Stick Sets. Fig. 1 shows a form of two-stick timbering that may be 
 used where the seam has a slight pitch and is so thin that the floor must be 
 blasted to secure entry height. To stiffen the collar, it must be thoroughly 
 wedged at d and at its joint with the leg e, by wedges /. Lagging is necessary 
 to prevent the coal falling into the entry. This form of timbering is good, pro- 
 vided the wedges / are tight so that the bulk of the pressure is transferred to 
 the leg e. The beveled joint will become tighter as the side pressure from the 
 coal increases. 
 
 FIG. 1 
 
 FIG. 2 
 
 A similar form of timbering is shown in Fig. 2, which is used in thicker seams 
 where the roof is good. As the joint between the post p and collar b is by no 
 means as strong as that shown in Fig. 1, this arrangement is more adapted to 
 holding back the coal than to supporting the roof. 
 
714 
 
 SUPPORTING EXCAVATIONS 
 
 The arrangement in Fig. 3 is adapted to thin, highly inclined seams. Even 
 if the top rock, or hanging wall b, is good, in order to prevent the leg c being 
 pushed into the roadbed, it is advisable to set its foot in a hitch in the coal and 
 
 FIG. 3 
 
 FIG. 4 
 
 to make a notched joint between it and the collar. The collars must be lagged 
 to keep back the overhead coal, and, if the top rock b is poor, the leg c may be 
 lagged as well. Seasoned lagging should be used in such places; split lagging 
 with the flat side laid next the leg c is preferable because the rounded side 
 is stronger in compression than in tension. 
 
 Three-Stick Sets. Fig. 4 shows the standard form of three-stick sets as 
 used in seams of moderate pitch where the sides are weak and require the use 
 of lagging. Where the sides are very weak the sets may be placed skin to skin, 
 but they are commonly set 3 or 4 ft. apart. 
 
 Fig. 5 shows the method of timbering where the dip is great, the bottom 
 hard, and the seam is not thick enough for full entry height. This method 
 avoids the cost of taking out enough rock to get in a set of timber having legs 
 of equal length. The shorter leg / is given a firm hold on the rock bottom. 
 
 Fig. 6 shows a form of timbering used in pitching seams where the coal is 
 soft and falls to a height greater than that required for the gangway. The 
 leg I on the high side is made long enough to reach up to the roof to support 
 the lagging, which keeps the soft coal from continually sliding down into the 
 gangway. The collar c strengthens the leg /. The coal is allowed to fall off 
 on the low side where no lagging is necessary. 
 
 Fig. 7 shows the method of timbering the levels in thin pitching seams, 
 when the top is supposed to be weak. The legs / and the collar c are made of 
 round timber about 12 in. in diameter, and are so jointed together that the 
 
 FIG. 5 
 
 FIG. 6 
 
 collar c will stand great pressure. The lagging a consists of round poles taken 
 direct from the woods, and usually from 3 to 6 in. in diameter. The poles are 
 used to keep the loose coal and roof from falling between the sets of timbers, 
 
SUPPORTING EXCAVATIONS 
 
 715 
 
 which are from 3 to 5 ft. apart. Where the lateral pressure is slight, planks p 
 are used. The road is made level by filling in the low side with refuse /, as 
 
 SHAFT TIMBERING 
 General Principles. The 
 
 general arrangement of shaft 
 timbers and some of the de- 
 tails thereof are illustrated 
 under the title Opening a Mine. 
 The nature and amount of the 
 timbering will vary with the 
 character of the ground pene- 
 trated. 
 
 In hard material, only such 
 timbers are introduced as are 
 necessary to furnish support 
 to the guides, pipes, wires, 
 etc. that are carried down the 
 shaft. In loose material, the 
 object of timbering is to give 
 support also to the sides of the 
 excavation. In watery strata, 
 the pressure of the water be- 
 hind the timber is another 
 point that must be considered. 
 Water encountered in the sink- 
 
 
 FIG. 7 
 
 ing of a shaft finds its way at once to the excavation or follows down behind 
 the lining and collects in the bottom of the shaft, unless kept out by the shaft 
 lining. If the lining is built tightly against the sides of the excavation, so as 
 to impede or stop the flow altogether, the water rises behind the lining to the 
 water level of the strata and the lining is subjected to a pressure dependent 
 on the head of water. The strength of the lining must be sufficient to with- 
 stand this pressure. In such cases, the following formula may be employed 
 to determine the thickness of white-pine lining that will resist a given head of 
 water: * = .016sV5 
 
 in which t = thickness of white-pine lining, in inches; 
 
 5 = clear unsupported span of timber, in inches; 
 d depth, or head, of water, in feet. 
 
 NOTE. While in the statement of this formula white-pine timber is used, 
 the same formula will give results that are practically correct for the other 
 varieties of timber used in shaft linings. 
 
 It must be remembered that the head of water supported by the curbing 
 does not mean the depth of the curbing below the surface, as the water rarely 
 if, ever, heads to the surface. 
 
 EXAMPLE. Find the thickness of white-pine 
 curbing required for a coffer dam when the depth 
 of the water head is 100 ft., the clear span of the end 
 plates of the shaft being 7 ft. 
 
 SOLUTION. Substituting the given values in the 
 formula, t = . 016 X (7X12) X V 100 = 13.44; hence a 
 14-in. timber would be used. 
 
 Timbering in Rock. Where a shaft, or a por- 
 tion of a shaft, is excavated from hard -rock strata, 
 the only timbering necessary is the cross-timbers, 
 or buntons, to support the guides in the hoisting 
 compartments of the shaft and the lines of pipes, 
 or wires. The buntons b, Fig. 1, are set in hitches 
 h cut in the rock face and firmly wedged in line, 
 one above the other, by wedges w. At times, the 
 hitches are cut square and those on one side made 
 deeper to permit the other end of the stick to be 
 placed in the hole opposite. 
 The buntons are spaced from 6 to 8 ft. apart, one above another, on each 
 end of the shaft, and between the several compartments of the shaft. When 
 it is desired to separate the compartments of the shaft, as in the caes of an air- 
 
 FIG. 1 
 
716 
 
 SUPPORTING EXCAVATIONS 
 
 way or manway, planks are spiked to the buntons or built between them to form 
 the partition. 
 
 Timbering in Loose Dry Material. In good ground, shafts have been sunk 
 to a depth of 200 to 300 ft. by using 3"X 12" planking set on edge, but beyond 
 
 this depth it is better to use 
 4-in. or 5-in. planks. When 
 an especially soft, wet, or crum- 
 bling stratum is met, such as 
 wet sand or fireclay, the plank- 
 ing is sometimes laid flatwise. 
 If the sides of the shaft are not 
 self-supporting and tend to 
 crumble into fragments of vary- 
 ing size, if boulders that are 
 likely to become detached are 
 found, or if the strata are 
 jointed and faulted, to preserve 
 the shaft and to avoid accident 
 from earth or rock falling to the 
 bottom from the side walls, it 
 is necessary not only to line the 
 entire excavation with plank, 
 but to support this planking by 
 heavy timber sets placed inside 
 the planking, as shown in Fig. 2. 
 These timber sets a are 
 placed at regular distances 
 apart and are separated by the 
 posts b. The lagging c, com- 
 posed of closely fitting planks, 
 may be driven in behind the 
 timber sets or it may be first, 
 placed in position and the 
 timber sets or frames added afterwards. Cross-buntons d are also inserted 
 in each set to separate the compartments. Where a greater strength of tim- 
 bering is required than is given by this form, the sets a may be placed one on 
 top of the other, i. e., skin to skin. 
 
 An open crib of timbers, similar to that shown in Fig. 3, may also be 
 employed in loose ground, the openings between the timbers being gradually 
 filled up compactly by the loose material. After the timbers have been placed 
 in position, triangular strips, or corner pieces, A are spiked to them in each 
 corner of the shaft. This open crib may be built either from the top down- 
 wards or from the bottom upwards. 
 
 Instead of building the timbering from the top downwards, it is frequently 
 built upwards from the bottom in sections of 10 to 15 ft., depending on the 
 character of the ground. The bottom of the shaft is carefully leveled with a 
 carpenter's level and straightedge; and, by measurements made from the plumb- 
 lines hung from the shaft corners, a set 
 of timbers is placed so that the inside is 
 in line with the edge of the sills, or shaft 
 templet. After the whole set is accu- 
 rately leveled and joined, wooden wedges 
 are driven between the timbers and earth 
 at each corner. The wedges should be 
 long and tapering, and should be driven 
 into position while the set is held in 
 place with a bar. Great care must be 
 taken to get this first set level and in 
 line with the shaft templet, as it is the 
 foundation for the other sets. After this 
 foundation set has been placed in position 
 and wedged, another set is placed on it, 
 leveled, and wedged in like manner. In _, 
 
 this manner, the work is continued until * IG - 
 
 the templet or next section of timbering is reached. If the sinker has measured 
 correctly and has made due allowance for the number of sets required to close 
 the distance between the shaft bottom and templet, his sets will close this space 
 
SUPPORTING EXCAVATIONS 
 
 717 
 
 FIG. 4 
 
 exactly. The inside edges of the planking are brought flush with the inside edges 
 
 of the templet, and iron straps, about 2 in. X i in. X 15 ft., provided with nail 
 
 holes are hung from the surface downwards, connecting all the planking and hang- 
 ing it from the templet. The straps or hangers are placed 
 
 on the sides and ends of the shaft at distances of 2 to 3 ft. 
 
 apart, and they break joints vertically as the timbering 
 
 proceeds. If a small space is left between the last set 
 
 and the templet and the planking does not close exactly, 
 
 a closing set is necessary. For this purpose, a regular set 
 
 is cut down to the required size by the rip saw or adz. 
 
 However, the sinker should make his measurements and 
 
 calculations so that no closing sets are required. 
 
 No cavities should be allowed to remain behind the 
 
 timbering after it is completed, except in ground that 
 
 swells. If cavities are found in the strata, or if more earth 
 
 has been taken out than was necessary, the space must be 
 filled with ashes, straw, etc. 
 
 Timbering in Swelling Ground. A form of timbering often 
 employed in swelling ground is a cribwork of heavy timbers, such 
 as is shown in Fig. 4. These timbers are notched together after 
 the fashion of a log cabin. One side of the timbers may be faced, 
 so as to form the face of the shaft, but the back of the timbers is 
 preferably left round. When the ground swells, the material 
 ._ more readily works out between the timbers, and can be removed 
 Hs from time to time, as it may be found necessary. An important 
 feature of the work in dealing with swelling ground is to keep the 
 material as dry as possible, because the moisture causes the swell- 
 ing. In such ground, a space at least 6 in. wide is sometimes cut 
 out all around the sides and ends of the shaft, and filled in loosely 
 with moss, straw, sand, or ashes, allowance being made for the 
 probable expansion of the ground. When the timbering, by bulg- 
 ing, shows signs of excessive pressure behind, the difficulty may be 
 overcome by carefully removing two or more planks from the shaft 
 at this point, and excavating such material as may be necessary, 
 all around behind the timbers. The manway thus formed should 
 be carefully drained by a pipe conducting the water to the sump or 
 other lodgment. This manway should be timbered and cleaned 
 out from time to time, as may be necessary; the bulged timbers 
 of the shaft should also be replaced by good ones. 
 
 Timbering in Very Wet Ground or Quicksand. In wet ground, 
 timbers should be closely joined. At times, it is desired to make 
 a water-tight joint between each set of timbers to keep the water 
 from entering the shaft; for this purpose, timbers have been laid 
 
 in cement, but better results are obtained by backing the timbers with cement. 
 
 A form of timbering that always gives good results, introduced for the first 
 
 time in the sinking of the Ladd 
 
 shaft at Ladd, Illinois, is that shown 
 
 in Fig. 5, which illustrates a section 
 
 of curbing passing through a stra- , . 
 
 turn of quicksand, and through soft efgStfi 
 
 material overlying the same. At a v.:: : .- 
 
 point above the soft material, the jSjjvs! 
 
 3"X8" curbing plank a employed feVx-t 
 
 for the shaft lining is laid flatwise, fjjji 
 
 increasing the thickness of the curb- 5&i$:s 
 
 ing from 3 to 8 in. When the 'S** 
 
 quicksand is reached, the 8-in. 
 
 plank is alternated by 6-in. plank, 
 
 forming the corrugated backing 
 
 shown at b; the effect of this rough 
 
 backing is to clog the drainage that 
 
 would otherwise find its way down 
 
 the back of the curbing, and greatly 
 
 reduces the amount of water enter- 
 ing the shaft. 
 
 FIG. 
 
 FIG. 6 
 
 . 
 
 The chief difficulty in sinking through quicksand is that arising from the 
 flow of the soft material into the excavation before the timbers can be placed 
 in position. To prevent this as far as possible, the excavation should be tim- 
 
718 
 
 SUPPORTING EXCAVATIONS 
 
 bered well down to the bottom of the shaft. Fig. 6 shows more or less accu- 
 rately the inflow of sand and the method of setting the timbers. The lower tim- 
 bers have been set, jacked up, 
 and spiked. Blocks a are used 
 to support the back of the lin- 
 ing. These blocks are knocked 
 out by the next set of timbers 
 when it is driven to its place. 
 It is necessary to provide a 
 temporary foundation for the 
 jacks, which in this case is af- 
 forded by the sills shown. The 
 form of lining employed is the 
 alternate narrow and wide 
 plank laid flatwise. To reduce 
 the flow of sand temporarily, 
 spiling has been driven between 
 the timbers: but the spiles must 
 be removed before they throw 
 too mucn weight on the lining. 
 
 p IG 7 To support the timber while 
 
 the jacks under the set are being 
 
 lowered far enough for a new timber to be placed over them, cleats are spiked 
 on the timbers as fast as each timber set is laid in place. If the timbers can- 
 not be forced into place by hand or driven with a sledge, a jack, similar to those 
 shown in Fig. 6, is used, being fastened to a piece of 6"X6" or 8"X8" timber, 
 about 1 ft. shorter than the inside dimensions of the shaft. 
 
 Square Frame at Foot of Shaft. When tbe bottom of the shaft is reached 
 and the sump has been made by carrying the excavation several feet below the 
 floor of the seam, a heavy substantial frame must be built for the support of 
 the shaft timbers. The cage landing is first made by placing two heavy square 
 timbers a, Fig. 7, under each hoistway. These timbers should be 10 in. X 12 in. 
 or 12 in. X 16 in., according to the size and weight of the cage, and should 
 occupy a position about under the rails on the cage. They are well bedded in 
 the strata on each side of the shaft, and set low enough to make the floor of the 
 cage, when the latter is resting on the timbers, level with the floor of the land- 
 ing. When this has been done in each hoistway, heavy longitudinal sills & 
 are laid over them, one at each side of the shaft; cross-timbers c are boxed into 
 the sills to keep them the right distance apart and to form a solid frame for 
 the cage landing. Substantial posts d are then set at the corner of each com- 
 partment. Heavy caps, or collars, e are framed to rest on these posts, and 
 cross-timbers / are 
 boxed into these caps 
 above. The whole 
 frame is brought to 
 such a height as will 
 correspond to the 
 height of the heading, 
 and the shaft timbers, 
 or lining, g are made 
 to rest on the top of 
 this frame. 
 
 Underneath the 
 cage timbers a heavy 
 planks are inserted so 
 as to cover the sump 
 to prevent material 
 from falling in and 
 avoid the necessity of 
 frequent cleaning. 
 Without a cover, 
 there is also the dan- 
 ger of animals falling 
 r_i _ A i _ I?. 
 
 FIG. 8 
 
 into the sump and being drowned before they can be got out. This cover 
 should be so arranged that it may be easily and quickly removed at any time. 
 Square-Set Timbering. Square-set timbering is adapted to large shafts or 
 heavy pressures. It is extravagant in the use of timber on account of both the 
 size and the quantity of timber required. The form of joint is simple, as the 
 
SUPPORTING EXCAVATIONS 
 
 719 
 
 timbers are for the most part boxed slightly into one another. Fig. 8 shows the 
 general construction of the timbering in a three-compartment shaft by square 
 sets; in it, some 
 of the timbers 
 are omitted for 
 the purpose of 
 showing the 
 form of joint 
 employed. At 
 A are shown the 
 wall plates ;atB, 
 the end plates; 
 at C, cross-bun- 
 tons; and at D, 
 posts or punch 
 blocks or stud- 
 dies. The joints 
 
 may be varied FIG. 9 
 
 as shown in Fig. 
 
 9. With the joint shown in (6), the cross-bunton is put in place from below. 
 The advantage of this is that, if the timbering must be kept close to the bot- 
 tom while sinking, the bunton going in from below can be left out at first, so 
 
 as to allow more room for the workmen. Fig. 10 
 
 shows another method of joining end and wall 
 
 plates, the post F being 
 
 boxed into the plates 
 
 both above and below. 
 
 In this figure, a 2-in. 
 
 strip S is shown on 
 
 which the lagging is to 
 
 rest. Numerous other 
 
 forms of joints are used 
 
 in square-set timbering, 
 
 but these will serve to 
 
 illustrate the principle, 
 p IG jo namely, that as little of 
 
 the timber should be 
 
 I 
 FIG. 11 
 
 cut out as possible, so as not to weaken the timber. When framing these 
 timbers, regard must always be had to the manner in which they are put to- 
 gether in the shaft. When the timbering is done from the top downwards the 
 sets are suspended by means of hanger bolts made of round-iron rods, bent to 
 a hook shape on one end and having a thread and nut on the other end, Fig. 11. 
 
 MISCELLANEOUS FORMS OF TIMBERING 
 
 Fig. 1 shows a method of placing drift sets in the case of very heavy or 
 swelling ground. Here a are the posts; c, the sills; b, the caps; d, the collar 
 braces that bear against both the caps and the posts; e, foot or heel braces 
 
 1 l 
 
 J 
 
 FIG. 1 
 
 FIG. 2 
 
 that bear against both the sills and the posts; /, diagonal braces that are halved 
 together and placed as shown. 
 
 Fig. 2 is a set employed in the case of an extra wide gangway, or parting, 
 there being a post set under the middle of the cap. This form of set may be 
 provided with a sill when the floor is soft. 
 
720 
 
 SUPPORTING EXCAVATIONS 
 
 Fig. 3 shows a form of drift set surrounded by bridging and used where 
 such bad ground is encountered as to necessitate forepoling. At a are shown 
 the posts; at b, the caps; at c, the sill of the regular set; at d, upright bridge 
 pieces; at e, a horizontal bridge piece separated from the set proper by blocks / 
 so as to provide spaces h around the regular set through which the spiles or 
 forepoles can be driven. 
 
 FIG. 3 
 
 FIG. 4 
 
 FIG. 5 
 
 Fig. 4 shows a form of drift set sometimes employed in very heavy or swell- 
 ing ground. This method of framing the timbers shortens each piece and 
 reduces the transverse strain on all the timbers. 
 
 Fig. 5 shows an ordinary drift set provided with a sollar for ventilation 
 purposes. An additional brace b is placed parallel to the cap c, and this is 
 covered with plank lagging a, so as to provide a passage above the regular 
 drift, which may be used as a return air-course. 
 
 FRAMING TIMBERS 
 
 Limiting Angle of Resistance. In Fig. 4, page 714, the legs of the timber 
 are inclined so that the pressure coming on the collar is transmitted equally 
 to both legs. If the legs are placed at different angles, the pressure will bear 
 unequally on them, the greater pressure coming on the leg making the smaller 
 angle with the vertical. The tendency for the foot of a post to slip increases 
 with the inclination ; and if the angle between the post and the vertical is more 
 than 20, the post is_apt to slip, but the legs are not apt to spread on a level 
 rock surface when this angle is less than 20. It is, of course, possible to block 
 the foot of the leg against the side of the gangway, but even then the hori- 
 zontal pressure against the foot of the post increases rapidly and it is advis- 
 able to keep the inclination of the legs less than 20 from the vertical. 
 
 When the pressure comes from four sides, four-stick timbering must be 
 used. In some instances, the legs are tenoned for a mortise in the sill, but this 
 is unnecessary if the angle the leg makes with the vertical does not exceed 15, 
 which, according to Morin's experiments, is the limiting angle of contact of 
 oak on oak when the fibers of the moving surface are perpendicular to the sur- 
 face of contact and those of the surface at rest are parallel to the direction of 
 the motion. In Fig. 7, page 711, the moving surface is the lower end of the 
 inclined leg and the surface at rest is the portion of the sill on which this end 
 of the leg rests. The friction of two surfaces that have been, for a consider- 
 able time, in contact and at rest, is different not only in amount, but also in 
 nature from the friction of surfaces in continuous motion. A jar or shock 
 producing an almost imperceptible movement of the surfaces of contact causes 
 the friction of contact at rest to pass to that which accompanies motion. 
 
 Placing Timber Sets. It is important in the framing of a set of timbers 
 to out the joints between the two pieces of timber so accurately that the bearing 
 surfaces are in close contact. The lower end of each leg must also be cut so 
 as to be in contact, over its whole surface, with the floor in order to get the full 
 benefit of the cross-section of the timber. When wedging the cap piece, care 
 should be taken to drive the wedges as uniformly as possible over the full length 
 of the cap piece; for if some wedges are driven more tightly than others, the 
 
SUPPORTING EXCAVATIONS 
 
 721 
 
 weight will be concentrated at these points, at which place the cap is apt to 
 break. In placing wedges, care should be taken to secure the roof without 
 throwing an unnecessary strain on any part of the timber set. 
 
 Timber Joints. Fig. 1 shows a joint sometimes used to resist pressure from 
 above rather than from the side. This joint is objectionable from the fact 
 
 mf 
 
 .... I 
 
 FIG. 1 
 
 FIG. 2 
 
 FIG. 3 
 
 that continued pressure on the collar a will cause it to sag and thus raise the 
 scarf b of the joint from the post c, throwing all the weight on the part d. This 
 has a tendency to split the post c and the cap a, as shown by the dotted lines; 
 if this occurs, the entire weight is thrown on the collar above the dotted line e, 
 and on the part of the post to the left of d, the part d and that below e being 
 useless in sustaining weight. The same bending trouble will take place, but to 
 a less extent, if the timbers are joined as in Fig. 2, unless the wedge / stiffens 
 the collar sufficiently to prevent its bending; it is doubtful, however, if sufficient 
 stiffening will occur when continued heavy pressure comes on the collar. In 
 case the collar a bends so as to open the joint b, the upper part above e is use- 
 less for sustaining pressure. The side wedge g is intended to keep the joint 
 tight. 
 
 The joint in Fig. 2 is better able to withstand pressure from above than 
 that in Fig. 1, for the pressure is along the fibers of the post c and not across 
 them. 
 
 The joints in Figs. 3 and 4 have proved very satisfactory in practice, as 
 the timbers are not so apt to split as when the joints shown in Figs. 1 and 2 are 
 used. 
 
 If the cap begins to sag, there is much less chance for the joint shown in 
 Figs. 3 and 4 to open than there is with the joint shown in Figs. 1 and 2, as 
 there are no sharp angles in the joint between the timbers a and c. The pres- 
 sure also comes on the faces b and d of the joint much more uniformly, and the 
 absence of the heel or sharp corner in the joint also greatly reduces the tendency 
 of the cap to split along the dotte'd line. In case the pressure is greater from 
 the side than the top, the leg is given an inclination less than 20 from the 
 vertical and a double-notched joint is made, as in Fig. 5. The foot of the leg 
 is placed in a hitch in the floor to prevent its being pushed inwards. 
 
 FIG. 4 
 
 FIG. 5 
 
 FIG. 6 
 
 If the leg a, Fig. 6, is let into the sill b as shown, the pressure p along the leg 
 may be resolved into the two components cd and ce. The more nearly verti- 
 cal the leg a is, the greater will be the component cd, which is resisted by the 
 cross-grain of the wood, and the stronger will be the joint. The tendency of 
 
 46 
 
722 SUPPORTING EXCAVATIONS 
 
 the leg a to slip is also less the more nearly vertical a is. If the leg a is bent 
 inwards, the heel / acts as a fulcrum of a lever and the corner e tends to split 
 off the block above the line eg. 
 
 If the leg a. Fig. 7, is jointed to the sill b as shown, there is less danger of 
 its slipping or of its splitting the timber than when the joint shown in Fig. 8 
 is used. The pressure p acting along the leg a, 
 Fig. 7, can be resolved into the two components, 
 one cd acting vertically and across the grain of the 
 wood, and the other ce acting parallel to the grain 
 of the wood. In this case, if the leg a bends to- 
 ward the right, the tendency is for the heel / to 
 split the sill along the line /g, but the length of 
 wood fiber fg in this case is longer than the length 
 of wood fiber eg in the joint shown in Fig. 6, and 
 there is, therefore, not the same danger of the 
 block above fg splitting off. Again, in case of a 
 sudden shock, the wood tends to slide along the 
 face fh, that is, perpendicularly to the direction in 
 which the pressure is transmitted along the leg. 
 Fir 7 The timber a could not, therefore, slide on the 
 
 timber b as readily with the joint in Fig. 7 as it 
 
 could with the joint in Fig. 6, where the angle of inclination between the 
 faces of the timber is greater. In other words, with the joint in Fig. 7, there 
 will be much more friction between the faces of the timber to oppose move- 
 ment than with the joint shown in Fig. 6; and to start a movement of the leg, 
 the jar must be much more severe. 
 
 The method of framing heavy shaft timbering is described under the head 
 of Square-Set Timbering. 
 
 CARE AND PRESERVATION OF TIMBER 
 
 CUTTING AND STORING TIMBER 
 
 Time to Cut Timber. The presence of much sap in the tree when it is 
 cut causes the timber to decay more rapidly than it would otherwise, owing to 
 the fermentation of the sap permitting the growth of fungi that feed on the 
 life of the timber. In growing timber, the sap ceases to run about the middle 
 of December and starts again about the middle of February. Timber cut, 
 therefore, in the months of December, January, and February will contain 
 the least sap and prove more lasting than the same timber cut at other times 
 of the year. The work of cutting timber in winter gives employment also to 
 farm hands during their idle season; moreover, the task of transporting tim- 
 ber on sleds to the mines or the railroads is" a much easier one in winter than 
 during the seasons when wagons must be used. 
 
 Peeling. Peeling timber is a simple and inexpensive method of increasing 
 its durability, and under some conditions is fairly effective. Bark retards 
 the loss of moisture from timber, and unbarked wood therefore offers more 
 favorable conditions for fungus growth than wood from which the bark has been 
 removed. Moreover, the space between the bark and the wood is an excellent 
 breeding place for many forms of wood-destroying insects. In dry workings, 
 the life of timber may be increased from 10 to 15% by peeling, although in wet 
 situations peeling seems to have little effect. 
 
 Besides increased durability, there are other advantages to be derived from 
 the use of peeled timber. The bark of unpeeled timber often flakes off soon 
 after placement, causing an accumulation of inflammable rubbish in the 
 workings, which must be removed at some expense. To peel timber in the 
 woods or at the shipping point effects a saving in freight and in cost of handling. 
 With loblolly and shortleaf pine the weight of bark usually amounts to from 8 to 
 10% of the original green weight. 
 
 Seasoning and Storing Timber. The durability of timber may in some 
 cases be increased by seasoning. In dry, well-ventilated workings the life 
 of seasoned timber is sometimes 25% greater than that of green timber. In 
 wet .locations, however, the effects of seasoning are counteracted by the 
 reabsorption of moisture. 
 
 Whenever practicable, timber should be seasoned in the woods or at the 
 shipping point, in order to realize, through loss of weight, a substantial saving 
 in the cost of freight and handling. 
 
SUPPORTING EXCAVATIONS 723 
 
 The timbers should not be permitted to lie on the ground after seasoning 
 operations are commenced, but should be placed on blocks so that they will 
 be exposed to a circulation of air. The blocks should not be so far apart that 
 the timbers will sag; and the timbers, if exposed to the sun, should be turned 
 regularly, otherwise they may check or warp. Sawed timbers should be 
 stacked up, with air spaces between the sticks; they should also be kept under 
 sheds when seasoning and before they are taken below ground. If this is 
 not possible, they should be stacked so that they will shed water. 
 
 The several lengths of timber should be stored together so that they can 
 be readily obtained as required. To prevent warping and checking, the tim- 
 ber should not be seasoned too quickly, as is frequently the case when artificial 
 heat is employed, or when the timber is exposed to a strong sun, especially 
 when the circulation of air is not sufficient. 
 
 PRESERVATION OF MINE TIMBER 
 
 Destructive Agencies. The relative importance of the various destructive 
 agencies affecting timber varies greatly with the conditions in the mines. 
 Under average conditions, the different destructive agencies cause the follow- 
 ing percentages of loss: Wear, 5%; breakage and fire, 20%; waste from all 
 causes, 25%; decay and insect attack, 50%. Dry rot and fungus growth are 
 diseases common to most timbers. Some timbers are more apt to be infested 
 with insects and suffer from this cause more than others, owing, probably, to 
 the nature of the wood or bark as furnishing food or nesting places for insects. 
 Climatic conditions have much to do with this trouble; in some climates, the 
 insects multiply rapidly and completely destroy the timber they infest. At 
 times, the bark of the timber is completely filled with the eggs and the larvee 
 of insects, and must be removed in order to protect the timber from their 
 inroads. 
 
 When wood is not properly seasoned, the sap is liable to ferment, especially 
 in a dry, warm place, and dry rot occurs, beginning in the center of the stick 
 and working outwards. In general appearance such a stick looks sound, 
 but by thrusting a knife blade into it the damage is discovered. Fresh-air 
 circulation, when the stick is away from decaying timber, is one preventive 
 of dry rot, as in such situations the stick seasons. 
 
 When timber is placed in warm, moist air, damp rot takes place; this is the 
 usual rot affecting mine timbers. It commences on the outside and gradually 
 finds an entrance into the interior of the stick through some check. The 
 destruction of a timber by damp rot is not so rapid as by dry rot and is notice- 
 able from the fungus growth on the outside of the stick. In mines, dry rot 
 occurs in the intake airways and in poorly ventilated workings, while damp 
 rot occurs in the return airways and damp rooms. When fungus of the damp- 
 rot species appears, it may be possible to save the timber and prevent the fun- 
 gus reaching the heart wood by washing the stick down with lime or alum water 
 from time to time. 
 
 General Principles of Timber Preservation. .The partial removal of 
 sap will retard decay, for which reason timbers are sometimes submerged for 
 several months, then removed and air-dried. A temperature of between 60 
 and 100 F. combined with moisture is favorable to decay; but mine timbers 
 must often be placed where such conditions prevail. It may be possible, by 
 special wood preservatives, to increase the life of timbers; but even then the 
 sap must be either dried or removed, as wood covered with paint before being 
 thoroughly seasoned will propagate dry rot in a warm, dry place, or damp rot 
 in a moist, warm place. With good sound timber, creosoted joints will pro- 
 long its life, especially if the ends have been submerged in creosote a month or 
 more. Different species of trees differ in their resistance to decay. Cedar, 
 tamarack, and locust are more durable than pine, oak, or cypress, although 
 in certain situations they may all have the same life. Contact with earth is 
 particularly destructive to timber; and nearness to decaying timber is a source 
 of disease. The principal means adopted to arrest the processes of decay 
 and preserve timber are creosoting, salting, and charring the timber. The 
 first two methods consist in impregnating the timber with cresote or a solu- 
 tion of salt so as to fill the pores. The acid acts to coagulate the albuminous 
 matter of the sap. By this means, the pores of the wood are filled with a 
 deposit of salt or with the coagulated albumen, which prevents the absorption 
 of moisture and arrests the process of decay in the timber. The acid also 
 destroys the organic life of the wood. In the third method, the charring of 
 the ends and surface of the timber closes the pores of the wood and prevents 
 the absorption of moisture; the charred surface of the wood will not then decay. 
 
724 SUPPORTING EXCAVATIONS 
 
 Attempts have been made to coat mine timber with some substance, as tar, 
 to prevent or retard its decay; in other cases, the timber has been treated with 
 chemicals with the same end in view. The objection to the use of creosote or 
 tar for preserving mine timbering is that they make the timber more inflam- 
 mable than it would otherwise be. Timbers are sometimes treated with solu- 
 tions of the chlorides or the sulphates of the various metals. When a regular 
 plant is installed for this W9rk, timbers are first placed in specially prepared 
 chambers from which the air is afterwards exhausted, and then the solution 
 for preserving the timber is forced in under pressure, the exhausting of the air 
 having reduced the pressure on the timber and opened the cells. After the 
 preserving material enters the chamber, it is forced into the pores of the wood 
 in such a manner as to thoroughly saturate it. 
 
 Before timber is treated with preservatives, it should be peeled, and, as a 
 rule, thoroughly seasoned. All timbers should be cut and framed to their 
 final dimensions and form before treatment, because the sawing and cutting 
 of treated timber frequently exposes untreated surfaces to attack by wood- 
 
 We are indebted to the reports of the U. S. Forest Service for the following 
 information. 
 
 Brush Treatments. A fairly effective and cheap treatment is to paint 
 timber with two or three coats of hot creosote or some similar preservative. 
 It is important that the wood be seasoned before treatment, for otherwise 
 checking may later expose untreated portions of the timber to fungus attack. 
 Care should, moreover, be taken to get the preservative well into all checks, 
 knot holes, and surface inequalities; otherwise decay is likely to develop at these 
 points. 
 
 The amount of preservative required for treatments of this character is 
 relatively small and no special equipment is needed. Brush treatments are 
 therefore advisable when the amount of timber to be treated is too small to 
 warrant the erection of even a small plant, or when it is necessary to restrict 
 the initial cost of treatment to the lowest possible figure. The main disad- 
 vantage of brush treatments is that the slight penetration secured is not enough 
 to insure the protection of the interior of the timber for any considerable period. 
 The thin coating of treated wood may be broken or split, or fungus spores may 
 enter through nail holes, checks, or splits, causing decay in the interior of the 
 timber, while the outside appears sound. 
 
 Open-Tank Treatments. A more effective method of treatment is the 
 open tank. In this the timber is first immersed in a tank of suitable capacity 
 containing the preservative, and the charge is then heated to a sufficiently high 
 temperature to drive off a portion of the air and moisture contained in the wood. 
 As excessive heating is likely to result in checks that will weaken the timber, 
 and as large quantities of preservative may be lost by volatilization, the maxi- 
 mum temperature of the hot bath should not, in the case of creosote oils, 
 exceed 220 F. and, if an aqueous salt solution is used, the temperature should 
 be kept slightly below the boiling point of the solution. Following the hot 
 bath, the timber is immersed in preservatives at a lower temperature, or it may 
 be left in the hot liquid, which is allowed to cool. 
 
 The treatment of timber by the open-tank process insures a greater pene- 
 tration of the wood by the preservative than does the brush method, and for 
 this reason has proved more effective. In general, it is well adapted for the 
 treatment of species that are easily impregnated. 
 
 Pressure Treatments. With many species, a satisfactory treatment can 
 be secured only by the use of pressure. The essential difference between the 
 
 E-tank process and the pressure processes is that in the former atmos- 
 ic pressure is relied on to secure the penetration of the wood, while in the 
 r the preservative is forced into the timber by artificial means. Owing 
 chiefly to the difficulty of impregnating many species of wood by the open-tank 
 process, the pressure treatments are the most widely used. 
 
 Pressure processes may be employed for either full-cell or empty -cell treat- 
 ment. The object of the former is to leave the treated portion of the wood 
 completely filled with the preservative, while the latter aims to inject the pre- 
 servative as deep into the timber but leave n9 free oil in the wood cells. The 
 oldest process of full-cell pressure treatment with creosote is known as Bethelliz- 
 ing. A similar treatment with zinc-chloride solution is called Burnetlizing. 
 
 Comparison of Open-Tank and Pressure Treatments. Experiments made 
 by the two principal processes upon different kinds of timber indicate: 
 
 1. Thoroughly seasoned loblolly and Pennsylvania pitch pine round mine 
 timbers may be satisfactorily impregnated by the open-tank process. 
 
SUPPORTING EXCAVATIONS 725 
 
 2% Green timber of these species is much more difficult to treat than sea- 
 soned timber. 
 
 3. Satisfactory results may be secured in the treatment of seasoned west- 
 ern yellow pine by the open-tank process, the sapwood of this species being 
 impregnated without difficulty. 
 
 4. In general, pressure treatments are more satisfactory than o^en-tank 
 treatments. By the former, the time of treatment is reduced considerably 
 and the preservative is more generally diffused through the timber. 
 
 5. Heart Douglas fir is impregnated with difficulty. 
 
 Cost of Open-Tank Plant. The open tank is the simplest type of apparatus 
 used for the impregnation of timber. The necessary equipment consists mainly 
 of an uncovered tank provided with a device for submerging the timber. The 
 tank may be so arranged that a fire can be built under it, but if a supply of 
 steam is available it should be equipped with coils for heating purposes. If 
 large timbers are to be treated, a derrick or gin pole is necessary for their con- 
 venient handling. A plant of this character, with an annual capacity of 100,000 
 cu. ft. may be erected at a cost of from $1,500 to $2,500. The low cost of an 
 open-tank plant places it well within the reach of most mine operators, and this, 
 perhaps, is its main advantage. 
 
 Cost of Pressure Plant. The cost of pressure plants depends chiefly on 
 their capacity. The total cost of a plant having a capacity of approximately 
 1,000 cu. ft. per run, or 750,000 cu. ft. per yr.* will amount to from $12,000 
 to $20,000. The following is a list of the main items of equipment: One 
 horizontal treating cylinder, 65 ft. long, with inside diameter of 6 ft. 2 in, 
 capable of withstanding an internal pressure of 175 Ib. per sq. in.; two vertical 
 measuring tanks, each of 15,000 gal. capacity; one storage tank of 50,000 gal. 
 capacity; one hoist engine; one pressure pump, capacity 150 G. P. M. at 175 Ib. 
 pressure per sq. in.; one air compressor, capacity 460 cu. ft. of free air per min. 
 at 20 Ib. pressure per sq. in.; sixteen cylinder cars; one zinc-chloride mixing tank 
 of 2,000 gal. capacity. Special attention should be given to the design and 
 construction of a storage yard of adequate capacity for both treated and 
 untreated material, as handling the timber before and after treatment is an 
 important factor in the cost of operation. It is also important to locate the 
 plant at a convenient point in the mining district, so that treated timber may 
 be readily distributed to points where it is to be used. 
 
 A pressure plant was designed by the Forest Service and erected by the 
 Anaconda Copper Mining Co. at Rocker, Mont. Its capacity is about 570 cu. 
 ft. of timber per run. The equipment is as follows: One treating cylinder 43 ft. 
 long and 6 ft. in diameter, working pressure 100 Ib. per sq. in.; one receiving 
 tank, 47 ft. long and 5 ft. in diameter; two measuring tanks, 12 ft. in diameter 
 and 17 ft. high; one general service pump, 360 G. P. M. at 125 Ib. per sq. in.; 
 one pressure pump, 60 G. P. M. at 125 Ib. per sq. in.; one vacuum pump 7 in. 
 X 10 in. X6 in., and jet condenser; eighteen cylinder cars; one hoist engine. 
 The total cost of the plant, erected, was approximately $15,000. 
 
 A plant designed by the Forest Service for the Tennessee Coal, Iron & 
 Railroad Co., and erected at McAdory, Ala., has a capacity of about 830 cu. ft. 
 of timber per run. The main equipment is as follows: One treating cylinder, 
 6 ft. in diameter and 65 ft. long, working pressure 100 Ib. per sq. in.; two meas- 
 uring tanks, 12 ft. in diameter and 18 ft. high; two storage tanks, 11 ft. in 
 diameter and 36 ft. long; one settling tank, 16 ft. X 6 ft. X 4 ft.; one pres- 
 sure pump, capacity 150 G. P. M. at 100 Ib. per sq. in.; one air compressor, 
 capacity 108 cu. ft. free air at 50 Ib. per sq. in.; one air reservoir 3 ft. in diam- 
 eter and 15 ft. long; one surface condenser, 230 sq. ft. of condensing surface; 
 twenty cylinder cars; one derrick and hoist engine. The total cost of this 
 plant, erected, including the necessary yard construction, amounted to approxi- 
 mately $12,000. 
 
 Cost of Treatment. The unit of cost handling timber at open-tank plants 
 is higher than at pressure plants, usually amounting to from 3 to 4 c. per cu. ft. 
 at the former and from 2 to 3c. per cu. ft. at the latter. These figures include 
 interest, depreciation, and operating charges, but not the cost of the preserva- 
 tive, which is by far the most important item. The accompanying table shows 
 the approximate costs of the untreated and treated loblolly pine gangway and 
 entry sets used in the Forest Service experiments in the mines of the Phila- 
 delphia & Reading Coal & Iron Co. One set consists of one 7-ft. collar, one 
 9-ft. leg, and one 10-ft. leg; average diameter of timber 13 in.; approximately 
 26 cu. ft. in one set. 
 
 *Annual capacity is based on two runs per day for 250 da. 
 
SUPPORTING EXCAVATIONS 
 
 BY T 
 VICE 
 
 
 i| 
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SUPPORTING EXCAVATIONS 727 
 
 Below is given, in detail, the cost of untreated and creosoted 16 ft. by 8 in. 
 Douglas fir shaft sets placed in the mines of the Anaconda Copper Mining Co. 
 These sets contain 1,127 ft. b. m. of Douglas fir squared timbers from the 
 Pacific coast, and 393 ft. b. m. of lagging. The average absorption secured 
 in the treatment of these timbers amounted to 4.5 Ib. of creosote per cu. ft. 
 
 Cost of Untreated Sets 
 
 1,127 ft. b. m. squared timbers, at $20.50 per 1,000 ft. b. m. . . $25.36 
 
 Framing timbers 13.50 
 
 Cost of lagging, at $15 per 1,000 ft. b. m 5.90 
 
 Switching and unloading charges .85 
 
 Cost of placing set 18.00 
 
 Total cost of untreated set in place $63.61 
 
 Cost of Treatment 
 Cost of treating, including interest, depreciation, fuel, and 
 
 labor charges $ 3.34 
 
 Cost of creosote, at 15. 6c. per gal.; absorption 4.5 Ib. per 
 
 cu. ft 8.03 
 
 Loading and unloading charges 1.23 
 
 Total cost of treatment $12.60 
 
 Total cost of treated set in place $76.21 
 
 These examples show that the cost of treating timbers, while a considerable 
 item, does not, when taken in conjunction with the cost of the timber and its 
 preparation" and placement, form an unduly high proportion of the whole cost. 
 The actual costs for other mines and other localities will, of course, differ more 
 or less from the figures just given, but they serve to illustrate the relation 
 between the cost of treated and untreated timbers under different conditions. 
 
 Durability of Treated Timbers. Tests to secure data on the comparative 
 durability of treated and untreated timber, begun by the Forest Service in 1906, 
 in cooperation with the Philadelphia & Reading Coal & Iron Co., have been 
 in progress for a sufficient period to produce results of practical importance. 
 The experimental timbers were standard round gangway or entry sets, treated 
 and untreated, each set consisting of a 9-ft. leg, a 10-ft. leg, and a 7-ft. cap or 
 collar, the average diameter of the timber being 13 in. The species used were 
 longleaf, loblolly, and shortleaf pine, Pennsylvania pitch pine, and red and 
 black oaks. 
 
 The treated sets included loblolly and shortleaf pine treated by the brush 
 method with creosote and carbolineum, by the open-tank method with various 
 preservatives, and by the pressure method with creosote and zinc chloride. 
 The accompanying table gives descriptions of the treated timbers. 
 
 Most of the timber was placed during 1906, 1907, and 1908; and inspections 
 were made in December, 1907; March, 1909; and July, 1910. 
 
 Owing to the conditions in the various collieries, it was not always possible 
 to make a complete inspection of all of the experimental timbers, nor was it 
 possible in all cases to procure complete data on the cause of failure of indi- 
 vidual pieces; but the condition of the timber as found in the various inspections 
 offers sufficiently accurate data to warrant the following conclusions: 
 
 1. All of the untreated material failed within from 1 to 3 yr. t while brush- 
 treated timber remained serviceable for from 3 to 4 yr. 
 
 2. The life of untreated peeled loblolly and shortleaf pine was from 10 
 to 15% greater than that of similar unpeeled material. 
 
 3. In dry, well- ventilated workings the average life of untreated seasoned 
 loblolly pine was approximately 25% greater than that of similar green material. 
 In wet locations, seasoned timber did not appear to outlast unseasoned material. 
 
 4. Loblolly and shortleaf pine, brush-treated with coal-tar creosote and 
 Avenarius carbolineum, proved to be from 50 to 100% more durable than 
 similar untreated material. Moreover, brush-treated loblolly and shortleaf pine 
 proved more serviceable than untreated longleaf pine, pitch pine, and red and 
 black oak. Brush treatment with Avenarius carbolineum was somewhat 
 more effective than similar treatment with coal-car creosote. 
 
 5. The condition of timber treated by the open-tank process with sodium 
 and magnesium chloride, although not comparing favorably with that of tim- 
 ber similarly treated with other preservatives, was better than that of the 
 brush-treated timbers. 
 
728 
 
 SUPPORTING EXCAVATIONS 
 
 WMOO 
 
 V 3 
 
 WPQ 
 
 Je? 
 
 So a 
 
 Fl 
 
 d-a ' 
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 1 
 SH 
 
 f 
 
 .g.S.g 
 
 6. Open- tank treat- 
 ments of green timber with 
 zinc chloride proved fairly 
 effective, but the tests indi- 
 cate that better results will 
 be secured with seasoned 
 material. About 13% of 
 the green timber treated 
 with zinc chloride by the 
 open-tank process showed 
 marked signs of decay after 
 4 yr., while no decay was 
 found after the same period 
 of service in seasoned ma- 
 terial similarly treated. 
 
 7. With the exceptions 
 noted, none of the impreg- 
 nated timbers showed signs 
 of decay after from 3 to 4 
 yr. service, although some 
 of them had failed from 
 crush and squeeze. 
 
 8. In some instances, 
 impregnated timber, re- 
 framed after treatment, 
 showed signs of decay. This 
 was probably due to the 
 cutting away of treated 
 material and the consequent 
 exposure of untreated por- 
 tions of the timber. 
 
 Economy in Use of 
 Treated Timbers. The 
 original cost of a green un- 
 peeled and untreated lob- 
 lolly pine gangway set, in- 
 cluding removal of old tim- 
 bers and placement of new 
 ones amounts to about 
 $8.50. The average life of 
 such a set is about 1 yr. 
 and 4 mo. At. the end of 
 this period the simple in- 
 terest charges on the ex- 
 penditure amount to $.57, 
 making the total cost up 
 to that time $9.07, and to 
 this must be added a re- 
 placement charge of $8.50. 
 The total charges for the 
 two installations and the 
 maintenance and simple in- 
 terest on the first installa- 
 tion up to this time amount- 
 ed to $17.57. After a 
 period of 2 yr. and 8 mo. 
 the interest charges on the 
 cost of the first installa- 
 tion amount to $1.14, and 
 on the first replacement to 
 $.57, making the total cost 
 up to this time $18.71. A 
 second replacement is then 
 necessary, but if a number 
 of sets are considered it is 
 unlikely that all of them will 
 fail at the same time. In 
 2 yr. the average total 
 
SUPPORTING EXCAVATIONS 729 
 
 charges against the untreated set amount to about $18.10. With a set 
 brush-treated with creosote, on the other hand, the charges amount to 
 $11.60, a saving of $6.50 due to the treatment. In 4 yr. this saving 
 amounts to $13.80, which represents the difference between $33, the total 
 cost of the untreated sets, and $19.20, the total cost of the brush-treated sets 
 for that period. The tests further indicate that brush treatment with carbo- 
 lineum proved more economical than brush treatment with creosote. The 
 fact that the initial cost of the timber at different periods is considered to be 
 the same makes the conclusions very conservative, as the price of mine timbers 
 will unquestionably continue to rise. On the other hand, a certain salvage 
 might have been allowed for removed props, which may be utilized for fuel or 
 sawed into lagging. As, under the conditions of the experiment, failure from 
 mechanical causes, such as crush and squeeze, was more common in treated 
 than in untreated props, the former would have a greater salvage value, and 
 the relative saving resulting from their use would be greater than that noted. 
 
 Because the impregnated timbers have not been in service long enough to 
 enable their average life to be determined, most of them being still sound 
 when last inspected, it is impossible to show the ultimate saving in money, 
 resulting from their use. Even for the period since their installation, however, 
 they have proved more economical than untreated or brush-treated material. 
 
 Not only will proper preservative treatment result in a direct saving in 
 money, but it will make less timber necessary for any given working. Further- 
 more, the use of treated timber makes it possible to utilize many of the inferior 
 and more rapid growing species, which, though possessing most of the require- 
 ments of high-grade structural timber, lack durability. Treated timber of 
 these species has in many cases proved more serviceable than high-grade 
 untreated material. Thus, in the Eastern and Southern States, treated loblolly 
 and shortleaf pines may take the place of untreated longleaf pine, while treated 
 red and black oaks may be substituted for untreated white oak. Douglas fir, 
 which is now extensively used in the West, may in turn be replaced by treated 
 hemlock, larch, or western yellow pine. Inferior grades of timber can usually 
 be bought for less than higher grades, and an additional saving thus realized. 
 
 Timber that is to be treated should, whenever possible, be round instead 
 of square, as the sapwood of most species is more easily impregnated than the 
 heartwood. Moreover, the use of round timbers will do away with the cost 
 of sawing and the consequent waste. 
 
 A further economy of waste may be effected by careful inspection, and a 
 rigid condemnation of all unsound material. This is especially important 
 where the timber is to be treated, for it is poor economy to apply an expensive 
 preservative treatment to defective material. 
 
 The utilization of waste mine timbers has sometimes proved profitable. 
 Sound sections of broken or partly decayed props have been sawed or split 
 into laggings, planking, etc., and in some cases it has been found profitable 
 to use this material for fuel or to sell it for pulp wood. In many cases such 
 methods afford a considerable saving and also provide a means of disposal 
 for waste. 
 
 Summary. Results of recent investigations may be summarized as follows : 
 
 1. Decay is, in general, the agency most destructive to timber used 
 in mines. 
 
 2. Although decay may often be retarded by peeling and seasoning, treat- 
 ment with a suitable preservative is more effective. 
 
 3. The average life of green, unpeeled, and untreated loblolly-pine gangway 
 sets, under the conditions of the experiments discussed, was less than 1J yr. 
 Brush treatments with creosote and carbolineum increased this to 3 and 4 yr., 
 while impregnation treatments with zinc chloride and creosote left from 70 
 to 90% of the timbers sound at the end of 4 yr. 
 
 4. The use of treated timber results in a saving in the cost of maintenance 
 of workings and a reduction in the amount of timber required and makes 
 possible the utilization of inferior species of wood. 
 
 5. Brush treatments are economical when the amount of timber to be 
 treated will not warrant the erection of a small open-tank or pressure plant, 
 or when only a short increase in service is required. 
 
 6. The open-tank process is adapted to the treatment of small quantities 
 of easily impregnated timber. When a large amount of material is to be 
 treated, a pressure process should be used. 
 
 7. Mine timbers impregnated with zinc chloride, and creosote oils have 
 shown the best results. Up to the present, no difference in their durability 
 has been noted. 
 
730 
 
 SUPPORTING EXCAVATIONS 
 
 8. An efficient system of inspection and careful supervision in the use of 
 timber will reduce waste and result in considerable economy. Necessary 
 waste can in many cases be utilized. 
 
 FIG. 1 
 
 H 
 
 STEEL AND MASONRY SUPPORTS 
 
 IRON AND STEEL PROPS 
 
 Cylindrical Cast-iron Props. Fig. 1 is a hollow iron prop made in two 
 sections with a sleeve a. This prop has been used in longwall workings where 
 it is necessary to draw the prop to let the 
 roof sag. By knocking up the sleeve, the 
 prop falls and can be pulled out of danger. 
 In case one or the other section of the prop 
 
 is buried by rock, it can usually 
 
 be recovered by the chain at- 
 tached, which is sufficiently 
 
 strong for recovering the end 
 
 from under the first fall. There 
 
 is considerable danger of the cast- 
 iron sleeve a splitting when pres- 
 sure conies on the prop. 
 
 Steel H-Beam Props. Steel 
 
 H-beam props, arranged as shown 
 
 in Fig. 2, have been used to a 
 
 limited extent in American mines. 
 
 The section shown at a is cut and 
 
 forged to form level bearings ; the 
 
 cost of such props is relatively 
 
 high. At d is shown a design in 
 
 which clips are formed by the 
 
 use of &-in. screen plates such 
 
 as are used at the breakers; in 
 
 this case the H section is simply 
 
 cut to length without other work; 
 
 this is also the case with the sec.- 
 
 tions shown at b and c, where 2-in 
 plank or plain steel plates, | or $ in. thick, 
 are used for bearings. These props may 
 be secured in place by wooden wedges. 
 
 Cast-iron Posts With I-Beam Caps. Cast-iron posts with I-beam caps have 
 been employed in a Staffordshire colliery in England. The posts were made 
 hollow and flanged at the ends as in Fig. 3 (o). A cast-iron chair a fits into the 
 post and receives the cap b. The chair was made for a 50-lb. rail, which was 
 reversed so that the head of the rail would slip into the horns of the chair as 
 shown and the bottom of the rail be upwards. The lagging c was of wood 
 and above this were placed planks d forming 
 a double lagging filled in above with waste to 
 make a tight joint with the roof rock. The 
 planks d placed on the lagging c saved timber. 
 
 STEEL ENTRY TIMBERS 
 Standard Forms. A set of timbers, whether 
 steel or wood, consists of two parts; the collar, 
 or cross-beam, and the legs, or posts. Under 
 certain conditions, the legs may be dispensed CW 
 
 with and the collars, which ordinarily are F r ^ 
 
 rolled I beams, may be set in hitches cut fn 
 
 the coal. Or the collars may be set upon wooden or hollow cast-iron legs, or 
 upon brick, masonry, or concrete walls. All of these methods have been suc- 
 cessfully tried in many places at home and abroad. However, the I-beam 
 collar or cap is generally, especially in entry timbering, set upon legs or posts 
 of steel. The legs are of two general types channel iron or H beam. The 
 former is illustrated in Fig. 1, which is called by the makers, the Carnegie 
 Steel Co., Style E. This form corresponds to installations in which steel I- 
 beam collars have been used with wooden posts, the top of the post being 
 cut to form a seat for the collar. The two channels forming the legs are 
 
 (6) 
 
 (d) 
 
 FIG. 2 
 
SUPPORTING EXCA VA TIONS 
 
 731 
 
 connected by bolts and separators, carry angle brackets at their tops on which 
 
 the collar rests, and foot on a steel plate towhich bars are riveted to hold 
 
 them firmly in place. Angles t . . . . ^ 
 
 riveted to their webs transmit 
 
 the load from the collar to the 
 
 legs, and bent angle lugs pre- 
 
 vent undue side motion. In 
 
 this form of construction, there 
 
 are but five pieces to be 
 
 erected: the single collar beam, 
 
 two legs, and two base plates. 
 
 If the footing is good, even the 
 
 base plates, shown in Fig. 2, 
 
 can be eliminated or plain plates 
 
 can be used instead of the 
 
 riveted bases. 
 
 The second type of leg, illus- 
 
 trated in Fig. 3, consists of an 
 
 H beam and in the combina- 
 
 tion shown is known by the 
 
 makers as Style F. The lug 
 
 angles at the top prevent side 
 
 motion and the bearing plates are perfectly plain, as shown in Fig. 4, although 
 
 base plates, Fig. 5, to which the legs may be bolted or riveted can be sup- 
 plied upon request. This is the simplest form of entry 
 timber and perhaps the one in most general use. It 
 should be noted, that where a broader bearing surface is 
 necessary, H beams may be used for collars in place of the 
 standard I beams. 
 
 Mr. R. B. Woodworth, in the Transactions of the Ken- 
 tucky Mining Institute, Dec., 1911, states as follows: "With 
 plain material at 1.25c. a Ib. f. o. b. cars Pittsburg, and the 
 usual cost for workmanship, the comparative costs of these 
 styles are shown in the two tables that follow, from which 
 
 p IG 
 
 FIG 2 
 
 can be seen at a glance how great a part attention to details may play in 
 
 the economic use of materials by the avoidance of unnecessary work in 
 
 fabrication. The sets in each 
 
 table are all of equivalent 
 
 theoretical strength. In the 
 
 first table, are given steel gang- 
 
 way supports for a very heavy 
 
 double-track gangway, collar 
 
 17 ft. long between legs, legs 
 
 10 ft. 6 in. high in the clear, 
 
 equivalent in strength to 24-in. 
 
 round, longleaf, yellow-pine 
 
 timbers. 
 
 In the second table are 
 given the steel gangway sup- 
 ports for a single-track gang- 
 way, collar 10 ft. long between 
 legs, legs 8 ft. high in the clear, 
 equivalent in strength to 15-in. 
 round, longleaf, yellow-pine 
 timbers. 
 
 "Figures in these two tables 
 
 do not include painting, cost of 
 
 FIG. 3 
 
 which varies with the kind of paint used, but may 
 be estimated at $2 per T. additional. Styles A, 
 B, D, and E, are various combinations of I-beam 
 collars and channel iron legs, while styles F, G, C, 
 and I have H-beam legs." 
 
 The details of another form of steel entry tim- 
 bers are shown in Fig. 6, where the legs are pin- 
 connected to the cap and not joined by angle bars. The cap piece a is an 
 I beam, while each leg b consists of two channel beams that rest in a 
 cast base c at the bottom. The top of each leg is fastened to the cap by 
 means of the pin d, held in place by the split cotters e. Iron wedges/ are also 
 
 FIG. 4 
 
 FIG. 5 
 
732 
 
 SUPPORTING EXCAVATIONS 
 
 
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SUPPORTING EXCAVATIONS 
 
 733 
 
 used to stiffen the connection between the cap and the leg. Several pinholes 
 are made in both the legs and the collars, so that the same set may thus be 
 used in several positions. In order that the legs may be given a desired batter 
 the legs of the posts fit into a cast shoe c 
 that has a cylindrical bottom, and this 
 bottom rests in a cast base g. This forms 
 a very easily adjustable set, for by means 
 of the base illustrated the legs can be given 
 any desired batter, and the set is then 
 stiffened by means of the wedges /. 
 
 Lagging used with steel timbering may 
 be of wood or, better, of boiler plate, or 
 corrugated sheets of buckle plates where 
 extreme strength is needed. The thin con- 
 crete slab, however, may well be used where 
 acid water is present, either plain or rein- 
 forced with expanded metal, wire-mesh 
 reinforcement, or plain rods or wire. 
 
 For pump houses, as shown in Fig. 7, 
 and for underground stables steel framing, 
 particularly in connection with concrete 
 lining, is daily growing in favor. In the 
 pump house shown, the simple steel fram- 
 ing took the place of heavy framed timbers 
 that it is necessary constantly to renew. 
 
 Relative Cost of Steel and Wood Tim- 
 bering. Owing to the movement of 
 
 FlG. 6 
 
 ^6 '\\23.8 /& 
 
 the strata overlying the pump room of the Dodson colliery, of the Plymouth, 
 (Pa.) Coal Co., it was decided to retimber it with steel. The original wooden 
 timbering consisted of 18-in. to 22-in. round sticks of white pine, yellow pine, 
 and oak placed 2 ft. center to center. A great deal of trouble was experienced 
 from these timbers becoming forced in close upon the pipe lines with the 
 possibility of breaking them. As new timbers were placed, they were put 
 in between the sets already in, so that eventually the pump room had timbers 
 practically skin to skin. It is estimated that the entire pump room was 
 retimbered in wood once a year. 
 
 The pump house is 100 ft. long, 8 ft. high in the clear, and 18 to 22 ft. wide. 
 Beginning with April 18, 1910, the seventy wooden sets of mine timbers were 
 replaced by forty-eight steel sets made up of 18-in., 55-lb., and 20-in. 65-lb. 
 I-beam collars and 6-in. H-beam legs, weighing 23.6 Ib. per ft. The last set 
 was installed about De- 
 cember 15, 1910. 
 
 From the following 
 statement it will be 
 noted that the total cost 
 for timbering once with 
 wood was $2,415, and 
 the total cost for tim- 
 bering in steel $2,889.09 , 
 or a difference in first 
 cost of not quite 20%. 
 The steel cost at the 
 mines slightly over two 
 and a half times the 
 cost of wooden sets, 
 and it also cost 33^% 
 more for placing. 
 Fewer sets were re- 
 quired, however, and 
 the ultimate rate was 
 thereby lessened. 
 
 The comparative FIG. 7 
 
 cost of the two instal- 
 lations is shown in the statement below, prepared by Mr. Haddock: 
 
 0-6 
 
 ^ Pump Mouse 30-0"Lony 
 ^ Square TJmter-5efs 
 ,f -}, j-0"c.foc. 
 
734 SUPPORTING EXCAVATIONS 
 
 Wood 
 
 Number of sets 70 
 
 Average diameter -of timber, inches 20 
 
 Quality of timber, yellow pine and oak. 
 
 Average weight per set, pounds 4,150 
 
 Cost per set f. o. b. cars mines $12.00 
 
 Cost per set for placing $22.50 
 
 Cost per set in place $34.50 
 
 Total cost for timbering $2,415.00 
 
 Life of timber set, year 1 
 
 Steel 
 
 Number of sets. 48 
 
 Size of collars, 18-in. beam , pounds 55 
 
 Size of collars, 20-in. beam, pounds 65 
 
 Size of legs, 6-in. H beam, pounds 23.6 
 
 Quality of steel, structural grade. 
 
 Average weight per set, pounds 1,483 
 
 Cost per set f. o. b. mines $31.47 
 
 Cost per set for placing $30.00 
 
 Cost per set in place $61.47 
 
 Total cost for timbering $2,889.09 
 
 The higher cost of placing the steel is due to three causes: 
 
 1. The charge of taking out the old timber, which, however, was insig- 
 nificant, as the steel was placed a set at a time by forepoling ahead, the con- 
 dition of the roof being very bad and there being loose material for an unknown 
 distance above. 
 
 2. Great care was taken with the steel to line it up properly and provide 
 a good base, which was made of a solid concrete wall built the full length of 
 the pump room on each side. This solid concrete base is unnecessary with the 
 wood and might have been omitted with steel, but its use means a real better- 
 ment in the construction. 
 
 3. The steel was placed without interfering with the operation of the 
 pumps, which necessitated very careful handling and added something to what 
 the expense would have been had the room been free from obstructions. 
 
 It is apparent that while the first cost of the steel construction is greater 
 than that of wood, it will have much more than paid for itself if its life extends 
 over 15 mo. only, and that every additional length of time it stands will mean 
 that much less in cost of maintenance. The first steel after being in place 
 16 mo. showed no sign of deflection in the collars, and what is better, no 
 evidence of fracture in the concrete where any overloading of the steel would 
 immediately show. 
 
 In 1908, at their Maxwell colliery, the Lehigh and Wilkes-Barre Coal Co. 
 timbered a double-track gangway with 20-in., 65-lb., I-beam collars 17 ft. long 
 between legs, and 8-in. H-beam legs 10 ft. 6 in. high in the clear, weighing, with 
 base plates, 1,720 Ib. per set. These took the place of wood sets made of 24-in., 
 round, yellow-pine timbers, the cost of which erected was $15 per set, weight 
 5,040 Ib., and the life of which was 2| yr. In view of their probable durability 
 the steel sets were erected on concrete bases which added to the cost, which 
 reached a total of $40 per set. Capitalized at 6% interest, the value of the 
 steel sets at the end of 15 yr. will be $95.86 each, while the capitalized value 
 -of the six wooden sets needed in that time will be $153.56. At the end of the 
 15 yr. the steel will have a scrap value per set of $12.03, while the wood will 
 be worth nothing, a saving by the use of steel of $69.73 per set or $4.65 per yr. 
 The use of steel in English mines has effected a saving of 2c. per T. of 
 coal mined. 
 
 At the No. 8 mine of the West Kentucky Coal Co., Sturgis, Ky., steel mine 
 timbers are used in the new slope, both main heading and air-courses. Sets 
 in use are Style F composed of 10-in., 25-lb., I-beam collar and 4-in., H-beam 
 legs. Sets a/e spaced 3 ft. on centers and lagged with oak plank 3 in. thick 
 on top and 2 in. thick on sides. Between the sets concrete is placed up to 
 4 ft. high. This makes a solid reinforced-concrete slope from the entrance 
 to the point where ribs are hard and top good. According to figures furnished 
 by Mr. W. H. Cunningham, general manager of the company, the comparative 
 costs of wood and steel for this mine were: 
 
 Wood. Yellow-pine creosoted; size 12 in.X12 in., 264 B. M. ft.; 
 cost at Sturgis $10.56 per set; cost in place $15.70; weight 1,575 Ib. 
 Wood. Native white oak; size 12 in.X12 in., 264 B. M. ft.; cost 
 at Sturgis $7.92; cost in place $13.06 per set; weight 1,340 Ib. 
 
SUPPORTING EXCAVATIONS 
 
 735 
 
 Steel. Cost of steel at Sturgis $9.75 per set; cost of placing $1; 
 cost of concrete per panel $5.16; total cost in place per set, steel 
 alone $10.75, steel concreted $15.91; weight of steel sets 425 Ib. 
 The saving in the use of steel without concrete over native white oak was 
 $2.31 per set; over yellow pine, $4.95. The excess cost of steel with concrete 
 over white oak was $2.85 per set; over yellow pine, 21c. This favorable com- 
 parison is due to the high unit cost of the wood and to the elimination of waste. 
 The safe uniformly distributed load on the wood collar is 19,200 Ib., on the 
 steel collar 26,000 Ib. The safe compressive strength of the steel leg is 43,200 
 Ib., while that of the wooden leg is 105,100 Ib.; in the one case more than ample, 
 in the other case out of all proportion. 
 
 Advantages of Steel Timbering. Among the benefits coming through 
 the use of steel timbering are: 
 
 1. Reduced Excavation. In the Lehigh and Wilkes-Barre installation the 
 same clear space inside was had with steel in an excavation 4 in. less in height 
 and 32 in. less in width than that needed with wooden timbering; in the Dodson 
 colliery, the space saved was 2 in. in height and 28 in. in width; and in the 
 West Kentucky installation, 2 in. in height and 16 in. in width. 
 
 2. Better Ventilation. The headings being larger, the ventilation is better, 
 and further, the absence of all stages of decay common to wooden timbers, 
 removes a serious source of vitiation of mine air. 
 
 3. Less Dust-Catchment Area. Steel mine timbers afford a much less area 
 for the lodgement of explosive coal dust than do wooden ones of the same 
 
 strength and are much more 
 
 easily cleaned. 
 
 4. Fireproof Character. 
 One of the greatest advantages 
 of steel timber consists in its 
 absolute incombustibility, ren- 
 dering it especially suitable for 
 the construction of underground 
 shanties, stables, pump and 
 engine rooms, etc. 
 
 Preservation of Steel Mine 
 Timbers. The corrosion of 
 structural-steel timbers within 
 the mine is not so serious as 
 above ground, as the conditions 
 of temperature, humidity, etc. 
 are practically uniform. Mine 
 timbering steel should not be 
 placed unpainted unless it is to 
 be covered with concrete. If 
 well painted before installation, 
 steel timbering, so far as rust is 
 concerned, should outlast the 
 life of the mine. After 17 yr. of use, the steel timbers installed in the 
 Sterns shaft, of the Susquehanna Coal Co. and in the pump room of the 
 Hazleton shaft colliery, No. 40 slope, of the Lehigh Valley Coal Co., are still 
 in use and in first-class condition. The steel timbering at the No. 1 shaft of 
 the Spring Valley (111.) Coal Co., is in good condition after 18 yr. use. Struc- 
 tural steel does not have the opportunity to corrode as does the steel in track 
 rails' underground and consequently lasts indefinitely. Rails are laid where 
 they come in direct contact with any acid mine water and, their tops being 
 polished by passing car wheels, are in the most unfavorable position to resist 
 corrosion. 
 
 The possible effect of acid mine water upon steel mine timbers has been 
 exaggerated. Tests under working conditions show that the careful selection 
 and application of good paint will prevent the destructive action of mine 
 water. The paint should be applied in two coats, the first of which should be 
 red lead or natural iron oxide and the second a good graphite. The coating 
 should be applied to a clean surface and should be well rubbed in. The paints 
 should be of the very best grade mixed in pure linseed oil, the weight of the 
 paint, in pounds, per gallon of oil being about three times its specific gravity. 
 
 MASONRY AND IRON SHAFT LININGS 
 
 Masonry Shaft Lining. Masonry shaft lining, which may consist of brick, 
 rock, or concrete, is used where timber is scarce or where the character of the 
 
 FIG. 
 
736 
 
 SUPPORTING EXCAVATIONS 
 
 strata is such as to render timber lining impracticable. A section only of a 
 shaft is sometimes thus lined, while the ordinary timber lining is used in the 
 greater part of the shaft. These linings are usually laid on a wedging curb 
 and are carried upwards in sections, as shown in Fig. 1. Each section is laid 
 on a ring a of cast iron or timber resting on a temporary shelf or seat b cut in 
 the rock. As the lower sections are built up, the shelf b supporting the masonry 
 above is cut away in places and the masonry below carried up to furnish the 
 necessary support for the upper section. In this manner, all the shelf is 
 finally cut away and replaced by the masonry of the lower section. 
 
 Tubbing. Tubbing is an English term applied to the metal, or sometimes 
 to the timber, lining of a circular shaft, and is particularly used when such 
 linings are employed to keep water from flowing into a shaft. The three kinds 
 of metal tubbing are: (1) that which is made in sections with outside flanges 
 and is simply wedged firmly into place by wedges placed between the tubbing 
 and the wall of the shaft; (2) that which is 
 made in sections and bolted together on the 
 inside both at the vertical and horizontal 
 joints; (3) that which is made up of com- 
 plete rings of cylinders bolted together by 
 means of horizontal flanges. 
 
 The metal tubbing a, Fig. 2, consists 
 of cast-iron segments varying in height 
 from 18 to 36 in. .according to the pressure 
 to be resisted. The segments are flanged 
 at top, bottom, and ends and $-in. pieces 
 of pine are put between them as they are 
 put in place, thus making tight joints both 
 horizontally and vertically. To prevent 
 breaking the metal lining by the pressure 
 of air or gas behind it, the metal is per- 
 forated; these holes are loosely plugged, so 
 that any particular pressure corning on 
 them will force out the plugs. At b is shown 
 a method of walling a circular shaft with 
 brick, the brick being laid on a cast-iron 
 wedge curb s. 
 
 Wood tubbing may be of two kinds: 
 (1) planks 2 or 3 in. thick placed vertical- 
 ly and having edges like barrel staves ; (2) 
 thick blocks similarly beveled and placed 
 vertically. At c is shown an example of 
 plank tubbing. The planks have timber 
 curves m placed inside them and spiked 
 to them. The curves are kept apart by 
 punch blocks n and are tied together and 
 fastened to the shaft sills I by the stringers 
 r. The sections of the shaft b and c are 
 shown supported on a rock bench while the 
 metal tubbing is being put in place below. 
 When a shaft has been lined up to the 
 rock bench, this is cut away and the metal 
 tubbing joined to the other portion of the 
 shaft lining by small metal sections, called 
 closers. 
 
 Ml " 
 
 I I I 
 
 I I -I 
 
 JUJ= 
 
 II I I I -I 
 
 FIG. 2 
 
 The following formula is given by Mr. W. Galloway for calculating the 
 proper thickness for. cast-iron tubbing, or for cement or brick lining: 
 
 ivhd 
 
 2(r+wh) 
 in which t = thickness of lining, in inches; 
 
 d = internal diameter of shaft, in inches; 
 h = head of water, in inches; 
 
 w = weight of cubic inch of water = -=^ = .0361 lb.; 
 
 l,7^o 
 r = 33}% (one-third) of crushing load per square inch of material 
 
 used. 
 
 The crushing strength of the material used should be determined in each 
 case by experiment, but the following may be used as a fair average value: 
 
SUPPORTING EXCAVATIONS 
 
 737 
 
 Pounds Per 
 Square Inch 
 
 Crushing strength of cast iron 80,000 
 
 Crushing strength of brick laid in lime mortar 1 ,000 
 
 Crushing strength of brick laid in cement and lime 1,500 
 
 Crushing strength of brick laid in best cement mortar 2,000 
 
 Crushing strength of concrete made from Portland cement and 
 
 1 mo. old 1,000 
 
 Crushing strength of concrete made from Rosendale cement 
 
 and 1 mo. old 500 
 
 Crushing strength of concrete made from Portland cement and 
 
 1 yr. old 2,000 
 
 Crushing strength of concrete made from Rosendale cement 
 
 and 1 yr. old 1,000 
 
 EXAMPLE. What should be the thickness of tubbing for a shaft 13 ft. in 
 diameter at a depth of 800 ft.: (a) for cast iron? (b) for brick, assuming a 
 mean crushing strength of 1,500 Ib. per sq. in.? (c) for concrete made from 
 Portland cement and 1 mo. old? 
 SOLUTION. 
 
 (a) /< 
 
 .0361X800X12X13X12 
 
 27,031 
 
 26,666 + 347 
 
 = 1 in 
 
 2 X 
 
 fM 
 
 L 
 
 +(.0361X800X12) 
 
 
 .0361X800X12X13X12 
 
 27,031 
 
 2X 
 
 , 
 -- 
 
 STEEL AND CONCRETE SHAFT LININGS 
 
 Steel Sets. The use of steel alone and not in connection with concrete 
 lining is unusual in shaft timbering. An illustration, however, is afforded by 
 the shaft at the Mt. Lookout colliery, of the Temple Iron Co., and illustrated 
 
 gjrjf 'Plate 
 
 at>'f every e'-o" 4 
 
 FIG. 1 
 
 in Fig. 1. The steel sets were used to reinforce the worn-out original wooden 
 sets, which were left in place. The steel sets consisted of 12-in. channels set 
 back to back, separated by anchor plates to catch in the wood of the original 
 lining, and double 6-in. channels to take the place of the 10"X12" buntons 
 47 
 
738 
 
 SUPPORTING EXCAVATIONS 
 
 FIG. 2 
 
 originally separating the compartments. It 
 would seem that instead of channels, H sec- 
 tions should have been used as better 
 adapted to resist compression than the 
 channels, as well as being lighter and, 
 hence, cheaper. 
 
 Steel Buntons. Steel, in place of wood, 
 is very commonly employed for buntons 
 even in shafts that are not lined with con- 
 crete. Some of the various forms are shown 
 in Fig. 2, and of these the H section ap- 
 pears the best and is the most generally 
 used. Steel buntons are fireproof, but cost 
 much more than wood; four times as much 
 if a section as light as 35 Ib. per ft. is used. 
 On the other hand, with proper care, they 
 will last indefinitely. 
 
 Concrete and Steel Shaft Linings. 
 Practically all concrete-lined shafts are 
 elliptic in section, the arch form being 
 adopted as better able to withstand pressure 
 than the rectangular. A full description 
 of the concrete-lined shaft at the Filbert 
 mine, of the H. C. Fnck Coke Co., Fayette 
 County, Pa., is given on page 230. 
 
 The rectangular, concrete-lined shaft of 
 the Bunsen Coal Co., near Clinton, Ind., is shown in Fig. 3. The buntons are 
 6"X8" concrete beams reinforced with a 6-in. 8-lb. channel. Where the shafts 
 pass through soft 
 ground, the ends are also 
 reinforced with the same 
 size channels. 'The lin- 
 ing is G in. thick through 
 firm material and 12 in. 
 through soft. The 
 guides are 6" X 8" yellow 
 pine bolted to the rein- 
 forced-concretebuntons. 
 The partitions in the air- 
 shaft at this mine are 8 
 in. thick and of rein- 
 forced concrete built 
 with American Steel and 
 Wire Co.'s No. 4 tri- 
 angular-mesh reinforce- 
 ment on 6"X8" bun- 
 tons reinforced with 
 channels as noted. 
 
 In the elliptical 
 shaft of the Tennessee 
 Coal, Iron, and Rail- 
 road Co., at Pratt mine 
 No. 13, near Ensley, 
 Ala., amassive, unrein- 
 forced concrete lining is 
 used with a minimum 
 thickness of 15 in. 
 through firm and 18 in. 
 through soft material. 
 The buntons are 6-in. 
 steel H sections, weigh- 
 ing 23.8 Ib. per ft., 
 spaced 6 ft. apart. The 
 guides are of the same 
 material as the buntons 
 and carry, bolted to 
 them, cast-steel safety 
 racks. FIG. 3 
 
HOISTING 739 
 
 HOISTING 
 
 Hoisting, or winding, engines may be driven by hand, horse, or mechanical 
 power. The mechanical power may be derived from engines, or motors, driven 
 by steam, electricity, gasoline, compressed air, water, etc. 
 
 There are two general classes of hoists: single and double. In the former, 
 there is but one cageway in the shaft and up this the cage and loaded car are 
 hoisted by an engine. After the load is dumped at the surface, the cage and 
 empty car descend through the same compartment, impelled by gravity, their 
 speed being controlled by the brakes on the engine drum. In double hoists, 
 there are two cages which travel in separate compartments, one ascending with 
 the loaded car as the other descends with the empty car. Double hoists are 
 the prevailing type, the use of single hoists being confined to prospecting shafts 
 and to unimportant operations in the metal-mining districts. 
 
 There is no essential difference between stationary engines used for hoisting 
 and for haulage. The chief distinction lies in the direction of application of 
 the power generated by the engine. In hoisting engines, the power is applied 
 vertically to raise a weight through a shaft; in haulage engines, the power 
 is applied in a horizontal or approximately horizontal direction to move a 
 weight along a track. Frequently, the same mechanism after having served 
 its purpose as a hoisting engine is used for haulage, and vice versa. 
 
 The subject of hoisting ropes is discussed under the head of Wire Ropes. 
 
 HAND- AND HORSE-POWER HOISTS 
 
 Hand- and horse-power hoists are of relatively small capacity and are almost 
 entirely used for prospecting, shaft sinking, or the like. 
 
 The -windlass, operated by one or two men, is frequently used for sinking 
 small shafts to depths of about 75 ft., where the loaded bucket weighs but 
 a few hundred pounds. In form, it is similar to the hoisting device used in 
 connection with water wells and consists of a wooden barrel, about 8 in. in 
 diameter and 4 or 5 ft. long, provided with a 1 to li-in. iron axle. This axle 
 is supported at either end in A-shaped wooden standards nailed or mortised 
 to a heavy timber base placed over the shaft. The necessary crank and 
 handle is attached to each end for applying the power. 
 
 For hoisting heavier weights, single- or double-geared iron crab winches 
 are used. In these, the power is transmitted to the drum or barrel by rack and 
 pinion, so that one man can raise 1 T. or more, but at the expense of speed. 
 These hoists are single and unbalanced, the bucket being hoisted by one or 
 two men and descends by gravity; its speed is controlled by loosening or 
 tightening the rope upon the drum. 
 
 For greater depths and heavier loads, horse whims, or gins, are used. These 
 consist essentially of a drum mounted on a shaft to which are attached one 
 or more cross-sweeps to each of which a horse or mule is hitched. Usually 
 the whim is placed a little distance from the shaft and is so arranged that the 
 movement of the car is regulated by two hand levers, which are connected to 
 the driving gear in such a way that the movement of the drum may be stopped 
 or reversed independently of the movement of the horse. One lever is moved 
 to hoist and the other to lower the load, and through their use overwinding 
 is prevented in case the animal does not stop on the instant. 
 
 In the better classes of whims, the drum is placed horizontally underground 
 or below a platform to be out of the way of the horses, motion being imparted 
 to it from a vertical shaft through beveled gearing. The vertical shaft is 
 provided with, two, four, or six sweeps to each of which one or two horses 
 may be hitched, so that as many as twelve animals may be used. With four 
 horses, 90 T. have been hoisted GOO ft. in 10 hr.; and with eight mules GO T. 
 have been hoisted 900 ft. in the same time. Some whims are provided with 
 gears for hoisting heavy loads at slow speed and lighter loads at high speed. 
 Such machines, at slow speed will hoist 2,400 Ib. 22 ft. per min.; and at fast 
 speed, 950 Ib. 55 ft. per min. 
 
740 HOISTING 
 
 STEAM-POWER HOISTING ENGINES 
 
 Hoisting engines are almost invariably of the duplex, or two-cylinder, type 
 with cranks set at right angles to one another and therefore have no dead 
 center; for which reason they can be quickly started from any position and 
 run more smoothly than single-cylinder engines. 
 
 Hoisting engines may be simple or compound, and tandem or cross-compound. 
 The first is by far the most extensively used in the shallow shafts prevailing 
 in the coal regions, where the shortness of the hoisting period and the frequent 
 reversals of the engines are not conducive to the economical use of high- 
 pressure steam expansively. In the metal-mining regions, where vertical lifts 
 of 1,000 ft. are usual, of 2,500 ft. fairly common, and where several of from 4,000 
 to over 5,000 ft. exist, refinements in compounding, etc. are successfully used. 
 Further, in metal-mining regions, the price of coal is such (from $4 to $10 and 
 more per ton) that it is imperative to secure all the energy possible from each 
 pound of fuel; while at coal mines and particularly at those where slack is used 
 under the boilers the cost of power has not, until comparatively recent years, 
 been thought worthy of consideration. 
 
 A hoisting engine may be of the slide-valve, piston-valve, or Corliss-valve 
 type and may be condensing or non-condensing. For a large hoisting engine, 
 a piston-valve gives a much better distribution of steam in the steam chest 
 than a slide-valve, but not so good as a Corliss valve. A hoisting engine, to 
 run condensing, should have an independent air pump and condenser; for if 
 the air pump is operated by the engine it will stop when the engine stops and 
 the vacuum will be lost, rendering the low-pressure piston, in some cases, 
 inadequate to pick up the load at the beginning of the next hoist. 
 
 In a hoisting engine, the drum on which the hoisting rope coils takes the 
 place of a flywheel, to a certain extent. The operation of hoisting is inter- 
 mittent in character, and in some cases the engine is so connected that it will 
 run only when operating the drum; in other cases it will run continuously, 
 either empty or under some other load than the hoisting load, the work of 
 hoisting being put on it, when needed, by means of a friction clutch connecting 
 the engine with the drums. Where an engine runs continuously, its surplus 
 power may be utilized for driving air compressors, fans, electric generators, 
 and other machinery; and, by thus concentrating the power, a higher grade 
 engine can be made available for hoisting purposes. 
 
 Second-Motion, or Geared, Hoisting Engines. In a second-motion engine, 
 power is transmitted from the engine shaft to the drum shaft through gearing. 
 This engine is particularly adapted for portable hoists, such as are used in 
 shaft sinking and similar temporary work, and for shallow mines, or mines 
 where a small t9nnage is raised. It is cheaper in first cost and in installation 
 than a first-motion hoisting engine, as a smaller engine does the same work, but 
 it cannot hoist as rapidly; there is also less liability of overwinding. Geared 
 engines are used ordinarily where a hoisting speed of 750 ft. per min. or less is 
 satisfactory, while first-motion engines are used for greater speeds. To hoist 
 the same load, a first-motion engine must be three to four times as large as a 
 second-motion engine, while the hoisting speed and cost will also be three to 
 four times as much. 
 
 The relative number of teeth in the gears may be varied so that the piston 
 speed may be made faster or slower or equal to that of the rope. The com- 
 monly used ratios vary from 1 to 3 to 1 to 5; that is, if the small gear-wheel 
 on the engine shaft has, say, 20 teeth, the large gear-wheel on the drum shaft 
 will have GO to 100 teeth, depending on the ratio, and it will require from three 
 to five revolutions of the engine to equal one of the drum. 
 
 If the ratio is exact, the teeth on the small gear come in contact with the 
 same teeth on the large gear during every revolution and cause excessive wear. 
 To equalize the wear, the number of teeth in the large wheel is commonly one 
 less or more than that demanded by the exact ratio. Thus, if the engine is 
 geared 1 to 5, while 20 teeth on the small wheel require 100 on the large wheel, 
 either 99 or 101 would be used. 
 
 Hoists are occasionally built with metal teeth in the pinion and wooden 
 teeth in the larger wheels. The larger wheels in such cases are cast with 
 mortises, into which are driven maple cogs that are made secure by wedges. 
 These wooden cogs, or teeth, wear well and are easily replaced when broken 
 without seriously interrupting hoisting operations; they are almost noiseless. 
 It a metal tooth breaks, the gear must be replaced, and hoisting must cease 
 until this can be done. In cut gears, the teeth are finished by machine; this 
 
HOISTING 741 
 
 adds slightly to the cost of these gears, but they are more serviceable than 
 rough, cast gears and make less noise. 
 
 Geared engines may have single or double drums, the former being in general 
 use at coal mines where the shafts are relatively shallow and the material is 
 hoisted frorn one level. Single-drum engines are commonly used in balance, 
 the drum being keyed directly to the shaft, one rope unwinding from the top 
 of the drum as the other rope winds up beneath it. Double-drum engines 
 may be used in balance, by leading the ropes as just indicated but on the 
 separate drums; or they may be used independently, each drum hoisting as 
 desired and both ropes leading on the drums alike, that is, both on top or both 
 underneath. 
 
 The wearing surfaces in hoisting engines, especially the main bearings, 
 should be made large and the engines proportioned to stand severe work. In 
 the case of two wide-faced drums on the shaft, it is sometimes necessary to have 
 a center bearing, which should be adjustable in every direction and kept as 
 nearly in line with the other bearings as possible. Owing to the difficulty of 
 keeping three bearings in line, and the danger of the shaft breaking in case the 
 bearings are not in line, it is well, where practicable, to omit the center bearing 
 and make the shaft as-short as possible and ample in diameter. 
 
 First-Motion, or Direct-Acting, Hoisting Engines. In first-motion hoists, 
 a pair of engines (right- and left-handed) are used with their cranks on the ends 
 of the same shaft as the drum, the cranks being set at angles of 90 with each 
 other to prevent the engines stopping on a dead center. A direct-acting 
 hoisting engine is used wherever the depth of the shaft or a large output demands 
 a high speed of hoisting. In coal-mining practice, their use was formerly limited 
 to the deepest shafts, but the large outputs required from modern mines have 
 caused them to be introduced at comparatively shallow shafts. 
 
 HOISTING ENGINES USING OTHER POWER THAN 
 STEAM 
 
 Compressed-Air Hoisting Engines. Where available, compressed air may 
 be used in place of steam for power as there is no essential difference in the 
 engines. Compressed air may be used exclusively or interchangeably with 
 steam, and should be reheated before entering the engine cylinders. In the 
 case of a compound engine, the reheater may be placed in the pipes leading to 
 the high-pressure cylinder; or, still better, it may be placed before each cylinder; 
 otherwise, the expansion will cause the moisture to freeze in the low-pressure 
 cylinder and stop the engine. 
 
 Where a hoisting engine is located on the surface and a boiler plant is 
 necessary, steam is generally preferable to compressed air, as the loss in efficiency 
 due to compressing the air is avoided. If, however, water-power is available, 
 it is frequently cheaper to use compressed air instead of steam, particularly 
 if compressed air is also used at the mine for coal cutters or rock drills; or if 
 for any reason it is necessary to place the hoisting engine at a distance from 
 the boiler plant, as there is much less loss of efficiency in carrying compressed 
 air than in carrying steam. For underground hoists, compressed air has many 
 advantages, particularly in gaseous coal mines. 
 
 Further data on compressed air will be found under that heading and under 
 the heading Haulage. 
 
 Gasoline Hoisting Engines. Gasoline hoists are adapted for sinking 
 prospecting shafts in mpuntainous districts where fuel is scarce and where an 
 easily portable engine is desirable. They are not generally used for permanent 
 hoists in mines of any great capacity. Their operation is essentially on the lines 
 of gasoline haulage motors, which are described under the heading Haulage. 
 The gasoline is injected into the engine cylinder in the form of a spray and is 
 there mixed with air and ignited by means of an electric spark, producing an 
 explosion that moves the piston. When starting the engine, the clutch is 
 released and the engine is rotated by pulling over the flywheel until it has 
 received the first impulse, which usually requires from one to two complete 
 turns. After receiving the first exptosion, the_ engine continues to operate, 
 drawing in a supply of gasoline and air and igniting it with an electric spark. 
 When operating the hoisting drum, the engineer first speeds up the engine 
 and then throws the clutch that controls the hoisting drum. Drums must 
 be well equipped with a powerful brake in the use of either gasoline or electric 
 hoists, to avoid accident due to the possible failure of the power. 
 
742 
 
 HOISTING 
 
 Hydraulic Hoisting Engines. Hoisting engines using the direct energy of 
 falling water as a source of power, while not infrequently employed in metal- 
 mining districts, are not known in the coal fields. 
 
 Electric Hoisting Engines. Electric hoists differ but slightly in mechanical 
 construction from those operated by steam. Owing to the high speed of the 
 ordinary motor, electric hoists are commonly double geared. The reduction 
 between the armature shaft and the intermediate shaft is ordinarily about 
 1 to 4; between the intermediate shaft and the drum gear it varies according 
 to the size of the drum and the hoisting speed desired . 
 
 Motors for heavy hoisting may be either of the alternating-current induc- 
 tion type or of the direct-current type. Alternating-current induction motors 
 are discussed under the subject of Electricity with further notes under Haulage. 
 When large direct-current motors are used at a distance from the power station, 
 the power is transmitted by alternating current to the point of its application 
 and is there transformed to direct current, usually by means of motor-generators. 
 
 The getting up of full speed (acceleration) and maximum load (coal and 
 weight of entire rope) produce what is known as a peak, or high point, in the 
 curve diagramming the power required from a hoisting engine; and the peak 
 load is often double the average load upon the engines. In electric hoisting 
 as the heating of the machines varies approximately as the square of the load 
 
 DC 
 
 Hoist Motor 
 
 FIG. 1 
 
 it is important in order to reduce the size (and consequently the cost of the 
 equipment) to make the load during the hoisting period as uniform as possible. 
 The partial equalization of the load is accomplished through the use of some 
 system of balanced hoisting, such as the Koepe describeci later. These systems, 
 however, do not perfectly balance the load during all portions of the run, and 
 various methods have been employed to produce what may be called an 
 electric balance so that the input of electric energy may at all times be equal 
 to the output of mechanical energy. 
 
 In the Ilgner system, shown in diagram in Fig. 1, a motor-generator set is 
 used for supplying power to the hoist motor, which is of the shunt-wound 
 direct-current type. The operation of the hoist is controlled by varying the 
 voltage of the generator, to which it is directly connected electrically. By 
 reversing the excitation of the generator, the direction of rotation of the motor 
 is also reversed. A flywheel is connected with the motor-generator set and 
 arrangements are made to automatically vary the speed of the set so that 
 during peak-load periods the speed of the set is decreased, and part of the 
 energy in the flywheel is used to assist the motor in driving the generator. 
 
HOISTING 
 
 743 
 
 When the load drops below a certain value, the speed of the set is gradually 
 increased and energy is again stored in the flywheel. By properly proportion- 
 ing the flywheel, assuming that the cycle of operation remains constant, it is 
 possible to keep the input to the hoisting plant within a few per cent, of the 
 average load. 
 
 An objection to the Ilgner system of hoisting is the expensive nature of 
 the hoisting plant, the addition of a motor-generator and flywheel increasing 
 the cost considerably. To overcome this feature and still provide for the 
 equalization of the input, a system has been introduced by the British Westing- 
 house Company which may be used under certain circumstances. This scheme 
 is shown diagrammatically in Fig. 2. The hoist motor in this system may be 
 either direct current or alternating current, depending on the source of supply. 
 The diagram of connections shows the arrangement of the plant with an alter- 
 nating-current source of supply. In parallel with the generators an equalizing 
 outfit is arranged, which consists of the direct-current machine coupled to the 
 flywheel, which is connected to the alternating-current system through a 
 rotary converter. 
 
 This equalizing equipment can be located anywhere that may be convenient, 
 it not being necessary to have it near the hoist. The operation is as follows: 
 When the hoist load exceeds the value for which the regulator is set, the field 
 
 A 
 
 J J 
 
 A 
 
 Automatic^ 
 Regulator 
 
 nierators 
 n 
 
 Rheostat 
 
 FlG. 2 
 
 of the equalizing machine is automatically strengthened, so that the speed tends 
 to drop and the machine is driven as a generator by the flywheel and delivers 
 energy through the rotary converters to the alternating-current system. The 
 rate at which the energy is delivered is dependent on the operation of the 
 regulator. When the demand drops below the value for which the regulator 
 is set, the field of the equalizing machine is automatically weakened; this 
 machine then runs as a motor and absorbs energy from the alternating-current 
 system through the rotary converter and speeding up the flywheel. In this 
 way the demand on the alternating-current system is kept practically constant. 
 When this system is used with a direct-current source of supply, the rotary 
 converter is omitted and the equalizing machine is connected directly to the 
 line. This arrangement, however, does not provide for controlling the hoist 
 motor, as does the Ilgner system, but it has the advantage that the equalizing 
 machine has only to deal with the loads in excess of the mean value for which 
 the regulator is set, and the cost is considerably reduced compared with the 
 former system. It also has the advantage that a failure of any part of the 
 equalizing equipment does not interfere with the operation of the hoist motor. 
 The application of this system is practically confined to cases where the rheo- 
 static control of the hoist motors offers no difficulties and where equalization 
 of input is all that is required. In the case of very large plants, however, the 
 
744 HOISTING 
 
 control question is of such importance that the Ilgner system is used almost 
 exclusively. 
 
 One important feature in connection with electric hoisting is the ease with 
 which safety devices can be arranged to prevent overwinding or overloading. 
 In connection with systems using either a motor-generator flywheel or the 
 Ilgner system of control, automatic devices have been arranged so that the 
 rate of acceleration is limited and the hoist is automatically retarded inde- 
 pendent of the operator, and as these devices are used every time the hoist 
 is operated they are necessarily kept in order. With such arrangements, over- 
 winding or starting up the hoist in the wrong direction is absolutely impossible, 
 and in view of these features the German mining authorities have allowed the 
 rate at which men may be hoisted to be increased from 1,200 ft. per min., which 
 is the maximum with steam-operated hoists with the best safety gears, to 
 2,000 ft. per min. with electric hoists, and the question has been under con- 
 sideration for some time of increasing this limit to 3,000 ft. per min. 
 
 BALANCED HOISTING 
 
 In hoisting through a double-compartment shaft and from a single level, 
 the weights of the ascending and descending cages and cars balance each other, 
 leaving unbalanced the weight of the load and that of the rope. The weight 
 of the load is uniform during the entire hoisting period, but that of the rope 
 is not. The entire weight of the rope must be raised at the beginning of the 
 hoist; at the middle of the hoist there is no rope weight to be considered, as 
 the two ropes (those attached to the ascending and descending cages, respec- 
 tively) are of the same length and, consequently, balance each other; and 
 at the end of the hoist, the weight of the rope is acting in favor of the load. 
 In fact, in extremely deep shafts, the weight of the rope attached to the de- 
 scending empty cage, may even exceed the weight of the load on the other cage 
 to such an extent as to tend to cause the engines to run away, necessitating 
 the shutting off of the steam and the application of the brakes in order to 
 prevent the loaded cage being carried into the head-sheaves. 
 
 In order to provide for the time necessary to load and unload the cages 
 at each end of the run, it is important to reach the full hoisting speed as soon 
 as possible. Further, as the maximum load must be raised at the outset, the 
 demand for power is much greater at the beginning of the hoist than at any 
 other time. Therefore, in order to provide > the power for getting up speed 
 under the maximum load (the two producing what is called a peak load), 
 hoisting engines must be made much larger than if the speed- of hoisting and 
 the load were uniform throughout the run. In hoisting from shallow shafts, 
 it is not customary to attempt to balance the load (that is, to make it uniform 
 throughout the hoisting period), the peak load being taken care of by pro- 
 portioning the size of the steam cylinders and drums, and without any very 
 serious increase in first cost or in operating expense. 
 
 Where the shaft is deep, the loads large, and the hoisting speed is necessarily 
 great in order to produce a large tonnage, some system of counterbalancing is 
 employed to render more uniform the demand for power upon the hoisting 
 engine. 
 
 As an illustration of unbalanced hoisting, assume that a load of 4,000 Ib. of 
 coal is to be hoisted in a double-compartment shaft 1,000 ft. deep by means 
 of a l|-in. crucible-steel rope weighing 3 Ib. per ft. (3,000 Ib. in all) which 
 winds upon a drum 7 ft. in diameter. It may be assumed, further, that the 
 car and empty cage weigh 3,000 Ib. each, and that friction is equal to 10% of 
 the load exclusive of that of the rope. The friction adds to the load to be 
 hoisted and decreases that to be lowered. 
 
 When the loaded cage is at the bottom of the shaft, the total weight to be 
 hoisted is that of the coal, the empty car and the cage, a total of 10,000 Ib. 
 To this must be added 10% for friction, or 1,000 Ib., and 3,000 Ib. for the 
 weight of the rope, or a grand total of 14,000 Ib. As the drum has a radius 
 of 3.5 ft., the total turning moment to be overcome by the engine is 14,000 
 X3.5 = 49,000 ft.-lb. But the engine is assisted by the weight of the empty 
 car and cage, or 6,000 Ib. From this must be deducted 10%, or 600 Ib. for 
 friction, leaving a net load of 5,400 Ib. assisting the engine, which is equivalent 
 to a C9unterbalancing moment of 5,400X3.5 = 18,900 ft.-lb. Hence, at the 
 beginning of the hoist the net load moment to be overcome by the engine is 
 49,000-18,900 = 30,100 ft.-lb. 
 
HOISTING 745 
 
 At the end of the hoist the weight on the loaded-cage side is lessened by 
 the weight of the rope, and is 11,000 Ib. This is equal to a total load moment 
 of 11.000X3.5 = 38,500 ft.-lb. On the empty side, the weight assisting the 
 engine is increased by the weight of the rope, 3,000 Ib., and is 8,400 Ib. This 
 is equal to a counterbalancing load moment of 8.400X3.5 = 29,400 ft.-lb. 
 Hence at the end of the hoist the net load moment to be overcome by the engine 
 is 38,500-29,400 = 9,100 ft.-lb. 
 
 Since the load moment upon the engine varies from 30,100 ft.-lb. at the 
 beginning of the run to 9,100 ft.-lb. at the end, in the assumed case the engines 
 must exert more than three times as much power at one time as at another. 
 Further, as the average load moment upon the engines is but 19,600 ft.-lb., and 
 the maximum load moment is 30,100 ft.-lb., but about 65% of their average 
 power is utilized. 
 
 Tail-Rope Balancing. Counterbalancing the weight of the hoisting ropes 
 may be accomplished by attaching to the bottom of one cage a rope of the 
 same size and weight as the hoisting rope, passing it under a pulley or sheave 
 wheel at the bottom of the shaft, and attaching the second end to the bottom 
 of the other cage. As the length of the balance rope is twice that of either 
 hoisting rope, the latter are exactly balanced. When this appliance is used, 
 the weight to be hoisted is uniform throughout the run and is equal to that of 
 the load and friction, because the cars and cages balance each other. Using 
 the foregoing illustration, the net load moment at starting is 30,100 ft.-lb. 
 From this must be deducted the load moment of the rope, which is 3,000X3.5 
 = 10,500 ft.-lb. Hence the net load moment, which is constant throughout 
 the run, is 30,100-10,500=19,600 ft.-lb. Hence, when the weight of the 
 hoisting ropes is counterbalanced, but about 65% of the power is required 
 to hoist as when the ropes are not balanced. 
 
 The use of the tail-rope gives its best results where hoisting is done from 
 one level only, and in deep hoisting it is impracticable because of the extra 
 weight which must be carried by the head-sheave axle and because of possible 
 excessive swaying of the rope. 
 
 Conical Drums. Conical drums are designed to make the work of the 
 engine throughout the hoist as nearly uniform as possible. To accomplish 
 this, when the cage is at the bottom of the shaft and the weight of the rope 
 is added to that of the cage and its load, the rope winds on that part of the 
 drum having the smallest diameter. As hoisting continues, the rope winds 
 on a gradually increasing diameter of drum, and when the cage is at the top 
 of the hoist and the load is only that due to the cage and the loaded car, the 
 rope is winding on that part of the drum having the greatest diameter; in this 
 way, the moment of the load at every point of the hoist remains approximately 
 the same. 
 
 The ratio of the larger radius R of a conical drum to the smaller radius r is 
 found as follows: 
 
 Let Wm = weight of material hoisted ; 
 
 We = weight of cage and car; 
 wr = weight of rope; 
 R = large radius of drum; 
 r = small radius of drum. 
 
 The moment of cage, car, load, and rope at the bottom of the shaft is 
 (wc+wt+wr)r. The moment of cage and car at the top of the shaft is w c R. 
 The net moment at beginning of hoist is (wc-\-Wm + Wr)r WcR. 
 
 When the loaded cage has arrived at the top and the other cage has reached 
 the bottom, the moment of cage, car, and load at the top is (w c -\-wm)R and the 
 moment of cage, car, and rope at the bottom is (w c -\- w r )r. The net moment 
 at end of hoist is (w c +wm)R (w c +Wr\r. 
 
 Finally, placing the moment at beginning of hoist equal to that at end of 
 hoist, and finding the value of the ratio of the two diameters which is equal 
 to that of the two radii, 
 
 ~ 2-U'c 
 
 EXAMPLE. Using the foregoing illustration, d = 7 ft.; w? = 4,000 Ib.; w c 
 = 3,000+3,000 = 6,000 Ib.; wr = 3,000 Ib.; it is required to find the larger 
 diameter of a conical drum for balanced hoisting. 
 
 SOLUTION. Substituting in the foregoing formula, 
 
 9 ft . 
 
746 
 
 HOISTING 
 
 From the equations representing the net load moment at the beginning of 
 hoisting, the net load moment upon the engines is (6,000+4,000+3,000) X 3.5 
 -6,000X4.8125 = 16,625 ft.-lb., which load moment is constant throughout 
 the hoist as when counterbalancing with the tail-rope is used, but with no 
 extra strain upon the head-sheave axle. 
 
 The use of the conical drum permits of the practical equalization of the 
 load on the engine during the entire hoisting period, and requires less power 
 in starting under load. 
 
 The disadvantages of the conical drum are as follows: To maintain a 
 certain average speed of hoisting, the speed toward the end of the hoist is of 
 necessity higher than the average and comes at a time when a slowing up 
 should be taking place, so that more care must be exercised when making the 
 landing. To prevent the rope from being drawn out of the grooves, the latter 
 must be made deep and with a large pitch, thereby increasing the width of the 
 face or length of the drum. In making a landing, when the rope is on the 
 conical face, the rope must be kept taut, as any slackness will permit the rope 
 to leave the groove, with the result that all the rope will pile up in the bottom 
 grooves of the drum allowing the cage to drop into the mine, unless it is resting 
 on the chairs. If there are several levels to be hoisted from, the equalizing 
 of the load on the engines can only be realized for one level; for all other levels 
 this advantage will be lost. For large depths, conical drums become very long 
 and require correspondingly long leads from head-frame to drum. To hold 
 
 the same amount of 
 rope, conical drums are 
 heavier than cylindrical 
 ones, and as a result, 
 the power required in 
 starting the load is 
 somewhat i n c r e a se d 
 owing to the greater 
 inertia of the rotating 
 parts. 
 
 Some of these disad- 
 vantages have been 
 overcome by making a 
 combination of cone 
 and cylindrical drums. 
 The drums are so des- 
 ignated that the land- 
 ing takes place only 
 when the rope is on the 
 cylindrical portion of 
 the drum. For deep 
 hoisting, the greater 
 diameter of the drum 
 and its length must be inconveniently large if the load is equalized. The 
 length and diameter" can be reduced by making one-half of the drum cylin- 
 drical and by having the rope from each end wind on the same cylindrical 
 portion of the drum. In all cases however, these modifications are made at 
 the expense of the equalization of the load on the engines, and it is not pos- 
 sible to obtain the latter without including some serious disadvantage. 
 
 There are certain objections to both cylindrical and conical drums: their 
 great size and weight, for large hoists, make them very expensive; their width 
 necessitates placing the engines far apart, which adds to the cost of the engines, 
 foundations, and buildings; the great weight of the drums is also objectionable, 
 because it forms a large part of the mass to be put in motion and brought to 
 rest at each hoist. 
 
 Flat Ropes and Reels. To overcome the objections to conical and cylin- 
 drical drums, _ flat ropes wound on reels, Fig. 1, may be used. In this case 
 the hub a is increased in diameter, above what 'is necessary for strength, to 
 such a size as is suitable to wind the rope on. It is then cored out from the 
 inside, so as not to contain too great a mass of metal. 
 
 The arms b of the reel extend radially from the hub to confine the rope 
 laterally when it is all wound on the drum. These arms are connected at their 
 outer ends by a continuous flange c, which is flared out, as shown at d, so as 
 to take in the rope easily, if it is deflected at all sidewise. 
 
 f In the larger-sized reels, the arms are bolted to the hub, and often the outer 
 rim connecting the arms is omitted. Hardwood lining was formerly used on 
 
 FIG. 1 
 
HOISTING 747 
 
 the arms under the impression that the wear on the rope would be less than with 
 bare iron arms, but sand and grit become embedded in the wood and grind 
 the rope. Polished iron arms with rounded corners and lubricated with oil or 
 tar are best. The end of the rope is fastened in a pocket e provided for it in 
 the hub. 
 
 The rope winds on itself so that the diameter of the reel increases as the 
 hoist is made and as the load due to the weight of the rope decreases. This 
 serves to equalize the load due to the rope in the same manner as the conical 
 drum. Two reels are generally put on the same shaft, and while one is hoist- 
 ing from one compartment of the shaft the other is lowering into another 
 compartment. The periphery of the hub where the rope winds should not be 
 round but of gradually increasing radius, for if a flat rope is wrapped about a 
 round hub the rope will have to abruptly mount itself at the end of the first 
 revolution and so on for every revolution. The radius of the hub should 
 increase at such a rate as to raise the rope an amount equal to its thickness 
 in the first wrap, so that it will wind on itself without jar at the point of 
 attachment, as well as on succeeding wraps. 
 
 In America, it is customary to wind on reels of small diameter, that is, 
 starting at 3 or 5 ft. and increasing to 8 or 12 ft.; but several large plants have 
 been built with reels starting at 8 ft. and increasing to 19 ft. In England, reels 
 have been made starting at 16 ft. and increasing to 20 or 22 ft. Such large 
 reels are easier on the rope but require large engines, as hoisting in balance is 
 used to only a slight extent. The large reel is easy on the rope, both from the 
 fact that it bends the rope but little and also gives less pressure on the bottom 
 wraps, as each wrap adds to the pressure. These reels are driven by means of 
 plain jaw or friction clutches. 
 
 The wear of a flat rope is excessive and the rope itself costs more than a 
 round rope of the same strength, does not last as long, and requires more care 
 and attention. 
 
 When calculating the dimensions of a reel for flat rope, the determination 
 of the size of the rope and of the large and small diameters of the reel must 
 proceed together. The smaller diameter d is that of the hub of the reel, and 
 the larger diameter D is that of the last coil of rope after the reel is full. The 
 large diameter D determines the length of the arms, b, Fig. 1. 
 
 EXAMPLE. Using a factor of safety of 9, what size of flat rope will be 
 required to hoist 5,000 Ib. of material in a skip weighing 3,000 Ib. through a 
 two-compartment shaft 2,000 ft. deep; and what will be the dimensions of 
 the reel? 
 
 SOLUTION. The load to be hoisted, allowing 10% for friction, is 8,800 Ib. 
 Assuming a 6"X*" rope with a breaking strength of 150,000 Ib., this will 
 weigh 5.1 Ib. per ft., or 10.200 Ib. for 2,000 ft. The total load will be 8,800 
 + 10,200=19,000 Ib. The factor of safety will be 150,000-7-19,000 = 7.8, 
 which is too low under the assumed conditions. 
 
 The breaking strength of an 8"X 3" rope is 200,000 Ib. This weighs 6.9 Ib. 
 per ft., or 13,800 Ib. for the entire rope. With this larger rope, the total load 
 will be 8,800+13,800 = 22,600 Ib., and the factor of safety will be 200,000 
 -T- 22,600 = 8.8, which is close enough for all practical purposes. Using the 
 formula given under the heading Conical Drums, 
 
 n . V 2X (3.000 + 13.800) +5.000 
 
 D = dX 2X3.000+5,000 = 3 ' 5d 
 
 that is, the diameter when the last coil is wound on the reel must be 3.5 times 
 that of the hub. 
 
 The area of the hub about which the rope is to coil is }W 2 , and the area 
 included in the outer coil of rope is iir> 2 ; hence, the area of the annular space 
 occupied by the rope is 
 
 l*>2-i7rd2=i7r(Z)2-d2) 
 
 Such values for D and d must be chosen that the equation of moments, D = 3.5d, 
 is satisfied, while the area of the annular space, iir(D 2 d 2 ), must correspond 
 to the space occupied by the given rope when coiled. In the assumed case 
 
 2 ooo X 12 
 
 2,000 ft. of rope \ in. thick requires ^^^ 12 ' 000 sq- in> m which to be 
 coiled. To satisfy the equation of moments, D must equal 3.5d; hence, to 
 satisfy both these conditions iir[(3.5rf) 2 -d 2 ] = 12,000; whence d = 37 in., or 
 3 ft. 1 in.; and Z? = 37X3.5 = 129.5 in., or 10 ft. 9i in. 
 
 The dimensions of the reel will then be: diameter of hub 3 ft. 1 in.; width 
 between flanges, 8| in., allowing i in. on each side of the rope for clearance; 
 diameter of the flanges where they flare, 10 ft. 9 j in. 
 
748 
 
 HOISTING 
 
 Koepe System. In its lightest form, a drum requires a large amount of 
 power to set it in motion, which power is absorbed by the brake and lost when 
 it is brought to rest again. Furthermore, with deep shafts requiring long 
 drums, the fleet, or angle that the rope makes with the head-sheave due to its 
 traveling from one end of the drum to the other, is not only a disadvantage 
 and possible cause of accident, but it is a source of wear. To overcome these 
 objections and also the great cost of large cylindrical or conical drums, the 
 Koepe system of hoisting, shown in Fig. 2, was devised by Mr. Frederick 
 Koepe. A single-grooved driving sheave a is used in place of a drum. The 
 winding rope b passes from one cage A up over a head-sheave, thence around the 
 sheave a and back over another head-sheave, and down to a second cage B; 
 it encircles a little over half the periphery of the driving sheave and is driven 
 by the friction between the sheave and rope. A balance rope c beneath the 
 cages and passing around the sheave d gives an endless-rope arrangement 
 with the cages fixed at the proper points. The driving sheave is stronger than 
 an ordinary carrying sheave, as it has to do the driving, and is usually lined 
 
 with hardwood, which 
 is grooved to receive the 
 winding rope, the depth 
 of the groove being gen- 
 erally equal to twice 
 the diameter of the 
 rope. Instead of being 
 placed parallel, the 
 head-sheaves are placed 
 at an angle with each 
 other, each pointing to 
 the groove in the driv- 
 ing sheave, thus reduc- 
 ing the side friction of 
 the rope on the sheaves. 
 The system has 
 been in successful oper- 
 ation since 1877, and 
 experiments made on it 
 have determined that, 
 with a rope passing only 
 one-half turn around 
 the drum sheave, the 
 coefficient of adhesion 
 with clean ropes is about 
 .3. If the ropes are 
 oiled, the adhesion be- 
 comes less, and some- 
 times slippage occurs, 
 producing not only wear 
 of the driving-sheave 
 lining but giving an in- 
 correct reading of the 
 hoist indicator and thus 
 possibly producing 
 overwinding, unless the 
 
 FIG. 2 
 
 position of the cage is indicated by marks on the rope, or unless the engineer 
 can see the cage. 
 
 At the end of the hoist, if the upper cage is allowed to rest on the keep, its 
 weight and the weight of the tail-rope are taken from the hoisting rope, and 
 there is then not enough pull on the hoisting rope to produce sufficient friction 
 with the drum sheave to start the next hoist. To prevent this trouble, the 
 keeps are dispensed with, or the rope is made continuous and independent of 
 the cage. To do this, crossheads are placed above and below each cage and 
 connected by ropes or chains outside of the cages. The bridle chains are then 
 hung from the top crosshead, and when the cage rests on the keeps, the weight 
 of the winding and tail-ropes remains on the driving sheaves. 
 
 With this system, only one driving sheave is necessary for the operation of 
 two compartments, and it is light, inexpensive to build, and very narrow, 
 admitting of a short sheave shaft and small foundations. This system permits 
 a perfect balance of rope and cage, so that the work to be done by the engine is 
 uniform, except for the acceleration, and consists only in lifting the material 
 
HOISTING 
 
 749 
 
 and overcoming the friction. There is no fleeting of the rope between the 
 driving sheaves and the head-sheaves. 
 
 The system has the following disadvantages, which prevent its being used 
 to any considerable extent: Liability to slippage of the rope on the drum; if 
 the rope breaks, both cages may fall to the bottom; hoisting from different levels 
 cannot be well done, for, since the cages are at fixed distances from each other, 
 the length of the rope is such that when one cage A is at the top, the other 
 cage B is at the bottom. If hoisting is to be done from the bottom, this 
 is satisfactory, but if hoisting is to be done from some upper level, cage B, 
 which is at the bottom, must be hoisted to that level to be loaded before it 
 can go to the top. Then, when cage B goes to the top with its load, cage A 
 must go to the bottom, wait there while cage B is being unloaded, and then 
 be hoisted to the upper level to receive its load. For each trip, therefore, the 
 time required for a cage to go from the bottom to the upper level and be 
 loaded is lost; and two movements of the engines are necessary for a hoist 
 instead of one. 
 
 Whiting System. In the Whiting system, two rope wheels placed tandem 
 are used in place of cylindrical or conical drums. As shown in Fig. 3, for a 
 two-compartment shaft the rope passes from one cage a up over a head-sheave c, 
 
 QIJ 
 
 FIG. 3 
 
 down under a guide sheave d, and is then wound 
 three times about the rope wheels e and /, to secure 
 a good hold, then around a fleet sheave g, and back 
 under another guide sheave h, up over another 
 head-sheave *", and down to the other cage b. 
 When the system is to be used for a single-com- 
 partment shaft, one end of the rope carries^ the 
 cage and the other end carries a balance weight, 
 which is run up and down in a corner of the shaft. 
 A balance rope below the cages, as shown, is gener- 
 ally used, though it is not as ^essential to the work- 
 ing of the system, as it is in the Koepe system. 
 When sinking a shaft, a balance rope cannot be 
 used as it interferes with the work at the bottom of the shaft. 
 
 The drums or wheels e and / are light, inexpensive, and narrow, thus per- 
 mitting short sheave shafts and small foundations. They are lined with 
 hardwood blocks, each lining having three rope grooves turned in it. The 
 main wheel e is driven by a hoisting engine, which may be either first- or second- 
 motion. The following wheel / is coupled to the main wheel by a pair of parallel 
 rods, one on each side, like the drivers of a locomotive. As the rope wraps 
 about the wheels e and / three times, there are six semi-circumferences of 
 driving contact with the rope, as compared with the one semi-circumference 
 in the Koepe system, and there is no slipping of the rope on the wheels. The 
 following wheel / is best tilted or inclined from the vertical an amount equal, 
 in the diameter of the wheels, to the pitch of the rope on the wheel, so that 
 the rope may not run out of its groove and may run straight from one wheel 
 to the other without any chafing between the ropes and the sides of the grooves. 
 
 The capacity of the wheels e and / is unlimited, while grooved cylindrical 
 drums, conical drums, and reels will hold only the fixed length of rope for 
 which they are designed. 
 
 As shown by the dotted lines, the fleet sheave g is arranged to travel back- 
 wards and forwards, in order to change the working length of the rope from 
 time to time to provide for an increased depth of shaft, and for changes in the 
 length of rope due to stretching and when the ends are cut off to resocket the 
 
750 HOISTING 
 
 rope. The fleet sheave g is moved a distance equal to one-half the change in 
 the length of rope. 
 
 Hoisting from intermediate levels can be readily done with the Whiting 
 system; for instance, if the cage a is at the top and cage b at the bottom, and 
 hoisting is to be done from some upper level, it is only necessary to run the 
 fleet sheave g out, and thus shorten the working length of the rope until cage b 
 comes up to the upper level. It can then be loaded and go to the top. While 
 cage b goes to the top, cage a descends to the same level, where it can be loaded 
 while cage b is being unloaded, and can then go directly to the top without any 
 lost time, as is the case in the Koepe system. 
 
 The system permits a perfect balance of rope and cage, so that the work to 
 be done by the engines is uniform, except for the acceleration, and consists 
 only in lifting the material and overcoming the friction. 
 
 There is no fleeting of the rope, so the rope wheels can be placed as close 
 to the shaft as may be desired. 
 
 This system was tried as early as 1862 in Eastern Pennsylvania, but it was 
 not used extensively because hoisting from great depths was not necessary, 
 since, for depths of less than 1,000 ft., cylindrical and conical drums are quite 
 satisfactory. Two of the Whiting hoists in the Lake Superior copper region 
 are among the largest hoisting plants in the world. Each of these consists of 
 a pair of triple-expansion, vertical, inverted-beam engines, driving direct a 
 pair of 19-ft. drums. The high-pressure cylinders are 20 in. in diameter, the 
 intermediate cylinders 32 in., and the low-pressure cylinders 50 in., and all six 
 of them have a 72-in. stroke. The rope used is a 2i-in. plow-steel rope and 
 hoists 10 T. of material at a trip, in one case from a depth of 4,980 ft. 
 
 Modified Whiting System. A modification of the Whiting system is 
 sometimes used in which a large drum keyed to the crank-shaft replaces the 
 small tandem drums, and even the slight probability of the rope slipping in 
 the Whiting system is thus obviated. One rope is 
 fastened to one end of the drum, and the other rope 
 to the other end in such a way that while one is wind- 
 ing on the other will be winding off the drum. One 
 rope passes directly to the head-sheave while the other 
 passes first around a fleet sheave, similar to that used 
 for the Whiting system, but preferably placed hori- 
 zontal, and thence to the head-sheave. This system 
 possesses the same advantages as the Whiting system 
 except that the depth of hoist is limited by the size 
 of the drum, and that there is a fleet of the rope. Up 
 to the limiting depth, as determined by the size of the 
 drum, this system can be used with equal economy for 
 any depth. This hoist, as well as the Whiting, is 
 therefore especially suitable for a place where one 
 F , mining company operates several mines, for it enables 
 
 the company to select one size for all their permanent 
 work, with all the advantages that come from duplicate machinery. 
 
 Despritz System. The general arrangement of the Despritz system is 
 shown in Fig. 4. A drum with a radius T is keyed to the same shaft as the 
 rope drum with a radius jR, and carries a small rope to which is attached a 
 chain whose length 2V is one-half of the distance between landings H . 
 
 The small rope is so wound on to its drum that at the commencement of 
 the hoist the chain is suspended at full length in a small compartment specially 
 provided. Immediately the hoisting commences, the small rope starts to 
 unreel, piling up the chain at the bottom of its compartment until the_ cages 
 reach their point of passing midway of the shaft, at which instant the hoisting- 
 rope loads balance, the piling up of the entire chain length is complete, and its 
 load moment on the main shaft is zero. At this instant, also, the small rope, 
 carrying the chain, has all unreeled from its drum and its point of _ fastening 
 is about to pass around underneath and take the rope into the position shown 
 by the dotted line. 
 
 Hence, as soon as the cages have passed each other the chain rope begins 
 to reel up again, extending the chain upwards until, at the termination of the 
 hoist, it again hangs at full length, giving a load moment of opposite sign 
 to that which it had at starting of the hoist. That is, during the first half 
 of the hoisting period the load moment of the chain on the drum shaft is plus, 
 while during the second half of the period it is minus. 
 If W= weight of hoisting rope per foot; 
 
 w = weight of chain per foot; 
 
HOISTING 
 
 751 
 
 l? = radius of rope drum, in feet; 
 T = radius of chain drum, in feet; 
 
 Monopol System. The system outlined in Fig. 5 is known as the Monopol. 
 An auxiliary drum of diameter equal to the winding drums, is keyed to the 
 main shaft and is of sufficient width to carry 
 two relatively small ropes, one of which is un- 
 derwound and the other overwound. 
 
 These ropes support a length of heavier 
 balancing rope in the position shown; this 
 balancing rope is usually a length of old hoist- 
 ing rope of the size used in the hoisting oper- 
 ations and which has been discarded on account 
 of wear. A glance at the diagram makes it 
 evident that if this balancing rope is adjusted 
 at the outset, so that each of its ends is in 
 position opposite one of the cages, as shown, 
 they will so remain whatever the position the 
 cages take during a hoisting period, and the 
 load moment on the drum shaft, so far as the 
 hoisting ropes are concerned, will be equalized 
 throughout. As in the former case, the weight 
 of the small rope can be neglected. 
 
 In practice either of the foregoing systems 
 requires that a small compartment be provided 
 for the accommodation of the balancing device. 
 This is usually partitioned off from one end of 
 
 i 
 
 FIG. 5 
 
 the pump compartment of the main shaft at a nominal expense. As for the 
 rest of the arrangements, almost any mechanic at the mines will find little 
 trouble in providing whatever may be required for the installation. 
 
 CALCULATIONS FOR FIRST-MOTION HOISTING 
 ENGINES 
 
 General Considerations. Owing to the fact that many of the resistances 
 that have to be overcome can only be estimated approximately, the determi- 
 nation of the horsepower required to hoist, as well as the dimensions of the 
 engines required for that purpose, cannot be made exactly. The usual pro- 
 cedure is to calculate an average or minimum horsepower by means of some 
 simple formula and then to add to this an amount that experience has indicated 
 to be necessary to provide for uncertainties both in resistances to be overcome 
 and in the future demands for power. The horsepower having been obtained, 
 the actual design of the engines should be left to a skilled mechanical engineer; 
 in fact, the entire matter, even including the calculation of the horsepower, is 
 more properly the work of the engine builder than the mine superintendent. 
 
 The methods involved in the solution of hoisting-engine problems are best 
 explained by the working out of the following example. 
 
 EXAMPLE. What should be the horsepower and dimensions of a first- 
 motion engine to hoist 1,500 T. of coal per da. of 8 hr. from a shaft 1,000 ft. 
 between landings under the following conditions: One-half hour is allowed 
 for delays of various kinds, 7 sec. for caging each trip, and 5 sec. each for 
 acceleration and retardation; the car holds 5,000 lb. of coal and weighs 2,500 lb.; 
 the cages weigh 4,000 lb. each; the drum is cylindrical, 8 ft. in diameter and 
 8 ft. wide; the head-sheaves are 8 ft. in diameter; the mean effective pressure of 
 the steam in the cylinder is 100 lb. per sq. in., the plant. has an efficiency 
 of .85% ; and the resistance of friction is taken to be the same as that required 
 to move a weight equal to 5% of the total load? 
 
 SOLUTION. 1. Hoisting Period. The operation of hoisting through a 
 shaft may be divided into three periods. First, a period of acceleration, during 
 which the load, rope drum, sheaves, moving parts of the engine, etc., are 
 brought from rest to full speed. Second, a full- or constant-speed period 
 during which the load is hoisted at the uniform velocity attained at the end 
 of the period of acceleration. Third, a period of retardation, during which 
 the load and moving parts are brought from full speed to rest. 
 
752 HOISTING 
 
 In practice, the time required for acceleration is variously estimated as 
 being equal to one-seventh of the net time of hoisting, as from 3 to 7 sec. 
 depending on the depth of the shaft and speed of hoisting, as the time required 
 for the drum to make, say, three revolutions, as the time required to hoist 
 the cage 50 or 150 ft. starting from rest, etc. The period of retardation is 
 usually taken to be equal in time to that of acceleration, although it may be a 
 little shorter. The full-speed period is the longest of the three, and consumes 
 about three-fourths of the net time of hoisting. 
 
 Because, in addition to raising the load, it as well as the drum, sheaves, and 
 moving parts of the machinery must be accelerated or brought up to full speed 
 from rest, the power required to hoist is very much greater during the period 
 of acceleration than at any later time; and hoisting engines should be designed 
 with this fact in view. 
 
 2. Net Time of Hoisting. The gross time actually devoted to hoisting 
 is 8- = 7.5hr. The weight of coal hoisted per hour = 1, 500 -J- 7.5 = 200 T. 
 As 5,000 Ib. = 2.5 T., the number of hoists per hour is 200^-2.5 = 80. As there 
 are 3,600 sec. in 1 hr., the gross time of hoisting per trip is 3,600-7-80 = 45 sec. 
 As 7 sec. is allowed for caging, the net time of hoisting is 45 7 = 38 sec. 
 
 3. Speed of Hoisting. Assuming that the acceleration, that is, the increase 
 in velocity of the cage, is uniform, the speed attained at the end of the period 
 of acceleration may be found from the formula, 
 
 H 1,000 . . , 
 
 in which = full speed of hoisting, in feet per second; 
 
 tf = distance between landings, in feet = 1,000; 
 / = net time of hoisting, in seconds = 38; 
 
 / = time of acceleration, in seconds = 5. 
 As the cage starts from rest and attains a velocity of 30.3 ft. per sec. at the 
 
 end of 5 sec., the space traversed during acceleration is -X/ = 75.75 ft., because 
 
 the average velocity is one-half the final. > 
 
 The acceleration, a is found from the formula a = v-r-t = 30.3-7-5 = 6.06 ft. 
 per sec. per sec. The space passed over during acceleration is not the same 
 for each of the 5 sec. In the first second, the cage is raised a distance of 
 but $a, or 3.03 ft.; during the second second, it is raised ia + o = 9.09 ft.; and 
 during each succeeding second it is raised a distance a = 6.06 ft. more. The 
 distances passed over in the single seconds making up the period of acceleration, 
 are, respectively, 3.03, 9.09, 15.15, 21.21, and 27.27 ft., the sum of which is 
 75.75 ft. as determined before. 
 
 The velocity attained at the end of any particular second is found from the 
 formula v = aL Thus, at the end of the fourth second, the velocity of the cage 
 is 6.06X4 = 24.24 ft. per sec.; that is, if the accelerating force ceased to act 
 at the end of the fourth second, the cage would enter the fifth second with 
 sufficient velocity to carry it 24.24 ft. But during the fifth second, the acceler- 
 ative force still acts, and adds $a or 3.03 ft. to the distance traveled. Similarly, 
 at the end of the fifth second, the cage, after traveling 27.27 ft. begins the sixth 
 second with a velocity sufficient to carry it 27.27 -fa = 30.3 ft. during that 
 second without further acceleration. 
 
 4. Revolutions of Drum per Minute. If D is the diameter of the rope 
 drum, in feet, the number of revolutions per minute made by it during the full- 
 speed period may be found from the formula, 
 
 30.3X60 1,818 . 
 rev. per .i.-..vm say, 72.5 
 
 The total number of revolutions made by the drum during acceleration or 
 retardation is 75.75-5-25.13 = 3, very nearly. The number of revolutions, 
 or fractions of a revolution, made by the drum during the individual seconds 
 of the acceleration period is found by dividing the distance passed over in any 
 second by the circumference of the drum. In the problem, the approximate 
 number of revolutions in each of the 5 sec. will be, respectively, |, $, f, I, 1&. 
 
 5. Friction in Hoisting. In well-designed and well-built first-motion 
 hoisting engines, the resistance due to friction should not exceed that due to 
 raising a weight equal to 5% of the total load including the weight of the 
 ropes, but in second-motion or geared hoists this resistance may amount to 
 7.5 to 10%. 
 
 The method of allowing for the effects of friction varies. By some, the 
 friction is added to the load and treated as part of it; by others, the area of the 
 steam cylinders is calculated on the basis of there being no friction and from 
 
HOISTING 753 
 
 10 to 15% added to this area as an allowance for friction, Probably the first 
 method is the more generally used. 
 
 In the problem, the total load to be moved is equal to the weight of the 
 (coal+2 cages+2 cars+2 ropes) = (5,000+8,000+5,000+4,000) =22.000 Ib. 
 At 5%, the resistance of friction is equivalent to raising a weight of 1,100 Ib. 
 
 6. Size of Hoisting Rope. The load on the rope is a maximum during the 
 first period of hoisting because, in addition to raising the load and overcoming 
 friction, there is a further resistance due to acceleration. 
 
 Assuming that the rope weighs 2 Ib. per ft., when the cage is at rest just 
 clear of the bottom, the load on the rope is equal to the weight of the (coal 
 + cage + car + rope) = (5,000+4,000+2,500+2,000 = 13,500 Ib.) As soon as 
 motion begins, the frictional resistance must be added, and the total load upon 
 the rope is 13.500X. 05+ 13,500 = 14,175 Ib. 
 
 If the acceleration of gravity g is taken as 32.2 ft. per sec. per sec., the 
 stress P on the hoisting rope during acceleration due fo raising the weight W 
 (load and friction) is 
 
 p=TF+ Xa = 14,175+^|-X6.06== 14,175+2,667 = 16,842 Ib. 
 
 The factor of safety commonly used in American practice in calculating 
 the strength of hoisting ropes is 5; hence, to sustain a load of 16,842 Ib., the 
 ultimate strength of the rope must be 84,210 Ib. The manufacturers' tables 
 show that the ultimate strength (breaking strength) of a li-in. extra cast-steel 
 rope weighing 2 Ib. per ft. is 86,000 Ib.; hence, it would be selected. 
 
 In choosing a rope of this size, no allowance is made for the strain due to 
 bending around the drum and sheaves, .which, if the same as the load on the 
 rope, is 13,500 Ib. The total strain on the rope during acceleration is, then, 
 16,842 + 13,500 = 30,342 Ib., and the true factor of safety is 86,000 -=-30,342 
 = 2.83. Although this seems a small margin of strength for live loads, Amer- 
 ican practice seems to warrant it. 
 
 7. Size of Drum. The manufacturers' tables indicate a minimum diameter 
 of 5 ft. for the drum and sheaves to be used with a l|-in. rope. While a drum 
 of this size might be used on contractors' hoists, a mine hoisting engine would 
 have drums 8 ft. or more in diameter. The greater the diameter of the drum, 
 the less will be its width for the same depth of hoist, the shorter will be the 
 drum shaft, and the less the strain upon it. Also, the greater the diameter of 
 the drum, the fewer will be the revolutions necessary to move the cage a given 
 distance and the less will be the piston speed of the engine. Further, large 
 drums reduce the bending strain on the rope and thus conduce to a longer 
 life. On the other hand, during acceleration, the power required to overcome 
 the inertia of the drum increases very rapidly with the increase in its diameter. 
 
 8. Ordinary Method of Calculating Power Required to Hoist. The usual 
 method of calculating the horsepower required to hoist is to multiply the 
 unbalanced load, in pounds, by the speed of hoisting, in feet per second, and 
 divide the product by 550. The unbalanced load is, in any case, taken as the 
 weight of coal and one rope, or, in the problem, as 7,000 Ib. To the unbalanced 
 load is added the friction, which is variously estimated as 5 or 10% of the total 
 weight being moved. Assuming the former figure, the resistance due to fric- 
 tion is 22.000X. 05= 1,100 Ib., making the total load 8,100 Ib. The speed of 
 hoisting should be taken at 30.3 ft. per sec. (1,818 ft. per min.), which allows 
 for the time lost in acceleration and retardation. With these data, the horse- 
 power is (8, 100X30.3) -T- 550 = 446.2. 
 
 Sometimes in calculating the speed of hoisting, the depth of the shaft is 
 divided by the total time of hoisting, which gives a speed of 1,000 -=-38 = 26.3 ft. 
 per sec. With this incorrect speed, the horsepower obtained is too low and 
 is (8,100X26.3)^550 = 387.3. 
 
 The horsepower, as thus obtained, is often divided by a factor representing 
 the assumed efficiency of the plant, and sometimes is further increased by an 
 arbitrary amount as an allowance for so-called contingencies. As will be 
 shown in paragraph 12, the horsepower determined by this method, no allow- 
 ance having been made for acceleration, is about one-half that really required 
 to hoist. 
 
 9. Piston Speed and Length of Stroke. The piston speed of hoisting engines 
 varies from 300 to 500 ft. per min., a commonly accepted value being 500 ft. 
 Because the engine makes two strokes for each revolution of the drum, if the 
 piston speed is called S, the length of stroke I may be found from 
 
 48 
 
754 HOISTING 
 
 In the foregoing, S is taken as 500 ft. per min., and the revolutions per 
 minute as determined in paragraph 4. 
 
 10. Dimensions of Engine to Produce a Given Horsepower. After the 
 power necessary to hoist and the piston speed have been determined, the total 
 area of cylinder necessary to yield the calculated horsepower at the mean effec- 
 
 Because there are two cylinders, each should have an area of 294. 492 -f- 2 
 = 147.246 sq. in. The diameter d of each cylinder will be d=> \/ z^- 
 
 if /oO4 
 
 = 13.7, say, 14 in. As the length of stroke is 42 in., the use of a 14"X 42" engine 
 is indicated. 
 
 By this method of calculation, no allowance is made for the power necessary 
 to accelerate the load and machinery, which frequently amounts to as much as 
 that required to raise the load. It is usually assumed that if one cylinder 
 will develop sufficient power to start the load, the power from two cylinders 
 will be great enough to accelerate it. This will commonly prove to be the case, 
 even if no allowance is made for the efficiency of the plant; although, to provide 
 for contingencies, it is advisable to make such an allowance. Thus, if a single 
 cylinder must be of a size sufficient to raise the entire load, it must have an area 
 of 294.492 or of 294.492-i- .85 = 346.46 sq. in., depending on whether the plant 
 is assumed to have an efficiency of 100% or of 85%. In the first case, d = 19.4, 
 say, 20 in., and in the second case d = 21 in. From this, the dimensions of the 
 engine will be 20 in.X42 in. or 21 in.X42 in., depending on the efficiency 
 assumed for the plant. These dimensions are very nearly those obtained by 
 the use of more accurate methods. 
 
 11. Resistance and Force in Hoisting. The resistance that must be overcome 
 in hoisting arises in part from raising the load and overcoming friction, and in 
 part from accelerating the load and machinery, particularly the drum and sheaves . 
 
 The friction is constant throughout the run and may be considered as a 
 portion of the load, or it may be included in an allowance made to cover the 
 various uncertainties entering into all calculations of this nature. If con- 
 sidered as a portion of the load, it may be estimated as 22.000X. 05= 1,100 Ib. 
 
 The unbalanced load is the weight of the coal and the hoisting rope. The 
 weight of the coal is constant throughout the run, but that of the rope decreases 
 as the loaded cage ascends. When the cages pass in the shaft, the ropes 
 attached to them are of equal length and their weights balance. Beyond the 
 passing point, the length and weight of the rope attached to the empty cage 
 becomes greater than that attached to the loaded cage and acts in favor of the 
 engine. Hence, because the weights of the rope wound off and wound on the 
 drum are equal, the unbalanced load at any instant is less than the original 
 load by twice the weight of the rope wound on the drum. For convenience in 
 calculation, the friction may be considered as part of the unbalanced load. 
 At the beginning of hoisting, the unbalanced load including friction, is 5,000 
 +2,000+1,100 = 8,100 Ib. At the end of the acceleration period when 75.75 ft. 
 of rope, weighing 2 Ib. per ft., has been wound upon and unwound from the 
 drum, the original load is reduced by 2X2X75.75 = 303 Ib., and is 7,797 Ib. 
 At the end of the full-speed period, 924.25 ft. of rope will have been wound 
 on the drum, and the load will be reduced by 2X2X924.25 = 3,697 Ib., and 
 will be 4,403 Ib. At the end of the period of retardation when the cage 
 comes to rest at the landing, all the rope will have been wound on the drum, 
 and the original load will be reduced by 2X2X1,000 = 4,000 Ib., and will be 
 4,100 Ib. These loads, all having a positive sign, are entered in the first 
 column of the following table. 
 
 The force, in pounds, required to accelerate the load is X a, in which W 
 
 is the total weight, or 22,000 Ib., placed in motion; a is the linear acceleration 
 
 22 000 
 or 6.06 ft. per sec. per sec.; and g is 32.2. The acceleration is then - ' 
 
 O.4.4 
 
 X 6.06 = 4,140 Ib. The retardation is equal to the acceleration, but has a nega- 
 tive sign ; this force is entered in the second column of the table with its proper 
 sign. The acceleration ceases as soon as the cage is moving at full speed. 
 The drum may be taken to weigh 25,760 Ib., and the force required to 
 
 accelerate it is 2 ~^X 6.06 = 4,848 Ib. 
 
HOISTING 
 
 755 
 
 The sheaves may be taken to weigh 805 Ib. each, and the force required to 
 
 OQC 
 
 accelerate them is 2X^^X6.06 = 303 Ib. 
 o2* 
 
 The total force required to accelerate the drum and sheaves is, thence, 
 4,848 + 303 = 5,151 Ib., and is the same in amount but negative in sign during 
 retardation. The algebraic sum of all the forces necessary to hoist and acceler- 
 ate are given in the fourth column of the table. A negative force indicates 
 that the resistance opposing it is acting to turn the drum and raise the load; 
 hence, the brakes must be applied to prevent the engine running away. 
 
 FORCES AND MOMENTS IN HOISTING 
 
 Period 
 
 Raising 
 Load 
 and 
 Friction 
 
 . Accelerating 
 
 Total 
 Force or 
 Resistance 
 
 Total 
 
 Moment 
 
 Load 
 
 Drum 
 and 
 Sheaves 
 
 Beginning acceleration . . 
 End acceleration 
 
 + 8,100 
 7,797 
 7,797 
 4,403 
 4,403 
 4,100 
 
 +4,140 
 4,140 
 
 -4,140 
 4,140 
 
 +5,151 
 5,151 
 
 -5,151 
 5,151 
 
 + 17,391 
 17,088 
 7,797 
 4,403 
 - 4,888 
 5,191 
 
 +69,564 
 68,352 
 31,188 
 17,612 
 -19,552 
 20,764 
 
 Beginning full speed 
 End full speed 
 
 Beginning retardation. . . 
 End retardation. . 
 
 
 12. Load Moments in Hoisting. The calculation of the area of the steam 
 cylinder of a hoisting engine is based on the principle that the force resisting 
 motion (or the resistance) multiplied by its lever arm, or'the distance through 
 which it acts, must equal the force producing motion multiplied by its lever 
 arm; the forces being expressed in pounds and the lever arms (or distances) 
 in feet. 
 
 The forces resisting motion at any instant are entered in the fourth column 
 of the table. Each has the same lever arm, which is the radius R of the drum, 
 or 4 ft. When the forces are multiplied by this lever arm, they give the total 
 moments, or load moments, in foot-pounds, which are given in the fifth column. 
 
 If the weights of the drum and sheaves are not known, the moments of the 
 force required to accelerate them may be calculated by formulas suggested by 
 Mr. Wilfred Sykes in the Transactions of the American Institute of Electrical 
 Engineers. The formula for the drum is Id = 100 R*X width, and for sheaves Is 
 = 25R 2 . The inertia Id or Is, when multiplied by the angular acceleration A a 
 of the drum and sheaves, gives the turning moment, which is the same as the 
 load moment. Thus, in the present problem, as R = 4 ft. and the width of the 
 drum is 8 ft., the inertia Id = 100X4 2 X8 = 12,800 Ib. As there are two sheaves, 
 their inertia will be 7j = 2X25X4 2 = 800 Ib. The inertia of the drum and 
 sheaves taken together is, therefore, 13,600 Ib. The angular acceleration is 
 equal to the linear acceleration a-i-radius of drum = 6.06^-4 = 1.515 radii per 
 sec. per sec. From this, the turning moment or load moment of the drum is 
 13,600X1.515 = 20,604 ft.-lb. 
 
 Suppose that it is desired to calculate the total moment at the end of 
 acceleration. The moment of the load is 7.797X4 = 31,188 ft.-lb., and that 
 of the force required to accelerate the load is 4,140X4 = 16,560. The sum of 
 these three moments is 20,604+31,188 + 16,560 = 68,532 ft.-lb., which corre- 
 sponds to the value in the last column of the table and which was determined 
 from the weights of the drum and sheaves. 
 
 If, as shown in the accompanying figure, a base line OO is divided to 
 correspond with the length, in seconds of time, of the various hoisting periods 
 there may be laid off above it the positive moments and below it the negative 
 ones. If the points so determined are joined by lines, there will result the 
 curve abed efg h, which may be called the curve of moments. This curve shows 
 graphically the variation in the load upon and the duty demanded of the 
 engine from second to second during the hoisting period. At the start, the 
 moments are a maximum, showing that the greatest power is required during 
 the first few seconds. At the end of acceleration, there is a very great drop 
 
756 
 
 HOISTING 
 
 in the load; in the present example it amounts to 55%. During the full- 
 speed period, the load drops regularly until at its end, and coincident with the 
 beginning of retardation, there is another great falling off in the load, which, 
 with its moment, becomes negative and tends to turn the engine. A large 
 amount of brake power is required during retardation; this power is supplied 
 by reversing the engine and turning steam gently into the cylinders against 
 the load and by the use of the brakes. As a result, for quick and heavy hoist- 
 ing, an engine must be run at much above its economical load. In fact, during 
 acceleration, the engine may -be called upon to deliver more than twice the 
 power required during full speed. In the present example, at the end of 
 acceleration when the cage is moving with a speed of 30.3 ft. per sec., the 
 horsepower exerted by the engine is (17,088X30.3) + 550 = 941.4. At the 
 beginning of full speed, the horsepower is (7,797X30.3) -7-550 = 429.5, or 
 about 46% of what it was during acceleration. At the end of full speed, the 
 horsepower drops to (4,403 X 30.3) -J- 550 = 242.5, and at the beginning of 
 retardation there is a further drop to (-4, 888X30.3) -7-550= -269.3 H. P. 
 It may be urged that the weight to be accelerated is not that of the entire 
 load, or 22,000 lb., but rather that attached to the loaded rope, or 13,500 lb., 
 because gravity accelerates the weight of the empty cage, car, and rope. If 
 this line of reasoning is carried farther, it follows that the weight to be acceler- 
 ated is that of the unbalanced load, or 7,000 lb. On the other hand, no account 
 has been taken in the calculation for the power necessary to overcome the 
 inertia of the crank, piston rod, etc., which in the aggregate is considerable, so 
 that it is undoubtedly true that the dimensions of an engine calculated on the 
 basis of accelerating a load of 22,000 lb. will be none too great for the work 
 demanded of it. In fact, it would seem advisable in any case to add something 
 to the area of the cylinders to provide for uncertainties in the resistances to 
 be overcome and for future demands for power. 
 
 The variation in the load and moments is of the greatest importance in 
 electric hoisting, because the motor is called on at the outset to furnish very 
 much more power than at the end of the full-speed period. /This reduces the 
 load factor, which is the ratio between the total energy used in hoisting a trip 
 under the given conditions and the energy required if the load and speed were 
 uniform and the motor working at its full rated capacity; and a low load factor 
 indicates low efficiency in the hoisting plant. 
 
 This great range in the demands for power, in the present example amount- 
 ing to nearly 1,250 H. P. in 38 sec., also indicates the importance of counter- 
 balancing the weight of the rope not only to reduce the unbalanced load to 
 be raised, but also, and more particularly, to cut down the excessive power 
 required to accelerate the load and machinery. 
 
 13. Determination of Engine Dimensions From Load Moments. If the 
 base line in the figure on this page is divided into revolutions instead of into 
 seconds, and perpendiculars are drawn through the points of division, the 
 average load moment for any revolutfon can be determined. This moment 
 divided by the crank radius of the engine gives the average pressure on the 
 crankpin for that revolution; from this, the required average piston pressure 
 is obtained. If the initial steam pressure is known, the point at which the steam 
 may be cutoff at any revolution can be obtained, and the steam consumption 
 per hoist can be accurately ascertained. Calculations of this nature, however, 
 are properly the work of the mechanical engineer and not of the mine foreman 
 or superintendent. 
 
 If the maximum load moments are known and the length of stroke has been 
 determined by assuming a piston speed, as in paragraph 9, the proper area 
 of cylinder may be found from the formula, 
 
 ML+MA 
 PNCRc 
 
HOISTING 
 
 757 
 
 in which A = area of a single cylinder, in square inches; 
 
 ML = moment of unbalanced load, coal, one rope, friction; 
 
 MA = moment of force required to accelerate total load, drum, two 
 
 sheaves, machinery; 
 P = mean effective pressure of steam in cylinders, in pounds per 
 
 square inch; 
 
 N = number of cylinders; 
 C = constant to reduce angular space passed through by crank to 
 
 that passed through by piston in the same time = .64; 
 Rc radius of crank circle, one-half length of stroke. 
 
 In the present problem, ML = 8, 100X4 = 32,400 ft.-lb.; MA - (4,140+5,151) 
 X4 = 37,164; P = 100 lb.; N = 2; C = .64; and Rc = 42 in.-j-2 = 21 in. = 1.75 ft. 
 Substituting in the formula, 
 
 32,400 +37,164 
 
 From this value of A, d is found to be 19.99, say, 20 in. The length of 
 stroke having been previously determined, the use of a 20"X42" engine is 
 indicated. In some cases an allowance is made for the efficiency of the plant. 
 In the present case, the efficiency has been assumed to be 85%; hence, the 
 proper area for the cylinders will be 310.55-7- .85 = 365.35 sq. in., and d = 21.6, 
 say, 22 in. With this allowance, the dimensions of the engine will be 22 in. 
 X42 in. 
 
 It is not unusual in calculations of this nature to assume a ratio r between 
 the length of stroke (length of cylinder) / and the diameter of cylinder d such 
 that l = rd. In this case, the diameter of cylinder may be found directly from 
 a modification of the preceding formula. A common value for r is 2, that 
 is, the length of stroke is made twice the diameter of the cylinder. The 
 formula for d (d 3 ) follows, its application being shown by using the preceding 
 data with a value of r = 2: 
 
 96(ML+MA) 96X (32,400+37.164) 
 
 *rPNC 3.14X2X100X2X.64 = 8 ' 307 ' 77 CU ' im 
 
 From this, d = 20.25 in., and l = rd = 2X20.25 = 40.5 in. A 21"X42" engine 
 would probably be selected, the extra power of the larger size being desirable. 
 
 CALCULATIONS FOR SECOND-MOTION HOISTING 
 ENGINES 
 
 When less than 200 to 250 H. P. is required to hoist, second-motion engines 
 are commonly preferred to first-motion engines because of their smaller size, 
 lower first cost, and generally greater ease in handling. Their small horse- 
 power limits their use to shallow shafts, those, say, not over 250 to 350 ft. deep, 
 where the net daily tonnage does not exceed 750 to 1,000, and where the speed 
 of hoisting is not more than 500 to 750 ft. per min. The standard or stock 
 sizes of second-motion engines are given in the following table, in which the 
 hoisting speed is the rate of travel of the cage and the horsepower is based on 
 a steam pressure of between 80 and 90 lb. 
 
 STANDARD SIZES OF SECOND-MOTION HOISTING ENGINES 
 
 Cylinders 
 
 
 Hoisting 
 
 Cylinders 
 
 
 Hoisting 
 
 
 Horse- 
 power 
 
 Speed 
 Feet 
 
 Minute 
 
 
 Horse- 
 - power 
 
 Speed 
 Feet 
 
 Minute 
 
 Diam- 
 eter 
 Inches 
 
 Stroke 
 Inches 
 
 Diam- 
 eter 
 Inches 
 
 Stroke 
 Inches 
 
 6 
 
 8 
 
 12 
 
 250 
 
 10 
 
 12 
 
 50 
 
 400 
 
 7 
 
 10 
 
 20 
 
 275 
 
 12J 
 
 15 
 
 75 
 
 450 
 
 81 
 
 10 
 
 30 
 
 350 
 
 14 
 
 18 
 
 100 
 
 450 
 
 9 
 
 10 
 
 35 
 
 350 
 
 16 
 
 18 
 
 150 
 
 450 
 
 81 
 
 12 
 
 40 
 
 375 
 
 18 
 
 24 
 
 200 
 
 550 
 
758 HAULAGE 
 
 Dimensions of Second-Motion Engines. While the load moments may be 
 determined in the same way as for first-motion hoisting engines, after which 
 the size of the cylinders may be calculated, it is not customary to do so. The 
 usual practice is to determine the horsepower by the method explained in 
 paragraph 8, an allowance being made for the time spent in acceleration and 
 retardation, and to select from the manufacturers' stock sizes an engine of 
 slightly more than the calculated horsepower. Thus, if an engine of 185 H. P. 
 is required, an engine with 18"X24" cylinders and rated at 200 H. P. will be 
 selected, the extra horsepower being desirable. As these engines cost from 
 $40 to $60 per H. P. (list prices, subject to discount) depending on the acces- 
 sories furnished, the cost of a few extra horsepower is not to be compared with 
 the increased efficiency gained through the use of the larger size. 
 
 The necessary diameter of cylinder to yield a given horsepower may be 
 calculated from the formula, 
 
 792.000 XH. P. 
 vPrGXR. P. M. 
 in which G = ratio of gearing, which is very commonly 3; 
 
 R. P. M. = revolutions of drum per minute; 
 
 and the other letters have the meanings previously given. The revolutions 
 of the crank-arm per minute are equal to the revolutions of the drum multiplied 
 by the gear ratio. That is, if the drum makes 50 rev. per min. and (7 = 3, the 
 revolutions per minute of the crank will be GXR. P. M. = 3X50 = 150. 
 
 In the ratio l = rd, r varies between 1.11 and 1.41, and should be taken to 
 be essentially the same as the ratio in the table for engines of the required 
 horsepower. 
 
 EXAMPLE. What should be the dimensions of a second-motion engine to 
 develop 200 H. P., when the mean effective pressure of the steam is 80 Ib. 
 per sq. in., the hoisting speed is 550 ft. per min., the drum is 6 ft. in diam., and 
 the gear ratio is 3? 
 
 SOLUTION. Here the revolutions per minute of the drum = 550 -i- (6X3.1416) 
 = 29.2, about, and r may be assumed as in the engine table to be as 18 : 24 or 
 as 1 : 1.33. Substituting in the formula, 
 
 792.000X200 
 3.14X80X1.33X3X29.2 ' ' 
 
 From this, d = 17.56, say, 18 in., and l = rd = 1.33X18 = 24 in. Hence the 
 dimensions of the cylinders are 18 in.X24 in. 
 
 In calculations relating to this type of engine, it is rarely necessary to 
 determine the accelerating force. Sufficiently accurate results may be obtained 
 by determining the horsepower required to hoist the unbalanced load (with 
 friction at 10%) at the sustained speed, and then to make one cylinder large 
 enough to do all the work. Where uncertainty exists as to the efficiency of 
 the plant or as to future possible increased demands for power, the determined 
 horsepower should be increased from 10 to 25% or more. 
 
 HAULAGE 
 
 RESISTANCES TO HAULAGE 
 
 Total Resistance to Haulage. The total resistance R, in pounds, which 
 must be overcome in bringing a car or a trip of cars from rest to full speed, may 
 be represented by the expression, 
 
 R=F+C+G+I 
 
 in which F = resistance due to friction, in pounds; 
 
 C = resistance due to curvature, in pounds; 
 G = resistance due to grade, in pounds; 
 1 1 = resistance due to inertia, in pounds. 
 When the trip is moving at a uniform speed, the resistance is 
 
 R=F+C+G 
 
 When the track is level, G = 0, and when it is straight C = 0. 
 Resistance Due to Friction. The frictional resistance to haulage is due 
 both to the friction of the wheels upon their axles, or car resistance, and to the 
 friction of the wheels upon the rails, or track resistance. It is customary to 
 consider these as one under the head of train resistance. On surface railroads, 
 it is found that the train resistance increases with the speed and is materially 
 
HA ULAGE 759 
 
 less for heavy than for light cars. The Baldwin Locomotive Works, quoting 
 the experiments of Prof. E. C. Schmidt, gives the following formula for the 
 resistance of freight cars, in pounds per ton, 
 
 in which W= weight of car, in tons; 
 
 V = velocity of train, in miles per hour. 
 
 The same authority gives the resistance for light standard-gauge and 
 narrow-gauge locomotives and tenders as 
 
 and for heavy standard-gauge locomotives as, 
 F = 4.3 + .003V2 
 
 Both in mine- and surface-railroad practice, it is found that the train 
 resistance depends on the diameter of the wheels, the kind of lubricant used 
 and the amount of lubrication, the kind of axles and journal boxes, the condi- 
 tion of the track, the presence or absence of curves, etc. A large journal bear- 
 ing reduces journal friction, and car wheels of large diameter roll more easily 
 than small ones over inequalities in the rails. Flat and grooved wheels add 
 materially to the resistance. With ordinary self-oiling wheels turning on 
 fixed axles, as used in bituminous coal mines, many experiments have shown 
 that the frictional resistance averages 30 Ib. per T., or 1.5%, when the cars 
 are properly oiled and kept in good repair. When the wheels are fixed and the 
 axles revolve in self-oiling journal boxes, the resistance should be under 20 Ib. 
 per T., or 1%. In surface-railroad practice, at low speeds, the resistance will 
 be from 4 Ib. to 10 Ib. per T., a working average being 6.5 Ib. In mines where 
 roller-bearing wheels are used, the resistance should not exceed 15 Ib. per T., 
 or .75%. Where the track is poor and wheels have much play on fixed axles, 
 the resistance may easily amount to 50, 60, or, in extreme cases, to 100 Ib. per T. 
 
 The track resistance is ordinarily but a small fraction of the total resistance 
 and may be found from the formula, 
 
 T SE 
 
 in which W = weight of car, in pounds; 
 
 r = radius of car wheel, in inches; 
 C = coefficient that, for iron wheels rolling on steel rails, is .02. 
 
 Thus the track resistance per ton of 2,000 Ib., when 20-in. wheels are used, 
 is (2,000 X .02) -h 10 = 4 Ib. 
 
 If a coefficient of friction /is assumed, the total frictional resistance may be 
 found from 
 
 F=fWcosX 
 in which W= weight of car; 
 
 X = angle of inclination of track. 
 
 If the track is level, X = 0, cos X = l, and F=fW. Where the pitch is 
 under 10%, say 5 30', no error of importance is made if this latter and more 
 simple formula is used. 
 
 EXAMPLE. What is the frictional resistance to moving a loaded mine car 
 weighing 8,000 Ib. on a level and on a slope of 20 when/= 1.5%? 
 
 SOLUTION. On a level track X = and F=fW=. 015X8,000 = 120 Ib. 
 On the slope, F = . 015 X 8,000 X. 937 = 112.5 Ib., about. 
 
 EXAMPLE. Assuming the conditions of the preceding problem, what 
 horsepower must be exerted to move the car at a rate of 2 mi. per hr. on a 
 level track? 
 
 SOLUTION. A speed of 2 mi. per hr. = (2 X 5.280) -r- 3,600 = 2.9 ft. per sec. 
 The work per second required to overcome a resistance of 120 Ib. is 120X2.9 
 = 348 ft.-lb. As 1 H. P. is equal to 550 ft.-lb. of work per sec., the required 
 horsepower will be 348 -=-550 = .63. 
 
 Resistance Due to Curvature. On surface railroads, it is customary to 
 compensate for the resistance due to curvature by reducing the grade by .03 to 
 .05 ft. per 100 ft. for each degree of curve. Thus, on an 8 curve, where the 
 grade would otherwise be, say, 2%, it would be reduced to (2.00 .05X8) 
 = 1.60%. 
 
 This correction is not made on mine roads, whereat is not generally possible 
 or even necessary to do so. Centrifugal force pressing the wheels against the 
 outer rail is the chief cause of curve resistance on surface railroads where the 
 speed is high, the cars heavy, the curves of long radius, and where, in particular, 
 the trucks being pivoted on king bolts, the axles are free to assume a position 
 in the direction of the radius of the curve. On mine roads, however, where 
 
760 HAULAGE 
 
 the speed is low, the cars light, the curves of small radius, and the axles are 
 fixed so that they cannot adjust their direction to that of the radius of the 
 curve, the chief cause of curve resistance is the binding of the wheels against 
 the rails. 
 
 The centrifugal force pressing the wheels against the outer rail of a curve 
 may be found from the formula, 
 
 c=~ 2 
 
 gr 
 in which W= weight of car or trip, in pounds; 
 
 v = velocity of car or trip, in feet per second; 
 r radius of curve, in feet. 
 
 EXAMPLE. A train weighing 400 T. is moving on an 8 curve at a speed 
 of 50 mi. per hr. What is the pressure against the outer rail? 
 
 SOLUTION. 400 T. = 800,000 Ib. A speed of 50 mi. per hr. = (SOX 5,280) 
 -7-3,600 = 73 ft. per sec. The radius of an 8 curve is about 717 ft., and g may 
 be taken at 32.2 ft. per sec. per sec. Substituting, 
 
 C=8 32'.2x7ir =20() ' 000 lb - a pp roximatelv 
 
 This is the total pressure of the train. If there are 8 cars each with two 
 four-wheel trucks, the pressure per truck is 200,000-7-16=12,500 lb., and for 
 each wheel bearing against the outer rail is 6,250 lb. 
 
 The following formula, based on 'experiments with mine cars moving at 
 usual speeds, gives the approximate average resistance due to curvature : 
 
 in which b = wheel base, in feet, and C, W, and r have the meaning given in 
 the preceding formula. 
 
 EXAMPLE. What will be the resistance to the passage of a motor weighing 
 20 T. (40,000 lb.), and having a wheel base of 10 ft., around a curve with a 
 radius of 200 ft.? 
 
 SOLUTION. By substituting in the formula, C = = 4( X> lb. 
 
 The preceding formula brings out the important point that, for equal 
 resistance, the sharper the curve the less must be the wheel base of the car. 
 Although not considered in the formula, it should be stated that for equal 
 resistance, the sharper the curve the less should be the gauge of the track. 
 
 Resistance Due to Grade. The grade or slope of a track may be expressed 
 in various ways. 
 
 1. As an angle made by the track with the horizontal. 
 
 2. As the ratio between the rise, taken as 1, or unity, and the horizontal 
 distance required to gain the rise; as 1 in 1, 1 in 5, etc. 
 
 3. As the rise in any horizontal distance, as a grade of 2 in. per ft., or of 
 6 in. per yd. 
 
 4. As a per cent.; this is a modification of 3, the horizontal distance being 
 taken as 100 ft. Thus a 2% grade is one in which the rise is 2 ft. per 100 ft., 
 or 105.6 ft. per mi. 
 
 5. As the rise in feet per mile of length of track; this is, also, a modification 
 of 3, the horizontal distance being taken as 1 mi. 
 
 Of these ways of expressing grades, the second and third are awkward and 
 practically obsolete. The first and fourth are in common use by mining engi- 
 neers, and the fourth and fifth by civil engineers. 
 
 If X = angle of slope, V = vertical rise, H = horizontal distance, and 5 
 = slope distance, then, 
 
 V V H 
 
 tan X = jj sin X = -= cos X = -= 
 
 V = H tan X = S sin X S = V cos X = H sec X H = V cot X = S cos X 
 
 The per cent, of grade is the tangent of the angle of inclination. A 10% 
 grade = angle whose tangent is .10000 = 5 43', about. A pitch of 7 58', the 
 tangent of which is .13995, equals a grade of .13995X100 = 13.995, say, 14%. 
 
 A 10% grade equals a rise of 5,280 X .10 = 528 ft. per mi. A grade of 460 ft. 
 per mi. equals one of (460-7-5,280) X 100 = 8.71%. 
 
 The resistance, due solely to the grade, which must be overcome in hauling 
 up an incline at a uniform speed is 
 
 G=Wsin X 
 
 On a level track, where sin X = sin = 0, G = and there is no resistance 
 due to the weight while the trip is moving at a uniform speed. In shaft hoist- 
 
HAULAGE 
 
 761 
 
 ing, where sin JV = sin 90 = 1, G=W and the resistance is equal to the total 
 load. 
 
 If the grade is expressed in feet per mile, instead of degrees, the formula 
 becomes, 
 
 G= PFXgrade in ft. per mi. X. 3788 
 
 If the grade is expressed as a per cent, instead of in degrees, the formula 
 becomes, G= WXper cent, of grade. This last relation is true only for com- 
 paratively flat grades, say, those not exceeding 10%, where the tangent and 
 sine of the angle of inclination are practically equal. 
 
 GRADE EQUIVALENTS 
 
 Per Cent. 
 
 4 
 
 Degrees 
 Minutes 
 
 Per Cent. 
 
 P ; 
 
 fs 
 *+$ 
 
 p. 
 
 r/1 W 
 
 1! 
 
 $ * 
 
 P S 
 
 Per Cent. 
 
 1 
 
 
 
 is 
 
 fefe 
 c. 
 
 Degrees 
 
 Minutes 
 
 .01 
 
 .53 
 
 .34 
 
 2.80 
 
 147.84 
 
 1 36.23 
 
 6.40 
 
 337.92 
 
 3 39.72 
 
 .02 
 
 1.07 
 
 .69 
 
 2.90 
 
 153.12 
 
 1 39.67 
 
 6.50 
 
 343.20 
 
 3 43.14 
 
 .03 
 
 1.58 
 
 1.03 
 
 3.00 
 
 158.40 
 
 1 43.10 
 
 6.60 
 
 348.48 
 
 3 46.56 
 
 .04 
 
 2.11 
 
 1.37 
 
 3.10 
 
 163.68 
 
 1 46.54 
 
 6.70 
 
 353.76 
 
 3 49.99 
 
 .05 
 
 2.64 
 
 1.72 
 
 3.20 
 
 168.96 
 
 1 49.97 
 
 6.80 
 
 359.04 
 
 3 53.41 
 
 .06 
 
 3.17 
 
 2.06 
 
 3.30 
 
 174.24 
 
 1 53.41 
 
 6.90 
 
 364.32 
 
 3 56.83 
 
 .07 
 
 3.70 
 
 2.41 
 
 3.40 
 
 179.52 
 
 1 56.84 
 
 7.00 
 
 369.60 
 
 4 .25 
 
 .08 
 
 4.22 
 
 2.75 
 
 3.50 
 
 184.80 
 
 2 .27 
 
 7.10 
 
 374.88 
 
 4 3.67 
 
 .09 
 
 4.75 
 
 3.09 
 
 3.60 
 
 190.08 
 
 2 3.71 
 
 7.20 
 
 380.16 
 
 4 7.09 
 
 .10 
 
 5.28 
 
 3.44 
 
 3.70 
 
 195.36 
 
 2 7.14 
 
 7.30 
 
 385.44 
 
 4 10.51 
 
 .20 
 
 10.56 
 
 6.88 
 
 3.80 
 
 200.64 
 
 2 10.57 
 
 7.40 
 
 390.72 
 
 4 13.93 
 
 .30 
 
 15.84 
 
 10.32 
 
 3.90 
 
 205.92 
 
 2 14.01 
 
 7.50 
 
 396.00 
 
 4 17.35 
 
 .40 
 
 21.12 
 
 13.75 
 
 4.00 
 
 211.20 
 
 2 17.44 
 
 7.60 
 
 401.28 
 
 4 20.77 
 
 .50 
 
 26.40 
 
 17.19 
 
 4.10 
 
 216.48 
 
 2 20.87 
 
 7.70 
 
 406.56 
 
 4 24.19 
 
 .60 
 
 31.68 
 
 20.63 
 
 4.20 
 
 221.76 
 
 2 24.30 
 
 7.80 
 
 411.84 
 
 4 27.60 
 
 .70 
 
 36.96 
 
 24.07 
 
 4.30 
 
 227.04 
 
 2 27.73 
 
 7.90 
 
 417.12 
 
 4 31.02 
 
 .80 
 
 42.24 
 
 27.50 
 
 4.40 
 
 232.32 
 
 2 31.16 
 
 8.00 
 
 422.40 
 
 4 34.44 
 
 .90 
 
 47.52 
 
 30.94 
 
 4.50 
 
 237.60 
 
 2 34.60 
 
 8.10 
 
 427.68 
 
 4 37.85 
 
 1.00 
 
 52.80 
 
 34.38 
 
 4.60 
 
 242.88 
 
 2 38.03 
 
 8.20 
 
 432.96 
 
 4 41.27 
 
 1.10 
 
 58.08 
 
 37.81 
 
 4.70 
 
 248.16 
 
 2 41.45 
 
 8.30 
 
 438.24 
 
 4 44.68 
 
 1.20 
 
 63.36 
 
 41.25 
 
 4.80 
 
 253.44 
 
 2 44.89 
 
 8.40 
 
 443.52 
 
 4 48.09 
 
 1.30 
 
 68.64 
 
 44.69 
 
 4.90 
 
 258.72 
 
 2 48.32 
 
 8.50 
 
 448.80 
 
 4 51.51 
 
 1.40 
 
 73.92 
 
 48.13 
 
 5.00 
 
 264.00 
 
 2 51.75 
 
 8.60 
 
 454.08 
 
 4 54.92 
 
 1.50 
 
 79.20 
 
 51.56 
 
 5.10 
 
 269.28 
 
 2 55.18 
 
 8.70 
 
 459.36 
 
 4 58.33 
 
 1.60 
 
 84.48 
 
 55.00 
 
 5.20 
 
 274.56 
 
 2 58.60 
 
 8.80 
 
 464.64 
 
 5 1.75 
 
 1.70 
 
 89.76 
 
 58.43 
 
 5.30 
 
 279.84 
 
 3 2.03 
 
 8.90 
 
 469.92 
 
 5 5.16 
 
 1.80 
 
 95.04 
 
 1.88 
 
 5.40 
 
 285.12 
 
 3 5.46 
 
 9.00 
 
 475.20 
 
 5 8.57 
 
 1.90 
 
 100.32 
 
 5.31 
 
 5.50 
 
 290.40 
 
 3 8.89 
 
 9.10 
 
 480.48 
 
 5 11.98 
 
 2.00 
 
 105.60 
 
 8.75 
 
 5.60 
 
 295.68 
 
 3 12.32 
 
 9.20 
 
 485.76 
 
 5 15.39 
 
 2.10 
 
 110.88 
 
 12.18 
 
 5.70 
 
 300.96 
 
 3 15.74 
 
 9.30 
 
 491.04 
 
 5 18.80 
 
 2.20 
 
 116.16 
 
 15.62 
 
 5.80 
 
 306.24 
 
 3 19.17 
 
 9.40 
 
 496.32 
 
 5 22.20 
 
 2.30 
 
 121.44 
 
 19.06 
 
 5.90 
 
 311.52 
 
 3 23.59 
 
 9.50 
 
 501.60 
 
 5 25.61 
 
 2.40 
 
 126.72 
 
 22.49 
 
 6.00 
 
 316.80 
 
 3 26.02 
 
 9.60 
 
 506.88 
 
 5 29.02 
 
 2.50 
 
 132.00 
 
 25.93 
 
 6.10 
 
 322.08 
 
 3 29.45 
 
 9.70 
 
 512.16 
 
 5 32.42 
 
 2.60 
 
 137.28 
 
 1 29.36 
 
 6.20 
 
 327.36 
 
 3 32.87 
 
 9.80 
 
 517.44 
 
 5 35.83 
 
 2.70 
 
 142.56 
 
 1 32.80 
 
 6.30 
 
 332.64 
 
 3 36.29 
 
 9.90 
 
 522.72 
 
 5 39.23 
 
 
 
 
 
 
 
 10.00 
 
 528.00 
 
 5 42.64 
 
 EXAMPLE. (a) What is the resistance opposing motion when a trip of cars 
 weighing 10,000 Ib. is moved upwards on a plane pitching 8. (b) If the 
 speed of the trip is 10 mi. per hr., what is the horsepower required to produce 
 this motion when the coefficient of friction / is .025? 
 
 SOLUTION. (a) As the trip is moving on a straight track at a uniform 
 speed, A and C are both equal to zero, and R = F-\-G. Substituting for F, 
 and G their values, 
 
 R=fW cosX+Wsin X = (.025X10,OOOX.99027) + (10,OOOX. 13917) 
 = 247.57+1,391.70 = 1,639.27 Ib. 
 
762 HAULAGE 
 
 (b) A speed of 10 mi. per hr. = (10X5,280)%- 3,600 = 14.7 ft. per sec. 
 Whence the foot-pounds of work in 1 sec. = 1,639.27X14.7 = 24,097.27. But 
 1 H. P. = 550 ft.-lb. of work in 1 sec., hence to move the trip up the grade at 
 a uniform speed of 10 mi. per hr. will require the expenditure of 24,097.27 
 -4-550 = 43.8 H. P. 
 
 Resistance Due to Inertia. The resistance due to the inertia of the trip is 
 frequently called the starting resistance because it exists only during the 
 period of acceleration and ceases as soon as the car is moving at a uniform 
 speed. The force necessary to overcome this resistance is not uncommonly 
 called the acceleration, although the word acceleration properly means the 
 gain in the velocity of the body in feet per second per second under the influence 
 of a constant force. During the time of its existence and application, the 
 accelerating force, in haulage problems, may be considered as constant and is 
 the same in value whether the load is moved horizontally, on an inclined track, 
 or vertically. 
 
 The force 7, in pounds, that constantly applied to a body will give it a 
 specified velocity uniformly accelerated from rest at the end of a specified 
 number of seconds, may be found from the formula, 
 , ,. W Wv Wv* 
 I = M a = a = - = - --- 
 g gt g2s 
 W 
 in which M= = mass of body, and the other symbols have the meaning 
 
 given them under Calculations f9r First-Motion Hoisting Engines. 
 
 EXAMPLE. (a) Neglecting friction, what force is required to bring a loaded 
 mine car weighing 5,000 Ib. from rest to a uniform speed of 8 mi. per hr. at 
 the end of 10 sec.? (b) What will be the maximum work per second and maxi- 
 mum horsepower during acceleration? 
 
 SOLUTION. (a) Here TF=5,000 Ib.; * = 10 sec.; = (5,280 X 8) -J- 3, 600 
 = 12 f t. per sec. ; a = 12 -j- 10 = 1 .2 f t. per sec. per sec. Substituting, 
 
 ,,^ = |2fxi.2-lS6,, about 
 
 (b) Because the speed during acceleration increases from to 12 ft. per 
 sec., the maximum work is done during the last second, and is 186X12 = 2,232 
 ft.-lb. From this, the maximum horsepower is 2,232-5-550 = 4.06. 
 
 It is to be noted that the average work performed and the average horse- 
 power required to perform this work during acceleration are one-half of the 
 maximum called for during the last second. 
 
 EXAMPLE. (a) What is the total resistance to be overcome in bringing a 
 trip of 10 loaded mine cars weighing 5,000 Ib. each, from rest to a speed of 
 8 mi. per hr. at the end of 10 sec.; the slope is 8, and the track is laid in a 
 10 curve? (b) What is the maximum work and- what is the maximum horse- 
 power required to do the work during acceleration? 
 
 SOLUTION. (a) The resistance to be overcome is equal to the sum of the 
 individual resistances and is, 
 
 W?|2 W 
 
 R = F+C+G+I=fW cos X+ ^-+W sin X+-~a 
 
 In the problem, it may be assumed that/=.02; 1^=5,000X10 = 50,000 Ib.; 
 X = 8; g = 32.2 ft. per sec. per sec.; v= (5,280 X 8) H- 3,600 = 12 ft. per sec.; 
 r = radius of an 8 curve = 717 ft., about; c = 12-f- 10 = 1.2 ft. per sec. per sec. 
 Substituting in the foregoing formula; 
 
 R = (.02 X 50,000 X .99027) + (^~ X ~) + (50,000 X .13917) + (x 1 .2) 
 
 = 990+312 + 6,958 + 1,863 = 10,123 Ib. 
 
 (6) The maximum work is at the end of the last second of acceleration 
 when the trip has acquired its full speed and is 10,123X12=121,476 ft.-lb. 
 As this work is performed in 1 sec., the horsepower is 121,476-5-550 = 221, about. 
 
 TRACKWORK* 
 
 Choice of Grade. The grade of entries is rarely a matter of choice, but is 
 determined by natural causes, particularly by the dip of the seam, the location 
 of the main haulage road with respect to the property lines, by the direction 
 and strength of the cleavage planes of the coal, etc. 
 
 * See further under Railroad Surveying. 
 
HAULAGE 763 
 
 Where possible the entries should be given a rising grade of from 6 in. 
 to 1 ft. per 100 ft. to insure good drainage, as the flow in the ditches will be 
 more or less impeded by material falling from overloaded cars, with road dirt, 
 etc. At shaft and slope bottoms, unless the cars are fed along by a chain haul 
 or some similar device, it is customary to give both the loaded and empty 
 tracks a favoring grade of about 1.25%, even if the roof and floor have to be 
 shot to do this. 
 
 Where capital is available, main haulage roads, which must last the life of 
 the property and along all or most of the length of which all the coal must 
 be moved, are graded with Almost the same care as first-class surface railroads. 
 More economical haulage is obtained where the grade is all in one direction, 
 and not alternately up and down hill, because of the excessive power temporarily 
 required to overcome the inertia and to bring the trip up to speed in pulling 
 out of swamps. A motor will deliver to the drift mouth no more coal than it 
 can pull over the sharpest grade, and for this reason it is not unusual to see the 
 output of a motor reduced to 50% of what it would be were a little money spent 
 in making the grades uniform. 
 
 Curvature. Curves on mine tracks are generally designated by the length 
 of their radius rather than by their degree of curvature, as is customary on 
 surface-railroad work. In fact, a curve of 50 ft. radius is the sharpest that 
 
 Kf\ 
 
 can be defined in terms of its deflection angle, because for it sin D= - = 1, 
 
 K 
 
 and D=180. 
 
 It is well to make all curves of as long radius as possible. Room turnouts 
 are commonly given a radius of 25 to 35 ft. ; turnouts from main-haulage roads 
 to cross- or butt-entries, a radius of 60 to 100 ft.; and where a curve is necessary 
 on a main-haulage road, its radius should be as great as possible, say, 150 to 
 200 ft., or more, in order to permit of high-speed traffic. 
 
 Rails on curves should not be sprung into place and then spiked, but should 
 be bent to the required radius with a rail bender, or jim-crow, as explained 
 under Railroad Surveying. The. marked difference in length between the 
 outer and inner rails on sharp mine curves may be found from the following 
 rule: 
 
 Rule. Multiply the gauge of the track by the length of the curve and divide 
 the product by the radius, all dimensions being given in feet. 
 
 EXAMPLE. What is the difference in length between the outer and inner 
 rails on a curve of 50 ft. radius and 100 ft. long, when the gauge is 3 ft. 6 in.? 
 
 SOLUTION. As 3 ft. 6 in. = 3.5 ft., the difference in length between the 
 outer and inner rails will be (3.5 X 100) -J- 50 = 7 ft. in. 
 
 With fixed axles and on a sharp curve, the running gear of a car or loco- 
 motive binds as the front wheel presses against the outside rail and the rear 
 wheel against the inside rail. To overcome this, the difference in gauge between 
 the car and the track is increased on curves. The amount of this increase 
 depends on the gauge of the track, the wheel base of the car, and the radius 
 of the curve, the maximum being limited, of course, by the tread of the 
 wheels. Experiments have shown that, with a narrow-gauge track having 
 sharp curves over which locomotives and cars with short wheel bases pass, a 
 good rule is to widen the gauge of the track ff in. for each 2| of curvature, that 
 is, on a 40 curve the track gauge should be increased 1 in. On the very sharp 
 curves frequently necessary in mines, the gauge should be widened as much 
 as the wheel tread will allow, and in some cases it is well to lay guard-rails 
 on the curves inside the rails, so that if one wheel mounts the track the other 
 will not follow, but will pull it back on to the track. 
 
 In motor haulage, in passing around curves the centrifugal force crowds 
 the outer wheel against the rails and tends to overturn the cars. To counter- 
 act this tendency, the outer rail is elevated by an amount proportionate to the 
 speed of the trip and the sharpness of the curve. 
 
 In rope haulage, as the pull of the rope on curves tends to overturn the 
 cars inwards, the inner instead of the outer rail is elevated. 
 
 On a slope haulage, however, operated by a single rope, when the weight 
 of the cars traveling on the slope is sufficient to draw the rope off the hoisting 
 drum, the rails on curves should be elevated on the outside, as the centrifugal 
 force only acts on the cars being lowered; the elevation in such a case should, 
 however, be moderate, so as not to interfere with the trip when being drawn 
 out by the rope, when, of course, the tendency is to tip the cars inwards. The 
 table on page 764 gives the elevation of rail for different degrees of curvature 
 and for a 42-in. track, assuming a speed of 10 to 15 mi. per hr. 
 
764 
 
 HAULAGE 
 RAIL ELEVATION 
 
 Degree 
 of Curve 
 
 Radius 
 of Curve 
 Feet 
 
 Elevation 
 of Outer 
 Rail 
 Inch 
 
 Degree 
 of Curve 
 
 Radius 
 of Curve 
 Feet 
 
 Elevation 
 of Outer 
 Rail 
 Inches 
 
 1 
 
 5,729.6 
 
 , 
 
 10.0 
 
 573.7 
 
 H 
 
 2 
 
 2,864.9 
 
 j 
 
 12.0 
 
 478.3 
 
 1 A 
 
 3 
 
 1,910.1 
 
 JL 
 
 15.0 
 
 383.1 
 
 if 
 
 4 
 
 1,432.7 
 
 A 
 
 18.0 
 
 319.6 
 
 1H 
 
 5 
 
 1,146.3 
 
 A 
 
 20.0 
 
 287.9 
 
 2-fg 
 
 6 
 
 955.4 
 
 if 
 
 60.0 
 
 100.0 
 
 4 
 
 7 
 
 819.0 
 
 I? 
 
 112.9 
 
 60.0 
 
 M 
 
 8 
 
 716.8 
 
 j 
 
 180.0 
 
 50.0 
 
 4f 
 
 9 
 
 637.3 
 
 i 
 
 
 
 
 It is not generally advisable to elevate the rail, more than 4$ in., as it is 
 not good practice to attempt to run trips around sharp curves at a high speed. 
 
 The rule for standard-gauge roads (4 ft. 8$ in. or 56$ in.) on surface and 
 for speeds of 25 to 35 mi. per hr. is to elevate the outer rail in. for each 
 degree of curvature. An approximate rule often given for narrower gauges 
 
 TABLE OF RAILS 
 
 (Carnegie Steel 
 
 
 o 
 
 
 s 
 
 
 
 & 
 
 For One Joint 
 
 For 1,000 T. of Rail 
 
 _- 
 
 ;> 
 
 
 pq 
 
 
 
 
 
 fel 
 
 8 
 
 i 
 
 o 
 
 V 
 
 1 
 
 5 
 
 Is 
 
 || 
 
 si 
 
 4, 
 
 Number 
 
 g 
 
 2 
 
 sj 
 
 f 
 
 I 
 
 "o " 
 
 o1 
 
 1?! 
 
 'SJu -o 
 
 5 
 
 a 
 
 
 .5? 
 
 OM 
 
 
 
 s *"* 
 CO 
 
 S 5 ! 
 
 * ^ 
 
 "3 ! <2 
 
 ? 
 
 !i 
 
 1 
 
 1 
 
 1 
 
 3 
 
 "o 
 
 J 
 
 
 
 'S'o 
 
 p 
 
 1 
 
 S 
 
 51 
 
 I? 
 
 
 
 
 
 
 
 
 
 * 
 
 ^ 
 
 
 CO 
 
 
 
 110 
 
 6 
 
 t 
 
 34 
 
 
 X4 
 
 5i 
 
 X- 
 
 v 
 
 99.50 
 
 
 5.60 
 
 105.10 
 
 1,892 
 
 11,350 
 
 61,760 
 
 100 
 
 5- 
 
 
 34 
 
 
 X4 
 
 5. 
 
 X 
 
 4 
 
 87.00 
 
 
 5.36 
 
 92.36 
 
 2,075 
 
 12,450 
 
 67.710 
 
 95 
 
 5- 
 
 iff 
 
 34 
 
 
 X4 
 
 5^ 
 
 X 
 
 Sg. 
 
 80.80 
 
 2 
 
 5.36 
 
 86.16 
 
 2,184 
 
 13,100 
 
 71,270 
 
 90 
 85 
 
 5 
 6] 
 
 j 
 
 34 
 34 
 
 
 X4 
 X4 
 
 5^ 
 5. 
 
 x- 
 
 4 
 \ 
 
 74.00 
 68.13 
 
 <5 
 
 
 
 5.20 
 5.20 
 
 79.20 
 73.33 
 
 2,305 
 2,441 
 
 13,830 
 14,640 
 
 75.230 
 79,660 
 
 80 
 
 5 
 
 
 34 
 
 
 X4 
 
 si 
 
 x 
 
 I 
 
 63.13 
 
 
 
 5.05 
 
 68.18 
 
 2,593 
 
 15,560 
 
 84,640 
 
 75 
 
 4-1 
 
 i 
 
 34 
 
 
 X4 
 
 5J 
 
 X- 
 
 4 
 
 58.50 
 
 
 4.96 
 
 63.46 
 
 2,766 
 
 16,590 
 
 90,270 
 
 70 
 
 4 
 
 
 34 
 
 
 X3 
 
 Si 
 
 X 
 
 4 
 
 54.64 
 
 
 4.76 
 
 59.40 
 
 2,963 
 
 17,780 
 
 96,720 
 
 65 
 
 
 v 
 
 24 
 
 
 X3 
 
 si 
 
 X 
 
 t. 
 
 35.55 
 
 
 3.18 
 
 38.73 
 
 3,192 
 
 12,770 
 
 104,200 
 
 60 
 
 4 1 
 
 . 
 
 24 
 
 
 X33 
 
 5^ 
 
 X 
 
 4 
 
 32.40 
 
 
 3.12 
 
 35.52 
 
 3,458 
 
 13,830 
 
 112,900 
 
 55 
 
 
 v 
 
 24 
 
 
 
 
 X 
 
 v 
 
 28.90 
 
 
 3.12 
 
 32.02 
 
 3,772 
 
 15,090 
 
 123,100 
 
 50 
 
 3' 
 
 
 24 
 
 
 X3- 
 
 5i 
 
 X 
 
 4 
 
 25.50 
 
 
 3.00 
 
 28.50 
 
 4,149 
 
 16,600 
 
 135,400 
 
 45 
 40 
 
 3i 
 
 3- 
 
 1 
 
 20 
 20 
 
 
 X3* 
 X3 
 
 si 
 
 5 
 
 x^ 
 
 
 
 18.75 
 16.10 
 
 
 2.90 
 2.90 
 
 21.65 
 19.00 
 
 5,148 
 5,790 
 
 20,590 
 23,160 
 
 150,500 
 169,300 
 
 35 
 
 3i 
 
 5 
 
 
 
 X2 
 
 4^ 
 
 
 
 12.10 
 
 ^2 
 
 1.74 
 
 13.84 
 
 6,618 
 
 26,470 
 
 193,500 
 
 30 
 
 3 
 
 
 16 
 
 
 X2 
 
 4 
 
 X- 
 
 
 10.45 
 
 "3 
 
 1.74 
 
 12.19 
 
 7,722 
 
 30,890 
 
 225,700 
 
 25 
 20 
 
 2- 
 
 2 
 
 
 16: 
 16 
 
 
 X2 
 X2 
 
 4 
 3^ 
 
 X 
 
 
 5.70 
 4.86 
 
 PQ 
 
 .97 
 .91 
 
 6.67 
 5.77 
 
 9,264 
 11,580 
 
 37,060 270,800 
 46.330 338,500 
 
 16 
 
 2 
 
 
 16 
 
 
 
 3 
 
 
 
 4.36 
 
 
 .865 
 
 5.225 
 
 14,480 
 
 57,920 423,200 
 
 14 
 
 2] 
 
 V 
 
 16 
 
 
 Xl^ 
 
 3 
 
 
 
 3.44 
 
 
 .865 
 
 4.305 
 
 16,540 
 
 66,180 
 
 483,600 
 
 12 
 
 2 
 
 
 16 
 
 
 
 3 
 
 X 
 
 
 3.44 
 
 
 .865 
 
 4.305 
 
 19,300 
 
 77,200 
 
 564,100 
 
 10 
 8 
 
 
 I 
 
 16: 
 
 
 Xli 
 Xli 
 
 II 
 
 x, 
 x, 
 
 t 
 
 2.60 
 2.00 
 
 
 .45 
 .45 
 
 3.05 
 2.45 
 
 23,170 
 28,960 
 
 92,680 
 115,800 
 
 677,300 
 846,400 
 
HAULAGE 
 
 765 
 
 is to make the elevation proportional to the gauge based on the amount given 
 for standard gauge. Thus, for a 36-in. gauge, the elevation would be about 
 two-thirds of the elevation for a 56-in. gauge of the same speed and curve. 
 
 The elevations of the outer rail given in the table correspond to the middle 
 ordinates of the respective curves for a chord of 20 ft. Hence, a common rule 
 to determine the amount of the elevation of the outer rail, for a speed of 15 mi. 
 per hr. for a 3-ft. gauge, is to measure the middle ordinate of a string 20 ft. long, 
 stretched as a chord on the gauge line of the outer rail. For higher or lower 
 speeds, make the length of the string proportional to the speed; thus, for a 
 speed of 12 mi. per hr., use a 16-ft. string, for 9 mi. per hr., a 12-ft. string, etc. 
 Also the elevation should be proportional to the gauge; thus, for a 30-in. gauge, 
 use five-sixths of the above elevation, etc. 
 
 The general rule is to begin to elevate the rail a short distance before the 
 curve begins, this distance depending on the amount of elevation required. It 
 is, however, not always practicable to do this in mine work. 
 
 Gauge of Track. The gauge of track selected must conform to local con- 
 ditions. The thickness of the seam and the character of roof and floor deter- 
 mine in a general way the size of the haulage roads, and consequently of the 
 mine cars that pass through them. The question of economical haulage 
 considers a minimum number of cars having a maximum capacity. As the 
 car length is limited by the necessarily short wheel base to about 10 ft., and 
 its height by the thickness of the seam and limit of easy hand loading, the 
 remaining dimension, or the width of the car, is usually the variable factor. 
 To obtain the maximum capacity required, the width of the car must be 
 increased, thereby requiring a broader gauge for stability. A broader gauge 
 
 AND ACCESSORIES 
 
 Company) 
 
 For 1,000 T. of Rail 
 
 For 1 Mi. Single Track 
 
 Weight in Gross Tons 
 
 Number 
 
 Weight, in Gross Tons 
 
 | 
 
 c 
 
 1 
 
 Total 
 Accessories 
 
 Pair of 
 Splice Bars 
 
 I 1 
 
 1 
 
 Splice Bars 
 
 J| 
 
 u 
 
 C/3 
 
 Total 
 Accessories 
 
 '3 
 
 Total 
 Complete 
 
 84.04 
 
 4.80 
 
 16.22 
 
 105.06 
 
 326 
 
 1 ,956 
 
 10,640 
 
 14.48 
 
 .83 
 
 2.80 
 
 18.11 
 
 172.29 
 
 190.40 
 
 80.56 
 
 5.03 
 
 17.78 
 
 103.37 
 
 326 
 
 1,956 
 
 10,640 
 
 12.66 
 
 .79 
 
 2.80 
 
 16.25 
 
 157.14 
 
 173.39 
 
 78.77 
 
 5.29 
 
 18.72 
 
 102.78 
 
 326 
 
 1 ,956 
 
 10,640 
 
 11.76 
 
 .79 
 
 2.80 
 
 15.35 
 
 149.29 
 
 164.64 
 
 76.15 
 
 5.39 
 
 19.75 
 
 101.29 
 
 326 
 
 1,956 
 
 10.64U 
 
 10.77 
 
 .76 
 
 2.80 
 
 14.33 
 
 141.43 
 
 155.76 
 
 74.26 
 
 5.71 
 
 20.94 
 
 100.91 
 
 326 
 
 1,956 
 
 10,640 
 
 9.92 
 
 .76 
 
 2.80 
 
 13.48 
 
 133.57 
 
 147.05 
 
 72.15 
 
 5.96 
 
 22.23 
 
 100.34 
 
 326 
 
 1 ,956 
 
 10,640 
 
 9.07 
 
 .75 
 
 2.80 
 
 12.62 
 
 125.71 
 
 138.33 
 
 72.28 
 
 6.25 
 
 23.70 
 
 102.23 
 
 326 
 
 1,956 
 
 10,640 
 
 8.52 
 
 .74 
 
 2.80 
 
 12.06 
 
 117.86 
 
 129.92 
 
 72.36 
 
 6.48 
 
 25.40 
 
 104.24 
 
 326 
 
 1 ,956 
 
 10,640 
 
 7.96 
 
 .71 
 
 2.80 
 
 11.47 
 
 110.00 
 
 121.47 
 
 50.63 
 
 4.65 
 
 27.36 
 
 82.64 
 
 326 
 
 1,304 
 
 10,640 
 
 5.17 
 
 .48 
 
 2.80 
 
 8.45 
 
 102.12 
 
 110.57 
 
 49.95 
 
 4.84 
 
 29.63 
 
 84.42 
 
 326 
 
 1,304 
 
 10,640 
 
 4.71 
 
 .46 
 
 2.80 
 
 7.97 
 
 94.29 
 
 102.26 
 
 48.60 
 
 5.28 
 
 32.33 
 
 86.21 
 
 326 
 
 1 ,304 
 
 10,640 
 
 4.20 
 
 .46 
 
 2.80 
 
 7.46 
 
 86.43 
 
 93.89 
 
 47.22 
 
 5.59 
 
 35.56 
 
 88.37 
 
 326 
 
 1,304 
 
 10,640 
 
 3.71 
 
 .44 
 
 2.80 
 
 6:95 
 
 78.57 
 
 85.52 
 
 42.99 
 
 6.69 
 
 39.51 
 
 89.19 
 
 364 
 
 1,456 
 
 10,640 
 
 3.04 
 
 .47 
 
 2.79 
 
 6.31 
 
 70.71 
 
 77.02 
 
 41.68 
 
 7,52 
 
 30.83 
 
 80.03 
 
 364 
 
 1,456 
 
 10,640 
 
 2.62 
 
 .47 
 
 1.94 
 
 5.03 
 
 62.86 
 
 67.89 
 
 35.84 
 
 5.43 
 
 32.29 
 
 73.56 
 
 364 
 
 1,456 
 
 10,640 
 
 1.97 
 
 .30 
 
 1.78 
 
 4.05 
 
 55.00 
 
 59.05 
 
 36.06 
 
 6.33 
 
 33.60 
 
 75.99 
 
 364 
 
 ,456 
 
 10,640 
 
 1.70 
 
 .30 
 
 1.59 
 
 3.59 
 
 47.14 
 
 50.73 
 
 23.67 
 
 4 10 
 
 40.32 
 
 68.09 
 
 364 
 
 ,456 
 
 10,640 
 
 .93 
 
 .16 
 
 1.59 
 
 2.68 
 
 39.29 
 
 41.97 
 
 25.13 
 
 4.96 
 
 48.74 
 
 78.83 
 
 364 
 
 ,456 
 
 10,640 
 
 .79 
 
 .16 
 
 1.53 
 
 2.48 
 
 31.43 
 
 33.91 
 
 28.24 
 
 576 
 
 32.30 
 
 66.30 
 
 364 
 
 ,456 
 
 10,640 
 
 .71 
 
 .15 
 
 .81 
 
 1.67 
 
 25.14 
 
 26.81 
 
 25.45 
 
 6.58 
 
 34.82 
 
 66.85 
 
 364 
 
 ,456 
 
 10,640 
 
 .56 
 
 .15 
 
 .77 
 
 1.48 
 
 22.00 
 
 23.48 
 
 29.69 
 
 767 
 
 40.61 
 
 77.97 
 
 364 
 
 ,456 
 
 10,640 
 
 .56 
 
 .15 
 
 .77 
 
 1.48 
 
 18.86 
 
 20.34 
 
 26.73 
 26.25 
 
 4.65 
 5.82 
 
 27.50 
 34.37 
 
 58.88 
 66.44 
 
 364 
 364 
 
 ,456 
 1,456 
 
 10,640 
 10,640 
 
 .42 
 .33 
 
 .07 
 .07 
 
 .43 
 .43 
 
 .92 
 
 .83 
 
 15.71 
 12.57 
 
 16.63 
 13.40 
 
766 
 
 HAULAGE 
 
 reduces wear and tear on tracks and rolling stock, and requires outside wheels, 
 which are cheap, easy to lubricate, and easy to replace. Cars with a relatively 
 narrow gauge run more easily around sharp curves, and they are generally 
 made with inside wheels. With wheels inside the frame, the capacity of 
 narrow-gauge cars may be made to almost equal that of cars of broader gauge, 
 but they lack the stability of the latter. With narrow gauges, shorter ties 
 can be used, reducing the amount of cutting in the bottom of a thin inclined 
 seam, and leaving more room available for ditching and for gob room, but 
 with a very narrow gauge too little room is given for the mules to tread, and 
 they frequently slip on the rails or inclines and at curves. 
 
 The most common track gauges in coal mines are 30, 36, 42, and 48 in., but 
 these are not absolute, as smaller and larger gauges are often employed. Gauges 
 less than 26 in. make the cars top heavy and gauges more than 48 in. require 
 large curves and extra wide haulage ways, room necks, etc. 
 
 In proportioning the gauge of a track to a given width of entry, provision 
 should be made, if possible, to allow for a passageway between the car and 
 the ribs, or at least between the car and one rib, so that a man and a mule 
 can pass between the car and the rib. 
 
 Rails. The size, that is, the weight per yard, of rails to be used depends 
 on the nature of the traffic. Nothing is gained by having rails of too light a 
 section. If the mine water is acid, light rails are soon eaten through, and in 
 any case they are apt to spring and cause wrecks, the cost of cleaning up which 
 will soon pay for the difference in cost of the heavier rails. 
 
 Main haulage roads, particularly where heavy motor or high-speed rope 
 haulage is used, are very commonly laid with rails weighing 50 to 60 Ib. per yd. 
 
 TABLE OF RAILS 
 
 (Carnegie Steel 
 
 
 ij 
 
 
 
 
 For One Joint 
 
 For 1,000 
 Tonnes of Rail 
 
 Is 
 
 t) g 
 
 C -JH 
 
 
 
 8 g 
 
 |i 
 
 I to 
 
 
 
 3j 
 
 43 
 
 
 Number 
 
 ll 
 
 *O M 
 
 il 
 
 li 
 
 Sj 
 
 CO ^ 
 
 V 
 
 |1 S 
 
 2 rn rd 
 
 Is g 
 
 v u 
 
 *!l 
 
 :|i 
 
 ! 
 
 1 
 
 13 
 
 '53 
 
 i 
 
 
 
 ll 
 
 p, 
 
 .,s j 
 
 oO j 
 
 
 I 1 
 
 
 a 
 
 
 
 
 
 "o 
 
 
 Cfl 
 
 
 54.56 
 
 155.60 
 
 864 
 
 19.0X121 
 
 140X14.3 
 
 45.13 
 
 
 2.54 
 
 47.67 
 
 1,854 
 
 11,124 
 
 49.60 
 
 146.00 
 
 864 
 
 19.0X114 
 
 140X14.3 
 
 39.46 
 
 
 2.43 
 
 41.89 
 
 2,040 
 
 12,240 
 
 47.12 
 
 141.30 
 
 864 
 
 19.0X114 
 
 140X14.3 
 
 36.65 
 
 jn 
 
 2.43 
 
 39.08 
 
 2,146 
 
 12,876 
 
 44.64 
 
 136.50 
 
 864 
 
 19.0X108 
 
 140X14.3 
 
 33.57 
 
 "3 
 
 2.35 
 
 35.92 
 
 2,270 
 
 13,620 
 
 42.16 
 
 131.80 
 
 864 
 
 19.0X108 
 
 140X14.3 
 
 30.90 
 
 pq 
 
 2.35 
 
 33.25 
 
 2,400 
 
 14.400 
 
 39.68 
 
 127.00 
 
 864 
 
 19.0X105 
 
 140X14.3 
 
 28.63 
 
 CO 
 
 2.29 
 
 30.92 
 
 2,550 
 
 15,300 
 
 37.20 
 
 122.20 
 
 864 
 
 19.0X102 
 
 140X14.3 
 
 26.54 
 
 
 2.25 
 
 28.79 
 
 2,718 
 
 16,308 
 
 34.72 
 
 117.50 
 
 864 
 
 19.0X95.2 
 
 140X14.3 
 
 24.78 
 
 
 2.16 
 
 26.94 
 
 2,916 
 
 17,496 
 
 32.24 
 
 112.70 
 
 610 
 
 19.0X95.2 
 
 140X14.3 
 
 16.10 
 
 
 .44 
 
 17.54 
 
 3,140 
 
 12,560 
 
 29.76 
 
 107.90 
 
 610 
 
 19.0X88.9 
 
 140X14.3 
 
 14.70 
 
 
 .42 
 
 16.12 
 
 3,410 
 
 13,640 
 
 27.28 
 
 103.20 
 
 610 
 
 19.0X88.9 
 
 140X14.3 
 
 13.10 
 
 
 .42 
 
 14.52 
 
 3,710 
 
 14,840 
 
 24.80 
 
 98.42 
 
 610 
 
 19.0X82.5 
 
 140X14.3 
 
 11.60 
 
 
 .36 
 
 12.96 
 
 4,080 
 
 16,320 
 
 22.32 
 
 93.66 
 
 508 
 
 19.0X76.2 
 
 140X14.3 
 
 8.50 
 
 
 .32 
 
 9.82 
 
 8,960 
 
 35,840 
 
 19.84 
 
 88.89 
 
 508 
 
 19.0X76.2 
 
 127X12.7 
 
 7.30 
 
 
 .32 
 
 8.62 
 
 10,080 
 
 40,320 
 
 17.36 
 
 84.13 
 
 410 
 
 15.9X63.5 
 
 114.3X12.7 
 
 5.50 
 
 
 
 .79 
 
 6.29 
 
 11,520 
 
 46,080 
 
 14.88 
 
 79.37 
 
 410 
 
 15.9X63.5 
 
 101.6X12.7 
 
 4.74 
 
 "8 
 
 .79 
 
 5.53 
 
 13.440 
 
 53,760 
 
 12.40 
 
 69.85 
 
 410 
 
 12.7X57.1 
 
 101.6X12.7 
 
 2.58 
 
 PQ 
 
 .45 
 
 3.03 
 
 16,140 
 
 64,560 
 
 9.92 
 
 66.67 
 
 410 
 
 12.7X50.8 
 
 88.9X12.7 
 
 2.20 
 
 <* 
 
 .41 
 
 2.61 
 
 20,160 
 
 80,640 
 
 7.94 
 
 60.32 
 
 410 
 
 12.7X44.4 
 
 88.9 X 9.5 
 
 1.98 
 
 
 .39 
 
 2.37 
 
 25,200 
 
 100,800 
 
 6.94 
 
 52.38 
 
 410 
 
 12.7X44.4 
 
 76.2X 9.5 
 
 1.56 
 
 
 .39 
 
 1.95 
 
 28,820 
 
 115,280 
 
 5.95 
 
 50.80 
 
 410 
 
 12.7X44.4 
 
 76.2X 9.5 
 
 1.56 
 
 
 .39 
 
 1.95 
 
 33,620 
 
 134,480 
 
 4.96 
 
 44.45 
 
 410 
 
 9.5X38.1 
 
 63.5X 7.9 
 
 1.18 
 
 
 .20 
 
 1.38 
 
 40,320 
 
 161,280 
 
 3.97 
 
 39.68 
 
 410 
 
 9.5X38.1 
 
 63.5 X 7.9 
 
 .91 
 
 .20 
 
 1.11 
 
 50,380 
 
 201,520 
 
HAULAGE 
 
 767 
 
 In motor haulage, it is recommended that the rails used weigh not less than 
 10 Ib. per yd. for each ton in weight coming on a single driver. Thus, a 20-T., 
 four-wheeled motor will have 5 T. on each wheel and will require a 50- Ib. 
 rail, which is light enough. 
 
 Side, cross, butt, or room entries, are commonly laid with 30- or 35-lb. rail, 
 as the motors used for gathering are light and their speed low. 
 
 In rooms, 16-, 20-, and 25-lb. rails are used, depending on the weight of the 
 loaded mine car and whether the gathering motor does or does not enter the 
 rooms. Wooden rails, from 16 to 20 ft. in length and 3 in.X4 in. or 4 in.XS in., 
 in section, and nailed to the ties with wire nails were formerly much used but 
 are now rarely seen. Room tracks, and in small mines the cross-entries, were 
 not infrequently laid with light wooden rails upon which were nailed strips of 
 strap iron about f in.XlJ in. in section. 
 
 Rule I. To find the weight of rail, in long tons (2,240 Ib,), required to lay 
 1 mi. of single track, multiply the weight of the rail, in pounds per yard, by ty, or 
 by 1.5714- 
 
 Rule II. To find the weight of rail, in long tons (2 #40 Ib.), required to lay 
 1 ,000 ft. of single track, multiply the weight of the rail, in pounds per yard, by 
 .29761. 
 
 Thus, the weight of 70-lb. steel for 1 mi. and for 1,000 ft. of single track will 
 be, respectively, 70X-V-=HO long tons and 70 X. 29761 = 20.833 long tons. 
 For lengths of track other than 1,000 ft., multiply the quantity required for 
 1,000 ft. by the ratio the given length bears to 1,000. Thus, for the materials 
 required for 600, 1,580, and 4,000 ft. of track, multiply the quantities of fish- 
 
 AND ACCESSORIES 
 
 Company) 
 
 For 1.000 Tonnes of Rail 
 
 For 1 Kilometer, Single Track 
 
 Num- 
 ber 
 
 Weight in Tonnes 
 
 Number 
 
 Weight in Tonnes 
 
 
 
 
 -a 
 
 
 j 
 
 52 
 
 *o rt 
 
 fi 
 
 
 i 
 
 t) 
 
 
 g 
 
 
 | 
 
 1 
 
 PQ 
 
 -2 
 
 1 
 
 *c3 o 
 
 W3 
 
 rt g 
 
 1 
 
 ' PQ 
 
 rt g 
 
 1 
 
 13 o 
 
 ,3 
 
 *c3 ~ 
 
 I 
 
 CO 
 
 I* 
 
 CO 
 
 m 
 
 *1 
 
 pq 
 
 a 
 
 CO 
 
 | 
 & 
 
 r 
 
 I 
 
 O w 
 
 d 
 
 *l 
 
 61,100 
 
 83.7 
 
 4.7 
 
 16.3 
 
 104.7 
 
 204 
 
 1,224 
 
 6,668 
 
 9.21 
 
 .52 
 
 1.78 
 
 11.51 
 
 109.12 
 
 120.63 
 
 67,200 
 
 80.5 
 
 5.0 
 
 17.9 
 
 103.4 
 
 204 
 
 1,224 
 
 6,668 
 
 8.05 
 
 .50 
 
 1.78 
 
 10.33 
 
 99.20 109.53 
 
 70,800 
 
 78.7 
 
 5.2 
 
 18.8 
 
 102.8 
 
 204 
 
 1,224 
 
 6,668 
 
 7.48 
 
 .50 
 
 1.78 
 
 9.76 
 
 94.24 104.00 
 
 74,700 
 
 76.2 
 
 5.3 
 
 19.9 
 
 101.4 
 
 204 
 
 1,224 
 
 6,668 
 
 6.85 
 
 .48 
 
 1.78 
 
 9.11 
 
 89.28 
 
 98.39 
 
 79,100 
 
 74.3 
 
 5.6 
 
 21.1 
 
 101.0 
 
 204 
 
 1,224 
 
 6,668 
 
 6.30 
 
 .48 
 
 1.78 
 
 8.56 
 
 84.32 
 
 92.88 
 
 84,000 
 
 73.0 
 
 5.9 
 
 22.4 
 
 101.3 
 
 204 
 
 1,224 
 
 6,668 
 
 5.84 
 
 .47 
 
 1.78 
 
 8.09 
 
 79.36 
 
 87.45 
 
 89,600 
 
 72.1 
 
 6.1 
 
 23.9 
 
 102.1 
 
 204 
 
 1,224 
 
 6,668 
 
 5.41 
 
 .46 
 
 1.78 
 
 7.65 
 
 74.40 
 
 82.05 
 
 96,000 
 
 72.3 
 
 6.3 
 
 25.6 
 
 104.2 
 
 204 
 
 1,224 
 
 6,668 
 
 5.06 
 
 .44 
 
 1.78 
 
 7.28 
 
 69.44 
 
 76.72 
 
 103,400 
 
 50.6 
 
 4.5 
 
 27.6 
 
 82.7 
 
 204 
 
 816 
 
 6,668 
 
 3.28 
 
 .29 
 
 1.78 
 
 5.35 
 
 64.48 
 
 69.83 
 
 112,000 
 
 50.1 
 
 4.9 
 
 29.9 
 
 84.9 
 
 204 
 
 816 
 
 6,668 
 
 3.00 
 
 .29 
 
 1.78 
 
 5.07 
 
 59.52 
 
 64.59 
 
 122,200 
 
 48.6 
 
 5.3 
 
 32.6 
 
 86.5 
 
 204 
 
 816 
 
 6,668 
 
 2.67 
 
 .29 
 
 1.78 
 
 4.74 
 
 54.56 
 
 59.30 
 
 134.400 
 
 47.3 
 
 5.5 
 
 35.9 
 
 88.7 
 
 204 
 
 816 
 
 6,668 
 
 2.37 
 
 .28 
 
 .78 
 
 4.43 
 
 49.60 
 
 54.03 
 
 149,360 
 
 76.2 
 
 11.9 
 
 40.0 
 
 128.1 
 
 400 
 
 1,600 
 
 6,668 
 
 3.40 
 
 .53 
 
 .78 
 
 5.91 
 
 44.64 
 
 50.36 
 
 168,000 
 
 73.6 
 
 13.3 
 
 32.6 
 
 119.5 
 
 400 
 
 1,600 
 
 6,668 
 
 2.92 
 
 .53 
 
 .29 
 
 4.74 
 
 39.68 
 
 44.42 
 
 192,000 
 
 63.4 
 
 9.1 
 
 34.2 
 
 106.7 
 
 400 
 
 1,600 
 
 6,668 
 
 2.20 
 
 .32 
 
 .19 
 
 3.71 
 
 34.72 
 
 38.43 
 
 224,000 
 
 63.7 
 
 10.7 
 
 36.3 
 
 110.7 
 
 400 
 
 1,600 
 
 6,668 
 
 1.90 
 
 .32 
 
 .08 
 
 3.30 
 
 29.76 
 
 33.06 
 
 268.800 
 
 41.7 
 
 7.3 
 
 43.6 
 
 92.6 
 
 400 
 
 1,600 
 
 6,668 
 
 1.03 
 
 .18 
 
 1.08 
 
 2.29 
 
 24.80 
 
 27.09 
 
 336,000 
 
 44.4 
 
 8.3 
 
 49.2 
 
 101.9 
 
 400 
 
 1,600 
 
 6,668 
 
 .88 
 
 .17 
 
 .98 
 
 2.03 
 
 19.84 
 
 21.87 
 
 419,800 
 
 49.9| 9.9 32.1 
 
 91.9 
 
 400 
 
 1,600 
 
 6,668 
 
 .79 
 
 .16 
 
 .52 
 
 1.47 
 
 15.88 
 
 17.35 
 
 480,360 
 
 45.0 11.3 
 
 35.2 
 
 91.5 
 
 400 
 
 1.600 
 
 6,668 
 
 .62 
 
 .16 
 
 .49 
 
 1.27 
 
 13.88 
 
 15.15 
 
 560,200 
 672,000 
 
 52.5 13.1 
 47.6 8.1 
 
 41.0 
 27.1 
 
 106.6 
 82.8 
 
 400 11,600 
 400 1,600 
 
 6,668 
 6,668 
 
 .62 
 .47 
 
 .16 
 .08 
 
 .49 
 .27 
 
 1.27 
 .82 
 
 11.90 
 9.92 
 
 13.17 
 10.74 
 
 839,600 
 
 45.9 
 
 10.1 
 
 33.9 
 
 89.9 
 
 400 
 
 1,600 6,668 
 
 .36 .08 
 
 .27 
 
 .71 
 
 7.94 
 
 8.65 
 
768 
 
 HAULAGE 
 
 WEIGHT OF RAILS, IN TONS OF 2,240 LB., REQUIRED TO LAY 1,000 FT. 
 SINGLE TRACK 
 
 Weight of 
 Rail 
 
 Tons For 
 1,000 Ft. 
 
 Weight of 
 Rail 
 
 Tons For 
 1,000 Ft. 
 
 Weight of 
 Rail 
 
 Tons For 
 1,000 Ft. 
 
 per Yard 
 
 of Track 
 
 per Yard 
 
 of Track 
 
 per Yard 
 
 of Track 
 
 8 
 
 2.381 
 
 40 
 
 11.905 
 
 75 
 
 23.321 
 
 12 
 
 3.571 
 
 45 
 
 13.393 
 
 80 
 
 23.809 
 
 16 
 
 4.762 
 
 50 
 
 14.881 
 
 85 
 
 25.298 
 
 20 
 
 5.952 
 
 55 
 
 16.369 
 
 90 
 
 26.786 
 
 25 
 
 7.441 
 
 60 
 
 17.858 
 
 95 
 
 28.274 
 
 30 
 
 8.929 
 
 65 
 
 19.346 
 
 100 
 
 29.761 
 
 35 
 
 10.417 
 
 70 
 
 20.833 
 
 110 
 
 32.737 
 
 plates, bolts, and spikes as well as rails, required for 1,000 ft. by .600, 1.58, 
 and by 4, respectively. 
 
 It will be noted that each increase of 5 Ib. per yd. in the weight of the rail, 
 increases by 1.488 (1.5, nearly) T., the quantity required to lay 1,000 ft. 
 of track. 
 
 The two following tables give the gross tons, of 2,240 Ib., required for 1 mi., 
 and the metric tonnes, or 2,204 Ib. (about) required for 1 km. of single track, 
 as well as the necessary fish-plates (splice-bars), bolts, nuts, and ties. It should 
 be especially noted that above 50 Ib. per yd. rails are 33 ft. long, the length 
 adopted by the American Railway Association in 1908, the American Railway 
 Engineering and Maintenance of Way Association in 1907, the American 
 Society of Testing Materials in 1907, and the American Society of Civil Engi- 
 neer's in 1908. The first table is based on 90% of rails to be 33 ft. long, and 
 10% not less than 24 ft. long, varying by even feet. Ties are to be placed to 
 centers or 2,640 ties per mile. Rails below 50 Ib. per yd. are furnished 30 ft. 
 long, and 10% not less than 20 ft. long. No excess has been allowed. The 
 second table is based on 90% of rails to be 10 m. long, with 10% varying down 
 to 8 m. in length. Ties are to be spaced 600 mm. to centers or 1,641 ties per 
 km. Rails below 24.80 km. per m. are furnished 5 m. long. No excess has 
 been allowed. For 1,000 ft. of single track, there will be required sixty-eight 
 30-ft rails, 68 pairs of splice bars, 272 bolts when four are used per joint, or 
 408 bolts when six are used per joint. 
 
 Ties. Main-entry ties should have at least a 5- to 8-in. face, and be 4 to 
 6 in. deep; their length will depend on the gauge of the track, but they slwuld 
 project from 8 to 12 in. on each side of the rail to give the roadbed stability 
 and the ties a resting surface for the transmission of weight to the roadbed. 
 The wood of main-track ties should be chestnut, oak, or hard pine. Locust 
 ties are very serviceable, but it is not probable that they can be had in sufficient 
 numbers to meet the demand. In case these woods are not to be had, other 
 woods will naturally take their place, but if such is the case their faces should 
 be enlarged. Sawed ties are not as durable as hewed ties with the bark removed. 
 
 On cross-entries where 20- to 30-lb. rails are used, the ties may have a 4- to 
 6-in, face and be 4 to 5 in. thick. In rooms, the ties need only be faced 3 or 4 in., 
 or sufficient to form a flat surface for the rail to rest on. 
 
 Steel ties for mine use are a comparatively recent introduction. In some 
 cases, channel or even I beams are used to which the rails are bolted, but the 
 common form of steel tie consists of some special rolled shape, frequently 
 corrugated, provided with a lug under which the outside edge of the base of 
 the rail fits. The rail is held in position by a clip that presses against the 
 inside base. In order to prevent slipping, the ties have small projections, 
 on the bottom, that cut into the floor. Owing to their thinness, steel ties 
 materially reduce the amount of brushing necessary in low seams. 
 
HAULAGE 
 SIZES AND QUANTITIES OF SPIKES* 
 
 769 
 
 
 
 Quantity 
 
 
 Size 
 Measured 
 Under 
 Head 
 Inches 
 
 Average 
 Number 
 
 oFloO Lb. 
 
 
 
 Weight of 
 Rail per 
 Yard 
 Pounds 
 
 Per 1,000 Ft. 
 
 Per Mile 
 
 
 
 
 I 
 
 
 
 Pounds 
 
 Kegs 
 
 Pounds 
 
 Kegs 
 
 
 2*Xf 
 
 1,342 
 
 300 
 
 1 
 
 
 1,575 
 
 71 
 
 8 to 16 
 
 3 Xf 
 
 1,240 
 
 324 
 
 1 
 
 
 1.710 
 
 8| 
 
 16 to 20 
 
 31X| 
 
 1.190 
 
 340 
 
 1 
 
 
 1,780 
 
 9 
 
 16 to 20 
 
 4 XI 
 
 1,000 
 
 360 
 
 Ij 
 
 
 2.090 
 
 10* 
 
 16 to 25 
 
 3JX& 
 
 900 
 
 445 
 
 2 J 
 
 
 2,350 
 
 11 
 
 16 to 25 
 
 4 X& 
 
 720 
 
 550 
 
 2- 
 
 
 2,910 
 
 14f 
 
 20 to 30 
 
 4*XA 
 
 680 
 
 590 
 
 3 
 
 
 3,110 
 
 15l 
 
 20 to 30 
 
 4 XI 
 
 600 
 
 670 
 
 3> 
 
 1 
 
 3,520 
 
 17f 
 
 25 to 35 
 
 4iXj 
 
 530 
 
 750 
 
 3 
 
 
 3,960 
 
 20 
 
 30 to 35 
 
 5 X* 
 
 450 
 
 880 
 
 4i 
 
 
 4,660 
 
 23 1 
 
 35 to 40 
 
 5 X& 
 
 400 
 
 980 
 
 5 
 
 
 5,170 
 
 26 
 
 40 to 55 
 
 5JX 
 
 375 
 
 1,112 
 
 Si 
 
 5,870 
 
 29| 
 
 45 to 100 
 
 NOTE. In ordering spikes, a reasonable allowance should be made for waste 
 For ordinary mine tracks with two spikes to the tie, divide by 2 the quantities 
 given in the table. For other spacing than 2 ft., proceed as follows: For 
 30 in., multiply the quantity of spikes by .80; for 28 in., by .858; for 26 in. by 
 .893; for 22 in., by 1.092; for 20 in., by 1.20; and for 18 in., by 1.334. 
 
 NUMBER OF TRACK BOLTS IN A KEG OF 200 LB. 
 
 Bolts 
 
 Size of Nuts 
 
 Bolts 
 
 Bolts 
 
 Size of Nuts 
 
 Bolts 
 
 Inches 
 
 Inches 
 
 in Keg 
 
 Inches 
 
 Inches 
 
 in Keg 
 
 
 X4i 
 
 H 
 
 square 
 
 195 
 
 
 X2* 
 
 1 square 
 
 654 
 
 
 X4 
 
 1 
 
 square 
 
 200 
 
 
 X3* 
 
 1 1 hexagonal 
 
 170 
 
 
 X3J 
 
 11 
 
 square 
 
 208 
 
 
 X3| 
 
 If hexagonal 
 
 237 
 
 
 
 11 
 
 square 
 
 216 
 
 
 
 1* hexagonal 
 
 228 
 
 
 X4 
 
 1 
 
 - square 
 
 305 
 
 
 X4 
 
 If hexagonal 
 
 220 
 
 
 X3i 
 
 1 
 
 square 
 
 329 
 
 1X3* 
 
 1 hexagonal 
 
 415 
 
 *X3* 
 
 1 square 
 
 576 
 
 
 
 
 SPACES BETWEEN ENDS OF RAILS 
 
 Temperature 
 When Laying 
 Track 
 
 Space to be 
 Left Between 
 Ends of Rails 
 Inch 
 
 Temperature 
 When Laying 
 Track 
 
 Space to be 
 Left Between 
 Ends of Rails 
 Inch 
 
 90 above zero 
 70 above zero 
 50 above zero 
 
 ! 
 
 30 above zero 
 10 above zero 
 10 below zero 
 
 1 
 
 * In this table the ties are placed 2 ft. center to center and four spikes are 
 placed in each tie. 
 49 
 
770 HAULAGE 
 
 FEET, BOARD MEASURE, IN MINE TIES OF VARIOUS LENGTHS 
 
 
 Length of Tie 
 
 Size of Tie 
 
 
 Inches 
 
 4 Ft. 
 
 5 Ft. 
 
 5 Ft. 
 
 6 Ft. 
 
 6 Ft. 
 
 7 Ft. 
 
 7 Ft. 
 
 8 Ft. 
 
 
 6 In. 
 
 OIn. 
 
 6 In. 
 
 OIn. 
 
 6 In. 
 
 OIn. 
 
 6 In. 
 
 OIn. 
 
 3X 5 
 
 5.6250 
 
 6.2500 
 
 6.8750 
 
 7.5000 
 
 8.1250 
 
 8.7500 
 
 9.3750 
 
 10.0000 
 
 4X 5 
 
 7.5000 
 
 8.3333 
 
 9.1667 
 
 10.0000 
 
 10.8333 
 
 11.6667 
 
 12.5000 
 
 13.8333 
 
 5X 5 
 
 9.3748 
 
 10.4167 
 
 11.4583 
 
 12.5000 
 
 13.5416 
 
 14.5833 
 
 15.6250 
 
 16.6667 
 
 4X 6 
 
 9.0000 i 10.0000 
 
 11.0000 
 
 12.0000 
 
 13.0000 
 
 14.0000 
 
 15.0000 
 
 16.0000 
 
 5X 6 
 
 11.2500 
 
 12.5000 
 
 13.7500 
 
 15.0000 
 
 16.2500 
 
 17.5000 
 
 18.7500 
 
 20.0000 
 
 6X 6 
 
 13.5000 
 
 15.0000 
 
 16.5000 
 
 18.0000 
 
 19.5000 
 
 21.0000 
 
 22.5000 
 
 24.0000 
 
 5X 7 
 
 13.1250 
 
 14.5833 
 
 16.0418 
 
 17.5000 
 
 18.9583 
 
 20.4167 
 
 21.8750 
 
 23.3333 
 
 6X 7 
 
 15.7500 
 
 17.5000 
 
 19.2500 
 
 21.0000 
 
 22.7500 
 
 24.5000 
 
 26.2500 
 
 28.0000 
 
 7X 7 
 
 18.3748 
 
 20.4167 
 
 22.4582 
 
 24.5000 
 
 26.5416 
 
 28.5833 
 
 30.6250 
 
 32.6667 
 
 6X 8 
 
 18.0000 
 
 20.0000 
 
 22.0000 
 
 24.0000 
 
 26.0000'28.0000 
 
 30.0000 
 
 32.0000 
 
 7X 8 
 
 21.0000 
 
 23.3333 
 
 25.6667 
 
 28.0000 
 
 30.3333 ! 32.6667 
 
 35.0000 
 
 37.3333 
 
 8X 8 
 
 24.0000 
 
 26.6667 
 
 29.3333 
 
 32.0000 
 
 34.6667 37.3333 
 
 40.0000 
 
 42.6667 
 
 7X 9 
 
 23.6250 
 
 26.2500 
 
 28.8750 
 
 31.5000 
 
 34.1250 36.7500 
 
 39.3750 
 
 42.0000 
 
 8X 9 
 
 27.0000 
 
 30.0000 
 
 33.0000 
 
 36.0000 
 
 39.0000 42.0000 
 
 45.0000 
 
 48.0000 
 
 9X 9 
 8X10 
 
 30.3750 33.7500 37.1250 
 30.0000 33.3333 36.6667 
 
 40.5000 
 40.0000 
 
 43.8750 47.2500 
 43.3333 ! 46.6667 
 
 50.6250 
 50.0000 
 
 54.0000 
 53.3333 
 
 9X10 
 
 33.7500 
 
 37.5000 
 
 41.2500 
 
 45.0000 
 
 48.750052.5000 
 
 56.2500 
 
 60.0000 
 
 10X10 
 
 37.5000 
 
 41.6667 
 
 45.8333 
 
 50.0000 
 
 54.1667 
 
 58.3333 
 
 62.5000 
 
 66.6667 
 
 NUMBER OF TIES PER 1,000 FT., AND PER MILE OF TRACK 
 
 Distance, Center to Center, in Inches 
 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 1,000ft 
 
 667 
 
 600 
 
 545 
 
 500 
 
 462 
 
 429 
 
 400 
 
 1 mi 
 
 3,520 
 
 3 168 
 
 2880 
 
 2,640 
 
 2,437 
 
 2,267 
 
 2,112 
 
 
 
 
 
 
 
 
 
 EXAMPLE. How many feet, board measure, in the ties required to lay 
 1,500 ft. of track, the ties being 6 ft. 6 in. long, 5 in.X6 in., and spaced 22 in. 
 
 between centers? 
 
 SOLUTION. 1,500 
 ft. = 1.5 thousands of feet. 
 From the two tie tables, 1 .5 
 X546X 16.25 = 13,308.75, 
 -say r 13,500 t. JB. M. 
 
 Entry Switches. In 
 large mines, the switches 
 connecting the main-road 
 tracks with those of the 
 cross-entries are of the 
 standard surface railroad 
 type, as described under 
 the heading Railroad Sur- 
 veying. In smaller mines, 
 the layout shown in Fig. 
 1 is commonly employed. 
 It will be noted that what 
 is known as a cast frog 
 
 p IG . i ^ is used and that the latch 
 
 rails are pivoted or bolted 
 
HAULAGE 
 
 771 
 
 FIG. 2 
 
 and so are not sprung into place as on surface roads. Owing to the limited 
 
 room for side tracks on mine roads, the lead of the switches is commonly much 
 
 less than on surface roads and generally consists of but a single length of rail. 
 
 Where either motor 
 
 or rope haulage is 
 
 used, the lead is 
 
 greater than where 
 
 the hauling is done 
 
 with mules. In this 
 
 latter case, the 
 
 switch rails may be _ JJ |f[f| flffl] (l||j < 
 
 any length up to 
 about 15 ft., de- 
 pending on the lead. 
 On side entries, the 
 length of the switch 
 points is frequently 
 but 2 or 3 ft., when 
 they are known as 
 latches. These 
 latches may con- 
 sist of a piece of 
 bar iron tapered to 
 a point so as to fit 
 more snugly against the rail, and may be held in place by a bolt through a 
 hole in the end. 
 
 The stub switch shown in Fig. 2 is in common use where mule haulage 
 is still employed, as it is much cheaper than the standard split switch, and 
 answers every purpose where speeds are low. The rails a and b are free to 
 swing from a point a little to the left of the last bridle, and their points slide 
 on flat iron plates spiked to the switch tie, which is broader and thicker than 
 the other ties. The frog may be of the plate or cast type, or may be made by 
 bending the rails composing the switch as shown in the figure. 
 
 Frogs. On first-class main roads, either standard types of surface railroad 
 
 frogs or plate 
 frogs, as shown 
 in Fig. 3, are 
 employed. The 
 latter consist of 
 rails of the same 
 section as those 
 used on the mine 
 FlG. 3 track, shaped 
 
 as shown in the 
 
 cut, and riveted to a heavy iron plate, usually i in. thick. The frog rails 
 are fish-plated and bolted to the track rails, and the plate is spiked to the ties 
 either at its sides or through holes in the plate. While these plate frogs may 
 be made by any competent blacksmith, it is much cheaper to buy them. 
 
 One form of cast frog is shown in Fig. 4 and another placed in a turnout 
 in Fig. 1. These frogs are cast in one piece and are inexpensive, but can only 
 be used for temporary work, as they soon work loose from the tie and require 
 constant attention. It is very difficult to get a straight workmanlike connec- 
 tion between them and the track rails, as they are not fish-plated thereto. 
 When the spikes once work loose, the ties must be shifted to bring new wood 
 under the lugs, as the spikes will not hold in the same holes. However, cast 
 frogs are largely 
 used on room entries 
 where mule haulage 
 is employed. The 
 frog shown in Fig. 
 5 is made by weld- 
 _ ing or bolting to- 
 
 FlG - 4 gether two rail ends FIG. 5 
 
 beveled so that they fit properly. An oak block a placed in the frog angle 
 between the rails helps to stiffen it. 
 
 Room and Branch Switches. In mines of large capacity where motor 
 haulage is employed on the cross-entries and gathering is done with motors, 
 the room switches are laid as carefully as those on the main haulage road, 
 
772 
 
 HAULAGE 
 
 with plate frogs, points, etc. The following figures show various forms of simple 
 switches often used where the cars are pushed by hand or hauled by mules, but 
 which cannot be used where motor haulage is employed. 
 
 Fig. 6 shows a room switch with a cast-iron frog / and fixed points a and b. 
 The advantages of this switch are fixed 
 points and the time saved when bringing 
 cars from the rooms. Unless the point a is 
 in line with the main track, the point b is 
 liable to derail the car or cause it to run into 
 the switch. This, however, can usually be 
 avoided by making the rail c somewhat 
 lower than the rail a, thus causing the car 
 while passing to cling to the rail c, and 
 readily pass between the point b and the 
 rail c, and at the same time causing the 
 wheel on the opposite side to take the rail a. 
 Another great trouble experienced with this 
 kind of switch is that where the wheels 
 
 FIG. 6 
 
 are allowed to remain on the cars after grooves have been worn in their treads, 
 the wheel will invariably follow the rail d. The point b should be higher 
 than the rail c, so that the tread of the wheel will not strike the rail c while 
 the car is leaving the switch. The rail c being lower than the rail a, it is 
 obvious that when a car is to be taken into the switch, the driver will have to 
 push the car toward the rail d, so that the wheel will take the rail b and the 
 flange of the wheel on the opposite side will pass between the point a and the 
 rail d. This form of switch is not applicable in the case of mechanical haul- 
 age, because it does not give an unbroken main line, which is essential to the 
 Steady movement of the trip. 
 
 -fill (U ill 
 
 FIG. 7 
 
 FIG. 8 
 
 The switch shown in Fig. 7 has loose latches b. Instead of a frog, a frog 
 latch c is used, which requires the lead rail a to be raised a certain height above 
 the rail of the main track, so that the latch c can be thrown across this rail. 
 The latch c is held in position at one end by a strong bolt, and at the other 
 end by a piece of iron spiked to a plank underlying the frog, as shown. By the 
 use of this switch, the main track is broken only at the point of switch. 
 
 Fig. 8 shows a form of switch giving an unbroken main track. The lead 
 rail of this switch has a fixed point; a frog latch c is used similar to that shown 
 in Fig. 7, and a switch latch a is 
 used on the follower rail. This 
 latch has a slight projection on its 
 under side to prevent its slipping off 
 the rail of the main track when in 
 use. This form of latch is unde- 
 sirable, since, if, by the negligence 
 of the driver the latch is not re- 
 moved after being used, it will 
 derail cars on the main road, since 
 
 it is not easily pushed aside by a _ Q 
 
 car passing out. r IG. 9 
 
 Fig. 9 shows a rough arrangement where a turnout or any other condition 
 requires the temporary use of a switch. The ordinary form for narrow gauges 
 consists of a movable rail a, about 6 ft. long, pivoted on a center ft. Where 
 the curve is not great, this arrangement acts admirably where cars are pushed 
 by hand, but for mule or locomotive haulage it is not recommended. The 
 dotted line shows the position of the rail a when the straight road is in use. 
 
HAULAGE 
 
 773 
 
 Fig. 10 shows a switch for permanent tracks in coal mines. No frog or 
 latch is required. By turning the lever h, the throw rod o moves the cranks ikm, 
 so that the rails r will face the rail df, the rail n will face the rail b, and the 
 rail g will face the rail/. The lead and other rails can be reduced to any required 
 length to suit circumstances. When the lead rail/d is from 12 to 16 ft. long, 
 and the other lengths are in proportion, the switch gives excellent results. It 
 should not be made of less than 20-lb. rail, and heavier will be better. The 
 objection to this switch is that the point of curve comes where the stub ends 
 of the rails face each other and the angle formed causes the car to lurch. 
 
 Diamond Switch. What is called a diamond switch in trackwork 
 is a double crossover, such as is shown in Fig. 11 (a), (6), and (c). The laying 
 out of a diamond switch is similar, as far as the calculation is concerned, to 
 the laying out of a turnout switch. A simple method, and one that is often 
 used in mine work, especially where track room is limited, is as a follows: 
 
 Through a central point a. Fig. 11 (a), midway between the two tracks, 
 draw two straight lines at right angles to each other, each making an angle 
 of 45 with the track rails. Extend these lines until each intersects lines drawn 
 through the points of switch c\, cz, cs, and a to which the latches come, if used, 
 and at right angles to the track rails at these points. These intersecting points 
 are the centers of the turnout curves, and are marked d\, dz, dz, and d^, respec- 
 tively. Where the diagonal lines cross the inner rails of the two tracks, bi, bz, bz, 
 and &< are the main-rail frog points. 
 
 It is evident that, in this construction, according to the distance between 
 the track centers, the diamond-frog points, at each side of the diamond, will 
 lie between the two tracks, as shown in (c), or they will be coincident with the 
 two inner rails of these tracks, as shown in (b), or they will lie within the track 
 rails, as shown in (a). 
 The position of these 
 frog points depends on 
 the length of the cross- m 
 ing or the distance be- 
 tween the opposite 
 switch points measured 
 on the main rail, as com- 
 pared with the distance 
 between the track cen- 
 ters. 
 
 Notes on Tracklay- 
 ing. As explained un- 
 der the heading Survey- 
 ing, it is advisable to 
 
 p IG 
 
 have the points (sights, sight plugs, strings, etc.) on which the entries are 
 driven set such a distance from the rib that they come over one of the 
 rails and may thus be used to aline the track. The distance the points 
 are set from the rib depends on the width of the car but is commonly from 
 2 ft. to 3 ft. By keeping one rail in line with the plugs, the ample and uniform 
 clearance demanded by the laws of most states may be maintained between the 
 side of the car and the other rib. 
 
 It is not customary to lay the permanent track as fast as the entries are 
 driven. Light rails spiked to widely spaced and unballasted ties laid on the 
 floor are used at first, and after the entry has advanced three or four rail 
 lengths (90 to 120 ft.) the permanent track is laid. 
 
 Before the ties are put down, the roadbed should be surfaced and brought 
 to grade. While this is not always done, it is the better practice except where 
 surfacing material must be brought from a distance, because by so doing the 
 roadbed will be firm from the outset and will not require attention because 
 of subsequent settling. 
 
 After the ties are placed at about the proper spacing, the rails are placed 
 upon them and fish-plated together. The ends of the ties should be lined 
 up so that on some one side their ends project a uniform distance, say 8 or 10 in. 
 from the rail. A preliminary lining up is given by the sight strings and before 
 the rails are laid in position, but the final lining of the ends of the ties is done 
 by measuring with a foot rule as the rail is about to be spiked to the tie. After 
 the rail lengths on one side of the entry are spiked, the rails for the other side 
 are laid in place and fish-plated together, and before being spiked are brought 
 to gauge. 
 
 In first-class entry work the track is ballasted with crushed stone as in 
 surface railroad practice and surfaced with finer material of the same kind. 
 
774 
 
 HAULAGE 
 
 Neither draw slate nor bottom rock make satisfactory ballast, particularly if 
 the mine is wet, as they soon disintegratein to an impervious clay that holds 
 water and becomes soft and mushy, a condition that results in the track soon 
 being out of line and grade. Under no circumstances should coal or bone 
 be used for ballast, as they soon are ground into powder and furnish an excellent 
 material for the propagation of a dust explosion. 
 
 In side-entry work, where the track is not ballasted and the ties are laid 
 upon a fireclay floor that is wet, they soon sink into it, and if animals travel 
 over such a roadbed, it soon becomes muddy and affords an insecure footing. 
 
 Where depressions in 
 the floor allow water to 
 accumulate, this state 
 of affairs is particularly 
 apt to occur, so that 
 especial attention 
 should be paid to the 
 ditching in order to drain 
 off the water. If the 
 water comes from the 
 roof and drips on the 
 track, the soft clay must 
 be dug out and ashes 
 substituted. The ashes 
 may absorb the moisture 
 and dry the fireclay to 
 such an extent as to 
 make the roadbed ser- 
 viceable, but in case 
 they do not, additional 
 ties should be put in so 
 that they are close to- 
 gether. If it is neces- 
 sary to place the ties 
 close together when the 
 road is first laid, only 
 a part of the ties are 
 spiked to the rails un- 
 til the track and bed 
 have been put in shape; 
 then the rails are spiked 
 fast to the other ties. 
 This forms a corduroy 
 roadbed and will afford 
 a fair roadbed and 
 track, although it may 
 need overhauling from 
 time to time as the clay 
 swells up and mixes 
 with the cinders. 
 
 In some mines that 
 have soft clay bottoms, 
 it is the custom to lay 
 mudsills of 3"X12" 
 plank parallel with the 
 track and on these to 
 place the cross-ties. The 
 planks are sometimes 
 placed skin to skin ; the 
 same care, however, is 
 necessary in this as in 
 the former case to pro- 
 
 FIG. 11 - 
 
 vide for drainage and to prevent the clay oozing up between the planks. 
 The ordinary spacing of ties on main entries is from 18 in. to 2 ft., measured 
 between the centers of the adjacent ties. In speaking of the spacing of ties, 
 the distance between the edges of the ties is sometimes used instead of the 
 distance between centers. Thus, if the ties have an 8-in. face and are spaced 
 2 ft. from edge to edge, there will be 2| ft. between the centers, which is too 
 great a distance for a roadbed on which there is a heavy traffic. 
 
HAULAGE 775 
 
 On cross-entries where mule haulage is employed, a distance of 2 to 3 ft. 
 between centers is allowable where 30-lb. rails are used. Ties for room track 
 have a 3- to 4-in. face and sufficient thickness to take the spike, and are placed 
 from 3 to 4 ft. apart, where the cars are pushed by hand, but where motors 
 enter the rooms the ties must be spaced as in entry work, but ballasting and 
 grading is rarely necessary. 
 
 On room entries, it is advisable to lay the room switches at the same time 
 the permanent track is put down. This prevents any subsequent interference 
 with traffic and, further, the work can be done much better when the track- 
 layers are not stopped by passing trips. If the rooms are driven on points set 
 a uniform distance apart along the entry, the room sight plugs may be used 
 by the tracklayer as a guide in placing the frogs. In many mines where the 
 rooms are evenly spaced and a standard frog, etc. are used, the entire switch 
 is purchased, all the lead, follower, switch, and point rails being cut to an 
 exact length and properly drilled for plating and bonding. This is a great 
 help toward securing a first-class track, as the frog at No. 1 room haying 
 been placed exactly, those on the rooms inside must of necessity come right. 
 
 Unless the pillars are to be drawn as soon as the rooms reach their limit, it 
 is customary to take up the room tracks and in some cases the frogs on the 
 entry, relaying them when pillar drawing is about to begin. Whether this is 
 a wise policy depends on circumstances. In wet mines where the rails may be 
 eaten by acid water, or where the roof is bad and the track is apt to be buried 
 under falls, or when 5 or 10 yr., or more may elapse before pillar drawing 
 begins, it is advisable to remove the rails from worked-up rooms and to use 
 them elsewhere. But where the mine is comparatively dry, the roof good, and 
 pillar drawing will begin in a year or two, the rails had better be left in place, 
 as the cost of taking up and relaying them will more than offset the interest 
 on the idle capital. 
 
 Rails should be stacked and not thrown in irregular piles. Three heavy 
 timbers should be laid upon level ground in such a way that they support the 
 ends and centers of the rails, which are placed side by side upon them. When 
 one row of rails is filled, additional and lighter timbers are laid upon it, and 
 another row filled, and so on, untiUhe stock on hand is neatly piled, each length 
 by itself. Ties-should be stacked in a similar way to props, as explained under 
 the heading Timbering. Both ties and rails are better kept outside the mine, a 
 day's or a week's supply being brought in at intervals as needed. 
 
 ANIMAL HAULAGE 
 
 Selection of Stock. While horses and ponies are generally used abroad 
 for mine haulage, mules are preferred in the United States, as being hardier, 
 less nervous, and more easily broken to their work. Large heavy mules with 
 long backs and relatively short legs can exert their strength to greater advantage 
 than short-bodied long-legged ones, although this is not always admitted. 
 Mere weight is not an indication of strength, as it may be due to fat, but a good 
 working weight, say up to 1,400 Ib. without clumsiness or thick hocks, is to be 
 desired in a mule. Perhaps the best mules come from Missouri and Kentucky 
 and, for mine use, have an average weight of about 1,200 Ib. and a height of 
 about 16 hands. 
 
 Mules from 4 to 6 yr. of age that have been worked are easier to break to 
 mine work than those without training of any kind. Mules are naturally 
 influenced by changes of water, diet, altitude, etc., and before being tried in 
 a mine should be given ample time to become accustomed to their new condi- 
 tions. If this was always done, probably a much smaller number would be 
 rejected as being unsuited to mine work, for a mule cannot be expected to work 
 when it is not well. 
 
 While some mules give absolutely no trouble when first taken into the mine 
 and will pull loads from the outset, the average mule has to be broken, and for 
 this purpose should be handled by two men, the driver and an expert in manag- 
 ing stock. At ffrst, the load should be light, the trips short, and the mule 
 not worked for more than 2 or 3 hr. The load, length of trip, and number of 
 hours worked may be increased daily. When properly harnessed and cared 
 for and, above all, kindly treated, the average mule soon learns his duties, 
 will back up to the trip without command, and will follow his driver's call 
 or whistle. 
 
 Feeding Mules. Mr. H. W. Hughes, gives the average daily ration at an 
 English colliery for 80 horses averaging 15 hands high, the figures covering 
 
776 HAULAGE 
 
 a period of 8 yr., as follows: Grain, 7.25 lb.: bran, 9.25 lb.; hay, 18.75 lb.; 
 total, 35.25 lb. The grain was composed of beans, 3 lb.; maize (corn), 2.75 lb.; 
 and oats, 1.50 lb. The last item was hay, 14 lb.; clover, 1 lb.; and straw, 
 3.25 lb. 
 
 The American mule appears to be fed about two-thirds as much as the 
 English horse. Mr. Chas. E. Bowron, gives the food allowance for mules at 
 several mines in Alabama and Tennessee, the first figures being pounds of hay 
 and the second, pounds of grain: 9.54 and 17.44, 7.92 and 19.20, 7.94 and 
 15.04, and 12.62 and 15.50. The total daily food allowance in these cases was 
 26,98, 27.12, 22.98, and 28.12 lb., respectively. It will be noticed that the 
 weight of the hay was about one-half that of the grain, reversing the usual 
 
 ractice. Mr. Bowron further gives the allowance for army mules during the 
 panish- American war as hay 14 lb. and grain 9 lb., and for the horses hay 
 14 lb. and grain 12 lb. 
 
 In the anthracite regions of Pennsylvania, the average ration for mules 
 from 1,000 to 1,200 lb. in weight is 12 lb. of grain and 15 lb. of hay. The 
 composition of the grain varies from two-thirds cracked corn and one-third 
 oats, to equal proportions of each. Corn is richer in fat-producing elements 
 than oats and is fed to give strength, but too much grain will cause acute 
 indigestion, paralysis of the walls of the stomach, and usually results in death. 
 A feed of bran once a week is recommended as a laxative: also a handful of pure 
 coarse ground salt twice a week. 
 
 Mules should be fed three times a day, although some large companies feed 
 but twice daily. On idle days, the food allowance may be reduced 25 to 30%. 
 Hay is digested chiefly in the intestines and grain in the stomach, hence, if 
 possible, a mule should be first watered, then given hay, and lastly grain. If 
 the water is given last, it washes the food into the intestines before it is acted 
 on by the gastric juices in the stomach. If the hay is given after the grain, 
 it carries the grain with it into the intestines. This order of feeding is not 
 always practicable in a mine and it is of advantage to place watering troughs 
 about the mine so that the mules can be watered during the day while at 
 work. As the feed is in the boxes when a mule is put in the stable at night, 
 there should also be water in his water trough so that he can drink at intervals 
 while feeding. Fresh food should never be placed on top of any left over from 
 the previous feeding. A mule should have plenty of water the first thing in 
 the morning, and care should be taken to have the water pure and the troughs 
 clean. 
 
 Care of Mules. Mine mules should have clean comfortable quarters, with 
 pure water and food. Their feet and legs should be washed every night and 
 their hocks dried ; and they should be combed regularly. Extreme care should 
 be taken that they are shod properly, and a competent shoer is imperative at 
 mines where many mules are used. If the mine is too small to warrant the 
 constant employment of a veterinarian, arrangements should be made for one 
 to visit the stables monthly to look over the stock, paying particular attention 
 to their feet. 
 
 The stable boss or mine foreman should inspect the harnessing of the 
 mules before they begin work. All parts of the harness must fit properly, 
 particularly the collar, which transmits the weight to the mule's shoulders; the 
 names, to which the traces are attached, should bear evenly upon the collar. 
 The traces should be of equal length and free from knots: many insert a coiled 
 spring between the trace and the car to take up the jar of starting. 
 
 Mules should not be worked more than one shift per day, and if overtime 
 is necessary, should be given a chance to rest the next day. If stabled under- 
 ground, they should, unless the expense is prohibitory, be brought to the 
 surface from the close of work Saturday until Monday morning. This pro- 
 cedure is not only humane, but the fresh air with the chance to run and roll in 
 the pasture and to nibble at the fresh grass, keeps the animals in health, adds 
 to their efficiency, and prolongs their life. 
 
 Estimates of the length of the working life of mine horses and mules vary 
 so widely that it seems impossible to give an average. Mr. Hughes, quoted 
 before, gives the average useful life of horses working in English mines as 
 more nearly 9 than 8 yr. This figure is based on 13 yr. experience at some large 
 collieries and should be considered authoritative. Mules seem to have a 
 much shorter working life than horses. Mr. Bowron assumes the average work- 
 ing life of a mule in the mines of the Birmingham, Alabama, district, to be 6 yr. 
 The records of the Fairmont Coal Co. for 1905, show that in that year, 26% of 
 their stock either died, was killed, or had to be disposed of on account of being 
 crippled or worn out. This shows a working life of between 3 5 and 4 yr. In 
 
HAULAGE 
 
 777 
 
 estimating the cost of mule haulage it is probably well to count on the life of a 
 mule as 5 yr., and that 10% of the stock is in the stable either sick or tempo- 
 rarily disabled. 
 
 Work of Mules. The amount of work that a mule can do is dependent 
 on the strength and condition of the mule, the condition of the track and 
 rolling stock, the relative sizes of paying and dead load hauled, length of trip, 
 presence or absence of grades that may be for or against the loads, etc. Mr. 
 Bowron gives the following figures for mines in Alabama and Tennessee; 
 
 WORK DONE BY MULES 
 
 Group 
 
 Average 
 Haul 
 Mile 
 
 Average 
 Output 
 Tons 
 
 Average Ton- Miles 
 per Mule 
 
 Net 
 Cost per 
 Ton- 
 Mile 
 
 Conditions 
 
 Gross 
 
 Net 
 
 1 
 2 
 3 
 
 4 
 
 .32 
 .37 
 .78 
 .64 
 
 513 
 861 
 502 
 
 887 
 
 12.4 
 24.8 
 41.4 
 38.3 
 
 6.9 
 13.8 
 23.0 
 21.4 
 
 35.7 
 17.9 
 10.7 
 11.5 
 
 Unfavorable 
 Average 
 Best 
 Average 
 
 The average haul is the distance traveled in bringing out the loaded car; 
 the total haul is twice this. In the columns headed Average Ton-Miles Per 
 Mule, the figures under the heading Net are for the paying load of coal hauled. 
 The figures in the column headed Gross are based on the assumption that the 
 car weighs 40% as much as the coal carried, but is carried twice as far. The 
 mines in Group 1 are four in number with unfavorable conditions caused by 
 short hauls, and steep adverse grades. In all but one of these mines, the mules 
 were employed solely for gathering. In the seven mines in Group 2 and the 
 two mines in Group 4, the mules were employed only for gathering, and average 
 conditions preyailed, the mines being fully developed, the hauls of fair length, 
 and the track in reasonable shape, etc. In the three mines of Group 3, mules 
 were used both for main-line haulage and gathering. A comparison of Group 2 
 with Groups 3 and 4 shows that better results are obtained when the hauls are 
 of fair length, as less time proportionately is taken up in changing trips. 
 
 It is estimated that a horse or mule will exert a tractive effort equal to 
 one-fifth of its weight at a speed of 2 to 4 mi. an hr. for 1,000 to 1,200 hr. per yr.. 
 say for 4 to 5 hr. per da. in a mining year of 200 to 220 da. In starting a load 
 from rest, a much greater effort is exerted for a limited time. 
 
 When gathering single cars, where the most distant room is not much over 
 J to | mi. from the parting, a mule should make two to three round trips per 
 hour, and bring in fifteen to twenty-five loads per day. In seams of moderate 
 thickness where the cars hold, say, 1.5 T., this means the delivery of a paying 
 load of from 22.5 to 37.5 T. per da. In thick seams, where the load is 2.5 
 to 3 T., the production per mule will vary between 60 and 75 T. 
 
 In hauling from an inside parting to the drift mouth, where the distance 
 is from to J mi., and the grades are such that a mule can haul two loaded 
 cars, one animal will deliver from thirty to forty loaded cars per day, equivalent 
 to a paying load of from, say, 45 to 100 T., depending on the size of the car. 
 
 These results cannot be obtained unless the management is competent, 
 and sees to it that the rails, roadbed, and cars are in first-class condition, that 
 the miners are properly distributed so that there are no unnecessary delays at 
 the face in waiting for loads, and that the mules are well fed, well shod, and 
 properly cared for. 
 
 When the seam is pitching and the entries are crooked with irregular grades 
 and the track is soft, as in the anthracite fields of Pennsylvania, no average 
 figures can be given because the conditions vary so from mine to mine, but, in 
 general, the efficiency of a mule is about one-half that of the same animal in 
 flatter and more regular seams. 
 
 Cost of Mule Haulage. In order to compare the cost of haulage at one 
 mine with that at another, haulage costs should be given in cents per ton-mile; 
 that is, the cost of hauling 1 T. of coal 1 mi. Further, the underground con- 
 ditions should be known, for it is possible that there is greater efficiency where 
 the cost is, say, 15 c. per T.-mi., than where it is but 10 c. 
 
778 HAULAGE 
 
 The cost of mule haulage is made up of three items; depreciation, feed 
 and care, drivers' wages. 
 
 If ten working mules per day are required for a given tonnage, eleven must 
 be provided, as one is practically certain to be laid up for the time being, either 
 sick or crippled. If the life of an American mine mule is but 5 yr., and his 
 cost is $250, $55 must be allowed annually per working mule for renewals, on 
 the basis that 10% of the stock is idle. 
 
 If the mule is fed 12 Ib. of corn and oats in equal proportions and 15 Ib. of 
 hay per day, his total food consumption will be 5,475 Ib. of hay and 2,190 Ib. 
 each of oats and corn per year. At $25 per T. for hay, 45 c. per bu. of 32 Ib, 
 for oats, and 80 c. per bu. of 56 Ib. for shelled corn, the individual cost of these 
 items will be $68.44, $30.80, and $31.29, or a total of $130.53 per yr. Allowing 
 for the feed of the idle mule, the annual cost per working mule will be $144.06. 
 The wages of the stable boss, harness, shoeing, services of veterinarian, etc., 
 will be fully $60 per yr. per mule at large mines and from $100 to $125 per yr. 
 at small ones. Allowing for the idle stock, probably $90 per yr. is a reasonable 
 charge. One working mule will therefore cost $55 for renewals, $144.06 foi 
 feed, and $90 for stable charges, etc., or a total of $289.06 per year of 365 da., or 
 79.2 c. per da. However, the mines do not run 365 da. per yr., the working 
 days averaging about 220. On this basis the fixed charges per working mule 
 per working day will be $289.06-7- 220 = $1.314. To this must be added the 
 driver's wages, which at present vary from $1.75 to $2.50, averaging, say, 
 $2.125, making the total cost per working mule per working day, $3.439. The 
 cost per ton of coal shipped is found by dividing the cost of all the mules by 
 the total tonnage. Thus, if ten mules at a total cost of 10X $3.439 = $34. 39 
 handle an output of 900 T., the cost per ton is $34.39 -f- 900 = 3.821 c. If 
 the average distance hauled is f mi., the cost per ton-mile per ton of output 
 is 3.821 X = 10.189 c. Since each mule delivers an average of 90 T hauled 
 f mi., the ton-mileage per mule is 90X1 = 33.75. Assuming the cars to 
 hold 2.5 T., the output requires the delivery of 900-7-2.5 = 400 cars per da. 
 If the cars weigh 1 T. each, the total weight handled by the ten mules per 
 day will be, coal 900 T.; outbound loaded cars 400 T.; inbound empty cars 
 400 T.; or a total of 1,700 T. hauled f mi. at a cost of $34.39. This is equiva- 
 lent to 637.5 T. hauled 1 mi. for ten mules, or 63.75 T.-mi. per mule, at a 
 cost of $34.39-7-1,700 = 2.02 c. per T. gross (cars and coal) of material hauled, 
 and $34.39-7-637.5 = 5.4 c. per T.-mi. 
 
 The haulage costs given by Mr. Bowron in the preceding table are based 
 on drivers' wages of $1.762; depreciation $25 per mule per year; feed and 
 stable attendance 34.9 c. per da. for 365 da.; interest 3.3 c. per da. for 365 da.; 
 making the total cost per working mule per working day, of which there were 276 
 in the year, $2.46. 
 
 In the reports of some coal mining companies, a charge of 50 c. per da. per 
 mule is made for all items other than drivers' wages. This is, obviously, 
 altogether too little. 
 
 Safe Grade for Mule Haulage. While the grade against empties on the 
 main haulways can be 1.5% the grade on cross-entries should not exceed .5 
 to 1%, where mules must gather cars in a hurry. If the mules are winded in 
 taking in empties, the loaded cars must necessarily come out slower, so that the 
 advantage gained by quick delivery of empty cars is offset by the loss of time 
 in returning the loaded cars. Often mine mules are injured by winding them 
 and then not giving them time to recover their breath for the return trip. The 
 driver has not so much control over his car and animal that he can stop instantly, 
 and if the mule lags or stumbles, the car will probably run against the mule and 
 injure its legs. A safe down grade for mule haulage should not exceed 3% and 
 great care will be needed in that case. On such steep grades, while the mule 
 can pull up the ordinary mine car, the brakeman or driver should run the car 
 down independent of the mule. A loaded mine car will slide on rails even 
 with four wheels spragged when the grade is 6 to 8% , depending on the condition 
 of the rails. 
 
 SELF-ACTING INCLINES* 
 
 In a self-acting incline, otherwise known as a gravity incline, gravity plane, 
 or simply, as an incline, the weight of a loaded car descending an inclined plane 
 is utilized to raise an empty car. In hilly regions, where the coal seams outcrop 
 at a considerable elevation above the valley, inclines are in common use to lower 
 
 * See also Slope Bottoms. 
 
HAULAGE 779 
 
 |; the loaded cars from the mine to the tipple. They are also, but far less fre- 
 ; quently, used underground to lower loaded cars from one level to another. 
 
 Tracks, Switches, Etc. The tracks upon inclines may be arranged in one 
 
 > of three ways. The best arrangement consists in two separate tracks thrpugh- 
 
 > out the entire length of the incline. Where the amount of coal handled is not 
 I large or where the capital is not available, it is quite common to use three rails 
 \ both above and below a parting or turnout midway of the incline where there 
 
 are four rails. That is, both above and below the parting where there are 
 two independent tracks, the middle rail of the three is common to both the 
 ascending and descending tracks. In the third arrangement, while there are 
 three rails above the parting, there are but two below_it. 
 
 Self-acting switches set by the mine cars are provided at both the top and 
 bottom of the incline where the rails join to form a single track, and similar 
 switches are used at both ends of the turnout on three-rail inclines. Safety 
 switches for derailing runaway cars are frequently used. These are usually 
 of the spring-latch type, which are closed by the ascending empty car and 
 open automatically after it has passed. They are thrown to permit the passage 
 of the loaded car by means of a lever at the head of the incline, the connection 
 between the switch and lever being made by wire or rods in the same manner 
 as that employed on surface railroads to throw distant switches. Safety 
 blocks are used at the top of the incline near the knuckle to prevent the cars 
 running away down the incline before they are attached to the rope. The 
 blocks may be heavy timbers placed by hand, or a more elaborate arrange- 
 ment of iron set by levers or automatically by the cars. 
 
 The weight of the rail used should be proportioned to that of the loaded 
 car. As the incline must last the life of the mine and all the coal shipped 
 must pass over it, rails weighing less than 50 Ib. per yd. are not to be recom- 
 mended where the loaded car weighs as much as 5,000 to 6,000 Ib. Lighter 
 rails may be used for lighter loads, but are hardly to be advised as the smaller 
 sections require a closer spacing of the ties, more attention on the part of the 
 repairmen, and are more apt to be bent in case a runaway trip jumps the track. 
 First-class ties should be used and the roadbed should have a uniform slope 
 and should be well ballasted. In fact, incline tracks should be laid with as 
 good material and with as much care as those on a main entry where motor 
 haulage is employed. In order to prevent the track creeping or sliding down 
 hill on steep pitches, every second or third tie is made long^enough to extend 
 across both tracks and its ends are anchored in hitches cut in the sides of the 
 excavation, are braced by posts firmly planted in the ground, or are held by 
 wire ropes or iron rods fastened to solid objects such as iron bolts sunk in a 
 ledge of rock, large trees, etc. Square notches should be cut in the base of the 
 rail at intervals of 10 or 15 ft. depending on the slope of the incline. These 
 notches should come upon the long or anchor ties, to which the rails are in 
 turn anchored by track spikes through the notches. 
 
 Rollers. Rollers for supporting the rope should be set closer together 
 than upon flat or upon steep inclines. Their distance apart varies from 12 to 
 18 ft., an average spacing being 15 ft. It is better to vary the spacing of the 
 rollers by a foot or more each way from the average, as this will, in a very great 
 measure, prevent the flapping of the rope which is so wearing upon it and 
 the rollers and which is almost sure to occur when the rollers are exactly the 
 same distance apart. The jolting of the cars shakes much coal from them, and 
 this soon fills the spaces between the ties and clogs the rollers and prevents 
 their turning. When the rollers are not free to revolve, the frictional resis- 
 tance to the passage of the rope and the wear upon it and the rollers is very 
 great; consequently, the track around the rollers should be cleaned frequently, 
 sometimes as often as once or twice a day. With tracks in fair shape and 
 rollers 12 to 15 ft. apart, actual tests have shown that the resistance due to 
 the friction of the rope in running empty cars down grades of from 3.8 to 
 6.2%, varied from 6 to 15% of the weight of the rope. 
 
 Ropes, Drums, Barneys, Etc. The strain on the hoisting rope is equal to 
 the force required to accelerate and hoist the load and to overcome friction, 
 and may be calculated by the formula R = F+G+I, as explained under the 
 heading Resistance to Haulage, noting that the weight of the rope must be 
 added to that of the car. As the wear on the rope from passing over idle 
 rollers, trailing on the ground, and the jerks due to dropping the trip over the 
 head of the incline is so great, a much higher factor of safety should be used 
 than in the case of shaft hoisting ropes; 10 is none too large. Ropes for inclines 
 are commonly made with six strands of seven wires each laid around a hemp 
 center (see section on Wire Rope) and those of the lang-lay and locked-coil 
 
780 HAULAGE 
 
 types are often favored because of their larger wearing surface and consequent 
 longer life. The rope is usually attached to the car by a chain 15 to 20 ft. 
 in length, socketed or clamped to the rope and provided with a clevis or hook. 
 Where the pitch is very steep and slope carriages or gunboats are used, bridle 
 chains similar to those used on shaft cages are attached to the corners of the 
 carriage or gunboat and to the rope at some point above the socket. 
 
 Where cars are attached to the rope by couplings they are subject to strains 
 that rack them while being pushed over the knuckle; there is possibility of acci- 
 dent from their running over the head of the incline before the rope is attached ; 
 time is lost in hooking the cars to and unhooking them from the rope; and 
 the rope is liable to be kinked and unduly strained in the hooking-on process. 
 To avoid these causes of wear and danger, it is a common practice, where con- 
 ditions are otherwise favorable, to attach to the end of the rope what is called 
 a barney. The barney consists of a small car or truck running on light rails 
 placed between those of the regular tracks of the incline. At the bottom of 
 the plane, the barney passes into the barney pit so that the mine car may pass 
 over it to the tipple. When cars are being hoisted, the barney comes out of 
 the pit and pushes the cars ahead of it up the incline. Similarly, at the top of 
 the incline, the cars are dropped against the barney and are held back by it 
 as they are lowered. A barney may be built of heavy timber or iron and must 
 have sufficient weight to prevent its being lifted from the track at the bottom 
 of the incline by the weight of the cars pushing against it. The face of the 
 barney should be covered for its full width and height by a sheet of heavy plate 
 iron to afford a wide bearing for the bumpers of the car. Cars intended for 
 use on inclines operated with barneys should have bumpers of larger face than 
 usual so that they may not ride or interlock while being raised or lowered. 
 To avoid the cost of a special track for the barney, one form of this device 
 is provided with wheels which have double grooves on their face and a lateral 
 play on their axles. For most of the trip the outer grooves of the wheels run 
 on the same track as the cars, but at the bottom of the incline the inner grooves 
 engage a supplementary barney track, the wheels are forced inwards on their 
 axles to accommodate themselves to the narrower gauge, and the barney passes 
 into the usual pit. 
 
 At the head of the incline, the ropes pass around a drum set, usually, at 
 such an elevation that the cars may pass under it, one rope winding on the drum 
 as the other winds off. The diameter of the drum is determined by the same 
 rules that apply in the case -of hoisting engines, and its width should be such 
 that when the cars are in the middle of the incline (but not on a turnout in 
 the case of three-rail inclines) the ropes will be in the centers of their respective 
 tracks. If the head of the incline is built upon a trestle, in order to secure 
 strength and steadiness and to avoid massive and expensive construction, it 
 is usual to place the drum below instead of above the car tracks. Where the 
 pitch is steep and a single drum is used upon which one rope winds on at the 
 top and the other winds off at the bottom, the upper rope will be so high if 
 the lead is short (that is, if the drum is near the knuckle) that the cars will be 
 lifted from the track as they drop over the knuckle. This difficulty can be 
 overcome by the use of two drums geared together so as to turn in opposite 
 directions. This allows the ropes to run off the same side of their respective 
 drums and at the same height above the track. The drums can then be placed 
 such a distance back from the knuckle and such a distance above the track that 
 the ropes are tangent to the rollers on the incline. This arrangement calls for 
 the use of two brakes, one for each drum, which, however, may be placed 
 close together on the same stand. Instead of drums, a pair of wheels each with 
 a series of parallel grooves on its face, may be employed. The rope is in one 
 piece and after making several turns around the pair of wheels has its end 
 hitched to the loaded and empty trips respectively or to barneys. These wheels 
 are set below the floor of the drum house at the head of the incline so that they 
 revolve horizontally, and their axles are vertical and in the center line between 
 the two incline tracks. They are made of such a diameter that the ropes are 
 in the center of the tracks; that is, the diameter is equal to the distance 
 between the center lines of the tracks. The greater the tension necessary to 
 prevent the rope from slipping, the greater is the number of grooves; four or 
 six are commonly used. Sometimes, to give a greater bearing surface between 
 the rope and the wheels, the rope is lapped in the form of a figure 8; but this 
 is to be avoided because of the undue bending strain thus thrown upon the rope. 
 
 The brakes controlling the speed of the drums must be very powerful, 
 strongly constructed, and continually watched that they may be in good and 
 effective condition. This is particularly necessary with steep pitches and 
 
HAULAGE 781 
 
 heavy loads, owing to the increase in the momentum as the pitch and the loads 
 increase and to the fact that the load is constantly increasing as the rope on 
 the load side winds from the drum while that on the empty side winds on it. 
 
 Grades and Their Effects. On short inclines where the difference between 
 the weight of the loaded and empty cars is considerable (say, those where the 
 length does not greatly exceed 500 ft. and the load is equal to or greater than 
 the weight of the car), a pitch of 3, equal to a grade of 5.24%, may be sufficient 
 to impart motion to the cars if they and the track are in first-class condition. 
 Where the incline is long or where the weight of the empty car bears a greater 
 ratio to that of the loaded car than that noted, pitches up to 10, or 17.64%, 
 may be necessary to start the trip. The greatest pitches on which cars can 
 generally be run without spilling their contents over the end gate are about 15 
 (26.8%), for cars with topping to 20 (36.4%), for cars loaded level full. In 
 some cases where the seam is thick enough to permit their use, cars with high 
 backs are employed where the incline is steep. Where the pitch exceeds, say, 
 20 and where the breakage of the coal is not objectionable (as where the mine 
 run coal is coked) the contents of several mine cars are dumped at the head of 
 the incline into a large sheet-iron car, or tank, called a gunboat or, sometimes, 
 a skip. These are not detached from the rope and are, of course, run in pairs in 
 balance, and dump or discharge automatically at the foot of the incline into 
 bins or upon screens. When breakage must be avoided and the pitch is too 
 steep to permit the cars being lowered in the usual way, they may be placed 
 upon a platform on wheels attached to the ropes. These platform cars are 
 variously known as slope carriages, dummys, etc. When these are used, the 
 tracks at both the head and foot of the incline are generally at right angles to 
 those on the plane so that the car rests sidewise on the rails of the carriage. 
 The loading and unloading of the carriage is performed in much the same way 
 as on a shaft cage; that is, the loaded car pushes off the empty car at the top 
 of the incline, and the empty car pushes off the loaded one at the bottom. If 
 the car is placed on the carriage endwise on instead of sidewise, particular 
 attention must be taken to lock it securely in place. 
 
 If the cars are attached to the rope in trips, the drawbars must be con- 
 tinuous and they and the couplings must be of heavier metal than in hauling 
 on a level. Further, the steeper the pitch and the longer the trip, the heavier 
 must be the couplings. When barneys are used, special couplings are not 
 necessary. 
 
 Conditions Unfavorable to Use of Inclines. Inclines requiring for their 
 operation a large number of cars, say, six or more, are expensive to operate 
 and maintain. Barneys cannot be used as the bumpers are practically certain 
 to interlock if the cars are pushed up a track that may not be in the best con- 
 dition. Further, as the barney must generally be placed the length of a trip 
 below the knuckle and the trip dropped down upon it, the strain upon the rope 
 and drum from the impact of the cars is so great as to be extremely dangerous. 
 Running a large trip attached to a rope also has objectionable features. The 
 cars must be very heavy in all their parts to withstand the strain upon the 
 couplings as the trip is pushed over the knuckle on the loaded side and as the 
 slack between the empty cars is taken up at the foot of the incline. For this 
 reason, the strain upon the rope and drum is great. The labor required at 
 both the top and bottom to handle such a large number of cars is excessive, 
 and its cost would pay a good interest on a rope haulage plant, retarding car 
 haul, or electric motor for transporting the coal from the mine to the tipple. 
 
 Inclines give excellent results at mines of limited output where the plane 
 is short and one-car trips can be run with barneys, but even under the most 
 favorable conditions it is a question for consideration if they may not well 
 be replaced by a retarding conveyer or car haul. 
 
 Calculations for Self -Acting Inclines. Because the same number of cars 
 is attached to each of the ropes, their weights balance and an incline will be 
 self-acting if the weight of the coal to be lowered is greater than the weight of 
 the rope to be raised together with the weight representing friction and other 
 resistances. The following formulas may be used in solving problems connected 
 with motion on self-acting inclined planes: 
 
 a = -jyg (sin X-fcos X) = " ? v = at, / = ? 
 
 These formulas, with the exception of the first, are the familiar ones appli- 
 cable to all cases of uniformly accelerated motion; s, however, is the length 
 of the incline. Because motion on an inclined plane is due solely to gravity 
 that component of it g sin X that acts parallel to the plane is the measure of 
 
782 HAULAGE 
 
 the acceleration. But this constant acceleration is diminished by the constant 
 resistance of friction fg cos X; whence, the net acceleration is the difference 
 of the two. 
 
 It is apparent that when sin X =/cos X, the plane is in equilibrium with the 
 
 p 
 forces on the two sides balancing, because then o = XgXO = 0, and when there is 
 
 no acceleration there can be no motion. From the relation sin X =/cos X, there 
 results =? =/, whence tan X =/. This is the general formula for equilibrium 
 
 COS A 
 
 on an inclined plane, for when tan X is greater than/, the plane is self-acting; 
 when tan X =/, the plane is in equilibrium ; and when tan X is less than /, the 
 plane is not self-acting and it will require more force than the weight of the 
 coal to overcome the friction. This formula is very valuable in making pre- 
 liminary calculations. 
 
 EXAMPLE. (a) If friction /is 4% (.04), can a plane pitching 2 be made 
 self-acting? (6) Friction remaining the same, can a plane pitching 8 be 
 made self-acting? (c) With friction as before, what is the least pitch at which 
 the plane will be self-acting? 
 
 SOLUTION. (a) Here, tan X = tan 2 = .03492, is less than /=. 04000 and 
 the plane is not self-acting. 
 
 (b) Here, tan X = tan 8 = .14054, is greater than /= .04000, and the plane 
 may be self-acting. 
 
 (c) Here it is required to find the angle of elevation of the plane when its 
 tangent is known. Since tan A"=/=.04000, X = 2 17' 27". At any greater 
 pitch, motion will result and the plane will be self-acting. 
 
 It does not follow, however, that^because motion is possible that a plane 
 can be operated in practice. Thus, in (c), while motion will result when the 
 pitch is increased to, say, 2 30', the number of cars that would have to be 
 handled in a trip would be so very great as to be impracticable from an operat- 
 ing standpoint. ( 
 
 After it has been determined, by the use of the preceding formula, that 
 the pitch is sufficient to permit of the plane being made self-acting, the number 
 of cars required in a trip to start motion on the plane is commonly found from 
 the formula, 
 
 R (sin A-+/COSA-) 
 C sin X- (C+2E)f cos X 
 in which, N = number of cars in trip; 
 
 C = weight of coal in loaded cars, in pounds; 
 E = weight of empty cars, in pounds; 
 R = weight of rope attached to empty trip, in ppunds. 
 
 In the formula, all the terms are known except /, which, while commonly 
 taken as .025 may be very much more, especially on flat inclines where the 
 rope sags on the ground between the rollers or where the track is in bad condi- 
 tion and the rollers so clogged with dirt that they do not turn. 
 
 EXAMPLE. How many cars will it require to start the trip on an inclined 
 plane 2,000 ft. long and pitching 8, when the car that weighs 2,500 Ib. carries 
 a load of like amount, the rope weighs 2 Ib. per ft., and the friction is 4 per 
 cent. (.04)? 
 
 SOLUTION. Substituting in the last formula, there results, 
 
 ,, 4,OOOX(.13917+.04X.99Q27) 
 
 = 2,500 X .19317 -(2,500+ 2X2,500) X. 04 X. 99027 C&rS 
 
 From this, it will require fifteen cars to start the trip. 
 
 In the formula, a = =^g (sin X /cos X), a = acceleration in feet per second 
 
 per second, produced by an unbalanced force C, which is weight of coal in 
 descending cars, in setting in motion weight W, which is weight of coal + 
 weight of qars+ weight of rope R+ weight of drum D. The formula may, 
 thence, be transformed to read 
 
 In a general sense it may be said that the weight of the coal C is the motive 
 power that sets in motion all the other weights including its own. 
 
 EXAMPLE. In the preceding example, assuming that the rope drum is 
 8 ft. m diameter and 10 ft. wide and weighs 32,000 Ib., and that there are 
 fifteen cars in a trip, (a) what will be the time of descent down the plane? 
 (o) What is the final speed, in feet per second and in miles per hour? (c) Fur- 
 
HAULAGE 783 
 
 ther, assuming that the speed is not allowed to exceed 25 mi. per hr., what 
 will be the capacity of the incline in an 8-hr, da., making the usual allowance 
 for delays, etc.? 
 
 SOLUTION. As there are fifteen loads of coal, C = 15X2,500 = 37,500 lb., 
 2E = 2X15X2,500 = 75,000 lb., # = 4,000 lb. f > = 32,000 lb., and (C+2E 
 
 +R+D) = 148,500 lb. 
 -. 04 X. 99027) = .81 ft. per sec. per sec. 
 From this the time of descent is / = 
 
 The final velocity reached at the foot of the incline will be # = .81X703 
 = 56.94 ft. per sec., or (3,600X56.94) ^5,280 = 38.8 mi. per hr. 
 
 As the speed is limited to 25 mi. per hr., or 36 ft. per sec., the brakes must 
 
 be applied at the end of /= = 44.4 sec., when the trip has traveled down 
 
 .ol 
 
 the incline a distance of s = - - = 799.2 ft. As retardation and accelera- 
 
 tion are equal, the time required to start and stop the trip will be 88.8 sec., and 
 the distance traveled during these periods will be 1,588.4 ft. The remaining 
 2,000 1,588.4 = 412.6 ft. of the trip will be made in 412.6-^-36 = 11.4 sec. 
 The entire time of descent will be 88.8+11.4 = 100.2 sec., or 1 min. 40 sec., 
 practically. 
 
 If 50 sec. is allowed for handling the ropes between trips, a trip will require 
 2% min., and 24 trips will be made in 1 hr. As (15X2,500) -f- 2,000= 18.75 T. 
 of coal is lowered each trip, the capacity of the incline will be 450 T. per hr. If 
 1 hr. a day is lost in various delays, the incline will handle an average net daily 
 output of 450X7 = 3,150 T. 
 
 In the example, the radius of gyration has been taken as equal to that of 
 the drum. The true radius of gyration is probably about AR, but the error 
 arising through the use of the larger and more easily obtained value is on the 
 safe side. 
 
 Profile of Inclines. If an incline is a plane of uniform pitch, as commonly 
 is the case, the weight of the descending trip constantly increases and that of 
 the descending trip decreases, as one rope winds off and the other winds on the 
 drum. Hence, the force F and, consequently, the acceleration a constantly 
 increase and, therefore, the force that must be applied through the brake to 
 keep the speed of the trip within the established limits greatly increases from 
 the start to the end of the run. 
 
 The most easily operated incline, that is, one on which the force applied 
 through the brake is constant, has a vertical tangent for such a distance below 
 the knuckle that the trip in descending it acquires the proper velocity; it also 
 has, from the end of this tangent to a point near the foot of the incline, the 
 shape of a curve such that the velocity of the descending trip is constant and, 
 hence, the brake resistance is uniform, and ends with a curve of such shape that 
 the velocity of the trip at the end of the run is just sufficient to carry it to 
 the tipple. 
 
 From the fact that after a trip has been started and has descended the 
 incline some distance much less weight is needed to keep it in motion, if the upper 
 end of the incline is given a greater pitch a much smaller trip may be set in 
 motion. In fact, relatively flat inclines can often be made to work only by 
 increasing the grade for from 25 to 75 ft. at the upper end to double or more 
 than double what it is on the body of the plane. This increased grade is known 
 as the steep pilch. All inclines, regardless of their pitch, terminate in a curve 
 that is tangent to the plane at one end and to the tipple floor at .the other. 
 The object of this curve is to reduce the speed of the trip to an amount just 
 sufficient to carry it to the dump. 
 
 JIG PLANES 
 
 A jig plane is a modification of the self-acting incline in which the weight 
 of a descending loaded car raises a counterweight running on wheels on a track, 
 and the descending counterweight raises the empty car. The counterweight, 
 or balance truck, runs on a track between and slightly below the rails of the 
 car track, and its weight is made equal to one-half the sum of the weights of 
 the loaded and empty cars or trips; that is, if ithe loaded car weighs 5,000 lb. 
 
784 HAULAGE 
 
 and the empty car 2,500 lb., the counterweight will weigh (5,000 + 2,500) 4- 2 
 = 3,750 lb. 
 
 In pitching seams, where the coal will not run by gravity in a chute or 
 where it will be broken if allowed to run, the jig is often employed with advan- 
 tage to lower loaded cars from the face to the gangway. For this purpose, a 
 sheave is arranged at the head of the track, near the face, between two posts 
 wedged firmly between the roof and floor. The rope is passed over this sheave, 
 one end is fastened to the balance truck, and the other end is coupled to the 
 car by any standard hitching. A brake wheel, securely fastened to one side of 
 the sheave, and a strong lever furnish the means of controlling the motion of 
 the car. Jig planes are generally used to drop single cars short distances. 
 Where the grade is so flat that two or more cars must be employed to impart 
 motion, a more cheaply installed and operated arrangement is generally possi- 
 ble. The rooms may be driven across the pitch on such a grade that a mule can 
 pull the empty car to the face, or the car may be drawn up by a block and 
 tackle operated by a mule or by a windlass, or by a rope passing over a sheave 
 at the head of the room track, one end of the rope being fastened to the car 
 and the other wound on a drum on the haulage motor, the drum being turned 
 by current from the entry wires while the motor is blocked on the rails. 
 
 Calculations for Jig Planes. While the formulas given under the head 
 of Self-Acting Inclines apply equally to jig planes, it is better to determine the 
 pitch of the track necessary to make the plane self-acting under the known 
 conditions. If the necessary pitch is greater than that of the seam, a jig 
 plane cannot be installed. The formula for the angle of pitch may be deduced 
 from that given for N, as follows: 
 
 - - 
 
 in which, F = friction in pounds = (C+B+R) Xf; 
 C = weight of loaded car, in pounds; 
 B = weight of balance car, in pounds; 
 R = weight of rope, in pounds. 
 
 EXAMPLE. It is desired to install a jig plane to lower a single loaded car 
 weighing 5,000 lb. a distance of 200 ft. from the face to the entry. If the empty 
 car weighs 2,000 lb., the rope 2 lb. per ft. t and friction is taken as .025, what 
 is the proper grade to make the plane self-acting? 
 
 SOLUTION. Here, F= (5,000+3,500+2 X 200) X. 025 = 222.5 lb.; C=5,000 
 lb.; B = (5,000+2,000)^2 = 3,500 lb.; 12 = 2X200 = 400 lb. Substituting in 
 the formula, 
 
 whence, X = 14 40'. On any greater pitch than this, the plane will be self- 
 acting, and on any lesser one it cannot be operated with one car, although it 
 may be by two or more. 
 
 EXAMPLE. With the conditions of the preceding problem, but with two- 
 car trips, on what pitch will the plane be self-acting? 
 
 SOLUTION. Here C = 10,000 lb.; B= (10, 000 +4, 000) -=-2 = 7, 000 lb.; 
 F= (10,000+7,000+400) X. 025 = 435 lb.; and # = 400 lb., as before. Sub- 
 stituting, 
 
 whence X 
 
 SLOPES AND ENGINE PLANES 
 
 Slopes. A slope is an inclined plane up which loaded cars are hauled on 
 one track by an engine of any convenient type at the same time as a corre- 
 sponding number of empty cars descend by gravity on a second and parallel 
 track. A slope, in many of its features, is a combination of the self-acting 
 incline and the standard double-compartment shaft. In all that relates to 
 track, rollers, the use of barneys or gunboats, slope carriages, etc., a slope is 
 identical with an incline; in all that relates to the motive power and the calcu- 
 lation of engine dimensions, a slope differs from a shaft only in that counter- 
 balancing is not attempted and that the weights moved must be multiplied by 
 sin X and the friction of the moving weights by cos X as in haulage on inclines 
 and for the same reason. It should be remembered, -however, that the inertia 
 of the drum and sheaves is not influenced by the inclination of the slope. 
 
 Slopes are the usual means of opening and operating pitching seams, and 
 are sometimes used underground in raising coal from a lower to a higher level. 
 
HAULAGE 785 
 
 While they are sometimes laid with three rails and a passing track, as some 
 inclines, all first-class main slopes are double-tracked throughout. The 
 profile of a slope is that of the dip of the seam slightly dished or concave at the 
 bottom to reduce the speed of the descending trip. At the surface, the slope 
 tracks are commonly extended upwards on a trestle having the same pitch as 
 the seam so that the knuckle is at the tipple platform, in order that the cars, 
 when released from the rope, may run by gravity to the dump. 
 
 The controlling factor in determining whether a certain grade is or is not 
 adapted to slope haulage, is that it must be sufficiently sharp to allow the 
 empty trip to run down by gravity dragging the rope after it. The proper 
 angle of slope is found from the formula tan X=f, for Self-Acting Inclines. 
 The coefficient of friction / should be made sufficiently great to allow for any 
 increase in resistance due to the clogging of the rollers by material dropped 
 from the cars. The pitch must also be steep enough to insure that the descend- 
 ing trip has at least the velocity imparted by the engine to the ascending 
 trip; otherwise, the empty rope will buckle and double on itself. 
 
 Both first- and second-motion engines are used for hoisting on slopes; the 
 choice between the two types is governed by the principles given under the 
 head of Hoisting. Slopes up to 500 or 600 ft. in length and of moderate pitch 
 are now generally operated with rope or chain hauls, the advantages obtained 
 through the regular delivery of single cars to the dump through the use of these 
 appliances more than offsetting their greater first cost. 
 
 Engine Planes. An engine plane is a single-track slope, without central 
 turnout, up which an engine pulls a loaded car as one operation and down 
 which, as a second operation, the empty car descends by gravity, dragging the 
 rope after it. There is frequent confusion in the use of the terms slope and 
 engine plane and what is always and rightly known as engine plane when on 
 the surface is miscalled a slope or a single-track slope when used underground. 
 
 The engines used on planes are commonly of the friction-clutch type. The 
 drum is thrown in when it is desired to hoist and thrown out and allowed to 
 turn on its shaft as the empty trip descends, its speed being controlled by 
 powerful brakes. When hoisting on a plane, the load is that of the loaded 
 trip and the weight of the rope, the latter diminishing uniformly as the rope 
 winds on the drum. When lowering, the load at the outset is that of the 
 empty trip but it is uniformly increased by the weight of the rope as the latter 
 unwinds from the drum. 
 
 The question of hoisting the load is merely one of installing a sufficiently 
 powerful engine, which must develop more power in engine plane than in slope 
 haulage because in the former there is no balancing of the moving weights. 
 In slope haulage, the inertia of the drum is overcome by the engine; but in 
 engine-plane haulage, this is true only in the case of the ascending loaded trip. 
 Hence, in engine-plane haulage the grade must be sharper than in slope haulage 
 because the empty trip must overcome the inertia of the drum. In both 
 forms of haulage, the length of the empty rope becomes constantly greater, 
 and the unchanging weight of the empty trip may not always be sufficient to 
 overcome the increasing rope resistance. For this reason and to attain an 
 average speed of, say, 10 mi. per hr., the grade of an engine plane should not 
 be less than 3%. 
 
 Flat slopes and planes are fully as unsatisfactory in operation as fiat self- 
 acting inclines. On the surface, their use may often be avoided by the employ- 
 ment of a motor running on a track laid on a flatter, but longer grade than the 
 plane. If motors cannot be employed and a plane must be used, it is better to 
 install a tail-rope or endless-rope system for its operation. Underground, where 
 their use is local and the amount of material handled over them is not great, 
 the use of flat slopes and planes is not so objectionable, although if short, and 
 cheap power is to be had, a mechanical haul of some kind is to be preferred. 
 
 ENDLESS-ROPE HAULAGE 
 
 In endless-rope haulage systems, a wire rope passes from the haulage-engine 
 drum to and through the main entry to a sheave at the end of the workings, 
 thence around the sheave and back along the main entry or a parallel entry 
 to the engine drum. The ends of the rope are spliced together, forming an end- 
 less rope to which the cars are attached singly by grips or in trips pulled by a 
 grip car. 
 
 As usually installed, the system requires two tracks, which may be laid in 
 the same entry if the roof is sound enough to permit the necessary width. 
 50 
 
786 HAULAGE 
 
 If the roof is bad, it is usually cheaper to lay single tracks in parallel entries of 
 standard width, using one road for inbound and the other for outbound traffic. 
 
 There are two general types of endless-rope haulage based on the speed of 
 the rope. In the low-speed system, which is the original type, the rope moves 
 continuously in the same direction at a rate of 2 to 4 mi. an hr.; there are 
 two separate tracks; the cars are attached to the rope singly at intervals of 
 100 to 200 ft.; and, as far as possible, there are as many inbound empty cars as 
 there are outbound loaded ones. In the high-speed system, the rope travels 
 at a rate of 15 to 25 mi. per hr.; the cars are attached to the rope in trips of 
 as many as fifty or more by means of a grip car; there is usually but one track, 
 which is used for both inbound and outbound traffic; and the direction of 
 motion of the rope is reversed to correspond to the direction in which the 
 trip is being moved. 
 
 The low-speed system has been highly developed in England, where the 
 cars, as well as the mine output, are relatively small, where the grades are 
 undulating and the curves numerous, where many branches (cross-entries) 
 must be worked from the main rope, and where there is not storage room at 
 the foot of the shaft for long trips of cars. While this requires much less 
 power than the high-speed system and insures a uniform and regular delivery 
 of loaded cars to the shaft bottom, it is costly in labor, as at least one attendant 
 is required at each branch. Although at such low speeds there is but little 
 danger of a car jumping the track, when such an accident does happen the 
 damage may be serious to both cars and rope, as there is no attendant to signal 
 promptly for the immediate stoppage of the rope. 
 
 The strain upon the rope in starting a car from rest varies as the square 
 of the rope's velocity, hence the higher the speed the greater must be the 
 diameter of the rope. Further, if the velocity is as great as 4 mi. per hr., the 
 ropes become flattened, kinked, and unduly strained, much sooner than at 
 velocities of 2 to 3 mi. per hr. For these reasons, the last-named speeds are 
 preferred for slow-moving ropes. When attaching it to the rope, the attend- 
 ant usually pushes the car by hand until it has acquired the velocity of the 
 rope before gripping it to the rope. Grips for low-speed haulage are very 
 largely of the automatic detaching type. 
 
 The high-speed system is in more general use in the United States where 
 the cars and the required output are large; where the track is straight and the 
 grades against the loads; where there are no branches; and where there is ample 
 storage room for long trips of cars. The system is economical in labor, as 
 no handling_of the trip is necessary except at the points of origin and delivery, 
 but it requires powerful engines to give the acceleration to the trip when 
 started on the heavy grades that usually prevail where this system is used. 
 The rope must be hearvier than in the low-speed system, the rails should weigh 
 60 Ib. or more per yard, the track must be kept clean and in perfect alinement, 
 and the cars must be of the best type. The amount of coal that may be 
 delivered by this system is practically only limited by the power of the engines, 
 particularly if inbound and outbound trips are run at the same time. At the 
 tipple, the long trips are fed into the dump by car hauls, imposing little if any 
 extra labor over that required when the low-speed system is used. 
 
 Endless-rope haulage is particularly adapted to mines where the entries 
 are level or have a slight uniform grade. In the low-speed system, the cars 
 should be fastened to the rope at regular intervals to make the load on the 
 engine constant and to insure a uniform delivery of cars to the tipple. How- 
 ever, owing to the delays incident to all mining operations, it is impossible 
 to keep the cars regularly spaced and they become bunched. Thus, the cars 
 may accumulate on a grade or on several grades in opposite directions and so 
 throw a variable load upon the engine, which makes its regulation very difficult 
 where the grades are not uniform in amount or direction. Where variable 
 grades occur, the rope will lift from the track in low places and may lash to 
 such an extent as to throw the cars from the track; while on an up-grade, the 
 rope will bear heavily on the rollers, producing excessive wear and greatly 
 increasing the friction. 
 
 General Arrangement of Endless-Rope Haulage Systems. Fig. 1 shows 
 the general arrangement of an endless-rope haulage system, which will answer 
 for either low or high speed. The rope passes back of the engine drums a and b 
 to the balance car c, where it is given a half turn around the sheave d. From d 
 the rope passes back past the engine drums and through the mine, where it is 
 supported on rollers, to the tail-sheave e which is carried on the balance car /. 
 After making a half turn around this sheave e, the rope returns along the 
 parallel track to the drum, thus completing the circuit. The balance cars are 
 
HAULAGE 
 
 787 
 
 intended to keep the rope tight. 
 The passage of the rope under 
 the pulleys g, over the pulleys 
 h, and to one side of the pulleys 
 *, is for the purpose of deflect- 
 ing it to the center of the mine 
 tracks. In the plan shown, the 
 rope k in going into the mine 
 pulls the empty cars / to the 
 curve m where they are un- 
 hooked and distributed to the 
 working places. At the same 
 point, but on the track , the 
 loaded cars are attached to the 
 outgoing rope p and hauled to 
 the curve q where they are un- 
 hooked and sent to the tipple. 
 
 Endless-Rope Haulage En- 
 gines and Drums. The engines 
 for an endless-rope haulage 
 plant are almost invariably of 
 the second-motion type and 
 may be fitted with plain slide 
 or Corliss valves; the latter is 
 preferred if the grades are vari- 
 able as they are more economical 
 in the use of steam and are auto- 
 matic. In the low-speed sys- 
 tem, the engines, if run contin- 
 uously in one direction, should 
 use steam expansively, and, 
 where the loads are variable, 
 should be provided with a fly- 
 wheel and governor. 
 
 There are generally two 
 narrow drums, arranged tan- 
 dem on separate shafts. One 
 of the drums is driven by gear- 
 ing and the other, frequently 
 called the follower, is turned by 
 the rope passing around it. 
 The drums vary in diameter 
 according to the size of rope, 
 size of engine, length of haul, 
 and should be of ample size to 
 reduce the bending strain on 
 the rope. The driven drum, 
 or follower, is sometimes inde- 
 pendent of the engine and made 
 smaller than the driving drum; 
 it is also sometimes permitted 
 to run loose on its shaft so that 
 the rope will lead .properly from 
 one groove to another. Drums 
 with a concave rim are some- 
 times used, but with such there 
 is considerable surging and jerk- 
 ing of the rope, and grooved 
 drums are preferable. The best 
 results appear to be obtained 
 when the drums are placed 12 
 to 15 ft. apart, in order that 
 there maybe a slight sag to the 
 rope and a better bite on the 
 drum. The number of grooves 
 on the driving pulley may be 
 two, four, or more, depending 
 on the strain coming upon the 
 
788 HAULAGE 
 
 rope; the follower pulley adds but little to the tension. To increase the 
 tension, the rope is sometimes bent around the drums in the form of a 
 horizontal figure 8, but the extra bending strain thus thrown on the rope 
 materially shortens its life. Because the tension on the different turns 
 of the rope gradually and uniformly decreases from the first to the last, the 
 wear on the lining of the grooves is not equal. This results in time in the 
 drum having as many diameters as it has grooves. The velocity of a point 
 on the circumference of the drum will be greater on the unworn grooves than 
 on the worn ones, and, as the rope and drum cannot travel at different speeds, 
 an increasingly violent rubbing action is set up between the rope and drum, 
 materially reducing the life of the former. To prevent this rubbing action, the 
 follower drum is sometimes made up of as many single drums as there are 
 grooves, each drum being free to revolve at a speed determined by that of the 
 groove opposite it on the solid driving drum. There are various forms of 
 differential drums on the market, designed to overcome the trouble under 
 discussion. In some of them, the lining of the grooves is free to move upon 
 the circumference of the drum and so to adjust itself to the variation in the 
 speed of the rope from groove to groove. 
 
 Rope-Tightening Arrangements. Owing to the stretching of the rope 
 under loads, balance- or tension- cars or sheaves are placed at both ends of the 
 rope line to keep it tight. The general arrangement is a& shown in Fig. 1. 
 The weight of the balance car is determined by experiment. Unless the track 
 upon which the balance car runs has considerable length, a piece must be cut 
 from the rope and a new splice made when the car reaches the end of the 
 track. In order to avoid the expense of blasting out an inclined track as 
 shown in Fig. 1, the balance car may be run on the grade of the entry and a 
 more than usually heavy counterweight employed; in which case the only 
 excavation necessary is that of the counterweight pit. The counterweight 
 is then supported from a pulley wheel riding on a chain. One end of the chain 
 is fastened to the balance car and the other end, after passing down into the 
 pit to form a loop upon which the pulley wheel rides, is carried up to and 
 around a small drum, which may be turned by worm-gearing operated by a 
 hand wheel. When the stretch of the rope has allowed the counterweight 
 to rest on the pit bottom, it is raised therefrom by winding some of the chain 
 upon the drum. 
 
 Grips and Grip Cars. Messrs. W. G. Salt and A. L. Lovatt, in the Trans- 
 actions of the Institution of Mining Engineers (England), give the following 
 as the seven essential qualities of a good grip, or clip, as it is called in England: 
 
 1. A clip must be sufficiently strong, with a margin of safety, to do the 
 work required and to withstand rough usage. If, however, the design of the 
 clip is too strong, the desired results will not be obtained; for if the tub or tubs 
 (car or cars) are derailed, serious damage might be caused to the rope or hauling 
 machinery if the clip does not act as a safety valve. 
 
 2. Its design and construction should be such that it can obtain and retain 
 a firm grip on the rope when it is attached. 
 
 3. The jaws of the clip should have a bearing of at least 70% on the 
 circumference of the rope and should embrace all the strands of the rope within 
 a minimum length of the clip jaw. 
 
 4. There should be a good margin for wear and the clip should be capable 
 of easy adjustment by the person using it. 
 
 5. The design and construction should be as simple as possible; the fewer 
 parts there are the better, and these should be such as to allow of the clip being 
 easily attached and detached from the rope with certainty, the detachment 
 being clean and certain. 
 
 6. The gripping surfaces should be so arranged as not to kink the rope 
 under working conditions. If the kink effect is reduced to a minimum the 
 wear on the rope will be reduced, and consequently the life of the rope will be 
 increased. 
 
 7. A clip should be capable of being automatically detached from the rope, 
 and ideally should be of such design as to work satisfactorily under any one or 
 all of the conditions prevailing at a mine. 
 
 The following controlling factors must be taken into account in the adoption 
 of a clip: Inclination, undulating or varying gradients, level roads, direction 
 of roads (straight or otherwise) ; and under- or over-rope haulage. 
 
 The article by Messrs Salt and Lovatt is reprinted in The Colliery Engineer 
 for Feb., 1914, and illustrates, compares, and criticizes the majority of the 
 grips used in England, where the slow-moving endless rope system with single 
 cars has been very successfully developed. 
 
HAULAGE 
 
 789 
 
 On undulating grades single grips have not proved universally successful, 
 and it is usually necessary to have grips at each end of the car to prevent its 
 running forwards or backwards and bending the rope at every change of grade. 
 
 Where the cars are run in trips instead of singly, grip cars are used. These 
 are four-wheeled trucks carrying the grip below the platform. The grip is 
 frequently of the jaw type with one fixed jaw; the movable jaw being brought 
 down upon the rope by a lever or by turning a hand wheel. In handling 
 heavy loads, the grip must be thrown in slowly so that the speed of the trip 
 is gradually accelerated from rest to that of the moving rope. This is, perhaps, 
 best accomplished by substituting for the jaw grip, the form used on street 
 railways, some suspension bridges, etc. This grip consists essentially of three 
 grooved wheels set in the same plane with their axles at the vertices of an 
 equilateral triangle. The rope runs tangent to the upper edge of two wheels 
 and tangent to the lower side of the other. As the axles of the wheels are 
 brought together by suitable mechanism a greater and greater pressure is 
 exerted upon the rope. At first the wheels revolve freely, but as the pressure 
 is increased they grip the rope more and more firmly at the same time imparting 
 an increasing velocity to the trip, until, when the grip wheels no longer revolve, 
 the trip is traveling at the same speed as the rope. Where grip cars are 
 employed, there is a device by which the frame carrying the grip wheels can 
 be raised a sufficient height to clear the rollers. In fact, any grip to be service- 
 able must pass over the track rollers, deflection sheaves on curves, and the like. 
 A grip-man rides on the grip car not only to handle the grip, but also to release 
 it and apply the brakes when needed. 
 
 Rollers and Sheaves. When 
 placing rollers on endless-rope haul- 
 age roads, the same precautions are 
 to be followed as when setting them 
 on inclined planes. The rollers are 
 very commonly hollow, cast-iron 
 cylinders 12 to 18 in. long, and 6 in. 
 in diameter, with raised rims to pre- 
 vent the rope running off them. 
 
 FIG. 2 
 
 Other rollers, 10 to 12 in. long, have a decidedly concave face to carry the 
 rope to a central groove. At the bottom of a dip, it is usually necessary 
 to have a roller in the roof to prevent the rope scraping against the roof; such 
 a roller may be of the types just described. Too much care cannot be taken 
 to see that the rollers are strongly and properly set and are in good condition 
 and free to revolve at all times. 
 
 Sheaves are a type of roller with their axles vertical and are used to guide the 
 rope around curves. When possible they are placed outside the rails on the inside 
 of the curve ; this arrangement permits the use of sheaves as large as 6 ft. in diame- 
 ter, thus greatly prolonging the life of the rope above what it would be if the 
 sheaves were in the center of the track where their diameter would be less than 
 one-half the track gauge. The sheave shown in Fig. 2, which may be set with 
 its axle inclined, is a very common form for use on the outside of curves. The 
 planking a is intended to guide the rope to the sheave and may be covered 
 with sheet iron held in place by bolts or nails with countersunk heads. 
 
 Where rollers or sheaves are placed outside the track on curves, some arrange- 
 ment is necessary to prevent the rope catching under the head of the rail as it 
 is deflected from the center line. A familiar arrangement consists of wedge- 
 shaped pieces of wood spiked to the ties, the highest point of the wedge rising 
 a little aoove the top of the rail. A wedge is placed on each tie and is set as 
 close to the rail as possible, leaving clearance < for the flange of the car wheel. 
 The face of the wedge, along which the rope slips into position, may be covered 
 with sheet iron held in place by spikes or bolts with countersunk heads. Numer- 
 ous devices similar to the one illustrated 
 in Fig. 3 are used for the same purpose. 
 The finger a, the lower end of which is 
 much the heavier, is pivoted at b so that 
 it normally hangs vertical. When the 
 rope presses against it, it assumes the 
 position shown in (b) , and after guiding 
 the rope over the rails, falls back to its 
 original position (a). Arrangements 
 must be made at all switches to prevent the rope being caught in the frogs. 
 Side-Entry Haulage. The endless-rope system is not readily adapted to 
 haulage on side or cross-entries. As ordinarily arranged, each entry has its 
 
 (a) 
 
 FIG. 3 
 
790 
 
 HAULAGE 
 
 own rope, which passes over a sheave at the face and makes a couple of turns 
 over a grip or driving wheel at the mouth. On the main entry is placed a 
 vertically turning wheel around which the main rope makes two turns to give 
 it sufficient power to turn the driving pulley on the side-entry haulage; this 
 it does by means of a friction clutch, which may be thrown in and out of gear. 
 There is usually a reducing gear so that the speed of the side-entry rope is less 
 than that of the main line. Loaded cars on the main line must be detached 
 from the rope on arriving at a cross-entry, because of the wheel around which 
 the main rope passes, and must be coupled on again after passing the entry. 
 Similarly, cars to be delivered to a side entry or which are received therefrom 
 must be uncoupled and coupled at the junction with the main line. On a level 
 track or on down grades, the cars on the main line will run past the branches 
 under their acquired momentum, but on sharp up grades this may not be possi- 
 ble. In any case, much labor is required at junctions and the grip must be 
 of a type that is quickly adjusted. 
 
 Overhead Endless-Rope Haulage. The overhead endless-rope haulage 
 system is a modification of the original low-speed type in which the rope is 
 carried over the cars instead of under them. As the cars are spaced from 100 
 to 200 ft. apart, it is unusual for the rope to sag low enough to drag either on 
 the track or on the rollers; hence, the wear on the rope is much less than when 
 it runs under the cars. 
 
 Most of the grips or clips used with an under-running rope may be used 
 with the overhead rope. A common form of grab, or dutch, is shown in Fig. 4, 
 where the rope rests in the groove a. The friction due to the motion of the 
 
 rope in the grab causes it to turn 
 slightly sidewise and grip the rope. 
 The heavier the car or the steeper the 
 grade, the more firmly will the grab 
 take hold of the rope. As the grab 
 is free to turn in the sockets b, it pulls 
 the car on an up grade and holds it 
 back on a down grade. When the 
 cars reach their destination, they are 
 automatically released by an increase 
 in the down grade and by the gradual 
 rise of the rope to an overhead sheave, 
 which lifts the rope from the grab and 
 allows the cars to run to the dump 
 by gravity. 
 
 The overhead endless-rope sys- 
 tem does not work very well on 
 curves, which should be made as short 
 
 FIG. 4 as possible so that one large wheel is 
 
 sufficient to carry the rope around 
 
 them. Branches may be worked by the overhead rope system by setting the 
 driving pulley conveying power to the side-entry pulley so that it will revolve 
 horizontally above the cars instead of vertically below them. As the rope 
 rises to pass around the pulley, the cars are, of course, automatically detached, 
 and, after passing over the cross-entry switches by gravity, are automatically 
 attached to the rope. The branch-entry driving pulley is operated by a friction 
 clutch as in the case of an under-running rope. 
 
 High Speed, or Reversing, Endless-Rope Haulage. In high-speed endless- 
 rope haulage, the rope is only in motion when the cars are being moved. At 
 the inside parting, the grip car pulling the trip is attached to the rope, which 
 is put m motion upon receipt of the proper signal at the engine room outside 
 the mine. At the tipple, a flying switch is usually made so that the cars can 
 run m by gravity, and the rope is stopped. After attaching the empty trip 
 to the grip car t> the rope is started in the opposite direction and the empty trip 
 hauled to the inside parting usually upon the same track used by the loaded 
 trip, but sometimes upon a separate track laid in a parallel entry. Where 
 but one track is used for traffic in both directions, the rope may be returned 
 upon rollers laid at one side of the main entry, or the return air-course or 
 manway may be used for the purpose. 
 
 There is no balancing of loads in this system and large and powerful engines 
 are required because there may be fifty or more cars in a trip running at a 
 speed of 15 to 25 mi. an hr. against grades of 3% and more. Balancing is 
 possible when two tracks are used and an empty trip leaves the tipple for the 
 mine at the same time a loaded trip leaves the inside parting for the tipple. 
 
HAULAGE 791 
 
 The high-speed and endless-rope and the tail-rope systems are used in the 
 United States on straight hauls too steep for motors and where a large output 
 is demanded. 
 
 Endless-Rope Haulage on Inclines. Either the underneath or overhead 
 endless- rope system is well adapted to lowering coal over an incline where the 
 grades are not too steep. The rope is given a sufficient number of turns around 
 the head-sheave to secure it against slipping. The head-sheave is a flat, 
 grooved wheel, similar to the driving drum ordinarily used, and its speed is 
 controlled by a brake. The diameter of the head-sheave and of the tail- 
 sheave at the foot of the incline is equal to the distance between the center 
 lines of the tracks, which is from 8 to 10 ft. Unlike ordinary incline haulage, 
 the rope is in balance, and as there are the same number of cars on each side 
 of the rope, they also will be in balance and the weight-producing motion, that 
 of the coal, is constant throughout the run; hence, less powerful brakes are 
 required than on ordinary inclines. Where the cars are not equally spaced, it 
 may possibly be necessary to install a small engine at the head of the incline 
 to keep the rope in motion at a speed of, say, 3 to 4 mi. per hr. 
 
 Calculations for Low-Speed, Endless-Rope, Haulage Engines. In deter- 
 mining the horsepower required of low-speed, endless-rope, haulage engines 
 it is usual to assume that the conditions demanded of the plant are perfectly 
 fulfilled and then to add a liberal amount for the power required to overcome 
 the irregularities and uncertainties always met in practice. Thus, it is assumed 
 that there are as many inbound empty cars as there are outbound loaded ones 
 and that they are equally spaced: that the track is level or has a uniform grade 
 either for or against the loaded side; that the rope is continuously in motion 
 and the cars will have the velocity of the rope when they are gripped thereto. 
 In practice, it may happen that at some given instant there are no inbound 
 empty cars, that the outbound loaded cars are badly bunched on a steep 
 adverse grade, where, the rope having for some reason been stopped, they 
 must be accelerated from rest to full speed. For these reasons, the engines 
 for low-speed, endless-rope haulage should have from two to three times the 
 horsepower calculated on the assumption that the conditions are perfectly 
 fulfilled. 
 
 The load to be moved is that of the coal, for the cars and rope are in balance. 
 To the weight of the coal must be added the friction based on the resistance to 
 motion of the entire rope and all the cars. The force required to accelerate 
 the system may be neglected. 
 
 EXAMPLE. In a low-speed, endless-rope, haulage system 5,000 ft. long, 
 the rope, which weighs 2 lb. per ft., has a speed of 3.5 mi. per hr. The grade 
 is undulating, but averages 2% (1 9') against the loads. The mine car, 
 which weighs 2,500 lb., holds 4,000 lb. of coal. If friction is estimated at 3%, 
 what will be the theoretical horsepower of the engines to deliver 180 T. of 
 coal per hr. to the tipple? 
 
 SOLUTION. The speed of the rope is (5,280X3.5)^-60 = 308 ft. per min. 
 There must be delivered to the tipple 1 80 -T- 60 = 3 T. or 3-7-2 = 1.5 cars of coal 
 per minute. As the rope travels 308 ft. per min., the cars will be spaced 308 
 -r- 1.5 = 205.3 ft. apart. There will be 5,000 -=-205.3 = 24.5, say, 25 cars on each 
 side of the rope. 
 
 The total weight in motion is, rope 2X5,000X2 = 20,000 lb.; coal, 25 car- 
 loads weighing 25X4,000 = 100,000 lb.; cars, 2X25 = 50, weighing 50X2,500 
 = 125,000 lb.; grand total, 245,000 lb. At 3%, the friction will be, 7,350 lb. 
 
 The formula for the horsepower is, 
 
 _ (W sin X+F cos X)S = (W tan X+F)S 
 
 33.000 33,000 
 
 since, on such a flat grade and for practical purposes sin X = tan X and cos X 
 = 1. 5 is the distance traveled by the rope, in feet per minute. 
 
 As W = 3 T. = 6,000 lb. per min., tan X = grade in per cent. = .02, F = 7,350 lb. 
 and 5 = 308 ft. per min., the theoretical horsepower required to keep the rope 
 and cars in motion is 
 
 _(W sin X+y)5_(6.000X. 02+7.350) X308 , 
 
 ' 33,000 33,000 
 
 If the rope should come to rest at a time when there were no inbound 
 empty cars and the loads were bunched on an adverse grade, it is probable 
 that 150 H. P., possibly more, might be required to get the system again 
 in motion. 
 
 Calculations for High-Speed, Endless-Rope, Haulage Engines. Because, 
 in high-speed, endless-rope haulage, the entire system "must be brought from 
 
792 HAULAGE 
 
 rest to full speed, the engines must be made sufficiently large to provide the 
 power required for acceleration. 
 
 EXAMPLE. A high-speed, endless-rope, haulage system is 1J mi. long. 
 The rope, which weighs 2 Ib. per ft., has a sustained speed of 15 mi. per hr. 
 at the end of 60 sec., starting from rest. The grip car weighs 5,000 Ib., the 
 empty car weighs 2,500 Ib. and carries 5,000 Ib. of coal. The grade averages 
 2% against the loads and friction is 2.5%. If but one track is used for haul- 
 age, how many cars must be run in a trip to give an output of 200 T. per hr., 
 and what must be the net horsepower of the engines? 
 
 SOLUTION. The full speed of the trip is (5,280X1.5) -=-3,600 = 22 ft. per 
 sec. The acceleration is fl = t>-f-/ = 22-f-60 = .367 ft. per sec. per sec., and the 
 retardation will be the same. During the joint periods of acceleration and 
 retardation, the trip will travel 2 X (22X60) -7-2 = 1,320 ft. in 2 min. = 120 sec. 
 The remaining (5,280X1.5) -1,320 = 6,600 ft. will be covered in 6,600 -=-22 
 = 300 sec., and the total time required to haul out the loaded trip will be 120 
 +300 = 420 sec., or 7 min. If 3 min. is allowed for coupling and uncoupling 
 and all delays, a trip will require 10 min. and six trips will be made per hour. 
 
 But for each loaded trip going out there must be an empty trip going in. 
 Hence, on a single-track system but three loaded trips per hour will be delivered 
 to the tipple. As each car carries 5,000 -J- 2 = 2.5 T. , 200 -^ 2.5 = 80 loaded cars 
 must be delivered each hour. The number of cars per trip will be 80 -5- 3 = 27. 
 
 The cars and the grip car will weigh 27 X (5,000+2,500) +5,000 = 207,500 Ib. 
 The rope will weigh 2X(5,280X1.5)X2 = 31,680 Ib. Hence, the total load 
 will be 239,180 Ib. As, on such a flat grade cos X=l, the friction will be 
 239, 180 X. 025 = 5,979. 5 Ib., at a speed of 22 ft. per sec., the horsepower neces- 
 sary to overcome friction will be (5,979.5X22) -7-550 = 239 H. P. 
 
 To haul the trip up grade will require, since for practical purposes sin X 
 - tan X = per cent, of grade, (Wtan XX 22) -i- 550= (207,500 X. 02X22) -*- 550 
 - 166 H. P. 
 
 To accelerate the entire system from rest to a speed of 22 ft. per sec. in 
 60 sec., will require the outlay, in force, of 
 
 f- 2 -f|f- X.36T-2,726,b. 
 
 The horsepower required to accelerate will be (2,726X22) -f- 550 = 104 H. P. 
 
 Thence, the total net horsepower required to overcome friction, to raise 
 the trip up the grade, and to accelerate the haulage system from rest to full 
 speed, will be 239 + 166+104 = 509 H. P. To allow for the friction of the 
 engines, their efficiency, future demands for power, at least 600 H. P. should 
 be provided, and 700 would be better. 
 
 NOTE. If, in the example, the system was double tracked, six loaded 
 trips of 14 cars each could be brought out per hour and as many equal size 
 trips of empties hauled in; the capacity of the plant would then be increased 
 from 81 to 84 cars. The horsepowers required to overcome the various resis- 
 tances would be, for friction 171 H. P., for grade 56 H. P., and for acceleration 
 76 H. P., a total of 303 H. P. Thus, double tracking the system and reducing 
 the loads, effects a saving in power of a trifle more than 40%. Similar economy 
 may be had by reducing the speed from 15 to 7.5 mi. per hr., but running 
 twenty-seven car trips as before. On the other hand, for the same expenditure 
 of power, the capacity of a double-track system should be about 60% more 
 than a single track. 
 
 TAIL-ROPE HAULAGE 
 
 General Arrangement. The tail-rope system of haulage resembles the 
 high-speed endless-rope system in that a single track is used upon which trips 
 of cars are run at high speed (6 to 25 mi. per hr.) in opposite directions. It 
 differs from the latter in that the rope is not continuous and that plain cylin- 
 drical drums and not driving and tightening pulleys are used on the haulage 
 engine. There are two ropes used in this system; a main or haulage rope and 
 a smaller tail-rope each winding and unwinding from its own drum, which 
 revolves freely on its shaft and may be thrown in gear by friction clutches. 
 When a loaded trip is to be hauled from the inside parting, the main rope is 
 coupled to the first car and the tail-rope to the last. Upon signal, the main- 
 rope drum is thrown in, the tail-rope drum is free on its shaft, and the engine 
 started. The main rope, which is wound entirely on the drum at the com- 
 pletion of the run, pulls the trip from the mine and the trip drags the tail- 
 rope after it unwinding it from its drum. The reverse process, the tail-rope 
 
HAULAGE 
 
 793 
 
 pulling the trip which, in turn, pulls the main rope, returns the empties to the 
 mine. 
 
 The general plan of a tail-rope plant with the engines placed underground 
 near the foot of the shaft 5 is shown in the accompanying figure. Here T is 
 the drum for the tail-rope, M that for the main rope, and w are the sheaves, 
 one of which is at the end of the main entry and one at the end of each side 
 entry or district. 
 Each side entry has 
 a rope reaching from 
 its mouth to a tail- 
 sheave w at or near 
 its inbye end and 
 back again to the 
 main entry ; the rope 
 is provided at each 
 end with couplings 
 similar to those on 
 the main-entry 
 ropes. When an 
 empty trip is to be 
 pulled into a side 
 entry, the main tail- 
 rope n is uncoupled 
 from the trip and 
 the branch rope / 
 coupled in its place. 
 The main tail-rope 
 is uncoupled at h 
 and the branch rope 
 g coupled to it. The 
 branch rope can 
 now pull the empties 
 and the .main rope 
 to the end of the side 
 entry, and the re- 
 verse operation will 
 haul the loads to 
 the mouth of the 
 side entry. If full 
 trips are pulled from 
 the side-entry part- 
 ing to the shaft bot- 
 tom, it is customary 
 to disconnect the 
 main-line ropes in- 
 bye n and run the 
 trips through to des- 
 tination without 
 stopping, effecting 
 a considerable sav- 
 ing in power in hav- 
 ing to accelerate the 
 system but once. 
 
 Engines, Drums, 
 Etc. Tail-rope 
 haulage engines are 
 almost always sec- 
 ond-motion or 
 geared, as the loads 
 and grades in mine 
 haulage are com- 
 monly too variable to permit of the successful use of first-motion engines. 
 Reversing gear is not needed, as the engines run continuously in the same direc- 
 tion, the direction of motion of the trip being controlled by throwing the 
 proper drum in gear. 
 
 The drums are necessarily of much smaller diameter than those of hoisting 
 engines, in order to keep the speed of the rope within the prescribed limits. 
 The flanges of the drums are also deeper than usual, as several coils of rope must 
 
794 HAULAGE 
 
 be wrapped upon one another, particularly if the haul is long. The brake 
 power should be ample, and the engineman must use care not to permit the idle 
 drum to turn too rapidly and thus pay off one rope more rapidly than the 
 engine is winding the other rope on its drum. Indicators must be provided to 
 show the location of the trip along the entry so that it may be stopped at the 
 mouth of any of the side entries as well as at the end of the main road. They 
 are 'also necessary where the direction of the grade varies, because, when the 
 grade changes to one in favor of the trip, steam must be shut off and the brakes 
 applied to prevent the trip over-riding the rope. 
 
 Sheaves, Rollers, Etc. The sheaves used for changing the direction of the 
 rope and the method of placing them under given conditions are the same in 
 endless- and tail-rope haulage. In some instances, large wood-lagged drums 
 are used in place of the ordinary iron deflection sheaves. These drums may be 
 as much as 6 ft. in diameter and 2 ft. wide, set with their axles vertical. When 
 the grooves become too deep, the drum is reversed end for end, thus subjecting 
 all parts of the lagging to wear and requiring less frequent renewals. There 
 is, however, a marked difference in the tail-sheaves employed in the two 
 systems. In endless-rope haulage, they are mounted upon a counterbalance, 
 or tightening car, which is employed to keep the rope at the proper tension; 
 in tail-rope haulage, the tail-sheaves, which are made of as large diameter as 
 possible and may revolve either horizontally or vertically, are very firmly 
 anchored, as the proper degree of tension is maintained by manipulating the 
 drums on the engine. 
 
 The track rollers are the same in the two systems. The tail-rope is usually 
 carried along one side of the haulage entry near the roof and upon short rollers, 
 the journals of which are supported by parallel uprights, 2 in.XS in. or a little 
 larger, which are firmly wedged between roof and floor. 
 
 Usually, 15 to 20 ft. of chain is used between the end of the rope and the 
 trip, to prevent injury to the rope through kinking when the trip is stopped. 
 Knock-off links, detaching hooks, etc., many of which are automatic, are in 
 use for rapidly uncoupling the rope from the trip. The selection of any auto- 
 matic device must be made with care, as accidents may arise through the 
 mechanism either acting at the wrong time or place or failing to act when and 
 where it should. 
 
 Signaling apparatus must be installed so that the engineer may be promptly 
 notified to stop or start the trip at any point in its course. At permanent 
 stations, such as the mai.n parting and the mouth and inbye end of side entries, 
 signals of the push-button type or telephones are commonly used. To signal 
 from any point along the main roads, two bare copper wires are suspended 
 about 6 to 9 in. apart along the side of the entry. By bringing the wires together 
 or by bridging the space between them with a piece of copper or iron, a signal 
 may be sent to the engine room. 
 
 Comparison of Endless- and Tail-Rope Haulage. Where the road is 
 straight, the grades uniform, and no branches are worked, there is little choice 
 between the high-speed endless-rope and the tail-rope haulage systems, except 
 that the latter requires 50% more rope, but, on the other hand, it can use a 
 simpler engine, as its direction of motion is not reversed. On curves, the 
 endless rope must be carried around small sheaves placed in the center of the 
 track; this arrangement is not nearly as satisfactory as in the tail-rope system 
 where large sheaves are placed outside the rails. On down-grades, since the 
 trip is attached to the rope at but one point (the grip car), there is always 
 the possibility of its over-riding and injuring the rope. The tail-rope system 
 is greatly the superior of the endless-rope in working branches, not only from 
 the standpoint t of labor, but of ease and efficiency. The horsepower demanded 
 of the engines is the same in either system. 
 
 The chief advantages of the ordinary, low-speed, endless-rope, haulage 
 system, are the regular delivery of single cars to the tipple permitting a better 
 regulation of labor than where the cars come in large trips; economy in instal- 
 lation, as the low speed does not demand the use of such large engines or such 
 heavy rails, ties, etc.; less liability of accident through the cars jumping the 
 track; less cost for upkeep, as the wear on the roadbed and rolling stock is 
 much less_at low than at high speeds; less power, and consequently less fuel, is 
 required ; it is more easily extended ; and requires one-third less rope. 
 
 The disadvantages of the low-speed endless-rope system are the cost of 
 laying and keeping up two sets of tracks, which, where the roof is poor may be 
 a serious matter even if parallel entries instead of one double-width entry are 
 used ; where branches must be worked, the cost for labor is high and the service 
 is not satisfactory; and it is not so efficient on crooked roads with undulating 
 
HAULAGE 795 
 
 grades as the tail-rope system for the reasons just given. Also, when the 
 workings become extensive and the haulageways long, the number of cars 
 required to keep up the output is excessive, and the large number of cars con- 
 siderably increases the strain on the rope and the power demanded of the 
 engine. 
 
 The tail-rope system is at a disadvantage in those states where the speed 
 of the trip is limited by law to 6 to 8 mi. per hr. Where the track and cars 
 are in poor condition and the entries are crooked a speed of even 8 mi. per hr. 
 may be excessive, but on modern roads, as maintained in first-class mines, and 
 with proper rolling stock, speeds of 20 mi. per hr. and more are perfectly 
 allowable; and high speed is an essential to the successful operation of tail- 
 rope haulage. 
 
 Calculations for Tail-Rope Haulage. The calculations for the horsepower 
 required in tail-rope haulage are made in the same way as those in high-speed 
 endless-rope haulage, provision being made for the power required to acceler- 
 ate the drum. In the event of the grades being variable, the power should 
 be sufficient to start and accelerate the trip on the most adverse grade. 
 
 STEAM-LOCOMOTIVE HAULAGE 
 
 The large volumes of dense smoke given off by the fuel, combined at times 
 with sulphur fumes and always with the exhaust steam, have prevented 
 the extensive use of steam locomotives in the bituminous mines of the United 
 States. For these reasons and because of the danger from fire, either through 
 igniting the timbers or methane, the use of these locomotives has been pro- 
 hibited by _ law in many states. In the anthracite regions of Pennsylvania, 
 where, until recent years, the coal worked was much thicker than in the bitu- 
 minous fields and where, also, the coal is smokeless, steam locomotives have 
 not proved so objectionable, and they are still quite extensively used for 
 underground haulage on return air-courses and on the surface for hauling 
 between the mine and the breaker, etc. 
 
 The steam locomotive possesses the advantages of low first cost, of not 
 requiring a power plant, as do compressed-air or electric locomotives, and of 
 being readily understood and operated by the average mine mechanic. The 
 last feature is of importance in securing an engine runner in outlying districts 
 where skilled labor is scarce. The advantage of carrying their own power, 
 that is, of being self-contained, is shared alike with compressed-air, gasoline, 
 and storage-battery electric locomotives. For the reasons given in the first 
 paragraph, they can only be used on return air-courses and not then if the 
 amount of gas present is at all considerable or if the mine is liable to sudden 
 outbursts of methane; hence, they are not adapted to gathering either from 
 rooms or from side entries. This necessitates the use of some power other 
 than steam for that purpose ; and the use of two kinds of power is not generally 
 economical and is to be avoided whenever possible. 
 
 Steam Mine Locomotives. Steam mine locomotives are generally similar to 
 the small locomotives used for switching on surface railroads. They have four or 
 six drivers, no pony truck or tender, and carry their water in a saddle tank over 
 the boiler and their coal in a box in the cab. When four drivers are used, all 
 have flanges; when six drivers are used, the middle pair are not flanged in order 
 that the locomotive may more readily pass around curves. The height of the 
 locomotive should be from 14 in. to 16 in. less than the thickness of the seam, 
 in order to give about 4 in. overhead clearance. 
 
 The wheel base of these locomotives, which must be as small as possible 
 to permit of easy passage around the sharp curves common in mines, varies 
 from 3 ft. in. on the small four-wheel engine weighing 8,000 lb., to 8 ft. 6 in. 
 on the largest six-wheel engine weighing 64,000 lb. These locomotives are 
 provided with reversing gear, couplers at both ends, and the sand box is arranged 
 to deliver sand to the rail when the engine is running in either direction. 
 
 The table on page 796 gives the manufacturers' dimensions, weights, power, 
 etc., of standard four-wheel steam mine locomotives. 
 
 Power of Steam Locomotives. The tractive force, or tractive effort, of a 
 locomotive is the total force developed by it that is available for moving a 
 load ; this depends on the size of the cylinders, the diameter of the driving wheels, 
 and the steam pressure. The tractive power of a locomotive is the measure of 
 its ability to pull a load and depends on the adhesion between the driving 
 wheels and the rails, which, in turn, depends on the weight of the locomotive 
 and the coefficient of friction. Under ordinary conditions, and also on a wet. 
 
796 
 
 HAULAGE 
 
 
 sanded rail, the adhesion or adhesive 
 power as it is generally called, is about 
 one-fifth the weight of the locomotive; 
 with favorable conditions and a dry 
 rail without sand, it is about one-fourth; 
 and on a well-sanded dry rail, about 
 one-third the weight. 
 
 If the tractive force of a locomotive 
 exceeds the adhesive power, the wheels 
 will slip and part of the tractive power 
 will be wasted. The power driving the 
 locomotive and the weight on the driv- 
 ing wheels must, therefore, be properly 
 proportioned to obtain satis factory 
 results, for if the cylinders of a steam 
 or an air locomotive are too large the 
 driving wheels will slip, showing that 
 there is too much power for the weight. 
 A locomotive in this condition is said 
 to be over 'Cylinder -ed. On the other 
 hand, if there is not enough power for 
 the weight, so that the wheels will not 
 move, the locomotive is said to be 
 under cylinder ed. The sustained trac- 
 tive power, that is, the power exerted 
 by a locomotive when traveling at its 
 normal speed and which is a measure 
 of the load it will pull continuously is 
 commonly taken as 25% of the weight 
 of the locomotive; and this, whether 
 the motive power is steam, compressed- 
 air, gasoline, or electricity. 
 
 The drawbar pull of a locomotive is 
 that portion of its tractive power that 
 is available for pulling a load; that is, 
 it is the total tractive power less the 
 power required to move the machine 
 itself. The drawbar pull may be meas- 
 ured by a dynamometer placed between 
 the locomotive and the first car of the 
 trip. The terms tractive power and 
 drawbar pull are often used to express 
 the same idea. While such use is never 
 strictly correct, on a level track the 
 weight of the locomotive is such a very 
 small proportion of the weight it can 
 pull, that the statement is practically 
 true. Thus, the hauling capacity of a 
 42,000-lb; locomotive is given by the 
 manufacturers as 1,255 T. on a level 
 track. As the weight of the locomo- 
 tive is but 21 T., or less than 2% of the 
 weight it can pull, the reduction to be 
 made from the tractive power to get 
 the drawbar pull is of no practical im- 
 portance. On an up grade, however, 
 while the tractive power remains the 
 same, the drawbar pull decreases rapidly 
 on account of the increased amount of 
 power required to run the locomotive 
 itself. 
 
 On long hauls, the average draw- 
 bar pull required should be well within 
 the rated pull, while, on short hauls 
 and for intermittent service, a locomo- 
 tive may be operated at its rated ca- 
 pacity. The sharpest grade against the 
 loaded trip should be used in calculat- 
 
HAULAGE 797 
 
 ing the size of a locomotive, and on a short grade, a locomotive may be worked 
 very close to the maximum adhesive power, or slipping point, as it is called. 
 The following empiric formula is C9mmonly used by manufacturers to 
 determine the tractive power of steam mine locomotives: 
 
 d 
 in which T = tractive power, in pounds; 
 
 D = diameter of cylinder, in inches; 
 
 L = length of piston stroke, in inches; 
 
 P = boiler pressure, in pounds per square inch; 
 
 d = diameter of driving wheels, in inches. 
 
 From this formula, it is apparent if the steam pressure is increased or 
 decreased, the tractive power will be similarly affected. Likewise, if the boiler 
 pressure remains the same, an increase in the diameter of the driving wheels 
 is accompanied by a decrease in the tractive power, and vice versa. Thus, 
 on surface railroads, freight locomotives which must have great tractive power 
 have relatively small drivers, whereas locomotives used in express service 
 where speed and not ability to haul heavy loads is of the greatest importance, 
 have large drivers. Taking the mean effective pressure of the steam in the 
 cylinders as 85% of the boiler pressure (.85) allows for the friction of the 
 locomotive itself; hence, on level roads the drawbar pull may be taken to be 
 the same as the tractive power calculated by the formula. The internal 
 frictional resistance of locomotives is usually taken as 6.5 to 7.5 Ib. per T. 
 of the weight on the drivers, while the tractive power is taken as 300 to 450 Ib. 
 per T. 
 
 EXAMPLE. What are the tractive power and drawbar pull of a steam mine 
 locomotive, weighing 14,000 Ib., with 6"X10" cylinders and drivers 23 in. in 
 diameter, when the boiler pressure is 140 Ib. per sq. in., both on a level track 
 and on a 2.5% grade? 
 
 SOLUTION. By substituting in the foregoing formula, the tractive power on 
 a level track is found to be 
 
 e^X IPX. 85X140 
 j= = 1, sou ID. 
 
 The drawbar pull may be taken as the same. 
 
 On the grade, while the tractive power is the same, the drawbar pull is less 
 than this by the amount of power required to move the locomotive itself up 
 grade, or by 14,000 X. 025 = 350 Ib. The drawbar pull on a 2.5% grade is, 
 thence, 1,860-350 = 1,510 Ib. 
 
 EXAMPLE. How many loaded cars weighing 7,500 Ib. each can be pulled 
 up a 2% grade by a locomotive weighing 25,000 Ib., if it has 9"X 14" cylinders, 
 28-in. drivers, and a steam pressure of 140 Ib.; the friction of the mine cars 
 being taken as 30 Ib. per T.? 
 
 SOLUTION. The tractive power, which may be calculated from the formula 
 or taken from the table, is 4,800 Ib. The resistance to motion, in pounds 
 per ton, is for friction 30 Ib. and for the grade 2,000 X. 02 = 40 Ib.; or a total 
 of 70 Ib. Whence the total tractive power of the locomotive on a 2% grade, 
 when expressed in terms of car resistance, is 4,820-f-70 = 69 T., very nearly. 
 Since the locomotive weighs 25,000 lb. = 12.5 T., the drawbar pull, in the 
 same terms, is 69.0- 12.5 = 56.5 T. Because each car weighs 7,500 Ib. = 3.75 T., 
 the locomotive can pull up the grade 56.5-7-3.75 = 15 cars. 
 
 The method just given assumes that the friction of the locomotive is the 
 same as that of the cars, which is not correct. The friction of the locomotive 
 is only about one-quarter that of a car and, as stated, is allowed for in the 
 formula by means of which the tractive power of the locomotive is calculated. 
 The following method may, then, be preferred: The power required to move 
 the locomotive up the grade is 25, 000 X. 02 = 500 Ib. Whence, the drawbar 
 pull is 4,820-500 = 4,320 Ib. The grade resistance per car is 7.500X.02 
 = 150 Ib. and the frictional resistance is 3.75X30= 112.5 Ib.; whence the total 
 resistance per car is 262.5 Ib., and the locomotive can haul 4,320 -T- 262.5 
 = 16+ cars. 
 
 In the foregoing calculations, no allowance is made for the power required 
 to accelerate the locomotive and train, n9r is such an allowance generally 
 necessary because of the slow speed of mine traffic and because the excess 
 of power that may be temporarily developed on a well-sanded rail is generally 
 ample to produce the acceleration. However, it may be readily calculated 
 when necessary. 
 
798 HAULAGE 
 
 EXAMPLE. If, in the last example, it requires 1 min. to bring the trip from 
 rest to the legal speed of 6 mi. per hr., how many cars can the locomotive pull 
 up grade? 
 
 SOLUTION. A speed of 6 mi. per hr. = (5,280X6)4-3,600 = 8.8 ft. per sec., 
 and the acceleration is a = Z>-H< = 8.8-7-60 = .147 ft. per sec. per sec. The 
 
 TTT O PC OOO 
 
 power required to accelerate the locomotive is a = -;^-X.147 = 114 Ib. 
 
 From this, the net drawbar pull is 4,320 114 = 4,206 Ib. The power required 
 
 7 500 
 to accelerate a mine car is ^r-r-X.147 = 35 Ib., and the total resistance of 
 
 O4.<& 
 
 each car is 262.5+35 = 297.5 Ib. Hence, the locomotive can, on this grade, 
 start a trip of 4,206 -f- 297.5 = 14+ cars and bring them to a speed of 6 mi. per 
 hr. at the end of 1 min. The gain in adhesion by sanding the rails will unques- 
 tionably permit of the locomotive accelerating the 15 cars which the preceding 
 example shows it can pull up the grade. 
 
 Speed of Steam-Locomotive Haulage. A locomotive cannot pull a maxi- 
 mum load at a maximum speed. As the load increases the speed decreases and 
 vice versa, but no general rule or formula can be given which exactly fixes the 
 relation between the load and the speed. Experience has shown that the rela- 
 tion between the load and speed of mine locomotives is approximately as follows: 
 
 Under usual track conditions, the speed in miles per hour attainable when 
 hauling a train as heavy as the locomotive can start, will be equal, to about 
 one-fifth the diameter of the driving wheels, in inches. 
 
 If the load is reduced to two-thirds to three-fourths of the maximum, the 
 speed will be about one-half the diameter of the driving wheels, in inches. 
 
 If the load is very light, say about one-eighth of the maximum, the speed 
 will be equal to or greater than the diameter of the drivers, in inches. 
 
 Thus, a locomotive with 30-in. wheels which can start a load of, say, 800 T. 
 on a level track, will pull this at a speed of 30-j-5 = 6 mi. per hr.; if the load is 
 reduced to, say, 550 to 600 T., the speed will be increased to about 50 -r- 2 
 = 25 mi. per hr.; and if the load is still further reduced to about 100 T., the 
 speed will rise to 30 mi. per hr., or more. 
 
 Horsepower of .Locomotives. The horsepower that may be developed by 
 a steam locomotive is usually calculated from the formula, 
 p _D*XLX.85PXS 
 
 dX375 
 
 that is, the horsepower of a locomotive is equal to the tractive power multi- 
 plied by the speed 5, in miles per hour, divided by 375. 
 
 COMPRESSED-AIR HAULAGE 
 
 As compressed-air locomotives are self-contained they, like steam and 
 storage-battery locomotives, can travel wherever tracks are laid. They have 
 the great advantage over steam locomotives that they cannot set fire to methane, 
 timber, or coal dust, and therefore may safely be used in gaseous, heavily 
 timbered, or dusty mines. There are no boilers or fireboxes, and hence fewer 
 repairs are needed ; there is no danger from boiler explosions, and they are more 
 easily and cheaply kept in repair than steam locomotives. As they do not give 
 off any smoke or injurious gas, they may be used in any part of any mine, and 
 for gathering, and their exhaust tends to improve the ventilation. On the 
 other hand, their use requires the installation of a more or less expensive 
 power plant, storage tanks or lines, pipe lines, etc., although only a part of the 
 entire outlay is chargeable to haulage where compressed-air coal-cutting 
 machines are used. They are not so high as steam locomotives of the same 
 tractive power and may therefore be used in thinner seams, but their greater 
 length prohibits their employment on sharp curves if the entries are narrow. 
 They are, also, no exception to the rule that locomotives of all types work 
 uneconomically on grades because of the large amount of power required to 
 propel the motor itself. A compressed-air haulage plant will generally cost 
 more than an electric plant of the same working capacity, but there is no danger 
 of electric shock where it is used, nor of igniting methane or coal dust by the 
 arc produced when electric power lines come in contact with one another or 
 with metal. 
 
 A compressed-air haulage plant consists of an air compressor driven by a 
 steam engine or by an electric or hydraulic motor, which compresses the air 
 to a pressure of 1,000 Ib. per sq. in. or more; a storage system for the air until 
 
HAULAGE 799 
 
 it is needed by the locomotive, which may consist of receivers or tanks, but is 
 usually the pipe line connecting the compressor with the charging stations 
 where the engine receives its supply of air; and one or more locomotives, which 
 may be either simple or compound. 
 
 Simple, or Single-Stage, Compressed-Air Locomotives. A compressed-air 
 locomotive has the driving and running gear of a steam locomotive, but the 
 boiler of the latter is replaced by a long, riveted, steel-plate, storage tank 
 containing the supply of air under a pressure of from 800 to 1,000 Ib. per sq. in. 
 These tanks vary from 26 to 42 in. in diameter, from 7 to 22 ft. in length, and 
 from 50 to 350 cu. ft. in capacity, their size depending on the air consumption 
 of the locomotive, which is determined largely "by the length of time it must 
 run without recharging. When necessary to reduce the height of the loco- 
 motive, the single tank may be replaced by two or more smaller ones, the 
 combined capacity of which is equal to the one large one. In cases where 
 the length of the haul requires unusual storage capacity and the size of the 
 locomotive is limited by the height or width of the entry or like practical 
 considerations, it is customary to use pressures up to 2,000 to 2,500 Ib. per 
 sq. in. The single riveted-steel tank is then replaced by a series of very heavy 
 seamless steel tubes about 9 in. in diameter; but these excessive pressures are 
 very rarely used about mines. 
 
 The air passes from the high-pressure, main storage tank to the auxiliary 
 tank or reservoir, which is about 9 in. in diameter and two-thirds as long as 
 the main tank. In this it is held at the working pressure of, usually, 140 Ib. 
 per sq. in., and passes from it directly to the cylinders. Between the tanks is 
 an automatic reducing valve and sometimes a stop-valve. The object of the 
 former is to maintain automatically a uniform pressure in the auxiliary reservoir 
 and consequently in the cylinders. The stop-valve, when used, is placed 
 between the storage tank and the reducing valve and is controlled by the same 
 lever as the throttle valve. When the latter is open the stop-valve is open, 
 thus admitting air to the auxiliary reservoir only as air is drawn from that into 
 the cylinders, and preventing leakage between the two. 
 
 The air passes from the auxiliary tank to the cylinders through a balanced 
 throttle valve, which permits of the maintenance of a constant working pres- 
 sure, prevents waste of air, and makes the locomotive more easily managed. 
 A stop- valve is placed between the auxiliary tank and the throttle valve to 
 prevent leakage of air past the latter into the cylinders. 
 
 These locomotives are provided with a safety valve, reversing gear, oil 
 cups, whistle, head- and tail-lights, sand box, and the other accessories of 
 steam locomotives. They may have either four or six drivers, the latter, 
 because of their relatively long wheel base, being the better adapted to long 
 straight hauls. The table on page 800 gives the dimensions of the standard, 
 or stock, sizes of these locomotives as made by the H. K. Porter Company, 
 Pittsbucg, Pa., although they have been largely displaced by the two-stage 
 motors described later. 
 
 Reheating Compressed Air. The efficiency of compressed air can be 
 greatly increased by reheating before admitting it into the cylinders, but in 
 haulage machinery the added complication of the mechanism needed for the 
 purpose is seldom justified by the saving in fuel or the increased efficiency, 
 except where the haul is very long or where the price of fuel is high. The 
 first condition rarely and the second never exists in coal-mining practice. The 
 air may be heated before entering the cylinders by partially filling the auxiliary 
 air-storage tank with water, which is kept hot by the injection of steam while 
 the main tanks are being filled at the charging station. Indirectly, this 
 method of heating increases the efficiency in another way; the moisture taken 
 up by the air from the hot water improves the lubrication in the valves and 
 cylinders. The cylinders of compressed-air locomotives are not lagged as are 
 those of steam-locomotives and, further, they are sometimes cast with the 
 outside corrugated so as to increase the surface exposed to the relatively warm 
 mine air. 
 
 The air may be effectively heated in a device known as an interheater, which 
 is explained under Compound Locomotives. 
 
 Compound, or Two-Stage, Compressed-Air Locomotives. There is no 
 essential difference in mechanical construction and accessories between the 
 simple, or single-stage, and the compound, or two-stage, compressed-air 
 locomotive. - In the latter, the air in the auxiliary reservoir is under 250 Ib. per 
 sq. in. pressure (as opposed to 140 Ib. in the simple locomotive) and passes 
 to a single high-pressure cylinder through the usual stop and throttle valves. 
 In the high-pressure cylinder, the air is expanded down from 250 to 50 Ib. 
 
800 
 
 HAULAGE 
 
 
 . 2 
 
 s 
 
 o 
 o 10 
 
 3 .fO CO 
 X 
 
 o ! 
 
 5 
 
 1.B 
 
HAULAGE 801 
 
 pressure and is reduced in temperature to about 140 P. below that of the 
 atmosphere or, say, from 60 above to 80 below zero. In order to restore as 
 much as possible of this lost heat to the air, the high-pressure exhaust passes 
 into an interheater, which consists of a cylindrical tank surrounding a number 
 of brass or aluminum tubes of small diameter. The exhaust from the low- 
 pressure cylinder, by means of a device like the exhaust nozzle of a steam 
 locomotive, draws the warm mine air through the thin tubes of the interheater, 
 and the high-pressure exhaust which is circulating around and between these 
 tubes is raised in temperature to within about 15 of that of the mine air 
 or, say, to 45 F. After being heated, the air is led to the low-pressure cylinder 
 or cylinders, where its pressure is reduced from 50 Ib. t9 that of the atmosphere, 
 and is then exhausted and used to draw air through the interheater, as explained. 
 In expanding from 250+14.7 = 264.7 Ib. pressure at 460 +60 = 520 tempera- 
 ture to 50 + 14.7 = 64.7 Ib. pressure at 460 80 = 380 temperature, both pressure 
 and temperature being absolute, one volume of exhaust air from the high- 
 pressure cylinder will be increased to -^~- X^ = 2.99 volumes. In the 
 interheater, the temperature is increased from 380 to 460+45 = 505 absolute, 
 and its volume from 2.99 to 2.99X~ = 3.97+, or to, say, 4 volumes. For 
 
 OoU 
 
 this reason, the area of the low-pressure cylinder or cylinders is made four 
 times as great as that of the high-pressure cylinder so that the work don in 
 them may be the same. 
 
 The cylinders _ are arranged in one of two ways. In the smaller locomo- 
 tives, there are single high-pressure and low-pressure cylinders, one on each 
 side, the latter having twice the diameter or four times the area of the former. 
 Consequently, the over-all width of the locomotive is greater on the low-pressure 
 than on the high-pressure side. In the larger locomotives, there are two 
 low-pressure cylinders arranged in tandem whose joint area is four times that 
 of the single high-pressure cylinder but whose diameters are to that of the 
 high-pressure cylinder as 1 : A/2, that is, as 1 : 1.414. The object of two, 
 instead of one, low-pressure cylinders is to reduce the over-all width on the 
 low-pressure side. 
 
 These locomotiyes are furnished with either four or six drivers, but the 
 latter, owing to their long wheel base and consequent stiffness on sharp curves, 
 are not recommended unless the haulage road is straight or the lightness of the 
 rail requires that the weight of the engine should be distributed over a greater 
 length of track. Where loaded cars must be pulled out of dip places to the 
 entry or where empty cars must be pulled to the face of a pitching room, the 
 locomotive is provided with a reel or drum holding from 300 to 1,000 ft. of wire 
 rope, the drum being turned by a small engine operated by compressed air 
 while the motor is blocked on the rails. For use in very narrow places, the 
 cylinders are placed between the drivers, that is, the locomotive is inside 
 connected. For exceptionally long hauls an extra supply of air may be carried 
 in a tender but as the weight of the latter reduces the paying load the loco- 
 motive can haul, it is better practice to increase the pressure in the main 
 storage tank 2,000 or 2,500 Ib., as heretofore explained. 
 
 The gain in efficiency through using two-stage instead of single-stage 
 expansion is very considerable, amounting to 40 and even 60% in cases. 
 
 Dimensions of Two-Stage Compressed-Air Locomotives. The following 
 table gives the dimensions of standard two-stage compressed-air locomotives 
 manufactured by the H. K. Porter Company, Pittsburg, Pa. In all cases, the 
 charging pressure is between 700 and 1,200 Ib. and the working pressure is 
 250 Ib. in the high-pressure and 50 Ib. in the low-pressure cylinder. The 
 tank pressure and capacity are adjusted by the manufacturer to suit local 
 conditions and requirements. The weight of the locomotive for the same 
 size of cylinders depends on the gauge of the track, capacity of the storage 
 tanks, etc. In special cases, the width outside the gauge line may be made 
 less than that given in the table. The height of the entry must be at least 2 
 in. more than that of the locomotive above the rail to provide the necessary 
 headroom. 
 
 The first four locomotives, which have one high- and one low-pressure 
 cylinder, make a class by themselves. By reason of their moderate storage 
 capacity and lightness they are adapted to gathering and the short wheel 
 base recommends them for use on crooked entries. They can be made for any 
 width of track and their height, which is not given in the table, is less for wide 
 then for narrow gauges. 
 
 51 
 
802 
 
 HAULAGE 
 
 ? si 
 
 v CO ** T-i ^ O 
 
 > TtH "* * O "* ^ * 2' 
 
 ,-lrH <N Q 1 ^ -2^^' 
 
 4* O-* 
 
 - _ 
 
 l-l rH (N O Q r-(rH O 
 
 * rtMH- 
 
 1C I-H O -^ 00 O5 '-' IM rti OO 01 ^ 11 ^^ 
 
 """" 
 
 g^-r^ 
 
 b 
 
 ^ cq ^Mc 
 
 g^ 
 .1 
 
 g 
 
 ss 
 
 Illll 
 
 
 
 
 1 511 
 
 
 Ui^llS 
 
 5 *g.--',*. po 
 
 ^ g +J > to w M 
 
 ^.^*'-eS.S:l 
 
 II 
 
 8 : 
 
 ty t/3 
 
 ;1IS 
 
 w 
 
 
 feS| 5 ^I'lfi - 
 
 i.a!il IB i22 E.'S'S'S 
 
 ZPp^J ^ WS^H^^rt 
 
HAULAGE 
 
 803 
 
 jlb 3 ggjgg 
 
 S 
 
 Heig 
 Main r 
 Weigh 
 Tracti 
 Lighte 
 Radius 
 Radius 
 
 The second four locomotives, all 
 but the first of which have two low- 
 pressure cylinders, have four drivers 
 and are standard for main line service. 
 
 The last four locomotives are also 
 standard for main line use, and are 
 the same as the preceding four except 
 that they have six drivers and conse- 
 quently are stiffer on curves. 
 
 Tractive Power of Compressed- 
 Air Locomotives. The tractive power 
 and drawbar pull of compressed-air 
 locomotives are calculated by the same 
 methods as those of steam locomo- 
 tives. Since the efficiency of the air 
 is increased by absorbing heat from 
 the cylinders, pipes, etc., at seven- 
 eighths cut-off, which is practically 
 full stroke, the cylinder pressure may 
 be taken as 98% of the auxiliary-tank 
 pressure and not as 85% of_the boiler 
 pressure as in steam locomotives. For 
 earlier cut-offs, the efficiency is less 
 than this; but in any case, for equal 
 cut-off, the efficiency of air is greater 
 than steam. The formula for the 
 tractive power of a compressed-air 
 locomotive, as modified from that of 
 a steam locomotive is, thence, 
 
 ^ 
 
 d 
 
 in which the symbols have the mean- 
 ings given for steam locomotives, ex- 
 cept p, which is the working pressure 
 in the auxiliary tank. 
 
 The tractive- power given in the 
 preceding tables is calculated by this 
 formula, but in practice, as in the case 
 of all self-contained haulage locomo- 
 tives, but 50 to 90% pf the theoretical 
 power can be continuously exerted 
 owing to poor track, imperfect lubri- 
 cation, etc. 
 
 Locomotive Storage Tanks. The 
 amount of air that a locomotive must 
 carry at high pressure in its main 
 storage tanks depends _in part on the 
 length of the run and in part on the 
 tractive effort that it must exert. 
 The length of the run is readily de- 
 termined and is twice the distance 
 from the charging station to the place 
 where the loaded trip is made up. 
 The tractive effort that the locomo- 
 tive exerts depends on the weight of 
 the empty and loaded cars that must 
 be hauled on the inbound and out- 
 bound runs, respectively, and the 
 grades that must be overcome. In 
 order, then, to determine the net 
 tractive effort at any part of the run, 
 it is necessary to have a profile of the 
 road showing the grades with their 
 amount and length. The tractive 
 effort required to overcome any grade 
 determines the average cylinder pres- 
 sure; this determines the point of cut- 
 
804 HA ULAGE 
 
 off; and this, in turn, determines the volume of air consumed per stroke of 
 the piston. The number of strokes of the piston made while moving any 
 distance multiplied by the volume of air consumed per stroke, gives the 
 total volume of air used during that part of the run. The sums of the volumes 
 of air required to overcome the various grades gives the total amount of air 
 required for the round trip; and to this 20% is added as an allowance for emer- 
 gencies. Storage capacity is provided for this volume of air when compressed 
 from four to six times the working or cylinder pressure. Favorable grades are 
 of much more importance in compressed-air than in steam haulage, because 
 in the former the locomotive must carry all its power (compressed-air) with 
 it, while in the latter the power (steam) is generated in the locomotive itself 
 while in motion. 
 
 Air is sometimes admitted to the cylinders throughout nearly full stroke 
 and consequently, as the exhaust is at high pressure, the efficiency is lower 
 than it should be. This practice is doubtless due to the tendency to use as small 
 a motor as possible for the service required, on account of the limited headroom 
 and narrow crooked gangways so common in mines. Better economic results 
 are obtainable, however, by using the air expansively and increasing the size 
 of the locomotive and the weight on the drivers; this is almost always done with 
 large locomotives. "Ample reserve power is available when necessary, because 
 full tank pressure can be admitted to the cylinders in starting a heavy load, or 
 in pulling on steep grades and sharp curves. 
 
 In using the air expansively, as can be done with properly proportioned 
 cylinders, there should be no trouble from freezing of the moisture. Although 
 the cold developed will produce a low cylinder temperature, as the initial work- 
 ing pressure is so much higher than that employed for pumps and other com- 
 pressed-air machinery, the expanded air becomes relatively dry, and the force 
 of the exhaust will be sufficient to keep the ports clear of accumulated ice. 
 To this end, the exhaust ports should be large, straight, and short. 
 
 Stationary Storage. The stationary storage system from which the main 
 storage tanks of a compressed-air locomotive are charged may consist of a pipe 
 line or of one or more storage tanks. For short hauls, the storage tank is 
 probably more convenient, but under all ordinary conditions the pipe line 
 from the air compressor to the locomotive charging station is made of a 
 diameter and strength sufficient to serve as a storage reservoir. The volume 
 of stationary storage is found from the formula, 
 
 " (P-P)' 
 
 in which V = volume of stationary storage, in cubic feet; 
 v volume of locomotive storage, in cubic feet; 
 P = pressure in stationary storage, in pounds per square inch; 
 p = pressure in locomotive storage, in pounds per square inch; 
 p' = pressure in locomoitve storage at time of charging, in pounds per 
 square inch. 
 
 EXAMPLE. The storage tanks of a compressed-air locomotive have a 
 capacity v of 160 cu. ft. at a pressure p of 800 Ib. per sq. in. If, at the time 
 of charging the pressure p' in the locomotive storage tanks is 250 Ib. and the 
 pressure P in the pipe line (stationary storage) is 1,000 Ib., what must be the 
 volume V of the stationary storage? 
 
 SOLUTION. By substituting the given values in the formula, 
 
 It should be noted that the pressure P in the pipe line is, in this case, 
 200 Ib. per sq. in. more than that in 'the locomotive storage tanks, in order 
 that the latter may be charged as speedily as possible. The time of charging 
 is about 1.5 min., during but 40 to 50 sec. of which the valve connecting the 
 pipe line to the locomotive is open. The pressure p' in the locomotive tanks 
 has here been taken' at 250 Ib., the same as the working or cylinder pressure 
 maintained in the auxiliary tank and to which it has been reduced from the 
 charging pressure of 800 Ib. in the main tank because of the air consumed by 
 the locomotive in doing its work. On short hauls, by reason of the small 
 consumption of air, _the pressure of that remaining in the locomotive storage 
 tanks _at charging time may be considerably more than the working pressure 
 as maintained in the auxiliary reservoir, but can hardly be less without reduc- 
 ing the tractive power of the locomotive. 
 
HA ULAGE 
 
 805 
 
 In the preceding example, if the pipe line from the compressor to the 
 charging station is, say, 4,000 ft. long, each linear foot must have a capacity of 
 
 = . 1 1 cu. ft. in order to store the 440 cu . f t. of air. From the accompany- 
 ing table of pipe suitable for compressed-air haulage plants, a 45-in. pipe, having 
 a capacity of .1105 cu. ft. per ft. of length, will be required. In order that 
 the time of charging may be as short as possible, the volume of the pipe line 
 storage is usually made two to three times that of the locomotive tanks, although 
 this ratio will depend on the line pressure and, in some measure, on the number 
 of locomotives and charging stations, the frequency of charging, etc. In the 
 example, the ratio of locomotive to pipe line storage capacity is 160 : 440 
 or 1 : 2.75. If there is but one charging station, the storage capacity is ample, 
 and the compressor is of sufficient size and power, the drop in pressure due to 
 charging one locomotive is practically certain to be recovered before another 
 can be coupled to the charging station. If there are several charging stations, 
 which may be in use at or about the same time, it is advisable to increase the 
 storage capacity of the line unless a wait of a few minutes is not of importance. 
 
 STANDARD STEAM AND EXTRA-STRONG PIPE USED FOR COM- 
 PRESSED-AIR HAULAGE PLANTS 
 
 
 
 Linear 
 
 Steam 
 
 Extra Strong 
 
 
 Trade 
 Diameter 
 Inches 
 
 Cubic 
 Feet in 
 1 Lin. 
 Ft. 
 
 Feet 
 Neces- 
 sary to 
 Make 
 1 Cu. 
 
 
 
 Trade 
 Diameter 
 Inches 
 
 Thick- 
 ness 
 
 Weight 
 per Foot 
 
 Thick- 
 ness 
 
 Weight 
 per Foot 
 
 
 
 Ft. 
 
 Inch 
 
 Pounds 
 
 Inch 
 
 Pounds 
 
 
 2 
 
 .0218 
 
 45.41 
 
 .15 
 
 3.61 
 
 .22 
 
 5.02 
 
 2 
 
 2* 
 
 .0341 
 
 29.32 
 
 .20 
 
 5.74 
 
 .28 
 
 7.67 
 
 2} 
 
 3 
 
 .0491 
 
 20.36 
 
 .21 
 
 7.54 
 
 .30 
 
 10.20 
 
 3 
 
 3* 
 
 .0668 
 
 15.00 
 
 .22 
 
 9.00 
 
 .32 
 
 12.50 
 
 3i 
 
 4 
 
 .0873 
 
 11.52 
 
 .23 
 
 10.70 
 
 .34 
 
 15.00 
 
 4 
 
 4J 
 
 .1105 
 
 9.05 
 
 .24 
 
 12.30 
 
 .35 
 
 17.60 
 
 4* 
 
 5 
 
 .1364 
 
 7.33. 
 
 .25 
 
 14.50 
 
 .37 
 
 20.50 
 
 5 
 
 &* 
 
 .1650 
 
 6.06 
 
 .26 
 
 16.40 
 
 .40 
 
 24.50 
 
 5J 
 
 G 
 
 .1963 
 
 5.10 
 
 .28 
 
 18.80 
 
 .43 
 
 28.60 
 
 6 
 
 If the length and diameter and, hence, the volume V of the storage line 
 are determined by piping already in place, the pressure P required in the pipe 
 line to instantly charge the locomotive may be found by transposing the 
 preceding formula, and is, 
 
 V ( 
 
 EXAMPLE. If the volume v of the locomotive storage tanks is 160 cu. ft.; 
 the full pressure p in the locomotive storage tanks is 800 Ib. per sq, in.; the 
 pressure remaining in these tanks at the time of charging is 250 Ib.; and the 
 storage line is 4,000 ft. of 4|-in. pipe, to what pressure must the air in the storage 
 line be compressied to charge the locomotive? 
 
 SOLUTION. A 4^-in. pipe has a volume of .1105 cu. ft. per ft. of length. 
 If this volume is taken as .11 cu. ft., that of the storage line 4,000 ft. long will 
 be 4,OOOX.11 = 440 cu. ft. = F. Substituting, 
 p = 160X(80Q-250)+440X800 
 440 
 
 Pipe Lines and Charging Stations. Pipe lines should be as straight as 
 possible and should not be placed in a trench and covered, as leakage is then 
 difficult to detect and general inspection is impossible. Expansion joints 
 are not necessary underground where the temperature is practically uniform 
 but one may be needed on the surface between the compressor and the mouth 
 of the mine. The lengths of pipe should be connected by heavy, threaded, 
 
806 HA ULAGE 
 
 screw couplings that are cqunterbored with an annular groove into which a 
 strip of soft metal can be driven to stop any leakage. Flanged or union coup- 
 lings should be placed at all charging stations and at intervals of 300 ft. or 
 so along the line. The ends of the pipe are riveted into recesses in the flanges 
 and are hammer-faced flush with the center bore. The flanges are also counter- 
 bored to hold a soft-metal or vulcanized-rubber gasket. The introduction of 
 these flange couplings permits of the easy repair, extension, or alteration of the 
 line. The pipe should be given one or more heavy coats of some non-corrosive 
 paint. 
 
 A valve should be placed between the C9mpressor and the pipe line, at 
 each charging station and at convenient points along the line, so that the 
 compressor or parts of the line may be inspected and repaired without loosing 
 any of the air in the pipes. Where the line runs down a shaft, a heavy cast tee 
 with several feet of pipe below it is placed at the bottom of the shaft to collect 
 water. A waste valve is inserted at the bottom of the pipe to permit the 
 water to be blown off. 
 
 The charging stations are simple in construction and repair. Attached 
 to the pipe line by a flange is a special tee to which is fitted a H-in. gate valve 
 having a short nipple into which is screwed a Moran flexible joint to which is 
 attached a short length of pipe. The Moran joint is of the ball-and-socket 
 type so that the pipe may be turned in any direction necessary to couple up 
 with the locomotive tanks. When not in use, the supply pipe is turned parallel 
 to the track. The locomotive is also provided with a pipe having ball-and- 
 socket joints and a gate valve opening into the locomotive tanks but which 
 closes as soon as the gate valve on the pipe line is closed to cut off the pressure. 
 A special coupling is used to connect the supply line and locomotive pipes. 
 This coupling cannot be broken as long as any pressure remains in the pipes 
 between the gate and check-valves, so a small globe valve is placed in the 
 line immediately above the gate valve in order to bleed off the remaining air. 
 All valves must be kept tight, packing must be replaced when worn out or lost, 
 and all joints and connecting pipes must be supported to prevent undue stress 
 coming upon them. 
 
 Air Compressors for Haulage Plants. The capacity of an air compressor 
 for a given plant depends on the number of locomotives, the capacity of their 
 tanks, and the length of time between chargings. The number of cubic feet F 
 of free air (air at atmospheric pressure, 14.7 Ib.) required to charge a loco- 
 motive may be found from the formula 
 
 14.7 .:. 
 
 in which the letters have the meaning of those in the preceding formula. 
 Having found F, the capacity of the compressor C in cubic feet of free air per 
 minute may be found from 
 
 in which n equals the number of charges in the time /. 
 
 EXAMPLE. A haulage system requires that the single locomotive in use 
 shall be charged three times an hour. The storage-tank pressure is 800 Ib. 
 and the pressure remaining in the tank at the time of charging is 250 Ib. If 
 the locomotive tanks have a capacity of 160 cu. ft., what must be the size 
 of the compressor in cubic feet per minute? 
 
 SOLUTION. Here z> = 160, = 800, ' = 250, = 3, and * = 60 min. By 
 substitution, 
 
 . ft., about 
 
 The required capacity of the compressor is, 
 3X00 
 
 Compressors for charging are of the three-stage type for pressures up 
 to 1,000 Ib. per in., and for higher pressures are usually four stage. They 
 are provided with intercoolers as explained under Compressed Air. 
 
 The horsepower required to compress the air may be found from the follow- 
 ing table. Thus, in the example, to compress 300 cu. ft. of air per min. to 
 800 Ib. in a three-stage compressor will require 3X32.5 = 97.5 H. P. 
 
HAULAGE 
 
 807 
 
 HORSEPOWER NECESSARY TO COMPRESS 100 CU. FT. OF FREE AIR 
 
 TO VARIOUS PRESSURES AND WITH TWO-, THREE-, AND 
 
 FOUR-STAGE COMPRESSORS 
 
 Gauge 
 Pressure 
 Pounds 
 
 Horsepower Necessary 
 
 Gauge 
 Pressure 
 Pounds 
 
 Horsepower Necessary 
 
 Two- 
 Stage 
 
 Three- Four- 
 Stage Stage 
 
 Two- 
 Stage 
 
 36.3 
 37.8 
 39.7 
 41.3 
 43.0 
 44.5 
 45.4 
 
 Three- 
 Stage 
 
 Four- 
 Stage 
 
 100 
 200 
 300 
 400 
 500 
 600 
 700 
 800 
 
 15.7 
 21.2 
 24.5 
 27.7 
 29.4 
 31.6 
 33.4 
 34.9 
 
 15.2 
 20.3 
 23.1 
 25.9 
 27.7 
 29.5 
 31.2 
 32.5 
 
 14.2 
 
 18.8 
 21.8 
 24.0 
 25.9 
 27.4 
 28.9 
 30.1 
 
 900 
 1,000 
 1,200 
 1,400 
 1,600 
 1,800 
 2,000 
 2,500 
 
 33.7 
 34.9 
 36.5 
 37.9 
 39.4 
 40.5 
 41.6 
 43.0 
 
 31.0 
 31.8 
 33.4 
 34.5 
 35.6 
 36.7 
 37.8 
 39.0 
 
 GASOLINE-MOTOR HAULAGE 
 
 Construction of Gasoline Locomotives. Gasoline locomotives, except for 
 the absence of a trolley pole, greatly resemble electric locomotives in appear- 
 ance as all their moving parts, gasoline tanks, engines', etc., are enclosed in 
 the same form of iron or steel casing in order to protect them from injury 
 from falling roof, collision, etc. These locomotives are, at present, made in 
 various sizes up to 20 T. in weight, those under 5 T. being generally used for 
 gathering. 
 
 The engines are of the four-cycle type, and usually have four cylinders, 
 although the larger ones may have six. The cylinders may be vertical or 
 horizontal, the latter construction being necessary in mines where the head- 
 room is limited. The engine shaft is placed lengthwise of the frame and is 
 connected by gearing to a cross- or jack-shaft near the front end of the loco- 
 motive. From the cross-shaft, power is transmitted to the axle of the nearest 
 pair of driving wheels either by spur gearing or by a chain passing around 
 sprocket wheels. The two pairs of drivers are connected either by rods, as in 
 steam or compressed-air locomotives, or by a chain drive passing over sprocket 
 wheels on each axle. By either arrangement, each axle is a driving axle and 
 the full power of the engines is utilized. There is no general or fixed ratio 
 between the weight, in tons, of a gasoline locomotive and the horsepower 
 developed by its engines. The various manufacturers, in their catalogs, indi- 
 cate a ratio of from 6 to 8 to even 10 engine horsepower to each ton weight of 
 the locomotive, but the engines are rated much below their capacity. Thus, 
 an engine rated in the catalog as, say, 40 H. P. will commonly develop 50 to 
 55 or more H. P. upon brake tests, and will exceed this if its speed is allowed 
 to exceed the 600 to 800 rev. per min., to which these engines are commonly 
 limited. 
 
 The smaller locomotives are made with low and high gears and the larger 
 ones, sometimes but not always, are made with low, intermediate, and high 
 gears, which allows of two and three speeds, respectively, both forwards and 
 reverse; and other speeds may be had by varying that of the engine. The 
 low gear, giving a speed of from 3 to 5 mi. per hr., is used while bringing the 
 trip from rest to full speed (accelerating) or while doing very heavy pulling, 
 while the high (or intermediate) gear is used under all ordinary conditions. 
 The speed changes are made by means of jaw clutches and the forward and 
 reverse motions by means of friction clutches, both mechanisms being operated 
 by levers from the engine cab. The transmission gearing is contained in an 
 oil-tight casing or box through which a continuous flow of oil is circulated 
 from the engine shaft, and which is in operation only while the locomotive 
 is in motion. 
 
 After circulating through the water-jackets surrounding the cylinders, the 
 cooling water passes to radiators or cooling tanks, being forced through the 
 
808 HA ULAGE 
 
 system by a small pump operated by gearing from the main engine-shaft. 
 The radiators are cooled by air from a small muitiblade fan placed on the 
 forward end of the engine shaft. The gasoline fuel is carried in two seamless 
 drawn-steel or copper tanks, which are provided with safety valves (thus giving 
 each tank two valves) to prevent leakage. It is almost always .arranged that 
 the tanks cannot be removed or charged except at a regular charging station, 
 which, in the case of drift mines, is always outside but near the opening. The 
 charging is done in a few minutes by removing the empty tanks and replacing 
 them with full ones, which hold about 5 gal. each. 
 
 The exhaust gases from the cylinders pass to some device intended to cool 
 them and to prevent back firing and the escape of sparks and flame to the 
 atmosphere. In most cases, this consists of a muffler provided with steel 
 tubes, baffle plates, wire gauze, etc., the gases being sometimes led over water 
 as an additional precaution against fire. The muffler also serves to make 
 the motor as nearly noiseless as possible. In one type of locomotive, the 
 exhaust is passed through a series of parallel perforated pipes contained in 
 what is called a deodorizing tank, which is filled with a liquid preparation 
 that extinguishes the flame and neutralizes the smell before the gases finally 
 escape. 
 
 The more recent types of these locomotives are provided with a self-starter, 
 which consists of an electric motor receiving current from a storage battery, and 
 which, by means of reducing gear, can be made to drive the crank-shaft of the 
 main engine. The storage battery is automatically charged by a generator 
 driven by the main engine, and requires no attention. The chief advantage 
 of the self-starter is that it allows the engines of the heavy locomotives, which 
 are difficult to start by hand particularly when cold, to be shut down when 
 the motor is not in motion, and to be readily started when the trip must be 
 moved. Not only does this effect a material reduction in fuel consumed, but 
 is of prime importance in that it prevents the pollution of the mine air by the 
 exhaust gases if the engine is kept in motion while the locomotive is still, the 
 common procedure when the self-starter is not used. The self-starting device 
 is also made a source of current for operating electric headlights. 
 
 These engines are provided with headlights, and tail-lights, a bell, one 
 or more sand boxes, and a whistle operated by compressed air. All have 
 efficient hand-brakes and some of the larger ones have a complete air-brake 
 system, the air being supplied by a small compressor operated from the engine 
 shaft, or otherwise. In this connection, the subject of Internal-Combustion 
 Engines, on page 532, etc., may be consulted. 
 
 Hauling Capacity and Fuel Requirements. The maximum tractive power 
 of a gasoline locomotive is exerted under low gear and may be taken as one- 
 fifth of its weight under ordinary conditions and as one-quarter under favor- 
 able ones. The tractive power under high gear is, in the case of locomotives 
 with two gears, about one-half that under low gear and should be made the 
 basis of estimating the size or weight of a locomotive to meet the prevailing 
 conditions. That is, power is sacrificed to gain speed. The drawbar pull, 
 resistance of the cars, etc., are figured in exactly the same way as for steam 
 locomotives. 
 
 Some choice in the matter of speed is offered. Thus the two-speed loco- 
 motives supplied by a leading manufacturer may be had with speeds of 3 and 6 
 or 4 and 8 mi. per hr., respectively. The 16-T. locomotive of the same maker 
 is offered with four combinations of speeds on the low, intermediate, and 
 high gears, respectively, of 3, 9, and 15, or 4, 12, and 20, or 5, 15, and 25, or 6. 
 18, and 30 mi. per hr. The relative speed ratios for low, intermediate, and 
 high gear are 1 : 3 : 5, or between the low and intermediate 1 : 3 and between 
 the intermediate and high 1 : If. While it is true that the increase in speed 
 is accompanied by a loss in drawbar pull, yet these locomotives under ordinary 
 conditions should pull at full speed under high gear the load they can start 
 and accelerate under low gear. In mine practice, the speed is very commonly 
 limited by law to 6 or 8 mi. per hr., but there seems no good reason why, in 
 main-line haulage where the track and equipment are in first-class modern 
 condition, that speeds of 20 and 30 mi. per hr. would not be perfectly safe. 
 
 The gasoline consumption of these locomotives depends on their size, the 
 loads hauled, the grades, the length of shift, and whether they are operated 
 continu9usly or intermittently. When operated continuously at full power, 
 the engines will probably use a pint, or a little less, gasoline per horsepower 
 per hour. Thus, a 10-T. locomotive with engines, say, of 62.5 H. P., will 
 burn 62.5X8 = 500 pt. = 62.5 gal. of gasoline per 8-hr, shift. But these loco- 
 motives are usually over-engined, so that on the heaviest grades they rarely 
 
HA ULAGE 809 
 
 exert more than three-fourths power. Further, no gasoline is used when 
 descending a grade nor, if provided with a self-starting device, when standing 
 waiting a trip, and but little is required for switching, etc. Experience has 
 shown that it is very unusual for the engines to develop for an entire shift 
 more than one-half their rated horsepower. In the example just cited, this 
 would reduce the gasoline consumption from 62.5 to 31.25, say, 30 gal. per shift, 
 which is at the rate of 3 gal. per T. of weight of the locomotive. This is a 
 maximum. One manufacturer estimates the daily fuel requirements at 8 
 to 10 gal. for a locomotive with 25-H. P. engines (one weighing 3.5 T.), and as 
 10 to 20 gal. for one with engines of 50 H. P. (weighing 8 T.). Mr. Carl Scholz, 
 speaking of the gasoline locomotives in his own mines, where average conditions 
 prevail, says: "The average consumption of gasoline and oil for an 8-hr, 
 shift on a 6-T. motor is about $2, gasoline costing 17 c. per gal." This would 
 indicate a fuel consumption of 12 gal. per shift, perhaps a little more, as the 
 amount paid for oil is not stated. At Gatliff, Tenn., a 5-T. motor uses 11 gal. 
 of gasoline in 9 hr. Available figures indicate that under average working 
 conditions the consumption of gasoline per shift is at the rate of 2 gal. per T. 
 of weight of the locomotive, although in some cases it may be as high as 2.5 gal., 
 and in rare instances 3 gal. It should be noted that the larger locomotives, 
 particularly when fitted with self-starting devices, require relatively less fuel 
 than the smaller ones, or those that must be started by hand. In comparison 
 with steam locomotives, a manufacturer states that the cost of fuel is about the 
 same for each type of motor for the same capacity. 
 
 Cost of Gasoline-Locomotive Haulage. At the No. 2 entry of the Roane 
 Iron Co., Rockwood, Tenn., the round-trip haul is 3 mi. with a uniform grade 
 of 1.5% in favor of the loads. The average weight of the empty cars is 1,400 lb., 
 of the loaded cars 3,640 lb., and the live load or weight of coal per car is 2,240 lb. 
 Ten 20-car trips of empties are hauled in and the same number of loads hauled 
 out from the mine in one shift. The inbound empties have a total daily weight 
 of 140 T., the outbound loads one of 364 T.; the total daily weight moved is 
 504 T., and that of the coal delivered to the tipple is 224 T. The following 
 are the details of the haulage costs by mule and by gasoline motor: 
 
 COST OF HAULAGE AT ROCKWOOD, TENN. 
 By mules: 
 
 4 drivers, at $1.65 $6.60 
 
 9 mules, at $.50 4.50 $11.10 
 
 By motor: 
 
 1 motorman, per day $2.05 
 
 1 coupler, per day 1.65 
 
 13 gal. gasoline, at 11 c 1.50 
 
 2 lb. carbide, at 4 c 08 
 
 J gal. gasoline engine oil, at 23 c .12 
 
 1 gal. transmission case oil .24 $ 5.64 
 
 Saving by motor $ 5.46 
 
 Or, 49.1%. 
 
 The cost per ton of coal delivered to the tipple is 4.955 c. by mules and 
 2.518 c. by locomotive. 140 T. of empties are hauled into the mine a distance 
 1.5 mi. and 364 T. of loads are hauled out the same distance. This is equal 
 to 504 T. hauled 1.5 mi. or 756 T. hauled 1 mi., at a cost of $11.10 or 1.468 c. 
 per T.-mi. by mules and $5.64 or .746 c. per T.-mi. by motor. If the cost 
 of hauling the live load of 224 T. of coal 1.5 mi. (equivalent to 336 T. moved 
 1 mi.) is considered, the cost per ton-mile by mules is 3.303 c. and by motor 
 1.678 c. In neither cost statement is any allowance made for depreciation, 
 repairs, renewals, interest on the investment, etc. As the majority of these 
 charges, particularly the first and third, are much greater in the case of mule 
 than motor haulage, the difference in favor of the locomotive will be greater 
 than that shown by the foregoing figures. 
 
 A 5-T. gasoline-haulage motor at the mines of the Southern Coal and Coke 
 Co., Gatliff, Tenn., handles 500 net T. of coal daily in 9 hr., working 22 da. 
 per mo. The average daily haul is 354 cars weighing 1,200 lb. when empty 
 and a little more than 4,000 lb. when loaded. The haul is from an inside 
 parting 2,500 ft., say mi. from the tipple, on an undulating road, which 
 varies in grade from 1.5% against the loads to 3.5% in their favor. The 
 details of mule and motor haulage are as follows; 
 
. 
 
 11 gal. g 
 Carbide, 
 
 810 HA ULAGE 
 
 COST OF HAULAGE AT GATLIFF, TENN. 
 1 gal. lubricating oil ............ .............. $ .15$ 
 
 i gal. gasoline engine oil ...................... .16 J 
 
 gasoline, at 14 c ....................... 1.54 
 
 use lights but little .................. .15 
 
 M9torman .................................. 2.50 * 
 
 Trip rider .................................. 1.83 
 
 Cleaning and repairs ......................... .40 
 
 6% int. on difference of cost of mules and motor. .52 
 
 Extra upkeep on track over mules ............. .50 
 
 Motor replaces 7 mules, at 42 c. per day for feed $ 2.94 
 
 Three drivers ............................... 7.23 
 
 Reduction to stable boss ...................... .35 
 
 Daily saving by use of motor .................. 2.76 
 
 $10.52 $10.52 
 
 The cost per ton of coal delivered to the tipple, on the basis of 500 T. per 
 da., is 2.104 c. by mules and 1.552 c. by gasoline motor. The empty cars have 
 a total weight of 212 T. and the loaded cars 708 T., making a total weight of 
 920 T. hauled | mi., which is equivalent to 460 T. moved 1 mi. The cost is, 
 hence, 2.287 c. per T.-mi. for mule haulage and 1.687 c. for locomotive haul- 
 age. On the basis of the live, or paying, load only, the cost for transporting 
 500 T. $ mi. (250 T. for 1 mi.) is 4.208 c. per T.-mi. by mules and 3.104 c. per 
 T.-mi. by locomotive. 
 
 A gasoline locomotive at the mine of the Mid valley Coal Co., Wilburton, 
 Pa., which displaces a steam locomotive and five mules, when making but 
 24 mi. per da., or about one-half its capacity, effects a saving over mule 
 haulage of 32.2%. The locomotive is rated at 9 T. and. uses 15 gal. of naptha 
 per day at a cost of 10 c. per gal., or $1.50 for fuel. It is estimated that the 
 consumption of gasoline would be 12 gal. per da., which, at 15 c. per gal., would 
 cost $1.80. For a period of 6 mo., during which 2 hr. of each 9 hr.-da. were 
 devoted to switching and were not properly chargeable to haulage, the average 
 daily mileage for the loaded and empty cars was 12 for each. The empty 
 cars weighed 2.5 T. and the total weight of them handled in 1 da. was 250 T. 
 The loaded cars weighed 5.5 T., and the total weight of them handled in 1 da. 
 was 550 T. The net weight of coal delivered to the mine mouth was, hence, 
 300 T. per da. The daily cost for motor haulage only was as follows: 
 
 COST OF HAULAGE AT WILBURTON, PA. 
 Wages of motorman and helper ......................... $3.35 
 
 15 gal. of naptha at 10 c ............................... 1.50 
 
 Lubricating oil ....................................... .12 
 
 Maintenance, $65.14 for 6 mo., 20 da. per mo .............. 54 
 
 Total ........................................... $5.51 
 
 The cost is, then, 1,837 c. per T. of coal delivered to the mine mouth, or 
 but 1.429 c. per T. if the cost of the time spent in switching is deducted. From 
 the figures furnished, there appear to have been an average of 12.5 trips per 
 day, and the length of haul was not far from 1 mi. With this understanding, 
 the cost per ton-mile was .687 c. for the combined weight of the loads and 
 empties (800 T.) and 1.429 c. per T.-mi. for the 300 T. of coal delivered. 
 
 At the plant of the Shade Coal Mining Co., Windber, Pa., the haulage cost 
 per ton of coal delivered to the tipple was 6.4 c. by mules and 3.15 c. by gaso- 
 line locomotive. On the ton-mile basis, the cost of mule haulage was 12.8 c. 
 and of gasoline haulage 3.79 c. for the coal delivered to the tipple. 
 
 Comparison of Gasoline and Other Types of Haulage Motors. Like other 
 self-contained locomotives (steam, compressed-air, and storage-battery elec- 
 tric), the gasoline motor has the advantage over the ordinary electric mine 
 locomotive operated through a trolley from overhead wires, that it can go 
 anywhere in the mine that the tracks are laid. As compared with the com- 
 pressed-air and overhead and storage-battery electric locomotives, it does not 
 require a more or less expensive plant for the generation of power. As com- 
 pared with the steam locomotive, it is as cheaply operated, does not so greatly 
 befoul and befog the air with unpleasant or dangerous gases, and when the 
 exhaust, carbureter, etc., are properly protected, is not so likely to ignite either 
 coal dust or methane. It -is questionable if the danger of igniting either of 
 
HA ULAGE 
 
 811 
 
 these explosive agents is as great with a well-designed and well-managed 
 gasoline motor as with the ordinary overhead-trolley electric locomotive. 
 
 The chief objections made to this type of locomotive relate to the cost of 
 power and the difficulty of obtaining competent operators and to the danger to 
 the health of the underground workers from the exhaust gases. When the 
 power-plant charges are considered in the cost of electric or compressed-air 
 locomotives, the cost of power for a gasoline locomotive will be found to be 
 very much less than for the other two types. On the other hand, if the mine is 
 already piped or wired for compressed-air or for electric coal-cutting machinery, 
 some study will be required to determine if the haulage can be done more 
 cheaply by gasoline motors than by those operated by the power already in 
 use. Competent operators are readily obtained from outside workers familiar 
 with motor trucks, the use of which as a substitute for horse-drawn wagons is 
 rapidly increasing. Attracted by the better wages prevailing in the mine, a 
 little training in the use of the gasoline locomotive and a familiarity with under- 
 ground work, makes them first-class motormen; The complaint that gasoline 
 locomotives will not take an overload as will electric locomotives does not seem 
 well-founded. It is a question of proportioning the engine power to the 
 weight of the locomotive, and a gasoline motor that has engine power enough 
 to slip its drivers, will pull as great a tonnage as any other locomotive of the 
 same weight. 
 
 It is unquestionably true, however, that a gasoline locomotive does dis- 
 charge into the mine air a certain amount of obnoxious and harmful gases, 
 carbon dioxide and carbon monoxide, respectively. At the 'same time, a 
 definite amount of oxygen is withdrawn from the air and used in the combustion 
 of the gasoline. The amount of these gases will depend on how well the 
 engine is working, and this, in turn, will, in a very great measure, depend on 
 the skill of the operator. The following analyses of mine air taken from work- 
 ings where a gasoline locomotive was used are furnished by Mr. A. J. King, 
 in an article read before the West Virginia Coal Mining Institute and reprinted 
 in the Colliery Engineer for October, 1913; the samples having been taken 
 by Mr. P. A. Grady, formerly mine inspector for the 12th District, West 
 Virginia. 
 
 ANALYSES OF MINE AIR AS AFFECTED BY EXHAUST OF 
 GASOLINE LOCOMOTIVES 
 
 Number of 
 Sample 
 
 C0 2 
 
 2 
 
 CO 
 
 CHt 
 
 N 2 
 
 1 
 
 .07 
 
 20.87 
 
 .03 
 
 .10 
 
 78.93 
 
 2 
 
 .11 
 
 20.92 
 
 .07 
 
 .13 
 
 78.77 
 
 3 
 
 .13 
 
 20.80 
 
 .06 
 
 .32 
 
 78.69 
 
 4 
 
 .09 
 
 20.78 
 
 .03 
 
 .33 
 
 78.77 
 
 5 
 
 .15 
 
 20.91 
 
 .05 
 
 .11 
 
 78.78 
 
 6 
 
 .15 
 
 20.86 
 
 .07 
 
 .10 
 
 78.82 
 
 Sample No. 1 was taken 80 ft. ahead of the air at the face of a room in which 
 the locomotive had been 5 min. with the engines running. The grade was 3% 
 in favor of the loaded car and 6,000 cu. ft. of air per min. was passing on the 
 entry. 
 
 Sample No. 2 was taken in the same place as sample 1, the locomotive 
 having been run up to the face and had pulled out a loaded car. 
 
 Sample No. 3 was taken at the face 210 ft. ahead of the ventilating current, 
 after the locomotive with its engines running had stood in the place for 5 min. 
 and then come out; the fumes were noticeable. 
 
 Sample No. 4 was taken in the same place, the locomotive having run to the 
 face and coupled to a loaded car which it pulled down a 3% grade in 1 min. 
 
 Samples Nos. 5 and 6 were taken on the entry, which had a cross-section 
 of 15 ft. by 5 ft., an area of 75 sq. ft., and through which 6,000 cu. ft. of air 
 per minute was passing. The samples were gathered after the ^locomotive had 
 been made to perform hard work by running up the entry, which had a grade 
 of 5%. 
 
 Mr. O. P. Hood, in the October, 1914, Bulletin of the American Institute of 
 Mining Engineers, gives the following table, which shows the amount of CO 
 and COz, in cubic feet per minute, given off by gasoline locomotives with 
 cylinders of various sizes, when running under both good and bad conditions. 
 
812 
 
 #4 ULAGE 
 
 So 8 
 a+J 
 
 *J* 
 
 II 
 
 3s 
 
 W3 
 
 >0 S 
 
 gjl 
 
 oo 2 
 
 ,0 
 
 ooooooooooooo 
 
 -lOCOOOt^-t^t^TfcooOCOTf 
 
 %$%%$ 
 
 
 lip a! 
 
 *s fi - s 
 
 H o 
 
 So.S 
 
 3 5 
 
 i Tj fll *V 
 
 fill 
 
 xxxxxxxxxxxxx 
 
 )U5 
 
 o 
 
HA ULAGE 813 
 
 Referring to the West Virginia experiments in the first of the preceding 
 tables and disregarding the CO, the greatest amount of gases foreign to normal 
 air is met in the third sample, which shows the presence of .45% of COz and CHi 
 combined, neither of which gases is poisonous even in very much larger amounts 
 than there shown. The dangerous gas is CO, the maximum amount of which 
 that maybe breathed fora short time and intermittently without injurious 
 effects is commonly stated to be .19%. When breathed continuously, air should 
 not contain more than .05% of this gas, and preferably but .025% unless those 
 exposed to its effects are in good health and are not working violently. All 
 the samples show less than the maximum, and the average of all is the safe 
 minimum of .05%. All the samples appear to have been taken in the inner 
 workings at places (the face of a room or entry) where the locomotive would 
 not usually go more than, say, once an hour, and probably not more than five 
 or six times a shift. In the intervals between trips, the CO would soon diffuse 
 even if there was no circulation of air, so that the mine cited was by no means 
 in a bad condition although every effort should be made to keep the content 
 of CO to .05%. In the mine in question, this could readily have been done by 
 increasing the volume of the air-current from 6,000 to 9,000 cu. ft. per min., 
 which would have raised the velocity of the air from 80 to 120 ft. per min.; and 
 neither the volume nor the velocity are high. Mr. King recommends that 
 where gasoline locomotives are used, in addition to the air that would ordinarily 
 be circulated through the entry, there should be a further amount of 1,000 cu. 
 ft. per min. for each ton in weight of the locomotive. 
 
 Mr. King's requirements are considerably in excess of those of one of the 
 leading manufacturers, who advocates that where the locomotive is in con- 
 tinuous operation there should be in circulation 800 to 1,000 cu. ft. of air per 
 min. per ton of weight of the locomotive, depending on whether the hauling is 
 done upon the intake or return. An occasional trip to a side entry or even to 
 a working place beyond the air will not require a material increase in the 
 quantity of air in circulation, as the normal volume of air in motion assisted 
 by diffusion will carry off the CO before a return trip is made to the same part 
 of the workings. On the other hand, it is admitted that if the consumption 
 of gasoline is the maximum, the air requirements will be doubled; but it is 
 stated that it appears impossible to consume this maximum under ordinary 
 normal conditions. 
 
 Mr. Hood's figures are of value in giving the quantities of harmful (COz) 
 and poisonous (CO) gases exhausted per minute by gasoline-locomotive engines 
 of various standard sizes when operating continuously with good and with bad 
 carburation. But haulage motors are not working continuously under full 
 load; in fact, they are idle so much of the time that the fuel consumption is 
 commonly about one-third the maximum, in rare cases rising to one-half. 
 Whether the air circulated shall be based on average or on extreme conditions 
 is a question for the mine manager. If extreme conditions are to be provided 
 for, the use of gasoline locomotives will be prohibited in many mines, where 
 the assumption of average conditions would permit it. The advocates of 
 gasoline haulage claim if extreme conditions (for no engines will be permitted 
 to work badly for a longer time than that required to shut off the fuel supply) 
 must be assumed in dealing with this type of locomotive, then electric haulage 
 should be prohibited because of the possibility of a fall of roof bringing down 
 the trolley wires with the consequent chance of a dust explosion through the 
 electric arc almost certain to be produced; and compressed-air and wire-rope 
 haulage should not be allowed as the compressor might explode or the trip 
 jump the track. 
 
 The variation in the quantity of air required by a motor in constant use 
 and, thus, consuming the maximum quantity of fuel, both when the carburation 
 is good and when it is bad and when the proportion of CO in the air is to be 
 kept at .10% and at .05% may be illustrated in the case of two locomotives 
 as follows: A 5-T. motor with 5"X 6" cylinders suitable for side-entry haulage 
 will require 3,300 cu. ft. per min of air when working properly if the CO in 
 the air is to be kept at .10% and 6,600 cu. ft. if the CO is to be kept at .05%. 
 The same motor, when working badly, will require nearly four times as much 
 air or 12,560 and 25,120 cu. ft., respectively, depending on the allowable per- 
 centage of CO. Similarly, a 9-T. motor with 6.5" X 8" cylinders and adapted 
 to main-line haulage will require 6,040 or 12,080, and 23,000 or 46,000 cu. ft. 
 per min. of air, depending on whether the carburation is good or bad and 
 whether the CO is to be kept at .10 or .05%. The range in air requirements 
 between the best and worst conditions of operation is from 3,300 to 25,120 cu. tt. 
 per min, in the case of the smaller locomotive, and in the case of the larger one, 
 
814 HA ULAGE 
 
 from 6,040 to 46,000 cu. ft. per min. Such an increase in the quantity of 
 air, the ratio being 1 to 8, cannot be made from time to time as it may be 
 temporarily needed, and must be permanently provided for in the ventilating 
 scheme of the mine. 
 
 Gasoline locomotives have been in use too short a time to have permitted 
 a solution of all the problems connected with their employment, and the 
 following suggestions in their selection and management may be of value: 
 
 1. Buy a high-grade motor from a responsible manufacturer and be guided 
 by his advice in its selection. 
 
 2. Do not use a larger motor than necessary to do the work; this will save 
 in first cost, in fuel consumption, and particularly in the amount of CO dis- 
 charged. 
 
 3. Use only high-grade gasoline and employ only experienced motormen, 
 who might be given a bonus for low fuel consumption ; this will lessen both the 
 fuel bill and the quantity of CO admitted to the air. 
 
 4. If possible, arrange the main-line haulage so that the grades favor the 
 outbound loads. If this is done, and the return air-current is made the haulage 
 road, the engines may be shut down and the loads dropped out by gravity, 
 saving in fuel and in CO discharged. The empties will be taken in under 
 power against the air, and the resultant velocity of the air-current will be 
 that of the inbound locomotive added to that ' of the outbound air. If the 
 velocities of the locomotive and the air-current are the same, this will double the 
 quantity of air passing the locomotive and may provide enough excess air to 
 take care of possible temporary bad carburation which is more apt to happen 
 under full than under part load. 
 
 5. Do not have the speed of the locomotive and the air-current the same 
 when they are moving in the same direction; to do so will cause a concentration 
 of gas around the locomotive, which will prove harmful to the motorman. 
 
 6. Where possible, avoid pulling from dip workings unless the air supply 
 is ample, because the maximum amount of gasoline is consumed and CO pro- 
 duced when starting up grade under full load. 
 
 7. Do not use the locomotive ahead of the air either in rooms or entries 
 more than necessary. It is in tight places that the effects of small amounts 
 of CO are the most marked. If compelled to enter such places, remain there 
 as short a time as possible, and do not allow the miners to return to the face 
 until some time has elapsed in order that the air-currents set up by the moving 
 trip and diffusion may have an opportunity to dilute the CO to the safe limit. 
 
 8. In event of carbureter troubles, shut off the gasoline instantly; an excep- 
 tion might be made when hauling against the full strength of the air-current. 
 
 9. Except in a strong air-current, do not allow the locomotive to stand 
 with the engines running; this precaution is particularly to be observed in places 
 ahead of the air. To this end, have the locomotive provided with a self- 
 starting device. 
 
 10. If the men complain of sickness, remove the locomotive from that 
 part of the mine until the reason for the trouble is found. Frequently a 
 slight adjustment of the ventilating current made by opening or closing a 
 regulator will remedy the trouble. 
 
 11. Overhaul and clean the locomotive thoroughly at the end of each 
 shift. Under no circumstances is it safe to use a locomotive underground 
 when the carbureter and ignition are out of order. 
 
 12. As the effects of CO upon the system are dangerous, the percentage 
 of it in the air must be kept as low as possible. Unfortunately, there are no 
 simple tests for this gas that may be applied by the miner or the foreman, and 
 the first indication of its presence is it ill effects. It might be well, then, at 
 the time of installing gasoline-motor haulage to employ a competent chemist 
 for a sufficient length of time to follow the locomotive to all parts of the mine 
 to secure samples for analysis of the air in the places the motor has been. 
 The expenditure of a few hundred dollars in taking and analyzing such samples 
 will either satisfy the management that the use of gasoline motors is perfectly 
 safe, or will suggest changes in the ventilating system or in the haulage schedules, 
 or in the use of certain roads for haulage, etc., that, if carried out, will make 
 the use of such motors unobjectionable. 
 
 Purification of the Exhaust. No satisfactory way of getting rid of the CO 
 in the exhaust of gasoline locomotives has as yet been devised. It is probable 
 that absorption by cuprous chloride (CuzCk), the reagent used for the purpose 
 in gas-analysis apparatus, -is not practicable because of the expense. 
 
 Solutions of lime or caustic soda or even plain water will absorb COz to a 
 certain extent, and at the same time will remove the odor. 
 
HA ULAGE 815 
 
 ELECTRIC-LOCOMOTIVE HAULAGE 
 
 GENERAL CONSIDERATIONS AFFECTING ELECTRIC HAULAGE 
 
 Advantages and Disadvantages of Electric Locomotives. All well-designed 
 and well-built haulage motors are practically equal in first cost, in the labor 
 cost of running, and in the cost of repairs, therefore, as an effective machine 
 for gathering and hauling coal, an electric locomotive possesses no marked 
 advantages over one propelled by steam, gasoline, compressed air, or storage 
 battery. The advantages and disadvantages commonly attributed to one 
 type of locomotive as compared with another, are in reality due more to the 
 power employed than to qualities inherent in the locomotive itself. 
 
 There is, however, one disadvantage possessed by the electric locomotive 
 that does not exist in the case of self-contained locomotives propelled by 
 steam, gasoline, or compressed air; it can be used only in those parts of the 
 mine where trolley wires have been hung for conveying the power and where, 
 at the same time, iron rails have been laid for the return circuit. This objection 
 has been largely overcome through the use of a combination trolley and storage- 
 battery locomotive, which can go anywhere in the mine; through the use of a 
 cable-reel locomotive, which can go the length of the cable beyond the end 
 of the trolley line; and through the use of the crab locomotive, which, while 
 standing on the main road and drawing current from the trolley line can pull a 
 car from a distance equal to the length of the rope carried on its rope drum. 
 
 So far as safety is concerned, the only locomotive that cannot possibly 
 ignite either methane or coal dust is one operated by compressed-air; and it 
 cannot cause death from shock. These are objections made rather unjustly 
 to the electric locomotive and should be charged against the means of conveying 
 power to it, the naked overhead trolley wire, and not to the locomotive itself 
 which, in its modern form, is an eminently safe machine. It may be argued 
 that the ventilating current should be sufficient to prevent the existence of 
 dangerous quantities of methane either in entries or rooms, that accumulations 
 of coal dust should be avoided, and that the mine should be watered or treated 
 with shale dust, and that men should be careful and not come in contact with 
 naked live wires, but while the_ first two conditions are successfully met in the 
 majority of mines and there is usually little danger of an electric spark or 
 arc igniting either methane or dust, there is always the possibility of this 
 happening even in the best-managed mines. The dangers of shock or death 
 through contact with live overhead wires can hardly be removed because of 
 the seeming impossibility of teaching the average mine worker to be even 
 reasonably careful. The possibility of setting fire to partitions, timbers, etc. 
 is so slight if even moderate care in properly insulating the wires is taken as to 
 be negligible. A danger chargeable to the locomotive itself may arise when an 
 unusually heavy trip is started or when the customary load is pulled up a 
 heavy grade. In both cases, it is usual to sand the rails and if too much sand 
 is used, the contact between the locomotive wheels and the rails for the return 
 circuit is broken, and the current will take a longer but easier path. This 
 may result in serious shock to the motorman, or if the current passes from the 
 locomotive through the drawbars of the cars and thence to the rail at some 
 unsanded place, those riding in the cars may be injured, powder in metallic 
 cans may be exploded, etc. The last is such a real danger, numerous acci- 
 dents having happened therefrom, that in many states it is prohibited by law 
 to transport powder in cars hauled by an electric locomotive. _This last_ danger 
 may be overcome in a very great measure by using a locomotive of a size pro- 
 portioned to the work, and then not overloading it. 
 
 Where many power-consuming machines are used in and around a mine, 
 rather than have each run by its own independent power generating engine r 
 it is cheaper and better to have a common power for all and to produce this 
 at some central plant and transmit it to the various points of application, and 
 it is the general adaptability of electricity to all power purposes that has led 
 to its extensive use in the operation of haulage locomotives. Electric energy 
 may be generated at any reasonable distance from the mine where power 
 may be had and may be easily and cheaply transmitted to any place needed 
 where it is available not only for the operation of haulage motors but also for 
 that of coal-cutting machinery, pumps, ventilating fans, shot-firing systems, 
 lighting etc. Hence, in mines where many power-requiring machines are 
 used, and particularly where these are scattered throughout the workings, 
 electricity is a favorite source of energy and, being used for all other purposes, 
 is used for haulage. On the other hand, in mines where, aside from haulage, 
 
816 
 
 H A ULAGE 
 
 power is required only to run the ventilating fan, it will unquestionably prove 
 cheaper in first cost and probably in operation to install a steam or gasoline 
 locomotive. Compressed air may also be transmitted from a central plant 
 and is available for the same purposes as electricity, except shot firing and 
 lighting and is further absolutely safe under all underground conditions, but a 
 compressed-air plant, including the piping, is more costly to install, extend, 
 and operate than an electric plant. 
 
 Current and Voltage. Direct current is generally used for electric haulage; 
 the pressure most commonly used is about 250 volts, although 500 volts has been 
 tried and is still used in some places. The objection to the higher pressure 
 is the greater danger of injurious or fatal shocks, as well as the greater difficulty 
 of insulating the wires from ground. The higher pressure can- be profitably 
 used only where all the passages through which the wires are strung are high 
 or roomy enough to permit placing the wires where there will be little danger 
 of contact with them, and dry enough to preserve the insulation. 
 
 Electric Generators. If the power house is near the mouth of the mine, 
 direct-current dynamos are generally used to generate the electric energy for 
 haulage purposes, and at the pressure used in the mine, 250 or 500 volts as the 
 case may be. It is frequently advantageous to locate the power house at some 
 distance from the mine, so as to take advantage of a water fall to generate 
 the power, or for other economic reasons; in such cases, in order to reduce the 
 cost of line copper, it is customary to transmit a high-voltage alternating 
 current to the mouth of the mine, or sometimes to the interior near where it 
 is to be used, there transform it in step-down transformers, and convert it by 
 means of rotary converters to direct current at ordinary mine voltage, after 
 which it is treated in the mine installation precisely as would be the case with 
 a direct current generated at the mouth of the mine. 
 
 Classes of Electric Locomotives. According to the kind of current used, 
 electric locomotives may be divided into direct-current, alternate-current, and 
 storage-battery locomotives. The direct-current locomotives are those in 
 general use in the United States and may be single or tandem. The standard 
 form of direct-current locomotive is used for main-line haulage; the modifica- 
 tions of it used for gathering are known as combination, cable-reel, and rope- 
 reel, or crab, locomotives. A special type, known as a rack or third-rail 
 locomotive, is used on heavy grades. 
 
 WIRING FOR ELECTRIC HAULAGE 
 
 Arrangement of Power Lines. In a shaft mine or a steep slope, insulated 
 feeder wires are run from the dynamo on the surface down the shaft or the 
 slope, or occasionally down a bore hole, into the mine, where they are connected 
 to the trolley wire and rails in the gangways; or, feeder wires may be con- 
 tinued along the haulage roads for a distance depending on the length of the 
 haulage road and the amount of electric current that must be carried. Where 
 
 the mine opening is a shallow slope 
 or a drift, the power is sometimes 
 carried into the mine by bare-wire 
 conductors fastened at intervals 
 to the caps, or legs, of the tim- 
 bers. If the mine opening is wet, 
 the power is transmitted through 
 lead-covered cables. In shafts, 
 the cables may be held in position 
 by wooden brackets placed on the 
 sides of the shaft, or suspended 
 from the top by block and tackle, 
 by means of which the cables may 
 be moved up or down. In a wei 
 shaft, the lead cable is carried far 
 enough into the mine from the 
 
 bottom of the shaft to be free from the shaft water, and is then connected with 
 the bare wire used in haulage. A main switch should be provided at the 
 foot of the shaft or the slope, so that the power can be turned off or on instantly. 
 Shape of Trolley Wire. Trolley wire is made with round, figure-8, or 
 grooved-cross-section, as shown in Fig. 1 (a), (&), and (c), respectively. The 
 round wire, shown at (a), has been generally used for the purposes of mine 
 haulage and for transmitting electric power into the mine. The preference for 
 mine work now inclines to the grooved form shown at (c). This wire is sup- 
 
 Ear 
 
 (a) 
 
 FIG. 1 
 
HA ULACE 
 
 817 
 
 ported by the clamp ears a, which fit into grooves in the sides of the wire just 
 above the center. The figure-8 wire, shown at (&), is liable to twist between 
 supports and throw; off the trolley; the round or the grooved wire, which is 
 practically circular in section, may be twisted without interfering in any way 
 with the trolley. When rounding curves, the figure-8 wire is also more liable 
 to pull or twist out of shape or out of the clamps entirely than either of the 
 other shapes. 
 
 Location of Wires. The trolley wire is located above the track, preferably 
 along one side and from 6 to 15 in. outside the rail, so as to be out of the way 
 of men and animals passing along the road. Where the roof is good, the trolley 
 wire may be supported directly from it. The trolley construction should be of 
 the most substantial nature, and the work of installation should be in charge 
 of an experienced man, as the care and thoroughness with which this is done 
 determine largely the successful operation of the plant. The mining laws of 
 many states provide that when the haulage road is used as a traveling way, 
 the trolley wire shall be set in an inverted wooden trough or boxing with sides 
 from 3 to 5 in. deep. Various provisions are made for the safety of men 
 compelled to pass and repass under the trolley wires at some particular point 
 as at the foot of a shaft, at a parting, etc. At such places it is not unusual to 
 compel the wires to be placed at their lowest point at least 6 ft. 6 in. above the 
 top of the rail. 
 
 Trolley Frogs. Fig. 2 (a) shows the under side of an overhead switch, or 
 trolley frog, used to guide the trolley wheel from one wire to another. This 
 is a simple V frog; it is shown in its natural position in (b). The trolley wires 
 are held by clamps b, and the span, or supporting, wires are attached to the 
 ears a. The frog must be placed with reference to the track so that the motion 
 
 c and 
 o the 
 
 of the locomotive, as it takes the switch, will have given the trolley an incli- 
 nation in the right direction before the trolley wheel strikes the frog. The 
 frog must also be hung level, or it will cause the wheel to leave the wire. 
 
 A simple method of finding the proper location for the trolley frog is shown 
 in Fig. 3. Measure the distance from the point of switch a to the fr 
 half way between these points make a chalk mark on the rail at b. 
 same on the straight rail, and mark the half- 
 way point d. Stretch a line from a to d and 
 one from e to b. Directly above their point of 
 intersection / is the place for the frog. 
 
 Resistance of Steel Rails. As the rails form 
 the return circuit for the electric current, they 
 must be considered in connection with the 
 voltage drop. The rail itself, on account of its 
 large cross-section, has a large current-carrying 
 capacity and the bonding should be done so 
 that no appreciable drop will take place in the 
 
 joints. The weight of rail, in pounds per yard, is fixed by traffic considera- 
 tions and is usually determined by allowing 10 Ib. per yd. for each ton of 
 locomotive weight per driving wheel. Thus, a 10-T., four-wheel locomotive 
 will have 10-7-4 = 2.5 T. on each driver and the required weight of rail will be 
 2.5X10 = 25 Ib. per yd. This formula gives the minimum weight of rail, but 
 much better results will be obtained by using the heavier rail recommended in 
 the accompanying table. 
 
 52 
 
 FIG. 3 
 
818 HAULAGE 
 
 SIZES OF LOCOMOTIVES, RAILS, AND BONDS 
 
 Weight of 
 Locomotive 
 Tons 
 
 Minimum Weight of Rail 
 per Yard and Size of Bond 
 
 Weight of Rail per Yard 
 Recommended and Size 
 of Bond 
 
 Rail 
 Pounds 
 
 Bond 
 Number 
 
 Rail 
 Pounds 
 
 Bond 
 Number 
 
 3 
 
 4 
 5 
 6 
 7 
 , 8 
 10 
 15 
 20 
 25 
 
 16 
 16 
 16 
 16 
 20 
 20 
 25 
 40 
 50 
 60 
 
 4 
 4 
 4 
 4 
 
 
 
 00 
 0000 
 0000 
 
 20 
 25 
 25 
 30 
 40 
 40 
 45 
 50 
 60 
 80 
 
 
 
 
 
 00 
 00 
 00 
 0000 
 0000 
 0000 
 
 RESISTANCE OF STEEL RAILS 
 
 The resistance of steel rails to the passage of an electric current varies 
 considerably with the composition of the metal. For the purpose of calculation 
 it is, however, common to take the specific resistance of steel rails as twelve 
 times that of copper. While this value may seem somewhat high, it is conser- 
 vative and will allow for the slight additional resistance at the joints. By using 
 the values from the following table, the rails can therefore be considered as 
 continuous. The resistance values given are for two rails in parallel; that is, 
 per mile of track. These values are based on the following formula : 
 
 ., 2.63 
 
 ohms per mile = : j j rr -r 
 
 weight of rail per yard 
 
 Bonding. The larger part 
 of the track resistance occurs 
 at the joints between the rails, 
 and as the fish-plates do not 
 form sufficient electric contact, 
 the ends of the rails at the joints 
 are always connected by a cop- 
 per conductor known as a bond. 
 The first of the two tables just 
 given shows that the area of 
 metal in the bond is essentially 
 the same as that in the trolley 
 wire. 
 
 There are many types of rail 
 bonds, but these may be divided 
 into two general classes; pro- 
 tected bonds, or those placed be- 
 tween the fish-plate and the rail, 
 and unprotected bonds, which 
 either span the fish-plate or are 
 placed under the rail. All 
 should be attached to the rail in such a way that the contacts between the 
 copper and steel are clean and bright when made. 
 
 Fig. 4 (a) shows a protected bond of the double-loop type, shaped so as to 
 give flexibility and at the same time allow openings for the track bolts. This 
 bond is made of thin copper strips on which copper terminals ab are cast. After 
 the terminals have been passed through the holes in the rail, they are com- 
 pressed by a special screw compressor, which forces the metal out sidewise 
 firmly against the sides of the holes. View (7>) shows this bond in position, 
 part of the fish-plate being cut away to expose the bond to view. The holes 
 through the rail for track bolts show through the loops of the bond. 
 
 Fig. 5 shows one form of unprotected bond. The copper terminals are 
 pressed into the holes in the rails by a powerful screw press, which expands 
 
 Weight of Rail 
 per Yard 
 
 Resistance per Mile 
 of Track 
 
 Pounds 
 
 Ohms 
 
 16 
 
 .1642 
 
 20 
 
 .1313 
 
 25 
 
 .1051 
 
 30 
 
 .0876 
 
 40 
 
 .0657 
 
 45 
 
 .0583 
 
 50 
 
 .0525 
 
 60 
 
 .0438 
 
 80 
 
 .0328 
 
HA ULAGE 
 
 819 
 
 All bonds 
 
 the metal in the hole so as to give complete contact with the rails, 
 should be inspected frequently, as they may work loose. 
 
 A poor return circuit, which is due to poor bonding, is responsible for much 
 of the motor trouble. If the voltage drops because of poor bonding or from 
 any other cause the amperes will be increased with the result that the armatures 
 will heat and possibly burn out. Poor bonding is commonly indicated by 
 the marked drop in the illuminating power of the headlight (which then burns 
 with a dull red glow) when a 
 trip is started. 
 
 Cross-Bonding. In addition 
 to the regular bonding at the 
 joints, the one line of rails 
 should be electrically joined, or 
 cross-bonded, to the other at 
 intervals of not more than 500 
 ft. and by conductors of the size 
 used for bonding. The object 
 of cross-bonding is to still pro- 
 vide a complete return circuit 
 in event of some of the rail 
 bonds jarring loose. Instead of 
 the standard form of cross- 
 bonding both the D., L., & W. 
 R. R. and the L. C. & N. Co. 
 have successfully used old wire 
 hoisting rope as a portion of 
 the return -circuit. The largest 
 size of rope is used on the main 
 haulage roads and H-in. rope 
 
 on the branches. The rope is FIG. 4 
 
 suspended near the bottom of 
 
 the props which carry the feed wire and is bonded to the rails every 250 to 
 300 ft. Where the rope has to be spliced, the abutting ends, after being thor- 
 oughly cleaned and brightened, are inserted in the opposite ends of short 
 pieces of lead pipe that are filled with solder. The attachments for bonding 
 the rope to the rail are made by soldering a clamp to the rope, using the 
 regular bonding hole on the rail. Tests have shown that the current-carrying 
 capacity of a Is-in. hoisting rope made of steel low in carbon and manganese 
 is the same as that of a rail weighing 30 Ib. per yd. 
 
 Feeders. Current is generally fed to the locomotive through an overhead 
 trolley system with the track rails forming the return circuit as explained. 
 In addition to the trolley wire, it is also almost always necessary to install 
 feeders to reduce the drop in voltage. A feeder is a heavy insulated or bare 
 
 copper cable suspended along one 
 side of the heading and is tapped 
 into the trolley wire at intervals 
 along the route. 
 
 In the early days of electric mine 
 haulage, the size of trolley wire was 
 much smaller than now used, the 
 size varying from No. to No. 0000. 
 The former is only used in small 
 one- or two-locomotive installa- 
 tions, and experience has shown 
 that a heavy trolley wire is of con- 
 siderable advantage. For this rea- 
 p IG ^ son the use of No. 0000 trolley wire 
 
 is now very common. 
 
 The size of the feeders depends on the length of the haul, the distribution 
 of the load, the current to be transmitted, and the permissible voltage drop. 
 Excessive drop is a very common cause for complaint in a mine using electric 
 haulage and it always pays to put sufficient copper in the feeders to prevent 
 the voltage at the locomotives from falling to too low a value. Low line 
 voltage makes it difficult to maintain the schedule and gives rise to trouble 
 with the motors, to say nothing of the cost of the power loss. As an approxi- 
 mate rule, the voltage drop from the point of supply to any locomotive should 
 be kept within 20%. 
 
 An approximate estimate of what the drop. in the rails will be can easily 
 
820 HA ULAGE 
 
 be formed at the outset by means of the table on page 818. The balance of 
 the drop will then give that allowed for the trolley and feeders combined, and 
 their cross-section can be determined from the following formula: 
 . . . , . 10.8XLX7 
 Area, in circular mills = - 
 
 in which L = distance between point of supply and load, in feet; 
 7= maximum current, in amperes; 
 Z? = drop in trolley and feeders, in volts. 
 
 From the value so found is subtracted the cross-section of the trolley, in 
 circular mils, the result being the required size of the feeders. The calculation 
 is easy, the only difficulty being the variation in the load both in magnitude 
 and position. 
 
 In order to illustrate the method of calculation assume the following 
 examples: 
 
 EXAMPLE 1. Find the size of feeder, if the voltage is 500; rails, 40 lb.; 
 trolley, No. 0000; length of road, 1 mi.; load, 400 K. W., bunched at end of 
 line; permissible drop, 20% = 100 volts. 
 
 SOLUTION. Resistance of 1 mi. of two 40-lb. rails = .0657; current = 400,000 
 ^500 = 800 amp.; drop in rails = 800 X. 0657 = 52.6 volts. This leaves a drop 
 of 100 52.6 = 47.4 to take place in the trolley wire and feeder. Assuming the 
 same conductivity of the material in these, their combined cross-section should 
 
 The trolley wire is No. 0000 and has a cross-section of 211,600 cir. mils. 
 Deducting this from the total cross-section of 965,000, leaves 965,000 211,600 
 = 753,400 or about 750,000 cir. mils. 
 
 EXAMPLE 2. Suppose that the total load of 400 K. W. is equally distributed, 
 what size of feeder is required? 
 
 SOLUTION. This is equivalent to an average load of 200 K. W. transmitted 
 over the whole circuit. The drop in the rails is now only half the former 
 value or 26.3 volts, leaving 100 26.3 or 73.7 volts to be consumed in the 
 trolley and feeders. Their combined cross-section will therefore be: 
 10.8X5,280X400 r 
 
 - ^-= -- = 310,000 cir. mils 
 7o.7 
 
 Deducting from this 211,600 cir. mils for the trolley leaves only about 
 100,000 cir. mils, which corresponds to No. feeder. 
 
 In making these calculations, attention must be paid to the carrying 
 capacity of the wires and cables. This must be kept in mind, because if the 
 lines are simply figured out on the basis of giving the allowable drop, the current 
 may be sufficient to overheat the wires. In most cases, however, the size of 
 wire necessary to keep the drop within the specified limits will be considerably 
 larger than necessary to handle the current without overheating. It is always 
 well, however, to compare the sizes obtained and the current carrying capacity, 
 which will be found in the wire table. 
 
 By referring to Example 1, it is seen that there is no danger of overheating, 
 but in Example 2 it will be necessary to increase the size considerably in the 
 section nearest the station where the current value is too high. 
 
 The pressure at which the current is supplied to the motors is limited by 
 considerations of safety. It would otherwise, of course, be desirable to use a 
 higher pressure, because this would mean a lower current, less drop and smaller 
 feeders for the same power. For this reason 500 volts is used in a few mine 
 haulage systems, although 250 volts evidently is somewhat safer in operating. 
 
 In mines of ordinary capacity, it will be uneconomical to use the direct- 
 current system only, when the current has to be transmitted for distances 
 over 1 mi., and many mines have during the last few years been changing 
 over their systems to a combination alternating current and direct current. 
 That is, alternating current is generated and transmitted at a higher voltage 
 to substations distributed along the tracks. In these substations, the alter- 
 nating current is changed to direct current by means of synchronous converters. 
 In this manner the 250- volt, direct-current supply can be brought near the 
 centers of distribution and the losses in the lines, feeders, and rails are consider- 
 ably reduced, also smaller size conductors can be used. 
 
 The following table shows the distance to which 100-K. W., three-phase 
 current can be transmitted over different sizes of wires at different potentials, 
 assuming an energy loss of 10%. A power factor of 85% is shown by the 
 table. 
 
HA ULAGE 
 
 
 t^OiO'OiOfMOt^'OiM 
 
 ooowdotocorHNco 
 
 5'-H'OO5eo 
 
 oooooo 
 T^ror^asoo 
 
 <6 
 
 821 
 
 EXAMPLE. What size of 
 wires should be used to de- 
 liver 500 K. W. at 6,000 
 volts, at the end of a three- 
 phase line 12 mi. long, allow- 
 ing energy loss of 10% and 
 a power factor of 85%? 
 
 SOLUTION. If the ex- 
 ample called for the trans- 
 mission of 100 K. W. (on 
 which the table is based), 
 look in the '6,000- volt 
 column for the nearest 
 figure to the given distance, 
 and take the size wire cor- 
 responding. But the ex- 
 ample calls for the trans- 
 mission of five times this 
 amount of power, and the 
 size of wire varies directly 
 as the distance, which in 
 this case is 12 mi. There- 
 fore, look for the product 
 5X12 = 60 in the 6,000-volt 
 column of the table. The 
 nearest value is 60.44 and 
 the size wire corresponding 
 is No. 00, which is, there- 
 fore, the size capable of 
 transmitting 100 K. W. over 
 a line 60.44 mi. long, or 500 
 K.W. over a line 12 mi. long. 
 
 If it is desired to ascer- 
 tain the size wires that will 
 give an energy loss of 5%, 
 or one-half the loss for 
 which the table is com- 
 puted, it is only necessary 
 to multiply the value ob- 
 tained by 2, for the dia- 
 meter varies directly as the 
 per cent, energy loss. 
 
 rl <N 50 CO <N CC 
 t-HNCO 
 
 222222 
 
 g<NCOO|OO 
 2,_ioqcOO>0 
 
 g - r 
 
822 HA ULAGE 
 
 DIRECT-CURRENT LOCOMOTIVES 
 
 Number and Arrangement of Motors. Direct-courrent electric locomotives 
 with two pairs of driving wheels may have one or two motors, while those 
 with three pairs of drivers commonly have three motors. 
 
 In the single-motor locomotive, the armature, which is set lengthwise of 
 the frame, is geared at each end to a driving axle with the result that both 
 pairs of wheels revolve at the same time and_ with the same speed. This 
 arrangement insures a high degree of adhesion with consequent strong tractive 
 effort, together with perfect distribution of the weight on the drivers and 
 good contact between the wheels and the rail. 
 
 There are two standard methods of mounting the motors in two-motor 
 locomotives. In the tandem mounting, one motor is placed between the axles 
 and the other between the forward axle and the front-end frame. In the 
 central, or inside, mounting, both motors are placed between the axles. The 
 tandem mounting permits of a short wheel base and is adapted for .light- and 
 medium-weight locomotives, which are commonly required to operate upon 
 sections of the track having short-radius curves. The central, or inside, 
 mounting requires a longer wheel base and is adapted for heavy locomotives 
 used in main-line haulage, where the roads are commonly straight or with 
 curves of long radius. With either arrangement, the locomotive frame is 
 proportioned to give an equal distribution of the weight between both pairs 
 of driving wheels. The motors may also be end mounted by placing each 
 motor in the space between the axle and the forward and rear frames, respec- 
 tively. This permits of a minimum wheel base, but is only used to meet 
 very unusual conditions. An advantage claimed for the two-motor locomotive 
 is that, in case of accident to one of the motors, the defective one may be 
 disconnected and the machine run with one motor to the repair shop or it may be 
 kept in operation although able to do less work. The advocates of the two- 
 motor machine also claim for it higher efficiency and better speed control 
 than is possible with the single-motor locomotive. 
 
 Six-wheel, three-motor locomotives of 15 to 25 T. weight may, to a certain 
 extent, be used instead of the tandem locomotives described on page 826, for 
 long and heavy runs over a main haulage road. Their application is, however, 
 more or less restricted, as on account of their greater length they may not 
 take the sttarp curves usually found in mine work. Where this is not objec- 
 tionable, locomotives of this kind have advantages, one being the possibility 
 of using lighter rails than for a two-motor locomotive of the same weight, due 
 to the equalization of the weight on all three pairs of driving wheels. To insure 
 this, irrespective of any irregularities of the track, three-motor locomotives 
 are supported from the journal-boxes, thus insuring at all times an even division 
 of the load among the three motors. The equalizing system also furnishes 
 a flexible suspension of the weight and produces an easy running locomotive, 
 greatly minimizing the wear and tear on the track and roadbed. The center 
 pair of wheels is generally furnished without flanges so as to prevent any 
 binding on the curves. 
 
 Construction of Motors. In the design and construction of mine loco- 
 motive motors, the following requirements are essential: Maximum capacity 
 within the gauge limitations; large overload capacity; accessibility for inspec- 
 tion and repair; large bearing surface to minimize wear; protection against dust 
 and moisture; accurate machining to insure interchangeability of parts; 
 rugged construction to withstand rough usage. 
 
 The motors are always of the series type and should preferably be equipped 
 with commutating poles. In this kind of motor, the same current passes 
 through the main-series and commutating-pole field coils. The torque exerted 
 and the speed at which it will run, depend on the flux entering the armature, the 
 number of conductors on the armature, and the amount of current flowing in 
 the winding. The flux, in turn, depends on the strength of the field magnets, 
 which in their turn depend on the number of turns in the field coil and the 
 amount of current flowing therein. The advantage of the commutating poles, 
 which are connected in series with the armature, lies in the fact that the electrical 
 and mechanical neutrals are made to coincide for all loads and for either 
 direction of rotation, thus assuring good commutation under all conditions 
 of operation. 
 
 The motor frames are split diagonally so that the upper part can be lifted 
 off, exposing the interior for inspection. The bearing heads are securely 
 clamped between the upper and lower frames, making it possible to readily 
 take out the armature for repairs. The laminations, armature windings, and 
 
HA ULAGE 823 
 
 commutator are all mounted on a common spider so that the shaft may be 
 removed without disturbing them, and interchange can therefore readily be 
 made. 
 
 The armature bearings are commonly of the Babbitt-lined, bronze-sleeve 
 construction, designed for oil and waste lubrication. The Babbitt is of such a 
 thickness that should it be melted from lack of lubrication, the shaft will be 
 supported by the sleeves before the armature strikes the pole pieces. 
 
 The use of ball bearings in mine-locomotive motors is a new feature. Where 
 they have been tried, they have given excellent results, and at present they bid 
 fair to displace the plain bearings for this class of service. The principal advan- 
 tage gained by the use of ball bearings is the small amount of lubricant required. 
 This lubricant being vaseline or some similar grease in small amounts, there is 
 very little possibility of its getting into the motor windings. There is a great 
 advantage in_this, as a large percentage of the motor troubles can be traced 
 directly to oil having worked its way into the windings. When properly 
 lubricated, ball bearings have another advantage, in that there is but a small 
 amount of wear. This decreases the liability of the armature coming down 
 on the pole faces with damaging results. 
 
 The field coils are held securely in place by spring-steel flanges, which are 
 pressed against the coils by the pole pieces when the latter are bolted in place. 
 
 Controllers. The controllers are of the rheostat magnetic blow-out kind. 
 A commutating switch is incorporated in the reverse cylinder, the handle of 
 which has four on-positions, two for each direction of motion, one with motors 
 in series and the other with motors in multiple. The main and reverse cylinders 
 are interlocked in the usual manner and the main cylinder provides for speed 
 regulation with motors in series or multiple. This system of control by per- 
 mitting motors to be started in multiple, allows them to exert their maximum 
 tractive effort independently, so that the slippage of one motor does not affect 
 the other a valuable feature for starting heavy trains. 
 
 When the operating handle is in the off-position, all parts of the motor 
 and rheostat equipment are dead and it is also impossible to retard the train 
 by bucking the motors a practice of motormen that is liable to cause trouble. 
 
 While single-end control may be considered standard, locomotives are often 
 built with a controller at each end, a construction often of advantage. 
 
 Frames. The general construction of electric mine locomotives involves 
 two distinct forms, one in which the side frames are placed outside the wheels, 
 and the other in which they are placed inside the wheels. 
 
 For a given track gauge, the outside frame allows the maximum space 
 between the wheels for the motors and other parts of the equipment, renders 
 the journal-boxes more accessible, and gives somewhat more space at the 
 operating end for the mototman. The inside frame restricts, to a certain 
 extent, the space between the wheels available for motors and other equipment, 
 but allows for the minimum overall width, a construction that is necessary 
 in those mines where the props are set close to the track or the space outside 
 the rails is otherwise limited. The wheels being outside the frame, this loco- 
 motive in case of derailment is somewhat more readily replaced. 
 
 The locomotives may be supplied with side frames of cast iron or rolled 
 steel plate, the latter construction being now the most generally used. Ihe 
 end frames as a rule consist of steel channels fitted with heavy wooden bumpers, 
 except on large locomotives where cast-iron bumpers may be advantageous 
 in order to get more dead weight. The bumpers and coupling devices must 
 be designed to suit the mine cars. 
 
 Wheels and Journals. The weight of the locomotive is ordinarily supported 
 from the journal-boxes on heavy helical springs. The journals are somewhat 
 similar to those on railway cars that have removable brasses and are lubricated 
 from oil cellars filled with waste. 
 
 The construction of the journal-boxes is such that the brasses can be removed 
 without disturbing the axles or frame stay-plates. On outside-frame loco- 
 motives, this is accomplished by jacking up the frame to relieve the pressure 
 on the journal-box spring and removing two vertical retaining plates. Ihe 
 inside-frame journal-boxes are fitted with a removable oil cellar, which can be 
 lowered for repacking. 
 
 Plate wheels are generally used for outside-frame locomotives, while for the 
 inside-frame construction spoked wheels are used, in order to give access to 
 the journal-boxes. 
 
 Chilled cast-iron and steel tires or rolled-steel wheels are in general use, 
 the first named being, however, the more common. These are approximately 
 60% cheaper than steel-tired wheels and 45% cheaper than those of rolled 
 
824 HAULAGE 
 
 steel. The higher cost of the steel wheels is, however, largely offset by the 
 fact that the treads can be refaced several times, if facilities are provided 
 therefor in the repair shop. 
 
 A somewhat increased adhesion is generally realized by the adoption of 
 steel wheels for mine service. While opinions differ greatly as to how much 
 this really, amounts to, it is generally conceded to be about 5%. A considerable 
 portion of this increased effort is often found to be due to the geater weight 
 of such wheels, and a comparison is difficult to make, as both the wheel tread 
 and rail are always subject to wide variations caused by moisture, nature of 
 the surface, amount and quality of sand used, etc. 
 
 Brakes. Several kinds of brake mechanisms are in use. In an exception- 
 ally strong and efficient one, the brake shoes are automatically locked in any 
 position in which they are left by the operator without the use of pawls or 
 ratchets. The brake shoes, made of cast steel, are removable in order to 
 insure a long life and in addition exert a dressing action on the wheel tread. 
 
 In certain instances where there is a heavy down grade, in order to be 
 sure of controlling the loaded trains, a special rail-grip brake is provided in 
 addition to the usual wheel brakes. Jaws are arranged to press the shoes 
 against a third rail, which is laid in the center of the track. This brake is 
 powerful enough to stop a train within a distance of 100 ft. on an 8% grade, 
 the train weighing 100 T., exclusive of locomotive, and running at a speed 
 of 8 mi. per hr. 
 
 Sand riggings are always provided, and the sand boxes so arranged that 
 the rails may be sanded ahead, when running in either direction. 
 
 Trolleys. In the standard mine trolley, the wheel is mounted in a swiveled 
 harp, which permits it to aline itself with the trolley wire, irrespective of the 
 direction of the pole. The pole is of wood and the lower end is inserted in a 
 swiveled base, which fits into sockets on either side of the locomotive. The 
 force of the compressed spiral spring is so applied to the pole that the pressure 
 of the trolley wheel against the wire is approximately uniform throughout 
 the limits of vertical variation and the swivel harp permits a wide lateral 
 variation of the wire. The pole being of wood is thoroughly nonconducting, 
 and is so located that the motorman can easily handle and reverse it without 
 leaving his position. The trolley cable terminates in a contact plug, which 
 fits in a receptacle placed on each side of the locomotive so that the change 
 from one side to the other is readily effected. 
 
 Some locomotives are made with two trolley poles, one at each side. 
 This construction is convenient in those mines, where for any reason it is 
 necessary to hang the trolley wire on the side opposite to the one where it 
 is usually placed. 
 
 Headlights. The headlights provided at each end of the locomotive, are 
 usually each fitted with a 32-c.p. incandescent lamp, which gives sufficient 
 illumination. A luminous-arc mine headlight is, however, manufactured, the 
 mechanism of which is simple and requires little attention. The upper electrode 
 is made of copper and lasts from 2,000 to 3,000 hr., while the lower one, 
 which is made of a composition of magnetite, lasts from 50 to 75 hr. 
 
 Capacity of Locomotives. Local conditions must be given a very careful 
 study in laying out a system of electric mine haulage. Not only should the 
 present output be considered but also the possibilities of increased output 
 and longer hauls. The number of cars to be handled per trip and per hour, 
 the time of lay-over, etc., must be correctly determined so as to result in the 
 most efficient operation. It is also important that the main-haul locomotives 
 have sufficient capacity to place on the parting enough empty cars per trip 
 to serve the gathering locomotives simultaneously in order to prevent any 
 reduction in the output from delays. 
 
 The amount of load that a locomotive is capable of hauling depends on 
 the weight of the locomotive, the adhesion between the driving wheels and the 
 track, the frictional resistance of the trailing load, and the curvature and 
 gradients of the track. 
 
 The adhesion varies greatly, depending on the condition of the surfaces 
 in contact, but experience has shown that with clean dry rails on a level track 
 the coefficient of adhesion can safely be assumed to be 20% for cast-iron wheels 
 and about 25% for steel-tired wheels. A 10-T. locomotive with steel-tired 
 wheels, for example, will develop on a straight level track a maximum tractive 
 effort of 10 X 2,000 X. 25 = 5,000 lb., before slipping the wheels. 
 
 With wet and slippery rails, when starting heavy trains or on steep grades, 
 sand is used to increase the adhesion, which by this means may be increased 
 to about 25 to 30% for cast-iron wheels and 30 to 33J% for steel-tired wheels. 
 
HA ULAGE 825 
 
 Due to excessive wear of wheels and other undesirable effects when it is used 
 too freely, sand should be limited in application to starting heavy trips and 
 climbing the steepest grades. It is therefore not advisable to load a locomotive 
 to its maximum tractive effort continuously, but about 10 or 15% reserve 
 capacity should preferably be left. 
 
 Only moderate acceleration and retardation are as a rule required in mine- 
 haulage service, .2 mi. per hr. per sec. being a sufficient value. This corre- 
 sponds to a force of about 20 Ib. per gross ton of the combined load and loco- 
 motive. This factor, however, is usually neglected unless the train is to be 
 started on a grade, as the slack can be taken up at the several couplings and 
 thus only one car at a time is actually started. Quite steep grades exist also 
 in the majority of cases, and the increased capacity of the locomotive to take 
 care of these is usually greater than the percentage increase in weight of the 
 locomotive demanded due to acceleration. 
 
 Where the service demands a high rate of acceleration, the weight of the 
 locomotive must be increased accordingly. The unit of acceleration is gener- 
 ally taken as 1 mi. per hr. per sec., and the force required to accomplish this 
 is about 95. Ib. per T. above the frictional resistance. 
 
 Frictional load resistance is caused by the friction of the wheel treads and 
 flanges against the rails and by the friction of the car journals. It may be 
 as low as 10 Ib. a T. or as high as 60 Ib., depending on the nature and condition 
 of the bearings, the size of rails, etc. For narrow-gauge roads with light 
 rails and ordinary mine cars, from 20 to 30 Ib. per T. is a fair figure. 
 
 For the locomotives, a resistance of from 12 to 15 Ib. per T. is quite common, 
 but this is generally such a small percentage of the total tractive effort that it 
 can be neglected. 
 
 The resistance due to curves can generally be neglected unless the curves 
 are very long or have a very short radius. Ordinarily, only a portion of the 
 trip will be on a curve at one time, so that the drawbar pull to be added should 
 be based only on the actual number of cars that are moving around the curve. 
 Many grades in mining work are so short that only a part of the trip can 
 occupy the up grade at one time, the balance of the trip being on a lesser grade, 
 on a level, or on a down grade. By accelerating to a high speed as the hill, is 
 approached, quite steep grades of short length may be mounted without diffi- 
 culty, and in such cases the locomotive can be worked close to the slipping point. 
 
 The resistance due to grades is always 20 Ib. per T. for each per cent, grade 
 and not only does a grade greatly increase the total train resistance, but it also 
 reduces the available drawbar pull of the locomotive, for of the total tractive 
 effort developed at the drivers, 20 Ib. per T. for each 1% grade is consumed 
 solely in driving the locomotive itself up the grade. 
 
 The size of a locomotive for a given load is therefore principally determined 
 by the limiting grade. For example, assume a trailing load of 80 T., a frictional 
 car and track resistance of 20 Ib. per T., and a track that is practically level 
 throughout with the exception of a stretch of 2% grade. The total train 
 resistance on the level portion of the track is SOX 20 = 1,600 Ib., but on the grade 
 it is 80 (20+2X20) =4,800 Ib., and in addition the force required for propelling 
 the locomotive up the grade. A 4- or 5-T. locomotive can easily handle this 
 on the level, while a 13- or 14-T. locomotive will be required to get it over 
 the grade. 
 
 Selection of Motors. Motors for mine locomotives are generally rated 
 on the 1-hr, basis; that is, the load that they will carry continuously for 1 hr. 
 without exceeding a certain specified temperature, usually 75 C. Standard 
 equipments are furthermore so selected that the motors will develop the rated 
 drawbar pull and speed of the locomotive on the above basis. Short overloads 
 of 15 or 20% can generally be taken care of, while at overloads of about 25% 
 the wheels will begin to slip. 
 
 The 1-hr, rating of a motor depends largely on the terminal capacity, while 
 the real capacity is its ability to perform its cycle of operations during the 
 entire day. The selection of the proper motor equipment on this basis, after 
 its weight has been decided on, involves a complete knowledge of the profile 
 of the road, the number of cars to be handled per trip and per hour, the weight 
 of the empty and loaded cars and the frictional resistance. The motor capacity 
 depends on the temperature that the windings will attain, and this in turn on 
 the average heating value of the current. As this is proportional to the square 
 of the current value, the average heating for an all-day service must be deter- 
 mined from the square root of the mean square of the current. 
 
 A motor is selected from the various sizes that will fit the locomotive in 
 question, and from the foregoing data and the characteristics of this motor 
 
826 HA ULAGE 
 
 equipment, the current and speed are obtained for each part of the cycle. 
 The current values are then squared and multiplied with the time during which 
 they last. To allow for the extra heating produced by the acceleration and the 
 switching and making up of trips at the ends of the run, about 10% should be 
 added to the sum of the time-current-squared values for fairly long runs and 
 about 15% for short runs. The sum of all these values is then divided by 
 the total time, including lay-overs, and the result is the average squared current 
 value. By taking the square root of this value, the root-mean-squared value 
 of the current for the complete cycle is obtained. If the continuous capacity 
 of the motor selected is below this value, a larger motor must be selected. As 
 the motor curves usually give values for one motor, the locomotive and trailing 
 weights, etc., should naturally be divided by two to give the weight each motor 
 will be required to handle. 
 
 The tendency to use larger motors than formerly is quite common and 
 is justified largely by the lower maintenance cost, but this can be carried too 
 far, especially in small mines where the cycle of duty is such that the motors 
 could not be overheated. In large mines, and especially for the long main- 
 haulage duties, a careful comparison of the required duty and the motor char- 
 acteristics should be made to insure a safe motor temperature. An approximate 
 rule, easy to remember, is that a total motor capacity of about 10 H. P. is 
 required for every ton the locomotive weighs. 
 
 Tandem Locomotives. In the past, a mining locomotive was generally 
 considered satisfactory so long as its motors could develop the torque required 
 for the necessary traction. Owing to the relatively short and infrequent runs, 
 heating was not the limiting feature, but as mine headings have increased in 
 length to 6 and 7 mi. in some cases, the motors that were formerly good for 
 runs of 1 and 2 mi. are no longer adequate for the longer service unless the 
 loads are correspondingly reduced. A reduction in loads is impossible, because 
 for the same output, the longer the runs the larger must be the trains, and 
 larger trains means larger motor capacity. The space mine locomotives can 
 occupy is limited by the gauge of the track, and the only way to increase 
 the hauling capacity is either to run two locomotives in tandem or to use 
 three-motor locomotives. 
 
 The weight of a large two-motor locomotive may furthermore be pro- 
 hibitive due to the track construction. On well-laid tracks having 50- or 
 60-lb. rails, 25- or 30-T. four-wheel, two-motor locomotives will operate success- 
 fully, but where lighter rails exist, it is inadvisable to concentrate the weight 
 on four drivers. Instead, therefore, of using a single 20-T. locomotive, two 
 10-T. locomotives coupled in tandem may be used, because while developing 
 the same tractive effort, with this combination the weight will be distributed 
 on eight driving wheels. 
 
 Cases are on record where large sums of money have been saved by the use 
 of tandem locomotives, where the increased lengths of hauls or tonnage neces- 
 sitated larger locomotive capacities. In one particular instance, it would have 
 been necessary to widen the funnel for many miles, while in another, seveial 
 miles of track would have had to be relaid with heavier rails. It is extremely 
 simple to-couple the locomotives in tandem. 
 
 The first, or primary, locomotive is provided with a four-motor controller 
 and the second, or secondary, locomotive, with a two-motor controller. The 
 two are electrically interconnected so that there is a complete control of all the 
 motors from the operating end of one. Similarly the brakes and sand valves 
 of both locomotives can be operated from the same place. 
 
 The Iocom9tives can also be operated singly as independent units by 
 separation, which requires but a few minutes, and only involves the pulling 
 out of the cable plugs, disconnecting the brake chain, and turning the primary 
 brake stand parallel to the end frame. 
 
 Cable-Reel Locomotives. ^Gathering locomotives of the cable-reel type 
 are provided with a conductor in the form of a flexible insulated cable that can 
 be connected to the trolley wire on the entry and through which current can 
 be conveyed to the locomotive when it is necessary for it to go beyond the end 
 of the trolley line. The arrangement is designed to do away with the cost of 
 stringing wires in the rooms as well as to overcome the danger of shock to the 
 miners. 
 
 The cable may be either single or double. The single cable is used where 
 the rooms are laid with steel rails, which are bonded to form the return circuit. 
 The double cable is used where the rails are of wood and the return circuit must 
 be made through the cable itself. 
 
 The cable reel may be driven mechanically from the axle, or by an inde- 
 
HA ULAGE 827 
 
 pendent motor. The mechanically driven cable reel is driven by a chain from 
 the locomotive axle. As the locomotive moves ahead the cable is paid out 
 automatically, being kept taut and the reel prevented from spinning by a 
 friction device. As the locomotive returns from the face, the reel is wound 
 through a clutch. In all cases, it is arranged that the tension on the cable 
 cannot exceed a safe amount. 
 
 The motor-driven reel is generally preferred particularly for gathering 
 on steep grades, because the motive power is independent of the axles, the 
 cable 'is always taut and there is no danger of its being run over should the 
 locomotive slide down grade with its wheels locked. The form and arrange- 
 ment of the cable reel and its motor vary somewhat. In one standard type 
 of gathering locomotive, the reel is drum shaped, is set above and on the end 
 frames in such a way that it does not project above the main casing of the 
 locomotive, and contains within it the necessary motor. In another standard 
 type, the reel is flat and turns horizontally on ball bearings on top of the loco- 
 motive. The reel is driven through a double reduction gearing by a small, 
 vertical, series-wound motor, the armature of which is, as a rule, provided 
 with ball bearings. The motor is connected directly across the line, with a 
 fuse and a switch inserted in the circuit, the former to protect against short- 
 circuits and the latter in case for some reason it should be desired to open the 
 circuit. A permanent resistance is also inserted in this circuit in order to limit 
 the heavy rush of current that would take place when the locomotive is stand- 
 ing still. The motor, however, has sufficient capacity to permit its being stalled 
 for any length of time without overheating. 
 
 The cable is generally about 500 ft. long, flexible, and heavily insulated 
 to withstand the wear to which it necessarily is subjected. The inner end is 
 connected to a collector ring on the underside of the reel and the outer end is 
 fitted with a copper hook for attaching to the trolley wire. A carbon brush 
 mounted on an insulated stud attached to the motor frame collects current 
 from the ring from which it is conducted to the controller circuit. 
 
 The arrangement and design of the reel motor is such that at all times it 
 will produce a tension on the cable. Thus, as the locomotive moves forwards, 
 the counter torque will produce a tension in the cable and cause it to pay out 
 evenly and drop along the roadbed without kinks. Owing to the braking effect 
 of this counter torque, the reel. will also come to a standstill when the loco- 
 motive stops; and as it starts on the return trip and the cable is slackened, the 
 motor action will immediately come into play and the reel will commence to 
 wind up the cable as the locomotive moves along, the peripheral rim speed of 
 the reel being higher than the linear speed of the locomotive. The operation 
 of the reel is thus entirely automatic and requires no controller, ratchet, or 
 clutch to be handled by the motorman, but leaves the motorman free to give 
 his entire attention to operating the controller and brakes and the proper 
 running of the locomotive. 
 
 Gathering locomotives are equipped with a regular mine trolley so that 
 they can be used in the same manner as regular hauling locomotives. When 
 the cable reel is not being used and the locomotive is collecting current through 
 the trolley pole in the regular way, the current flow through the reel motor 
 is cut off by throwing the reel and trolley switch to the trolley side. 
 
 Crab Locomotives. Crab, or traction-reel, locomotives carry a reel or drum 
 mounted in a similar position to that of a cable-reel locomotive, but upon 
 which is wound 350, 500, or more feet of wire rope. In operation, the loco- 
 motive remains on the entry with the brakes set, and the rope is dragged to 
 the face and coupled to the loaded car by the motor helper; when the reel 
 motor is started, the car is pulled to the entry. If the rope is long enough to 
 reach from the entry to the face of the room, where it is passed around a sheave, 
 and back again to the entry, this locomotive may be used to pull empty cars 
 up a grade to the face. Crab locomotives are in general use in mines where 
 the room track is too weak to sustain the weight of the motor, or where the 
 working places are on such a pitch that the locomotive cannot propel itself 
 in them. 
 
 Combination Cable-Reel and Crab Locomotives. Gathering locomotives 
 are sometimes built with both a cable and a rope reel. By the use of the 
 cable, the locomotive itself can enter any place where the track is suitable 
 and the grades are not too steep, and on heavy pitches the locomotive can 
 stand on the entry and pull cars to it by means of the wire rope. 
 
 Rack-Rail Locomotives. Traction locomotives may be used on short 
 grades of 5%, but above that they are not to be considered. To handle trips 
 on heavy grades without resorting to rope haulage, rack- or third-rail loco- 
 
828 HA ULAGE 
 
 motives are often employed. In these, the teeth of steel gear wheels carried 
 on the axle of the locomotive and turned by an electric motor, engage slots 
 cut in an iron bar (the rack rail) laid between the track rails, thus mechanically 
 pulling the locomotive forward up the grade. As the hauling capacity of the 
 locomotive does not depend on its adhesion but on the horsepower developed 
 by its motors, it tnay be made much lighter than the trolley locomotive with a 
 corresponding gain in the weight it is able to haul. 
 
 The rack rail may be either live or dead. In the first case, the current for 
 operating the locomotive is carried by the rack rail; in the second, the current 
 is received from an overhead trolley wire and returns through the rails of the 
 regular track. 
 
 A combination rack and traction locomotive is also made, which is arranged 
 to run as a rack locomotive on grades and as a traction locomotive on a level, 
 where no rack rail need be laid. 
 
 Rack-rail locomotives are planned on the unit system; that is to say, any 
 number of units of 50, 100 H. P., etc., may be run as a single locomotive where 
 the grades and the loads warrant it. 
 
 Operation of Electric Locomotives. Before an electric mining locomotive 
 is put into service, it should be inspected to see that all parts are in proper 
 condition. It should be well oiled and the sand boxes should contain plenty of 
 dry sand. The sand levers and brakes should be tried to see that they are 
 operating satisfactorily, and the controller should be on the off-position before 
 the trolley pole is put on. 
 
 When starting the locomotive, the current should be thrown on gradually 
 and due consideration paid to the load that the locomotive is to haul. The 
 slack in the couplings will often relieve the starting condition so that it will 'not 
 be necessary to start all the cars in the train simultaneously. The controller 
 should be advanced from one notch to another, quickly, being allowed to 
 remain on one point until the locomotive has gathered" speed to correspond , 
 when it is moved quickly to the next notch, etc. If, however, the controller 
 is advanced too rapidly and the wheels begin to slip the controller must not be 
 thrown backwards one or two steps but must be thrown off quickly, completely, 
 and advanced again in the usual manner. If the control is moved backwards 
 slowly, arcing at the contact fingers may cause burning and blistering. 
 
 The controller is only intended for starting duty and the locomotive should 
 not be run continuously with the controller on intermediate position, as this is 
 liable to cause a burn-out of the resistance or other damage to the controller. 
 
 If the locomotive runs too fast with the controller in the on-position and 
 the motors in parallel, the motors should be placed in series or the current 
 thrown on for a short time and then off, letting the locomotive coast. 
 
 When it is necessary to brake, the controller should be thrown to the 
 off-position before the brakes are applied. The controller should not be used 
 for braking, by reversing the motors, except in case of emergency. This 
 practice is sometimes resorted to, but is very severe on the motors, controllers, 
 and in fact on the entire equipment. Reversing the motors when running at 
 full speed is apt to break the gears and spring the armature shaft. 
 
 Troubles of Electric Locomotives. 1. Failure to Start. The most com- 
 mon cause of a motor failing to start is broken connection in the electric circuit 
 in the motors, the trolley, the track return, the circuit-breaker, controller, or 
 resistance grids. If the open circuit is in the motors, the defective part 
 can be located by raising the brushes of each motor commutator successively, 
 with the controller in the multiple position and the current applied. If, how- 
 ever, neither of the motors will operate when so connected, the opening is in 
 some other part of the electric circuit than the motors. An examination to 
 determine this is best made by the use of a bank of lamps, one end of which 
 is connected to the trolley wire and the other end applied to different parts of 
 the circuit beginning with the trolley harps and taking the circuit step by step 
 until the open circuit is passed. 
 
 When the open circuit is found to be in the field coils in one of the motors, 
 it is necessary to cut this motor out of circuit and drive the locomotive with 
 the other motor. Only half the customary load should then be hauled, 
 although the locomotive will, to a great extent, protect itself, as the wheels 
 connected to the driving motor will have a tendency to slip, which of course will 
 determine the amount of load that the locomotive is 'capable of hauling. The 
 defective motor is best cut out by removing its brushes. 
 
 Failure to start may also be due to faulty connections causing the motors 
 to buck each other. This will cause a heavy current and the fuse or circuit- 
 breaker will blow, It is readily corrected by reversing the brush leads on one 
 
HA ULAGE 829 
 
 motor. Grounding the current may also prevent a locomotive from starting, 
 while on the other hand mechanical troubles are often the cause; for example, 
 the brakes may not be released, the gears may be broken, the bearings stuck 
 or seized, etc. 
 
 If the locomotive jumps or does not start up smoothly, the trouble is 
 generally short circuits in the starting resistance, wrong or open connections, 
 controller troubles, etc. 
 
 2. Excessive Heating. Heating may be due to the motors being over- 
 loaded when hauling heavy trips, and can then only be remedied by reducing 
 the load or by providing larger locomotives. 
 
 Low voltage is a very common cause of a motor not developing its rated 
 capacity causing overheating due to slower speed, breakdowns, etc. This may 
 be the result of insufficient copper in the overhead wires, poor bonding of the 
 rails, poor connections in the circuit or insufficient prime mover or generator 
 capacity. 
 
 A short circuit in any armature turn will cause a circulation of heavy 
 current therein, followed by excessive heating. This current is due to the 
 transformer action of the field coils acting as primary and the short-circuited 
 armature turns as secondary. The trouble can generally be detected by the 
 smell of burning insulation or by the hand, as the short-circuited coils will be 
 much warmer than the other part of the armature. As a temporary remedy, 
 the short-circuited coils can be open circuited at the commutator and dis- 
 connected from it, the commutator being bridged at this point to close 
 the gap. 
 
 Short-circuited field turns will cause the motor to speed up, particularly 
 at light loads. This tendency to speed up will cause the motor to take an 
 excessive current, causing overheating of the defective motor armature. The 
 defective coil can be located by feeling with the hand, as it will be much cooler 
 than the others. This is due to the reduced number of turns, which decreases 
 the resistance of the coil and consequently the amount of loss therein. When 
 a field coil is found to be short circuited so as to affect the operation of the 
 motor, the coil should be removed and replaced by a new one. 
 
 Burn-out from excessive heating is also caused by the armature coming 
 down on the pole faces. The remedy for this is, of course, only to give more 
 attention to the motor bearings, keeping them properly lubricated and by 
 frequently checking the air gap to see if the armature is getting dangerously 
 close to the pole faces. 
 
 3. Sparking. Excessive sparking at the brushes is frequently caused by 
 an open circuit in the armature winding. Such sparking may often become 
 so violent as to cause the motors to flash over at the commutator. An exami- 
 nation will show that the commutator segments, between which the open circuit 
 occurs, are blackened and slightly burned. If the open circuit is not taken 
 care of at once, it is liable to cause a flat spot on the commutator, requiring 
 turning. Temporary relief can be had by bridging the open circuit at the 
 commutator. 
 
 Short-circuited field turns, if affecting a large number of turns, are also 
 liable to cause excessive sparking at the brushes. 
 
 Commutator troubles are a very common cause of sparking and com- 
 mutators should be kept free from oil and dirt. If they become very rough 
 from overheating and excessive sparking, it may be necessary to smooth 
 them with sandpaper, and if this does not help, returning is the remedy. 
 
 Trouble with the commutators is often due to careless handling of the 
 locomotive, such as operating it with a defective controller or a defective 
 resistance. When a resistance is found to have a broken grid, a new one 
 should be put in at once. The method sometimes resorted to of short circuiting 
 a broken grid should not be allowed, except for temporary work, for when 
 doing so, a large percentage of the resistance may be cut out of one or more of 
 the steps, causing the motors to take excessive current when those points on 
 the controller are reached. This will cause the locomotive to start with a 
 jerk and very likely burn the commutator and brushes, besides being hard on 
 the gears and other mechanical parts of the locomotive. 
 
 4. Grounds. When a ground occurs in a motor, whether it is confined to 
 the armature, field coils, or commutator, it will cause the circuit-breaker or 
 fuse to blow, and it will not be possible to keep the circuit-breaker closed 
 without holding it in, which should never be done. 
 
 Motors will also sometimes show a ground when tested with a voltmeter 
 or a bank of test lamps, but otherwise will operate satisfactorily. It is then 
 evident that there is a leakage path formed somewhere, and if the motors 
 
830 HAULAGE 
 
 are not inspected and thoroughly cleaned to remove this partial ground it is 
 only a short time before a permanent ground can be expected. 
 
 When a ground occurs, the motor containing it should be cut out of service 
 and the locomotive operated by the other motor until such time as the ground 
 can be located and remedied. 
 
 ALTERNATING-CURRENT LOCOMOTIVES 
 
 Alternating-current locomotives may be either single or three phase. 
 Single-phase locomotives require but one overhead trolley wire, as in direct- 
 current haulage, whereas three-phase locomotives require two trolley wires, 
 the track rails forming the third leg of the circuit. Three-phase locomotives 
 are not generally recommended for underground use because of the difficulty 
 of maintaining and insulating two trolley wires, the increased complication of 
 the switches where two wires are used, etc. 
 
 The single-phase locomotive, taking all its current from one phase of the 
 supply system, produces an unbalanced load on the line, but this should not 
 seriously affect a power station of good capacity. In extensive haulage 
 installations, by taking the power for the various sections of the main line and 
 for the various branches from different phases of the supply line, it is possible 
 to practically balance the load. 
 
 The three-phase locomotive sometimes used at American mines for outside 
 haulage, is similar in general construction and appearance to the direct-current 
 machine. It has, however, either two trolley poles or a pantagraph trolley 
 making sliding contact with the wires. These locomotives may be had up to 8 
 to 10 T. in weight and for the standard frequencies and voltages. They are 
 provided with two-torque induction motors, with suitable starting resistances 
 in the rotor circuit, so that reduced speeds may be had for starting (accelera- 
 tion), switching, etc. As the induction motor is a constant-speed machine, the 
 locomotive tends to maintain the speed for which it is geared regardless of the 
 load or grades. The high-speed of the induction motors necessitates a double- 
 gear reduction and consequently a different method of mounting than is used 
 in the direct-current machine. 
 
 The advantage of the three-phase locomotive is in the saving in the cost of 
 converters and the power lost in converting from alternating to direct 
 current. The high voltages so often used with them are extremely dangerous. 
 
 STORAGE-BATTERY LOCOMOTIVES 
 
 For gathering coal, storage-battery locomotives are recommended where 
 the grades are not severe ; where the speed does not exceed 3 5 to 4 mi. per hr. ; 
 where the hauls are short, say not over mi., and where the service is inter- 
 mittent; that is, where the locomotive is idle a good portion of the time, as 
 when waiting on empties or loads. These locomotives are not at present 
 advised for main-line haulage where the travel is long because the practically 
 continuous service requires a locomotive of a price and over-all dimensions 
 that is commonly prohibitory. In size, these locomotives range from 2 
 to 10 T., a common size for gathering being 4 T.; however, a 20-T. locomotive 
 of this type has been built. In the majority of cases, the battery is carried on 
 the same truck as the motor and is an integral part of the locomotive, but in 
 some of the larger machines designed for long hauls, heavy work, and the 
 like _ conditions requiring more nearly continuous service, the batteries are 
 carried on a trailing truck, tender, or battery car; the weight of which reduces 
 the hauling capacity of the locomotive. Recharging is done at night with 
 usually a little "livening up" during the noon hour or other idle times. Where 
 separate battery cars are used, a fresh one may be coupled to the locomotive 
 at the time the exhausted one is taken away to be recharged. One type 
 of these locomotives is built to use current from the ordinary overhead trolley 
 wire where such exists, thus saving the batteries for use in parts of the mine 
 where current is not to be had. This locomotive is also arranged with suitable 
 switches so that the batteries may be charged from the trolley circuit at the 
 same time the motor is being run in the ordinary way. 
 
 The weight of a locomotive required to give the necessary adhesion to 
 haul the load is calculated in the same way as for any other kind of locomotive. 
 The calculation of the battery capacity or power is not easily made and requires 
 a careful study of the grades, loads, and distances, from which may be cal- 
 culated the foot-pounds of work the locomotive must perform. In this calcu- 
 lation, perhaps the most important point is estimating the ratio of the actual 
 discharge rate of the battery cells to the normal rate of discharge. This 
 
VENTILATION OF MINES 831 
 
 depends on the length of time the locomotive is developing the maximum 
 drawbar pull or some other high value of the drawbar pull that is sustained 
 for any considerable length of time. The value finally selected depends largely, 
 if not entirely, on the judgment and experience of the individual. It is gener- 
 ally considered safe to make this ratio 1 : 3, although on flat grades where 
 the maximum pull is exerted only at starting and for a second or two, the 
 ratio may be as high as 1 : 5. The foot-pound of work may be reduced to 
 kilowatt-hours on the basis of 1 ft.-lb. = .000000377 K. W.-hr. In ordinary 
 estimates, it may be assumed that the kilowatt-hours per ton-mile of load are 
 .125 for a level track, which includes the losses in the battery and locomotive. 
 
 VENTILATION OF MINES 
 
 CHEMICAL AND PHYSICAL PROPERTIES OF GASES 
 
 CHEMISTRY OF GASES 
 
 Matter and Its Divisions. Matter is the substance of which all things are 
 composed and may be denned as anything that possesses weight or occupies 
 space. There are three divisions of matter: 
 
 A mass is a body of matter of a size to be appreciable to the senses. 
 
 A molecule is the smallest particle of matter into which a mass may be 
 divided by physical means; it is the smallest particle of matter that is capable 
 of a separate existence. The exact size of a molecule cannot be determined 
 but it is so small that the most powerful microscope would tail to recognize 
 it. Lord Kelvin calculates that if a single drop of water was magnified until 
 it appeared as large as the earth (approximately 8,000 mi. in diameter), the 
 molecules in the drop would appear to have a size between that of a baseball 
 and a small shot. 
 
 An atom is the smallest particle of an element that can enter into a chem- 
 ical reaction and cannot further be divided. As a rule, atoms are incapable of 
 existing in a free state, and are generally found in combination with other atoms, 
 either of the same or of different kinds. 
 
 Atoms unite to form molecules, and molecules unite to form masses. 
 
 Classes of Matter. An element is a mass of matter composed of the same 
 kind of molecules which, in turn, are composed of the same kind of atoms. 
 Thus, two atoms of hydrogen unite to form a molecule of hydrogen and an 
 inconceivable number of molecules of hydrogen unite to form a mass, say, 
 an ounce or a pound of hydrogen. In the case of an element, the mass, mole- 
 cule, and atom are of the same kind. 
 
 A compound, or chemical compound, is a mass of matter composed of the 
 same kind of molecules, but the molecules are composed of two or more atoms 
 of different kinds. Thus a mass of methane is composed of molecules of 
 methane, which are each composed of one atom of carbon and four atoms 
 of hydrogen. 
 
 A mixture is a mass of matter composed of two or more different kinds of 
 molecules, the one molecule being composed of different atoms than the other 
 or others. Thus, afterdamp is a mixture of molecules of oxygen, nitrogen, 
 carbon dioxide, carbon monoxide, and usually one or more other gases, the 
 molecules of each of which are composed of characteristic atoms. 
 
 There are at present (1915) 83 definitely known elements having properties 
 more or less clearly understood, together with a number more the identifica- 
 tion or characteristics of which are in doubt. 
 
 Forms of Matter. The atoms composing a molecule are held together 
 by chemical affinity, and molecules composing a mass are held together by 
 cohesion. In addition, molecules of all matter are acted upon by an opposing 
 force, repulsion, which tends to drive them apart. Repulsion is not inherent 
 in the mass, but is an induced or applied force that is largely the result of heat 
 or the temperature of the body. 
 
 All matter exists in one of three forms, solid, liquid, or gaseous, according 
 to the predominance of the attractive or the repulsive forces existing between 
 the molecules. For example, water exists as ice, or in a solid form, when the 
 attractive force exceeds the repulsive force between its molecules. As the 
 temperature is raised or heat is applied, the ice assumes the liquid form due 
 to the more rapid vibration of the molecules of which it is composed. In 
 
832 VENTILATION OF MINES 
 
 other words, the repulsive force existing between the molecules is increased, 
 and the result is a liquid. If the temperature is raised still further by apply- 
 ing more heat, the vibration of the molecules becomes yet more rapid, the 
 repulsive force is increased between the molecules, and a gas or vapor called 
 steam is formed. 
 
 Changes in Matter. Matter cannot be destroyed but its form may be 
 changed or, if a chemical compound, it may be broken up into its component 
 elements. Changes affecting the form or state of matter brought about by 
 physical causes, as heat, pressure, electricity, etc., and affecting only the 
 molecules of a body are physical changes; changes affecting the atoms in a 
 molecule, by which they are rearranged or combined in new ways are chemical 
 changes. Physical changes always accompany chemical changes, a change 
 in the arrangement or relations between the molecules of matter usually pre- 
 ceding a change in the arrangement of the atoms in the molecule. Thus, the 
 change from ice to water to steam is a physical change due to heat; if the heat 
 is still further increased, the molecules of water will be decomposed into hydro- 
 gen and oxygen gas, which is a chemical change. 
 
 Symbols and Formulas. It is usual to express the names of the elements 
 by letters called symbols. The letters selected are the first one of the name 
 or the first and some letter following it. While in the majority of cases, the 
 letters are taken from the common name of the element, in others the symbol 
 is derived from its Latin or other name. Thus, the symbol for iron is Fe, 
 derived from the Latin ferrum, and for tungsten is W, from -wolfram, an earlier 
 name. The symbols for antimony, gold, silver, tin, copper, sodium, potas- 
 sium, and mercury, are similarly derived from the Latin. Two atoms of an 
 element, as hydrogen, may be written either 2H or Hz. 
 
 A formula is the expression of the composition of a molecule by means of 
 the symbols of the elements entering into it, the number of atoms of each kind 
 in the molecule being denoted by subscripts. Thus, the formula for methane 
 is CH4, which indicates that a molecule of this gas is composed of one atom 
 of carbon (symbol C) and four atoms of hydrogen (symbol H). When there 
 are no subscripts, it is understood that but one atom is present in the mole- 
 cule, as in CO, which is composed of one atom each of carbon and oxygen. 
 Two molecules of methane would be written 2CHt, three molecules 3CHt, etc. 
 
 The symbol for the element hydrogen is H, and the formula for the molecule 
 of hydrogen is Hz, since each molecule of this gas contains two atoms as explained 
 in the next paragraph. 
 
 Atomicity of Elements. By atomicity is meant the number of atoms in 
 a molecule. The rare atnwspheric gases, argon, helium, krypton, neon, and 
 xenon are monatomic; that is, their molecules contain but one atom. Hence, 
 for these gases, the symbols A, He, Kr, Ne, and Xe, respectively, represent 
 either one atom or one molecule. 
 
 The common atmospheric gases, hydrogen, nitrogen, and oxygen are 
 diatomic, or their molecule is composed of two atoms. In these cases, the 
 symbols for the atoms are, respectively, H, N, and O, and the formulas for the 
 molecules are Hz, Nz, and Oz. While sulphur is letr atomic at temperatures 
 of more than 800 C. and hexatomic at about 500 C. and its molecule is thence 
 St or Se, it is commonly written S, as if monatomic, in questions of mine gases. 
 The same is true of carbon, which is either diatomic or tetratomic. 
 
 Chemical Reactions. A chemical reaction is any change in the arrangement 
 of the atoms in a single molecule of a substance or in the atoms of several 
 molecules of different substances brought about by external agencies. The 
 agencies affecting the arrangement of the atoms in a molecule or molecules are 
 heat, electricity, and chemical affinity. In any reaction, no matter is destroyed. 
 There are always the same number and kind of atoms after the reaction as 
 before it took place, but their combination, one with the other, to form mole- 
 cules is different. 
 
 Chemical Equations. A chemical equation is the expression of the equality 
 between atoms before and after a chemical reaction takes place. The first, 
 or left-hand, member of the equation gives the formula and the number of 
 molecules or atoms of the substance acted upon or the two or more substances 
 that react upon one another, while the second, or right-hand, member gives 
 the formula and the number of molecules of the substance or substances formed 
 by the reaction. 
 
 There are atomic and molecular equations. The former, which are the 
 simpler, show the relation between the atoms concerned in a reaction. The 
 atomic equation for the burning of carbon in air is written C-\-2O = COz. 
 The molecular equation for the same reaction is C-\-Oz = COz. From the first 
 
VENTILATION OF MINES 
 
 833 
 
 equation, when the weight of carbon burned is known, there may be calculated 
 the weight of oxygen required for the combustion and that of the carbon 
 dioxide formed. If the weights per cubic foot of O and COi are known, the 
 volumes of these gases concerned in the reaction may then be calculated. 
 The molecular equation, however, shows that the volume of oxygen consumed 
 is the same as that of the carbon dioxide produced; hence, but one volume 
 calculation need be made. 
 
 Atomic Weight. The absolute weight of an atom is not known, but the 
 relative weights of the atoms are known in most cases with a high degree of 
 accuracy. As hydrogen gas is the lightest known substance, it is made the 
 basis of comparison, and the relative weights of the atoms of the other elements 
 are referred to it. Thence, the atomic weight of an element is the ratio between 
 the weight of its alom and that of an atom of hydrogen. The atomic weight 
 of oxygen = 15.88 when hydrogen = 1. Oxygen is a very common constituent of 
 chemical compounds and hydrogen rather unusual; hence, for ease in calcu- 
 
 THE ELEMENTS WITH THEIR SYMBOLS AND ATOMIC WEIGHTS 
 
 (0 = 16) 
 
 Element 
 
 Symbol 
 
 Atomic 
 Weight 
 
 Element 
 
 Symbol 
 
 Atomic 
 Weight 
 
 Aluminum 
 Antimony 
 
 Al 
 Sb 
 A 
 
 27.10 
 120.20 
 39.88 
 
 Molybdenum . . 
 Neodymium . . . 
 Neon 
 
 Mo 
 Nd 
 Ne 
 
 96.00 
 144.30 
 20.20 
 
 Arsenic 
 
 As 
 Ba 
 
 74.96 
 137.37 
 
 Nickel 
 Niton 
 
 Ni 
 Nt 
 
 58.68 
 222.40 
 
 Bismuth 
 
 Bi 
 B 
 
 208.00 
 11 00 
 
 Nitrogen 
 
 N 
 Os 
 
 14.01 
 190.90 
 
 Bromine 
 
 Br 
 
 Cd 
 
 79.92 
 112.40 
 
 Oxygen 
 Palladium 
 
 
 Pd 
 
 16.00 
 106.70 
 
 Caesium 
 Calcium 
 Carbon 
 
 Cs 
 Ca 
 
 Q 
 
 132.81 
 40.07 
 12 00 
 
 Phosphorus. . . . 
 Platinum 
 
 P 
 
 Ft 
 K 
 
 31.04 
 195.20 
 39.10 
 
 Cerium 
 
 Ce 
 Cl 
 
 140.25 
 35 46 
 
 Praseodymium . 
 
 Pr 
 Ra 
 
 140.60 
 226.40 
 
 Chromium 
 
 Cr 
 
 52.00 
 
 Rhodium 
 
 Rh 
 
 102.90 
 
 Cobalt 
 Columbium 
 Copper 
 Dysprosium 
 Erbium 
 Europium 
 Fluorine 
 Gadolinium 
 Gallium 
 Germanium 
 Glucinum 
 Gold 
 Helium 
 Holmium 
 
 Co 
 Cb 
 Cu 
 
 % 
 
 Eu 
 
 Gd 
 Ga 
 Ge 
 Gl 
 Au 
 He 
 Ho 
 
 58.97 
 93.50 
 63.57 
 162.50 
 167.70 
 152.00 
 19.00 
 157.30 
 69.90 
 72.50 
 9.10 
 197.20 
 3.99 
 163.50 
 
 Rubidium 
 Ruthenium .... 
 Samarium 
 Scandium 
 Selenium 
 Silicon 
 Silver 
 Sodium 
 Strontium 
 Sulphur 
 Tantalum 
 Tellurium 
 Terbium 
 Thallium 
 
 Rb 
 Ru 
 
 Sa 
 Sc 
 Se 
 Si 
 Ag 
 Na 
 Sr 
 S 
 Ta 
 Te 
 Tb 
 Tl 
 
 85.45 
 101.70 
 150.40 
 44.10 
 79.20 
 28.30 
 107.88 
 23.00 
 87.63 
 32.07 
 181.50 
 127.50 
 159.20 
 204.00 
 
 Hydrogen 
 Indium 
 
 H 
 In 
 
 1.008 
 114.80 
 
 Thorium 
 Thulium 
 
 Th 
 Tm 
 
 232.40 
 168.50 
 
 Iodine 
 Indium 
 Iron 
 
 Krypton 
 Lanthanum 
 
 I 
 Ir 
 Fe 
 Kr 
 La 
 Pb 
 
 126.92 
 193.10 
 55.84 
 82.92 
 139.00 
 207 10 
 
 Tin 
 Titanium 
 Tungsten 
 Uranium 
 Vanadium 
 
 Sn 
 Ti 
 W 
 U 
 V 
 Xe 
 
 119.00 
 48.10 
 184.00 
 238.50 
 51.00 
 130.20 
 
 Lithium 
 Lutecium 
 Magnesium 
 Manganese 
 Mercury 
 
 Li 
 Lu 
 Mg 
 Mn 
 Hg 
 
 6.94 
 174.00 
 24.32 
 54.93 
 200.60 
 
 Ytterbium 
 Yttrium 
 Zinc 
 Zirconium 
 
 Yb 
 Yt 
 Zn 
 Zr 
 
 172.00 
 89.00 
 65.37 
 90.60 
 
 53 
 
834 
 
 VENTILATION OF MINES 
 
 lating, chemists have found it advisable to consider the atomic weight of 
 oxygen as 16, in which case that of hydrogen is 1.008, the ratio of 15.88 : 1 being 
 the same as 16 : 1.008. When the atomic weights are based on oxygen =16. 
 those of all the elements must be multiplied by 1.008 if they have been deter- 
 mined on the basis hydrogen =1. The foregoing table of atomic weights is 
 based upon oxygen =16, and is taken from the report of the International 
 Committee of Atomic Weights for 1914. All the elements in the list are 
 known, and there have been omitted therefrom sundry of the radioactive 
 elements as actinium, polonium, radiothorium, etc., which are, as yet imper- 
 fectly identified. 
 
 Molecular Weight. The molecular weight of any substance, elementary 
 or compound, is equal to the sum of the atomic weights of the atoms in its 
 molecule. It is customary, in all but precise calculations, to use the approxi- 
 mate rather than the exact atomic weights. The following are the approximate 
 atomic weights generally used for the elements occurring in mine gases, the 
 exact weight when oxygen = 16 being given in parenthesis: Carbon 12 (12); 
 hydrogen 1 (1.008); nitrogen 14 (14.01); oxygen 16 (16); sulphur 32 (32.07). 
 For illustration, the molecular weight of sulphuric acid, HzSOt, is found as 
 follows: 
 
 Approximate Exact 
 
 #2 = 2X 1= 2 Ht = 2X 1.008= 2.016 
 
 5=1X32 = 32 5=1X32.07 =32.070 
 
 04 = 4X16 = 64 04 = 4X16 =64.000 
 
 Molecular weight = 98 Molecular weight = 98.086 
 
 The following table gives the names, formulas, and molecular weights of 
 the elementary (oxygen, nitrogen, and hydrogen) and the compound gases 
 that may be met in mines. For all ordinary purposes, the approximate mole- 
 cular weights may be used. 
 
 FORMULAS AND MOLECULAR WEIGHTS OF COMMON GASES 
 
 Name of Gas 
 
 Formula 
 of 
 Molecule 
 
 Molecular Weight 
 When 
 
 = 16 
 
 # = 1 
 
 Approximate 
 
 Acetylene 
 
 CzHz 
 COz 
 CO 
 C*H 6 
 CzH* 
 Hi 
 H Z S 
 CHt 
 NO 
 Nt 
 N0 2 
 
 02 
 
 50 2 
 H-D 
 
 26.016 
 44.000 
 28.000 
 30.048 
 28.032 
 2.016 
 34.086 
 16.032 
 30.010 
 28.020 
 46.010 
 32.000 
 64.070 
 18.016 
 
 25.82 
 43.67 
 27.79 
 29.82 
 27.82 
 2.00 
 33.82 
 15.91 
 29.78 
 27.80 
 45.66 
 31.76 
 63.58 
 17.88 
 
 26 
 44 
 28 
 30 
 28 
 2 
 34 
 16 
 30 
 28 
 46 
 32 
 64 
 18 
 
 Carbon dioxide 
 Carbon monoxide 
 Ethane 
 
 Ethylene 
 
 Hydrogen 
 
 Hydrogen sulphide .... 
 Methane 
 
 Nitric oxide 
 Nitrogen 
 
 Nitrogen dioxide 
 
 Oxygen 
 Sulphur dioxide 
 
 Water, vapor 
 
 Percentage Composition. The actual weights of the various elements in 
 a given weight of a chemical compound are proportional to the weights of the 
 atoms of each element in a molecule of the compound. 
 
 EXAMPLE. What is the percentage composition of methane, CHi, and how 
 many pounds of carbon, C, and hydrogen, H, are there in 5 Ib. of this gas? 
 
 SOLUTION. From the foregoing table, the weight of a molecule of CHt 
 is 16, of which 12 parts by weight (1X12) is C, and 4 parts by weight (4X1) 
 is H, From this, the percentage of C in a molecule of CH t is (12 -M 6) X 100 
 = 75; and of H , is (4 -=- 16) X 100 = 25. 
 
 In 5 Ib. of CH t there are 5X. 75 = 3.75 Ib. of C, and 5X. 25 = 1.25 Ib. of H. 
 
 Weights of Substances Concerned in Reactions. The actual weights of 
 
VENTILATION OF MINES 835 
 
 the substances entering into any chemical reaction are proportional to the total 
 molecular weights of the substances concerned in the reaction. 
 
 EXAMPLE 1. (a) How many pounds of oxygen are required to burn 5 Ib. 
 of methane; (&) how many pounds of carbon dioxide and water vapor will be 
 produced? 
 
 SOLUTION. (a) The molecular equation for the reaction may be written 
 
 Cfh + 2Oz = COz + 2HsO 
 Molecular weights, 16 + 64 = 44+36 
 
 Dividing by 16, 1+4 = 2.75+2.25 
 
 The molecular weights may be taken from the preceding table or may 
 be calculated from the approximate atomic weights. Since the reaction is 
 based upon a known weight of CHi, the molecular weights are divided through 
 by the molecular weight of CHi to reduce the relative weight of that gas to 
 unity or 1. The reaction may be read: Four pounds of O are required to 
 burn 1 Ib. of C#4, the reaction producing 2.75 Ib. of COz and 2.25 Ib. of HiO. 
 Since it requires 4 Ib. of O to burn 1 Ib. of CHi, to burn 5 Ib. of CBt will require 
 5X4 = 201b. of 0. 
 
 (b) Since 1 Ib. of CH* in burning produces 2.75 Ib. of COz and 2.25 Ib. of 
 HiO, 5 Ib. of this gas will produce 5X2.75 = 13.75 Ib. of COz and 5X2.25 
 = 11.25 Ib. of HzO. 
 
 Note that the sums of the atomic weights on both sides of the equation are 
 the same and equal to 80. Also that the actual weight of the substances burned 
 is the same as that of the substances produced; thus 5 Ib. of CHt+20 Ib. of O 
 = 25 Ib., and 13.75 Ib. of COa+11.25 Ib. of H*0 = 25 Ib. 
 
 EXAMPLE 2. How mdny pounds of carbon monoxide must be burned in 
 oxygen to produce 10 Ib. of carbon dioxide, and how many pounds of oxygen 
 will be required? 
 
 SOLUTION. The molecular equation for the reaction is 
 
 2CO+0 2 = 2C0 2 
 Molecular weights, 56+32 = 88 
 Dividing by 88, .636 +.364 = 1 
 
 The molecular weights taken from the table or calculated are divided 
 by 88, the weight of two molecules of COz, since it is the absolute weight of 
 that gas that is required. It is apparent that to produce 10 Ib. of COz, 10 
 X. 636 = 6.36 Ib. of CO must be burned in 10X. 364 = 3.64 Ib. of O. 
 
 Volumes of Gases Concerned in Reactions. As equal volumes of all gases 
 contain the same number of molecules, all gaseous molecules are of the same 
 sbe, whence the volumes of the gases concerned in any reaction are directly 
 proportional to the number of molecules of the respective gases involved. 
 
 EXAMPLE 1. How many cubic feet of oxygen will 100 cu. ft. of carbon 
 monoxide consume in burning to carbon dioxide, and how many cubic feet of 
 the latter gas will be produced? 
 
 SOLUTION. The molecular equation is written 
 II I II 
 
 The Roman numerals written above the formulas for the gases, represent 
 the number of molecules of each concerned in the reaction. Hence, two 
 volumes of CO combine with one volume of O to produce two volumes of COz. 
 In this reaction there has been a condensation since three volumes are reduced 
 to two. On the other hand, there are six atoms on each side of the equation, 
 and the molecular weights are 88 on each side. Since CO combines with 
 one-half its volume of O, it follows that 100 cu. ft. of CO will combine with 
 50 cu. ft. of O to form 100 cu. ft. of COz. 
 
 EXAMPLE 2. How many cubic feet of oxygen are required for the complete 
 combustion of 100 cu. ft. of methane, and how many cubic feet of carbon 
 dioxide and vapor of water will be produced? 
 
 SOLUTION. The molecular equation is written 
 I II I II 
 
 The volume of the O will be twice that of the CHt. and the volumes of 
 the COz and HzO will be equal, respectively, to those of the CHt and O. Hence, 
 to burn 100 cu. ft. of CHt will require 200 cu. ft. of O, and there will be pro- 
 duced 100 cu. ft. of CO 2 and 200 cu. ft. of HzO. 
 
 Volumes of Gases When Burned in Air. When gases are burned m air, 
 in order to compute the volume of the products of combustion exactly, account 
 must be taken of the nitrogen in the atmosphere. The exact ratio by volume 
 of the oxygen to the nitrogen in the air is 1 : 3.782; that is, for every molecule 
 of oxygen there are 3.782 molecules of nitrogen, From this, the formula for 
 
836 VENTILATION OF MINES 
 
 air may be taken to be (O2+3.7822V2), and may be substituted for the molecule 
 of oxygen Oz in all reactions where it occurs. Where exactness is not required, 
 it is usual to assume the : N ratio in the air as 1 : 4, and to write the formula 
 (O 2 _|_42V2). It should be noted that the foregoing are, strictly speaking, not 
 formulas, but indicate, rather, the composition of a definite mixture of oxygen 
 and nitrogen, which is known as air. 
 
 EXAMPLE 1. What is the percentage, by volume, of methane in firedamp 
 at its most explosive point? 
 
 SOLUTION. By introducing the formulas for the ratio of oxygen and 
 nitrogen in the air, the equation for the combustion of methane is, 
 
 CHt+2(Oz+3.782Nz) = C0 2 +2fl2O+7.5642V2 
 Relative volumes, 1 2 X (1+3.782) 1 2 7.564 
 Relative volumes, 1 9.564 1 2 7.564 
 
 From this, one volume of CHi combines with 9.564 volumes of air and 
 forms 10.564 volumes of firedamp. The proportion of methane in the mixture 
 is (1 -T- 10.564) X 100 = 9.46%. 
 
 EXAMPLE 2. Using the approximate O : N ratio for air, what is the per- 
 centage composition of the afterdamp of an explosion of CO? 
 
 SOLUTION. The molecular equation may be written 
 
 2CO+ (02+42V 2 ) = 2C0 2 +4AT 2 
 Relative volumes, 2 5 24 
 
 In the six parts of afterdamp there will be g = 1 = 33.33% of COz and f = | 
 = 66.67% of N. 
 
 Weight and Volume of Gases in Reactions. When the volume, in cubic 
 feet, of 1 Ib. of gas is known, the volumes and weights of the gases concerned 
 in a reaction may be obtained through the use of the ordinary formulas. The 
 volume of 1 Ib., in cubic feet, of the principal gases is given in a following table. 
 
 EXAMPLE. Using the exact molecular weights _ when O = 16, what are the 
 weights and volumes, in cubic feet, of the gases involved in the burning of 
 1 Ib. of carbon in oxygen? 
 
 SOLUTION, The molecular equation is 
 
 Relative volumes, I I 
 
 C+ Oz = COz 
 
 Molecular weights, 12+32 = 44 
 Dividing by 12, 1 +2.67 = 3.67 
 
 Inspection shows that 2.67 Ib. of are required to burn 1 Ib. of C, and 
 that 3.67 Ib. of COz are produced; further, the volume of the O required is 
 the same as that of the COz produced. From the table on page 837, the volume 
 of 1 Ib. of is found to be 11.208 cu. ft.; hence, 2.67 Ib. will have a volume 
 of 2.67 X 11.208 = 29.93 cu. ft. Further, as the volume of 1 Ib. of COz is 8.103 
 cu. ft., 3.267 Ib. will occupy 3.67X8.103 = 29.94 cu. ft. 
 
 It will be noted that the volumes of oxygen and carbon dioxide as calculated 
 are practically equal. This is as it should be as the relathe volumes are the 
 same, as is shown by the equation representing the reaction. In fact, in 
 reactions between gases or into which gases enter, it is only necessary to calcu- 
 late the volume of one of the gases; that of the others may be told from the 
 relative volumes given by the equation. The volumes of the gases will always 
 be equal or some simple multiple as 1, 2, 3, etc., of one another. 
 
 PHYSICS OF GASES 
 
 Avogadro's Law. Equal volumes of all perfect gases, whether simple or com- 
 pound, contain the same number of molecules when each are under the same con- 
 ditions of temperature and pressure. From this law it follows: 
 
 The molecules of all perfect gases are of the same size. 
 
 A given volume of any perfect gas is as much heavier than the same volume 
 of hydrogen as its molecular weight is greater than the molecular weight of hydrogen, 
 or, more simply, the weight of 1 cu. ft. of any gas is proportional to its molecular 
 weight. 
 
 Avogadro's law and its two corollaries do no apply to either solids or liquids, 
 and do not hold strictly true for all gases at all temperatures, but they are of 
 much practical value in chemistry and physics. It has been found that the 
 density and specific gravity of gases calculated on the assumption of the correct- 
 ness of this law, do not in all cases, agree with the observed density and specific 
 gravity. 
 
 Density of Gases. The density of a gas is the ratio between the weight 
 of a unit volume of the gas and that of the same volume of hydrogen, measured 
 at a temperature of 32 F. and under a barometric pressure of 29.92 in. of 
 mercury. Density is sometimes defined as the specific gravity of a gas referred 
 
VENTILATION OF MINES 
 
 837 
 
 to hydrogen instead of to air as the standard. The following statements, based 
 on the assumed correctness of Avogadro's law and the fact that the molecule 
 of hydrogen is diatomic (composed of two atoms) are correct when the atomic 
 weights are based on H = 1 . 
 
 1. The density of any simple diatomic gas is equal to its atomic weight. 
 
 2. The density of any compound gas is equal to one-half its molecular 
 weight. 
 
 The values in the table are calculated from the atomic weights and in 
 numerous instances do not agree with the observed values, which they probably 
 would do if Avogadro's law was strictly correct. 
 
 DENSITY OF GASES AT 32 F. AND 29.92 IN. OF MERCURY 
 
 Gas 
 
 Formula 
 
 Density 
 
 Exact 
 
 Approximate 
 
 Acetylene 
 Air 
 
 C 2 ff2 
 
 C0 2 
 CO 
 C 2 H S 
 CzHi 
 Hz 
 HtS 
 CH t 
 NO 
 Nt 
 NOz 
 Ot 
 S0 2 
 H,O 
 
 12.910 
 14.359 
 21.835 
 13.895 
 14.910 
 13.910 
 1.000 
 16.915 
 7.955 
 14.890 
 13.910 
 22.830 
 15.880 
 31.795 
 8.940 
 
 12 
 14 
 22 
 14 
 15 ' 
 14 
 1 
 17 
 8 
 15 
 14 
 23 
 16 
 32 
 9 
 
 Carbon dioxide 
 
 Carbon monoxide 
 Ethane 
 
 Ethylene 
 Hydrogen 
 
 Hydrogen sulphide 
 
 Nitric oxide 
 Nitrogen 
 
 Nitrogen dioxide 
 Oxygen 
 
 Sulphur dioxide 
 
 Water vapor 
 
 
 Air being a mixture and not a true gas has, strictly speaking, no 'density, 
 but the values given are convenient in certain calculations. 
 
 Water vapor cannot exist at 32 or at any temperature below the boiling 
 point unless the pressure is less than 29.92 in. The figures given are theoretical 
 but, as in the. case of air, are useful at times. 
 
 Specific Gravity of Gases. The specific gravity of a gas is the ratio of its 
 weight to that of an equal volume of air, measured at a temperature of 32 F. 
 and a pressure of 29.92 in. of mercury. 
 
 SPECIFIC GRAVITY, WEIGHT, AND VOLUME OF GASES AT 32< 
 AND 29.92 IN. OF MERCURY 
 
 F. 
 
 Gas 
 
 Symbol 
 
 Observed 
 Specific 
 Gravity 
 
 Weight of 
 1 Cu. Ft. 
 Pound 
 
 Volume of 
 1 Lb. 
 Cubic Feet 
 
 
 CiHz 
 
 .9056 
 
 .07309 
 
 13.682 
 
 Air 
 
 
 1.0000 
 
 .08071 
 
 12.390 
 
 Carbon dioxide 
 Carbon monoxide 
 Ethane 
 Hydrogen 
 Hydrogen sulphide 
 
 COt 
 
 CO 
 H 6 
 
 1.5291 
 .9670 
 1.0494 
 .0696 
 1.1912 
 
 .12341 
 .07805 
 .08470 
 .00621 
 .09614 
 
 8.103 
 12.813 
 11.806 
 177.904 
 10.401 
 
 Methane 
 
 cm 
 
 .5545 
 
 .04475 
 
 22.346 
 
 
 N 
 
 .9674 
 
 .07808 
 
 12.807 
 
 Olefiant gas (ethylene) 
 
 CiHt 
 
 .9852 
 1.1054 
 
 .07952 
 .08922 
 
 12.575 
 11.208 
 
 Sulphur dioxide 
 
 
 2.2131 
 
 .17862 
 
 5.598 
 
838 
 
 VENTILATION OF MINES 
 
 As in the case of the densities, the observed specific gravities determined 
 by experiment, do not generally agree with the theoretical specific gravities 
 determined from the weight of 1 cu. ft. of air and of hydrogen and the molecular 
 weight of the gases. This want of agreement between the observed and 
 calculated specific gravities will affect the weights per cubic foot and volumes 
 per pound calculated from them. The preceding table is based on observed 
 specific gravities and the weight of 1 cu. ft. of air of .08071 Ib. at 32 F. and 
 29.921 in. of mercury pressure. 
 
 Atmospheric Pressure. The pressure of the air upon an object on the 
 surface of the earth is equal to the weight of the column of air extending from 
 the object to the upper limits of the atmosphere, a distance variously estimated 
 as from 45 to 200 mi. The pressure of the atmosphere decreases with the 
 elevation of the place above sea level and increases with the distance below it. 
 At sea level, when the temperature is 32 P., the atmospheric pressure is 
 14.697 Ib. per sq. in. This pressure of 14.697 Ib., which is commonly taken 
 as 14.7 Ib., is often called an atmosphere. 
 
 Measurement of Atmospheric Pressure. The pressure of the atmosphere 
 may be measured by the height of a column of air of uniform density, or that 
 of a column of water (water gauge) or of mercury (barometer), necessary to 
 produce such pressure. The following table gives the heights of the columns 
 of these various substances necessary to produce a pressure of 14.697 Ib. per 
 sq. in. (one atmosphere) at a temperature of 32 F. 
 
 EQUIVALENT HEIGHTS OF COLUMNS OF AIR, WATER, 
 AND MERCURY 
 
 Pressure per 
 Square Inch 
 Pounds 
 
 Height of Column to Produce Pressure 
 
 Air 
 Feet 
 
 Water 
 Feet 
 
 Mercury 
 Inches 
 
 14,697 
 .491 
 .433 
 .036 
 
 26,220 
 
 876 
 772 
 64 
 
 33.942 
 1.134 
 1 
 
 A or 1 in. 
 
 29.921 
 
 1 
 .882 
 .074 
 
 The pressure per square foot due to 1 in. of the water and mercury columns 
 is 5.2 and 70.7 Ib., respectively. 
 
 The height of the air column corresponding to 1 in. of the water gauge is, 
 more exactly, 64.43 ft., at 32 F. and barometer 29.921 in. Note that in the 
 following table the temperature is 60 and barometer 30 in. 
 
 CORRESPONDING MERCURY AND AIR COLUMNS, AND PRESSURE 
 PER SQUARE FOOT FOR EACH INCH OF WATER COLUMN 
 
 
 
 Air 
 
 Pressure 
 
 
 
 Air 
 
 Pressure 
 
 Water 
 Gauge 
 
 Mercury 
 Column 
 
 Column 
 Feet 
 
 Pounds 
 per 
 
 Water 
 Gauge 
 
 Mercury 
 Column 
 
 Column 
 Feet 
 
 Pounds 
 per 
 
 Inches 
 
 Inch 
 
 (T. 60, 
 B. 30") 
 
 Square 
 Foot 
 
 Inches 
 
 Inch 
 
 (T. 60, 
 B. 30") 
 
 Square 
 Foot 
 
 1 
 
 .0735 
 
 68 
 
 5.2 
 
 6 
 
 .4412 
 
 407 
 
 31.2 
 
 ,2 
 
 .1471 
 
 136 
 
 10.4 
 
 7 
 
 .5147 
 
 475 
 
 36.4 
 
 3 
 
 .2206 
 
 204 
 
 15.6 
 
 8 
 
 .5882 
 
 543 
 
 41.6 
 
 4 
 
 .2941 
 
 272 
 
 20.8 
 
 9 
 
 .6618 
 
 611 
 
 46.8 
 
 5 
 
 .3676 
 
 340 
 
 26.0 
 
 10 
 
 .7353 
 
 679 
 
 52.0 
 
VENTILATION OF MINES 
 
 839 
 
 WATER COLUMN, AND PRESSURE PER SQUARE FOOT FOR EACH 
 INCH OF MERCURY COLUMN 
 
 
 
 Pressure 
 
 
 
 Pressure 
 
 Barometer 
 Inches 
 
 Water 
 Column 
 Feet 
 
 Pounds 
 per 
 Square 
 Inch 
 
 Barometer 
 Inches 
 
 Water 
 Column 
 Feet 
 
 Pounds 
 per 
 Square 
 Inch 
 
 1 
 
 1.13 
 
 .49 
 
 16 
 
 18.13 
 
 7.84 
 
 2 
 
 2.27 
 
 .98 
 
 17 
 
 19.27 
 
 8.33 
 
 3 
 
 3.40 
 
 1.47 
 
 18 
 
 20.40 
 
 8.82 
 
 4 
 
 4.54 
 
 1.96 
 
 19 
 
 21.53 
 
 9.31 
 
 5 
 
 5.67 
 
 2.45 
 
 20 
 
 22.67 
 
 9.80 
 
 6 
 
 6.80 
 
 2.94 
 
 21 
 
 23.80 
 
 10.29 
 
 7 
 
 7.93 
 
 3.43 
 
 22 
 
 24.93 
 
 10.78 
 
 8 
 
 9.06 
 
 3.92 
 
 23 
 
 26.07 
 
 11.27 
 
 9 
 
 10.20 
 
 4.41 
 
 24 
 
 27.20 
 
 11.76 
 
 10 
 
 11.33 
 
 4.90 
 
 25 
 
 28.33 
 
 12.25 
 
 11 
 
 12.46 
 
 5.39 
 
 26 
 
 29.47 
 
 12.74 
 
 12 
 
 13.60 
 
 5.88 
 
 27 
 
 30.60 
 
 13.23 
 
 13 
 
 14.73 
 
 6.37 
 
 28 
 
 31.73 
 
 13.72 
 
 14 
 
 15.87 
 
 6.86 
 
 29 
 
 32.87 
 
 14.21 
 
 15 
 
 17.00 
 
 7.35 
 
 30 
 
 34.00 
 
 14.70 
 
 Barometers. The aneroid barometer and its use in determining elevations 
 is described on page 140. The mercurial barometer is often called the cistern 
 barometer; or. when the lower end of the tube is bent upwards instead of the 
 mouth of the tube being submerged in a basin, it is known as the siphon bar' 
 ometer. The instrument is constructed by filling a glass tube 3 ft. long, and 
 having a bore of \ in. diameter, with mercury, which is boiled to drive off the 
 air. The thumb is now placed tightly over the open end, the tube inverted, and 
 its mouth submerged in a basin of mercury. When the thumb is withdrawn, 
 the mercury sinks in the tube, flowing out into the basin, until the top of the 
 mercury column is about 30 in. above the surface of the mercury in the basin, 
 and after a few oscillations above and below this point, comes to rest. The 
 vacuum thus left in the tube above the mercury column is as perfect a vacuum 
 as it is possible to form, and is called a Torricelli vacuum, after its discoverer. 
 There being evidently no pressure in the tube above the mercury column, 
 and as the weight of this column standing above the surface of the mercury 
 in the basin is supported by the pressure of the atmosphere, it is the exact 
 measure of the pressure of the atmosphere on the surface of the mercury in 
 the basin. If the experiment is performed at sea level, the height of the 
 mercury will be found to average about 30 in.; at higher elevations it is less, 
 while below this level, it is greater. Roughly speaking, an allowance of 1 in. of 
 barometric height is made for each 900 ft. of ascent or descent from sea level 
 (see Barometric Elevations). A thermometer is attached to each mercurial 
 barometer to note the temperature of the reading, as it is customary in all 
 accurate work with this instrument to reduce each reading to an equivalent 
 reading at 32 F., which is the standard temperature for barometric readings. 
 
 Mercury expands about .0001 of its volume for each degree Fahrenheit. 
 To reduce, therefore, a reading at any temperature to the corresponding 
 reading at the standard temperature of 32 F., subtract TU^ of the observed 
 height for each degree above 32; or, if the temperature is below 32, add T^J 
 for each degree. 
 
 Thus. 30.667 in. at 62 F. is equivalent to a reading of 30.555 in. at 32 F., 
 
 since 30.667 - 
 
 X (30.667) = 30.667 - .092 = 30.555 in. 
 
 A scale is provided at the top of the mercury column with its inches so 
 marked upon it as to make due allowance for what is called the error of capacity. 
 In other words, the inches of the scale are longer than real inches, since the 
 level of the mercury in the basin rises as it sinks in the tube, and vice versa. The 
 top of the mercury column is always oval, convex upwards, owing to capillary 
 attraction, and the scale is read where it is tangent to this convex surface. 
 
840 VENTILATION OF MINES 
 
 Relation Between Volume and Temperature of Gases. The pressure 
 remaining the same, the volume of a given weight of any gas is proportional to 
 its absolute temperature. (Gay-Lussac's, or Charles' law.) 
 
 The meaning of absolute temperature is explained on page 353. For general 
 purposes, the absolute zero is taken as 460 and not at its exact value of 
 -459.64 F. 
 
 If V = volume of a gas at absolute temperature T; 
 
 i> = volume of same gas at absolute temperature t; 
 the proportion may be written 
 
 V:v=T:t (1) 
 
 EXAMPLE. If 10,000 cu. ft. of air at 32 F. is heated to 60 F. in passing 
 through a mine, what is the increased or expanded volume, the pressure remain- 
 ing constant? 
 
 SOLUTION. Here, F= 10,000, T = 460 +32 = 492, t = 460 +60 = 520, and it 
 is required to find v; substituting in formula 1, 10,000 : t> = 492 : 520; whence, 
 
 v = 10,OOOX^= 10,569 cu. ft. 
 4y*j 
 
 Relation Between Volume and Pressure of Gases. The pressure remaining 
 the same, the volume of a given weight of any gas is inversely proportional to its' 
 absolute pressure. (Mariotte's, or Boyle's law.) 
 
 Absolute pressure is the pressure above that of a perfect vacuum to which 
 a gas may be subjected and is equal to the pressure of the atmosphere at the 
 particular time and place added to the pressure as recorded by a gauge or 
 other instrument. Thus, at sea level and under ordinary atmospheric con- 
 ditions, a gauge pressure of 100 Ib. is equal to an absolute pressure of 114.697 Ib. 
 per sq. in. At a place 5,000 ft. above sea level, where the average reading of 
 the barometer is, say, 24.9 in. corresponding to a pressure of 12.22 Ib. per 
 sq. in., 100 Ib. gauge pressure is equal to 112.22 Ib. absolute. 
 
 If V = volume of a gas under an absolute pressure P; 
 
 v = volume of same gas under an absolute pressure p; 
 then, V : v=p : P (2) 
 
 EXAMPLE 1. It is estimated that the open and abandoned workings of a 
 mine have a volume of 1,000,000 cu. ft. Should the barometer fall from 
 29.5 to 29.0 in., what volume of air and gas would be forced out of the gob 
 and into the airways, the temperature remaining unchanged? 
 
 SOLUTION. As the barometer measures absolute pressures, in this example, 
 the volumes are inversely proportional to the readings of the barometer. 
 Hence, V = 1,000,000, P = 29.5, = 29.0, and it is required to find v; substi- 
 tuting in formula 2, 1,000,000 : v = 29.0 : 29.5; whence, 
 
 = 1,000,000X^ = 1, 017,250 cu. ft. 
 
 The volume of gas and air forced into the airways will be 17,250 cu. ft. 
 
 EXAMPLE 2. When the atmospheric pressure is 14.7 Ib. per sq. in., how 
 many cubic feet of free air must be compressed to a gauge pressure of 80 Ib. 
 to fill a cylinder having a capacity of 20 cu. ft., the temperature remaining 
 unchanged? 
 
 SOLUTION. A gauge pressure of 80 Ib., under the given conditions, is equal 
 to an absolute pressure of 80+14.7 = 94.7 Ib. Hence, V = 20, P = 94.7, p = 14.7, 
 and it is required to find v; substituting in formula 2, 20 : y = 14.7 : 94.7; 
 whence, 
 
 v = 20 Xj|^ = 128.84 cu. ft. 
 
 Relation Between Volume, Temperature,. and Pressure of Gases. When 
 both the temperature and pressure of a gas are changed, the change in volume 
 is directly proportional to the change in absolute temperature (Gay-Lussac's 
 law) and inversely proportional to the change in absolute pressure (Mariotte's 
 law). By combining the formulas 1 and 2, there results, 
 V:v=Tp:tP (3) 
 
 EXAMPLE. A certain volume of air measures 100 cu. ft. at 32 F. and a 
 pressure of 14.7 Ib. per sq. in.; what will be the volume of the air if the temper- 
 ature is increased to 90 F., and the pressure reduced to 10 Ib. per sq. in.? 
 
 SOLUTION. Here, F=100, T = 460+32 = 492, P = 14.7, * = 460+90 = 550, 
 
VENTILATION OF MINES 841 
 
 = 10, and it is required to find ; substituting in formula 3, 100 : i> = 492 
 X10 : 550X14.7; whence, 
 
 Relation Between Weight, Temperature, and Pressure of Gases. The 
 
 weight of 1 cu. ft. of a gas is the reciprocal of its volume per pound, or W= -~ 
 
 and w = -, from which V = and v = . Substituting the values of V and v 
 in formula 3 and rearranging, there results, 
 
 W:w = tP:Tp (4) 
 
 EXAMPLE. If 1 cu. ft. of carbon monoxide weighs .0781 Ib. at 32, barom- 
 eter 29.92 in., what will be the weight of the same volume of gas at a temper- 
 ature of 90, barometer 28.00 in.? 
 
 SOLUTION. Here J^=.0781, T = 460 + 32 = 492, P = 29.92, J = 460+90 
 = 550, p = 28.00, and it is required to find w. Substituting in formula 4, 
 .0781 : w = 550X29.92 : 492X28.00; whence, 
 
 Another method of determining the weight of 1 cu. ft. of a gas at any 
 temperature and pressure is given toward the end of the next section. 
 
 Weight and Volume of Air and Gases. The weight of 1 cu. ft. of dry air 
 at 32 F. and a pressure of 29.921 in. of mercury or 14.697 Ib. per sq. in., is 
 .08071 Ib. avoir. Although not a true gas but a mixture of gases, the weight 
 per cubic foot of air decreases as the temperature increases and the pressure 
 decreases, and vice versa. 
 
 The usual formula for finding, approximately, the weight W of 1 cu. ft. of 
 air when the temperature t, in degrees Fahrenheit, and the height B of the 
 barometer, in inches, are given, is, 
 
 Tr _1.3273B 
 460-H 
 
 The denominator of the fraction is the absolute temperature, and 1.3273 
 is the weight of 1 cu. ft. of air under a pressure of 1 in. of mercury and at a 
 temperature of 1 F., absolute ( 459 P.). 
 
 When the pressure P, in pounds per square inch, is given, W may be found 
 from 
 
 '2 7P 
 
 The factor 2.7 is obtained by dividing 1.3273 (formula 5) by the weight of 
 1 cu. in. of mercury, .4912 Ib. 
 
 EXAMPLE 1. What is the weight of 1 cu. ft. of dry air at 90 F., barometer 
 28 in.? 
 
 SOLUTION. Substituting in formula 5, 
 
 EXAMPLE 2. What is the weight of 1 cu. ft. of dry air at a temperature 
 of 10 below zero, when the pressure is 10 Ib. per sq. in.? 
 SOLUTION. Substituting in formula 6, 
 2.7X10 27 
 
 When the specific gravity of a gas is known, its weight per cubic foot under 
 any conditions of temperature and pressure may be found by first finding the 
 weight of 1 cu. ft. of air under the same conditions, and multiplying this result 
 by the specific gravity of the gas. 
 
 EXAMPLE. The specific gravity of carbon monoxide is .967; what is the 
 weight of 1 cu. ft. of this gas at 90 and 28 in.? 
 
 SOLUTION. Using formula 5, 
 
 Tr = 1 ' 3273X28 X. 967-. 0676 X Q ft 7= nflRi Ib. per cu. ft. 
 This is the same result as was obtained in the example illustrating formula 4. 
 
842 
 
 VENTILATION OF MINES 
 
 VOLUME AND WEIGHT OF AIR AT SEA LEVEL AT DIFFERENT 
 TEMPERATURES 
 
 Temperature 
 Degrees 
 
 Fahrenheit 
 
 Volume of 
 1 Lb. 
 Cubic Feet 
 
 Weight of 
 1 Cu. Ft. 
 Pound 
 
 Temperature 
 Degrees 
 Fahrenheit 
 
 !"! 
 
 ' Weight of 
 1 Cu. Ft. 
 Pound 
 
 Temperature 
 Degrees 
 Fahrenheit 
 
 Volume of 
 1 Lb. 
 Cubic Feet 
 
 Weight of 
 1 Cu. Ft. 
 Pound 
 
 
 
 11.583 
 
 .08633 
 
 100 
 
 14.103 
 
 .07091 
 
 260 
 
 18.135 
 
 .05514 
 
 10 
 
 11.834 
 
 .08450 
 
 110 
 
 14.355 
 
 .06967 
 
 270 
 
 18.387 
 
 .05439 
 
 20 
 
 12.086 
 
 .08273 
 
 120 
 
 14.607 
 
 .06846 
 
 280 
 
 18.639 
 
 .05365 
 
 32 
 
 12.390 
 
 .08071 
 
 130 
 
 14.859 
 
 .06730 
 
 290 
 
 18.891 
 
 .05294 
 
 40 
 
 12.590 
 
 .07943 
 
 140 
 
 15.111 
 
 .06618 
 
 300 
 
 19.143 
 
 .05224 
 
 45 
 
 12.712 
 
 .07864 
 
 150 
 
 15.363 
 
 .06509 
 
 310 
 
 19.387 
 
 .05158 
 
 50 
 
 12.843 
 
 .07786 
 
 160 
 
 15.615 
 
 .06041 
 
 320 
 
 19.647 
 
 .05090 
 
 55 
 
 12.969 
 
 .07711 
 
 170 
 
 15.867 
 
 .06302 
 
 330 
 
 19.892 
 
 .05027 
 
 60 
 
 13.095 
 
 .07637 
 
 180 
 
 16.119 
 
 .06204 
 
 340 
 
 20.151 
 
 .04963 
 
 65 
 
 13.221 
 
 .07564 
 
 190 
 
 16.371 
 
 .06108 
 
 350 
 
 20.395 
 
 .04903 
 
 70 
 
 13.347 
 
 .07493 
 
 200 
 
 16.623 
 
 .06016 
 
 360 
 
 20.655 
 
 .04841 
 
 75 
 
 13.473 
 
 .07422 
 
 210 
 
 16.875 
 
 .05926 
 
 370 
 
 20.899 
 
 .04785 
 
 80 
 
 13.599 
 
 .07354 
 
 220 
 
 17.127 
 
 .05839 
 
 380 
 
 21.159 
 
 .04726 
 
 85 
 
 13.725 
 
 .07286 
 
 230 
 
 17.379 
 
 .05751 
 
 390 
 
 21.404 
 
 .04672 
 
 90 
 
 13.851 
 
 .07220 
 
 240 
 
 17.631 
 
 .05672 
 
 400 
 
 21.663 
 
 .04616 
 
 95 
 
 13.977 
 
 .07155 
 
 250 
 
 17.883 
 
 .05592 
 
 450 
 
 22.923 
 
 .043624 
 
 Diffusion of Gases. The rale or velocity of diffusion between air and a gas, 
 or between different gases, is inversely proportional to their specific gravities or 
 densities. (Graham's Law.) 
 
 Diffusion is the gradual mixing of one gas with another when bodies of them 
 are brought into direct contact or when the wall of the vessel containing them 
 is a porous membrane through which they can pass. Diffusion does not 
 depend on stirring or mechanical mixing, although assisted thereby. Thus, 
 when methane is given off at the floor of a seam, the tendency of the gas to 
 rise owing to its extreme lightness greatly assists its rapid diffusion by bringing 
 a greater number of molecules of air and gas in contact in a given time. A 
 feeder in the roof or other high point may give off gas more quickly than 
 diffusion can take place, particularly where the air-current is sluggish, in which 
 case there will be formed a body of pure methane. Similarly, an accumula- 
 tion of blackdamp may be formed near the floor or in some other low place 
 where the current is feeble and the gas is given off more rapidly than it can 
 diffuse. 
 
 Diffusion continues until the gases are uniformly mixed, and when so mixed 
 the gases cannot be separated. As. stated in Graham's law, the greater the 
 difference in the specific gravities of two gases, the more rapidly will they 
 diffuse or mix. Thus, carbon dioxide will mix with air more rapidly than will 
 nitrogen. 
 
 The rate of diffusion of one gas with respect to another may be found by 
 comparing their rates of diffusion with respect to air. Thus, the rate of 
 diffusion of carbon dioxide with respect to methane is .812 -5-1.344 = .604, and 
 of oxygen with respect to hydrogen is .949 -7-3.830 = .248. 
 
 The volumes of the various gases that will diffuse in the same time are 
 proportional to their respective rates of diffusion. Thus, 1,344 volumes of 
 methane will diffuse in the same time as 1,000 volumes of air or 812 volumes 
 of carbon dioxide. 
 
 The rates of diffusion may also be calculated by comparing the densities 
 of the gases with 'respect to hydrogen. The density of air and carbon dioxide 
 are, respectively, 14.359 and 21.835, whence the rate of diffusion of carbon 
 dioxide with respect to air is Vl4.359-f-21.835= V^657614 = .811, which agrees 
 very closely with the observed rate of .812. 
 
 In the accompanying table, it will be noted that the observed and theo- 
 retical rates of diffusion agree very closely, except in the case of hydrogen 
 sulphide. 
 
VENTILATION OF MINES 
 
 843 
 
 RATES OF DIFFUSION AND TRANSPIRATION OF GASES COMPARED 
 TO AIR 
 
 Gas 
 
 Specific 
 Gravity 
 
 Rate of Diffusion 
 
 Rate of 
 Trans- 
 piration 
 
 Theoretical 
 
 Observed 
 
 Hydrogen 
 
 .0694 
 .5545 
 .9670 
 .9674 
 1.0000 
 1.1054 
 1.1817 
 1.5291 
 
 3.7965 
 1.3428 
 1.0169 
 1.0166 
 
 .9511 
 .9199 
 .8087 
 
 3.830 
 1.344 
 1.015 
 1.014 
 
 .949 
 .950 
 .812 
 
 2.066 
 1.639 
 1.034 
 1.030 
 1.000 
 .903 
 1.458 
 1.237 
 
 Methane 
 
 Carbon monoxide 
 
 Nitrogen 
 Air 
 
 Oxygen 
 Hydrogen sulphide 
 Carbon dioxide 
 
 Occlusion and Transpiration of Gases. All coals in the seam contain 
 a greater or less amount of various gases that are given off as the coal face 
 is exposed in mining. It has commonly been supposed that these gases were 
 occluded, or hidden, in the coal under great pressure, but there seems, reason 
 to doubt this as a universal rule (see under Formation of Methane). In any 
 case, the escaping gases are not occluded, a term that refers to the probable 
 condensation and perhaps existence of a gas in a quasi-metallic state in the 
 pores of a metal, as hydrogen in the pores of the metals palladium or platinum. 
 The conditions that have held the gas in the coal or adjoining rocks are largely 
 closeness of grain in the coal and imperviousness of the clay in the roof shales. 
 The pressure of the occluded gases is often as high as 10 to 40 or more atmos- 
 pheres (see Properties and Sources of Methane). 
 
 Transpiration refers to the more or less steady outflow of gas from the 
 pores of the coal at the working face. The rate of transpiration of the various 
 mine gases, air being the unit, is given in the preceding table. Although the 
 relative rates are not the same, the order of the gases in transpiration is the 
 same as in diffusion, except in the case of the very heavy hydrogen sulphide 
 and carbon dioxide. The rate of transpiration varies with the pressure under 
 which the gas exists and decreases as the temperature decreases but not in the 
 same ratio, and is independent of the specific gravity of the gas. 
 
 The rates of transpiration is of importance in determining the nature of the 
 gas mixtures found in mines. Thus, 1,639 volumes of methane will transpire 
 in the same time as 1,237 volumes of carbon dioxide and there is, thence, a 
 tendency to increase the proportion of the former and decrease that of the 
 latter in the airways. This difference in the rate of transpiration has made 
 difficult the accurate determination of the different gases present in different 
 coals. The principal occluded gases are methane, nitrogen, and carbon dioxide. 
 In some coals, methane formed 93% of the occluded gas; in others, nitrogen 
 formed 91%; while in others, carbon dioxide formed 54%. Oxygen rarely 
 exceeds 4 or 5% and is usually much less. Analyses of occluded gases, both 
 face and blowers, are given under Firedamp. 
 
 The transpiration of gas from coal seams varies widely in its nature, often 
 being accompanied by a sharp crackling and a hissing sound; in extreme cases 
 the pressure is so great as to dislodge the coal from the face. Usually, the 
 gases issue without noise either from the pores in a newly exposed working face , 
 or through blowers, which are the exposed ends of larger openings or crevices 
 in the seam or its containing rocks (see Properties and Sources of Methane). 
 
 Humidity. The amount of water, as vapor, that may be contained in 
 a given volume of air depends on the temperature, and is greater at high than 
 at low readings of the thermometer. When air contains all the moisture it 
 can at any given temperature, it is said to be saturated. -When the temper- 
 ature of saturated air is lowered, some of the vapor is condensed and deposited 
 upon surrounding objects in the form of drops of water. When the temper- 
 ature is raised, the air is no longer saturated and is capable of taking up more 
 moisture from the mine workings until it becomes saturated at the higher 
 temperature. The gallons of water contained in 100,000 cu. ft. of saturated 
 air is given in the following table. 
 
844 
 
 VENTILATION OF MINES 
 
 GALLONS OF WATER IN 100,000 CU. FT. OF SATURATED AIR AT 
 TEMPERATURES FROM -20 F. TO +100 F. 
 
 Temperature 
 Degrees F. 
 
 % $ 
 ftQ J 
 0,0^ 
 
 III 
 
 cTcS 
 
 Temperature | 
 Degrees F. | 
 
 8,0 J 
 
 its 
 
 3S% 
 
 13-| 3 
 
 o o 
 
 Temperature! 
 Degrees F. 
 
 w 1o 
 Q<O <u 
 nX&i 
 
 oo'.S 
 
 SOXI 
 cS"-" 3 
 
 o o 
 
 Temperature 
 Degrees F. 
 
 Gallons per 
 100,000 
 Cubic Feet 
 
 Temperature 
 Degrees F. 
 
 b t? 
 
 a 8(S 
 O.H 
 
 SO.Q 
 ea *-" 3 
 
 o o 
 
 -20 
 
 .284 
 
 5 
 
 1.044 
 
 29 
 
 3.172 
 
 53 
 
 7.751 
 
 77 
 
 17.099 
 
 19 
 
 .298 
 
 6 
 
 1.094 
 
 30 
 
 3.312 
 
 54 
 
 8.023 
 
 78 
 
 17.643 
 
 18 
 
 .315 
 
 7 
 
 1.149 
 
 31 
 
 3.462 
 
 55 
 
 8.306 
 
 79 
 
 18.202 
 
 17 
 
 .336 
 
 8 
 
 1.205 
 
 32 
 
 3.618 
 
 56 
 
 8.592 
 
 80 
 
 18.776 
 
 16 
 
 .354 
 
 9 
 
 1.265 
 
 33 
 
 3.756 
 
 57 
 
 8.891 
 
 81 
 
 19.365 
 
 15 
 
 .373 
 
 10 
 
 1.329 
 
 34 
 
 3.902 
 
 58 
 
 9.199 
 
 82 
 
 19.971 
 
 14 
 
 .395 
 
 11 
 
 1.397 
 
 35 
 
 4.051 
 
 59 
 
 9.516 
 
 83 
 
 20.594 
 
 13 
 
 .416 
 
 12 
 
 1.466 
 
 36 
 
 4.206 
 
 60 
 
 9.843 
 
 84 
 
 21.232 
 
 12 
 
 .440 
 
 13 
 
 1.537 
 
 37 
 
 4.366 
 
 61 
 
 10.179 
 
 85 
 
 21.888 
 
 11 
 
 .462 
 
 14 
 
 1.611 
 
 38 
 
 4.530 
 
 62 
 
 10.525 
 
 86 
 
 22.564 
 
 10 
 
 .488 
 
 15 
 
 1.688 
 
 39 
 
 4.701 
 
 63 
 
 10.880 
 
 87 
 
 23.254 
 
 9 
 
 .514 
 
 16 
 
 1.767 
 
 40 
 
 4.878 
 
 64 
 
 11.249 
 
 88 
 
 23.964 
 
 8 
 
 .541 
 
 17 
 
 1.849 
 
 41 
 
 5.059 
 
 65 
 
 11.626 
 
 89 
 
 24.694 
 
 7 
 
 .568 
 
 18 
 
 1.931 
 
 42 
 
 5.246 
 
 66 
 
 12.015 
 
 90 
 
 25.439 
 
 6 
 
 .569 
 
 19 
 
 2.022 
 
 43 
 
 5.439 
 
 67 
 
 12.415 
 
 91 
 
 26.207 
 
 5 
 
 .633 
 
 20 
 
 2.114 
 
 44 
 
 5.639 
 
 68 
 
 12.824 
 
 92 
 
 26.994 
 
 4 
 
 .666 
 
 21 
 
 2.215 
 
 45 
 
 5.845 
 
 69 
 
 13.248 
 
 93 
 
 27.800 
 
 3 
 
 .704 
 
 22 
 
 2.320 
 
 46 
 
 6.059 
 
 70 
 
 13.686 
 
 94 
 
 28.629 
 
 2 
 
 .743 
 
 23 
 
 2.428 
 
 47 
 
 6.278 
 
 71 
 
 14.132 
 
 95 
 
 29.477 
 
 1 
 
 .782 
 
 24 
 
 2.539 
 
 48 
 
 6.507 
 
 72 
 
 14.594 
 
 96 
 
 30.346 
 
 
 
 .823 
 
 25 
 
 2.655 
 
 49 
 
 6.740 
 
 73 
 
 15.066 
 
 97 
 
 31.239 
 
 + 1 
 
 .865 
 
 26 
 
 2.779 
 
 50 
 
 6.979 
 
 74 
 
 15.556 
 
 98 
 
 32.156 
 
 2 
 
 .906 
 
 27 
 
 2.905 
 
 51 
 
 7.229 
 
 75 
 
 16.054 
 
 99 
 
 33.098 
 
 3 
 
 .948 
 
 28 
 
 3.035 
 
 52 
 
 7.487 
 
 76 
 
 16.569 
 
 100 
 
 34.058 
 
 4 
 
 .996 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Relative humidity, which is often called humidity, is the ratio of the 
 quantity of water vapor present to the quantity necessary to saturate the space 
 occupied by the air, at the given temperature and pressure. When air is 
 saturated, its relative humidity is 100%. At any relative humidity, the 
 amount of water actually present in a given volume of air may be found by 
 multiplying the amount required to saturate the air at the specified temperature 
 by the relative humidity. 
 
 EXAMPLE 1. A current of 60,000 cu. ft. of air a min. is entering a mine; 
 its temperature is 20 F. and humidity 65%. What is the quantity of water 
 brought into the mine in 1 min., in 1 hr., and in 1 da. of 24 hr.? 
 
 SOLUTION. From the preceding table, 100,000 cu. ft. of saturated air 
 at 20, contains 2.114 gal. of water. At 65% relative humidity, this volume 
 of air will contain 2.114 X. 65 = 1.3741 gal., and 60,000 cu. ft. will contain 
 six-tenths of this quantity, or 1.374 IX. 6 = .82446 gal., which is the quantity 
 of water brought into the mine in 1 min. In 1 hr. there will be .82446X60 
 = 49.4676 gal., and in a 24-hr, da. there will be 49.4676X24 = 1,187.2224 gal. 
 
 EXAMPLE 2. If, in example 1, the return air-current has a temperature 
 of 65 and a relative humidity of 98%, what is the quantity of water absorbed 
 from the mine workings in 1 min., 1 hr., and 1 da.? 
 
 SOLUTION. At 98% humidity, 60,000 cu. ft. of air contains 11.626X.98 
 X. 6 = 6.83609 gal. At 20 F. and 65% humidity, the same quantity of air 
 contains .82446 gal. (example 1); hence, there is absorbed by the air-current 
 in its passage through the mine, 6.83609 -.82446 = 6.01 143 gal. a min.; 6.01143 
 X 60 = 360.6858 gal. an hr., and 360.6858X24 = 8,656.4692 gal. a da. 
 
 Psychrometers or Hygrometers. A psychrometer, or hygrometer, is an 
 instrument for measuring the quantity of aqueous vapor in the air. The 
 standard type involves the determination of the temperature of evaporation 
 and consists of two similar thermometers usually mounted on the same frame, 
 one called the dry bulb and the other the -wet bulb. Below the wet bulb is a 
 small jar for water. In order to take an observation, a small muslin sack is 
 
VENTILATION OF MINES 
 
 845 
 
 fixed around the wet bulb, its end extending down into the jar from which 
 the water is drawn by capillary attraction. The thermometers are exposed to 
 a current of air that has a velocity of 15 ft. or more per sec. If the relative 
 humidity of the air is less than 100%, that is, if the air is not saturated, some 
 of the water on the muslin sack is evaporated, a certain amount of heat is 
 absorbed by evaporation, and the temperature of the wet-bulb thermometer 
 is reduced to a point at which the amount of heat absorbed by evaporation is 
 just equal to that received from the surrounding air. From the readings 
 of the two thermometers, by reference to suitable tables, the relative humidity 
 and, consequently, the aqueous vapor per cubic foot of air may be calculated. 
 
 The sling psychrometer is the form in common use in mines. It consists of 
 two thermometers mounted side by side in a case provided with a cover. The 
 instrument has a handle at the top by which it may be given a whirling motion 
 to secure a velocity of the wet bulb of 15 ft. a sec. or more. The muslin sack 
 is moistened at the time of making the observation, which is repeated until 
 the results agree. 
 
 The hygrodeik is a form of psychrometer in which the thermometers are 
 attached to a fan-shaped wooden frame, on which are a series of curves and 
 radial lines placed between the thermometers. By properly placing a pointer 
 suspended from the upper part of the frame according to the readings of the 
 two thermometers, the relative humidity may at once be taken from one of 
 the scales, thus obviating any calculations. 
 
 In the hair hygrometer, the rapid change that takes place in the length 
 of a strand of hair with changes in the amount of moisture in the air, is utilized 
 to move a pointer by means of a delicately adjusted lever arm. 
 
 A hygrograph is an instrument by which the variations in relative humidity 
 are automatically recorded. It consists of a hair psychrometer, the pointer 
 of which carries on its end an inking arrangement so that it can trace a line 
 on section paper wrapped on a revolving cylinder turned by clockwork. In 
 this way, a permanent and continuous record is obtained. The readings of 
 a hair psychrometer are not always reliable, and the instrument should be 
 standardized by comparison with the regular wet-bulb instrument, at various 
 temperatures and degrees of saturation. 
 
 MINE GASES 
 
 ATMOSPHERIC AND MINE AIR 
 
 Atmospheric Air. Sir William Ramsay gives the following as the com- 
 position of ordinary air: 
 
 COMPOSITION OF PURE AIR 
 
 Name of Gas 
 
 By Volume 
 
 By Weight 
 
 Exact 
 
 Approximate 
 
 Exact 
 
 Approximate 
 
 
 20.941 
 78.1221 
 .937/ 
 
 20.94 
 79.0G 
 
 23.024 
 75.5391 
 1.437 / 
 
 23.02 
 76.98 
 
 Nitrogen 
 Argon 
 
 Total . 
 
 100.000 
 
 100.00 
 
 100.000 
 
 100.00 
 
 
 In the column headed Approximate, the argon and nitrogen are considered 
 as one gas, as is usually done. With the argon occur certain very rare gases 
 similar to nitrogen whose proportions, by volume, Ramsay estimates to be: 
 Helium, .0004%; krypton, .028%; neon, .0123%; xenon, .005%. 
 
 In addition to these normal gases, air always contains a certain amount of 
 carbon dioxide and water vapor, the former averaging .03 to .04%, and the 
 latter depending on the temperature and relative humidity. At certain times 
 and in certain places, traces of ammonia, oxides of nitrogen, sulphur dioxide, 
 and even hydrogen are found in air. The composition of the air is constant 
 regardless of the altitude. 
 
846 VENTILATION OF MINES 
 
 Mine Air. Mine air does not differ from atmospheric air, except that in 
 its passage through the mine, the ventilating current gives up a certain amount 
 of oxygen to the coal and to the various processes of combustion (breathing of 
 men and animals, burning of lamps, etc.), and receives a certain amount of 
 other gases in place thereof; always carbon dioxide, usually methane, rarely 
 carbon monoxide, and very rarely or in extremely minute amounts, ethane, 
 olefiant gas, nitrous oxide, sulphur dioxide, hydrogen sulphide, hydrogen, and 
 possibly hydrocarbons higher than ethane. The carbon dioxide, methane, 
 and carbon monoxide are generally known as mine gases, as the others are 
 found in very small amounts or under unusual conditions. The constituent 
 of air that usually varies the most between the intake and the return is the 
 absolute humidity, meaning by this term, the actual amount of water con- 
 tained in a given volume of the air-current. Regardless of the relative humidity 
 of the intake, that of the return is rarely less than 90% and is very commonly 
 more than this; further, this is generally true in mines of any size whatever 
 may be the outside temperature. That is, whether the air enters at 20 and 
 50% humidity or 80 and 95% humidity, it will usually leave the mine with 
 a saturation of 90% or more at a temperature between 55 and 65. 
 
 In passing through well-ventilated mines, the air-current will rarely lose 
 more than .5 to .75% of oxygen and gain about the same amount of carbon 
 dioxide and methane. At the larger American mines, a chemist is employed 
 to regularly analyze the return air, and any deficiency in oxygen or dangerous 
 increase in carbon dioxide and, more particularly, methane is promptly rectified 
 by increasing the ventilating current. 
 
 In Great Britain, the mine code of 1914 provides: "A place shall not be 
 deemed to be in a fit state for working or passing therein if the air contains either 
 less than 19% of oxygen or more than li% of carbon dioxide." 
 
 OXYGEN 
 
 Properties and Sources. Oxygen has an atomic symbol of O and a mole- 
 cular formula of Oz. It is but slightly soluble in water, 100 volumes of which 
 take up 4.11 volumes of the gas at 32 and 2.83 volumes at 68. It is taste- 
 less, odorless, and colorless and is the supporter of life and combustion. Its 
 chemical and physical constants have been given in preceding tables. 
 
 Oxygen is the most abundant element in nature, composing, by weight, 
 23.02% of the atmosphere, 85.79% of all water, and 47.17% of the rocks of 
 the solid crust of the earth. It constitutes 49.85%, or practically one-half, of 
 all matter existing between the upper limits of the earth's atmosphere and the 
 lower depths of its crust. It is not produced by any of the ordinary chemical 
 processes or changes going on in mines, but is absorbed or consumed in prac- 
 tically all of them. Small amounts are given off by the pores of the coal, by 
 blowers, etc. 
 
 Effect of Oxygen on Life. Oxygen is essential to life, forming in the lungs 
 with the hemoglobin of the blood an unstable chemical compound known as 
 oxy hemoglobin, which gives arterial blood its bright red color. In its passage 
 through the body, the oxyhemoglobin parts with its oxygen and is converted 
 into hemoglobin, which gives the familiar dark purple color to venous blood. 
 
 At rest, an average man breathes sixteen to eighteen times a minute and 
 takes into the lungs at each respiration 30.5 cu. in. of air. When working 
 moderately, there will be about twenty-five respirations a minute, which may 
 be increased to as many as sixty when the work is very violent, as in running. 
 Of the oxygen passing into the lungs, 10 to 35% is consumed in the processes 
 of the body, the rest being exhaled with the nitrogen inhaled in the air together 
 with the carbon dioxide formed in the tissues. Exhaled breath contains from 
 2.6 to 6.6% of carbon dioxide, with an average of about 4%. The proportion 
 of carbon dioxide is less during sleep, although it changes but little with changes 
 in the amount of oxygen in the air, as long as breathing is free. 
 
 The effect upon life of diminishing the proportion of oxygen in the air 
 depends on whether its place is taken by nitrogen or carbon dioxide. When 
 carbon dioxide is not present, the effects produced upon a miner by a simple 
 deficiency in the percentage of oxygen are the same as those produced by the 
 great diminution in atmospheric pressure at high altitudes (Haldane). Quot- 
 ing further from Haldane: A diminution (of oxygen in the air) from 20.93% 
 to 15% is by itself practically without effect on men, though a candle would 
 be instantly extinguished in such air. As the diminution increases further, 
 certain effects begin, however, to be produced. The first symptoms usually 
 noticed are that any great muscular exertion is less easy, and that it is apt to 
 cause slight dizziness and unusual shortness of breath. A person not exerting 
 
VENTILATION OF MINES 
 
 847 
 
 himself will, as a rule, not notice anything unusual until the oxygen percentage 
 has fallen to 10%. The breathing then usually begins to become deeper 
 and more frequent, the pulse more frequent, and the face somewhat dusky. 
 At 7%, there is usually distinct panting, accompanied by palpitations, and the 
 face becomes a leaden blue color. At the same time the mind becomes con- 
 fused and the senses dulled, although the person breathing the air may be quite 
 unaware of the fact. Muscular power is also greatly impaired. At a slightly 
 lower percentage, there is complete loss of consciousness . . . . In air 
 containing no oxygen, loss of consciousness occurs within 40 sec. or less, without 
 any previous warning symptom (see Effect of Carbon Dioxide on Life). 
 
 Pure oxygen may be inhaled for a long time without danger and is fre- 
 quently administered in cases of suffocation, carbon monoxide poisoning, etc. 
 
 Effect of Oxygen on Combustion. As the proportion of oxygen in the air 
 is lessened, lamps burn more and more dimly until they finally go out. The 
 amount of oxygen that will sustain combustion is influenced by the amount 
 of moisture and carbon dioxide present. Thus, a lamp will be extinguished 
 sooner when the air is moist and the oxygen has been replaced by carbon 
 dioxide than when the air is dry and nitrogen is the only inert gas present. 
 
 A residual atmosphere is one that remains after a flame burning in it has 
 so reduced the amount of oxygen that it is finally extinguished. The following 
 table, from Clowes and the Bureau of Mines, gives the residual atmospheres 
 in which flames of various burning substances were finally extinguished. 
 
 COMPOSITION OF RESIDUAL ATMOSPHERES THAT EXTINGUISH 
 FLAME 
 
 Flame 
 
 Percentage Composition of Atmosphere 
 
 COi 
 
 2 
 
 Nt 
 
 
 6.30 
 4.35 
 2.95 
 12.25 
 4.90 
 
 2.30 
 3.25 
 3.00 
 3.00 
 3.00 
 
 11.70 
 14.90 
 16.24 
 13.35 
 11.35 
 5.50 
 15.60 
 13.90 
 16.60 
 16.50 
 15.82 
 
 80.50 
 80.75 
 80.81 
 74.40 
 83.75 
 94.50 
 82.10 
 82.85 
 80.40 
 80.50 
 81.18 
 
 Alcohol, absolute 
 Candle 
 
 Carbon monoxide 
 Coal gas 
 
 Hydrogen 
 Methane 
 
 Natural gas 
 
 Paraffin, lamp oil 
 Wolf lamp, bonneted 
 
 Wolf lamp, unbonneted 
 
 
 Clowes sums up the results of his experiments as follows: 
 
 1. Wick-fed flames require atmospheres of very similar composition to 
 extinguish them; while gas-fed flames require atmospheres of widely different 
 composition. 
 
 2. Nitrogen must be added in larger proportion than carbon dioxide in 
 order to extinguish the same flame (see Effect of Carbon Dioxide on Com- 
 bustion). 
 
 3. The minimum proportion of extinctive gas that must be mixed with air 
 in order to extinguish a flame is independent of the size of the flame. 
 
 4. The composition of an atmosphere that will at once extinguish a lamp 
 placed in it is not the same as the residual atmosphere resulting from the 
 lamp burning out in pure air. In the case of wick-fed flames, however, the 
 difference is not great. 
 
 5. The flames of candles and lamps, when they are extinguished by burn 
 ing in a confined space of air, produce an atmopshere of almost identical com- 
 position with that of air expired from the lungs. 
 
 6. The extinctive atmospheres produced by the combustion of the flames 
 of candles and of lamps, and the air expired from the lungs after inspiring 
 fresh air, are respirable with safety. 
 
 7. The extinction of an ordinary candle or lamp flame is not necessarily 
 indicative of the unsuitability of an atmosphere to maintain life when it is 
 breathed. 
 
848 VENTILATION OF MINES 
 
 Absorption of Oxygen by Coal. The experiments of the Bureau of Mines 
 and of others show that coal bottled in air under ordinary atmospheric pres- 
 sure rapidly absorbs oxygen until, after a few days, there remains often only 
 1 or 2% of oxygen in the free gas in the bottle. At the same time a certain 
 proportion of the oxygen unites with the substances in the coal to form carbon 
 dioxide, but this process, at least during the comparatively short time of the 
 experiments accounts for only a small part of the oxygen entering the coal. 
 
 The effect of the gradual absorption of oxygen with the formation of 
 greater or less amounts of carbon dioxide is to form blackdamp with the 
 nitrogen remaining in the air, as explained under Blackdamp. 
 
 NITROGEN 
 
 Properties and Sources. Nitrogen has an atomic symbol of 2V and a 
 molecular formula of TVz. It is odorless, colorless, and tasteless, and supports 
 neither life nor combustion. In the atmosphere, it serves to dilute the oxygen 
 and, in combinations like ammonia, is a source of plant food. It is about 
 one-half as soluble in water as oxygen, 100 volumes of water taking up 2.03 vol- 
 umes of the gas at 32 and 1.40 volumes at 68. The chemical and physical 
 constants of nitrogen have been given in the preceding tables. 
 
 Small quantities of nitrogen are given off by the pores of the coal. It is 
 the product of feeders and blowers, rarely as pure nitrogen, but mixed with 
 considerable amounts of carbon dioxide, forming blackdamp. Feeders of 
 methane, also, contain variable amounts of this gas. Small quantities may be 
 present in the leakage from natural gas wells that have been drilled and improp- 
 erly cased through the coal. It is found chiefly, and to the extent of 20 to 55%, 
 in the products of combustion of explosives; the percentage depending on the 
 kind of explosive and the conditions under which it is fired. 
 
 While composing 79.06% by weight of the atmosphere, nitrogen constitutes 
 but .03% of the matter existing between the upper limit of the atmosphere 
 and the lower limit of the earth's crust. Owing to the absorption of oxygen 
 in the various chemical processes going on in mines, the proportion of nitrogen 
 in mine air is usually greater than in that at the surface. 
 
 Effect of Nitrogen on Life. Nitrogen is distinctly negative in its action 
 and is not in any way poisonous. The effect of gradually increasing the .per- 
 centage of nitrogen or, what is the same thing, decreasing the proportion of 
 oxygen in mine air, is to cause death by suffocation (see Effect of Oxygen on 
 Life). 
 
 Effect of Nitrogen on Combustion. Pure nitrogen instantly extinguishes 
 combustion of any kind. Increasing proportions of nitrogen in the air with 
 the accompanying decreasing proportions of oxygen cause a flame to burn 
 with diminishing brilliancy until it is finally extinguished (see Effect of Oxygen 
 and Effect of Carbon Dioxide, Respectively, on Combustion). 
 
 Atmospheres deficient in oxygen and high in nitrogen and methane and, 
 commonly, carbon dioxide, are very common in old workings. In these old 
 workings, a lamp may not burn although breathing is without discomfort, but 
 if sufficient fresh air is mixed with these gob atmospheres they may become 
 highly explosive; or they may be explosive in one part of the workings and 
 not in another. 
 
 CARBON DIOXIDE 
 
 Properties and Sources. Carbon dioxide, formerly known as carbonic acid, 
 carbonic-acid gas, blackdamp, chokedamp, stythe, etc., has a formula of COz, 
 is colorless and odorless, has a slight acid taste especially when dissolved in 
 water, and is not combustible. It is very soluble in water, 100 volumes taking 
 up 179.6 volumes of the gas at 32 and 90.1 volumes at 68. The chemical 
 and physical constants are given in preceding tables. 
 
 Under ordinary working conditions, carbon dioxide is produced in the 
 mine by the breathing of men and animals, by the burning of oil, acetylene, 
 gasoline, and explosives, by the decay of vegetable and animal matter, and by 
 the slow oxidation of the coal. Small amounts of this gas are produced by 
 feeders and blowers occurring in the roof, floor, or face, by transpiration from 
 the coal being mined, by escape from the water of underground streams wherein 
 it has been held under pressure, and by chemical reaction between water carry- 
 ing carbonates in solution and acid minewater. However, the amotint of 
 carbon dioxide thus added to the air of a well-ventilated mine is insignificant 
 and is, according to Haas, not over .02 to .03%, so that normal mine air should 
 not contain over .06 to .07% of this gas. 
 
VENTILATION OF MINES 849 
 
 Under unusual conditions, carbon dioxide is produced by spontaneous 
 combustion of coal as in gob fires, by mine fires of any kind, and by explosions 
 of methane and coal dust. While it may be formed by the burning or explosion 
 of carbon monoxide, its origin in this way is highly improbable, as over 13% 
 of monoxide is necessary for the purpose. 
 
 Owing to its high specific gravity, carbon dioxide naturally tends to collect 
 along the floor and in dip workings, but this tendency is resisted by its diffusive 
 properties, so that the gas is commonly distributed uniformly through the air 
 of a working place. When concentrated at the floor it is because it is given off 
 there faster than diffusion and the ventilating currents can remove it. As 
 Haldane states, warm air laden with carbon dioxide from breathing and burning 
 will keep at the top of the rise. 
 
 Effect of Carbon Dioxide on Life. Carbon dioxide is not actively poisonous 
 like carbon monoxide, hydrogen sulphide, etc., in that it does not combine with 
 the hemoglobin of the blood or cause degeneration of the brain cells or the 
 like, but in sufficient quantities it does have a toxic effect. That is to say, 
 atmospheres in which a deficiency of oxygen is accompanied by a corresponding 
 excess of carbon dioxide are more injurious than those where the oxygen 
 deficiency merely results in increasing the proportion of nitrogen present. 
 Messrs. Priestly and Haldane explain this as follows: " At ordinary atmos- 
 pheric pressure, the breathing always regulates in such a way as to keep the 
 percentage of carbonic acid (COz) in the air cells (alveoli) of the lungs constant. 
 Each individual has his own exact percentage; but on an average there is 
 about 5.6% of carbonic acid in the alveolar air of man. The regulation is 
 almost astoundingly exact for each person. 
 
 "If air containing carbonic acid is breathed, the respirations become 
 deeper, in such a way that the alveolar carbonic-acid percentage still remains 
 practically the same, if possible. If, for instance, there is 2% of carbonic 
 acid in the air, the breathing will need to be about 50% deeper than before. 
 This difference would not be noticed by the person. If there is 5% of carbonic 
 acid in the air, it requires much panting to keep the alveolar carbonic-acid 
 percentage nearly constant; if there is 6 or 7%, it is, of course, quite impossible 
 to maintain a normal alveolar carbonic-acid percentage, and great distress is 
 produced, as the blood becomes abnormally charged with carbonic acid, to 
 which the body is exquisitely sensitive. 
 
 "It is carbonic acid, and carbonic acid alone, which regulates our breathing 
 under normal conditions. The supposed ill effects of a small percentage of 
 carbonic acid in the inspired air are wholly imaginary, as a very slight increase 
 in the depth of breathing at once compensates for the extra carbonic acid. 
 So long as the efforts of the lungs to adjust themselves to the change in the 
 amount of carbonic acid in the air are not attended with discomfort, the person 
 is in no danger." 
 
 The same authority says that "carbon dioxide produces no very noticeable 
 effect until it amounts to more than 3% (3% COz and 97% air = 3% CO*. 
 20.4% Oz, 76.6% Nz), which is more than is often met in mine air just extinctive 
 of lights. With an increasing proportion, the breathing becomes noticeably 
 deeper and more frequent; at about 5 or 6% (5% CO* and 95% air = 5% COz, 
 20% Oz, 75% A^), there is marked panting accompanied by increased frequency 
 of pulse. At about 10% (10% COz and 90% air =10% COz, 18.9% Oz, 71.1% 
 Nz), there is violent panting, throbbing, and flushing of the face. Headache 
 is also produced, especially noticeable on return to fresh air. Beyond 10%, 
 carbon dioxide begins to have a narcotic effect, and at 25% (25% COz and 
 75% air = 25% COz, 15.8% Oz, 59.2% Nz} death may occur after several hours; 
 but as much as 50% may be breathed for some time without fatal effects, to 
 judge from experiments on animals." 
 
 In commenting upon a certain blackdamp, Mr. E. M. Chance says: "With 
 10% of oxygen, the effects produced will be more dangerous from the deficiency 
 of oxygen than from the 4% of carbon dioxide. In fact, the 4% of carbon 
 dioxide will prolong life by creating deeper and more frequent respiration. 
 In breathing atmospheres containing 2% or 3% carbon dioxide and, say, 
 10% or 12% oxygen, the respiration will be better and the man will be more 
 resistant to the gas than if he breathed the air without the carbon dioxide." 
 
 Modern investigations show that a certain amount of carbon dioxide is 
 distinctly stimulating to respiration and, in cases of suffocation, it is not 
 unusual to administer the dioxide at the same time as oxygen, because the 
 increased depth of breathing through the effort of the lungs to adjust themselves 
 to the proper alveolar percentage of carbon dioxide, naturally draws into them 
 more of the desired oxygen. 
 54 
 
850 
 
 VENTILATION OF MINES 
 
 Effect of Carbon Dioxide on Combustion. Strictly, it is the lack of oxygen 
 and not the presence of carbon dioxide or other inert gas that causes a lamp 
 flame to dim and finally go out. However, the experiments of Haldane, 
 Clowes, Clement, and others show that when a loss of oxygen is accompanied 
 by an increase in carbon dioxide, a flame is extinguished more quickly than 
 when a deficiency in oxygen merely causes an increase of nitrogen. The 
 following table, abridged from Clement, shows the effects on the explosive range 
 of methane by decreasing percentages of oxygen and increasing percentages 
 of carbon dioxide. The explosions were made in a steel explosion chamber 
 by an electric spark and are believed to approximate results that would be 
 obtained in the mines. In any case, the amount of nitrogen in the air may 
 be found by subtracting from 100%, the sum of the percentages of oxygen, 
 carbon dioxide and methane. 
 
 EXPLOSIVE RANGE OF MIXTURES OF METHANE AND CARBON 
 DIOXIDE 
 
 Atmosphere 
 Contains 
 
 Methane 
 Explodes 
 
 Atmosphere 
 Contains 
 
 Methane 
 Explodes 
 
 2 
 Per 
 Cent. 
 
 C0 2 
 Per 
 Cent. 
 
 Lower 
 Limit 
 Per 
 Cent. 
 
 Upper 
 Limit 
 Per 
 Cent. 
 
 2 
 Per 
 Cent. 
 
 C0 2 
 Per 
 Cent. 
 
 Lower 
 Limit 
 Per 
 Cent. 
 
 Upper 
 Limit 
 Per 
 Cent. 
 
 19 
 
 
 5.5 
 
 13.5 
 
 16 
 
 20.0 
 
 6.7 
 
 9.6 
 
 19 
 
 20 
 
 6.4 
 
 
 16 
 
 30.0 
 
 7.4 
 
 8.1 
 
 19 
 
 50 
 
 8.0 
 
 10.8 
 
 15 
 
 
 5.9 
 
 9.6 
 
 18 
 
 
 5.7 
 
 12.8 
 
 15 
 
 16.0 
 
 6.9 
 
 8.7 
 
 18 
 
 20 
 
 6.4 
 
 11.8 
 
 15 
 
 21.0 
 
 7.5 
 
 7.5 
 
 18- 
 
 48 
 
 8.5+ 
 
 10.0 
 
 14 
 
 
 6.2 
 
 8.2 
 
 17 
 
 
 5.7 
 
 11.8 
 
 14 
 
 12.5 
 
 7.3 
 
 7.5 
 
 17 
 
 20 
 
 6.4 
 
 10.3 
 
 14 
 
 13.5 
 
 6.9* 
 
 7.2* 
 
 17 
 
 43. 
 
 8.3 
 
 8.7 
 
 13 
 
 
 6.3 
 
 7.1 
 
 16 
 
 
 5.8 
 
 10.7 
 
 13 
 
 2.0 
 
 6.6 
 
 6.8 
 
 The effect of increasing percentages of carbon dioxide, that of the oxygen 
 remaining unchanged, is to shorten the explosive range of methane by raising 
 the lower and reducing the upper explosive limit. Immediately after the 
 explosive limits coincide, there is so much carbon dioxide present that an 
 explosion is not possible. The lower the oxygen percentage in the air, the 
 less carbon dioxide is required to make the atmosphere inexplosive. Further, 
 the dioxide appears to be more active in reducing the upper explosive limit 
 than in raising the lower one. 
 
 According to J. F. Clement, the author of the foregoing table, the difference 
 in the effects of carbon dioxide and nitrogen on the explosive limits of methane 
 is due to the marked difference in the specific heats of the two gases. The 
 mean molecular heats of carbon dioxide and nitrogen between and 650 C. 
 are, respectively, 10.6 and 7.2. A given volume of carbon dioxide will absorb, 
 therefore, 10.6 -r- 7.2 = 1.47 times as much heat, practically 50% more, as the 
 same volume of nitrogen while being heated to 650 C., the ignition temperature 
 of methane. An amount of carbon dioxide may, thence, be eventually reached 
 where its cooling effect is so great that the temperature of the surrounding air 
 will be below the ignition point of methane. 
 
 Similar reasoning shows that the amount of heat required to raise the 
 temperature of an excessive percentage of carbon dioxide may be so great 
 that the products of combustion of an oil flame may be cooled below the 
 ignition point of the oil; and when this is passed, the lamp goes out. As the 
 cooling is gradual as the percentage of carbon dioxide increases, so is the 
 diminution of the light given out by the lamp, which is proportional to the 
 rate of combustion of the oil. A reduction of 1% in the oxygen normally in 
 
 * Note that these are burnings and not explosions. 
 
VENTILATION OF MINES 851 
 
 the air causes a loss of 30% jn the light emitted by oil flame. Clowes states 
 that when 2% of carbon dioxide is present, the hydrogen flame begins to change 
 from reddish to pale blue, whereas 10% is necessary to reduce the size of an 
 oil flame and 15% to extinguish it. A reduction in the oxygen to 16% causes 
 the acetylene flame to become yellow. 
 
 Blackdamp. The term blackdamp is commonly applied by the miner to 
 carbon dioxide and by others to a mixture of that gas and air in which the 
 proportion of carbon dioxide is so large that a lamp will not burn in it. 
 
 Strictly, there is no such gas as blackdamp, and the term is now used to 
 describe a residual atmosphere, resulting from the slow absorption of oxygen 
 by the coal and by the processes of oxidation always taking place underground. 
 Was it not for the fact that in these processes of absorption and oxidation a 
 certain amount of carbon dioxide is given off, the resulting mine atmosphere 
 would be one of pure nitrogen. On this understanding, blackdamp is mine 
 air deficient in oxygen but containing an excess of nitrogen, with (usually) 
 or without carbon dioxide. 
 
 However, certain chemists like Haldane and those of the Bureau of Mines 
 regard blackdamp as a more or less distinct gaseous mixture containing, on an 
 average, from 90 to 85% of nitrogen and 10 to 15% of carbon dioxide, with 
 seldom less than 5% or more than 20% of the latter. The chemical and 
 physical properties of such a mixture, both by itself and when associated with 
 air, will depend on the relative proportions of the two gases. Thus, a black- 
 damp mixture high in carbon dioxide will have a much more marked effect 
 upon life and combustion than when the mixture is largely or entirely nitrogen; 
 pure blackdamp is lighter than carbon dioxide and is lighter than air when the 
 proportion of carbon dioxide is less than 5.25%. If a small amount of methane 
 is associated with the blackdamp, the resulting mixture will almost always be 
 lighter than air. As illustrating the variable composition of blackdamp, 
 Haldane cites that at the Grotto del Cane, near Naples, as being pure carbon 
 dioxide and that at a metal mine in Colorado as being pure nitrogen; between 
 these extremes, the two gases may exist in any proportion. 
 
 The following analyses from Haldane illustrate the composition of air and 
 blackdamp mixtures and the methods of computation. 
 
 In the first form, the amounts of the gases are reported in the ordinary way; 
 in the second, the oxygen with the proper amount of nitrogen to form air is 
 reported as such, and the remainder of the nitrogen together with all the 
 carbon dioxide is reported as blackdamp. 
 
 AIR FROM OLD WORKINGS, HAMSTEAD COLLIERY 
 As Analyzed Air-Blackdamp Ratio 
 
 Oxygen ............... 3.35 A - /Oxygen ......... 3.35\ 1fim 
 
 Nitrogen ............. 84.03 Air \Nitrogen ........ 12.65 / lb<UU 
 
 Carbon dioxide ........ 5.25 T,, t,j orv ,^f Nitrogen ........ 71.38\ 7R R o 
 
 Methane ............. 7.33 Blackdamp \ Carbon dioxide .. 5.25 / 76 ' 63 
 
 Carbon monoxide ....... 04 Methane ............... 7.33 
 
 Carbon monoxide ........ 04 
 
 100.00 
 
 100.00 
 
 In the preceding analysis, the blackdamp is composed of 93.2% nitrogen 
 and 6.8% carbon dioxide. 
 
 AIR FROM A DISUSED END, DOLCOATH TIN MINE, CORNWALL 
 
 As Analyzed Air-Blackdamp Ratio 
 
 Oxygen ............... 17.99 ../Oxygen ......... 17.99"l R r q ~ 
 
 Nitrogen ............. 78.83 Air \ Nitrogen ........ 67.94 / 85 ' 93 
 
 Carbondioxide ....... .38 Blackdain M 14-07 
 
 100.00 
 
 100.00 
 
 In the preceding analysis, the blackdamp is composed of 77.6% nitrogen 
 and 22.4% carbon dioxide. 
 
 In the section headed Firedamp are numerous analyses of gaseous mixtures 
 given off by the face, blowers, feeders, etc., the majority of which contain 
 blackdamp. The constituents of these, and similar mixtures, may be combined 
 in the same way as the foregoing. 
 
 Haldane's Blackdamp Indicator. Haldane's blackdamp indicator is based 
 upon the fact that the distance above the bottom of a tube at which a lighted 
 
852 VENTILATION OF MINES 
 
 taper is extinguished bears a constant relation to the amount of oxygen in the 
 air or, conversely, to the amount of inert impurities present. The apparatus 
 consists of a glass tube 7 in. long and | in. in diameter with a vertical scale on 
 its face which is graduated in percentages of blackdamp and the corresponding 
 percentages of oxygen. The blackdamp graduations run from to 10.5% and 
 the corresponding oxygen graduations from 20.9 to 18.8%. A lighted taper, 
 fg in. in diameter is introduced into the bottom of the tube and is moved 
 upward until it is extinguished, when the percentage of blackdamp present is 
 read directly from the scale. Since an excess of moisture or of nitrogen affects 
 the flame in a similar way to carbon dioxide, the indicator records the sum of 
 the inert impurities in the mine air. As methane elongates the flame, the 
 device is better adapted to use in non-gaseous mines. The instrument is 
 graduated to correspond with air saturated with moisture at 64 F. (about 
 2% of moisture) as this is a fair average of temperature and humidity con- 
 ditions in mines. Provided the temperature and humidity do not vary greatly 
 from those just named, it is found that the indications of the instrument may 
 be relied upon to within about .2% of oxygen and 1% of blackdamp. The 
 instrument may be graduated for any other conditions of temperature and 
 humidity. 
 
 Below 18.8% of oxygen, the taper will no longer burn in the tube nor will 
 it burn without it when the oxygen is below 18.2% (13% of blackdamp) unless 
 held horizontally when it will burn until the oxygen has been reduced to about 
 17.2% (18% of blackdamp). 
 
 CARBON MONOXIDE 
 
 Properties and Sources. Carbon monoxide, formerly known as carbonic 
 oxide, carbonic-oxide gas, and whitedamp, has a formula CO, is odorless, color- 
 less, and tasteless, and supports neither life nor combustion. It burns with 
 a bright bluish flame and is explosive when mixed with air in the proper pro- 
 portions. The gas is so extremely poisonous that its presence in mine air 
 indicates conditions that should be investigated and remedied at once. 
 
 The burning of coal dust suspended in the air or lodged on the roof, floor, 
 and ribs, at the time of a mine explosion, is the greatest and most dangerous 
 source of carbon monoxide, a gas that has probably caused more deaths, 
 certainly more at one time, than have all the other mine gases combined. 
 
 Insignificant amounts of carbon monoxide are given off by certain coals 
 either because they are occluded in the pores of the seam or because they 
 result from the slow oxidation of the coal. Rollin T. Chamberlain investigated 
 the gases given off by coals when bottled in a vacuum. The gases from small 
 lumps from the Mansfield mine, Carnegie, Pa., contained .22% CO at the end 
 of 1 mo.; analyses made at the end of 10 and of 20 da. showing none of the 
 gas. The gases from Monongah, W. Va., coal crushed to pass through a 
 ten-mesh sieve, showed .20% of carbon oxide for the first 6 wk., .16% CO for 
 the next 10 wk., and 2.86% CO for the final 10 wk. of the half year during which 
 the tests were carried on. In these instances, the coal used was the Pittsburgh, 
 or No. 8, containing over 30% volatile matter. It was found that the finer 
 the coal, the more gas was given off. The amount of gas thrown into the mine 
 air in this way is top small to be detected by analysis in the return. 
 
 Under all conditions of working, gasoline-haulage motors produce gases 
 containing carbon monoxide. When the carburation is poor, the proportion of 
 the gas is high and, if the ventilation is defective, may be a source of grave 
 danger. Proper operation of the motor and sufficient ventilation will generally 
 prevent trouble from this cause. 
 
 Carbon monoxide may be produced by the explosion of methane when 
 the percentage of the latter gas in the air is between the limits of maximum 
 explosibility and the upper explosive limit or between 9.46 and, say, 13%. 
 The amount of the gas thus produced increases as the percentage of methane 
 approaches the upper explosive limit (see Combustion Products of Methane). 
 
 Carbon monoxide is produced by the detonation of all kinds of explosives 
 in amounts ranging from 2 to 35% of the volume of the gases resulting there- 
 from, depending on the composition of the explosive, the care used in handling 
 it, and the conditions under which it was fired. Ordinarily, under proper 
 conditions of management, the carbon monoxide produced in this way is not 
 dangerous and cannot be detected in the return air. 
 
 The gases from black powder exploded in a vacuum contain from 2 to 12% 
 of carbon monoxide, with an average of about 6%. In mining operations, 
 however, the presence of coal dust will increase the proportion of the gas to 
 18 to 20% and to 35% in some cases. The proportion given off is found to 
 
VENTILATION OF MINES 853 
 
 decrease as the pressure decreases and the amount of moisture present increases. 
 Haas states that the gases from black powder will yield on an average 18% 
 of the monoxide, and that 1 Ib. of powder will produce 1 cu. ft. of the gas. 
 Should 12 Ib. of powder be exploded in a place 6 ft. X 15 ft., and such amounts 
 are sometimes used in solid shooting, the gases, if confined within a distance 
 of 10 ft. from the face, would cause the air to contain 1.33% of carbon monoxide ; 
 an amount that would be fatal in a few minutes. 
 
 In the case of a standing shot, the cracks and crevices of the coal are com- 
 monly filled with a combustible gas, which is frequently ignited by the lamp 
 of a miner returning too soon to the face. It has commonly been supposed 
 that this gas is carbon monoxide, but Mr. Haas suggests that it is probably 
 some hydrocarbon distilled from the coal by the intense heat of the explosion, 
 and that the monoxide produced was all burned immediately after the blast 
 was discharged. 
 
 Some permissible explosives, notably those of the ammonium nitrate class, 
 yield no carbon monoxide when detonated in a vacuum. However, when 
 fired in the presence of coal dust, as in a mine, they will yield from 6 to 36% of 
 the gas, the higher figures being extreme. 
 
 Abel and others have shown that the explosion of nitroglycerine does not 
 yield any carbon monoxide, but the tests of the Bureau of Mines indicate the 
 presence of as much as 28.4% CO in the gases from exploding 40% strength 
 nitroglycerine dynamite and 34.6% in the gases of the same explosive when 
 of 60% strength. A 60% strength low freezing dynamite yielded as much 
 as 47.4% CO, in the gases. The explosion products from ammonia and gelatine 
 dynamites contain from to 4% CO. However, when these explosives are 
 improperly used, that is, when all or a part of the charge is burned and not 
 exploded, the amount of carbon monoxide in the gases is greatly increased. 
 In a test by the Bureau of Mines, the gases from a 40% strength gelatine 
 dynamite contained 3% CO when the explosive was detonated and 13.7% when 
 it was burned. 
 
 The gases from selected permissible powders and dynamites should cause 
 no trouble from carbon monoxide if the explosives are properly used with detona- 
 tors of ample strength, if the air supply at the face is good, and if a reasonable 
 time is allowed for the gases to mix with the air before returning to the face 
 after a shot. 
 
 While the Bureau of Mines (Miner's Circular 14) states that natural gas 
 does not contain carbon monoxide, from which it follows that the leakage 
 from an improperly cased well drilled through the seam cannot be a source 
 of this gas, other analysts have found from to .4% CO in natural gas from 
 Pennsylvania and West Virginia, from to .5% in that from Ohio and Indiana, 
 and an average of 1% in that from Kansas. 
 
 Carbon monoxide is invariably present in the gases from gob fires. These 
 fires are caused by the spontaneous combustion of the coal through the slow 
 oxidation of piles of slack and bone coal left behind in the workings where 
 the air supply is sufficient to furnish the necessary oxygen, but is not great 
 enough to carry away all the heat formed by the chemical processes going on 
 (see under Spontaneous Combustion and Mine Fires). 
 
 Should a gob fire burst into flame through an increase of the air supply, or 
 should a fire in the ordinary sense start in the timber or in the coal, large 
 volumes of carbon monoxide will be given off because, in the confined workings 
 of a mine, it is not possible for there to be enough air present to furnish all the 
 oxygen required to burn the carbon to carbon dioxide. Either a portion of the 
 carbon is burned to the monoxide directly, ir it is burned to the dioxide, a 
 part or all of which is at once reduced to monoxide. Numerous deaths have 
 been caused by the carbon monoxide from extensive mine fires being carried 
 into the workings in mines, where under usual conditions, the air current was 
 ample. 
 
 Effect of Carbon Monoxide on Life. While perhaps not so poisonous as 
 hydrogen sulphide and nitrogen dioxide, carbon monoxide is formed under so 
 many more conditions and to a so much greater extent that it is commonly 
 considered the most dangerous of mine gases. 
 
 The poisonous effect of the gas is due to its absorption by the hemoglobin 
 of the blood (with which it forms an unstable chemical compound) which has 
 200 to 300 times the affinity for carbon monoxide that it has for oxygen, and to 
 the extent that the blood is saturated with monoxide to that extent it cannot 
 carry the oxygen required by the tissues. The Committee on Resuscitation 
 from Mine Gases of the American Medical Association, in speaking of the 
 effects of illuminating gas which contains much carbon monoxide, says; If the 
 
854 VENTILATION OF MINES 
 
 amount of hemoglobin combined with carbon monoxide exceeds a figure between 
 60 and 70%, so that only 30 to 40% is available for the transportation of 
 oxygen, and if the patient has been in this condition for f hr. or more, degen- 
 erative processes will have started in the brain from lack of oxygen and death 
 or serious nervous or mental impairment will certainly follow. According to 
 Wabner, when the saturation reaches 67% (two-thirds) death is practically 
 certain and is inevitable when the saturation is 79%. Haldane says that when 
 death occurs gradually, the hemoglobin is usually about 80% saturated. 
 
 The absorption of carbon monoxide by the blood changes its color from 
 deep purple red to a very characteristic pale or rose shade. This distinctive 
 coloring is noticeable in the lips and other parts of the body where the skin 
 is thin, and for this reason the bodies of those who have died from monoxide 
 poisoning commonly present a very lifelike appearance, entirely different from 
 the pallid, leaden look accompanying death from other causes. 
 
 The effect of carbon monoxide is not cumulative, and for each per cent, of 
 the gas in the air there is a fixed degree of saturation of the hemoglobin, as 
 shown in the table on page 858. Thus, breathing air containing .04% of 
 carbon monoxide will result in the blood becoming 30% saturated; and indefi- 
 nite exposure will not increase this degree of saturation unless the percentage 
 of the gas in the air is increased. Nasmith and Graham have shown that 
 animals may be hardened to the effects of carbon monoxide so that after several 
 weeks' exposure to gradually increasing proportions of the gas, they are able to 
 live in atmospheres that would kill them at the outset. In the case of man, 
 however, the inhalation of small amounts of this gas while at work during 
 the day does not render him immune, as the blood is purified at night by breath- 
 ing fresh air. 
 
 Haldane says, "The symptoms of carbon-monoxide poisoning are essentially 
 the same as those produced by air deficient in oxygen, and vary according to 
 the degree of saturation reached by the blood. The onset of the symptoms is 
 very insidious, there being only slight shortness of breath and palpitations, but 
 hardly any discomfort; and the senses, power of judgment and of movement, 
 are commonly much impaired before the person is aware of anything being 
 wrong. In some cases there is much excitement, but often there is simple 
 drowsiness and stupidity. The symptoms are, in some respects, similar to 
 those produced by alcohol. One curious fact is that in carbon-monoxide, as in 
 alcoholic, poisoning sudden exposure to cool fresh air may greatly increase 
 the symptoms. Death seems often to be immediately brought about by 
 attempts to escape rapidly up inclines, ladders, etc." In several instances 
 in American mines, the victims of a dust explosion have been able to make 
 their way as much as mi. from their working places before being overcome 
 by the carbon monoxide in the afterdamp. 
 
 The rapidity with which carbon monoxide will overcome a person and 
 whether death or disablement will follow, depends on the percentage of gas in 
 the air and the length of time it has been breathed, and on the rapidity of 
 breathing which, in turn, depends on the violence of his exertions, and on 
 the shortage of oxygen or presence of inert gases as carbon dioxide in the 
 mine air. When the blood is saturated with carbon monoxide to the extent 
 of 50%, a man is too weak to walk. As Haldane points out, the blood of a 
 man will take up about 2 pt. of the monoxide, and of the gas inhaled about 
 60% is absorbed by the hemoglobin. A man at rest inhales about 10 or 12 pt. 
 of air a min., and should this air contain .10% CO, the absorption of the gas 
 would be at the rate of .007 pt. a min., requiring 2.25 hr. to produce one-half 
 saturation and total disability. A man walking breathes about three times as 
 much air as when at rest and would be disabled in 1 hr. or less, and when 
 running in from 20 to 30 min. As 50% saturation is the maximum with 
 .10% CO, death does not follow. Haldane's experiments showed that with 
 .20% CO in the air, it required 70 min. for the blood of a man at rest to become 
 50% saturated, and \ hr. when walking. The same degree of saturation 
 would probably be reached in 10 to 15 min. when running. Since the maximum 
 saturation for .02^, CO is a trifle over 70%, death is practically certain if the 
 patient is unconscious when found and degeneration of the brain cells has 
 set in. If the air contains .30% CO, 50% saturation of the blood and uncon- 
 sciousness will take place in hr. or less when at rest, in 10 to 15 min. when 
 walking and proportionately less when running. If at rest, with this per- 
 centage of carbon monoxide, the blood will become fully saturated (.30% CO 
 = 80% saturation) in a little more than $ hr., and death is certain. According 
 to Wabner, when there is 1% CO in the air, saturation will require but 5 to 
 6 min., even supposing the ill-ventilated place does not already contain other 
 
VENTILATION OF MINES 855 
 
 injurious gases or impoverished air, which will generally be the case in the pit. 
 Death, of course, takes place. 
 
 Haldane gives the following as effects of percentages of carbon monoxide 
 less than .10%: Even .01% may prove injurious where the oxygen is below 
 21% and where considerable quantities of carbon dioxide are present, as in 
 afterdamp; .02% will produce a saturation of the blood to the extent of 20% 
 resulting in a slight tendency to dizziness and shortness of breath on exertion; 
 with .05% giddiness on exertion will result after hr. exposure; and with .07% 
 there will be vertigo on the slightest exertion . 
 
 When the air is deficient in oxygen or contains notable amounts of carbon 
 dioxide, breathing is deeper and more frequent and a greater amount of carbon 
 monoxide is inhaled and absorbed in a given time than would otherwise be 
 the case. Such atmospheres are common after dust explosions, and members 
 of a rescue party entering them are either more quickly overcome by the same 
 percentage of gas or are finally overcome by a less percentage than if the air, 
 except for the presence of the monoxide, was otherwise normal. It must not 
 be overlooked, however, that members of a rescue party have probably been 
 exposed for some time to atmospheres containing appreciable amounts of 
 this gas, so that when they enter a place where the content of carbon monoxide 
 is fairly high, their blood is already partly saturated, and they naturally 
 succumb more quickly than if entering from fresh air. 
 
 The percentage of this gas that may be safely allowed as a permanent 
 constituent of mine air is very low indeed, certainly under .01%, as such air 
 is commonly deficient in oxygen and contains carbon dioxide and methane 
 as well. The maximum percentage that may be breathed for considerable 
 time without producing permanent injurious after-effects is commonly placed 
 at .05%. This percentage, although causing giddiness when working, results 
 in a saturation of the blood not to exceed one-third, from which recovery, in 
 fresh air, is rapid. 
 
 In severe cases of carbon-monoxide poisoning, death usually takes place in 
 a few hours, although life may be prolonged for a few days or weeks; but 
 recovery is not unknown. Such recovery is very slow and the patient may 
 develop chronic pains in the head and legs, and impaired eyesight or dis- 
 ordered brain; and there appears to exist a tendency to pneumonia, etc. Even 
 in mild cases, where complete recovery is made, the process is extremely 
 slow, requiring from several hours to weeks, depending on the length of expo- 
 sure; the milder attacks are accompanied by violent headaches, nausea, and 
 vomiting, and the more severe ones by spasms, cramps, and the like, in addition. 
 
 The Committee of the American Medical Association, previously quoted, 
 says further, "As hemoglobin gives up carbon monoxide very rapidly in atmos- 
 pheres free from the gas, if the patient is still breathing when discovered, the 
 mere inhalation of fresh air without the use of artificial respiration and the 
 administration of oxygen will restore him unless the degeneration of the brain 
 tissues has set in, in which case no amount of oxygen will prevent either death 
 or serious mental derangement should the patient survive. Owing to the fact 
 that it is impossible to tell at the time the patient is discovered or for an hour 
 or two afterwards whether the critical point (degeneration of the brain cells) 
 has been reached, it is of the greatest importance to begin resuscitation at 
 once and preferably by administering oxygen, which removes the monoxide 
 five times as fast as air alone." The Committee does not recommend the 
 general use of appliances for mechanically stimulating breathing, the suction 
 required to produce exhalation being very injurious to the delicate tissues of 
 the lungs and say that the apparatus should be used not longer than 5 or 
 6 min. at a time, and should be alternated with the manual method alone, or 
 in gas cases, combined with oxygen inhalation. 
 
 Explqsibility of Carbon Monoxide. Carbon monoxide will not support 
 combustion but instantly extinguishes a flame placed in it. It is, however, 
 explosive over a very wide range. Authorities differ as to the explosive 
 limits, but they are generally taken to lie between 13 and 15.5% (lower limit) 
 and 75% (upper limit) in air. For complete combustion- by means of an 
 electric spark, Blair fixes the limits at 16.5 and 75%, and Clowes gives 13 and 
 75% when the gas is ignited in the ordinary way and from below (see Relative 
 Explosibility of Methane and Other Gases). The equation for the burning 
 of carbon monoxide in air is 2CO + (O2+3.7822V2) = 2C02+3.7822W, from this, 
 the maximum explosive point is reached when there is 29.45% of the gas 
 in air. 
 
 A certain amount of moisture is necessary for the explosion of carbon 
 monoxide; it is claimed as much as 5% for the maximum explosive effects. 
 
856 VENTILATION OF MINES 
 
 The reaction is a double one. First, Cp+HzO = COz+Hr, the hydrogen 
 immediately combining with the oxygen in the air by the action, 2Hz + Oz 
 = 2HyO. If it is true that carbon monoxide enters into a dust explosion, which 
 appears doubtful, in an absolutely dry mine an explosion of this gas would 
 not be possible. 
 
 The explosive limits of whitedamp mixtures (air and carbon monoxide) 
 may be lowered by the addition of a gas of a lower explosive limit, as methane 
 or hydrogen, and this is true even when the percentage of the added gas is 
 below its own explosive limit. Similarly, the addition of carbon monoxide 
 to firedamp mixtures (air and methane) will raise the higher explosive limit of 
 the last-named gas. 
 
 Explosions of carbon monoxide are very rare if they occur at all, not only 
 because the lower explosive limit is so high but also because such large amounts 
 of the gas are usually accompanied by still larger amounts of nitrogen or 
 carbon dioxide, which so reduce the percentage of oxygen that there is not 
 enough of it to combine with the monoxide in explosive proportions. Inves- 
 tigations appear to sustain the view of Mr. Haas that the burnings and explo- 
 sions that sometimes follow the placing of a lamp in the crevices of a standing 
 shot are due not so much to carbon monoxide given off by the powder as to 
 hydrocarbons distilled from the coal by the heat of the explosion. 
 
 Detection of Carbon Monoxide. Flame Test. In the laboratory, for equal 
 percentages, carbon monoxide gives a flame cap identical with that of methane. 
 The .30% which is exceedingly dangerous is without effect on the flame of 
 the ordinary safety lamp and the 2%, which is the limit of detection by the 
 skilled observer (very many firebosses cannot detect less than 3%), will pro- 
 duce unconsciousness in 30 sec. or less in one who is running, as a fireboss on 
 his rounds. Further, in examining old workings where gob fires exist or in 
 opening a mine that has been sealed to extinguish a fire, the observer will have 
 been breathing for some time air containing gradually increasing amounts of 
 the monoxide, so that his blood will be partly saturated and himself be more 
 susceptible to its effects some time before he reaches a point where the gas will 
 show in the safety lamp. It is unquestionably true that no observer, unless 
 wearing some one of the types of rescue apparatus, ever detected carbon 
 monoxide in the mine with a standard safety lamp and lived to describe his 
 observations. In the Clowes hydrogen lamp, .25% of CO gives a plainly visible 
 cap $ in. in height, but as Mr. Clowes says it is impossible to distinguish 
 between the cap made by the poisonous monoxide and the non-poisonous 
 methane; so that the hydrogen flame test is not distinctive. 
 
 Potain and Drouin Method. The apparatus employed by Potain and 
 Drouain consisted of a long tapered tube connected with a supply of mine air 
 to be tested and dipping to the bottom of an outer tube containing the reagent 
 composed of 10 cu. cm. of a .01% solution of palladium chloride, and two 
 drops of hydrochloric acid. When the mine air is drawn through the outer 
 tube by an aspirator, the reagent (which is about 8 in. in depth) is discolored 
 by the palladium precipitated by the carbon monoxide if present. The per- 
 centage of carbon monoxide is determined by comparing the volume 9f mine 
 
 air taken with that 
 
 REACTION OF CO ON PtCU 
 
 Percentage 
 of CO 
 in Air 
 
 Reaction Visible After 
 
 Time in 
 which Paper 
 Turns Black 
 Minutes 
 
 Minutes 
 
 Seconds 
 
 .010 
 
 11 
 
 
 60 
 
 .025 
 
 5 
 
 
 32 
 
 .050 
 
 3 
 
 
 16 
 
 .075 
 
 2 
 
 
 12 
 
 .100 
 
 1 
 
 
 9 
 
 .250 
 
 
 44 
 
 6 
 
 .500 
 
 
 26 
 
 4 
 
 .750 
 
 
 20 
 
 3 
 
 1.000 
 
 
 16 
 
 2 
 
 2.000 
 
 
 15 
 
 2 
 
 of a standard mix- 
 ture of air and car- 
 bon monoxide re- 
 quired to produce an 
 equal discoloration 
 in another similar 
 bulk of the reagent. 
 The method will de- 
 tect the presence of 
 .01% of CO. 
 
 Simonis Method. 
 In the Simonis 
 method, mine air 
 previously freed, if 
 necessary, from the 
 sulphides of ammo- 
 nia or hydrogen by 
 passing through a 
 solution of copper 
 sulphate or sul- 
 phuric acid, is drawn 
 
VENTILATION OF MINES 
 
 857 
 
 through a tube in which is placed a strip of paper saturated with the chloride 
 of either platinum or palladium. Carbon monoxide, if present, will decompose 
 the chloride and turn the paper first brown and then black in a length of 
 time proportional to the amount of gas present: .01% of CO being detectible. 
 The table gives the lengths of time required by various percentages of carbon 
 monoxide in air to discolor and blacken the test paper saturated with platinum 
 chloride which is rather more sensitive than palladium chloride. J. R. Camp- 
 bell has modified the process by placing a wet sponge in the bottom of the 
 receptacle, thus permitting the use of dry instead of moist test papers. Any 
 number of papers may be prepared in advance for, in use, they will absorb 
 enough moisture from the sponge to permit of the reaction. When used in 
 the mine, air is forced through the apparatus by a pump or India-rubber 
 inflator, but fairly good results may be obtained by merely exposing the 
 instrument to the mine air for any desired length of time. As little as .01% 
 of CO may be thus detected, 
 
 Use of Canaries or Mice. In recovery work after a mine explosion, the 
 existence of dangerous amounts of carbon monoxide in the afterdamp is com- 
 monly determined by the effect of the gas upon mice or canaries carried in a 
 cage by some one of the exploring party. When advancing with the air, the 
 last man should carry the animals, and when moving against the air, the first 
 man, so that they may be exposed to the air and its effects on them noted 
 before the men enter it. Canaries are preferred to mice as they are more 
 sensitive to the action of the gas, and their signs of distress while perched are 
 more easily noted than those of mice who are apt to crouch in a corner of the 
 cage. If a mouse is used, it must be made to move from time to time by 
 tilting the cage, poking it with a stick, etc., so that, while moving, its symptoms 
 may be noticed. The rate of breathing, number of heart beats, etc., in a mouse 
 or canary, are so much more rapid (pulse about 700 to 1,000 beats a min.) than 
 in a man, that the effects of the gas on them is much more rapid. 
 
 The accompanying table from the Bureau of Mines gives the effect on mice 
 and canaries of varying percentages of carbon monoxide, and should be com- 
 pared with the effect of similar amounts on men, as previously given. Thus, 
 when exposed to an atmosphere containing .20% CO it will require ? hr. for the 
 blood of a man walking to become 50% saturated, at which stage the legs will 
 give way; but a canary similarly exposed showed signs of distress in 1.5 min., 
 and fell from his perch in 5 min. In using canaries as guides to the presence 
 of the monoxide, certain facts must be remembered. In the excitement of 
 rescue work, the unskilled observer may entirely fail to note in the canary the 
 preliminary symptoms of poisoning that would be clear to the trained man; 
 
 EFFECT OF CO ON MICE AND CANARIES 
 
 Mice 
 
 Canaries 
 
 Per 
 
 
 Per 
 
 Effect 
 
 Cent. 
 
 Effect 
 
 Cent. 
 
 CO 
 
 
 CO 
 
 .16 
 
 Very slight distress at end of 
 
 .09 
 
 Very slight distress at end of 
 
 
 hour. 
 
 
 Ihr. 
 
 
 .20 
 
 Distress in 8 min.; partial 
 
 .12 
 
 Weaker at end of 1 hr. 
 
 than 
 
 .31 
 
 collapse in 15 min. 
 Distress in 4 min.; collapse in 
 
 .15 
 
 after exposure to .9% 
 Distress in 3 min.; fell 
 
 from 
 
 
 7 min.; lost muscular pow- 
 
 
 perch in 18 min. 
 
 
 
 er in 35 min. 
 
 
 
 
 .46 
 
 Distress in 2 min.; collapse in 
 
 .20 
 
 Distress in 1? min.; fell 
 
 from 
 
 
 4 min. 
 
 
 perch in 5 min. 
 
 
 .57 
 
 Distress in 1 min.; collapse in 
 
 .29 
 
 Fell from perch in 2\ min 
 
 
 
 2 min.; muscular power lost 
 in 7 min.; death in 16 min. 
 
 
 
 
 .77 
 
 Distress in 1 min.; muscular 
 
 
 
 
 
 power lost in 6| min.; death 
 
 
 
 
 
 in 12 J min. 
 
 
 
 
858 
 
 VENTILATION OF MINES 
 
 and the ability of even trained men to detect these early symptoms varies con- 
 siderably. There is also a marked difference in the resisting power to carbon- 
 monoxide poisoning of canaries, some birds showing no more distress at the end 
 of 6 min. than others did in 2 min. For this reason, either a bird should be 
 selected which previous tests has shown to be sensitive to the gas, or several 
 birds should be taken along. It would also appear that small percentages of 
 carbon monoxide (say .10%) which in the course of 1 hr. or so seriously affect 
 men, are often without any influence at all on the canary. For these reasons, 
 while actual distress or disablement on the part of the bird are unfailing signs 
 of the presence of the gas, these signs should net be waited for, and the display 
 by any member of such symptoms of poisoning as dizziness, shortness of 
 breath, weakness of the legs, impairment of sight, etc., should lead to the 
 immediate withdrawal of the entire party. 
 
 Blood Tests. The so-called blood test, while giving excellent results in 
 determining whether carbon monoxide is or is not present in the air or blood, is 
 not definite when the percentage of gas is required. For this determination, a 
 chemical analysis should be made in the regular way. To make the blood 
 test, one to three drops of blood secured from a healthy animal or by pricking 
 the finger are shaken up with enough water to make about a 1% solution 
 (1 part of blood in 100 of water). This results in a buff-colored solution, which 
 is equally divided between two test tubes, which are corked. One test tube is 
 set aside for comparison, and through the cork of the other are inserted two 
 glass tubes, one of which is long enough to reach nearly to the bottom of the 
 test tube, the end of the other being above the level of the solution. A glass 
 bottle filled with the suspected air is connected with the long tube and suction 
 applied at the end of the short one. This will exhaust the air from the bottle 
 and cause it to bubble up through the test solution, which will be colored a 
 distinctive pink shade if any carbon monoxide is present. The colors will be 
 more distinctly visible if the two tubes are compared against a brightly lighted 
 white background. The same result may be obtained by shaking one of the 
 blood solutions for 10 min. or so in a bottle containing the suspected air. The 
 presence of the gas in the blood may be told by preparing solutions of equal 
 strength (same quantity of blood and water) of the blood of the supposedly 
 poisoned person and that of a healthy person or animal; the latter for com- 
 parison, as before. 
 
 To obtain an approximate idea of the percentage of carbon monoxide in 
 the air, Haldane recommends the following: Prepare a solution of normal 
 blood and fill two test tubes with it as already described. Set one of the 
 tubes aside, and thoroughly saturate the other with illuminating gas, which con- 
 tains large quantities of the monoxide, by bubbling the gas through the solution 
 and shaking them together for about 10 min. This will give a buff-colored 
 solution containing no carbon monoxide and a pink solution saturated with it: 
 and these are the two ends of the scale. A mouse is exposed in the suspected 
 air in the mine for from 10 to 15 min. and then killed in the place, as its rembval 
 to fresh air, while alive, would greatly reduce the amount of the gas in its 
 blood and thus invalidate the test. As much of the mouse's blood is taken as 
 was required to make the test solutions, and it is diluted to the same degree. 
 By comparing, against a white background, the color of the mouse-blood 
 solution with that of the two test solutions, it can be approximately determined 
 if its blood is jfo, j&, etc., saturated. The amount of carbon monoxide in the 
 air can then be determined from the following table. 
 
 PER CENT. OF CARBON MONOXIDE IN AIR CORRESPONDING TO 
 
 VARIOUS PERCENTAGES OF SATURATION OF BLOOD 
 
 SOLUTION 
 
 Blood 
 
 Carbon Monoxide 
 
 Blood 
 
 Carbon Monoxide 
 
 Saturation 
 
 in Air 
 
 Saturation 
 
 in Air 
 
 Per Cent. 
 
 Per Cent. 
 
 Per Cent. 
 
 Per Cent. 
 
 10 
 
 .012 
 
 60 
 
 .12 
 
 20 
 
 .025 
 
 70 
 
 .19 
 
 30 
 
 .040 
 
 80 
 
 .30 
 
 40 
 
 .060 
 
 90 
 
 .70 
 
 50 
 
 .080 
 
 
 
VENTILATION OF MINES 859 
 
 As it is only necessary that the test solution should have a clearly perceptible 
 color, one drop of blood may be sufficient. The test may be used to estimate 
 the amount of the gas in the blood of a person suffering from gas poisoning, by 
 taking as much blood from the patient as was used in making the test solution 
 and diluting it to the same degree. As noted, if the patient has been, uncon- 
 scious for hr. or more and his blood is found to be over 60% saturated, it is 
 more than probable that degeneration of the brain cells has set in and that no 
 amount of oxygen or other respiratory treatment would have effected his 
 recovery. 
 
 By measurihg the quantity of a normal solution of carmine that is required 
 to color the mouse-blood solution to the same intensity as the solution satu- 
 rated by means of _ illuminating gas, it is possible to make a very accurate 
 quantitative determination of the amount of carbon monoxide present. The 
 method, while delicate, is not used to any great extent, ordinary methods by 
 absorption being preferred. 
 
 Spectroscopic Methods. A portable pocket spectroscope for the detection 
 of carbon monoxide has been devised by a German firm. A sample of the 
 suspected air is obtained in the ordinary way and to it are added a few drops of 
 a very weak solution of blood which is supplied with the instrument. After 
 being well shaken the blood solution is examined with the spectroscope. 
 Whether CO is present or not, two dark bands will be seen in the yellow and 
 green parts of the spectrum between the Frauenhofer lines D and E, the 
 position of which is specially marked on the scale of the spectroscope. If no 
 carbon monoxide is present these bands will disappear on adding to the original 
 solution a drop or two of colorless ammonium sulphide (diluted), and in their 
 place and between them will appear one broad band which shades off at the 
 edges. If carbon monoxide is present the two_ bands are but very slightly 
 altered in appearance by the addition of ammonium sulphide and they are not 
 replaced by a single band. In the one case the oxyhemoglobin is decomposed 
 by ammonium sulphide and in the other the carboxyhemoglobin is not affected 
 by that reagent. 
 
 METHANE 
 
 Properties and Sources. Methane, otherwise known as light carburetted 
 hydrogen, marsh gas, firedamp, or simply as gas, has a formula CHt, is odorless, 
 colorless, tasteless, and non-poisonous, and will not support life or combustion. 
 From the mining standpoint, it is the most important member of the paraffin 
 series of gases whose general formula is C n Hz n +2 in which n is the number of 
 atoms of carbon in a molecule of any one of these gases. Methane burns with 
 a blue flame similar to that of carbon monoxide, and like that gas is explosive 
 when mixed with air in the proper proportions. 
 
 Methane is given off by the pores of the coal in practically all mines, 
 although often in amounts that can only be detected by careful analysis. Gas 
 so contained in the coal is commonly, but incorrectly, spoken of as occluded, a 
 term strictly referring to gas absorbed and possibly condensed in the pores of 
 a metal, as hydrogen in palladium. The amount of gas given off by the seam 
 is very variable, and depends, in a great measure, on the opportunity it has 
 had to escape naturally from the coal. Thus, more gas may be expected in the 
 inner workings than near the outcrop, in a shaft than in a drift mine, and at 
 great than at shallow depths. In the deep European mines, the Prussian Fire- 
 damp Commission found that from 357 to 2,400 cu. ft. of methane are given 
 off per ton of coal mined; and, in France, Chesneau reports 1,377 cu. ft. of gas 
 per ton of coal mined at the Herin mine, Anzin, and 882 cu. ft. at Ronchamp. 
 Similar figures for American mines are not available, but may be readily cal- 
 culated when the output of the mine and the volume of the air current and its 
 content of methane are known. Thus, in a mine producing 1,000 tons a day, 
 when the return has a volume of 100,000 cu. ft. a min., which contains .30% of 
 CH 4 , the volume of gas per ton of coal mined is (60 X 24X100,000 X. 003) -r- 
 l,000 = 432cu. ft. 
 
 Many coals continue to give off gas for months after being mined and 
 explosions of methane have occurred on shipboard by taking a lighted torch 
 into the bunkers where the boiler coal is stored. Samples of coal bottled in 
 a vacuum continue to give off gas for from 5 to 1 yr., the gas escaping more 
 rapidly from finely crushed than from lump coal. The volume of gas given 
 off by the coal is much greater during the first few days after mining than 
 later. From American coals, Chamberlain obtained a volume of gas equal 
 to .9 to 2.3 times that of the sample before crushing. Lump coal yielded 
 but .5 to .9 their volumes of gas under similar conditions. Analyses of the 
 gases given off by coal will be found under Firedamp. 
 
860 
 
 VENTILATION OF MINES 
 
 These so-called occluded gases exist under a pressure that is more or less 
 proportional to the thickness of the cover upon the coal and, according to 
 the European investigations recorded in the accompanying table, is frequently 
 as great as 10 to 16 atmospheres (150 to 240 Ib. per sq. in.). Pressures over 
 40 atmospheres, or about 600 Ib. per sq. in., have been noted. The figures 
 in the second column of the table are the depths of the boreholes, or the dis- 
 tance back from the face and in the solid coal where the pressure was measured. 
 
 PRESSURE OF OCCLUDED GAS 
 
 Name of Mine 
 
 Depth of Hole 
 Feet 
 
 Pressure 
 Pounds 
 
 Elmore mine, main bed 
 
 8.53 
 
 4.36 
 
 Hetton mine, Hutton bed 
 Eppleton mine Hutton bed 
 
 8.98 
 46.90 
 
 6.96 
 36.14 
 
 Balden mine, Bensham bed 
 Harris Navigation mine 
 
 31.85 
 32.80 
 
 71.41 
 22.04 
 
 Methyr Vale mine 
 
 49.20 
 
 39.67 
 
 Celynen mine . . . . . . 
 
 54.48 
 
 68.32 
 
 Harton mine (1,214 ft. deep) 
 
 16.24 
 
 196.30 
 
 Harton mine . . . 
 
 27.55 
 
 230.44 
 
 Harton mine 
 
 37.13 
 
 294.45 
 
 Methane is given off by blowers, otherwise known as feeders or bleeders, 
 which are streams or jets of gas issuing from cracks and crevices in the coal 
 face or in the floor or roof. These blowers seem to follow some well-defined 
 line of fracture in the measures or some fissure or clay vein and, as they fre- 
 quently give off gas under high pressure for many months, they are probably 
 connected with some underlying reservoir or porous stratum filled with gas. 
 In many cases, because of the high pressure, the gas in escaping makes a 
 singing noise, which resembles the pattering of light rain upon leaves. 
 
 Methane is frequently found along the line of clay veins and similar irregu- 
 larities, probably following the line of separation between the material filling 
 the vein and the rocks through which it cuts. In many cases, the gas is found 
 under high pressure just after the clay vein is pierced, whereas none, or but 
 normal quantities are found between it and the crop line. Gas may be found 
 within an area bounded by clay veins or by the dykes of igneous rock common 
 in some of the western coal fields. In such cases, if the mine has not hitherto 
 generated gas and, consequently, the necessary precautions to cope with it 
 have not been made, the sudden piercing of a clay vein or dyke and the unex- 
 pected release of large volumes of gas has led to serious accidents. 
 
 Sudden outbursts of gas in large quantities and under great pressure some- 
 times take place. These may be caused by the gas finding its way through 
 vertical crevices or cleats to cavities of considerable horizontal extent, so that 
 the gas pressure is distributed over a wide area. As the mine openings approach 
 such a locality, the pressure manifests itself by bursting the coal from its posi- 
 tion in the face and throwing it into the entries, in some cases completely 
 blocking them. These outbursts are frequently preceded and accompanied 
 by thunderings and poundings, the former for several days before the gas 
 actually escapes. 
 
 Whether the outbursts of gas so frequently accompanying bumps (bounces) 
 are a cause or an effect of the throwing of large masses of coal into the- workings 
 as a result of a sudden rending of the pillars, is not satisfactorily decided. The 
 weight of evidence, however, indicates that bumps are due to the sudden release 
 of pressure in the overlying rocks, and that the shattering of the coal and 
 roof, and sometimes the floor, sets free the contained gas and opens any pockets 
 or crevices in which it may be stored. If pillars are left too small or their 
 drawing has been carried too far, the tendency to slowly and regularly settle 
 (and possibly to bring on a squeeze) may be resisted by a strong roof until 
 such a time as the limit of its strength is reached when it will suddenly give 
 and as suddenly crush the coal over an area of a few hundred square feet or 
 several acres. When the resistance becomes adjusted to the pressure, the 
 crushing will cease; therefore, unless the place is entirely closed, bumps may 
 be repeated in the same or adjacent areas as the roof pressure accumulates. 
 The outbursts mentioned in the first part of the paragraph produce results 
 similar to bumps, but on a smaller scale. 
 
VENTILATION OF MINES 861 
 
 In Belgium, large volumes of gas under very high pressure and accom- 
 panied by a peculiar porous coal dust are found in large chambers or pockets. 
 When a reservoir of this kind is accidentally tapped by a heading, an outrush 
 of large volumes of gas and coal dust occurs with great suddenness, filing 
 the workings immediately, and causing enormous damage. Thus, according 
 to Wabner, at the Agrappe colliery in Belgium, more than 500,000 cu. yd. of 
 gas and a great mass of coal dust broke out into a heading at a depth of 2,000 ft., 
 blocking up all the workings and the shafts, and taking fire at the pit mouth 
 destroyed the head-frame and surface plant. After the first rush of gas had 
 subsided, violent explosions occurred, completely closing the shafts and killing 
 or injuring 112 men. Similar explosions have occurred in other mines in 
 the same country. The Belgian measures have been subjected to very heavy 
 horizontal pressure, which has resulted in the formations slipping over and past 
 one another, the irregular line of fracture producing pockets in which the gas 
 accumulated, and in which pockets were large quantities of dust resulting from 
 the grinding of the coal by the rock movement. 
 
 Methane is often released in unusual quantities from the rocks during 
 a squeeze or a creep, by a heavy fall of roof or a general breaking or settling 
 of the overburden accompanying and following pillar drawing. 
 
 In some mining districts, the leakage under great pressure from improperly 
 cased oil and gas wells drilled through the workings, is a source of methane 
 as it constitutes 50% or more of natural gas. 
 
 Black powder does not usually produce any methane but many safety 
 (permissible) powders and high explosives yield from a trace to as much as 
 5% of it when exploded in the laboratory. Analyses of the combustion pro- 
 ducts of explosives are given on page 670. When used in the mine in contact 
 with coal, and particularly when slack is used for tamping, all powders yield 
 important amounts of methane (5 to 10% or more of the gases of combustion), 
 which may be in part distilled from the coal by the heat of the explosion, and 
 in part result from chemical combination between the elements in the powder 
 and those in the coal. 
 
 Methane is found in the gases from mine fires and in the afterdamp of 
 explosions, where it is distilled from the coal by heat. 
 
 Analyses of combinations of methane and various gases will be found 
 under Firedamp. 
 
 Formation of Methane. Coal seams are formed by the slow alteration of 
 vegetable matter in the presence of moisture and in the absence of air; heat 
 generated by pressure, commonly assisting in the process. The alteration has 
 resulted in the formation of various hydrocarbons, the chief of which is methane. 
 While, in the course of ages, most of the gas has escaped through the over- 
 lying rocks, large quantities still remain. Methane may be formed wherever 
 moist vegetable matter is protected from the air, as in swamps and peat bogs and 
 the bottom of stagnant ponds, where it may be seen bubbling up through the 
 water; whence the name marsh gas. It is suggested that methane is yet being 
 formed in some seams where the processes of alteration have not been com- 
 pleted; but this has not been proved. 
 
 All methane does not originate in coal seams. It occurs in mines of salt 
 and strontia, in beds of clay and sandstone, invariably accompanies the pro- 
 duction of petroleum, and always forms the bulk of natural gas, even when 
 these substances are found many hundreds of miles from any coal field. In 
 mining regions, natural gas is often met in sands (more or less porous sand- 
 stones) several hundred to several thousand feet below the lowest coal bed. 
 These facts have led Mr. Haas to hold, for northern West Virginia at least, that 
 methane does not originate in the coal, but in the natural-gas sands many 
 feet below. In these deep sands, the natural gas is under a pressure pro- 
 portional to the depth, a pressure in many instances as great as 1,500 Ib. and 
 often reaching 2,000 to 3,000 Ib. a sq. in. Because of this pressure, the gas 
 is forced slowly upwards and meeting the seam, is held in the pores of the 
 coal. This view of Mr. Haas' explains why the deeper seams are more gaseous 
 than the higher ones, why one mine in a district may produce much gas and its 
 neighbor but little, and why feeders from the floor and bottom of the seam 
 are more lasting than those from the roof and the top of the bed. 
 
 Occurrence of Methane in Mines. After prolonged exposure, the occluded 
 methane is largely given off by the seam so that in active workings, at least, 
 the gas is more commonly found at or near the face of the rooms and entries 
 than nearer the drift mouth or the foot of the shaft. Unless diffused or removed 
 by the air-current as fast as it escapes, the extreme lightness of methane tends 
 to its concentration near the roof; and in workings being driven to the nse, 
 
862 VENTILATION OF MINES 
 
 and it is commonly looked for there. When slowly given off near the floor, 
 diffusion will distribute it uniformly through the air of the place; and when 
 once mixed it will not again separate. The same is true of gas coming from 
 the roof, but the diffusion is not so rapid. When issuing from the top, the gas 
 under the influence of a gentle air-current will often flow in a thin sheet or 
 layer next the roof, rising into and remaining in any cracks or crevices. In 
 entries, gas will accumulate behind any obstruction in the air; thus, it will be 
 found at the roof between the collars of parallel sets of timbers. 
 
 The volume and velocity of the air-current have much to do with the 
 concentration of gas in one part or another of the workings. In rooms, where 
 the air is apt to be stagnant, and particularly beyond the last break-through, 
 accumulations of methane are usual. In such places, the gas often tails out 
 or tails back from the face; that is, at the face it will extend down from the 
 roof for, say, 3 ft. and thence gradually decrease in depth outwards towards 
 the break-through where none may be found. Bodies of what is known as 
 standing gas will accumulate in old workings where there is little or no circu- 
 lation of the air. In some cases, the oxygen will be so reduced through absorp- 
 tion by the coal or the percentage of methane may be so high that an explosion 
 is not possible in the old workings, but should the gas escape into the air-current 
 an explosive mixture may result. Gas is very often a source of trouble in pillar 
 drawing, accumulating above the falls of roof where it is entirely out of reach 
 of the sluggish air-currents which, possibly, may be circulating through the gob. 
 This pillar gas (as well as standing gas in old workings) may be forced into the 
 airways with disastrous results by a heavy fall of roof or by the reduced at- 
 mospheric pressure, which is marked by a fall of the barometer. 
 
 Effect of Methane on Life. As methane is not concerned with breathing, 
 like carbon dioxide, and does not combine with the hemoglobin of the blood, 
 like carbon monoxide, it is without active effect on life. When unusually large 
 amounts are present, it acts in the same way as an excess of nitrogen, reducing 
 the percentage of oxygen available for breathing which becomes more and more 
 difficult and finally impossible. Wabner states that methane produces suf- 
 focation when constituting 50% of the inhaled air, while Guibal places the 
 limit at 33%. 
 
 Explosibility of Methane. Methane, like carbon monoxide, will either 
 burn or explode when mixed in the proper proportions with air. The temper- 
 ature of ignition of methane is variously stated to be 650 C. (1,202 F.) by 
 Demanet, 740 C. (1,364 F.) by Brunck, 780 C. (1,436 F.) by Koehler. 
 The Bureau of Mines gives the igniton temperature in air as 650 to 750 C. 
 (1,202 to 1,382 F.); and in oxygen, 536 to 700 C. (1,033 to 1,292 F.). 
 
 The percentage of methane in the air necessary to produce either a burning 
 or an explosion depends on the means taken to ignite the gas, on the presence 
 of other combustible or inert gases, on the amount of oxygen and water vapor 
 in the air, on the temperature and pressure, etc. With low percentages of 
 methane, owing to the cooling effect of a large body of air, the burning will 
 extend only a very short distance from the cause of ignition, as when the 
 gas is detected in the flame of a safety lamp. As the percentage of gas increases, 
 the inflammation extends farther and farther from 'its origin until it entirely 
 permeates the gaseous mass. A point is then reached when the burning is 
 instantaneous and an explosion occurs; this marks the lower explosive limit. 
 Later, as the percentage of gas increases, the maximum explosive point is 
 reached. When this is passed, the still increasing percentage of methane in the 
 air is accompanied by explosions of less and less violence, until the higher, or 
 upper, explosive limit is reached. From this point to the upper inflammable 
 limit, the phenomena are the same, but in reversed order, to those leading 
 from the lower inflammable to the lower explosive limit. 
 
 As it is a difficult matter to tell just when a very rapid burning becomes 
 an explosion, authorities differ in the values assigned to the explosive limits 
 of methane in air. Blair gives the limits as 6.1% and 12.8% for ignition by 
 an electric spark when complete combustion results. Doctor Brunck states 
 that below 6% and above 15% an explosion cannot take place. The Bureau 
 of Mines notes that 5.5% of gas in air will explode, but not with violence, and 
 that an incomplete burning sometimes results with as little as 4.5%. Similarly, 
 the Bureau has secured slight burnings with as much as 20% of methane. 
 Clowes places the explosive limits at 5 and 13% when the gas is ignited from 
 below, and at 6 and 11% when ignition is from above, and remarks that the 
 lower figures (5 and 6%) represent the least amount of gas that will always 
 burn, and under certain conditions will explode. The maximum explosive 
 point is reached when the air contains 9.46% of methane. 
 
VENTILATION OF MINES 
 
 863 
 
 The determination of the exact explosive limits of the gas is not a matter 
 of first importance, that is, it makes little difference in practical ventilation 
 whether the lower limit is 5.5 or 7.1%, as either figure is far beyond the amount 
 that can be tolerated in the presence of bituminous-coal dust, which is com- 
 monly fixed at not more than 1%, one of the largest producers requiring that 
 the return air in its mines shall not contain more than .30% of methane. 
 
 Methane can only be ignited by a flame or an electric arc and not by dark 
 heat alone, although explosions have been attributed, as at the Belleyue mine, 
 Alberta, Can., to ignition of methane by sparks produced by rocks striking one 
 another during a fall of roof. Sparks from the old-time flint mill, or wheel, used 
 for lighting in gaseous mines are, also, believed to have originated gas explosions. 
 
 The explosion of methane is not instantaneous when it is raised to the 
 ignition point, but requires an appreciable time interval. This fact is taken 
 advantage of in the use of high and permissible explosives the flame of which is 
 so short that notwithstanding its high temperature, it goes out before it has 
 time to ignite the gas. 
 
 A decrease in the pressure makes the gas less explosive. According to 
 Brunck, a mixture of air 7.5% of methane that explodes with violence at 
 atmospheric pressure (30 in. of mercury) cannot be made to explode if the pres- 
 sure is reduced to 8 in. of mercury. Similarly, an increase in pressure as well as 
 one in temperature renders the gas more explosive ; hence at great depths, where 
 the barometer stands at, say, 33 to 34 in. and the thermometer registers possibly 
 100 F., a lower percentage of gas will be explosive than in surface workings. 
 
 As the other combustible gases have a much wider explosive range (see table 
 below) and lower ignition temperature than methane, their presence in- 
 creases the liability of a firedamp mixture to explode. On the other hand, 
 inert gases like nitrogen and carbon dioxide by shortening the explosive range 
 of methane and by their cooling effect on the products of combustion, materially 
 reduce the liability of occurrence of such explosions. The presence of gases 
 having a maximum explosive point greater than that of methane as well as 
 that of inert gases, raises the maximum explosive point of firedamp. Since 
 mine air is commonly deficient in oxygen, the explosive limits of methane in it 
 are usually higher than in pure air, one authority placing them at 7.14 and 
 16.67%, respectively, and another stating that the maximum degree of explosi- 
 bility is reached when the methane is one-eighth to one-ninth of the air, that 
 is, from 12.5 to 11.1%. 
 
 The statement sometimes made that an addition of one-seventh (14.3%) 
 of carbon dioxide to a volume of air and methane at its most explosive point 
 (CHt, 9.46%; air, 90.54%) entirely prevents its explosion seems contrary to 
 the facts as the resulting mixture, which has the composition COz 12.51%, 
 Oz 16.60%, N* 62.61%, CHt 8.28%, is well within the explosive limits as given 
 in the following table. 
 
 It has been shown by Baker that an explosion of gas is not possible when 
 it and the air are absolutely dry, moisture playing the part of a catalytic agent, 
 as noted under Explosibility of Carbon Monoxide. However, the condition 
 of absolute dryness does not exist in mines and cannot be brought about therein. 
 
 LIMITING EXPLOSIVE MIXTURES OF VARIOUS EXPLOSIVE GASES 
 WITH AIR 
 
 Combustible Gas Used 
 
 ^Percentage of Gas Mixed 
 With Air 
 
 Method of 
 Kindling 
 
 Lower 
 Explosive 
 Limit 
 
 Upper 
 Explosive 
 Limit 
 
 Methane. . . . 
 
 /5 
 U 
 J6 
 19 
 9 
 6 
 13 
 4 
 3 
 
 13 
 11 
 29 
 22 
 55 
 72 
 75 
 22 
 82 
 
 Upwards 
 Downwards 
 Upwards 
 Downwards 
 Upwards 
 Upwards 
 Upwards 
 Upwards 
 Downwards 
 
 Coal gas, Nottingham 
 Water' gas artificial 
 
 Hydrogen 
 Carbon monoxide 
 
 Ethylene, olefiant gas 
 
 Acetylene . . . 
 
 
864 
 
 VENTILATION OF MINES 
 
 The above table from Clowes gives the relative explosibility of methane 
 and other gases. Clowes notes that the determination of the limits for acetylene 
 is complicated by a somewhat explosive separation of the acetylene itself into 
 its elements. The composition of the coal gas was: Olefins, 5.3%; hydrogen, 
 48.2%; carbon monoxide, 6.6%; methane, 34.2%; oxygen, .2%; nitrogen, 5.5%. 
 The total combustible gases were 94.3%, inert gases 5.7%. The composition 
 of the water gas was: Hydrogen, 49.6%; carbon monoxide, 40.8%; carbon 
 dioxide, 2.6%; nitrogen, 7.0%. The total combustible gases were 90.4%, 
 inert gases, 9.6%. Combustion was effected in tubes, by means of a Bunsen 
 burner, the flame being held both below and above the body of the gas. The 
 conditions, in the main, were not unlike those that might be met in the mine. 
 
 The probability of an explosion is greatest in the case of those gases having 
 a wide explosive range, because it is possible to form with them a greater 
 number of explosive mixtures. For this reason, methane with an explosive 
 range of 5 to 8% is the least dangerous gas, and hydrogen, with a range of 
 67% is the most dangerous. Also, methane is less dangerous than the other 
 gases because its temperature of ignition is higher, and it is more slowly kindled. 
 However, methane is in the end the most dangerous gas from the viewpoint of 
 possible explosions because of its general occurrence; the other gases are found 
 but rarely or in very small amounts, and carbon monoxide, notwithstanding its 
 wide range of explosibility, is dangerous solely because of its intensely poisonous 
 properties. 
 
 Firedamp. Firedamp originally meant the gas methane and later was 
 modified to mean an explosive mixture of methane and air, Methane rarely 
 occurs in a pure state being associated with small amounts of ethane, ethylene, 
 nitrogen, etc., and the word firedamp is now very commonly defined as a mix- 
 ture of explosive mine gases, very largely methane but often, if not always, 
 mixed with other hydrocarbons and small amounts of inert gases. As, with 
 the exception of the rare gas hydrogen, all mine gases are heavier than methane, 
 the specific gravity of firedamp is higher than that of pure methane, and may 
 reach above .7. 
 
 The. following analyses, from Chamberlain, are of firedamp given off by 
 coal when bottled in a vacuum. 
 
 COAL FROM FACE, NAOMI MINE (GAS COAL, PITTSBURGH, PA., 
 DISTRICT) 
 
 Gas 
 
 First 
 3 Wk. 
 
 4 Wk. 
 Later 
 
 10 Wk. 
 
 Later 
 
 9 Wk. 
 
 Later 
 
 Carbon dioxide 
 Carbon monoxide \ 
 
 1.05 
 
 .83 
 
 .63 
 
 .60 
 
 Olefins J 
 Paraffins . . 
 
 1.03 
 55.39 
 
 .29 
 84.96 
 
 .84 
 91.39 
 
 1.13 
 
 87.89 
 
 A . /Oxygen 
 Aa \Nitrogen . . 
 
 .51 
 1.91 
 
 .35 
 1.32 
 
 .50 
 1.89 
 
 .40 
 1.51 
 
 Nitrogen, excess 
 
 40.11 
 
 12.25 
 
 4.75 
 
 -8.47 
 
 Relative volumes 
 
 100.00 
 .21 
 
 100.00 
 .20 
 
 100.00 
 
 .28 
 
 100.00 
 .21 
 
 COAL FROM FACE, NO. 1 NORTH SHAFT, NANTICOKE, PA. 
 (ANTHRACITE) 
 
 Gas 
 
 First 
 Week 
 
 Second 
 Week 
 
 Third 
 Week 
 
 Fourth 
 Week 
 
 Carbon dioxide 
 
 .02 
 
 
 .17 
 
 
 Olefins 
 
 .51 
 
 .78 
 
 .87 
 
 .29 
 
 Paraffins. . 
 
 86.86 
 
 93.99 
 
 94.19 
 
 98.58 
 
 A f Oxygen 
 
 .04 
 
 
 
 .07 
 
 Air \Nitrogen 
 Nitrogen, excess 
 
 .15 
 12.42 
 
 5.23 
 
 4.77 
 
 .26 
 
 .80 
 
 Relative volume 
 
 100.00 
 1.22 
 
 100.00 
 .99 
 
 100.00 
 
 100.00 
 
 .81 
 
VENTILATION OF MINES 
 
 865 
 
 In the preceding analyses, by olefins is meant gases of the type of ethylene, 
 CzHt, and by paraffins, gases of the type of methane and ethane, CH^ and CtH 6 , 
 respectively. In the Naomi analysis, whatever carbon monoxide may have 
 been present is grouped with the olefins, and its absence in the Nanticoke 
 analysis is noticeable. Mr. Chamberlain states that certain differences 
 observed in making the analyses can be explained by the presence of ethane 
 (in the paraffins) in proportions of a trace to four parts of ethane to 100 parts 
 of methane. So far as his tests went, the bituminous coals yielded more ethane 
 than the single sample of anthracite (Nanticoke); in fact, the analyses of 
 several anthracite gases indicated that instead of there being paraffins higher 
 than methane, that small amounts of hydrogen were present. 
 
 The following table gives the composition and volume of gases (firedamp) 
 issuing from some Welsh coals when heated in a vacuum to 212 F. 
 
 GASES ENCLOSED IN THE PORES OF COAL AND EVOLVED IN A 
 VACUUM AT 212 F. 
 
 (Thomas) 
 
 
 
 
 
 
 
 Quantity 
 
 Name of Colliery 
 
 Quality 
 
 COz 
 
 
 
 cm 
 
 N 
 
 fecS 
 
 1 
 
 
 
 
 
 
 
 iji 
 
 o fc^ 
 
 
 
 
 
 
 
 *ijj 
 
 f ft | 
 
 
 
 
 
 
 
 p, 
 
 u w 
 
 Navigation 
 
 Steam 
 
 13.21 
 
 .49 
 
 81.64 
 
 4.66 
 
 250.0 
 
 80 
 
 Dunraven 
 
 Steam 
 
 5.46 
 
 .44 
 
 84.22 
 
 9.88 
 
 218.0 
 
 70 
 
 Cyfarthfa 
 
 Steam 
 
 18.90 
 
 1.02 
 
 67.47 
 
 12.61 
 
 147.0 
 
 47 
 
 Bute 
 
 Steam 
 
 9.25 
 
 .34 
 
 86.92 
 
 3.49 
 
 375.0 
 
 120 
 
 Bonville's Court 
 
 Anthracite 
 
 2.62 
 
 
 93.13 
 
 4.25 
 
 555.0 
 
 178 
 
 Watney's. 
 
 Anthracite 
 
 14.72 
 
 
 84.18 
 
 1.10 
 
 600.0 
 
 192 
 
 Plymouth Iron Works 
 
 Bituminous 
 
 36.42 
 
 .80 
 
 
 62.78 
 
 55.9 
 
 18 
 
 Cwm Clydach 
 
 Bituminous 
 
 5.44 
 
 1.05 
 
 63.76 
 
 29.75 
 
 55.1 
 
 18 
 
 Bettwys 
 
 Bituminous 
 
 22.16 
 
 6.09 
 
 2.68 
 
 69.07 
 
 24.0 
 
 8 
 
 The following table gives a series of firedamp analyses from Le Chatellier, 
 some of them being of blowers, others from bore holes, etc. 
 
 ANALYSES OF FIREDAMP 
 
 (Le Chatellier) 
 
 Locality 
 
 CE t 
 
 C0 2 
 
 N 
 
 O 
 
 Analyst 
 
 Dunraven mine, blowers. . . . 
 
 96.70 
 
 .47 
 
 2.79 
 
 
 J. W. Thomas 
 
 Dunraven mine, bore hole. . 
 
 96.50 
 
 .44 
 
 3.02 
 
 
 J. W. Thomas 
 
 Garswood mine. 
 
 84.16 
 
 .86 
 
 12.30 
 
 2.65 
 
 W. Kellner 
 
 Garswood mine, blowers. . . . 
 
 88.86 
 
 .41 
 
 8.90 
 
 1.83 
 
 W. Kellner 
 
 Glamorgan mine, blowers . . . 
 
 93.01 
 
 .27 
 
 5.94 
 
 .78 
 
 . W. Kellner 
 
 Dombran mine, blowers. . . . 
 
 95.11 
 
 .48 
 
 4.07 
 
 .34 
 
 f Austrian Firedamp 
 
 Karwin mine 
 
 94.59 
 
 .18 
 
 4.48 
 
 .75 
 
 \ Commission 
 
 Karwin mine, blowers 
 
 99.10 
 
 .20 
 
 .70 
 
 
 
 Hruschau mine 
 
 79.16 
 
 .19 
 
 17.04 
 
 .61 
 
 
 Hruschau mine, blowers. . . . 
 
 87.93 
 
 .83 
 
 10.25 
 
 .99 
 
 
 Peters wald mine, blowers. . . 
 
 90.00 
 
 .15 
 
 9.25 
 
 .60 
 
 
 Segen Gottes mine 
 
 83.51 
 
 1.17 
 
 15.02 
 
 .30 
 
 Sauer 
 
 Segen Gottes mine, bore hole 
 
 87.16 
 
 1.11 
 
 11.73 
 
 
 Sauer 
 
 Liebe Gottes mine, bore hole 
 
 77.69 
 
 3.77 
 
 18.48 
 
 .06 
 
 Sauer 
 
 The following table from Schondorrf 
 65 
 
 entirely of firedamp from blowers. 
 
866 
 
 VENTILATION OF MINES 
 ANALYSES OF FIREDAMP FROM BLOWERS 
 
 Locality 
 
 CH* 
 
 CzH 6 
 
 H 
 
 COz 
 
 N + 
 
 Bonifacious mine at Kray, Essen 
 
 90.94 
 
 
 1.40 
 
 .30 
 
 7 36 
 
 Consolidation mine at Schalk, Westphalia 
 Konig mine at Neunkirchen, Saarbuck. . . 
 
 Oberkirchen mine at Schaumburg 
 
 Cavities in the roof, Lothringen mine at 
 Castrop Westphalia 
 
 89.88 
 84.89 
 f 60.46 
 \ 93.66 
 
 27 95 
 
 1.62 
 37.64 
 
 .88 
 
 5.84 
 2.11 
 
 1 35 
 
 .67 
 .65 
 2.56 
 .63 
 
 45 
 
 3.61 
 12.84 
 
 4.80 
 70 25 
 
 New Iserlohn mine at Lawgendren, West- 
 phalia 
 
 / 4.75 
 \ 4.00 
 
 .06 
 
 .09 
 
 1.34 
 .40 
 
 65.00 
 95 00 
 
 
 
 
 
 
 
 The following analyses from Chamberlain are of feeder gas from American 
 mines; the last being that of a gas issuing under high pressure from a standpipe 
 at Luzerne, near Wilkesbarre, Pa. In this case, C n Hz n , is the general formula 
 for the olefin series of gases of which ethylene, or olefiant gas, is a type. When 
 so used, the formula means that the gases, while present, were not separately 
 determined. In the same way, the other paraffin gases, of which the general 
 formula is C n Hz n +z, were not determined but are included with the methane. 
 
 ANALYSES OF FIREDAMP FROM FEEDERS 
 
 Locality 
 
 CH* 
 
 COz 
 
 CO 
 
 C n Hzn 
 
 Air 
 
 Nt 
 
 Excess 
 
 Cardiff, 111 
 
 90.42 
 
 2.04 
 
 
 .20 
 
 6.02 
 
 1.32 
 
 
 
 
 
 
 
 
 Cardiff, 111 
 
 92.17 
 
 2.39 
 
 
 
 !6 
 
 263 
 
 2 55 
 
 
 
 
 
 
 
 
 Luzerne, Pa 
 
 91.31 
 
 1.59 
 
 .04 
 
 .49 
 
 1.10 
 
 4.65 
 
 The following series of analyses of a firedamp mixture that could be 
 explosive under proper conditions is given by Mr. G. A. Burrell. The analyses, 
 made day by day, show the change in the atmosphere in an enclosed area in an 
 anthracite mine, a part of which was sealed off to prevent entrance of a fire 
 in progress in a neighboring district. The gases were not contaminated by the 
 products of combustion of the fire as a heavy roof fall prevented the escape 
 of the gases from the one to the other, and thus fairly represent the change 
 in mine air away from the ventilating current. On the first two days, there 
 was a leakage of air into the enclosed area, and after this was stopped the 
 change in the imprisoned air was much more rapid. 
 
 GASES FROM AN ENCLOSED AREA IN AN ANTHRACITE MINE 
 
 
 
 Percentage of 
 
 Sample 
 Number 
 
 Date 
 
 
 
 
 
 
 
 
 
 COz 
 
 CO 
 
 Oz 
 
 CtH 
 
 Nz 
 
 1 
 
 Oct. 31 
 
 2.2 
 
 
 15.0 
 
 14.0 
 
 68.8 
 
 2 
 
 Nov. 1 
 
 2.3 
 
 
 14.6 
 
 18.1 
 
 65.0 
 
 3 
 
 Nov. 2 
 
 2.6 
 
 
 6.2 
 
 24.2 
 
 67.0 
 
 4 
 
 Nov. 2 
 
 2.9 
 
 
 5.7 
 
 29.3 
 
 62.1 
 
 5 
 
 Nov. 3 
 
 2.8 
 
 
 4.1 
 
 34.9 
 
 58.2 
 
 6 
 
 Nov. 6 
 
 2.6 
 
 
 5.0 
 
 53.0 
 
 41.4 
 
 The following analyses from Mr. Austin King give the composition of some 
 firedamps from the Connellsville, Pa., bituminous-coal region. The very large 
 
VENTILATION OF MINES 
 
 867 
 
 amounts of ethylene, carbon monoxide, and hydrogen in the first two samples 
 is noticeable. Mr. King also furnishes the following analyses of gases escaping 
 from bore holes 'drilled from the surface to drain the gob. 
 
 ANALYSES OF FIREDAMP, CONNELLSVILLE REGION 
 
 Samples Taken From 
 
 Percentage of 
 
 C0 2 
 
 CzH t 
 
 2 
 
 CO 
 
 Fh 
 
 C//4 
 
 Nz 
 
 Drill hole in coal f 
 Crevice in roof, fac 
 Return airway of n 
 
 ice 
 
 .30 
 1.70 
 
 1.50 
 1.30 
 
 1.60 
 
 1.80 
 18.40 
 
 1.30 
 .90 
 
 7.35 
 2.04 
 
 79.60 
 63.27 
 6.50 
 
 8.25 
 28.99 
 75.10 
 
 2 main entry 
 lain entry . . 
 
 ANALYSES OF GAS FROM DRILL HOLES 
 
 Remarks 
 
 COz 
 
 CzHi 
 
 02 
 
 CO 
 
 H 2 
 
 CzH 6 
 
 CH* 
 
 Nz 
 
 Hole, 525 ft. deep. 
 Hole, 406 ft. deep. 
 Same, 1 yr. later . . 
 Hole, 474 ft. deep. 
 
 2.50 
 5.20 
 1.80 
 4.60 
 6.90 
 
 .10 
 
 10.40 
 3.20 
 14.90 
 4.20 
 9.20 
 
 .20 
 .40 
 
 1.35 
 14.16 
 
 1.60 
 
 11.90 
 12.64 
 2.20 
 8.80 
 38.30 
 
 73.85 
 78.96 
 71.68 
 67.52 
 48.50 
 
 Firedamp is usually found in the same relative positions in the workings as 
 methane. However, the presence of large amounts of gas heavier than methane 
 may make firedamp heavier than air and give it a tendency to collect on the 
 floor. Thus, a gaseous mixture composed of 54.1% of methane and 45.9% of 
 carbon dioxide has the same weight as air. Any increase in the percentage of 
 carbon dioxide over 45.9 will make the mixture heavier than air and, if diffusion 
 is not taking place, the firedamp will accumulate on the floor. 
 
 Combustion Products of Methane. When pure methane is exploded in 
 air the reaction is Ctf4+2(O 2 +3.7822V 2 ) = CO 2 +2# 2 O + 7.564.ZV 2 . The com- 
 position of the afterdamp is 15.1% COz, 12.3% vapor of water HzO, and 72.6% 
 Nz. As soon as the water vapor condenses, the remaining gas is a blackdamp 
 with the composition i !7.2% COz and 82.8% Nz. This reaction holds good for all 
 burnings and_ explosions of methane as long as there is an ample supply of 
 oxygen; that is, from the lower inflammable limit (about 5%) to the maximum 
 explosive point (9.46%). 
 
 _ As the percentage of methane in the air rises above the maximum explosive 
 point and the supply of oxygen is less than that required for complete com- 
 bustion, an increasing proportion of the methane is burned to carbon monoxide 
 and hydrogen, the reaction probably being 2C# 4 + (02+3.782^) = 2CO + 4ff 2 
 + 3.782A/2. It is also probable that portions of the methane are burned to 
 
 PRODUCTS OF EXPLOSION OF METHANE IN AIR 
 
 Percentage of Methane in Air 
 
 
 9.46 
 
 10.03 
 
 10.94 
 
 12.00 
 
 Carbon dioxide 
 Carbon monoxide 
 Hydrogen .... 
 
 15.10 
 
 10.16 
 2.13 
 1.39 
 
 8.35 
 4.47 
 3.66 
 
 4.80 
 3.90 
 3.50 
 
 Water 
 
 12 30 
 
 
 
 
 Nitrogen . 
 
 72.60 
 
 86.32 
 
 83.52 
 
 82.20 
 
 Methane, etc 
 
 
 
 
 2.50 
 
868 VENTILATION OF MINES 
 
 carbon monoxide without the formation of hydrogen by this reaction. 
 +3(O2+3.782Af 2 )=2CO-| : 4tf2O + 11.3462V2. It is not possible to determine 
 the percentage composition of the afterdamp in these cases as the relative 
 proportions of the methane burned to carbon dioxide, and to carbon monoxide, 
 and hydrogen, respectively, cannot be known. 
 
 The first column gives the composition of the afterdamp as calculated from 
 the reaction for complete combustion. The second and third columns repre- 
 sent the results of investigations by Mr. G. A. Burrell, of the Bureau of Mines. 
 The figures in the fourth column are from the French firedamp commission 
 as quoted by Chamberlain. The sums total but 96.9% and indicate the 
 presence of some unconsumed methane and other hydrocarbons. Mr. Burrell 
 notes that no acetylene, olefin hydrocarbons, or unburned methane were found 
 in the products of combustion. 
 
 The results of the French firedamp commission in some measure support 
 the contentions of Doctor Broockmann, of Bochum, who, according to Wabner, 
 has shown that the product of the imperfect combustion of methane is ethylene 
 (olefiant gas, CzHt), and not carbon dioxide. The reaction for the explosion 
 in oxygen would probably be written, 2CHt+02 = CzH4,+2HzO. In dis- 
 cussing Doctor Broockmann's work, Chamberlain says: A mixture of air 
 and firedamp containing from 10.8 to 13.5% of marsh gas he found to give 
 two separate flames. Expecting to find some carbon monoxide formed as the 
 result of the first flame, Broockmann removed the products of the first com- 
 bustion, in an exploding mixture of methane and air, before the appearance 
 of the second flame; but in no case found a trace of carbon monoxide. Instead, 
 the heat of the first combustion converted the unconsumed methane into 
 acetylene and hydrogen. These doubtless furnished the fuel for the second 
 flame. 
 
 In the case of the formation of acetylene and hydrogen, the reaction for 
 explosion in oxygen, would be, 2CHt+O2 = C2H2+Hz+2HzO. From the 
 evidence in hand, it would appear that the explosion of methane in a deficient 
 air supply, that is when there is more than 9.46% methane in the air, results 
 ordinarily in the formation of carbon monoxide and hydrogen, but that under 
 certain conditions some acetylene and olefiant gas may be formed. One of 
 these conditions for the formation of ethylene or acetylene would appear to 
 be a percentage of methane approaching the upper explosive limit. 
 
 Effect of Atmospheric Changes on Escape of Firedamp. The pressure of 
 the atmosphere is not constant, but is subject to fluctuations depending on the 
 condition of the atmosphere. Besides these, there are fluctuations that are 
 more or less regular and are called barometric variations. There is both a 
 yearly and a diurnal, or daily, variation. Of these two, the more important 
 and the more regular is the daily variation, in which the barometer attains a 
 maximum height from 9 to 10 o'clock A. M., and a minimum about 4 o'clock p. M. 
 Other maximum and minimum readings are obtained at 10 P. M. and 3 A. M., 
 respectively; but these are not as pronounced as those occurring in the day- 
 time. The daily barometric variations range from .01 to .08 in. 
 
 A reduction in atmospheric pressure (fall of the barometer) permits, or 
 tends to permit, an increase in the outflow of gas, and an increase in atmospheric 
 pressure (rise of the barometer) reduces the outflow. Although at its point 
 of escape face and blower gas are but little above atmospheric pressure, a 
 short distance within the solid the pressure may be from five to forty or more 
 atmospheres, whereas standing gas in old workings is under atmospheric 
 pressure only. For this reason, a change in pressure has much more effect 
 on the escape of gas from the gob than from the face, although the lengthening 
 of the flame of a burning blower during periods of low barometer and its 
 shortening when the barometer is high which are due to an increase and decrease, 
 respectively, in the amount of escaping gas are well known. 
 
 In connection with barometric fluctuations the following points should 
 be noted: Changes in the outflow of gas always take place before the corre- 
 sponding change in the barometer, and from 1 to 6 hr. in advance thereof. 
 This appears to be due to the fact that an air-and-gas column is much more 
 sensitive to slight changes in pressure than one of mercury. Thus, the table 
 on page 838 shows that 1 in. of mercury = .491 Ib. a sq. in. = 876 ft. of air, and 
 for a given change in the mercury column, the one in the air column is 876 X 12 
 = 10,512 times as great. One reason for the discontinuance of the barometer 
 warnings in England was that they did not arrive until the danger was passed. 
 In an extensive country like the United States, the well-known Daily Weather 
 Maps of the Weather Bureau can be utilized in this connection. Thus, an 
 area of low barometer, say, in Arizona, will probably not reach Illinois or 
 
 
VENTILATION OF MINES 869 
 
 Pennsylvania for 24 to 36 hr. t giving ample time to make any necessary changes 
 in the ventilation. The reason why these maps have not received extended 
 use is possibly due to the facts that the average American mine is shallow and 
 non-gaseous, and provided with ample ventilation. 
 
 Increases in the outflow of gas due to working the mine should not be 
 confused with those due to changes in atmospheric pressure. As pointed out 
 by Messrs. Evans and Hutchinson, the amount of gas given off by the face is 
 a minimum at the beginning of the shift, increases to a maximum at its end 
 and then decreases to a minimum at the beginning of the next morning shift. 
 This is due to the fact that by day fresh faces of coal are constantly being ex- 
 posed, and does not concern the escape of gas from the gob. For the same 
 reason, a mine producing 2,000 or 3,000 tons a day gives off more gas than 
 one mining but 1,000 tons. Rapidity of working, however, does not affect the 
 outflow of gas from the gob. 
 
 The more rapid the change in the barometer, the greater will be the increase 
 or decrease in the /outflow of gas. When the pressure falls a certain amount 
 and then remains constant for some time, the increased outflow of gas gradu- 
 ally diminishes as the pressure of the gas in the coal adjusts itself to that 
 of the atmosphere. The outflow does not become as low as before the fall 
 until the pressure returns to its original amount. The greater the pressure of 
 the gas in the pores of the coal, the less will be the effect of atmospheric changes 
 on its escape. Standing gas in old workings is more dangerous when changes 
 of pressure take place than face or blower gas, as large volumes of it may be 
 forced into the airways. 
 
 Afterdamp. Strictly speaking, afterdamp and blackdamp are one and the 
 same gaseous mixture (COz and N), the one being formed with extreme rapidity 
 by the explosion of methane or coal dust (or both), and the latter very slowly 
 by the gradual absorption of oxygen and the giving off of carbon dioxide by the 
 coal. Afterdamp, however, is a convenient term in indicating that the black- 
 damp mixture it defines is found after rather than before an explosion. Owing 
 to the general insufficiency of oxygen for complete cormTustion and the universal 
 presence of coal dust in mine workings, afterdamp probably always contains 
 more or less carbon monoxide, and the presence of this gas may be used to 
 distinguish it from blackdamp formed in the ordinary way. Unfortunately, it 
 is not possible to give representative analyses of afterdamp, because in the 
 time between an explosion and the arrival of a chemist, the mine atmosphere 
 will have materially changed and correct samples cannot be obtained. Doctor 
 Haldane says that afterdamp may be assumed to contain about 80 to 85% N, 
 12 to 14% O, 4 to 6% C0 2 ,.6 to 1.5% CO, together with small amounts of SOz, 
 HiS, and unconsumed CHi. Such an analysis indicates, roughly, a composi- 
 tion of 62% air, 38% blackdamp composed of 87% N and 13% CO 2 , and the 
 amounts of the other gases previously named, and is a typical air-blackdamp 
 mixture. 
 
 Afterdamp, at least by the time rescue parties arrive upon the scene, is 
 very rarely extinctive of lights and so must contain at least, say, 17.5 to 18% 0; 
 considerably more than the figures given by Doctor Haldane. Neither is the 
 atmosphere always extinctive immediately after an explosion as is proved by 
 the numerous instances in which the lamps of the killed have been found 
 either burning or exhausted of oil. 
 
 Whether the breathing of afterdamp results fatally or not depends almost 
 entirely on the amount of carbon monoxide present, for, except for this gas, 
 the afterdamp quoted from Dr. Haldane is not necessarily deadly, although 
 extinctive of lights. In anthracite mines, where the dust is inert, carbon 
 monoxide is derived from the imperfect combustion of methane, but in bitu- 
 minous mines where, frequently, no gas is concerned in. the explosion, the 
 monoxide comes from the imperfect combustion of the carbon of the coal, 
 from the reduction of carbon dioxide to carbon monoxide by incandescent 
 carbon and, more likely, by the imperfect combustion of the various hydro- 
 carbons distilled from the coal by the intense heat of the explosion. As no 
 two explosions are alike in the relative proportions of methane (or coal dust) 
 and air concerned, so does the amount of monoxide in the resultant afterdamp 
 vary from amounts that are merely injurious to those that are almost immedi- 
 ately fatal, Doctor Haldane's figure of 1.5% probably well representing the 
 average maximum. 
 
 In some cases, depending on the incompleteness of the explosion, the after- 
 damp will contain unburned methane, small amounts of hydrogen, and possibly 
 traces of acetylene. The oxides of nitrogen may be found in minute quantities 
 in afterdamp as a result of the burning of explosives and if black powder has 
 
870 VENTILATION OF MINES 
 
 been one of these, traces of sulphur dioxide and hydrogen sulphide as well. 
 Vapor of water is always a product of the explosion of hydrocarbon gases 
 and, as stated, some moisture seems essential to the explosion of all gases. 
 
 Detection of Methane. Some miners having long familiarity with methane 
 claim to be able to feel the presence of large amounts of the gas, and others 
 attribute to it a peculiar odor and a taste like apples. It is impossible to give 
 any reason for these claims as the pure gas is odorless and tasteless and its 
 effect on respiration is the same as that of nitrogen. The claim that the gas 
 can sometimes be seen is not altogether unreasonable, the visibility being due 
 to the irregular refraction of the light rays from a lamp while passing through 
 layers of methane or of firedamp of varying densities. 
 
 The gas is universally detected in mine workings by the use of some form 
 of safety lamp, in rare cases a so-called mechanical gas detector has been used. 
 For accurate determinations of the methane content of the return air and the 
 control of the ventilation of a mine as a whole, the larger corporations now 
 cause chemical analyses of the mine air to be made daily or more often if 
 necessary. 
 
 THE RARER MINE GASES 
 
 General Considerations. A number of gases, either by reason of their 
 existence in mine air being disputed or doubtful, or by their occurrence under 
 very unusual conditions or in such small amounts that they can be detected 
 only locally and not when distributed through the ventilating current, are 
 known as the rarer mine gases. These gases are ethane and ethylene and the 
 higher members of the paraffin and olefin series of gases, and hydrogen, all of 
 which may occur associated with methane in firedamp; acetylene, which is 
 sometimes found as a combustion product of methane in a deficiency of oxygen ; 
 hydrogen sulphide and sulphur dioxide which may be formed by the burning of 
 certain explosives, by mine fires, and by certain natural chemical processes; 
 and several of the oxides of nitrogen, which are found in the combustion prod- 
 ucts of various explosives. 
 
 The part that any of these gases plays in the general scheme of mine venti- 
 lation is insignificant, and most of them are of little more than theoretical 
 interest. Ethane, ethylene, and other members of their series are not easy 
 to detect, and it is possible that their more general occurrence will be demon- 
 strated when more accurate methods of analysis are employed. On the other 
 hand, many competent chemists doubt their existence in mine air after special 
 and exhaustive searches for them. 
 
 Ethane and Other Paraffin Gases. Ethane, formula Czfle, the next higher 
 than methane in the paraffin series of gases having the general formula 
 C n Hz n +t, is believed to be a fairly common constituent of firedamp, although 
 its presence is denied or doubted by numerous competent observers. The 
 Prussian Firedamp Commission reported a sample of firedamp containing 
 37.62% of ethane, but the maximum noted in American mines rarely exceeds 
 .25 to .50%. Chamberlain found from a trace to 4 parts of ethane to 100 parts 
 of methane in the gases given off by American coals when bottled in a vacuum, 
 while Porter and Orvitz and Parr and Barker could find no trace of it in many 
 samples of coal from Illinois and other states, and Brunck (Germany) and 
 Harger (England) either could not find the gas or claim that its existence has 
 not been definitely proved. As the gas is formed under the same natural 
 conditions as methane, there seems no good reason why it should not be found 
 in firedamp. The gas is given off by the face and by blowers, but it may 
 enter the mine through leakage from wells of natural gas which usually con- 
 tains from 3 to 6% of ethane and as high as 16% in the case of that piped to 
 Pittsburgh, Pa., from the West Virginia fields. 
 
 Ethane is odorless, colorless, and tasteless, is slightly heavier than air, and 
 is non-poisonous but, like methane and nitrogen, is suffocating in sufficient 
 quantities. The gas is combustible, burning with a somewhat more brilliant 
 flame than methane, and is explosive at a lower temperature (968 to 1,166 F.) 
 according to the reaction 2C2#6+7O2 = 4CO2+6.H2O. The explosive range of 
 the gas does not appear to have been determined, but its point of maximum 
 explosibility in air is fixed by Brunck at 5.6%. When present with methane, 
 it makes the firedamp mixture more easily explosive, but not to a great extent 
 owing to the relative difference in the amounts of the two gases. 
 
 Whether insignificant amounts of. the next higher paraffin gases, propane 
 CsHs and butane CiHw, are or are not associated with ethane in the methane 
 of firedamp is a very much unsettled question. The chemical and physical 
 properties of these gases and their effect on firedamp mixtures are very similar 
 
VENTILATION OF MINES 871 
 
 to those of ethane. In chemical analyses, they are commonly determined with 
 the methane or ethane and are sometimes reported as paraffins. 
 
 Ethylene and Other Olefin Gases. Ethylene, otherwise known as ethane, 
 and olefiant gas, formula Ctlh, is the principal member of the olefin series of 
 gases having the general formula C n Hz n . It is, perhaps, a rather more abun- 
 dant constituent of some firedamps than ethane, although such a large maximum 
 as 37.62% has not been reported for it. Chamberlain found .02 to .26% of 
 ethylene and ethylene and carbon monoxide jointly, respectively, in feeder 
 gas from Cardiff, 111., and .49% of ethylene in gas escaping from a borehole 
 near Wilkes-Barre, Pa. Small amounts of ethylene are not uncommon in 
 natural gas; it is a usual constituent of producer and by-product coke-oven 
 gas, and to its presence is due the illuminating power of coal gas distilled 
 from coal. 
 
 Ethylene is colorless, has a slight ethereal odor, and is said to have a 
 mild sweetish taste. It is a trifle lighter than air, is non-poisonous although 
 suffocating like nitrogen and methane, is combustible, and is explosive between 
 the limits of about 4 and 22% in air according to the reaction (in oxygen) 
 C2#4+3O2 = 2CO2+2# 2 O. The gas ignites and burns with a very brilliant 
 flame at about 1,020 F., its point of maximum explosibility being reached 
 when it constitutes 5.21% of the air. 
 
 As with ethane, the tendency of ethylene is to increase the explosibility 
 of firedamp mixtures, but its influence is not as great as it rarely forms as 
 much as 1% of a body of explosive gases. 
 
 It is possible that trifling amounts of propylene, CsHe, and butylene, CtHs, 
 the next higher gases in the olefin series are present with ethylene. If so, they 
 have not been separately determined but are included in the ethylene or are 
 reported under the head of olefin or C n Hin gases. 
 
 Hydrogen. Hydrogen, with an atomic symbol of H and a molecular for- 
 mula Hz, is of quite general occurrence in small quantities in mines. Based 
 on published analyses, the gas is not a common constituent of face or feeder 
 gas, although Mr. Austin King reports 2.04% in the gases taken from a crevice 
 in a mine roof and 7.35% in the gases from a hole drilled into the solid. From 
 a trace to as much as 8 or 9% are found in the crevices of the coal face after 
 blasting, where it is formed in part as an incomplete-combustion product of 
 the powder and in part by distillation of the coal. It appears to be always 
 present in amounts up to 2% or more in the gases from gob and ordinary mine 
 fires, and is an almost universal constituent of the afterdamp of coal-dust 
 explosions where it results from distillation from the coal or the incomplete 
 combustion of methane and other- hydrocarbons. It is found in natural gas 
 sometimes to the extent of 25 to 30%, commonly forms nearly or fully one-half 
 of coal gas, and is present in large amounts in all types of manufactured gas. 
 
 Hydrogen is odorless, colorless, and tasteless, is the lightest substance 
 known, is non-poisonous but is suffocating like methane, etc. It is com- 
 bustible and is explosive between the limits of 5 and 72% in air, having the 
 greatest explosive range of any of the true mine gases. It ignites at a tempera- 
 ture between 1,030 and 1,130 F., and burns with an almost colorless bluish 
 flame and with the production of intense heat, according to the reaction (in oxy- 
 gen) 2#2 + O2 = 2H?O. As the water vapor condenses, the afterdamp from the 
 explosion of pure hydrogen in air is nitrogen only. 
 
 As its explosive range is much wider and it occurs so much more frequently 
 and abundantly, its effect in increasing the explosibility of firedamp mixtures 
 is much more marked than that of any other gas. 
 
 Acetylene. Acetylene, formula C2.H2, is the only gas of the series having 
 the general formula C n //2n-2, that is found in mines. It is reported only as 
 a constituent of afterdamp resulting from the explosion of methane in a marked 
 deficiency of oxygen. Acetylene, and the next higher gas in the same series, 
 allylene CaH*, are minor constituents of coal gas. 
 
 Acetylene is colorless, tasteless, and has an ethereal odor that has by some 
 been likened to that of geranium. It is slightly poisonous and is suffocating. 
 It is combustible and is explosive between the limits of 3 and 82% in air, 
 having, probably, the greatest explosive range of any gas. It ignites at about 
 900 P.. and burns with an intensely brilliant flame and much smoke except 
 in properly designed burners, according to the reaction (in oxygen) 2CzHz+ 
 
 --. 
 
 Hydrogen Sulphide. Hydrogen sulphide, formula H 2 S, and otherwise 
 known as sulphuretted hydrogen, or stinkdamp, is colorless, has a sweetish taste 
 and a very distinctive odor of decayed eggs, as little as .01% in air being 
 capable of detection by this means. The gas is even more poisonous than 
 
872 VENTILATION OF MINES 
 
 carbon monoxide, is combustible, and is explosive with violence when present 
 to the extent of 12.5% in air, the point of maximum explosibility being reached 
 at 14.2%. The reaction for its burning in oxygen is 2HzS+3Oz = 2.H2O + 2SO2. 
 
 Hydrogen sulphide is produced in mines by the burning of black powder 
 and those of the higher explosives of less than 40% strength that contain 
 sulphur as a combustible. The amount of this gas in powder smoke varies from 
 a trace to as much as 15 to 20% or more, the proportion, in a great measure, 
 depending on the amount of moisture present. It is also formed by the decay 
 of animal and vegetable substances containing sulphur, by the action of acid 
 waters on metallic sulphides (particularly iron pyrites), by the heating of 
 sulphides in the presence of moisture as in gob fires, by the distillation of coal 
 containing sulphur when the hydrogen and sulphur unite directly, and by the 
 reducing action upon sulphates of bacteria in foul and stagnant water. When 
 absorbed by water, the gas is readily given off on stirring, and care should be 
 taken not to .disturb a pool known or supposed to contain it. Very small quanti- 
 ties of the gas are sometimes found in feeder and blower gas, and it is, at other 
 times, carried into the mine in solution in water from the containing rocks. 
 
 The gas is an irritant poison affecting the nostrils and other approaches to 
 the lungs, the eyes, brain, and all the tissues, although, unless in large amount 
 it does not appear to effect a change in the blood as does carbon monoxide. 
 One of the first symptoms of very small amounts is irritation of the air-passages 
 accompanied by an inflammation of the eyes, which feel as if full of dust. In 
 larger amounts, according to Lehmann, the gas causes nausea, giddiness, cold 
 skin, labored breathing, irregular action of the heart, and pains in the stomach. 
 Death follows quickly after unconsciousness (which comes very rapidly in 
 cases of hydrogen-sulphide poisoning), and is frequently accompanied by 
 delirium, convulsions, and lockjaw. As little as .05% will prove fatal if 
 breathed for some time, .07% in 1 hr.,and .20% in a few minutes. The after- 
 effects of this poisoning, like those of carbon monoxide, are frequently severe, 
 long continued, and even permanent. 
 
 One of the immediate effects of hydrogen sulphide in dangerous quantities 
 is a deadening of the sense of smell, which ceases to be a guide to the detection 
 of the gas. A simple test for the presence of this gas may be made by dipping 
 a piece of paper in acetate of lead (sugar of lead) , and allowing it to dry. Upon 
 exposure to air containing even a trace of the gas, the paper is immediately 
 blackened by the formation of lead sulphide. 
 
 Sulphur Dioxide. Sulphur dioxide, formula SOz, appears to be formed 
 during mine fires by the burning of coals containing pyrites by the reaction 
 (in oxygen) 4:FeSz+llOz = 2FezO3, + 8SOz, and possibly by the decomposition 
 of sulphates previously formed by the slow oxidation of pyrites according to 
 the reaction, 2FeSO4 = FezO3+SO 2 +SO3. 
 
 Sulphur dioxide is colorless, has a suffocating irritating smell, and a pro- 
 nounced taste. It is more than twice as heavy as air and is incombustible, 
 sometimes being used instead of carbon dioxide to extinguish mine fires. 
 
 The gas is very soluble in water forming, it is believed, sulphurous acid by 
 the reaction HzO [ + SOz = HzSOs. As the gas is absorbed by the moisture in 
 the throat, nostrils, etc., it is probably as sulphurous acid and not as sulphur 
 dioxide that this gas acts on the system. The gas appears to decompose the 
 red corpuscles of the blood, is fatal in extremely small amounts, and its symp- 
 toms in producing irritation of the air-passages, lungs, eyes, etc., with accom- 
 panying congestion, are similar to those of hydrogen sulphide. However, much 
 smaller amounts of it than of the sulphide are dangerous. Thus, Lehmann 
 says that as little as .001% produces some slight irritation of the mucuos mem- 
 brane and respiratory organs, which is pronounced when the percentage rises 
 to .003. In the case of rabbits, .04% causes congestion of the chest and 
 inflammation of the air-passages and eyes, and .10% causes death in a few 
 seconds. 
 
 Nitric Oxide and Nitrogen Di9xide. When high explosives containing 
 nitroglycerine and nitro-substitution compounds are burned rather than 
 exploded, they do not yield carbon dioxide and nitrogen but their gases of 
 combustion contain large quantities of carbon monoxide and nitric oxide, NO, 
 which latter, on contact with air is at once converted into the red fumes of 
 nitrogen dioxide NOz, by the reaction 2NO + Oz = 2NOz. Haldane shows that 
 when nitroglycerine is exploded, the gases of combustion contain 63.2% COz 
 and 31.6% Nz, but when burned in the presence of its own gases, they con- 
 tained 35.9% CO and 48.2% NO. Clarence Hall found in the gases resulting 
 from the burning of ordinary 40% strength gelatine dynamite, 13.7% CO, 
 11.3% NO, and .6% NO 2 , 
 
VENTILATION OF MINES 873 
 
 The conditions causing the burning, all or in part, of nitro-explosives 
 instead of their detonation, are poor quality of the explosive, improper tamp- 
 ing, the use of detonators of insufficient strength of or defective fuses, and the 
 actual burning of a quantity of the explosive by a fire carelessly started. 
 
 Haldane claims that nitrous fumes, NOz, are even more poisonous than 
 those of HzS and says that no gas met in mines is so treacherous in its effects. 
 These fumes act as an irritant to the eyes, nose, and throat not dissimilar to 
 that of hydrogen sulphide and sulphur dioxide, but whereas the after-effect of 
 recovery from the last-named gas is a temporary catarrh, with nitrous fumes 
 there is great danger of intensely acute bronchitis, which is often fatal. While 
 temporary irritation and apparent recovery may be experienced at the time of 
 exposure, these are frequently followed by the development of bronchitis in 
 a few hours and this is frequently fatal in 2 da. Mice forced to breath air 
 containing but .05% of thesaifumes for 1 hr., and which apparently recovered, 
 died within 24 hr. of bronchitis. 
 
 Nitrous fumes are easily detected by their smell, even when greatly diluted, 
 and care should be taken in returning to the face if this smell is at all notice- 
 able. Minute traces of the gas may be detected by exposing in the suspected 
 air a paper soaked in a solution of starch and potassium iodide; if any nitric 
 oxide is present, the starch is at once turned blue by the iodine set free. 
 
 EFFECT OF HEAT AND HUMIDITY ON MINE WORKERS 
 
 The mean annual underground temperature of the mines of the United 
 States is probably about 10 more than that of the surface, and is between 
 60 and 65 F. The causes making for this increase in temperature are the heat 
 given off by men and animals, by the burning of lamps, by the oxidation of 
 animal and vegetable substances (as the decay of timber), by the slow oxidation 
 of the coal, by gob fires whether active or smoldering, by the detonation of 
 explosives, and by the interior heat of the earth. In deep mines, the effect 
 of increasing heat with increasing depth is of prime importance in raising 
 underground temperatures. Below the level of no annual variation which, in 
 temperate climates is some 60 ft. below the surface, the temperature increases 
 at a rate of from 1 F. in 100 ft. to 1 F. in 60 ft., or about 1 F. for each 80 ft. 
 of descent. A mine 1,000 ft. deep in a region as western Pennsylvania and 
 Ohio, where the mean annual temperature is about 55, may reasonably be 
 
 expected to have an average temperature of 55+ (""HQ ) = 67, about, 
 
 due to the interior heat of the earth alone. To this must be added an always 
 uncertain amount, perhaps as much as 2 to 3, for the heat arising from the 
 other causes named. 
 
 Whether the temperature of the ventilating current will be greater or less 
 than the temperature established by the preceding conditions depends on its 
 initial temperature and its velocity. Radiation from the side walls is constant 
 but slow and rapid currents of air will not absorb as much heat as those moving 
 slowly; consequently, at the face or in any tight place the temperature is 
 much, often 5 or 10, greater than on the entries where the air is circulating 
 freely. Haas found that in a certain mine entry 4,000 ft. long, over 30,000 
 B. T. U. a min. were radiated from the sides, which is equivalent to the heat 
 derived from burning more than 1 T. of coal a day. In regard to the initial 
 temperature of the air, Scholz found at certain mines in the Middle West that 
 during summer, when the temperature outside averages 85 F. for 24 hr., with a 
 maximum of 95 to 100, the mine temperatures fluctuated between 70 and 78 ; 
 and that during winter, with a temperature of 40 to 50 outside, the mine 
 temperatures ranged from 60 to 67, the exact temperature necessarily depend- 
 ing somewhat on the extent of the mine. As the average annual temperature 
 of the region in question cannot be far from 55, it would appear that at : 
 times (even in winter) the temperature of the mine is considerably above t 
 annual for the place. 
 
 As long as the mine air is dry, or relatively so, men can work m temperatures 
 as high as 90 and even 100 without much discomfort or impairment of health, 
 as the perspiration is rapidly absorbed by the air-currents. But it has been 
 shown that, regardless of the outside temperature and humidity, the return 
 air is usually saturated to the extent of 90% or more, except in the and regions 
 of the West, where the humidity may fall to 85%. Haldane states that in 
 still and moist air it is hardly possible for men to do continuous hard work at 
 temperatures of. 80 t-> 85 even when stripped to the waist. At temperatures 
 
874 VENTILATION OF MINES 
 
 above 90, by the wet bulb, it is only possible to work for short periods, and 
 it becomes increasingly difficult to remain in the place even without working. 
 Haldane found that at a temperature of 93 in still and saturated air and 
 doing practically no work, his temperature rose 5 in 2 hr. and was still rising 
 rapidly when he found it necessary to go out. 
 
 SAFETY AND OTHER LAMPS 
 PRINCIPLE AND ORIGIN OF SAFETY LAMPS 
 
 Description. In a safety lamp, the flame of the burning illuminant is iso- 
 lated from direct contact with the mine air by a wire gauze, or a glass and gauze 
 cylinder, which is closed at the top where it is covered by a hood to which is 
 attached a ring or hook for carrying. As a further means of isolating the flame, 
 there may be two or more gauzes with an air space between each, and in prac- 
 tically all lamps the outer gauze is surrounded by a shield, called a bonnet, 
 which is provided with perforations or slots. The various parts of the lamp 
 are securely held together by the necessary standards and screw, soldered, or 
 riveted joints. 
 
 Dates of Discovery. The principle of isolating the flame of the lamp was 
 evolved by Dr. William R. Clanny in the spring of 1813, although his, the first 
 safety lamp, did not receive its final and successful trial until Oct. 16, 1815. 
 The principle of the bonnet was demonstrated on Nov. 28, 1815, by George 
 Stephenson; and on Dec. 15 of the same year, Sir Humphrey Davy announced 
 the use of the wire gauze. 
 
 Principles of the Safety Lamp. Although the last to be made public, the 
 principle discovered by Davy is the first in importance. This principle is that, 
 while a wire gauze of fine mesh entirely surrounding the flame will permit the 
 free entrance of air within the lamp, yet in its outward passage through the 
 gauze the burning gas is broken up into a series of fine jets and is so reduced 
 in temperature by the cool metal that its flame is extinguished and, hence, 
 cannot ignite firedamp mixtures outside the lamp. 
 
 In Stephenson's lamp, the_ burning gas was extinguished not by a cool 
 metal gauze, but by bringing it in contact with the inert products of combustion 
 that were held in the upper part of the lamp between the bonnet and the gauze. 
 While, in modern lamps the bonnet plays in a greater or less degree the part 
 for which it was originally intended, its chief use is to prevent the direct impact 
 against the gauze of air-currents of high velocity which might extinguish the 
 lamp or, what is more dangerous, might force the flame against or through 
 the gauze and thus cause an explosion. When the blanketing effect of the 
 original bonnet is desired, it is now generally accomplished through the use of 
 double or triple gauzes as in the Marsaut lamp. 
 
 Safety lamps are not absolutely safe in the sense that they may be burned 
 indefinitely in explosive mixtures of gas and air. In comparison with the 
 unprotected candles that they replaced or with modern open lights, they are 
 relatively safe in that the warning of the presence of a dangerous amount of 
 gas afforded by its burning within the lamp, gives the miner time to withdraw 
 before an explosion takes place. 
 
 Early Classification of Safety Lamps. Safety lamps were formerly divided 
 into two general classes, those designed for testing for gas and those intended 
 for working lamps, the construction of the former being such that they were 
 the more sensitive to gas. This distinction in usage and construction is now 
 rarely made, and at any particular mine the same kind of lamp is commonly 
 used by fireboss and miner alike. The reason for this is that none but special 
 lamps in the hands of skilled observers can detect the less than 1 % of gas that 
 is dangerous in the presence of explosive coal dust. Such being the case, there 
 is nothing to be gained in providing a fireboss with a dangerous lamp (all sen- 
 sitive lamps are unsafe) t9 detect 2.5% of gas when a safe lamp will detect, 
 say, 3%; as these proportions of gas are equally dangerous when coal dust is 
 present and equally harmless when it is not. 
 
 Approved Safety Lamps. An approved safety lamp possesses those features 
 that a mining department or legislature declares essential in lamps to be used 
 within its jurisdiction. The features considered essential vary, but both here 
 and in Europe, to be approved, a lamp must have a bonnet. The Davy lamp, 
 not being safe with or without a bonnet, is not permitted in Europe, but is 
 allowed in a few American states for gas testing, although the number of states 
 permitting it is decreasing. 
 
VENTILATION OF MINES 875 
 
 SAFETY-LAMP CONSTRUCTION 
 
 Specifications. Mr. J. W. Paul sums up the structural requirements of 
 safety lamps as follows: 
 
 1. The framework should be rigid and well made so that it will not get 
 out of shape when roughly handled; 
 
 2. If the lamp has a glass chimney, the upright rods (standards) should 
 be of such number and so spaced that a straightedge, or ruler, placed against 
 any two adjacent rods will not touch the glass; 
 
 3. If a lamp has no bonnet, the gauze should be protected with rods in 
 the same manner as the chimney, as indicated in 2; 
 
 4. The lock should be such as will require, .when locked, a special device 
 for unlocking; 
 
 5. The glass chimney should have a smooth and even wall throughout, 
 should be of the best quality, and should have its ends ground truly parallel 
 and at right angles to the axis of the chimney. The chimney should bear the 
 trade-mark of the manufacturer; 
 
 6. When the lamp is assembled there should be no openings between the 
 outside and the interior of the lamp except those in the gauze or other heat- 
 absorbing device, such as a perforated plate or cylinder in which the size of 
 the perforations corresponds with that of the gauze openings; 
 
 7. The handle of the lamp should be either an open ring or a hook, strongly 
 made and not easily bent in the hand; 
 
 8. The construction of the lamp should be such that its parts are made 
 in standard uniform sizes and fit so intimately that should any part be omitted 
 in assembling its absence would be easily detected by the most casual inspection ; 
 
 9. There should be an expansion ring or equivalent device used with the 
 glass chimney so that the chimney when heated can expand without breaking 
 any part of the lamp;- 
 
 10. In the selection of a safety lamp, carefully examine each of the dis- 
 assembled parts to ascertain defects or improper construction; if any such is 
 discovered, the entire lamp should be rejected. 
 
 Design of Safety Lamps. As pointed out by Hughes, Marsaut and others 
 have shown that a certain relation should exist between the volume contained 
 within a lamp and the gauze surface open for the escape of the products of 
 combustion resulting from an internal explosion, as experiments have proved 
 that the ignitions of explosive mixtures outside the lamp by explosions within 
 it become less frequent as the open surface of the gauze is enlarged. 
 
 Marsaut also proved that: (1) A lamp of small diameter (such as a Davy) 
 does not readily pass an explosion, as the volume of gas that can be exploded 
 is insignificant. (2) A lamp without a glass is more secure against the effects 
 of internal explosions than a lamp with a glass cylinder, as the latter confines 
 the gases at the time of an explosion and acts like a cannon; it is, therefore, 
 advisable to reduce both the height and the diameter of the glass. (3) A wire 
 gauze of conical shape is more secure against the transmission of internal 
 explosions than is one of cylindrical shape and of the same capacity. (4) Gases 
 resulting from combustion play, a certain part in preventing external explo- 
 sions and it might, therefore, not be advisable to guide them by a chimney. 
 (5) A descending current of feed-air prevents the filling up of glass lamps with 
 an explosive mixture, and occasions the formation of an inexplosive and elastic 
 cushion at the bottom of the lamp. 
 
 Materials of Construction. With the exception of the gauze and glass, 
 the various parts of safety lamps are made of brass or, where lightness is 
 required, of aluminum or magnalium. Where iron enters into the construc- 
 tion, it is usually in the standards and hood. 
 
 Safety-Lamp Gauzes. The main gauze of safety lamps is of 28 mesh; 
 that is, there are 28 openings in 1 lin. in. or 784 openings in 1 sq. in. If made 
 of No. 28 (B. W. G.) wire .014 in. in diameter as is usual, 1 sq. in. of the gauze 
 will be about two-thirds (.6151 sq. in.) metal and one-third (.3849 sq. in.) 
 openings. As exceptions to the use of this standard gauze, those in the Marsaut 
 and Chesneau lamps have 934 and 1,264 openings per sq. in., respectively. 
 
 Gauzes are commonly made of iron wire, although copper is sometimes 
 used. The latter is rather more durable than iron as it does not rust or burn 
 out so quickly, but it becomes hot and passes the flame sooner than iron as it 
 has a higher specific heat. 
 
 The gauze cylinder must not exceed a certain size, which Davy fixed m his 
 original lamp as 2 in. in diameter and 7 in. high (contents 22 cu. in.), otherwise 
 the burning of the large volume of gas within it will heat the gauze, and par- 
 
876 VENTILATION OF MINES 
 
 ticularly the top, to a point where it will no longer cool the flame sufficiently 
 to prevent its igniting gas outside the lamp. In modern lamps, the diameter 
 of the gauze is about the same as that of the original Davy, but its height is 
 less and varies from 4 to 5 in., as the lower part is replaced with glass. In 
 lamps built on the Eloin principle, that is in those lamps that take air in 
 through ports below the flame and are thence known as underfeed or under- 
 draft lamps, as all the gauze is available for the discharge of the combustion 
 products, it may be made much smaller than in a lamp of ordinary construc- 
 tion. The Ashworth-Hepplewhite-Gray lamp, Fig. 1, e, page 885, is an example 
 of a lamp with a relatively small gauze. 
 
 As the top of the gauze receives the full effects of the flame, it is often 
 reinforced by what is known as a gauze cap or smoke gauze. This consists of a 
 cylinder of standard gauze closed at the top, which fits snugly over the main 
 gauze for about one- third its length. The upper part of this cap is sometimes 
 crimped or indented so that it may not be pushed too far down upon the main 
 gauze as it is desirable to leave a small space between the tops of the two. 
 
 The gauze of the early lamps was always cylindrical, but in many modern 
 lamps it is in the form of a truncated cone; a shape commonly followed where 
 there is more than one gauze. 
 
 Safety Lamp Glasses. Although Clanny and Stephenson used glass in 
 front of their original (1815) lamps to increase the light-giving power, the pres- 
 ent form of safety lamp in which a glass cylinder entirely surrounds the flame 
 and is surmounted by a cylinder of gauze is due to Dr. Clanny who appears 
 to have combined ideas original with both Davy and Stephenson. In a gen- 
 eral way, modern lamps may be said to be Davy lamps in which the lower por - 
 tion of the gauze cylinder is replaced with one of glass; or to be Stephenson 
 lamps, the perforated metal cylinder being replaced by one of gauze. 
 
 Glasses are commonly cylindrical, but in the Ashworth-Hepplewhite-Gray 
 lamp they have the shape of an upward-tapering truncated cone. This form 
 allows the upward diffusion of the light, at least in pary, and thus permits of 
 a closer inspection of the roof without having recourse to the very dangerous 
 practice of turning the lamp on one side. t 
 
 Multiple Gauzes. Some safety lamps are made with two or even three 
 gauzes, one within the other, with a small air space between; and lamps so 
 made are known as multiple-gauze lamps. The inner gauze is always conical 
 but the outer gauze may be cylindrical or conical with a little more slope than 
 the inner one so that there may be more air space between the gauzes at the top 
 than at the bottom. The intention of multiple gauzes is to interpose one or 
 more curtains or screens of inert gases between the flame of any gas burning 
 in the lamp and the outside air. These screens are formed by the retention 
 of the products of combustion in the spaces between the several gauzes. The 
 multiple gauze is the modern development of the original Stephenson prin- 
 ciple of preventing the outward passage of the flame by smothering it in inert 
 gases, and adds greatly to the safety of the lamp. 
 
 The effect of these gas screens is to impede the free upward and outward 
 passage of the products of combustion simultaneously reducing the amount of 
 oxygen admitted to the flame and the amount of oil burned in a given time. In 
 other words, they reduce the draft and thus increase the tendency of the lamp 
 to smoke and diminish the illuminating power. The reduction in illuminating 
 power increases with the number of gauzes. Thus, the Marsaut lamp, Fig. 1, d, 
 page 885, with three gauzes has an illuminating power 20 to 25% less than 
 the same lamp with two gauzes. In lamps admitting air on the Eloin principle 
 and which, in consequence, have a strong natural draft, the reduction in 
 illuminating power through the use of multiple gauzes is considerably less 
 than in lamps drafted in the ordinary way. With multiple gauzes, the gauze 
 cap (smoke gauze) is rarely used. 
 
 Safety-Lamp Bonnets. A bonnet consists > of a metal cylinder entirely sur- 
 rounding the gauze of the safety lamp, and is intended to prevent the direct 
 impact of air-currents of high velocity against the gauze, as explained under 
 Principles of the Safety Lamp. The surface of the bonnet is usually smooth, 
 but in the Wolfe lamp, Fig. 1, /, page 885, it is corrugated. The bonnet is 
 perforated or slotted with a varying number of holes arranged in various ways 
 and which are designed to permit access of air to and egress of combustion 
 products from the lamp. In some bonnets, the slots are indented on one side 
 or arranged on the corrugations (Wolfe lamp) so that the air enters tangentially 
 and not directly against the gauze. In the early Davy lamp, the screening 
 effect of the bonnet was secured, but only in part, by the use of a semicircular 
 shield that could be slipped in front of the flame when moving against the air. 
 
VENTILATION OF^ MINES 877 
 
 The fewer the perforations or slots, the greater the blanketing effect of 
 the bonnet and the more nearly it approaches a series of gauzes in its influence 
 on the circulation of air within the lamp and on its light-giving power. Lamps 
 with tight-fitting bonnets are easily extinguished when exposed in high per- 
 centages of gas, the flame being smothered by the large volume of combustion 
 products held back by the imperfect circulation. 
 
 In the Ash worth-Hepplewhite- Gray lamp, a double bonnet is used, and 
 double- and triple-gauze lamps are always bonneted for general use and com- 
 monly so when employed for gas testing. f 
 
 Circulation of Air in Safety Lamps. Air is admitted to safety lamps in three 
 ways. 
 
 In the Davy lamp, Fig. 1, a, page 885, the air enters at the bottom of the 
 gauze, which extends below the top of the wick tube, and the products of 
 combustion pass upwards and out through the top of the gauze. 
 
 In underdraft lamps (Eloin principle) as in Fig. 1, e, page 885, the air 
 enters below the flame through gauze-protected ports, and the products of 
 combustion follow the same course as in the Davy lamp. 
 
 In the majority of lamps, Fig. 1, b, c, and d, page 885, the air enters at the 
 base of the gauze above the glass and must pass downwards to the flame. 
 
 Lamps of the first two classes, in which the air follows what may be called 
 the natural course (as in an ordinary chimney) are sensitive to small amounts 
 of gas, are apt to flame readily, are adapted to gas testing but not to general 
 use, and are unsafe in air-currents of any but very low velocity unless provided 
 with bonnets or multiple gauzes. When so equipped, underfed lamps are ex- 
 cellent for general use, but are not so sensitive to gas as otherwise. 
 
 In the third class, the air in passing down to the lamp flame conflicts with 
 the ascending products of combustion with the formation of eddy currents, 
 which may cause the lamp to flicker and smoke, thus making it less sensitive 
 to gas and decreasing its illuminating power. In the Mueseler lamp, Fig. 1, c, 
 page 885, the flame is surmounted with a conical sheet-iron chimney, which 
 increases the draft and causes the air to circulate in a natural course. Follow- 
 ing the arrows, the air enters through the base of the gauze, passes down beside 
 the chimney to the wick, and the products of combustion pass up the chimney 
 and thence out through the upper part of the gauze (see Mueseler lamp). It 
 should be noted that a bonnet or a series of multiple gauzes interferes with the 
 rapidity but not with the direction of air circulation. 
 
 In order to detect thin layers of gas near the roof without the dangerous 
 necessity of turning the lamp on one side, of waving it to and fro, or of brushing 
 the top air down upon it with a cap, several special constructions are employed. 
 In the Ashworth-Hepplewhite-Gray lamp, the standards are hollow and air 
 can, when needed, be drawn down through them by closing the regular entrance 
 ports at the base of the lamp. A device for the same purpose that may be 
 attached to ordinary lamps consists of an L-shaped pipe about in. in diameter, 
 the short arm of which is attached to a special port in the lamp below the flame 
 while the long arm projects upwards into the gas. An improvement on the 
 preceding is used by Mr. Joseph Smith, general superintendent of the Stag 
 Canon Fuel Co., at Dawson, N. Mex. The device consists of a small, double- 
 acting pump the discharge end of which may be directly connected to the 
 base of any of the standard forms of safety lamps. By means of a number of 
 5-ft. lengths of f-in. gas pipe which may be screwed together until their com- 
 bined length is sufficient to reach the top of the highest falls and then attached 
 to the suction end of the pump, samples of air from otherwise inaccessible 
 places may be drawn into and through the lamp. For the same purpose 
 Sir William Garforth uses a rubber bulb with a strong metal nozzle. In the 
 base of the safety lamp is a tube with a self-closing valve. When testing for gas, 
 the bulb is placed in a cavity in the roof or other place where gas is suspected, 
 and is filled with the firedamp by compression in the usual way. The gas is pre- 
 vented from escaping by holding a finger over the nozzle and the lamp is taken to 
 some safe place where the end of the buib is inserted in the tube in the lamp, 
 opening the valve in so doing, when the gas may be squeezed upon the flame. 
 
 Wick Tubes, Wicks, Etc. The wick tube of a lamp may be round or flat. 
 When flat, one side is commonly made with one or more grooves to reduce the 
 fricti9n when the wick is adjusted in height and to provide a space for the cir- 
 culation of the air that the oil may ascend. The top of the tube should be 
 set about in. above the base of the glass for, if set too low, the shadow cast 
 on the ground by the body of the lamp is increased; and if set too high, the 
 amount of light diffused upwards is decreased. In many lamps, m one side of 
 the wick tube is a narrow slot in which the point of the picker is inserted to 
 
878 VENTILATION OF MINES 
 
 adjust the wick. This slot should be as narrow and as short as possible, other- 
 wise the oil will be vaporized and possibly ignited at the side rather than at 
 the top of the tube. In some lamps, the wick remains stationary and the 
 height of the flame is adjusted by raising or lowering a sheath that fits over the 
 wick tube; and, in other lamps, the wick is contained in an adjustable sheath 
 sliding within a fixed wick tube. In either case, the sheath is adjusted by 
 turning a screw attached to the bottom of a shaft passing through the oil 
 chamber. 
 
 Wicks are round 05 flat to correspond with the wick tube. They are made 
 of strands of cotton yarn very lightly twisted or plaited (flat wicks) to form a 
 bulk but slightly greater than the inside dimensions of the wick tube. Wicking 
 should be thoroughly dried before use, as moisture impedes the flow of oil and 
 reduces the illuminating power of the flame. 
 
 The picker used for cleaning the wick should sweep the entire top of the 
 wick tube with a motion somewhat inclined to the horizontal. 
 
 Igniters, or Relighters, for Safety Lamps. An igniter is a device for relight- 
 ing a safety lamp without opening it. In the igniter commonly used with the 
 Wolf lamp, the match is a narrow strip of paraffined paper in which are inserted 
 small lumps of fulminate at intervals of about % in. The coiled match is 
 contained in a flat metal box inserted in a special receptacle in the bowl. The 
 igniter proper consists of a piece of spring steel doubled on itself, one end of 
 which is provided with fine teeth to engage the match. By raising the rod 
 attached to the igniter, the teeth catch in the match and push its end slightly 
 above the level of the wick. When the rod is suddenly pulled downwards by 
 means of the head at the bottom of the oil chamber, the teeth of the igniter 
 explode one of the fulminate caps thus igniting the match, which burns until 
 level with the top of the wick tube. In a similar igniter, a friction match is 
 held against a feed-screw by a steel spring. The upper part of the feed-screw 
 carries a wheel with sharp teeth that strike against and ignite the match when 
 a button on the lower end of the feed-screw is turned. In other igniters, 
 phosphorus is used in place of fulminate to light the match. 
 
 Electric relighters are used in some standard lamps. Where light oils, as 
 naptha, giving off vapors are burned, a low-tension current is used to heat 
 to incandescence a platinum wire placed immediately over the wick tube. 
 For the heavier colza and seal oils, a series of sparks produced by a high-tension 
 current are passed over the wick tube. The current is taken into the lamp 
 through a carefully insulated conductor passing through the bowl, the body of 
 the lamp furnishing the return circuit. (See Protector Lamp and Hailwood 
 Lamp.) 
 
 The property of alloys of cerium of sparking when brushed by a milled 
 wheel has been taken advantage of in the design of safety-lamp igniters. The 
 alloy commonly employed is one of iron and cerium which, when struck by the 
 milled wheel after the manner of a flint against steel, often throws off unburned 
 particles of metal, which may lodge against the gauze. If these are subse- 
 quently ignited, sufficient heat may be developed to fire the gas outside the 
 lamp. To overcome this difficulty, the American Safety Lamp Co. uses an 
 alloy of cerium and magnesium and a positive igniting device. In the older 
 igniters of this type, a series of small sparks are struck by turning the milled 
 wheel until the lamp is lit. In the improvement, a spring attached to the 
 igniter is compressed by turning the head of a stem projecting below the bowl. 
 When the tension of the spring reaches a certain amount, the wheel is released 
 and revolves with such rapidity that the spark is practically a continuous 
 flame, which ignites the wick at once. 
 
 Many have advised against the relighting of lamps in the presence of 
 explosive amounts of gas, and particularly so if the lamp burns naphtha because, 
 in a few seconds after being extinguished, the gauze may become filled with 
 highly combustible vapors that may explode and pass the flame when the 
 igniter is applied. The long series of tests made with the Wolf lamp go to show 
 that this claim is not well founded. Others object to placing an igniting 
 device in the hands of miners and irresponsible boys and hold that an electric 
 relighter, which can only be applied at a lamp station, is to be preferred to 
 other types. 
 
 Locks for Safety Lamps. Locks for safety lamps are made on one of three 
 general plans. 
 
 1. The lamp may be locked by a screw pin, catch, or similar device that 
 may be opened by a key. While locks of this type cannot be opened acci- 
 dently, they may be readily unlocked by any one even without a key. This 
 form of lock is now rarely used. 
 
VENTILATION OF MINES 879 
 
 2. The lock may be constructed so that it may be opened by any one, but 
 any attempt to do so extinguishes the light or is revealed in some way. 
 
 3. The lamp may be locked by a device operated by electricity or com- 
 pressed air, and can only be opened by means of special appliances kept in the 
 lamp room at the surface or at a relighting station in the mine. 
 
 To the second class belongs the lead-plug lock. The lower part of the 
 lamp is encircled with a movable ring to which is attached a hinged lock that 
 drops over a projecting lug on the bowl. A lead plug is inserted in the lug and 
 is punched flat; the punch used for the purpose stamping the latter or date 
 for the day on the lead. 
 
 In the "Protector" lock, the wick tube is surrounded by a close-fitting 
 collar of the same height held in place by a steel pin (lock bar) fastened by a 
 piece of spring steel. In order to remove the lock bar, it is necessary to unscrew 
 the bowl to reach the spring, but in so doing the wick tube (and wick) is drawn 
 down through the collar and the lamp extinguished. In other locks of this 
 class, the unscrewing of the bowl brings into action a cap, or extinguisher, that 
 smothers the flame. 
 
 In the third class are several magnetic and compressed-air locks. In the 
 Wolf lock, the tooth on the end of a pawl pivoted at its center is forced by a 
 spring into a socket in the bowl when the latter is screwed into place. To 
 unlock the lamp, the poles of a powerful horseshoe magnet are applied to poles 
 in the base ring of the lamp. The current passes through the spring into 
 the pawl, which causes the end opposite the tooth to move inwards thus 
 releasing the tooth from its socket and permitting the bowl to be unscrewed. 
 When the lamp is released from the magnet, the spring forces the tooth into 
 its original position so that when the bowl is screwed into place, it is locked 
 automatically. 
 
 In the Hailwood lock, the ring holding the glass is provided on the under 
 side with ratchet teeth into which engages an iron lock-bolt, which is held in 
 an upright position by a strong spring resting on a movable iron guard plug, 
 the latter resting on a solid shoulder formed in a recess in the bowl. To 
 unlock the lamp, the nose of an electromagnet in which a current is generated 
 by operating a treadle is placed against the guard plug and is pressed upwards. 
 As soon as the plug comes in contact with the lock-bolt, it secures a strong 
 magnetic hold upon it. Depressing the pedal draws down the guard plug and 
 with it the lock-bolt, releasing it from the teeth in the glass ring and per- 
 mitting the unscrewing of the bowl. The lamp may be locked automatically by 
 simply screwing up the bowl. 
 
 To open the ordinary air lock, the suction end of a small air pump is applied 
 to the mouth of the recess in which the lock-bolt fits. On operating the pump 
 by a treadle, the vacuum created draws the bolt outwards against the pressure 
 of the spring holding it in place, and permits unscrewing the _ bowl. The 
 Hailwood air-lock differs from the preceding in that the positive pressure 
 (not suction, or a vacuum) of compressed air is used to force back the bolt. 
 In this lock, the spring holding the bolt in place may be made to withstand a 
 pressure as high as 250 Ib. so that the pressure of the air in the power mains 
 is not sufficient to open the lamp. 
 
 Oils for Safety Lamps. Because of their colorless sensitive flame, alcohol 
 and even hydrogen are burned in some special forms of safety lamps designed 
 for the determina^n of small percentages of methane. Ordinarily, some kind 
 of illuminating oil is used both in working and in testing lamps. 
 
 The principal illuminating oils of vegetable origin are pressed from the 
 seeds of the cotton and rape plants, the crude oil being treated with acid, 
 washed, etc., to remove various mucilaginous substances that would otherwise 
 cake on the wick. The purified or refined oils are commonly known as winter 
 oils as their temperature of solidification is much below that of the crude 
 
 Refined cottonseed oil has a specific gravity between .922 and .926 and 
 solidifies at from about 33 to 50 F. 
 
 Rape, or as otherwise called, colza oil is extracted from the seeds of several 
 species of the genus Brassica of the Cruciferas, or mustard, family. These 
 plants are extensively cultivated in all parts of the world, except in the United 
 States, for the illuminating oils contained in them. The species commonly 
 cultivated are Brassica napus, or rape, the B. campestris, or rutabaga, and, to 
 a less extent, the B. oleracea, or cabbage. The oils extracted from these plants 
 differ slightly in their properties but are all sold as rape or colza oil, the latte 
 name being derived from the word cole, or kohl, meaning cabbage. Colza 
 oil has a specific gravity of .913 to .915 and solidifies at about 15 F., con- 
 
880 
 
 VENTILATION OF MINES 
 
 siderably below cottonseed oil. The illuminating power of vegetable oils is 
 low and may be increased and the incrustation of the wick decreased by the 
 addition of one-half their volume of kerosene (ordinary coal oil). 
 
 Whale and seal oil extracted from the blubber of the respective animals 
 are largely used in safety lamps, but not to the same extent as lard oils. Animal 
 oils, like vegetable oils, do not possess great illuminating power, although this 
 depends on their purity. The British Accidents in Mines Commission recom- 
 mends the use of a mixture of one-third refined petroleum (kerosene) and 
 two-thirds rape or seal oil as being cheaper and having the same illuminating 
 power as the best colza oil while not forming such a hard cake or crust on the 
 wick. The Commission considered seal as superior to colza oil in maintaining 
 a more uniform height of flame for a longer time without retrimming. 
 
 Of the distillation products of petroleum, the so-called light oils are largely 
 used in safety lamps because of their high illuminating power. The oils used 
 and the temperatures at which they are distilled are, gasoline below 140 F., 
 naphtha between 140 and 230 F., and benzine between 230 and 302 F.; 
 kerosene, which is distilled between 302 and 572 F., is used only when mixed 
 with non-volatile animal and vegetable oils. 
 
 As these oils are highly volatile, their volatility decreasing in the order 
 of the temperatures at which they are distilled, their fumes have been con- 
 sidered as a source of danger, but this has been disproved by long and safe 
 use of lamps burning naphtha and by the researches of Watteyne and Stassart 
 in Belgium. These gentlemen found that when benzene was used, there was 
 a slightly greater tendency of the lamps to heat and, in some cases, of the 
 glasses to crack, but these in no way involved a passing of the flame or a 
 deterioration of the lamp. Their photometric observations showed that the 
 average illumination of the best oil (animal or vegetable) fed lamp was but 
 .4 candlepower as opposed to .87 candlepower of the benzene-burning lamp 
 with underfeed draft. Special tests have shown that the Wolfe lamp burning 
 naphtha or benzene is safe under any conditions of use; thus, when the oil 
 vessel of a burning lamp was heated to 180 F., the lamp was extinguished 
 and without danger. 
 
 The illuminating power of safety-lamp oils varies so widely according to the 
 purity of the oil, the kind of lamp used, the conditions of burning, etc., that it is 
 not possible to give exact figures as to their relative light-giving value. The 
 following figures are average of many determinations of the light power of 
 various oils burned in a Clanny lamp when referred to a standard candle 
 burning 120 grains of spermaceti an hour: Standard candle, 1.00; English 
 rape oil, .32; best quality colza oil, .47; seal oil, .35; two parts of rape oil and 
 one of kerosene, .30; various grades and makes of so-called safety lamps oils, 
 .51, .43, and .48, respectively. 
 
 Illuminating Power of Safety Lamps. The illuminating power of a safety 
 lamp depends on the illuminant used and on the construction of the lamp. 
 As its flame is not surrounded with glass, the Davy gives less light than any 
 other lamp except the Stephenson and so (aside from being unsafe) is unsuited 
 for working purposes. 
 
 RELATIVE ILLUMINATING POWER OF SAFETY LAMPS 
 
 Lamp 
 
 Candle- 
 power 
 
 Lamp 
 
 Candle- 
 power 
 
 Ashworth-Hepplewhite-Gray 
 Clanny 
 
 .75 
 34 
 
 Hailwood, burning naphtha 
 
 1.00 
 45 
 
 Davy, common 
 Davy, Jack 
 
 .15 
 .08 
 
 Marsaut, two gauzes 
 Mueseler, Belgian 
 
 .55 
 .36 
 
 Davy, in case 
 Evan Thomas 
 
 .16 
 .43 
 
 Mueseler, English 
 Stephenson 
 
 .32 
 .10 
 
 Hailwood, burning oil 
 
 .67 
 
 Wolf, burning naphtha .... 
 
 1.00 
 
 A free circulation of air, which is best secured by an underfeed draft, 
 insures a better supply of oxygen, removes the combustion products more 
 quickly, and thus increases the lighting power of the lamp. Bonnets and 
 multiple gauzes (see the two types of Marsaut lamp in the table) while increas- 
 ing the safety of the lamp, reduce its illuminating power through impeding 
 the circulation. 
 
VENTILATION OF MINES 881 
 
 The table gives the relative illuminating power of various safety lamps 
 referred to a standard candle (burning 120 gr. of spermaceti an hour) as unity. 
 The oils used were mostly colza or seal oil, and the results are averages only 
 and are not to be taken as exact and absolute. 
 
 According to Hughes, Marsaut found that the illuminating power of a lamp 
 when the oil chamber is made of brass is but 70% of that of the same lamp 
 when the chamber is made of iron, which appears to be due to the greater 
 heat conductivity of the brass by reason of which the lamp bottom gets much 
 hotter than if it was made of iron and the oil becomes viscous and will not flow. 
 
 TESTING FOR METHANE 
 
 Desirable Features in Lamps for Testing and for General Use. The fol- 
 lowing are considered desirable features in a safety lamp for gas testing: 
 
 1. The flame should be clear, steady, and free from smoke, that the gas 
 cap may be more plainly observed and, to make the indications afforded by 
 the cap of value, atmospheric conditions should be the same within and without 
 the lamp. Alcohol and naphtha, particularly when burned in lamps with 
 underfeed draft, afford a better and less smoky flame than animal or vegetable 
 oils burned in a lamp drafted above the glass in the ordinary way, see under 
 Circulation of Air and Oils for Safety Lamps. 
 
 2. A construction such that when the lamp is exposed to air-currents of 
 high velocity, the flame will not be blown against or through the gauze to its 
 injury or cause the ignition of gas outside the lamp. This is secured through 
 the use of bonnets, multiple gauzes, etc. 
 
 3. There should be no bright surface behind the flame, reflections from 
 which may interfere with the visibility of the cap. Secured by giving the metal 
 parts a dull finish, careful selection of the glass, etc. 
 
 4. Ability to detect thin layers of gas near the roof, see Circulation of 
 Air in Safety Lamps. 
 
 5. A scale for measuring the height of a flame cap so as to more accurately 
 determine the percentage of gas in the air. The use of the scale is based on the 
 assumption that a cap of given height always corresponds to a definite per- 
 centage of gas in the air. While this may be true in the laboratory where the 
 scale is adjusted to flames obtained by burning known proportions of pure 
 methane in pure air, it is rarely, if ever, true in the mine where deficiency of 
 
 .oxygen, the presence of blackdamp and coal dust, and varying conditions of 
 pressure, temperature, and humidity tend to alter the cap for the same per- 
 centage of gas in the air. That is, a cap, say, 1 in. in height obtained in the 
 mine indicates a different per cent, of gas, and usually a greater one, than the 
 same cap in the laboratory. Further, the conditions within the lamp where 
 the air is more or less mixed with combustion products cannot be the same as 
 in the mine. 
 
 The following are essential features in lamps for general use, that is, in 
 working lamps: 
 
 1. The lamp should give the maximum light consistent with safety; this 
 is secured by the use of the proper illuminant and construction. 
 
 2. The lamp should be safe in air-currents of high velocity; this is secured 
 through the use of bonnets, multiple gauzes, etc. 
 
 3. The lamp should be strong in all its parts so that it may not be easily 
 broken through careless handling or in minor accidents, and should be simple 
 in construction so that it can easily be taken apart for cleaning and as easily 
 assembled when it is done. 
 
 4. The lamp should be capable of being securely locked so that it cannot 
 be opened by unauthorized persons or at any but some appointed place. 
 
 5. The lamp should not be as sensitive to gas as one used for testing. A 
 lamp that rapidly fills with flame in the presence of explosive mixtures 
 and must be as rapidly removed therefrom to prevent the passage of the flame 
 through the gauze or the extinction of the light, requires constant watching, 
 and is unfitted for a working lamp. The same construction that makes a lamp 
 safe in strong air-currents also makes it less sensitive to gas. 
 
 6. The lamp should diffuse light upwards so that the roof may be inspected 
 without turning the lamp on one side. 
 
 7. The lamp should be provided with an appliance for relighting without 
 opening it. The tests of Watteyne and Stassart showed that the explosion 
 relighter causes external explosions in rare instances, but that the phosphorus 
 igniter does not. It has been demonstrated that, as long as the glass is not 
 broken, the gauze punctured, etc., internal relighting is safe provided a proper 
 igniter is used. 
 
 56 
 
882 
 
 VENTILATION OF MINES 
 
 Testing tor Gas. When a safety lamp is brought into an atmosphere con- 
 taining methane, the presence of the gas is indicated by a bluish halo or cap 
 surrounding and surmounting the lamp flame. The ordinary lighting flame 
 of the lamp is rarely used in gas testing as it does not show a cap but merely 
 an increase in length in the presence of methane, and this increase cannot well 
 be measured unless the length of the flame in fresh air is first observed. The 
 same is true of what is sometimes called an intermediate flame about one-half 
 the height of the ordinary flame. 
 
 The flame commonly used for testing is made by screwing down the wick 
 until the yellow color of the wick has disappeared and nothing but a faint 
 blue cap remains on the burner. This is sometimes spoken of as a cap, cap- 
 flame, blue cap, testing flame, non-luminous flame, etc., and is from | to J in. 
 high, depending on the illuminant used, type of lamp, etc. 
 
 A blue cap, wholly or partially visible, and which should not be confused 
 with that due to gas, is frequently seen above the testing flame. This is 
 commonly called the fuel cap, and has been supposed to be due to the burning 
 of the volatile products of the lamp fuel driven off by the heat. Briggs, how- 
 ever, has shown that the fuel cap is the outer of the three layers or parts into 
 which any flame may be divided, occurs with solid as well as with liquid fuels, 
 and that it is intensified only by the vapors given off when the lamp is hot. 
 The fuel cap appears as a halo and, in order not to be deceived by it, the 
 observer should become accustomed to its appearance in fresh air. 
 
 To test for methane, hold the lamp in an upright position with one hand and 
 with the other screening the eyes from the body of the flame, slowly raise the 
 lamp toward the roof and watch closely for the first appearance of the cap. 
 When this is observed, the lamp should be promptly but cautiously drawn 
 down, while the distance of the lamp from the roof is noted; this gives the 
 depth of the gas in the place. When sufficient gas is present, or the lamp is 
 raised too quickly, the entire gauze sometimes fills with flame; a condition 
 known as faming. When this occurs, the lamp must be handled with great 
 care. An explosion of gas within the lamp is very likely to take place when 
 it is withdrawn from a body of gas into fresh air, and this may be communi- 
 cated to the outside gas unless the lamp is properly made. Bonneted lamps are 
 more liable to internal explosions than those not bonneted, but, owing to the 
 restricted circulation in the lamp, are far less likely to pass the flame to the 
 outside. 
 
 Height of Gas Cap. With the same lamp, burning the same illuminant, 
 with the same wick, and using the same height of flame, as long as the air is 
 pure and is not contaminated with carbon dioxide or excess nitrogen, there 
 is a fixed height of cap for each per cent, of methane present. However, 
 if the lamp, illuminant, wick, or height of flame is changed, or if the propor- 
 tion of inert gases in the mine air is varied, there will be a change in the height 
 of the cap made by the same percentage of gas so that, unless all the condi- 
 tions are constant or are known, it is not possible to tell whether a cap of a 
 certain height is due to the presence of, say, 1 or 2.5% of methane. Prof. 
 G. R. Thompson, Leeds University, gives the following table for the heights 
 of gas caps in different lamps, using different oils, etc. 
 
 HEIGHT OF GAS CAPS IN DIFFERENT LAMPS 
 
 Lamp 
 .No. 
 
 Wick and Oil Used 
 
 Percentage of Gas 
 in Mixture 
 
 1 
 
 2 
 
 3 
 
 Height of Cap, 
 Inches 
 
 1 
 2 
 3 
 
 Circular wick, .23 in. in diameter, burning 
 paraffin oil 
 
 .200 
 
 .520 
 .175 
 
 .30 
 
 .67 
 .50 
 
 0.4 
 
 1.1 
 1.0 
 
 Flat wick, .65 in. wide, burning naphtha (boil- 
 ing point, 55C.) 
 
 Flat wick, .55 in. wide, burning colza oil 
 
 The following figure shows the height, in centimeters and in inches, of the 
 gas cap corresponding to various percentages of gas and pure air as observed 
 
VENTILATION OF MINES 883 
 
 in the naphtha-burning lamps now so generally used for testing and general 
 purposes. 
 
 The gas cap in lamps like the Davy of Clanny burning sperm or colza 
 oil are so very small and difficult to distinguish when the percentage of 
 methane is reduced to 2.5%, that it is considered impossible for the most 
 skilled observer to detect less than 2% of gas with these lamps, and 3% is 
 about the limit for the average man. For small percentages of methane the 
 naphtha flame is much more sensitive than the oil, and with it as little as 
 1 % of gas may be detected. 
 
 To avoid adjusting the flame in each working place, fire bosses should 
 carry a second lamp with normal flame or, better, may use a storage-battery 
 portable electric lamp. 
 
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 2% 3% 4% 
 
 CARE OF SAFETY LAMPS 
 
 Cleaning Lamps. The following suggestions in regard to cleaning standard 
 naphtha-burning safety lamps are selected from J. W. Paul. 
 
 1. Each workman should have his own lamp, marked with a distinctive 
 number corresponding to that on a hook or the lamp rack. When a lamp is 
 turned in at the end of a shift, if it is in bad condition or has been tampered 
 with, it should be set aside for later detailed examination. If the lamp is 
 returned in normal condition, it should be unlocked and the bowl, gauzes, 
 and globe loosened and hung on a rack. 
 
 2. All removable parts should be detached and the fount sent to the filling 
 station, which should be separated from the lamp room by fireproof parti- 
 tions with iron or steel drop doors. 
 
 3. The gauze should be brushed inside and out and blown, preferably with 
 compressed air, until all wires are clean, holes freed from dirt, etc. Gauzes 
 with broken wires, enlarged holes, etc., should be crushed and thrown aside. 
 New gauzes should be thoroughly burned to remove the grease in order to 
 prevent flaming on the outside in the presence of an explosive mixture of 
 gas and air. 
 
 4. The glass should be wiped with a damp and dried with a clean, dry 
 cloth until free from all oil or moisture. Gaskets should be whole, should 
 fit, and should be free from grit or dirt. 
 
 5. The bonnet should be brushed until free from soot or dust. 
 
 6. The lower-ring gauze of underdraft lamps should be brushed and if holes 
 or broken wires are found, should be discarded or sent to the repair shop. < 
 
 7. The igniter should be tested to see if it is in working order, whether it is 
 supplied with tape (match), and whether it fits in its receptacle "so that there 
 is no unnecessary opening from the outside to the inside of the lamp. 
 
 8. Only enough gasoline should be used to saturate the cotton in the bowl, 
 
884 VENTILATION OF MINES 
 
 and the outside thereof should be wiped clean. The use of special filling 
 tanks is to be recommended. Naphtha or gasoline of the best quality 
 should be used; its specific gravity should be 0.70 to 0.72. 
 
 9. Before the lamp is assembled, the picker should be in condition for use 
 and should not hang below the bottom of the bowl or it may be bent. 
 
 10. After the lamp has been assembled the wick should be lit, adjusted 
 to a low flame, and the tightness of the joints tested by blowing against 
 them; leakage will be shown by the wavering of the flame. Compressed- 
 air coils in which the lamp may be placed are recommended. 
 
 11. It is advisable to place the lighted lamp in a testing box containing 
 an explosive atmosphere. 
 
 Assembling Lamps. Some of the common errors made in assembling 
 lamps are: Leaving out one or both gaskets, or using broken gaskets; plac- 
 ing gaskets in underfed lamps so as to exclude the air from below; leaving 
 out one of the gauzes in double-gauze lamps; placing on top of the glass an 
 expansion ring designed to be placed below it; failing to screw up the bowl 
 sufficiently to make a tight fit between the glass globe and the gaskets; 
 leaving out the igniting device without plugging the stem hole; omitting the 
 deflection rings that prevent air from blowing directly into the lamp; omitting 
 the shield or bonnet; using a defective gauze. 
 
 Failure of Safety Lamps. Aside from want of atten^n to the precautions 
 noted under Assembling Lamps, other reasons for the failure of safety lamps, 
 that is, the ignition by the lamp of the gas outside it are: Exposure to air 
 currents of greater velocity than those for which the lamp was designed; 
 permitting the gas to burn within the lamp until the gauze is red hot and 
 its cooling property destroyed; allowing the lamp to smoke until the pores 
 of the gauze become clogged with soot which will heat and possibly burn, or 
 the coating of the gauze with oil, grease, or coal dust with the same result; 
 holding the lamp on one side so that the flame strikes upon and heats the 
 gauze; allowing the glass to be broken by water dropping on it or in any 
 other way; puncturing the gauze. 
 
 _ A little-recognized cause of lamp failure is the presence of fine and explo- 
 sive dust in the air. Dust fine enough to pass through the meshes of the 
 gauze may be ignited within the lamp, pass through the gauze and ignite 
 firedamp or dust mixtures outside the lamp. Ashworth found that a Davy 
 lamp, that would not cause an external explosion in 4.5% of gas when the 
 air was moving 370 ft. per min. and was free of dust, passed the flame and 
 caused an explosion in 10 sec. when only the ordinary amount of dust was 
 floating in the air. 
 
 Relighting Stations, Lamp Houses, Etc. In large mines it is customary to 
 have lamp stations with a man in attendance to see to the relighting, renewal, 
 etc., of the safety lamps. These stations are usually located at the mouth of 
 each principal entry and are the headquarters of the district fire boss when 
 not on his rounds. 
 
 Lamp houses, where safety lamps are received from and delivered to the 
 men and where they are cleaned, repaired, etc., vary in size and completeness 
 of equipment depending upon the number of lamps handled daily At 
 almost all mines it is customary to store the oil in a separate building or in a 
 fireproof room, pumping out the daily requirements into one or more filling 
 tanks in the lamp room proper. At large mines, the lamp room is fitted with 
 revolving brushes and a small air compressor for cleaning and testing lamps, 
 a gas testing box, etc. The system employed in handling lamps varies 
 widely. Generally the lamps are numbered and, where possible, the lamp 
 number and that of the miner's check correspond. Lamps are often turned 
 in merely by being hung on a hook with a number corresponding to that by 
 the lamp, to which they are returned by the lampman in time for the morning 
 shift. In other cases, the lamps are placed in separate compartments in a 
 large cabinet. The compartments are sometimes locked, each miner having 
 his own key, and commonly are open on the back or lamp room side so that 
 the lampmen may easily remove the lamps for cleaning and as easily return 
 them to the right place. Not infrequently, the lamps are handed out per- 
 sonally through a window in the fashion of ordinary supplies. 
 
 STANDARD TYPES OF SAFETY LAMPS 
 
 Davy Lamp. The Davy lamp (Fig. 1, a, page 885) consists of the usual 
 oil vessel, or bowl, to which is secured by three standards a gauze cylinder 
 surmounted by a gauze cap (smoke gauze). The cylinder is made of stand- 
 ard wire gauze, is generally 1 J in. in diameter and, with its cap is about 6 in. 
 
VENTILATION OF MINES 
 
 885 
 
 high. Air enters all around the lamp, below the flame, and passes out at 
 the top of the gauze as shown by the arrows. In the fire-boss Davy, the oil 
 chamber is quite small and the gauze does not exceed 5 in. in height; in the 
 pocket Davy, the gauze is 3^ to 4 in. high. 
 
 Marsaut 
 
 rnj. i 
 
 Davy lamps are often provided with an upward-sliding metal shield 
 encircling the gauze for two-thirds of its circumference as a protection in 
 
886 VENTILATION OF MINES 
 
 strong air currents. Owing to the free admission of air these lamps give a 
 good flame for testing and are sensitive to gas. At one time they were in 
 universal use for gas testing, but they are so very unsafe that their use for 
 any purpose is prohibited in Europe and in most of the United States. The 
 unbonneted Davy will pass the flame in air currents moving at more than 6 ft. 
 per sec. or 360 ft. per min. (4 mi. per hr.), a less speed than that maintained 
 by the average fire boss in making his rounds. 
 
 In the tin-can Davy, the gauze was surrounded by a tin case with a glass 
 window; later, the tin can was replaced by a brass case having an all-around 
 glass window. In the Jack Davy, the tin case was replaced by a glass cylin- 
 der (either within or without the gauze) reaching the entire length of the 
 gauze. In another form, a low glass cylinder, held in place by a spring or 
 screw, was made to slide up or down over the gauze. When provided with a 
 bonnet over the upper part of the gauze, this last form of Davy was, at one 
 time, very popular in the United States. Some of the numerous types of 
 bonneted Davy lamps have withstood air velocities as high as 1,200 ft. per 
 min. (14 mi. per hr.) and even more in the case of the tin-can Davy. The 
 Scotch Davy was distinguished by the greater diameter (nearly 3 in.) of the 
 gauze which was closed at the top by a conical copper cap. The lamp was 
 provided with a hook at the side, instead of a ring at the top, for carrying, 
 and had a flat wick with a small shield beside it as a protection against the 
 wind. Davy lamps are designed to burn animal or vegetable oils only. 
 
 Stephenson Lamp. The original Stephenson lamp consisted of a glass 
 chimney closed by a perforated copper cap and surmounted by a perforated 
 copper shield. The space between the cap and the shield filled with the 
 inert products of combustion which, from lack of oxygen, extinguished the 
 flame of any gas burning within the lamp before it could reach the outside air. 
 
 The more modern lamp of this name resembles the Davy in appearance 
 as it uses the same gauze, but without the gauze cap. Instead, within the 
 main gauze is a conical glass chimney, closed at the top with a perforated 
 copper cap, which may be raised from the bottom so as to admit air more 
 freely at the base of the flame. 
 
 Stephenson lamps are often called Geordie lamps. 
 
 Clanny Lamp. The original Clanny lamp consisted of a cylindrical metal 
 case (height about 3 times the diameter) the front of which was replaced with 
 glass and in which an ordinary candle burned. Air was forced into the lamps 
 by a bellows, through a water seal. The top of the lamp was closed by a 
 tapering copper cap like an inverted funnel, the opening in which was too 
 small to permit passage of the flame. 
 
 The simplest form of the modern Clanny lamp is essentially a Davy lamp 
 in which the lower portion of the gauze is replaced with a glass cylinder 
 about 2 in. high, as in Fig. 1, b, page 885. As in all lamps where the air 
 enters above the gauze (see arrows), there are conflicting air currents which 
 interfere with the formation of a perfect cap, cause a tendency to smoke, 
 and unfit the lamp for delicate testing. The unbonneted Clanny is not safe 
 in air currents moving over 8 ft. per sec. or 480 ft. per min. (5 mi. per hr.). 
 There are, however, many forms of bonneted Clanny lamps, some of which 
 are safe in currents moving 2,000 ft. or more per min. (22f mi. per hr.). 
 
 Evan Thomas Lamp. There are several lamps of this name, all of which are 
 modifications of the Clanny. The original Evan Thomas lamp was of the un- 
 derdraft type, being provided with a double steel bonnet above a double glass 
 chimney. Air was drawn in at the top, descended between the bonnets and 
 glasses, and entered the lamp below the flame through gauze- protected ports. 
 The lamp was of excellent illuminating power, but the tendency of the glass 
 to crack by the heat of the gas burning within it led to its abandonment. 
 
 The present lamp is a bonneted Clanny with the addition of a device to 
 control the air, which commonly takes the form shown in the Deflector Lamp 
 Fig. 2. In another form, a deflector ring placed around the base of the gauze, 
 throws the entering air upward. The gauze is protected by a very deep 
 gauze cap at the top between which and the top of the bonnet are deflectors 
 throwing the products of combustion downward. The result of this con- 
 struction is that only a very small part of the gauze is exposed to the action 
 of gas burning within trie lamp and the retention of the products of combus- 
 tion, on the Stephenson principle, in the upper part of the lamp, materially 
 adds to its safety in explosive mixtures. This last form of lamp is said to 
 have safely withstood an explosive current moving at the rate of 3,200 ft. 
 per min. (36.3 mi. per hr.). The lamp burns oil and gives a good light, but 
 has a tendency to smoke. 
 
VENTILATION OF MINES 
 
 887 
 
 FIG. 
 
 Deflector Lamp. A deflector lamp is, strictly, not a distinct type but is 
 any one of the standard lamps t9 which is added a device known as a deflector 
 that is designed to control the direction of the air currents. As shown in Pie 
 2, where it is applied to a bonneted two-gauze 
 Marsaut lamp, the deflector consists of a brass 
 shield a midway between the outer gauze and the 
 bonnet and about 1 J in. high. About J in. above 
 the top of this shield is the bottom of an angle 
 ring b. This ring fits closely to t'he gauze, its top 
 flange entirely closing the space between the gauze 
 and the bonnet. The air follows the course shown 
 by the arrows and is thrown directly upon the 
 flame. As the air is heated by passing over the 
 warm deflector and gauze, the draft, rate of com- 
 bustion of oil and, consequently the illumination 
 are improved. The deflector is said to fit the 
 lamp for burning in air containing a much higher 
 percentage of carbon dioxide than is otherwise 
 possible. 
 
 Bull's Eye, or Mauchline, Lamp. The bull's 
 eye, or Mauchline, lamp is a Clanny in which the 
 glass is replaced by a metal cylinder fitted up 
 like a bull's eye lantern, with a lense at one end 
 and a reflector behind the flame at the other. In 
 each side, at the height of the flame, is a gauze- 
 protected circular port through which gas caps 
 may be observed. The lamp is not generally 
 bonneted, throws a good light directly ahead and 
 was designed, primarily, for the use of mine sur- 
 veyors. 
 
 Marsaut Lamp. The Marsaut lamp. Fig. 1, 
 d, is a Clanny lamp with two or, usually, three 
 conical gauzes to afford protection against strong 
 air currents and, particularly, internal explosions. The lamp has a tendency 
 to smoke and heats quickly, but the confinement of the products of combustion 
 between the gauzes, on the Stephenson principle, adds much to the safety 
 of the lamp. The unbonneted lamp is considered safe in air currents moving 
 not faster than 600 ft. per min. (7 mi. per hr.). The bonneted Marsaut is 
 one of the safest of lamps and easily withstands velocities of 3,000 ft. per 
 . min. (34 mi. per hr.), and more. The table on page 880 shows that the two- 
 gauze lamp has about 22 % more illuminating power than that with three 
 gauzes. 
 
 Mueseler Lamp. The Mueseler Lamp, Fig. 1, c, page 885, is a Clanny 
 lamp with an interior conical sheet-iron chimney which increases the draft, 
 separates the products of combustion from the entering air, increases the 
 security of the lamp against internal explosions, and decreases its tendency 
 to flame. The unbonneted type, shown in the figure, may be considered 
 safe in an air current having a velocity not greater than 600 ft. per min. 
 (7 mi. per hr.). 
 
 There are two types of the bonneted Mueseler, the Belgian and the English, 
 which differ only in the dimensions of the chimney. In the former, which is 
 the official or approved lamp in Belgium, the chimney must have a total 
 height of 4.6 in. and must be so placed that its bottom is .85 in. above the 
 top of the wick tube and its top 3.55 in. above the horizontal gauze which, 
 surrounding the chimney at the level of the top of the glass, divides the upper 
 from the lower part of the lamp. The object of the horizontal gauze is to 
 prevent any burning gas passing upwards between the chimney and the main 
 gauze. The chimney of the English Mueseler is set higher above the flame 
 than that of the Belgian and the area of its upper end is much larger. The 
 Belgian lamp, in the tests of the Royal Accidents Commission (English), 
 was extinguished without harm after a few seconds exposure to explosive 
 air currents moving at the rate of 2,880 ft. per min. (32.7 mi. per hr.), while, 
 in every instance, the English lamp caused an explosion; in fact, the English 
 lamp failed when the velocity exceeded 1,000 ft. per min. (11.3 mi. per hr.). 
 The Mueseler lamp is sensitive to air currents striking it obliquely, and these 
 sometimes blow the air circulating in the lamp from its regular course with 
 danger of an explosion. The lamp is easily extinguished if held at a slight 
 angle from the vertical as the products of combustion then pass upwards 
 
888 VENTILATION OF MINES . 
 
 between the chimney and the gauze and, mixing with the entering air, 
 smother the flame. The statement that the Mueseler lamp is safe in air 
 currents moving 100 ft. per sec., or 68.1 mi. per hr., seems hardly credible. 
 
 Ashworth-Hepplewhite-Gray Lamp. The Ashworth-Hepplewhite-Gray 
 lamp, familiarly known as the A-H-G or as the Gray lamp, is shown in Fig. 
 1, e, page 885. The lamp is a bonneted Clanny with underdraft, air entering 
 through gauze-protected ports or through a gauze ring entirely surrounding the 
 lamp at and below the level of the flame. Admission of air to the gauze ring 
 or gas ports is through the standards which are hollow. The openings at the 
 top of the standards are closed by a plate which may be revolved over them, 
 and those at the base are closed by slides. When used for testing, the cover 
 plate is revolved until the tops of the standards are open and the bottom 
 openings are closed by slipping the slides down over them, the air then 
 following the course shown by the arrows. This construction permits the 
 testing of thin layers of gas near the roof. When used as a working lamp, 
 the top openings are closed by the cover plate and the slides at the base of the 
 standards are pushed up. In some types of this lamp there are three instead 
 of four standards, only one of which is hollow, the others being of thin wire 
 so as not to impede the light. The conical glass and short conical gauze 
 permit the upward diffusion of light. In some cases the steel bonnet is 
 cylindrical instead of as in the figure, but it is always closed by a truncated 
 cone which reduces the area of the top of the opening and better controls the 
 circulation and prevents downward currents. The opening in this cone is 
 protected by a perforated dome or cap which, in some lamps, is extended 
 downwards like an ordinary bonnet to the level of the top of the glass. The 
 lamp is intended for burning colza or similar oils, has high illuminating power 
 (see following table), is said to be safe in air currents traveling 6,000 ft. per 
 min. (68.1 mi. per hr.), and is generally considered a most excellent lamp. 
 
 Wolf Lamp. Fig. I,/, page 885, shows the Wolf lamp as used in the United 
 States, The lamp burns naphtha or gasoline and, hence, assisted by its con- 
 struction, gives a maximum of light and permits the detection of small per- 
 centages or methane. It uses a magnetic lock (see Locks for Safety Lamps), 
 has an internal ignition device (see first paragraph on Igniters, or Relight- 
 ers) , and has an underdraft. 
 
 The lamp is of the Clanny type with the double conical gauzes of the Mar- 
 saut, and usually has a corrugated bonnet, the openings in which are so ar- 
 ranged that air currents strike tangentially and not directly upon the gauze. 
 Air for combustion enters through gauzes or a gauze ring at the base of the 
 glass chimney, the openings being protected from direct contact of air cur- 
 rents by a baffle ring^. The wick is held in a sheath moving within the wick 
 tube and may be adjusted by turning the screw at the base of the lamp. 
 
 The baffle ring and bonnet are made in various forms so that the external 
 appearance of Wolf lamps varies considerably. Some of these lamps have 
 the overdraft of the Clanny; in some the igniter box is circular; in others, a 
 lead in place of a magnetic lock is used; some are arranged to burn colza; 
 others burn alcohol, have the Chesneau scale attachment, and are adapted for 
 testing for small percentages of gas. While such variations and adaptations 
 are common in the lamp as used in Europe, they are practically unknown 
 in the United States. 
 
 The Wolf is a most excellent lamp, and is safe in air currents containing 
 9 % of methane when moving 3,600 ft. per min. (41 mi. per hr.). 
 
 Protector Lamp. The Protector lamp is not a separate type but is a modi- 
 fied Clanny, Marsaut, or Mueseler lamp designed to burn colzaline, a light 
 oil obtained by the purification of colza; and is provided with an electric 
 igniter. The wick tube, or burner, is double with a narrow annular space 
 between the two tubes. In the inner tube is a stationary cotton wick extend- 
 ing down into the bowl which contains a piece of sponge for absorbing and re- 
 taining the oil fuel. The lamp is lit electrically by means of a platinum wire 
 connected to two terminals, one of which is connected with a contact on 
 the bottom of the bowl, the framework of the lamp forming the return 
 circuit. A low-tension current from a battery is sufficiently powerful to 
 heat the wire to the ignition point of the colzaline vapor, which, as it forms, 
 passes up the annular space between the inner and outer wick tubes and is 
 burned around the head of the stationary wick. The flame is regulated by 
 screwing the bottom of the lamp up or down, and is extinguished if an at- 
 tempt is made to unscrew the bottom completely, as explained under Locks 
 for Safety Lamps (Protector Lock). 
 
 Hailwood Lamp. The Hailwood lamp is designed to burn naphtha or 
 
VENTILATION OF MINES 889 
 
 gasoline. It is essentially a bonneted Clanny lamp with the double gauze of 
 the Marsaut and an underdraft protected by a baffle ring. The lamp is pro- 
 vided, as desired, with either the magnetic or the compressed-air lock (de- 
 scribed under Locks for Safety Lamps). The lamp is relit in a special gas- 
 proof, gauze-protected chamber by means of an electric spark which jumps 
 the gap between the top of the wick tube and the end of an upright insulated 
 copper wire through which the current enters the lamp. The wick tube is 
 flat and is surrounded by a sliding sheath by means of which the lampman 
 may adjust the flame as desired but which is so arranged that it is impossible 
 for the miner to raise the flame to such a height that it may be drawn through 
 the gauze. The ordinary, or burning, wick is fed with naphtha by a perma- 
 nent feeding wick which extends down into the bowl and which is pressed 
 against the ordinary wick by a spring. Owing to its construction and to the 
 illuminant used, the lamp gives a most excellent light and also permits the 
 detection of low percentages of methane. In the Belgian government tests 
 the lamp successfully withstood air currents containing 8 % of methane when 
 moving 900 m., or 2,952 ft., per min. (33.5 mi. per hr.), regardless of the 
 angle at which the air struck the lamp. 
 
 The Hailwood oil-burning lamp differs in a few details from the naphtha- 
 burning lamp just described. The picker, which is of copper and through 
 which an electric current may be passed, is provided with two prongs or 
 arms, one of which is used to snuff or trim the lamp wick and the other to 
 convey the current to the wick tube when it is desired to relight the lamp. 
 Other lamps of this name, designed more particularly for gas testing, are of 
 the Mueseler type but with a glass instead of a metal chimney on the back 
 and inner side of which is a piece of metal as a background against which to 
 better view the gas caps. 
 
 SPECIAL TYPES OF SAFETY LAMPS 
 
 Clowes Hydrogen Lamp. The Clowes hydrogen lamp is essentially an 
 A-H-G lamp with a somewhat taller chimney and an attached device for 
 burning hydrogen. A seamless copper tube is inserted in the bowl beside 
 the wick tube and is connected either below or at the 
 side of the lamp with a small portable cylinder a (Fig. 
 3) containing hydrogen. The cylinder, which is about 
 5 in. long and 1 in. in dia- 
 meter, is attached to the 
 lamp by the clip b and the 
 screw e. In testing for gas, 
 the valve d is opened, the 
 hydrogen enters the lamp 
 and is ignited at the mouth 
 of its burner by the oil 
 flame, which is then pulled 
 down by the picker until it 
 is extinguished. By means 
 of the valve d, which regu- 
 lates the supply of hydro- 
 gen, the height of the test- 
 ing flame is adjusted until 
 its top coincides with a 
 scale not shown in the 
 figure, the adjustment be- 
 ing made in air free from 
 methane. The scale con- 
 sists of a number of cross- 
 bars in a ladder-like frame 
 placed in front of the flame. 
 The heights of the cross- 
 bars (which appear as dark 
 lines against the flame) 
 mark the heights of the gas 
 
 FIG. 3 
 
 FIG. 4 
 
 caos corresponding to various percentages of pure methane burning in pure 
 air. The hydrogena ttachment is designed to render possible the detection 
 of 1 to 3 % of gas; for higher percentages, the oil flame is used. With i % of 
 gas the cap is in. high, and with 2 % of gas about l| in. 
 
 Stokes Alcohol Lamp. The Stokes alcohol lamp, Fig. 4, is a modification 
 of the A-H-G lamp in which a small alcohol flame is introduced beside the 
 
890 
 
 VENTILATION OF MINES 
 
 regular oil flame. The small alcohol bowl a is screwed beneath the regular 
 oil bowl and is provided with a long wick tube b. When the screw plug c 
 is removed and the alcohol lamp screwed in place its wick is lit by the oil 
 flame d which is then extinguished by drawing down the wick with the picker. 
 In other respects the lamp is the same as the Clowes. The alcohol is not as 
 persistent as the hydrogen flame and is more easily extinguished in gas; on 
 the other hand, it is more stable in gas than the oil flame but is more easily 
 blown out by the wind. The lamp is designed to detect from $ to 3 % of gas. 
 Pieler Lamp. The Pieler lamp, Fig. 5, is essentially a Davy lamp with 
 an exceptionally tall gauze, and is arranged to burn alcohol. The flame is 
 surrounded by a short conical metal bonnet or shade reaching up about 2 in. 
 from the bottom of the gauze, and into coincidence with the top of which the 
 tip of the lamp flame is brought by adjusting in fresh air. Affixed to the 
 lamp standards is a slotted metal plate, each slot marking the height of gas 
 cap corresponding to a certain percentage of pure gas in air. The lamp in 
 the cut is designed to indicate percentages of gas from } to 1?%, increasing 
 
 FIG. 5 
 
 FIG. 6 
 
 by %. When the cap reaches the top of the scale plate, 2 % of gas is pres- 
 ent. The lamp illustrated is unbonneted. The bonneted Pieler greatly 
 resembles the Chesneau lamp, Fig. 6, in external appearance, as the scale 
 plate is replaced by a glass plate inserted in the bonnet, on which are etched 
 lines corresponding to the height of the flame caps. 
 
 The Pieler lamp is extensively used in Austria (where it originated) and 
 Germany, but it is of limited application in the United States. The lamp, 
 like all of the Davy type, is unsafe in air currents of any but low velocity, 
 Beyond 2% of gas, the lamp is useless as the gauze which is Sin. high fills 
 with flame. Where the gaseous conditions are unknown, it is advisable to 
 make a preliminary test with an 9rdinary lamp, as the Pieler is practically 
 certain to pass the flame if placed in an explosive mixture of gas and air. 
 
 The absorptive power of the cotton, with which the bowl of the lamp is 
 filled, is commonly great enough to modify the height of the flame cap and 
 consequently^ affect the accuracy of the[determinations. Furthermore, after 
 a determination has been made, the heat remaining in the gauze assists in 
 the volatilization of the naturally volatile alcohol, so that for 20 to 30 min., 
 or until it thoroughly cools down, the lamp cannot be used f9r a second test 
 as there will be an artificial atmosphere of alcohol vapor within the gauze. 
 
 Chesneau Lamp. The Chesneau lamp, Fig. 6, of French origin, is a 
 bonneted Clanny with underdraft and is designed to burn alcohol. In the 
 
VENTILATION OF MINES 891 
 
 figure, c is one of the openings through which air has access to the gauze 
 ring surrounding the lamp below the wick tube. The cylinder a plays 
 the same part as the conical shield in the Pieler lamp, and the lamp flame, 
 when a test is to be made, is adjusted to the level of its top, that is, to the base 
 of the main gauze. The gauzes in this lamp have 1,264 openings per sq. in. 
 In the front of the bonnet is inserted a mica window d with a scale on either 
 side. One scale is graduated in millimeters for measuring the height of the 
 gas cap, and the other is graduated in the corresponding percentages of gas. 
 A sliding shield d can be adjusted to the exact height of the cap, thus per- 
 mitting of much more precise readings. 
 
 The Chesneau lamp is much superior to the Pieler in that it is safe in air 
 currents moving over 2,000 ft. per min., and requires but 30 to 90 sec. to 
 cool down between tests; but, as in the Pieler lamp, the accuracy of the tests 
 is somewhat interfered with by the absorptive power of the cotton in the bowl. 
 It should be noted, however, in the Chesneau as in the Pieler lamp so long 
 as the physical condition of the cotton is the same as when the lamp was 
 standardized, its indications are accurate. 
 
 Stuchlick Acetylene Safety Lamp. The Stuchlick acetylene safety lamp, 
 an Austrian invention, is essentially a Clanny lamp designed to generate 
 and burn acetylene gas. The bowl of the lamp is double and consists of an 
 outer carbide box in a groove in which slides an interior water vessel, the 
 two being connected by a flexible siphon tube. The water vessel can be 
 raised and lowered within the carbide box, and is held in position by a 
 spring and screw. The lamp, which weighs about 3 lb., is held together by 
 screwing on the bowl. 
 
 After the carbide box is two-thirds filled with calcium carbide, the water 
 vessel is pushed down to its lowest position and filled with water. The lamp 
 is then assembled. In the lowest position of the water box the level of the 
 water in it is below that of the opening into the carbide box, and the genera- 
 tion of acetylene is not possible. As the water box is raised, water flows 
 through the siphon tube into the carbide box and the acetylene then given 
 off enters the burner through a small pipe within the flexible tube. Any 
 excess of gas is carried back into the water vessel and thence to the open air, 
 the flexible pipe, which has a hydraulic joint, acting as a safety valve. In 
 testing for gas, the flame is adjusted for height by a screw which moves the 
 gas nipple in the burner. 
 
 One per cent, of methane in air is easily detected by the green halo which 
 surrounds the acetylene flame, which, in dangerous percentages of gas, is 
 extinguished by the products of combustion. One-third pound of calcium 
 carbide and one filling of the water box will furnish a light for 8 hr. at a less 
 cost than benzene. 
 
 Tombelaine Acetylene Safety Lamp. The Tombelame lamp is an under- 
 draft and bonneted Clanny with double gauzes, the inner of which extends 
 downward over the flame similarly to the Mueseler chimney so that any 
 sudden enlargement of the acetylene flame will not break the glass. The 
 bowl of the lamp is double, the inner cylinder holding the carbide and the 
 outer the water. In use, the inner cylinder after being filled with carbide 
 is screwed into place and the bottom of the lamp placed in water which 
 flows into the water holder through openings designed for the purpose. The 
 amount of water entering the carbide chamber, the flow of acetylene to the 
 burner, and the height of flame are regulated by a thumbscrew in the base 
 of the lamp. The lamp weighs 1.5 kg. (3.3 lb.), has an illumination of about 
 6 c.p., and will burn 11 hr., with a slightly greater consumption of acetylene 
 than the Stuchlick lamp. 
 
 GAS INDICATORS AND GAS-SIGNALING DEVICES 
 Use and Principles. Gas indicators are designed to more exactly deter- 
 mine the amount of methane in mine air than does the ordinary safety lamp. 
 These devices are based on the use of some one of the well-known physical or 
 chemical properties of gases, such as: The difference in the density or in the 
 rate of diffusion of methane and air; the heat generated by the burning ot 
 methane or the contraction in volume of its products of combustion; the 
 increased brilliancy of platinum or palladium wire, or their increased elec- 
 trical resistance when heated in the presence of methane; the absorption of 
 methane by platinum or palladium sponge, etc. 
 
 In addition to the foregoing are colored glass, various chemicals, loops ot 
 wire, etc., the use of which is intended to make more distinctly visible the 
 gas cap formed in the ordinary safety lamp. 
 
892 VENTILATION OF MINES 
 
 While, in the main, based upon correct principles, these devices, with few 
 exceptions, have been discarded as being too cumbersome or costly; as 
 requiring top much time or skill in their manipulation; or as being inaccurate 
 under practical mining conditions while meeting the perfect ones in the labora- 
 tory. This last objection is the most serious, and it is clear that any appa- 
 ratus which is standardized under certain atmospheric conditions and for 
 pure methane and pure air, as it would be in the laboratory, cannot give 
 correct readings in the mine where the atmospheric conditions may be and 
 usually are widely different and where, above all, the air is certain to be more 
 or less deficient in oxygen and contaminated with nitrogen, carbon dioxide, 
 etc. 
 
 In a signaling device or system numerous gas indicators placed at points 
 in the workings where methane is apt to accumulate are electrically connected 
 with some central station, as the superintendent's office. When methane 
 is present, the indicators become operative, closing their respective circuits 
 and thus ringing bells or moving pointers at the central station. 
 
 Gas-signaling systems have never proven satisfactory. The indicators 
 fail for the reasons previously stated and, as they are not instantaneous in 
 their action, never give warning of gas until some time after it has accumu- 
 lated. They are particularly at fault in that they announce the presence 
 of gas only at points where an indicator is placed and, as it is impossible to 
 entirely cover the workings with indicators, a dangerous accumulation of 
 gas may exist within a few feet of one of these appliances. Further, indi- 
 cators of the type that glow in the presence of methane are dangerous, even 
 when enclosed in safety-lamp gauze. 
 
 Experience thus far has shown that for the detection of gas at the face 
 nothing is better adapted than a standard safety lamp, and for accurate 
 percentage determinations, chemical analysis should be relied upon. 
 
 Liveing Indicator. The Liveing indicator consists of two coils or spirals 
 of platinum wire of equal electrical resistance enclosed in separate glass- 
 ended cylinders set facing each other and about 4 in. apart. One of the 
 cylinders, which is tightly sealed, is filled with pure air, and the other is made 
 of standard safety-lamp gauze. Between the spirals is a wedge-shaped 
 mirror for reflecting their image upward through the small glass window of 
 the box containing the apparatus. By applying suction (by the mouth or a 
 small air pump) to the end of a rubber tube attached to the box, mine air is 
 drawn into the apparatus through another tube which is made long enough 
 to reach places not readily accessible, as cavities in the roof, etc. 
 
 When an electric current, generated by turning the handle of a small 
 magneto placed in the bottom of the box, is passed through the spirals they 
 glow with equal intensity, if no methane is present. If, however, gas is 
 present, the spiral within the gauze cylinder will glow more brightly. The 
 mirror is then moved until the images of the two spirals as viewed through 
 the window appear of equal intensity, when the percentage of gas may be 
 read from a graduated scale over which the mirror passes. 
 
 Repeated heating of the gauze-encased spiral alters its electrical conduc- 
 tivity to such an extent that it soon becomes necessary to adjust the zero 
 point of the scale in fresh air before a test is made. This is done by heating 
 up the coils and shifting the mirror until the images appear of equal bright- 
 ness; the zero of the scale is then made to coincide with the position of the 
 mirror. 
 
 Coquillon's Indicator. Coquillon's indicator consists of a glass tube in 
 which is a loop of palladium wire that can be heated to incandescence by a 
 small battery contained within the same box as the tube. If a measured 
 quantity of mine air containing methane is introduced into the tube and the 
 electric current is applied, all the gas will be burned and the contraction in 
 volume of the products of combustion is a measure of the percentage of gas 
 present. This indicator is really an apparatus for making a rapid analysis 
 of mine air. 
 
 Le Chatelier's Indicator. Le Chatelier's indicator, while differing from 
 Coquillon's in a few minor details, is chiefly distinct in the use of platinum 
 for palladium wire. 
 
 The indicators devised by Maurice, Monier, and some others are based 
 upon the same principle as Le Chatelier's. 
 
 Turquand's Indicator. Turquand's indicator consists of a glass U-tube of 
 fine bore about one-half filled with mercury. The ends of the tube are 
 inserted in a metal block in such a way that there is a small space between 
 the top of each arm of the tube and the bottom of a porous stopper inserted 
 
VENTILATION OF MINES 893 
 
 in the corresponding holes in the block. In one of these spaces is an absorb- 
 ent to distinguish between methane and carbon dioxide, and in the other is a 
 coil of palladium wire that can be made to glow by passing an electric 
 current through it. Normally, the mercury stands at the same level in the 
 two arms of the tube, but when methane or other hydrocarbon gases that 
 are absorbed by hot palladium wire enter through the porous stopper, heat 
 is generated and the thread of mercury is pushed down one leg and up the 
 other, the difference in level of the columns of mercury being a measure of 
 the amount of gas present. 
 
 The Swan indicator is of this type, but employs the expansion of a column 
 of mercury by the heat liberated by the absorption of methane by a glowing 
 platinum wire, to show the percentage of gas present upon a graduated scale. 
 
 Ralph's Indicator. Ralph's indicator employs a differential galvanometer, 
 in one coil of which is a piece of platinum wire enclosed in standard safety- 
 lamp gauze so that it may safely^ be exposed in air containing methane. 
 When no gas is present and an electric current is passedthroughtheapparatus, 
 the needle or indicator of the galvanometer is not deflected as the resistance 
 of the two coils is the same. When methane is present, its absorption 
 by the platinum wire increases the resistance in that coil, and the needle is 
 deflected by an amount proportional to the percentage of gas in the air. 
 
 This indicator is the basis of some signaling systems in which the variation 
 in resistance is made to extinguish a distant light, to place a distant buzzer 
 in action, etc. 
 
 Garforth-Walker Indicator. That the amount of methane required to 
 make a platinum wire glow when an electric current is passed through it is 
 proportional to the thickness of the wire is made the basis of an indicator 
 devised by Mr. S. F. Walker for Sir William Garforth. Several small glass 
 tubes are fixed inside the protecting glass of any portable electric lamp. 
 The tubes are arranged to be easily replaced, are enclosed in safety-lamp 
 gauze, and contain platinum wire of a gauge or thickness proportional to 
 the percentage of gas in air that each particular tube is intended to indicate. 
 At the entrance to each tube is a self-closing_ valve that can be pushed open 
 by the metal nozzle of a rubber bulb which is filled with the mine air to be 
 tested, the insertion of the nozzle automatically switching on the current 
 to the wire. After sufficient time is allowed for the wire to reach the proper 
 temperature, the contents of the bulb are squeezed out, the wire glowing if the 
 percentage of methane corresponding to the particular tube is present. In 
 testing, the tube with the coarsest wire, which indicates the greatest per- 
 centage of gas, is used first; if the percentage of gas is not great enough to 
 make this wire glow, tubes with successively finer wires are used until one 
 is found that is sensitive to the percentage of gas present. Palladium 
 may be used to advantage in place of platinum wire. This apparatus is still 
 in the experimental stage. 
 
 Ansell's Indicator. Ansell's indicator consists of a cylindrical chamber, 
 one side of which is formed by a movable diaphragm of porous unglazed 
 earthenware and the other by a stationary graduated dial or plate to the 
 center of which is pivoted a hand or needle, the apparatus somewhat resem- 
 bling an aneroid barometer in appearance. When exposed to a mixture of 
 methane and air, the gas diffuses through the porous diaphragm more rapidly 
 than the air passes out, causing a difference in pressure on the two sides with 
 a resultant outward movement of the diaphragm. By means of mechanism, 
 the motion of the diaphragm is made to move the needle over the circular 
 scale on the edge of the dial on which the percentage of methane may be 
 read off. After making a test, the needle must be set back to zero by expos- 
 ing the apparatus in pure air, a process requiring considerable time. 
 
 In some indicators of this type the diaphragm is placed midway between 
 the ends, one of which is porous while the other carries the scale. 
 
 The action of all indicators of this type becomes absolutely unreliable if a 
 deficiency of oxygen or an excess of carbon dioxide or moisture or a rise or 
 fall of temperature affects the density of the air, as the rate of diffusion 
 is then changed from that prevailing when the instrument was standardized. 
 Clowes has shown that when 4 % of coal gas and 3 % of methane was present, 
 the indicator showed but 1.71 % of the latter gas; also, that when absolutely 
 pure air was heated, the indicator showed it to contain 4 % of gas, and that 
 when the same air was cooled the indicator gave a minus reading of the same 
 amount. 
 
 The indicators devised by Libin, McCutcheon, Webster, and some others 
 are of this type. 
 
894 VENTILATION OF MINES 
 
 William's Methanometer, William's methanometer, which resembles the 
 previously mentioned Ralph indicator, consists of a pair of thermo-electric 
 couples connected with a galvanometer. Each couple is enclosed in porous 
 material, that surrounding one of them being impregnated with platinum- 
 black to absorb methane. The couples may be brought to the temperature 
 at which platinum-black is most sensitive to methane by means of a battery 
 current and, if no gas is present, the needle of the galvanometer remains 
 stationary. If, however, gas exists, the temperature of the couple surrounded 
 by platinum-black will be raised through its absorption of methane, its 
 resistance will be changed and the needle of the galvanometer will be deflected 
 in proportion to the amount of gas present. The indicator is made in port- 
 able form for fire bosses and may be used as the basis of a signaling system 
 when connected to the necessary wires for transmitting the indications of 
 the needle to a distance. 
 
 Aitkin's Indicator. In the Aitkin indicator two thermometers are sus- 
 pended side by side in the same frame, the bulb of one being covered with 
 platinum-black (spongy platinum). In pure air the readings of the ther- 
 mometers will be the same, but if methane is present its absorption by the 
 platinum-black causes a rise in temperature which is indicated by the proper 
 thermometer and which is a measure of the percentage of gas. The appara- 
 tus is not accurate in that the platinum-black rapidly deteriorates through 
 the absorption of moisture and through the deposition of dust on its surface 
 and, further, because platinum is insensitive to low percentages of gas when 
 cold. 
 
 An indicator of this type was at one time attached to the Sussmann port- 
 able electric lamp. 
 
 Beard-Mackie Sight Indicator. The Beard- Mackie sight indicator is a 
 device for making visible and more accurately measuring the height of the 
 caps made by small percentages of gas. While it may be applied to any 
 safety lamp, it is commonly used in connection with the Davy or with those 
 having an underdraft. The indicator, which resembles a ladder in appear- 
 ance, consists of two upright standards between which are strung a series 
 of fine wires, the lowest being of brass and the others of platinum. The 
 standards are soldered to a brass washer which fits over the neck of the wick 
 tube or, better, which is pivoted so that the indicator may be swung into 
 the flame only when a test is to be made. The latter construction prevents 
 the sooting of the wires through continued contact with the flame, which is 
 the greatest drawback to the use of this indicator. In testing, the lamp 
 flame is adjusted in fresh air until the lowest, or standard, wire is just aglow. 
 The platinum wires are so spaced that when $ % of methane is present the 
 lowest of them will glow, when 1 % is present both the first and second, and 
 similarly up to the last wire which indicates 3 % of gas. 
 
 Brigg's Wire Loop. Brigg's wire loop which is intended to delumine, or 
 remove the color from the lamp flame in order that the gas cap may be more 
 distinctly visible, may be applied to any safety lamp and is not patented. 
 The device consists of a piece of 22-gauge copper wire bent into a loop, the 
 longer axis of which is equal in width to the wick of the safety lamp. The 
 loop is supported upon an upright brass standard extending through the lamp 
 bowl so that it may be swung in or out of the flame. In testing, the flame 
 is left at its normal working height. As soon as the loop is swung into it the 
 flame, this, without being reduced in size, loses its yellow color and the 
 cap, if methane is present, in as little as \ % of gas becomes visible and that 
 of % of gas may be measured. 
 
 By dipping the loop in a solution of chloride of zinc a green coloration is 
 imparted to the lamp flame, to the so-called fuel cap (if present) and, to a 
 less extent, to the gas cap. This action improves the indications consider- 
 ably, but the chloride of zinc soon burns off. The loop, however, sometimes 
 gives a fairly strong green flame without this treatment, especially if it has 
 not been used for some days, and it generally gives a very faint one. 
 
 The flame may be intensified by introducing 1 or \\% of carbon tetra- 
 chloride into the lamp oil or naphtha, at a cost of roughly \ c. a shift. The 
 tetrachloride does not affect the working flame, but when the loop is moved 
 into it the flame becomes green from the copper chloride and the gas cap, 
 if present, a bright blue from the copper oxide formed. 
 
 Cuninghame-Cadbury Indicator. In the Cuninghame-Cadbury indicator 
 a small sheet of asbestos is secured on a holder in much the same way as the 
 Brigg's wire loop so that it may be moved in or out of the normal, or but 
 " itly reduced, flame of the lamp. The asbestos, which is twice steeped 
 
VENTILATION OF MINES 895 
 
 in a strong solution of carbonate of soda, is placed about i in. above the 
 wick, and enters the flame for about two-thirds the thickness of the same. 
 In pure air a slight fuzzy yellow, or orange, halo will appear around the flame 
 toward the upper part of the asbestos. If methane is present, the halo will 
 be surmounted by a yellowish conical cap the length and distinctness of 
 which depends on the per cent, of gas. In some cases a perpendicular scale 
 for measuring the he ght of gas caps is attached to the snuffer pin so that it 
 can be temporarily moved into position when testing. It is stated that the 
 use of this device, which is not patented and may be attached to any safety 
 lamp, permits the detection of as little as 5 % of gas. 
 
 Colored Glass Indicators. In order to cut off the yellow light and thus 
 render the cap more distinctly visible, Mr. A. L. Steavenson suggests that 
 a sheet of blue glass be interposed between the flame and the eye, or that a 
 pair of blue glass spectacles be worn while testing. 
 
 To do away with the reflection of the flame and cap in the polished glass 
 of the ordinary safety lamp which often interferes with the accuracy of the 
 test, a strip of dull-surfaced metal may be placed back of the flame. The 
 same result may be obtained by making a strip of soot or smoke down one 
 side of the glass after it has been cleaned. As an additional precaution, all 
 metallic surfaces, such as the bowl, standards, etc., that can in any way 
 reflect the flame may be given a dull finish. 
 
 Forbes Indicator. The F9rbes indicator consists 9f a brass tube about 6 
 in. long in which moves a piston the position of which, in terms of the per 
 cent, of methane in the air, is indicated by a pointer and scale. In the 
 mouth of the tube is fixed a tuning fork that makes 512 vibrations a second 
 and emits a corresponding sound when fresh air is forced through the tube 
 by moving the piston. If the density of the air is lowered by the presence 
 of methane, the length of stroke of the piston and the corresponding yolume 
 of air required to produce a note of equal depth is not the same as in pure 
 air, the difference being measurable on the scale. In making tests an al- 
 lowance is necessary for changes in the density of the air due to variations 
 in temperature. 
 
 Firedamp Whistle. In the firedamp whistle the attempt is made to esti- 
 mate the percentage of methane in the air by the difference in the sound 
 emitted by a metal pipe when air currents of different densities are blown 
 through it. When pure air is used, the pipe, which is about 10 in. long and 
 2 in. in diameter, emits a certain tone, but as the density of the mine air 
 decreases as the proportion of methane in it increases, the tones become 
 higher and tremulous. The device, which is an adaptation of the Forbes 
 indicator, can hardly be considered reliable, as changes in temperature and 
 pressure, or a deficiency in oxygen, or an increase in carbon dioxide or nitro- 
 gen, will affect the density of the air as well as changes in the methane 
 content. 
 
 Hardy Indicator. In the Hardy indicator there are two separate pipes, 
 alike in every respect, one of which is blown with pure air and the other 
 with the mine air to be tested. The number of vibrations per second made 
 by the pipes is made the measure of the percentage of methane present. 
 The same objections apply to this indicator as to the Forbes and to the fire- 
 damp whistle. 
 
 Shaw Gas-testing Machine. In the Shaw machine, a graduated beam 
 operated by a crank and connecting arm raises and lowers the pistons in 
 two vertical cylinders known as the air and gas cylinders, respectively. 
 The larger, or air, cylinder is fixed in position, while the smaller, or gas, 
 cylinder may be shifted along a graduated slide in such a way that the length 
 of travel of its piston and consequently the volume of its discharge may be 
 varied. Both cylinders discharge into a small combustion cylinder in front 
 of which a gas jet is burning and one end of which is movable outward against 
 a gong. As a preliminary operation it is necessary to determine the per- 
 centage of some readily available gas (as illuminating gas) that must be 
 mixed with pure air in order to produce an explosion. To do this, pure air 
 and pure illuminating gas are pumped from their respective cylinders until 
 the mixture delivered to the combustion chamber is feebly explosive as 
 evidenced by a slight ringing of the gong when the mixture is lit and exploded 
 by the gas jet. This requires several determinations, much shifting of the 
 gas cylinder to secure the proper ratio of gas to air, and consumes a good deal 
 of time. 
 
 If mine air in place of pure air is pumped from the air cylinder into the 
 combustion chamber, less and less illuminating gas will be required to make 
 
896 VENTILATION OF MINES 
 
 the mixture explosive as the percentage of methane in the air increases. A 
 rubber bag containing mine air is connected with the air cylinder and the 
 position of the gas cylinder shifted until the mixture from the two cylinders 
 as delivered to the combustion chamber is of the same explosive intensity as 
 the mixture of pure air and gas. From the position of the gas cylinder in 
 either case may be calculated the percentage of illuminating gas required to 
 produce an explosion both with pure and with mine air. A simple proportion 
 then gives the percentage of methane in the mine air. 
 
 This apparatus is bulky, expensive, and slow, but at one time had a 
 considerable following through intensive advertising. It is no longer used. 
 
 Hauger and Pescheux Gas-signaling Apparatus. In the signaling appara- 
 tus devised by Hauger and Pescheux, an extremely sensitive balance carries 
 on one end a tightly sealed vessel of pure air and on the other a tray of the 
 same area and weight as the air vessel. If the composition of the atmosphere 
 is changed in any way, its density will vary according to the percentage of 
 gas invading it and, as the composition of the air in the closed vessel is 
 unaltered, the equilibrium of the balance will be destroyed. If the gases 
 invading the atmosphere are lighter than air the air chamber will descend, 
 but if they are heavier than air it will ascend. Attached to the beam is a 
 needle dipping in a cup of mercury which, immediately on disturbance of 
 the balance, closes an electric circuit that may be made to ring a bell or set 
 a danger signal at any distance from the apparatus. To allow for the dis- 
 turbing influences of changes in atmospheric temperature and pressure, two 
 compensators are attached to the beam. One of these is an aneroid barom- 
 eter which acts on a multiplying lever which in turn changes the position 
 of a rider which slides along a thread. To compensate for changes in tem- 
 perature, a bimetallic spiral is made to act on a lever which, in its turn, shifts 
 the position of a rider on the beam. 
 
 Low Gas-signaling Apparatus. The low signaling apparatus consists of 
 two wires arranged in V-shape and held in tension by a bar and spring. One 
 wire is of platinum and carries at short intervals lumps of spongy platinum; 
 the other is of iron and brass in such proportions that its coefficient of expan- 
 sion is the same as that of the platinum for equal changes of temperature. 
 As long as the wires contract and expand equally they are kept in tension by 
 the spring referred to, but should the platinum wire sag by reason of its 
 more rapid expansion, an arrangement of springs and multiplying mechanism 
 closes an electric circuit which may be made to give a determined signal at 
 any distance. When the apparatus is exposed to hydrocarbon gases they 
 are absorbed by the spongy platinum, the platinum wire is heated, expands 
 and sags, and rings the alarm as stated. 
 
 ELECTRIC SAFETY LAMPS 
 
 The ordinary .safety lamp is subject to many disadvantages, and several 
 explosions have been traced to imperfections in these lamps or to their 
 unintentional breakage. To obviate these disadvantages many varieties 
 and models of so-called electric safety, lamps all of which employ a small 
 storage battery, have been devised. 
 
 Such lamps must provide safety against ignition of mine gases, a steady 
 and uninterrupted production of light for at least one shift and should be of 
 practically foolproof construction. Since such lamps are exposed to ex- 
 tremely rough usage in the hands of inexperienced men, even slight mechan- 
 ical or electrical weaknesses may result in a total failure of the light supply. 
 Furthermore, to guard against the opening of the lamp while in the mine 
 most such lamps are provided with some means, such as a lock, which pre- 
 vents anyone from tampering with or dismounting the apparatus. These 
 locks may be either in the nature of an ordinary padlock or a type of mag- 
 netic lock such as is often used on naphtha-burning safety lamps. 
 
 Points of Danger in an Electric Safety Lamp. Experiments both in this 
 country and in Germany have demonstrated that the only point of danger 
 in a portable electric lamp is the glowing filament. Sparks obtained by the 
 making or breaking of the electric circuit are not of- sufficient strength to 
 ignite an explosive mixture. It is unnecessary, therefore, to provide against 
 sparking at the switch or other connections between the battery and the 
 lamp. The lamp filament under ordinary conditions is enclosed in a vacuum 
 bulb, and the danger of igniting mine gases is present only when this bulb is 
 broken without rupturing the filament. Several methods may be employed 
 for preventing such a contingency. The two most commonly used, however, 
 are a spring which instantly forces the lamp out of its socket, thus instantly 
 
VENTILATION OF MINES 897 
 
 breaking electrical connections, and a fuse which blows the moment the 
 bulb is fractured. 
 
 Types of Electric Safety Lamps. There are two general types of electric 
 safety lamp. These may be designated as hand lamps and cap lamps; the 
 former strongly resembles in appearance an oil-burning safety lamp, while 
 the latter is modelled after the open-flame cap lamp extensively employed 
 in this country. Although many varieties of each have been placed on the 
 market, all models of the same type strongly resemble each other and a 
 description of one will apply with only minor variations as to constructional 
 features to all lamps of its particular type. 
 
 The Ceag Lamp. The Ceag lamp won first prize in the competition con- 
 ducted by the British government in 1912, since which time it has been 
 accepted by practically all European governments 
 and has been approved by the U. S. Bureau of 
 Mines. This lamp is illustrated in Fig. 7. As 
 described by Mr. H. O. Swoboda its construction 
 is as follows: 
 
 The bulb is covered with a heavy glass dome D, 
 which is protected by four heavy steel rods H, held 
 together by a sheet-steel roof 7. A substantial 
 hook is attached to this roof. Thus the miner can 
 either stand the lamp on the ground or hang it to 
 a post in the immediate neighborhood of his work- 
 ing place. The bottom part, made of heavy cor- 
 rugated galvanized sheet steel, contains the stor- 
 age battery. By turning the upper part on the 
 lower the miner can turn the light on and off. The 
 incandescent lamp rests in a socket which is 
 pressed upward by a spiral spring O against 
 another spring P between the bulb and the glass 
 dome D, providing a complete spring support and 
 preventing breakage even with the most severe 
 shock. Electric connection is established for one 
 pole through the socket spring O and for the other 
 pole by another smaller spring E inside the socket 
 spring and insulated from it. In case the bulb 
 breaks the socket spring pushes the socket up- 
 ward, and as the inner spring does not expand as 
 much as the socket spring the circuit is inter- 
 rupted. Another safety device has been added, 
 but it is not shown in this illustration. This con- 
 sists of a fuse which blows the moment the bulb 
 of the incandescent lamp is broken. This elimi- 
 nates the possibility of obtaining sparks or getting 
 the filament to glow in case the miner should 
 attempt to push the bulb back into its normal 
 position. It also protects the battery from being 
 short-circuited for any length of time in case the 
 leads to the bulb have become short-circuited " 
 during the accident. FIG, 7 
 
 The rotating movement of the upper part of the lamp upon the lower is 
 limited by a soft-iron pin M, which acts as a magnetic lock. This pin can be 
 withdrawn in the charging room by a strong electromagnet, and when this 
 is done the upper and lower parts of the housing separate and the battery 
 can be removed for charging. The storage battery consists of a single round 
 lead cell with concentric electrodes inside a cylindrical vessel A covered with 
 a waterproof lid of the same material. The holes in the terminal sockets 
 contain bushings made of acidproof metal into which removable terminals 
 Pi and P 2 are fitted. These terminals are pressed upward by the terminal 
 springs W\ and Wi against the contact segments K\ and Kz of the switch, 
 carrying in this manner the current to the incandescent lamp. Terminals 
 and springs can be easily taken out and cleaned by washing in warm water. 
 In charging storage batteries gases develop which must have an oppor- 
 tunity to escape. It is therefore impossible to make the cells air-tight. An 
 ordinary opening would allow the acid to run out in case the cell were upset. 
 The center of the cell is therefore equipped with a celluloid tube B which 
 communicates by means of a small side tube F with the upper part of the 
 cell where the gases collect. The gases, therefore, may pass from the cell 
 57 
 
898 
 
 VENTILATION OF MINES 
 
 through the side tube F and finally through the center tube C to the open, 
 while any particles of acid will be deposited in the cylinder B. Even if the 
 cell is turned upside down no acid can escape and the lamps will burn upside 
 down without leaking. 
 
 The weight of this lamp in standard size is 5 Ib. Its height, not including 
 hanger, is 10J in., while its largest diameter is 3| in. The lamp consumes 
 0.85 amp. at 2 volts. The battery has a capacity of 16 amp.-hr. and the 
 maximum charging current should not exceed 2 amp. This general design, 
 however, is built in four sizes, ranging from 1* to 5 Ib. in weight and in 
 capacities ranging from 4 to 16 hr. for one discharge and producing a light 
 ranging from 0.75 to 3 c.p. 
 
 Special Forms of the Ceag Lamp. A number of modifications of the Ceag 
 lamp have been developed. Lamps are made for rescue parties, cages, 
 
 FIG. 12 
 
 powder magazines, shaft lighting, shaft inspection, loading places, blasting; 
 also for head and tail lamps of trips. The lamp shown in Fig. 8 is similar 
 to the standard design, but has the incandescent lamp mounted on one side 
 and combined with a reflector projecting the light in one direction. _ This 
 lamp is used for inspection and for a head and tail lamp. It is made in the 
 same capacities as the standard lamp. 
 
 The shaft lamp shown in Fig. 9 is arranged with an adjustable arm carry- 
 ing the incandescent lamp and is made to furnish from 8 to 24 c.p., burning 
 from 7 to 12 hr. on one charge, according to size. 
 
 Fig. 10 is another type of shaft lamp without the adjustable arm. It is 
 made for 8 to 12 c.p. and to furnish light from 10 to 15 hr. on one charge. 
 
 Fig. 11 is constructed to project light downward. It is built for from 8 to 
 32 c.p. and for a length of discharge of from 7 to 15 hr. 
 
 Cap Lamps. Naked-flame cap lamps have ^ng been used in this country, 
 and it is but natural that the miner should desire an electric lamp of similar 
 utility. The lamps developed to meet this demand are essentially of two 
 
VENTILATION OF MINES 
 
 899 
 
 parts, the storage battery being carried on the belt while the lamp proper is 
 attached to the cap, the two being connected by a suitable flexible cable. 
 Such a lamp is shown in Fig. 12, while Fig. 13 shows the general principles 
 of construction. The incandescent lamp bulb is mounted inside a parabolic 
 reflector provided with a lens. A ball joint may also be incorporated in the 
 design, permitting the wearer to direct the light beam where it is most 
 needed. The flexible cable connecting the battery to the lamp is heavily 
 insulated and in addition is armored at both ends where the liability of 
 bending short is the greatest. Furthermore, an alloy with a low melting point 
 is employed in this cable so that in case of accident to the lamp and the pos- 
 sible short-circuiting of the battery, this alloy will melt and destroy the 
 short-circuit before a sufficient temperature has been attained to render 
 the ignition of mine gases possible. 
 
 FIG. 14 
 
 Charging Stations. After a shift in the mine an electric safety lamp must 
 be left at the lamp house to be cleaned and recharged. Special charging 
 racks have been designed for this purpose, one or more charging circuits 
 being employed. Each circuit should be equipped with a switch, a rheostat 
 and an ammeter. The rheostat should be provided with surplus resistance 
 so that less than a full complement of cells may be charged. A portable 
 voltmeter of suitable capacity, say 3 volts, should also be provided so that 
 readings may be taken on each individual cell. After charging, cleaning and 
 reassembling, the lamps are placed in special racks from which the miners 
 remove them when starting a new shift. 
 
900 VENTILATION OF MINES 
 
 Electric charging stations or lamp houses, particularly if many lamps are 
 to be handled, follow the same general principles of design as do those where 
 oil-burning safety lamps are used. No special arrangements need, however, 
 be made for the storage and handling of dangerous inflammable oils. Fig. 
 14 shows a lamp house designed to accommodate 4,000 lamps. It contains 
 a charging room with 20 racks, three small motors for buffing and cleaning 
 and a distribution board with a watt-hour meter. There is also a store 
 room for receiving the lamps when they are ready for service, and a repair 
 shop. A small room is also employed for a number of ordinary safety lamps 
 to be used by the fire bosses. To secure reliability of service it is essential 
 that care and intelligence be employed in the maintenance and repair of 
 any electric safety lamp. 
 
 ACETYLENE LAMPS 
 
 Acetylene, C 2 H 2 , is formed by the action of water on calcium carbide, 
 Ca.Cz, by the reaction CaC 2 + 2H 2 O = Ca(OH) 2 + C 2 H 2 . The calcium 
 carbide is made by fusing together lime and coke in the electric furnace. 
 Commercial carbide frequently contains small amounts of calcium sulphide 
 and, rarely, minute traces of calcium phosphide which will form hydrogen 
 sulphide and phosphide, respectively, with water. Both of these gases are 
 extremely poisonous, but their percentage in mine air, when derived from 
 acetylene lamps, is so insignificant as to be negligible. 
 
 While the carbide of magnesium yields about 50% more acetylene than 
 the carbide of calcium, it is too costly for commercial use. 
 
 Acetylene ignites at 896F. and burns with an extremely white flame to 
 carbon dioxide and vapor of water, the reaction for combustion in oxygen 
 being 2C 2 H 2 + 5O 2 = 4CO 2 + 2H 2 O. When the oxygen content of the air 
 is reduced to 16% the acetylene flame becomes distinctly yellow, and at 
 12 to 13 % of oxygen it is extinguished. 
 
 The standard acetylene, or carbide, lamp consists of a small water tank 
 screwed on top of a container which is about half filled with small lumps of 
 calcium carbide. The inflow of water and, consequently, the production of 
 gas, is regulated by a valve operated from the top or the side of the lamp. 
 The lamp is usually provided with a reflector behind the flame, and the burner 
 is similar to that employed in a jet for burning ordinary illuminating gas, 
 no wick being used. 
 
 While there are many shapes and sizes of acetylene lamps, the common 
 form is about 4 in. high and weighs, when charged, about 6 oz. The average 
 consumption of carbide is about 4 oz. per 8-hr, shift at a cost of 2.5 c. with 
 carbide at 10 c. per Ib. Mr. G. W. Pfeiffer gives the relative cost per man 
 per shift for various types of lamps at a Mexican mine, where the price of 
 materials is greater than in the United States, as: Mixture of coal- and lard- 
 oil, 6 c.; miners' oil, 15 J c.; acetylene, 5 c. 
 
 The Bureau of Mines states that ordinary carbide lamps when fitted with 
 a reflector and with a flame 1 to 1J in. long give a candlepower head-on of 
 4.2 to 6.2 and at right angles to the flame of .87 to 1.45. Without a reflector, 
 the head-on candlepower of these lamps averages 1.9 to 2.15 and at right 
 angles 1.9. In comparison, the maximum average candlepower of miners' 
 and drivers' oil-burning lamps is stated to be 1.4 to 1.9. 
 
 Carbide should be kept in tightly sealed canisters and the contents of the 
 container should not be thrown at random about the mine as there will 
 usually be some unconsumed carbide in it which, in contact with water, may 
 generate sufficient acetylene to start a fire if this gas should be accidentally 
 ignited; special metal tanks should be provided at convenient intervals into 
 which the exhausted carbide may be thrown. 
 
 EXPLOSIVE CONDITIONS IN MINES 
 
 In the ventilation of gaseous seams, the air current may be rendered 
 explosive by the sudden occurrence of any one of a number of circum- 
 stances that cannot be anticipated. Among these are the following: (1) 
 Derangement of the ventilating current. (2) Sudden increase of gas due to 
 outbursts, falls of roof, feeders, fall of barometric pressure, etc. (3) Pres- 
 ence of coal dust thrown into suspension in the air, in the ordinary working of 
 the mine, or by the force of blasting at the working f^ce, or by blown-out, 
 or windy shots. (4) Pressure due to a heavy blast, or any concussion of the 
 air caused by closing of doors, etc. (5) Rapid succession of shots in close 
 workings. (6) Accidental discharges of an explosive in a dirty atmosphere. 
 
VENTILATION OF MINES 901 
 
 Any or all of these causes may precipitate an explosion at any moment. 
 Hence, the condition of the air current should be maintained far within the 
 explosive limit. The explosive conditions vary considerably in different 
 coal seams. The nature of the coal and its enclosing strata, its friability 
 and inflammability, together with the character of its occluded gases, deter- 
 mine, to a large extent, the explosive conditions in the seam. Experience 
 in any particular seam or district must always be the best guide and furnish 
 the best standard for determining the exploding power of any given lamp 
 flame. For example, a 2-in. flame may be comparatively safe in a small mine 
 where the coal is hard and not particularly inflammable, while a IJ-in. flame 
 cap would be considered unsafe in mines where the conditions are more 
 favorable to the^generation of gas and formation of coal dust. The daily 
 output of the mine and the general care that is enforced upon the miners 
 at the working face are factors that should always be considered and taken 
 into serious account in determining explosive conditions. 
 
 Derangement of Ventilating Current. -The flow of the air current must be 
 uniform and continuous. Doors must be kept closed, since the mere setting 
 open of a door, for a short period of time, may be enough to make an explo- 
 sive condition possible. Any contemplated change in the current, by the 
 erection of brattices, air bridges, stoppings, etc., should be carefully con- 
 sidered before the work is begun, and every precaution adopted to secure the 
 safety of the men. Derangement of the current may occur through a fall 
 of roof upon the main airway, by which the area of the airway is reduced, 
 which results in the ^reduction of the quantity of air traversing the mine. 
 If this fall is not noticed at once, serious results may happen. The utmost 
 vigilance is therefore required on the part of fire bosses and all connected with 
 mine workings. The failure of the ventilating apparatus is another source 
 that gives rise to the derangement of the current. As a rule, furnaces are 
 not now employed for the ventilation of gaseous seams. There are, however, 
 some furnaces in use in such seams, and these require constant attention lest 
 the fire should burn low. Upon any accident occurring to the ventilating 
 machinery, notice should at once be given to the inside foreman, and the 
 men withdrawn as rapidly as possible. 
 
 A sudden increase of gas may occur at any time in a gaseous seam, owing 
 to an outburst, which suddenly yields a large volume of gas and may render 
 the mine air in that section extremely explosive. The men working on the 
 return of such a current must be hastily withdrawn, and all open lights 
 extinguished. A heavy fall of coal in the mine workings or in the airways, 
 or the tapping of a large gas feeder, produces the same effect in a less degree. 
 The nearer to the face of the workings the fall of roof takes place, the more 
 liable it is to be followed with a large flow of gas, inasmuch as the gas near 
 the face has not had time to drain off, as in the case of old workings. This 
 fact is always true in reference to new workings in a gaseous seam. The gas 
 continues to flow freely for a considerable period, when its flow gradually 
 decreases until it about ceases. When a large feeder has been tapped, it 
 may be plugged for a time, if necessary, but the better practice is to allow it 
 to flow freely and diffuse into the air current, which should be sufficiently 
 increased to dilute the quantity of gas given off and to render it inexplpsive. 
 The men upon the return air should be notified. It is dangerous practice to 
 light these feeders. 
 
 When there is a large area of abandoned workings in the mine, any con- 
 siderable fall of barometric pressure is usually followed by an outflow of gas 
 from the gobs or waste places of the mine. A fall of 1 in. in 5 hr. represents 
 a very rapid decrease of barometric pressure. At all large collieries there is, 
 or should be, a good standard barometer located upon the surface near the 
 shaft. In many cases, these barometers are self-recording, and are often 
 provided with an automatic alarm that gives warning whenever a fall of 
 barometric pressure occurs. This warning should at once be conveyed to 
 the men in the workings, and every precaution adopted to avoid evil results. 
 The fact is fairly well established that a fall of atmospheric pressure is not 
 followed by an outflow of gas from the mine workings for the space of, say, 
 3 hr. after such fall occurs. This statement^must be regarded with caution, 
 however, as it largely depends on the condition and extent of the abandoned 
 workings. Where these are full of gas, its expansion affects the condition of 
 the airways much more quickly than in cases where these workings places 
 are partly ventilated. 
 
 Effect of Coal Dust in Mine Workings. According to the inflammability 
 of the coal the presence of coal dust in a finely divided state becomes a 
 
902 VENTILATION OF MINES 
 
 dangerous factor. Certain coals are friable and easily reduced to fine dust 
 which in the course of ordinary operations becomes stirred up and is sus- 
 pended in the air. _ For a long time it was a much disputed question whether 
 the presence of this dust was a dangerous factor unless some gas was also 
 present in the atmosphere. Evidence secured in numerous investigations 
 following explosions that have occurred during recent years have established 
 the explosibility of coal dust when acted upon by a flame of sufficient inten- 
 sity, beyond the slightest doubt. The exact action of the flame on such 
 dust is but imperfectly understood, but the action once started is continuous 
 as long as the explosive medium is available. Naturally, quantities of 
 methane will greatly^ increase the violence, but its presence is unnecessary 
 to produce an explosion. 
 
 Regarding the prevention or the checking of gas and dust explosions the 
 Bureau of Mines in numerous experiments has proved that an explosion 
 cannot originate from thoroughly wet coal dust, but that it is not easy to wet 
 piles of coal dust even with well-humidified air currents. This is an impor- 
 tant feature. When a saturated air current passes through a mine it dampens 
 the roof, floor, and sides, but the coal dust itself when in accumulations 
 appears to repel moisture; even with long exposure dust like that from the 
 Pittsburgh seam takes up only 1 or 2 % of moisture, though the walls and floor 
 may become damp. The surprising result of experiments makes it evident 
 that it is necessary to remove coal-dust accumulations, so that, after a pas- 
 sageway has been well dampened, any particles of dust falling on wet sur- 
 faces will themselves become wet. It has been observed after some dust- 
 explosion disasters that the explosion has traversed entries in which there was 
 standing water along the bottom, but on the other hand examination of the 
 benches and projections along the sides of such entries has disclosed quantities 
 of dry dust. Also it has been observed that timbers frequently carry on 
 their upper surfaces quantities of dust sufficient to propagate an explosion. 
 Consequently, the Bureau emphasizes two precautions, namely, first remove 
 all accumulations of dry dust and then keep the entries wet or use a coating of 
 rock dust. There will then be little danger of explosion. 
 
 One of the principal mediums for distributing coal dust about the mines 
 is the mine car. It is often loaded so high that the coal strikes the timbers 
 or roof and is so jarred that it falls to the roadway where it is ground to a 
 powder by men and mules. Tight cars should be used wherever possible. 
 Gateless cars are used in Europe except in Wales and Scotland and revolving 
 tipples are employed for dumping them. By proper arrangement the coal 
 is thus discharged with little breakage. In the case of a downcast shaft the 
 shaking screens in the tipple should not be placed immediately adjacent to 
 the shaft and if they are already near it, vacuum dust collectors should be 
 installed 9ver the screens and chutes. 
 
 Otherwise, a large quantity of duat may be drawn down the shaft. In a 
 certain mine in England in which rock dust was used to counteract the 
 danger of coal dust a thick film of coal dust was observed on top of the rock 
 dust, the deposit extending for a distance of 500 or 600 ft. from the shaft. 
 Had it not been for the light-colored rock dust the deposit could not have 
 been seen. The coal dust had been collecting for only 2 mo. subsequent to 
 the time when the rock dust had last been laid. This mine has since put in 
 vacuum dust collectors over its screens. In many of the recently built 
 European plants it is the practice to place the screening plant 100 to 200 ft. 
 distant from the downcast shaft. 
 
 The Bureau of Mines in Technical Paper No. 56 has outlined a number of 
 preventive methods to be used in soft-coal mines for fighting the coal-dust 
 danger. Naturally, there is but one way to prevent any coal-dust explo- 
 sions, and that is to wet or wash down all rooms or haulageways where coal 
 dust is likely to accumulate and to keep such places in a moist condition. 
 This is often impossible and impractical, but the following methods suggested 
 by the Bureau of Mines are all highly commendable. 
 
 Humidifying the Air Current. With the humidifying system the intake 
 air current is so saturated or supersaturated as to carry the moisture into 
 the mine in minute but constant quantities every minute of the day. The 
 amount of water vapor that air will carry or support varies with its tempera- 
 ture. For example, if 3,300 cu. ft. of air will support 1 Ib. of water at freez- 
 ing or 32F. then at 62 it will support 3 Ib. and a current of air of 3,300 cu. 
 ft. per min. entering a mine at 32F. would absorb moisture up to its capacity 
 at 62 or whatever the temperature may be. Thus ordinarily the current of 
 air takes up and carries away 20 Ib. per min. or about 2$ gal. per min., which 
 
VENTILATION OF MINES 
 
 903 
 
 would be over 3,500 gal. per day. This going on for months makes a mine 
 more and more dry. No ordinary sprinkler system will entirely overcome 
 this for the air will only absorb nK>isture. As it becomes heated it expands 
 and dries. On the other hand, moisture in saturated air entering a mine at a 
 higher temperature than that within will condense over the sides and roof 
 of the haulageways and working places, thereby depositing water instead of 
 withdrawing it. This principle seems to 
 be the solution for the coal-dust problem 
 from a humidifying standpoint. In this 
 connection, the Colorado Fuel and Iron 
 Co. installed radiators and steam pipes 
 in the intake of its coal mines in southern 
 Colorado, the radiators to raise the tem- 
 perature of ingoing air, and the steam 
 pipes to inject the necessary moisture in 
 the form of steam. 
 
 The percentage of saturation obtained 
 will depend upon the volume of air en- 
 tering the mine and its temperature, the 
 heating surface of the radiator and the 
 amount of moisture supplied. That is, 
 the larger the volume and the lower the 
 outside temperature, the greater the 
 heating surface and amount of moisture 
 will have to be to give the same results. 
 
 Another method of supplying a mine 
 with a preheated and humidified venti- 
 lating air is suggested by the operation 
 and tests of an evaporative condenser 
 installed at the central power plant of a 
 group of mines near Pittsburg, to handle the exhaust steam from turbo gen- 
 erators. This suggestion is made in contradistinction to the steam jet and 
 steam coil heating method. 
 
 The condenser referred to for the purpose of humidifying air, consists of 
 a nest of 900 vertical, 1^-in. diameter copper tubes, 19_ft. long, fixed top 
 and bottom in suitable headers. The tubes are housed in on two sides, as 
 
 FIG. 1 
 
 ft 
 
 and, 
 
 toPullfopor from Condenser i 
 it to Mine for Ventilation 
 
 Man way 
 
 Exhaust 
 
 Haulage Way 
 
 Exhaust 
 
 FIG. 2. Arrangement of Entries, 
 Fan Blowing 
 
 ran to Pull vapor from 
 
 Condenser thru Mine 
 
 Man way 
 
 FIG. 3. Arrangement of Entries, 
 Fan Exhausting 
 
 shown in Fig. 1, one side being left open for the admission of air, which is 
 drawn in and around the tubes, by a fan placed opposite the open side. 
 The vapor generated by the evaporation of water, with which the tubes 
 are mechanically wetted, is picked up by the air as it passes around the tubes. 
 Where the arrangement of a mine's power equipment will permit,_ it is 
 suggested that the usual mine fan be made to perform the double service of 
 
904 VENTILATION OF MINES 
 
 drawing the air around condenser tubes, where it takes on heat and moisture 
 in proportion to the work of condensation, as well as through the mine 
 By test performance, the amount of water evaporated per pound of steam, 
 condensed is approximately 1 Ib. Figures 2 and 3 will indicate the arrange- 
 ment of the connections to a condenser, fan, and mine, when blowing or 
 exhausting. 
 
 Many variations of the condenser as described could be used for the sug- 
 gested purpose, but the evaporative kind seems especially adapted, inasmuch 
 as the air required to maintain its efficiency obtains its heat and humidity 
 in a single operation. 
 
 It is conceded that cold air must be heated and have a sufficient amount of 
 moisture given to it, to prevent it from absorbing moisture from the mine, as 
 it gradually becomes heated during its passage through the air-courses, 
 thereby increasing its moisture-carrying capacity. The assumption is made 
 that, if the air supplied to a mine be heated to the mine's normal temperature, 
 and that be also given a high relative humidity, it will issue from that mine 
 having practically the same temperature and humidity. It is further as- 
 sumed that, should it be possible to sufficiently heat and humidify the re- 
 quired amount of ventilating air, somewhat in excess of the mine's normal 
 temperature, and give it a proportional burden of humidity, an amount of 
 moisture would be given off by the air, as its temperature is adjusting itself 
 to that of the mine. The basis for the last assumption lies in the nil effect 
 that any quantity of heat given off by the ventilating air, so treated, would 
 have towards raising the normal temperature of a mine. 
 
 However, any interchange of heat that might take place, from air to the 
 walls of a mine, would tend to diminish the moisture-carrying capacity of 
 the air, and would result in the deposit of a certain amount of moisture. The 
 possibility of conditioning sufficient ventilating air, and the amount of 
 exhaust steam required to perform the work, can be judged from the result 
 of a series of problems, the results of which can be displayed graphically 
 by means of curves. _ 
 
 By virtue of a suitable condenser, the air used as a vehicle to carry off 
 the vapor, equal to the amount of water placed on the tubes necessary to 
 effect condensation within them, produces in one operation a preheated and 
 humidified atmosphere. It seems possible to adjust the degree of heat and 
 humidity imparted to air passing through such a condenser to such a degree 
 that the comfort of the miner would in no way be affected. By so doing, 
 however, it might be necessary to forego some inches of vacuum which might 
 otherwise be available at the engine in order to maintain the adjustment. 
 Where a sufficient horsepower of exhaust steam is not at hand, the amount 
 of coal required under a boiler, working at 60 % efficiency, to produce low- 
 pressure steam used in coils to heat air, is approximately 6J T. per 24 hr., 
 for a unit of 100,000 cu. ft. of ventilating air per min. In such an arrange- 
 ment, it must be understood that the air is humidified by a second operation 
 and does not come into direct contact with the steam formed in the boiler. 
 
 From a hygienic standpoint, mine ventilating air treated in the manner 
 described would, to a considerable extent, bring about the same results that 
 are claimed for devices now being used to condition air used to ventilate 
 public buildings, assembly halls, and many up-to-date residences. 
 
 Considering the many factors entering into the successful operation of 
 such an air-tempering device, when adapted to the general mine proposition, 
 it is quite difficult to draw definite conclusions; however, the foregoing matter 
 possesses sufficient merit to warrant consideration of mine operators. 
 
 Hygrometers. The use of the hygrometer is in its infancy for observations 
 in coal mines and while the complete rotary sling hygrometer or psychrome- 
 ter is undoubtedly the most accurate for obtaining humidity readings, it 
 is too delicate an instrument to carry around underground. The hygrometer 
 shown in Fig. 4 is inclosed in a carrying case which converts it into a pocket 
 instrument that is not liable to become broken when carried about in the 
 mine. The wet and dry thermometers are inserted in each side of a split 
 cylindrical case which is readily closed or opened by a handle. It is easy to 
 swing but it is not so quick as the sling hygrometer. The thermometers 
 are mounted on springs to lessen the danger of breakage, and this, with the 
 case, makes a handy arrangement for underground observations. 
 
 Recording hygrometers, giving a single record of the relative humidity 
 have been in use for a long time. Engineers have appreciated the distinct 
 advantage of having a record of both the dry-bulb temperature and the 
 wet-bulb temperature independently but simultaneously on the same chart. 
 
VENTILATION OF MINES 
 
 905 
 
 Such an instrument has the added advantage in the ease with which its 
 accuracy can be checked with a standard thermometer at all times. The 
 importance of proper conditions of temperature and humidity is being more 
 and more appreciated in its effect on coal dust. 
 
 The recording hygrometer illustrated in Fig. 6 consists of two sensitive 
 bulbs mounted in tandem back of the case, the wet bulb being jacketed and 
 kept moist by maintaining water at a constant level in a trough beneath the 
 bulb. The pen arms are attached directly to shafts concentric with the 
 
 FIG. 5 
 
 helical tube bulbs. The case is 
 mounted on a swivel bracket en- 
 abling the swinging of the instru- 
 ment at right angles to the wall 
 or support, and giving easy ac- 
 cess to the inverted glass bottle 
 serving as a water reservoir. It 
 is made to cover ranges between 
 the freezing and boiling points of 
 water (32 to 212F. or 0-100C.). 
 The principle of the construc- 
 tion of the recording hygrometers 
 is shown in Fig. 5. In the cut A 
 represents the reservoir, the tube 
 B, the dry bulb which records the 
 atmospheric temperature, and C 
 the wet bulb which is covered 
 with a special jacket leading 
 down into trough D, containing 
 water. The bulb C is always 
 cooler than B due to the evap- 
 oration of the water. The evap- 
 oration increases or diminishes 
 
 FIG. 6. Recording Hygrometer ^ .__ . 
 
 according to the amount of moisture in the air Tak ing ^difference 
 between the two thermometer readings and consulting the table that is 
 
906 VENTILATION OF MINES 
 
 explosive condition of the air would necessarily have to be close to the limit, 
 in order for such a slight occurrence to precipitate an explosion. The factor 
 of pressure as increasing the explosiveness of gaseous mixtures should be 
 considered and constantly borne in mind. 
 
 Rapid Succession of Shots in Close Workings. It constantly happens that 
 two, three, or more shots are fired by means of fuse or touch squibs in a 
 single chamber or heading,, where the circulation of air is not always the 
 best. The practical effect is that a considerable quantity of carbonic-oxide 
 gas, CO, is produced by the firing of the first shot, and this gas does not have 
 time to diffuse or become diluted by the air current before it is fired by the 
 flame of the following shots. An explosion may often be precipitated by 
 such an occurrence, if the workings are at all dusty. Two shots at the most 
 are all that should be fired at one time in a close chamber or heading. 
 
 Mine explosions are commonly the result of the ignition of firedamp with 
 an open lamp, or coal dust exploding after being set in motion by an explo- 
 sion of gas, blown out shot, fall of roof or a rush of air and an electric arc. 
 Numerous other cases of explosions are recorded but are not in the class 
 commonly referred to as mine explosions. 
 
 Before the coal-dust theory was advanced and proven, it was believed 
 that wherever the greatest damage was done, was the point where the 
 explosion originated. This is by no means always the case. 
 
 QUANTITY OF AIR REQUIRED FOR VENTILATION 
 
 The quantity of air required for the adequate ventilation of a mine cannot 
 be stated as a rule applicable in all cases. Regulations that would supply a 
 proper amount of air for ventilation of a thick seam would be found to cause 
 great inconvenience if applied without modification to the workings in a 
 thin seam. Likewise, the ventilation of an old mine with extended workings, 
 a large area of which has been abandoned, and in many cases not properly 
 sealed off, will require, naturally, a larger quantity of air per capita than a 
 newly opened mine or shaft. The natural conditions existing in rise and 
 dip workings, with respect to the gases that may be liberated or generated in 
 those workings, call for the modification of the quantity of air required in 
 each case. For example, dip workings, where mucn blackdamp is generated, 
 will require a larger quantity of air, or higher velocity at the working face, 
 to carry off such damps; and rise workings, liberating a large amount of 
 marsh gas, will likewise require a higher velocity at the working face. On 
 the other hand, a reversal of these conditions, such as a large quantity of 
 marsh gas being liberated in dip workings, or a similar amount of blackdamp 
 being generated in rise workings, will require a comparatively low velocity 
 of the air at each respective working place. 
 
 Quantity Required by State Laws. The quantity of air required by the 
 laws of the several states is generally specified as 100 cu. ft. per man per 
 min., and in many cases an additional amount of 500 cu. ft. per animal per 
 min. is stated. This quantity is in no case stated as the actual amount of 
 air required for the use of each man or animal, but is only the result of experi- 
 ence, as showing the quantity of air required for the proper ventilation of 
 the average mine, based on the number of men and animals employed. The 
 number of men employed in a mine is an indication of the extent of the work- 
 ing face, while the number of animals employed is an indication likewise of 
 the extent of the haulage roads, or the development of the mine. These 
 amounts refer particularly to non-gaseous seams. 
 
 The Bituminous Mine Law of Pennsylvania specifies that there shall be 
 not less than 150 cu. ft. per min. per person in any mine, while 200 cu. ft. 
 are required in a mine where firedamp has been detected. 
 
 The Anthracite Mine Law of Pennsylvania specifies a minimum quantity 
 of 200 cu. ft. per min. per person. Each of these laws contains modifying 
 clauses, which specify that the amount of air in circulation shall be sufficient 
 to "dilute, render harmless, and sweep away" smoke and noxious or dan- 
 gerous gases. Some mining companies specify the amount of air that must 
 pass the last breakthrough and that the breakthrough shall not be more than 
 a certain distance from the face of room or heading. One such company 
 operating several mines in a region where mine explosions are fairly frequent 
 has never had an explosion. Its rule is to have 12,000 cu. ft. of air per min. 
 passing the last breakthrough which must not be over 100 ft. from the work- 
 ing face. 
 
 Quantity of Air Required for Dilution of Mine Gases. To determine this 
 requires a knowledge of the quantity of gas generated or liberated in the 
 
VENTILATION OF MINES 907 
 
 workings. The quantity of air for dilution should be ample, and should be 
 such as not to permit the condition of the current to approach the explosive 
 point. The ventilation should be ample at the face. 
 
 Quantity of Air Required to Produce the Necessary Velocity of Current at 
 the Face. This consideration modifies considerably the quantity of air 
 required for the ventilation of thick and thin seams. The velocity of the 
 current is dependent not only on the quantity of air in circulation, but on the 
 area of the air passage. This area is quite small in thin seams, and often very 
 large in thick seams. As a result, the velocity is often low at the face of 
 thick seams, and insufficient for the proper ventilation of the face, although 
 the quantity of air passing into such a mine may be very large. A certain 
 velocity of the current is always required in order to sweep away the gases. 
 This velocity depends on the character of the gases and the position of the 
 workings. Heavy damps are hard to move from dip workings where they 
 have accumulated; and, likewise, lighter damps accumulating at the face 
 of steep pitches are hard to brush away, and the velocity of the current in 
 these cases must be equal to the task of driving out these gases. 
 
 ELEMENTS IN VENTILATION 
 
 The elements in any circulation of air are (fl) horsepower, or power ap- 
 plied; (b) resistance of the airways, or mine resistar.ee, which gives rise to 
 the total pressure in the airway; (c) velocity generated by the power applied 
 against the mine resistance. 
 
 Horsepower or Power of the Current. The power applied is often spoken 
 of as the power upon the air. It is the effective power of the ventilating 
 motor, whatever this may be, including all the ventilating agencies, whether 
 natural or otherwise. The power upon the air may be the power exerted by 
 a motive column due to natural causes, or to a furnace, or may be the 
 power of a mechanical motor. The power upon the air is always measured 
 in foot-pounds per minute, which expresses the units of work accomplished 
 in the circulation. 
 
 Mine Resistance. The resistance offered by a mine to the passage of an 
 air current, or the mine resistance, is due to the friction of the air rubbing 
 along the sides, top, and bottom of the air passages. This friction causes the 
 total ventilating pressure in the airway, and is equal to it. Calling the 
 resistance R, the unit of ventilating pressure (pressure per square foot) p, 
 and the sectional area of the airway a, we have, R = pa; that is to say, the 
 total pressure is equal to the mine resistance. 
 
 Velocity of the Air Current. Whenever a given power is applied against a 
 given resistance, a certain velocity results. For example, if the power u 
 (foot-pounds per minute) is applied against the resistance pa, a velocity v 
 (feet per minute) is the result; and since the total pressure pa moves at 
 the velocity v, the work performed each minute by the power applied is the 
 product of the total pressure by the space through which it moves per 
 minute, or the velocity. Thus, u = (pa)v. 
 
 Relation of Power, Pressure, and Velocity. The relation of these ele- 
 ments of ventilation is not a simple relation. For example, a given power 
 applied to move air through an airway establishes a certain resistance and 
 velocity in the airway. The resistance of the airway is not an independent 
 factor; that is to say, it does not exist as a factor of the airway independent 
 of the velocity, but bears a certain relation to the velocity. Power always 
 produces resistance and velocity, and these two factors always sustain a fixed 
 relation. 
 
 This relation is expressed as follows: The total pressure or resistance varies 
 as the square of the velocity; i.e., if the power is sufficient to double the 
 velocity, the pressure will be increased 4 times; if the power is sufficient to 
 multiply the velocity 3 times, the pressure will be increased 9 times. Thus, 
 we observe that a change of power applied to any airway means both a 
 change of pressure and a change of velocity. 
 
 Again, since the power is expressed by the equation u = (pa)v, and since 
 pa, or the total pressure, varies as v 2 , the work varies as v 3 . From this it 
 follows that, if the velocity is multiplied by 2, and, consequently, the total 
 pressure by 4, the work performed (pa)v will be multiplied by 2 s = 8. We 
 thus learn that the power applied varies as the cube of the velocity. 
 
 MEASUREMENT OF VENTILATING CURRENTS 
 
 The measurement and calculation of any circulat9n in a mine airway 
 includes the measurement of (a) the velocity of the air current, (b) of pres- 
 
908 
 
 VENTILATION OF MINES 
 
 sure, (c) of temperature, (d) calculation of pressure, quantity, and horsepower 
 of the circulation. 
 
 These measurements should be made at a point in the airway where the 
 airway has a uniform section for some distance, and not far from the foot of 
 the downcast shaft or the fan drift. 
 
 Measurement of Velocity. For the purpose of mine inspection, the veloc- 
 ity of the air current should be measured at the foot of the downcast, at the 
 mouth of each split of the air current, and at each inside breakthrough, in 
 each split. These measurements are necessary in order to show that all the 
 air designed for each split passes around the face of the workings. 
 
 The measurement of the velocity of a current is most conveniently made 
 by means of the anemometer. This instrument consists of a vane placed 
 in a circular frame and having its blades so inclined to the direction of its 
 motion that 1 ft. of lineal velocity in the passing air current will produce 1 
 re volution of the vane. These revolutions are recorded by means of several 
 pointers, each having a separate dial upon the face of the instrument, the 
 motion being communicated by a series of gearwheels arranged decimally to 
 each other. Most anemometers are provided with a large central pointer 
 that makes 1 revolution for each 100 revolutions of the vane. The dial for 
 this pointer is marked by 100 divisions, which record the number of lineal 
 feet of velocity. In very accurate work with the anemometer, certain con- 
 stants are used as suggested by the instrument maker, but these constants 
 are of little value in ordinary practice and are of doubtful value even in more 
 accurate observations. 
 
 The measurement of the velocity of an air current must necessarily 
 represent only approximately the true velocity in the airway. The air 
 travels with a greater velocity in the center of the airway , and is retarded at 
 the sides, top, and bottom by the friction of these surfaces. Hence, the 
 air to a large extent rolls upon these surfaces, which naturally generates an 
 eddy at the sides of airways. When measuring the air, the anemometer 
 should be held in a position exactly perpendicular to the direction of the 
 current, and moved to occupy different positions in the airway, being held 
 an equal time in each position, or it may be moved continuously around 
 the margin of the airway, and through the central portion. 
 The person taking the observation should observe the caution 
 of not obstructing the area of the airway by his body, as the 
 area is thereby reduced, and the velocity of the current in- 
 creased. The area of the airway is accurately measured at 
 the point where the observations are taken. 
 
 To obtain the quantity of air passing (cubic feet per minute) , 
 multiply the area of the airway, at the point where the velocity 
 is measured, by the velocity. 
 
 EXAMPLE. The anemometer gives a reading of 1,320 ft. in 
 2 min., the height of the airway is 6 ft. 6 in., and its average 
 width 8 ft. 8 in. What volume of air is passing in the airway 
 per minute? 
 
 6* X 81 X 
 
 37,180 cu. ft. per min. 
 
 The measurement of the ventilating pressure is made by 
 means of a water column in the form of a water gauge. 
 
 Water Gauge. The water gauge is simply a glass U-tube 
 open at both ends. Water is placed in the bent portion of the 
 tube, and stands at the same height in both arms of the tube 
 when each end of the tube is subjected to the same pressure. 
 If, however, one end of the tube is subjected to a greater 
 pressure than the other end, the water will be forced down in 
 FIG. 7 that arm of the tube, and will rise a corresponding height in 
 the other arm, the difference of level in the two arms of the 
 tube representing the water column balanced by the excess of pressure to 
 which the water in the first arm is subjected. An adjustable scale grad- 
 uated in inches measures the height of the water column. The zero of the 
 scale is adjusted to the lower water level, and the upper water level will 
 then give the reading of the water gauge. One end of the glass tube is 
 drawn to a narrow opening to exclude dust, while the other end is bent to 
 a right angle, and passing back through the standard to which the tube is 
 attached, is cemented into the brass tube that passes through a hole in the 
 partition or brattice, when the water gauge is in use. The bend of the tube 
 
VENTILATION OF MINES 
 
 909 
 
 is contracted to reduce the tendency to oscillation in the height of water 
 column (see Fig. 7). 
 
 When in use, the water gauge must be in a perpendicular position. It may 
 be placed upon a brattice occupying a position between two airways, as 
 shown at A, Fig. 8. The brass tube forming one end of the water gange is 
 inserted in a cork, and passes through a hole bored in the brattice. The 
 water gauge must not be subjected to the direct force of the air current, as 
 in this case the true pressure will not be given. Fig. 8 shows the instrument 
 as occupying a position in the breakthrough, between two entries. It will 
 be observed that the water gauge records a difference of pressure, each end 
 of the water gauge being subject to atmospheric pressure, but one end in 
 addition being subject to the ventilat- 
 ing pressure, which is the difference of 
 pressure between the two entries. The 
 water gauge thus enables us to measure 
 the resistance of the mine inbye from 
 its position between two airways. If 
 placed in the first breakthrough, at the 
 foot of the shaft, it measures the entire 
 resistance of the mine, but if placed at 
 the mouth of a split, it measures only 
 the resistance of that split. It never 
 measures the resistance outbye from its 
 position in the mine, but always inbye 
 (see Calculation of Pressure). 
 
 Calculation of Mine Resistance. 
 The mine resistance is equal to the 
 total pressure pa that it causes. This 
 mine resistance is dependent upon 
 three factors: (a) The resistance k 
 offered by 1 sq. ft. of rubbing surface 
 to a current having a velocity of 1 ft. 
 per min. The coefficient of friction k, 
 or the unit of resistance, is the resist- 
 ance offered by the unit of rubbing sur- 
 face to a current of a unit velocity. This unit resistance has been variously 
 estimated by different authorities (see following table). The value most 
 universally accepted, however, is that known as the Atkinson coefficient 
 (.0000000217). (b) The mine resistance, which varies as the square of the 
 velocity, (c) The rubbing surface. Hence, if we multiply the unit resist- 
 ance by the square of the velocity, and by the rubbing surface, we will 
 obtain the total mine resistance as expressed by the formula pa = ksv 2 . 
 
 TABLE OF VARIOUS COEFFICIENTS OF FRICTION OF AIR IN MINES. 
 
 Pressure per 
 
 Sq. Ft. Decimals 
 
 of a Pound. 
 
 J. J. Atkinson's treatise 0000000217 
 
 A. Devillez in Ventilation des Mines: 
 
 Forchies 00000000821 1 
 
 Crachet-Picquery 000000008928 
 
 Grand Baisson 000000008611 
 
 Average of 2, 3, and 4 000000008585 
 
 Used in Ventilation des Mines 000000009511 
 
 Arched Tunnels 000000002113 
 
 Along a working face of coal 
 
 G. G. Andre, Atmosphere of Coal Mines 
 
 Peclet, Cheminee (Devillez, p. 112) 
 
 D. K. Clark 
 
 According to Goupilliere's Cours d' Exploitation des Mines, 
 
 FIG. 8 
 
 000000014266 
 .000000022424 
 .000000003697 
 . 000000002272 
 
 W Fairlev 00000001 
 
 T Stanlev TameV " .00000000929 
 
 D. Murgue J . ^ iTf ! 1 1-!.! ; ! ! T! 1! ! ; .; 000000008242 
 
 It will be observed that J. J. Atkinson's coefficient is greatly in excess of 
 any other, with the exception of Andre's. Fairley's is derived from an 
 
910 VENTILATION OF MINES 
 
 average taken between Atkinson, Devillez, and Clark, and, undoubtedly, it 
 is an exceedingly simple coefficient to work out calculations with, as it will 
 save a great mass of figures. James, in his work on colliery ventilation, 
 reduces the coefficient still further on the authority of the Belgian Mine 
 Commission, but he gives a most unwieldy figure to use. 
 
 Atkinson's figure is the one most in use, and if it is too high, it errs on the 
 side of safety, and it is always advisable to have plenty of spare ventilating 
 capacity at a mine. For this reason, and until a regular and thorough inves- 
 tigation, made by a commission of competent men, provides a standard coef- 
 ficient, we prefer to abide by Atkinson's coefficient, and it is used in all our 
 calculations. 
 
 Calculation of Power, or Units of Work per Minute. If we multiply the 
 total pressure by the velocity (feet per minute) with which it moves, we 
 obtain the units of work per minute, or the power upon the air. Hence, u = 
 pav = ksv 3 , which is the fundamental expression for work per minute, or 
 power. 
 
 The Equivalent Orifice. This term, often used in regard to ventilation, 
 evaluates the mine resistance, or, as will be seen from the equation given 
 below for its value, expresses the ratio that exists between the quantity 
 of air passing in an airway and the pressure or water gauge that is produced 
 by the circulation. This term was suggested by M. Daniel Murgue, and 
 refers to the flow of a fluid through an orifice in a thin plate, under a given 
 head. The_formula expressing the velocity of flow through such an orifice 
 is v = \/2gh> multiplying both members of this equation by A, and substi- 
 tuting for the first member Av, its value q, we have, after transposing and 
 
 correcting for vena contracta, A - - t in which .62 is the coefficient 
 
 .&2VWh 
 
 for the vena contracta of the flow. Reducing this to cubic feet per minute and 
 inches of water gauge represented by *', we have, finally, the equation A = 
 
 . 0004 X . By this formula, Murgue has suggested comparing the flow of 
 
 V i 
 
 air through a mine to the flow of a fluid through a thin plate; since, in each 
 case, the quantity and the head or pressure vary in the same ratio. Thus, 
 applying this formula to a mine, Murgue multiplies the ratio of the quantity 
 of air passing (cubic feet per minute) and the square root of the water gauge 
 (inches) by .0004, and obtains an area A, which he calls the equivalent 
 orifice of the mine. 
 
 Potential Factor of a Mine. (Proposed by T. J. Beard.) Equations 8 and 
 27 pages 370^-371, give, respectively, the pressure and the power that will 
 circulate a given quantity of air per minute in a given airway. These 
 equations may be written as equal ratios, expressed in factors of the current 
 
 and the airway, respectively: thus, = , and = , which show that 
 
 q* a 3 t q> c 
 
 the ratio between the pressure and the square of the quantity it circulates in 
 any given airway is equal to the ratio between the power and the cube of the 
 quantity it circulates. Solving each of these equations with respect to q, 
 we have the following: 
 With respect to pressure, 
 
 With respect to power, 
 
 Hence we observe that, in any airway, for a constant pressure, the quan- 
 tity of air in circulation is proportional to the expression a \/ ; and, for a 
 
 \fes 
 
 a 
 constant power, the quantity is proportional to the expression $/ , which 
 
 terms are called the potentials of the mine with respect to pressure and 
 
 Q Q 
 
 power, respectively; and their values ~j= and a/- are the potentials of the 
 
 VP V" 
 
VENTILATION OF MINES 
 
 911 
 
 THE FOLLOWING TABLE OF WATER GAUGES WILL BE FOUND OF ASSISTANCE 
 IN CALCULATING THE AMOUNT OF AIR REQUIRED FOR MINE WORKINGS 
 
 
 
 
 P. 
 
 $ 
 
 o 
 
 8 
 
 
 
 
 k 
 
 o 
 a 
 
 in 
 
 | 
 
 a 
 
 I 
 
 
 
 <u 
 
 &<% 
 
 i 
 
 o 
 
 a 
 
 '' 
 
 '*< 
 
 . 
 
 co 
 
 
 
 | 
 
 S.b 
 
 S-~ 
 
 M 
 
 c a 
 
 o 
 
 
 
 1*8 
 
 |"o 
 
 sp 
 
 rt 
 
 
 
 o 
 
 0*0 
 
 si 
 
 O 
 
 '.p w 
 
 11 
 
 fc 
 
 P 
 
 
 
 O 
 
 8 
 
 11 
 
 fg 
 
 S*"" 1 
 
 
 ' 
 
 a 
 
 |l 
 
 If 
 
 I* 
 
 |<g 
 
 I 3 
 
 1 
 
 
 
 !* 
 
 So- 
 
 w 
 
 "o 3 
 
 JM 
 
 0.1 
 
 0.52 
 
 8.32 
 
 0.05 
 
 520 
 
 0.016 
 
 5.1 
 
 26.52 
 
 424.32 
 
 2.94 
 
 26,520 
 
 0.800 
 
 0.2 
 
 1.04 
 
 16.64 
 
 0.12 
 
 1,040 
 
 0.031 
 
 5.2 
 
 27.24 
 
 435.84 
 
 3.02 
 
 27,240 
 
 0.825 
 
 0.3 
 
 1.56 
 
 24.96 
 
 0.17 
 
 1,560 
 
 0.048 
 
 5.3 
 
 27.56 
 
 440.96 
 
 3.04 
 
 27,560 
 
 0.835 
 
 0.4 
 
 2.08 
 
 33.28 
 
 0.23 
 
 2,080 
 
 0.063 
 
 5.4 
 
 28.08 
 
 449.28 
 
 3.10 
 
 28,080 
 
 0.850 
 
 0.5 
 
 2.60 
 
 41.60 
 
 P. 28 
 
 2,600 
 
 0.079 
 
 5.5 
 
 28.60 
 
 457.60 
 
 3.17 
 
 28,600 
 
 0.866 
 
 0.6 
 
 3.12 
 
 49.92 
 
 0.34 
 
 3,120 
 
 0.081 
 
 5.6 
 
 29.12 
 
 465.92 
 
 3.23 
 
 29,120 
 
 0.884 
 
 0.7 
 
 3.64 
 
 58.24 
 
 0.40 
 
 3,640 
 
 0.110 
 
 5.7 
 
 29.64 
 
 474.24 
 
 3.30 
 
 29,640 
 
 0.900 
 
 0.8 
 
 4.16 
 
 66.56 
 
 0.46 
 
 4,160 
 
 0.128 
 
 5.8 
 
 30.16 
 
 482 . 56 
 
 3.38 
 
 30,160 
 
 0.913 
 
 0.9 
 
 4.68 
 
 74.88 
 
 0.51 
 
 4,680 
 
 0.141 
 
 5.9 
 
 30.68 
 
 490.88 
 
 3.40 
 
 30 680 
 
 0.930 
 
 .0 
 
 5.20 
 
 83.20 
 
 0.58 
 
 5,200 
 
 0.159 
 
 6.0 
 
 31.20 
 
 499.20 
 
 3.44 
 
 31,200 
 
 0.940 
 
 .1 
 
 5.72 
 
 91.52 
 
 0.63 
 
 5,720 
 
 0.173 
 
 6.1 
 
 31.72 
 
 507.52 
 
 3.50 
 
 31,720 
 
 0.962 
 
 .2 
 
 6.24 
 
 99.84 
 
 0.70 
 
 6,240 
 
 0.188 
 
 6.2 
 
 32.44 
 
 519.04 
 
 3.55 
 
 32,440 
 
 0.983 
 
 .3 
 
 6.76 
 
 108.16 
 
 0.75 
 
 6,760 
 
 0.205 
 
 6.3 
 
 32.76 
 
 524.16 
 
 3.61 
 
 32,760 
 
 0.993 
 
 .4 
 
 7.28 
 
 116.48 
 
 0.80 
 
 7,280 
 
 0.225 
 
 6.4 
 
 33.28 
 
 532.48 
 
 3.67 
 
 33,288 
 
 .000 
 
 .5 
 
 7.80 
 
 124.80 
 
 0.86 
 
 7,800 
 
 0.236 
 
 6.5 
 
 33.80 
 
 540.80 
 
 3.73 
 
 33,800 
 
 .024 
 
 .6 
 
 8.32 
 
 133.12 
 
 0.92 
 
 8,320 
 
 0.252 
 
 6.6 
 
 34.32 
 
 549.12 
 
 3.81 
 
 34,320 
 
 .042 
 
 .7 
 
 8.84 
 
 141.44 
 
 0.99 
 
 8,840 
 
 0.268 
 
 6.7 
 
 34.84 
 
 557.44 
 
 3.87 
 
 34,840 
 
 .056 
 
 .8 
 
 9.36 
 
 149.76 
 
 1.03 
 
 9,360 
 
 0.283 
 
 6.8 
 
 35.36 
 
 565.76 
 
 3.92 
 
 35,360 
 
 .071 
 
 .9 
 
 9.88 
 
 158.08 
 
 1.10 
 
 9,880 
 
 0.299 
 
 6.9 
 
 35.88 
 
 574.08 
 
 3.98 
 
 35,880 
 
 .083 
 
 2.0 
 
 10.40 
 
 166.40 
 
 1.15 
 
 10,400 
 
 0.315 
 
 7.0 
 
 36.40 
 
 582.40 
 
 4.01 
 
 36,400 
 
 103 
 
 2.1 
 
 10.92 
 
 174.72 
 
 1.21 
 
 10,920 
 
 0.331 
 
 7.1 
 
 36.92 
 
 590.72 
 
 4.10 
 
 36,920 
 
 .120 
 
 2.2 
 
 11.44 
 
 183.04 
 
 1.27 
 
 11,440 
 
 0.348 
 
 7.2 
 
 37.64 
 
 602 . 24 
 
 4.17 
 
 37,640 
 
 .140 
 
 2.3 
 
 11.96 
 
 191.36 
 
 1.32 
 
 11,960 
 
 0.362 
 
 7.3 
 
 37.96 
 
 607.36 
 
 4.19 
 
 37,960 
 
 .150 
 
 2.4 
 
 12.48 
 
 199.68 
 
 1.38 
 
 12,480 
 
 0.378 
 
 7.4 
 
 38.48 
 
 615.68 
 
 4.24 
 
 38,480 
 
 .166 
 
 2.5 
 
 13.00 
 
 208 . 00 
 
 1.44 
 
 13,000 
 
 0.390 
 
 7.5 
 
 39.00 
 
 624.00 
 
 4.30 
 
 39,000 
 
 .181 
 
 2.6 
 
 13.52 
 
 216.32 
 
 1.50 
 
 13,320 
 
 0.409 
 
 7.6 
 
 39.52 
 
 632.32 
 
 4.40 
 
 39,520 
 
 .193 
 
 2.7 
 
 14.04 
 
 224 . 64 
 
 1.56 
 
 14,040 
 
 0.425 
 
 7.7 
 
 40.04 
 
 641.12 
 
 4.45 
 
 40,040 
 
 .213 
 
 2.8 
 
 14.56 
 
 232.96 
 
 1.61 
 
 14,560 
 
 0.441 
 
 7.8 
 
 40.56 
 
 648.96 
 
 4.50 
 
 40,560 
 
 .230 
 
 2.9 
 
 15.08 
 
 241.28 
 
 1.68 
 
 15,080 
 
 0.456 
 
 7.9 
 
 41.08 
 
 657.28 
 
 4.56 
 
 41,880 
 
 .242 
 
 3.0 
 
 15.60 
 
 250.60 
 
 1.72 
 
 15,600 
 
 0.471 
 
 8.0 
 
 41.60 
 
 665.60 
 
 4.52 
 
 41,600 
 
 1.262 
 
 3.1 
 
 16.12 
 
 257.92 
 
 1.80 
 
 16,120 
 
 0.490 
 
 8.1 
 
 42.12 
 
 673.92 
 
 4.68 
 
 42,120 
 
 1.274 
 
 3.2 
 
 16.64 
 
 266.24 
 
 1.84 
 
 16,640 
 
 0.504 
 
 8.2 
 
 42.84 
 
 685.44 
 
 4.70 
 
 42,840 
 
 1.300 
 
 3.3 
 
 17.16 
 
 274 . 56 
 
 1.89 
 
 17,160 
 
 0.520 
 
 8.3 
 
 43.16 
 
 690.56 
 
 4.76 
 
 43,160 
 
 1.308 
 
 3.4 
 
 17.68 
 
 282.88 
 
 1.96 
 
 17,680 
 
 0.536 
 
 8.4 
 
 43.68 
 
 698.88 
 
 4.82 
 
 43,680 
 
 1.320 
 
 3.5 
 
 18.20 
 
 291.20 
 
 2.01 
 
 18,200 
 
 0.551 
 
 8.5 
 
 44.20 
 
 707.20 
 
 4.87 
 
 44.200 
 
 1.340 
 
 3.6 
 
 18.72 
 
 299 . 52 
 
 2.08 
 
 18,720 
 
 0.567 
 
 8.6 
 
 44.72 
 
 715.52 
 
 4.96 
 
 44,720 
 
 1.360 
 
 3.7 
 
 19.24 
 
 307.84 
 
 .13 
 
 19,240 
 
 0.583 
 
 8.7 
 
 45.24 
 
 723.84 
 
 .02 
 
 45,240 
 
 1.370 
 
 3.8 
 
 19.76 
 
 316.16 
 
 .20 
 
 19,760 
 
 0.600 
 
 8.8 
 
 45.76 
 
 732.16 
 
 .08 
 
 45,760 
 
 1.386 
 
 3.9 
 
 20.28 
 
 324.48 
 
 .25 
 
 20,280 
 
 0.614 
 
 8.9 
 
 46.28 
 
 740.48 
 
 .16 
 
 46,280 
 
 1.400 
 
 4.0 
 
 20.80 
 
 332.80 
 
 .30 
 
 20,800 
 
 0.631 
 
 9.0 
 
 46.80 
 
 747.80 
 
 .20 
 
 46,800 
 
 1.415 
 
 4 1 
 
 21.32 
 
 341.12 
 
 .36 
 
 21,320 
 
 0.646 
 
 9.1 
 
 47.32 
 
 758.12 
 
 .25 
 
 47,300 
 
 1.432 
 
 4\2 
 
 21.84 
 
 349.44 
 
 .42 
 
 21,840 
 
 0.661 
 
 9.2 
 
 48.04 
 
 768.64 
 
 .28 
 
 48,040 
 
 1.452 
 
 4.3 
 
 22.36 
 
 357.76 
 
 .46 
 
 22,360 
 
 0.677 
 
 9.3 
 
 48.36 
 
 773.76 
 
 .33 
 
 48,360 
 
 1.465 
 
 4.4 
 
 22.88 
 
 366.08 
 
 .54 
 
 22,880 
 
 0.693 
 
 9.4 
 
 48.88 
 
 782.08 
 
 .43 
 
 48,880 
 
 1.481 
 
 4.5 
 
 23.40 
 
 374.40 
 
 .58 
 
 23,400 
 
 0.709 
 
 9.5 
 
 49.40 
 
 790.40 
 
 .45 
 
 49,400 
 
 1.500 
 
 4.6 
 
 23.92 
 
 382.72 
 
 .65 
 
 23,920 
 
 0.724 
 
 9.6 
 
 49.92 
 
 798.72 
 
 .50 
 
 49,920 
 
 1.513 
 
 4.7 
 
 24.44 
 
 391.04 
 
 .71 
 
 24,440 
 
 0.740 
 
 9.7 
 
 50.44 
 
 807.04 
 
 .60 
 
 50,440 
 
 1.525 
 
 4.8 
 
 24.96 
 
 399 . 36 
 
 .80 
 
 24,960 
 
 0.753 
 
 9.8 
 
 50.96 
 
 815.36 
 
 .66 
 
 50,960 
 
 1.542 
 
 4.9 
 
 25.48 
 
 407 . 68 
 
 .83 
 
 25,480 
 
 0.773 
 
 9.9 
 
 51.48 
 
 823.68 
 
 5.72 
 
 51,480 
 
 1.560 
 
 5.0 
 
 26.00 
 
 416.00 
 
 .87 
 
 26,000 
 
 0.789 
 
 0.0 
 
 52.00 
 
 832.00 
 
 5.74 
 
 52,000 
 
 1.600 
 
 NOTE. The table is based on 1 cu. ft. of water weighing 62.4 Ib. 
 umn of water 1 in. in depth and 1 sq. ft. in area equals 5.2 ID. 
 
 A col- 
 
912 VENTILATION OF MINES 
 
 current with respect to pressure and power, respectively. These factors, it 
 will be observed, evaluate the airway, as they determine the quantity of air 
 a given pressure or power will circulate in that airway (cubic feet per min- 
 ute). By their use the relative quantitites of air any given pressure or 
 power will circulate in different airways are readily determined. The rule 
 may be stated as follows: 
 
 Rule. For any given pressure or power, the quantity of air in circulation is 
 always proportional to the potential for pressure, or the potential for power, as 
 the case may be. 
 
 This rule finds important application in splitting (see Calculation of 
 Natural Splitting). In all cases where the potential is used as a ratio, the 
 relative potential may be employed by omitting the factor k\ or it may be 
 employed to obtain the pressure and power in several splits by multiplying 
 the final result by k (see Formulas 26, 27, etc., page 914). 
 
 EXAMPLE. 20,000 cu. ft. of air is passing in a mine in which the airway 
 is 6 ft. X 8 ft., and 10,000 ft. long, under a certain pressure; it is required to 
 find what quantity of air this same pressure will circulate in a mine in which 
 the airway is 6 ft. X 12 ft., and 8,000 ft. long. 
 
 Calculating the potential X p with respect to the pressure for each 
 of these mines, or airways, we have, using the ^relative potential, 
 
 / , 6X J __ =.62845, and X 2 = 6X12\/- 6X12 ^I 
 2(6 + 8)X 10,000 \2(6 + 12)X8,000 
 
 = 1.1384. Since the ratio of the quantities is equal to the ratio of the 
 potentials with respect to pressure, in these two mines, we write the propor- 
 
 . 
 tion 20,000 : q 2 : : .62845 : 1.1384, and g2 = .' = 36,229 cu. ft. 
 
 ,O^o4o 
 
 per min. 
 
 EXAMPLE. 20,000 cu. ft. of air is passing in a mine in which the airway 
 is 6 ft. X 8 ft., and 10,000 ft. long, under a certain power; it is required to 
 find what quantity of air will be circulated by this same power in a mine in 
 which the airway is 6 ft. X 12 ft., and 8,000 ft. long. 
 
 We calculate the potential X u with respect to power for each of these 
 
 mines, using, as before, the relative potential. Thus, X\ 
 
 = . 7337, and Xz = = 1.0905. Then, in this case, since the 
 
 <^/2 (6 + 12) X 8,000 
 
 ratio of the quantities is equal to the ratio of the potentials with respect 
 to power, we write the proportion, 20,000 : qz : : .7337 : 1.0905, and 
 
 20,000X1.0905 , 
 ff2 = ~~ = 29,726 cu. ft. per mm. 
 
 / uO / 
 
 The following table will serve to illustrate the use of the formulas em- 
 
 Eloyed in these calculations. It will be observed that there are several 
 )rmulas for quantity, and for velocity, and for work or horsepower, but 
 in each respective case the several formulas are derived by simple transposi- 
 tion of the terms of the original formula, and are tabulated here for conven- 
 ience. Choice must be made in the use of any of these formulas, according 
 to the known terms in each example. Thus, an example may ask: What 
 pressure will be produced in passing a given quantity of air thro gh a certain 
 mine, the size and length of the airways being given? We then use the 
 
 formula p = . But if the question asks what quantity of air a given 
 
 pressure will produce in this same mine, we use the formula q= AnT X-o. 
 
 It will be observed that this second formula is a simple transposition of the 
 first. 
 
 In like manner the question may be asked, what power will produce a 
 certain quantity of air in a certain airway; and the expression used, in this 
 
 case, is = . Or the question may be asked, what quantity of air will 
 be produced in a given airway by means of a certain power or work applied 
 to the airway. In this case the formula used is q = a^-^-. If the question 
 asks for the power required to produce a given velocity in a given airway, 
 
VENTILATION OF MINES 
 
 913 
 
 the formula employed is u=ksv*. ^All of these formulas are derived by com- 
 bining the simple formulas p = , q = av, and u = qp. 
 
 To illustrate the use of the formulas, we take as an example an under- 
 ground road, 5 ft. wide by 4 ft. high, and 2,000 ft. in length, and calculate the 
 value of each symbol or letter, assuming a velocity of 500 ft. per min. 
 
 
 Symbol 
 
 Value of Symbol 
 for this Particular 
 Example 
 
 Area of airway (5 ft. X '4 ft.) 
 
 a 
 h 
 
 20 sq. ft. 
 2 959 H p 
 
 Coefficient of frictionf 
 Length of airway 
 
 k 
 I 
 
 .000000021 7 Ib. 
 2 000 ft 
 
 Perimeter of airway, 2(5 ft. -f- 4 ft.) 
 Pressure (Ib. per sq. ft.) . . . 
 
 o 
 p 
 
 18 ft. 
 9 765 Ib 
 
 Quantity of air (cu. ft. per min.) 
 Area of rubbing surface 
 Units of work per minute (power) 
 Velocity (ft. per min.) 
 
 Q 
 s 
 u 
 
 V 
 
 10,000 cu. ft. 
 36,000 sq. ft. 
 97,650 ft.-lb. 
 500 ft. 
 1 87788 in 
 
 Equivalent orifice of the mine 
 
 A 
 
 X u 
 
 2.919 sq. ft. 
 217 16 units 
 
 Potential for pressure 
 Weight of 1 cu. ft. of downcast air 
 
 X v 
 
 w 
 M 
 
 3,200 units 
 . 08098 Ib. 
 120 5 ft 
 
 Depth of furnace shaft 
 Average temperature of the upcast column . . 
 Average temperature of the downcast column. 
 
 D 
 T 
 t 
 
 306.77 ft. 
 350F. 
 32F. 
 
 * A horsepower is equal to 33,000 units of work. 
 
 t This coefficient of friction is an invariable quantity, and is the same in 
 every calculation relating to the friction of air in mines. 
 
 NOTE. The water gauge is calculated to five decimal places to enable all 
 the other values to be accurately arrived at. In practice it is only read to 
 one decimal place. 
 
 FORMULAS 
 
 On the right side of each formula the various calculations, based on the 
 example given, are worked out in figures. 
 
 To Find: 
 
 d 
 fc 
 
 Formula 
 
 Specimen Calculation 
 
 Rubbing surface 
 of an airway. 
 (Sq. ft.) 
 
 1 
 
 s = lo 
 
 2,000X18 = 36,000 sq. ft. 
 
 Area of an air- 
 
 
 . <7 
 
 10.000 
 
 way. (Sq. ft.) 
 
 
 a ~v 
 
 
 Velocity. (Ft. 
 
 
 v 9 
 
 10,000 
 
 per min.) 
 
 3 
 
 a 
 
 20 
 
 
 
 \I U 
 
 \/ 97 ' 65 500ft 
 
 
 4 
 
 V ~\ks 
 
 \.000000021 7X36,000 ' 
 
 
 
 \E 
 
 .1 9.765X20 
 
 
 5 
 
 "-\^ 
 
 u 
 
 \.0000000217X36.000 * 
 97,650 
 
 
 
 V ~pa 
 
 9.765X20 * 
 
 58 
 
914 
 
 VENTILATION OF MINES 
 
 To Find: 
 
 o 
 ^ 
 
 Formula 
 
 Specimen Calculation 
 
 Pressure. (Lb. 
 
 * 
 
 ksv* 
 
 .0000000217X36,000X5002 ?65 lb 
 
 per sq. ft.) 
 
 
 P a 
 ksq* 
 
 .0000000217 X 36,000 X 10,000^ 
 
 
 
 P 03 
 tt 
 
 203 
 = 9.765 lb. 
 
 97,650 ^ 
 
 
 10 
 
 11 
 
 1 
 
 * Q 
 p = Mw 
 p = 5.2 
 
 *= 52 
 
 io;ooo * 
 
 120.58 X. 08098 = 9.765 lb. 
 5.2 X 1.87788 = 9.765 lb. 
 
 10 ' 0002 0-651b 
 
 
 
 * XJ 
 
 q* 
 
 217.163 ' 
 
 /lo.oooy 
 
 
 
 P ~x7> 
 
 U,200,> 9 ' 76 ' lb< 
 
 Water gauge. 
 (In.) 
 
 14 
 
 <=h 
 
 2^5.1^88^ 
 
 0* 
 
 Resistance of an 
 airway. (Total 
 
 15 
 
 1 f* 
 
 pa = ksv* 
 u 
 
 .0000000217 X 36,000 X 500 2 = 195.3 lb. 
 97,650 
 
 pressure, Ib.) 
 
 
 pa- v 
 
 500 
 
 Quantity. (Cu. 
 ft. per rain.) 
 
 17 
 
 1 ^ 
 
 q = av 
 u 
 
 20 X 500 = 10,000 cu. ft. 
 97 ' 650 = 10000cu ft 
 
 
 
 q ~P 
 
 9.765 1 ' 
 
 
 
 \/^Vfl 
 
 ~J 9.765X20 
 
 
 
 q ~ \ks Xa 
 
 \.0000000217X36.000 A 
 = 10,000 cu. ft. 
 
 
 on 
 
 ^/""va 
 
 ^/ 97,650 
 
 
 21 
 
 q ~ \ks Xa 
 ff = X-^ 
 
 \.0000000217X 36,000 A 
 = 10,000 cu. ft. 
 
 217.16X -^97,650 = 10,000 cu. ft. 
 
 
 22 
 23 
 
 <7 = -^/X p 2 M 
 q = X P Vp 
 
 -Y/3.20Q2X 97,650 = 10,000 cu. ft. 
 3,200 X V9.765 = 10,000 cu. ft. 
 
 Units of work 
 per minute, or 
 power on the 
 air. (Ft.-lb. per 
 min.) 
 
 24 
 25 
 26 
 
 07 
 
 u=*avp 
 u = qp 
 u = ksv* 
 
 ksq<> 
 
 20X500X9.765 = 97,650 ft.-lb. 
 10,000X9.765 = 97,650 ft.-lb. 
 
 .0000000217 X 36,000 X 500* 
 = 97,650 ft.-lb. 
 
 .0000000217 X 36,000 X 10,000" 
 
 
 
 a 3 
 
 203 
 = 97,650 ft.-lb. 
 
VENTILATION OF MINES 
 
 915 
 
 To Find: 
 
 d 
 
 
 Formula 
 
 Specimen Calculation 
 
 Units of work 
 per minute, or 
 power on the 
 
 28 
 oq 
 
 =/z33,000 
 
 u-- 
 
 2.959X33,000=97,650 ft.-lb. 
 10,0003 
 
 air. (Ft.-lb. per 
 min.) 
 
 ?(-> 
 
 X U 3 
 
 u Q3 
 
 217.163 y7 ' 0<j( 
 10,0003 __ nfi 
 
 
 
 XS 
 
 3,2002 - 97 ' 650 fL - lb - 
 
 
 71 
 
 h~ U 
 
 97 '650 
 
 
 
 " 33,000 
 
 33,000 ~ 2 - 959IL r - 
 
 Power potential. 
 
 S 9 
 
 x* a 
 
 20 
 
 
 33 
 
 \/ks 
 
 Xu~ \P 
 
 ^/.0000000217X36,000 
 
 ^/Io^oo~2 0171flur 
 
 
 9 <1 
 
 \/> 
 
 Xu = q 
 
 10-000 n 171Gun 
 
 
 
 ^ 
 
 \X97.650 
 
 Pressure poten- 
 tial (Units ) 
 
 JK 
 
 Xn -a\t~ 
 
 o V/ 20 
 
 
 36 
 
 a Mks 
 Y q 
 
 \.0000000217X36.000 
 = 3,200 units. 
 
 10,000 
 
 
 
 VP 
 
 V9-765 
 
 Equivalent ori- 
 
 37 
 
 A .0004*7 
 
 .0004 X 10,000 _o 910 . q ft 
 
 fice. (Sq. ft.) 
 
 
 Vi 
 
 Vl. 87788 
 
 Motive column, 
 
 3^ 
 
 A/ 7)V T ~ l 
 
 ?0fi 77 V 35 "~ 32 T'O'ift 
 
 downcast air. 
 (Ft.) 
 
 
 ^ X 459+r 
 A/ * 
 
 77X 459 + 350 ] 
 9.765 
 
 
 
 7# 
 
 .08098 ~ UO<5 t> 
 
 Motive column, 
 
 
 M DV r ~* 
 
 306 77 X 35 ~ 32 1937ft 
 
 upcast air. 
 (Ft.) 
 
 
 X 459 + < 
 If p 
 
 !06<77X 459 + 32 198 ' 7ft - 
 9 - 7 65 a10 o 7f . 
 
 
 
 M ~w 
 
 .04915 ] 
 
 Variation of the Elements. In the illustration of the foregoing table, we 
 have assumed fixed conditions of motive column, as well as fixed conditions 
 in the mine airways. It is often convenient, however, to know how the 
 different elements, as velocity v, quantity q, pressure p, power u, etc., will 
 vary in different circulations; since we may, by this means, compare the 
 circulations in different airways, or the results obtained by applying different 
 pressures and powers to the same airway. These laws of variation must 
 always be applied with great care. For example, before we can ascertain 
 how the quantity in circulation will vary in different airways, we must 
 know whether the pressure or the power is constant or the same for each 
 airway. The following rules may always be applied: 
 
 For a constant pressure: v varies as VrS 1 varies as a\ r (relative 
 potential for pressure). 
 
916 VENTILATION OF MINES 
 
 For a constant power : v varies as -77=; q varies as g (relative potential 
 
 for power). 
 
 For a constant velocity : q varies as a; p varies as ; u varies as /o. 
 
 c 
 
 For a constant quantity: v varies inversely as a; p varies inversely as X u 3 
 (potential for power); u varies inversely as X u 3 (potential for power) or 
 directly as p. 
 
 For the same airway: The following terms vary as each other: v, q, 
 
 VP- -v^- 
 
 SIMILAR AIRWAYS 
 
 r = length of similar side, or similar dimension 
 
 For a constant pressure : v varies as \ j; q varies as r 2 X \y; r varies 
 
 as lv 2 , or 
 
 For a constant power: v varies as -* ; q varies as rX A^'-y; r varies as 
 
 i 
 
 , or -\flq 3 , 
 
 For a constant velocity: q varies as r 2 ; p varies as ; u varies as lr; r 
 
 ,- I u 
 varies as v q * it or r- 
 
 P I 
 For a constant quantity: v varies inversely as r 2 ; p and u vary inversely as 
 
 T ; r vanes as - f or -. 
 
 FURNACE VENTILATION 
 
 P (motive column) varies as D; q varies as \^D 
 FAN VENTILATION 
 
 It has been customary in calculations pertaining to the yield of centrifu- 
 gal ventilators to assume as follows: q varies as n\ p varies as w 2 ; u varies 
 as n 3 . 
 
 More recent investigation, however, shows that when we double the speed 
 we do not obtain double the quantity of air in circulation; or, in other words, 
 the quantity does not vary exactly as the number of revolutions of the fan. 
 Investigation also points to the fact that the efficiency of centrifugal ventila- 
 tors decreases as the speed increases. To what extent this is the case has 
 not been thoroughly established. The variation between the speed of a 
 fan and the quantity, pressure, power, and efficiency, as calculated from 
 a large number of reliable fan tests, may be stated as follows: 
 
 For the same fan, discharging against a constant potential: q varies as 
 ". p varies as n 1 -' 4 . Complement of efficiency (1 K) varies as n- 425 . 
 
 The efficiency here referred to is the mechanical efficiency, or the ratio 
 between the effective work qp and the theoretical work of the fan. 
 
 Quantity Produced by Two or More Ventilators. In the development of 
 a mine, it often happens that the means used for producing a ventilating 
 current becomes inadequate for the production of the quantity of air required 
 as the extent of the workings increases. To increase the circulation, it is 
 often proposed to duplicate the ventilating apparatus in use by adding 
 another fan or furnace similar to the one already in operation. This means 
 an increase of ventilating power, which, of course, produces an increase in 
 the quantity of air in circulation. Assuming that no change is made in 
 the course of the circulation of the air through the mine, any increase of 
 quantity will require an increase of power in proportion to the cube of the 
 ratio in which the quantity is increased, as is shown by the following com- 
 parison of power and quantity for a given airway: 
 
 If KI represents the power on the air for a given airway when a quantity 
 
 <ji is circulating, MI= 8S8L = _ ?1 s ; jf M2 represents the power on the air 
 
VENTILATION OF MINES 917 
 
 when a quantity 32 is circulating through the same airway, u 2 = ^ = 
 
 As the same airway is considered in each case, k, s, and a are the same and 
 
 Ul Ql^ 
 
 by canceling, = - or MI : uz qi* : qz 3 ; that is, for the same airway, the 
 
 power is proportional to the cube of the quantity, or the ratio between 
 the powers for two quantities of air equals the cube of the ratio between the 
 quantities. For example, if the quantity is to be doubled, the quantity 
 ratio is then 2 and the power ratio is 2 3 = 8. That is to say, it will require 
 eight times the power to double the quantity of air in the same mine or 
 airway. This shows that two fans of the same size and running at the same 
 speed will not produce double the quantity of air circulated by one of these 
 fans alone. 
 
 When two or more ventilating motors are employed, it is evident that the 
 total power producing the circulation is equal to the sum of the powers of 
 the several motors. 
 
 Now, calling the quantities produced by several motors working separately 
 on the same airway gi, 32, etc., the powers of these several motors MI, uz, etc., 
 and the total quantity produced when all the motors are working together, 
 
 Q> Q3 (^) =afll3 O + 323 (S) + etC> r> dividin S both members of the 
 equation by , Q 3 = gi 3 + <72 3 + etc., and, finally, 
 
 This formula shows the quantity of air produced by the combined action 
 of two or more ventilating motors working on the same mine or airway, and 
 which, when working alone, produce the quantities qi, 32, etc., in the same 
 mine or airway. 
 
 EXAMPLE. A fan ventilating a certain mine is capable of producing 
 42,600 cu. ft. of air when operated alone, and another fan ventilating the 
 same mine will produce 57,400 Cu. ft. when working alone; what quantity 
 of air will be produced in this mine when both fans are in operation, assuming 
 that the general conditions in the mine remain the same? 
 
 SOLUTION. Substituting the given quantities in the formula, and calling 
 the unknown quantity x, the total quantity of air produced by the com- 
 bined action of the two fans 
 
 x = -y/42,6003 + 57,4003 = 64,300 cu. ft. per min. 
 
 The installation of two fans side by side at the mouth of the same return 
 is very unusual, but the installation of a second fan called a "booster" 
 at some point in the interior of the workings is a fairly common practice. 
 Boosters unquestionably increase the amount of air in circulation by aiding 
 the main fan to overcome the frictional resistances of exceptionally long 
 air-courses, but their operation is expensive for the reasons explained. They 
 are permissible in ventilating headings that will have but a short life, or 
 even main workings which are shortly to be abandoned, but should not be 
 tolerated as part of the permanent eouipment of a mine. It is frequently 
 the case that a booster is installed when the cleaning up of the return air- 
 courses to their proper normal width would have permitted the main fan 
 to have supplied the necessary quantity of air, and more cheaply. 
 
 DISTRIBUTION OF AIR IN MINE VENTILATION 
 
 When a mine is first opened, the air is conducted in a single current 
 around the face of all the headings and workings, and returns again to the 
 upcast shaft, where it is discharged into the atmosphere. As the develop- 
 ment of the mine advances, however, it becomes necessary, to divide the air 
 into two or more splits or currents. This division or splitting of the air- 
 current is usually accomplished at the foot of the downcast, or as soon as 
 possible after the current enters the mine. There are several reasons why 
 
918 VENTILATION OF MINES 
 
 the air current should be thus divided. The most important reason is 
 that the mine is thereby divided into separate districts, each of which has 
 its own ventilating current, which may be increased or decreased at will. 
 Fresh air is thus obtained at the face of the workings, and the ventilation is 
 under more perfect control. It often happens that certain portions of a mine 
 are more gaseous than others, and it is necessary to increase the volume of 
 air in these portions, which can be readily accomplished when each district 
 has its own separate circulation. Again, the gases and foul air are not 
 conducted from one district to another, but each district is supplied with 
 fresh air direct from the main intake. Should an explosion occur in any 
 part of the mine, it is more apt to be confined to one locality when a mine is 
 thus divided into separate districts. Another consideration is the reduced 
 power necessary to accomplish the same circulation in the mine; or the 
 increased circulation obtained by the use of the same power. 
 
 Requirements of Law in Regard to Splitting. The Anthracite Mine Law of 
 Pennsylvania specifies that every mine employing more than 75 persons 
 must be divided into two or more ventilating districts, thus limiting the 
 number that are allowed to work on one air current to 75 persons. The 
 Bituminous Mine Law of Pennsylvania limits the number allowed to work 
 upon one current to 65 persons, except in special cases, where this number 
 may be increased to 100 persons at the discretion of the mine inspector. 
 
 Practical Splitting of the Air Current. When the air current is divided into 
 two or more branches, it is said to be split. The current may be divided one 
 or more times; when split or divided once, the current is said to be traveling 
 in two splits, each branch being termed a split. The number of splits in 
 which a current is made to travel is understood as the number of separate 
 currents in the mine, and not as the number of divisions of the current. 
 
 Primary Splits. When the main air current is divided into two or more 
 splits, each of these is called a primary split. 
 
 Secondary Splits. Secondary splits are the divisions of a primary split. 
 
 Tertiary Splits. Tertiary splits result from the division of a secondary 
 split. 
 
 Equal Splits of Air. When a mine is spoken of as having two or more equal 
 splits, it is understood to mean that the length and the size of the separate 
 airways forming those splits are equal in each case. It follows, of course, 
 from this that the ventilating current traveling in each split will be the 
 same, inasmuch as they are all subject to the same ventilating pressure. 
 When an equal circulation is obtained in two or more splits by the use of 
 regulators, these splits cannot be spoken of as equal splits. 
 
 IJnequal Splits of Air. By this is meant that the airways forming the 
 splits are of unequal size or length. Under this head we will consider (a) 
 Natural Division of the Air Current; (b) Proportionate Division of the Air 
 Current. 
 
 Natural Division of the Air Current. By natural division of air is meant 
 any division of the air that is accomplished without the use of regulators; or, 
 in other words, such division of the air current as results from natural means. 
 If the main air current at any given point in a mine is free to traverse two 
 separate airways in passing to the foot of the upcast shaft, and each 9f these 
 airways is free or an open split, i.e., contains no regulator, the division of 
 the air will be a natural division. In such a case, the larger quantity of air 
 will always traverse the shorter split of airway. In other words, an air cur- 
 rent always seeks the shortest way out of a mine. A comparatively small 
 current, however, will always traverse the long split or airway. 
 
 Calculation of Natural Splitting. It is always assumed, in the calculation 
 of the splitting of air currents, that the pressure at the mouth of each split, 
 starting from any given point, is the same. Since this is the case, in order 
 to find the quantity of air passing in each of. several splits starting from a 
 common point, the rule given under Potential Factor of a Mine is applied. 
 This rule may be stated as fallows: 
 
 The ratio between the quantity of air passing in any split and the pressure 
 Potential of that split is the same for all splits starting from a common point. 
 Also, the ratio between the entire quantity of air in circulation in the several 
 splits and the sum of the pressure potentials of those splits is Hie same as the 
 above ratio, and is equal to the square root of the pressure. 
 
 Expressed as a formula, indicating the sum of the pressure potentials 
 
 (Xi+X 2 + etc.) by the expression SX P , this rule is ~- = = \/J~. Hence, 
 
VENTILATION OF MINES 919 
 
 Q 2 Q3 
 
 P = (ZX ) 2 a U = (I.X )2 ex P ress the pressure and power, respectively, 
 absorbed by the circulation of the splits. These are the basal formulas for 
 splitting, from which any of the factors may be calculated by transposition 
 They will be found illustrated in the table at the end of this section. We will 
 give here two examples only, showing the calculation of the natural division of 
 an air current between several splits. We have, from the above formulas 
 
 -5T,- 
 
 EXAMPLE. In a certain mine, an air current of 60,000 cu. ft. per min. 
 is traveling in two splits as follows: Split A, 6 ft.XS ft., 5,000 ft. lone- 
 split B, 5 ft.XS ft., 10,000 ft. long. It is required to find the natural divi- 
 sion of this air current. 
 
 Calculating the relative potentials for pressure in each split, we have 
 
 for split A, Xi = 48\- = 8888 
 
 ' 
 
 for split B, X 2 = 40\ __ _ = .4961 
 
 \2(5 + 8) 10,000 
 and substituting these values, we have, 
 
 X 60,000 = 38,506 cu. ft. per min.; 
 
 and 32 = ^1^X60,000 = 21,494 C u. ft. per min. 
 
 i.oo4y 
 
 EXAMPLE. In a certain mine, there is an air current of 100,000 cu. ft. per 
 min. traveling in three splits as follows: Split A, 6 ft. X 10 ft., 8,000 ft. long; 
 split B, 6 ft. X 12 ft., 15,000 ft. long; split C, 5 ft. X 10 ft., 6,000 ft. long. Find 
 the natural division of this current of air. 
 
 Calculating the respective relative potentials with respect to pressure, 
 we have / - - 
 
 for split A, Xi = 60\ _ _ = .9185; 
 \2(6 + 10) X 8,000 
 
 for split B, X 2 = 72\/ _ ^ _ = .8314; 
 \2(6 + 12) X 15.000 
 
 for split C, X 3 = 5Q\f. 50 = .8333. 
 
 . \2(5 + 10) X 6,000 
 " ils, we have SX P = .9185 + .8314 + 
 jing rule, we have 
 
 31 =^g|X 100,000 = 35,556 cu. ft. per min.; 
 
 CO 1 A 
 
 32 = ^^X100,000 = 32,184 cu. ft. per min.; 
 53 = ^^X100,000 = 32,260 cu. ft. per min. 
 
 A.dOOZ 
 
 . , 
 
 Adding these potentials, we have 2X P = .9185 + . 8314 + . 8333 = 2.5832. 
 Then, applying the foregoing rule, we have 
 
 
 Total, 100,000 
 
 Proportional Division of the Air Current. It continually happens that 
 different proportions of air are required in the several splits of a mine than 
 would be obtained by the natural division of the air current. It is usually 
 the case that the longer splits employ a larger number of men, and require a 
 larger quantity of air passing through them. They, moreover, liberate a 
 larger quantity of mine gases, for which they require a larger quantity of air 
 than is passing in the smaller splits. The natural division of the air current 
 would give to these longer splits less air, and to the shorter ones a larger 
 amount of air, which is directly the reverse of what is needed. On this 
 account, recourse must be had to some means of dividing this air propor- 
 tionately, as required. This is accomplished by the use of regulators, of 
 which there are two general types, the box regulator and the door regulator. 
 
 Box Regulator. This is simply an obstruction placed in those airways that 
 would naturally take more air than the amount required. . It consists of a 
 brattice or door placed in the entry, and having a small shutter that can be 
 opened to a greater or less amount. The shutter is so arranged as to allow 
 the passage of more or less air, according to the requirements. The box 
 regulator is, as a rule, placed at the end or near the end of the return air- 
 
920 VENTILATION OF MINES 
 
 way of a split. It is usually placed at this point as a matter of convenience, 
 because, in this positipn, it obstructs the roads to a less extent, the haulage 
 from the back entry in this split being carried over to the main haulway, 
 through a crosscut, before this point is reached. The difficulty, however, 
 can be avoided, in most cases, by proper consideration in the planning of the 
 mine with respect to haulage and ventilation. The objection to this form 
 of regulator is that, in effect, it lengthens the airway, or increases its resist- 
 ance, making the resistance of all the airways, per foot of area, the same. 
 It is readily observed that, by thus increasing the resistance of the mine, 
 the horsepower of the ventilation is largely increased, for the same circula- 
 tion. This is an important point, as it will be found that the power required 
 for ventilation is thus increased anywhere from 50% to 100% over the 
 power required when the other form of regulator can be adopted. 
 
 Door Regulator. In this form of regulator, which was first introduced by 
 Beard, the division of the air is made at the mouth of the split. The regu- 
 lator consists of a door hung from a point of the rib between two entries, 
 and swung into the current so as to cut the air like a knife. The door is 
 provided with a set lock, so that it may be secured in any position, to give 
 more or less air to the one or the other of the splits, as required. The posi- 
 tion of this regulator door, as well as the position of the shutter in the box 
 regulator, is always ascertained practically by trial. The door is set so as 
 to divide the area of the airway proportionate to the work absorbed in the 
 respective splits. The pressure in any split is not increased, each split 
 retaining its natural pressure. 
 
 Calculation of Pressure for Box Regulators. When any required division 
 of the air current is to be obtained by the use of box regulators, these are 
 placed in all the splits, save one. This split is called the open, or free, split, 
 
 and its pressure is calculated in the usual way by the formula p= 
 
 a 3 
 
 The natural pressure in this open split determines the pressure of the entire 
 mine, since all the splits are subject to the same pressure in this form of 
 splitting. 
 
 First, determine in which splits regulators will have to be placed, in order 
 to accomplish the required division of the air. Calculate the natural pres- 
 sure, or pressure due to the circulation of the air current, for each split, 
 
 kso^ 
 when passing its required amount of air, using the formula p = . The 
 
 split showing the greatest natural pressure is taken as the free split. In each 
 of the other splits, box regulators must be placed, to increase the pressure 
 in those splits; or, in other words, to increase the resistance of those splits 
 per unit of area. 
 
 EXAMPLE. The ventilation required in a certain mine is: 
 
 split A, 6 ft. X 9 ft., 8,000 ft. long; 40,000 cu. ft. per min. 
 split B, 5 ft.XS ft., 6,000 ft. long; 40,000 cu. ft. per min. 
 split C, 9 ft.X9 ft., 8,000 ft. long; 10,000 cu. ft. per min. 
 split D, 6 ft.XS ft., 10,000 ft. long; 30,000 cu. ft. per min. 
 In which of these splits should regulators be placed, to accomplish the 
 required division of air, and what will be the mine pressure ? 
 
 Calculating the pressure due to friction in each split when passing its 
 required amount of air, we find, 
 for split At 
 
 for split B, ^.0000000217X2(5 + 8)6.000X40.000^^^ 
 for split C, f ..0000000217X2(+Q)8 t OOOX10.000, L176 
 
 for split P ^..0000000217X2(6+8)10.000X30.000., 49>45 ^ pef gq ft 
 48 3 
 
 Split B has the greatest pressure, and is theref9re the free split. Box 
 regulators are placed in each of the other splits to increase their respective 
 pressures to the pressure of the free split or the mine pressure. Therefore, 
 the mine pressure in this circulation is 84.63 Ib. per sq. ft. 
 
 The size of opening in a box regulator is calculated by the formula for 
 determining the flow of air through an orifice in a thin plate under a certain 
 head or pressure. The difference in pressure between the two sides of a box 
 regulator is the pressure establishing the flow through the opening, which 
 
VENTILATION OF MINES 921 
 
 corresponds to the head h in the formula v<=^/2gh. This regulator is 
 usually placed at the end of a split or airway, and since the regulator in- 
 creases the pressure in the lesser splits so as to make it equal to the pressure 
 in the other split, the pressure due to the regulator will be equal to the 
 ventilating pressure at the mouth of the split, less the natural pressure or 
 the pressure due to friction in this split. Hence, when the position of the 
 regulator is at the end of the split, the pressure due to friction in the split is 
 
 first calculated by the formula p = -, and this pressure is deducted from 
 
 the ventilating pressure of the free or open split, which gives the pressure 
 due to the regulator. This is then reduced to inches of water gauge, and 
 
 substituted for i in the formula A '- - . The value of A thus obtained is 
 
 y 
 
 the area (square feet) of the opening in the regulator. 
 
 EXAMPLE. 750,000 cu. ft. of air is passing per min. in a certain mine, in 
 two equal splits, under a pressure equal to 2 in. of water gauge, and it is 
 required to reduce the quantity of air passing in one of these splits, by a box 
 regulator placed at the end of the split, so as to pass but 15,000 cu. ft. per 
 min. in this split. Find the area of the opening in the regulator, assuming 
 that the ventilating power is decreased to maintain the pressure constant 
 at the mouth of the splits after placing the regulator. The size and length 
 of each split is 6 ft. X 10 ft. and 10,000 ft. long. 
 
 The natural pressure for the split in which the regulator is placed will be 
 
 ksq* .0000000217X2(6 + 10)10,000 X 15,0002 f 
 P = --=- (6X10)3 - - 7 ' 233 lb - P er "I- ^ 
 
 7 2*^*^ 
 Then, -^ir^ 1 - 4 in> of water gauge (nearly), due to friction of the air 
 
 " 
 current in this split. And, 2 1.4 = .6 in. water gauge due to regulator. 
 
 .00040 .0004X15,000 . 
 Finally, A = ~ = - - = 7.746 sq. ft., area of opening. 
 
 V-6 V.Q 
 
 Size of Opening for a Door Regulator. The sectional area at the regulator 
 is divided proportionately to the work to be performed in the respective splits 
 according to the proportion A i : A 2 : : u\ : uz. Or since Ai-\-Az = a, we have 
 
 Ai : a : : u\ : u\-\-ui, and Ai=* - Xa. This furnishes a method of pro- 
 
 UI+U2 
 
 portionate splitting in which each split is ventilated under its own natura 1 
 pressure. The same result would be obtained by the placing of the box 
 regulator at the intake of any split, thereby regulating the amount of air 
 passing into that split, but the door regulator presents less resistance to the 
 flow of the air current. The practical difference between these two forms 
 of regulators is that in the use of the box regulator each split is ventilated 
 under a pressure equal to the natural pressure of the open or free split, 
 which very largely increases the horsepower required for ventilation of 
 the mine; while in the use of the door regulator each split is ventilated under 
 its own natural pressure, and the proportionate division of the air is accom- 
 plished without any increase of horsepower. This is more clearly ex- 
 plained in the following two paragraphs, and the table showing the com- 
 parative horsepowers of the two methods. 
 
 Calculation of Horsepower for Box Regulators. By the use of the box 
 regulator, the pressure in all the splits is made equal to the greatest natural 
 pressure in any one. This split is made the open or free split, and its natural 
 pressure becomes the pressure for all the splits, or the mine pressure. This 
 mine pressure, multiplied by the total quantity of air in circulation (the sum 
 of the quantities passing in the several splits), and divided by 33,000, gives 
 the horsepower upon the air, or the horsepower of the circulation. Thus, 
 in the first example given on page 920, in which for split B the pressure 
 = 84.63 lb. per sq. ft. and the total quantity of air passing per minute 
 is 12,000 cu. ft., we have 
 
 Calculation of Horsepower for Door Regulators. In the use of the door 
 regulator, each split is ventilated under its own natural pressure, and, 
 hence, in the calculation of the horsepower of such a circulation, the power 
 of each split must be calculated separately, and the sum of these several 
 
922 
 
 VENTILATION OF MINES 
 
 powers will be the entire power of the circulation. For the purpose of 
 parison, we tabulate below the results obtained in the application of 
 two methods of dividing the air in the above example 
 
 com- 
 these 
 
 Splits 
 
 Natural 
 Division 
 
 Required 
 Division 
 
 Horsepower 
 
 Door 
 Regulator 
 
 Box 
 Regulator 
 
 Split A , 6 ft. X 9 ft., 8,000 ft. long . 
 Split B, 5 ft. X 8 ft., 6,000 ft. long . 
 Split C, 9ft.X9ft., 8,000 ft. long. 
 Split D, 6 ft. X 8 ft., 10,000 ft. long . 
 
 Totals. . . 
 
 28,277 
 22,360 
 47,423 
 21,940 
 
 40,000 
 40,000 
 10,000 
 30,000 
 
 64 . 145 
 102.582 
 .356 
 44.955 
 
 102.582 
 102 . 582 
 25.645 
 76 . 936 
 
 120.000 
 
 120,000 
 
 212.038 
 
 307.745 
 
 SPLITTING FORMULAS 
 
 The following table of formulas will serve to illustrate the methods of 
 calculation in splitting. The example assumes the same airway as that given 
 on page 912 and used to illustrate the table of formulas, pages 913, 914 and 
 915 but the air current is divided, as specified in the table: 
 NATURAL DIVISION 
 
 Primary Splits. Split (1) =4 ft.XS ft., 800 ft. long. Split (2) =4 ft.XS 
 ft., 1,200 ft. long. 
 
 To Find: 
 
 Formula 
 
 Specimen Calculation 
 
 Potential for 
 pressure. 
 
 35 
 41 
 
 P + etc.). 
 
 (1) 
 
 on A/ 20 lOfiO 
 
 U \.0000000217X 14,400 3>U51 
 
 "f}\l 20 
 
 ~ \.0000000217X 21,600 ' 
 5,060 + 4,131=9,191. 
 
 Natural divi- 
 sion. 
 
 g== ^XO. 
 
 (1) 
 (2) 
 
 |^|~X 10,000 = 5,505 cu. ft. 
 
 
 Or the natural division may be calculated from the pressure at the mouth 
 of the several splits by using Formula (23) ; thus, 
 
 
 23 
 
 q = X P \/P. 
 
 (1) 5,060 Vl- 1838 = 5,505 cu. ft. 
 (2) 4.131V1- 1838 = 4,495 cu. ft. 
 See formula (42). 
 
 
 
 t, Q * 
 
 10,000* 11S3Slb 
 
 
 
 (2Xp) 2 
 
 9.19P - 1 ' 18 ' 
 
 
 
 u Q3 
 
 10,0003 
 
 
 
 (SXp) 2 
 
 9.191 2 11>8ti8 units. 
 
 a 
 
 44 
 
 Q=2X P VP. 
 
 9, 191 Vl-1838 = 10,000 cu. ft. 
 
 
 45 
 
 Q--<^(2X,)*u. 
 
 -Y/9,191 2 X 11,838 = 10, 000 cu. ft. 
 
 Increase of 
 quantity due 
 
 
 n 2Xp v 
 
 Q 1 Q1 
 
 V 1O 000 S 7 cu ft 
 
 to splitting. 
 (Pressure con- 
 stant.) 
 
 4b 
 
 C?= v -Xg<>. 
 
 Xp-O 
 
 cJ.zUU 
 
 Increase in 
 quantity due 
 to splitting. 
 (Power con- 
 stant.) 
 
 47 
 
 -'X(GF? 
 
 \,Ap_o/ 
 
 10,000 ^/(|^) 2 - 20,205 cu. ft. 
 
s 
 
 VENTILATION OF MINES 
 
 923 
 
 sS 
 
 ^ 
 
 2 
 
 i^i 
 
 >' 
 
 oo 
 
 -?- 
 
 -^ 
 
 o 
 
 
 ra 
 
 l-i 
 
924 
 
 VENTILATION OF MINES 
 
 Secondary Splits. (1) 4 ft.X5 ft., 800 ft. long. (2) 4 ft.X5 ft., 500 ft. 
 long. (3) 4 ft. X 5 ft., 400 ft. long. (4) 4 ft. X 5 ft., 300 ft. long. 
 
 The calculation is often shortened, when many splits are concerned, by 
 
 using the relative potential, omitting the factor k; but the final result must 
 
 then be multiplied by k to obtain the pressure or power; or, these factors 
 
 must be divided by k, when finding the quantity, as m formulas (49) to (51). 
 
 PROPORTIONATE DIVISION 
 
 Primary Splits (only). (1) 4 ft.XS ft., 800 ft. long = 3, 500 cu. ft. (2) 
 4 ft. X 5 ft., 1,200 ft. long = 6,500 cu. ft. 
 
 To Find: 
 
 o 
 fc 
 
 Formula 
 
 Specimen Calculation 
 
 Pressure due to 
 friction. 
 
 13 
 
 '- 
 
 (1) 
 (2) 
 
 3 ' 5 2 17315 Ib 
 
 5,0602 ' 7 ' 
 6 ' 5 2 17571b 
 
 4.13P ' lb> 
 
 To accomplish this division of air, the pressure in split (1) must be in- 
 creased by means of a regulator to make it equal to the pressure in the 
 free or open split (2), and, hence, the pressure due to the regulator is equal 
 to the difference between the natural pressures in these splits. 
 
 Pressure due to 
 the regulator 
 in split (1). 
 
 53 
 
 ,*-. 
 
 2.4757 - .47845 = 1 .99725 Ib. 
 
 Area of the 
 opening in 
 regulator. 
 
 37 
 
 00040 
 
 .0004 X 3,500 _ 22505q ft 
 
 3 vr' 
 
 A /1 .99725 
 
 \ 5.2 
 
 Secondary Splits. (1) 4 ft. X 5 ft., 800 ft. - 3,500 cu. ft. (2) 4 ft. X 5 ft. , 
 500 ft. - 6,500 cu. ft. (3) 4 ft. X 5 ft., 400 ft. -4,000 cu. ft. (4) 4ft.X5ft., 
 300 ft. - 2,500 cu. ft. 
 NOTE. When using the relative potential, multiply the result by k, to 
 obtain the pressure, or the power. 
 
 Pressure due to 
 friction. Free 
 split second- 
 pressure. 
 
 13 
 
 ^ 
 
 ("H 0000000217^-- ^ 47S4R 1h 
 
 
 (-) .0000000-17^ 942g j => 1.0314 Ib. 
 / 4,000 \ 2 
 
 \1.0541/ 
 ( \) OOOOOOO17^ ^bvv \ OQ1 ^fi 1K 
 
 
 Since the natural pressure in (3) is greater than that in (4), (3) is the free 
 split, and its natural pressure is the pressure for the secondary splits. The 
 pressure for the primary splits is then found by first adding the pressures in 
 (2) and (3), and if their sum is greater than the natural pressure for (1), it 
 becomes the pressure for the primary splits, or the mine pressure. If the 
 natural pressure for (1) is the greater, this is made the free split, and its 
 natural pressure becomes the primary or mine pressure. In this case, the 
 secondary pressure must be increased by placing a regulator in split (3). 
 
 Prim a r y o r 
 mine pressure. 
 
 
 pi + ps 
 
 1.0314 + .31248 = 1.34388. 
 
 Pressure due to 
 the regulators. 
 
 
 0/+V/-,, 
 
 (4) 
 (1) 
 
 .31248 - .091546 = .220934 Ib. 
 (1.0314 + .31248) -.47848 
 = .86540 Ib. 
 
 Areas of open- 
 ings in the 
 regulators. 
 
 37 
 
 
 (4) 
 (1) 
 
 .0004X2,500 10511 ._ ft 
 
 -4/.220934 
 
 \ 5.2 
 .0004 X 3,500 ^34300.., ft 
 
 
 ^^8654 
 
VENTILATION OF MINES 925 
 
 METHODS AND APPLIANCES IN THE VENTILATION 
 OF MINES 
 
 Ascensional Ventilation. Every mine, as far as practicable, should be 
 ventilated upon the plan known as ascensional ventilation. This term refers 
 particularly to the ventilation of inclined, seams. The air should enter the 
 mine at its lowest point, as nearly as possible, and from thence be conducted 
 through the mine to the higher points, and there escape by a separate 
 shaft, if such an arrangement is practicable. Where the seam is dipping 
 considerably and is mined through a vertical shaft, the upcast shaft should 
 be located as far to the rise of the downcast shaft as possible. The intake air 
 is then first conducted to the lowest point of the dip workings, which it 
 traverses upon its way to the higher workings. In the case of aslope 
 working where a pair of entries is driven to the dip, one being used as the 
 intake and the other the return, there being cross-entries or levels driven at 
 regular intervals along the slope, the air should be conducted'at once to the 
 inside workings, from which point it returns, ventilating each pair of cross- 
 entries from the inside, outwards. Where the development of the cross- 
 entries or levels is considerable, their circulation is considered separately, 
 and a fresh air split is made in the intake at each pair of levels. In all 
 ventilation, the main point to be observed is to conduct the air current first 
 to the inside workings, from whence it is distributed along the working face 
 as it returns toward the upcast. 
 
 General Arrangement of Mine Plan. Every mine should be planned with 
 respect to three main requirements, viz.: (a) haulage; (b) drainage; (c) 
 ventilation. These requirements are so closely connected with one another 
 that the consideration of one of them necessitates a reference to all. The 
 mine should be planned so that the coal and the water will gravitate towards 
 the opening, as far as possible. There are many reasons, in the consideration 
 of non-gaseous mines, why the haulage should be effected upon the return 
 airways. The haulage road is always a dusty road, caused by the traveling 
 of men and mules, as well as by the loss of coal in transit, which becomes 
 reduced to fine slack and powder. If the haulage is accomplished upon the 
 intake entry or air-course, this dust is carried continually into the mine and 
 working places, which should be avoided whenever possible. When the 
 loaded cars move in the same direction as the return air, the ventilation of 
 the mine is not as seriously impeded. It is often the case that fewer doors 
 are required upon the return airway than upon the intake, which is a feature 
 favorable to haulage roads. Again, in this arrangement, the hoisting shaft 
 is made the upcast shaft, which prevents the formation of ice, and conse- 
 quent delay in hoisting in the winter season. The arrangement, however, 
 presupposes the use of the force fan or blower, since if a furnace or exhaust 
 fan is employed, a door, or probably double doors, would have to be placed 
 upon the main haulage road at the shaft bottom, which would be a great 
 hindrance. 
 
 In the ventilation of gaseous mines, however, other and more important 
 considerations demand attention. The gaseous character of the return 
 current prevents making the return airway a haulageway. In such mines, 
 the haulage should always be accomplished upon the intake air, as any other 
 system would often result in serious consequences. In such gaseous mines, 
 men and animals must be kept off the return airways as far as this is 
 possible. 
 
 As far as practicable, ventilation should be accomplished in sections 
 or districts, each district having its own split of air from the main intake, and 
 its own return connecting with the main return of the mine. Reference 
 has been made to this under Distribution of the Air in Mine Ventilation. 
 This splitting of the air current is accomplished preferably by means of an 
 air bridge, either an under crossing or an over crossing. There are, in 
 general, three systems of ventilation, with respect to the ventilating motor 
 employed: (a) natural ventilation: (b) furnace ventilation; (c) mechanical 
 ventilation. 
 
 Natural ventilation means such ventilation as is secured by natural means, 
 or without the intervention of artificial appliances, such as the furnace, 
 or any mechanical appliances by which the circulation of air is maintained. 
 In natural ventilation, the ventilating motor or air motor is an air column 
 that exists in the downcast shaft by virtue of the greater weight of the 
 downcast air. This air column acts to force the air through the airways 
 
926 VENTILATION OF MINES 
 
 of the mine. An air column always exists where the intake and return 
 currents of air pass through a certain vertical height, and have different 
 temperatures. This is the case whether the opening is a shaft or a slope; 
 since, in either case, there is a vertical height, which in part determines 
 the height of air column. The other factor determining the height of air 
 column is the difference of temperature between the intake and return. 
 The calculation of the ventilating pressure in natural ventilation is identical 
 with that of furnace ventilation, which is described later. 
 
 Ventilation of Rise and Dip Workings. We have referred to the air column 
 existing either in vertical shafts or slopes as the motive column or venti- 
 lating motor. Such an air column will be readily seen to exist in any rise 
 or dip workings within the mine, and may assist or retard the circulation 
 of the air current through the mine. It is this air column that renders the 
 ventilation of dip workings easy, and that of rise workings correspondingly 
 difficult, depending, however, on the relative temperature of the intake and 
 return currents; the latter usually is the warmer of the two, which gives 
 rise to the air column. The influence of such air columns must always be 
 taken into account in the calculation of any ventilation. This is often 
 neglected. 
 
 The influence of air columns in rise or dip workings, within the mine, 
 becomes very manifest where, from any reason, the main intake current is 
 increased or decreased. For example, a mine is ventilated in two splits, a 
 rise and a dip split; a current of 50,000 cu. ft. of air is passing in the main 
 airway, 30,000 cu. ft. passing into the dip workings, and 20,000 into the rise 
 workings. A fall of roof in the main intake airway, or other cause, reduces 
 the main current from 50,000 to 35,000 cu. ft. _ Instead, now, of 21,000 cu. ft. 
 going to the dip workings and 14,000 to the rise workings, we find that this 
 proportion no longer exists, but that the dip workings are taking more than 
 their proportion of air, and the rise workings less. Thus, the circulation 
 being decreased to 35,000 cu. ft., the dip workings will probably take 25,000 
 cu. ft., and the rise workings 1 10,000 cu. ft. On the other hand, had the 
 intake current been increased instead of decreased, the rise workings would 
 then take more than their proportion, while the dip workings would take 
 less. The reason for this distribution is evident; suppose, for example, the 
 intake or mine pressure is 3 in. of water gauge, and in the dip workings 
 there is in. of water gauge acting to assist ventilation, while a like water 
 gauge of | in. in the rise workings acts to retard ventilation. The effective 
 water gauge in the dip workings is therefore 3J in., while the effective 
 water gauge in the rise workings is 2J in., or they are to each other as 7 : 5. 
 If, now, the mine pressure is decreased to, say, 2 in., the effective rise and 
 dip pressure will be, respectively, 2$ in. and l in., or as 5 : 3. _ We observe, 
 before the decrease, the dip pressure was J, or 1.4, times the rise- pressure, 
 while after the decrease took place in the mine pressure, the dip pressure 
 became , or 1.66, times the rise pressure. The relative quantities passing in 
 the dip split before and after the decrease took place, as compared with the 
 quantities passing in the rise split, will be as the \/l-4 : \/1.66, showing an 
 increase of proportion. Now, instead of a decrease taking place in the mine 
 pressure, let us suppose it is increased, say, from 3 in. to 4 in. The effective 
 pressures in the dip and rise workings will then be, respectively, 4 in. 
 and 3 1 in., or they will be to each other as 9 : 7, instead of 7 : 5. Here we 
 observe that the dip pressure is If, or 1.15, times the rise pressure, instead 
 of 1.4. The relative quantities, therefore, passing in the dip split, before 
 and after the increase of the mine pressure, as compared with the quantities 
 passing in the rise split, will be in the ratio of -\/\A : \/i.l5 f showing a 
 decrease of proportion. We observe that any alteration of the mine pres- 
 sure by which it is increased or decreased does not affect the inside dip or 
 rise columns, and hence the disproportion obtains. In case of a decrease of 
 the mine pressure, the dip workings receive more than their proportion 
 of air, and in case of an increase of the mine pressure, they receive less 
 than their proportion of air. 
 
 Influence of Seasons. In any ventilation, air columns are always estab- 
 lished in slopes and shafts, owing to the relative temperatures of the outside 
 and inside air. The temperature of the upcast, or return column, may always 
 be assumed to be the same as that of the inside air. The temperature of the 
 downcast, or intake column, generally approximates the temperature of the 
 outside air, although, in deep shafts or long slopes, this temperature may be 
 changed considerably before the bottom of the shaft or slope is reached, and 
 
VENTILATION OF MINES 927 
 
 C9nsequently the average temperature of the downcast, or intake, is often 
 different from that of the outside air. The difference of temperatures will 
 also vary with the seasons of the year. In winter the outside temperature is 
 below that of the mine, and the circulation in shafts and slopes is assisted 
 since the return columns are warmer and lighter than the intake columns 
 for the same circulation. In the summer season, however, the reverse of 
 this is the case. The course of the air current will thus often be changed 
 When the outside temperature approaches the average temperature of the 
 mine, there will be no ventilation at all in such mines, except such as is 
 caused by accidental wind pressure. 
 
 In furnace ventilation the temperature of the upcast column is increased 
 above that of the downcast column by means of a furnace. The chief 
 points to be considered in furnace ventilation are in regard to the arrange- 
 ment and size of the furnace. Furnace ventilation should not be applied to 
 gaseous seams, and in some cases is prohibited by law. It is, however, in 
 use in may mines liberating gas. In su9h cases the furnace fire is fed by a 
 current of air taken directly from the air-course, sufficient to maintain the 
 fire, and the return current from the mine is conducted by means of a dumb 
 drift, or an inclined passageway, into the shaft, at a point from 50 to 100 ft. 
 above the seam. At this point, the heat of the furnace gases is not sufficient 
 for the ignition of the mine gases. The presence of carbonic-acid gas in the 
 furnace gases also renders the mine gases inexplosive. In other cases 
 where the dumb drift is not used, a sufficient amount of fresh air is allowed 
 to pass into the return current to insure its dilution below the explosive 
 point before it reaches the furnace. 
 
 Construction of a Mine Furnace. In the construction of a mine furnace, a 
 sufficient area of passage must be maintained over the fire and around the 
 furnace to allow the passage of the air current circulating in the mine. The 
 velocity of the current at _ the furnace should be estimated not to exceed 
 20 ft. per sec. and the entire area of passage calculated from this velocity. 
 Thus, for a current of 50,000 cu. ft. of air per min., the area of passage 
 through and around the furnace should be not less than 
 
 This is a safe method of calculation, notwithstanding the fact that the 
 velocity of the air is often much more than 20 ft. per sec., yet the volume 
 of the air is largely increased owing to the increase of temperature. 
 
 The length of the furnace bars is limited to the distance in which good 
 firing can be accomplished, and should not exceed 5 ft. The width of the 
 grate will therefore determine the grate area. The grate area must, in every 
 case, be sufficient for the heating of the air of the current to a temperature 
 such as to maintain the average temperature of the furnace shaft high enough 
 to produce the required air column, or ventilating pressure, in the mine. 
 The area A of the grate of the furnace is best determined by the formula 
 
 A = XH. P., in which A = grate area in square feet; H. P. = horse- 
 
 power of the circulation; and D = depth of shaft in feet. The horsepower 
 for any proposed circulation may always be determined by dividing the 
 quantity 9f air (cubic feet per minute) by the mine x *potential X v , and cubing 
 and dividing the result by 33,000; thus 
 
 The furnace should have proper cooling spaces above and at each side; 
 upon one side, at least, should be a passageway or manway. The furnace 
 should be located at a point from 10 to 15 yd. back from the foot of the shaft, 
 at a place in the airway where the roof is strong. This is well secured 
 by railroad iron immediately over the furnace. A good foundation is 
 obtained in the floor, and the walls of the furnace carried up above the 
 level of _the grate bars, when the furnace arch is sprung. If possible, a 
 full semicircle should be used in preference to a flat arch. The sides and 
 arch of the furnace should be carried backwards to the shaft; this is neces- 
 sary in order to prevent ignition of the coal. The walls and arch are con- 
 structed of firebrick a sufficient distance from the furnace, and afterwards 
 of a good quality of hard brick; the shaft is also lined with brick or protected 
 by sheet iron a sufficient height to prevent the ignition of the curbing. 
 
 Air Columns in Furnace Ventilation. As previously stated, natural ven- 
 tilation and furnace ventilation are identical, in so far as in each the venti- 
 
928 VENTILATION OF MINES 
 
 lating motor is an air column. This air column is an imaginary column of 
 air whose weight is equal to the difference between the weights of the upcast 
 and downcast columns. The upcast and downcast columns in furnace 
 ventilation are sometimes referred to as the primary and secondary columns, 
 respectively. The primary or furnace column is, in nearly every case, a 
 vertical column, and consists of a single air column whose average tempera- 
 ture is easily approximated. According to the manner of opening the 
 mine, whether by shaft, slope, or drift, the secondary column may be a 
 vertical column in the shaft, an inclined column in the slope, or an outside 
 air column in case of a drift opening. Again, it is to be observed that in 
 case of a slope opening where the top of the furnace shaft is much higher 
 than the mouth of the slope, and the dip of the slope is considerable, the 
 secondary column consists of two columns of different temperatures, an 
 outside air column and the slope column. These two parts of the secondary 
 column must be calculated separately, and their sum taken for the weight of 
 the secondary column. The level of the top of the furnace shaft determines 
 the top of both the primary and secondary columns, whether these columns 
 are in the outer air or in the mine. The weight of the upcast or primary 
 column is largely affected by its gaseous condition. For example, if the 
 return current from the mine is laden with blackdamp COz, its weight will 
 be much increased, since this gas is practically 1$ times as heavy as air, 
 while, if laden with marsh gas, or firedamp mixture, its weight will be con- 
 siderably reduced. These causes decrease and increase, respectively, the 
 ventilating pressure in the mine. 
 
 Inclined Air Columns. In a slope opening, the air column is inclined; it 
 is none the less, however, an air column, and must be calculated in the same 
 manner as a vertical column whose vertical height corresponds to the amount 
 of dip of the slope. Fig. 9 shows a vertical shaft and 
 a slope, the air column in each of these being the 
 same for the same temperature. The air column in 
 all dips and rises must be estimated im like manner, 
 by ascertaining the vertical height of the dip. 
 
 Calculation of Ventilating Pressure in Furnace 
 Ventilation. The ventilating pressure in the mine 
 FIG. 9 airways, in natural or in furnace ventilation, is 
 
 caused by the difference of the weights of the 
 
 primary and secondary columns. Air always moves from a point of higher 
 pressure towards a point of lower pressure, and this movement of the air is 
 caused by the difference between these two pressures. In this calculation 
 each column is supposed to have an area of base of 1 sq. ft. Hence, if we 
 multiply the weight of 1 cu. ft. of air at a given barometric pressure, and 
 having a temperature equal to the average temperature of the column, by 
 the vertical height D of the column, we obtain not only the weight of the 
 column but the pressure at its base due to its weight. Now, since the venti- 
 lating pressure per square foot in the airway is equal to the difference of the 
 weights of the primary and secondary columns, we write 
 /1.3253XB 
 
 459+? 459 + r 
 
 EXAMPLE. Find the ventilating pressure in a mine ventilated by a 
 furnace, the temperatures of the upcast and downcast columns being, 
 respectively, 350F. and 40F., the depth of the upcast and downcast shafts 
 being each 600 ft., and the barometer 30 in. 
 
 Substituting the given values in the above equation, we have 
 
 - 1.3253X30X600( ig Jp 55 - ^350) - 18- 32 Ib. per sq. ft. 
 
 Calculation of Motive Column or Air Column. It is often convenient to 
 express the ventilating pressure P (pounds per square foot) in terms of air 
 column or motive column M, in feet. The height of the air column M is 
 
 equal to the pressure p divided by the weight to of 1 cu. ft. of air, or M 
 
 The expression for motive column may be written either in terms of the 
 upcast air or of the downcast air, the former giving a higher motive column 
 than the latter for the same pressure, since the upcast air is lighter than 
 that of the downcast. As the surplus weight of the downcast column of air 
 produces the ventilating pressure, it is preferable to write the air column in 
 terms of the d9wncast air, or, in other words, to consider the air column as 
 being located in the downcast shaft, and pressing the air downwards and 
 
VENTILATION OF MINES 929 
 
 through the airways of the mine. If we divide the expression previously 
 given for the ventilating pressure by the weight of 1 cu. ft. of downcast air 
 
 ( 459-Uj )' we obtain for the motive column, after simplifying, M = 
 
 \459 + TV * ^' which is the ex P ress ' on for motive column in terms of the 
 downcast air. 
 
 If, on the other hand, we divide the expression for the ventilating pressure 
 by the weight of 1 cu. ft. of upcast air ' 3 > we obtain M = 
 
 (459+l) * Dt whic ^ is the ex P ression for motive column in terms of the 
 upcast air. 
 
 Influence of Furnace Stack. To increase the height of the primary or 
 furnace column, a stack is often erected over the mouth of the furnace shaft. 
 The effect of this is to increase the ventilating pressure in the mine in pro- 
 portion to the increased height of the primary column, and to increase the 
 quantity of air passing in the mine in proportion to the square root of this 
 height. Thus, the square root of the ratio of the heights of the primary 
 column, before and after the stack is erected, is equal to the ratio of the 
 quantities of air passing before and after the erection of the stack. Or, 
 calling these quantities gi and 52, and the height of stack d, we have 
 
 \l D + d =, ^ or = \l D + d 
 
 MECHANICAL VENTILATORS 
 
 A large number of mechanical ventilators have been invented and applied, 
 with more or less success, to the ventilation of mines. The earliest type of 
 ventilator was the wind cowl, by which the pressure of the wind at the sur- 
 face was brought to bear effectively upon the mine airways by the action of 
 a cowl whose mouth could be turned toward the wind; this was naturally 
 very unreliable. The waterfall was also extensively applied at one time, but 
 its application could only be made where there was \a reliable source of 
 water supply, and where the drainage of the mine could be effected through 
 a tunnel, or where' the mine opening could be placed in connection with 
 such a waterfall outside of the mine. Where these conditions are obtained, 
 as is the case in some mountainous districts, the waterfall is still in use, as 
 it is an effective means of ventilation, and is economical. Its application, 
 however, must be limited to the ventilation of small mines. The steam jet 
 is another mechanical device for producing an air current in the mine. The 
 steam is allowed to issue from a jet at the bottom of an upcast shaft, and, 
 by the force of its discharge, causes an upward current in the shaft. Its use, 
 however, is very limited, and is practically restricted to the ventilation of 
 shafts while sinking. In this connection it may be mentioned, however, 
 that the discharged steam from the mine pumps, where practicable, may be 
 conducted into the upcast shaft; or the discharge pipe from the pumps may 
 be carried up the upcast shaft, its heat increasing the temperature of the 
 shaft, and thereby increasing the motive column and the ventilation. 
 
 Fan Ventilation. Mechanical motors of this type present two distinct 
 modes of action in producing an air current: (a) by propulsion of the air; 
 and (6) by establishing a pressure due to the centrifugal force incident to 
 the revolution of the fan. Fans have been constructed to act wholly on 
 one or the other of these principles, while others have been constructed to 
 act on both of these principles combined. 
 
 Disk Fans. The action of this type of fan resembles that of a windmill, 
 except that in the latter the wind drives the mill, while in the former the 
 fan propels the air or produces the wind. This type of fan consists of a 
 number of vanes radiating from a central shaft, and inclined to the plane of 
 revolution. The fan is set up in the passageway between the outer air and 
 the mine airways. Power being applied to the shaft, the revolution of the 
 vanes propels the air, and produces a current in the airways. The fan may 
 force the air through, or exhaust the air from, the airways, according to the 
 direction of its revolution. This type of fan is most efficient under light 
 pressures. It has found an extensive application in mining practice, and has 
 a large number of devotees, but has been replaced to a large degree in the 
 ventilation of extensive mines. This type of fan acts wholly by propulsion. 
 
930 VENTILATION OF MINES 
 
 Centrifugal fans include all fans that act solely on the centrifugal principle, 
 and those that combine the centrifugal and propulsion principles. The 
 action of the fan, whether by centrifugal force alone, or combined with 
 propulsion, depends on the form of the fan blades. In this type of fan, the 
 blades are all set at right angles to the plane of revolution, and not inclined, 
 as in the disk fan just described. The blades may, however, be either radial 
 blades, sometimes spoken of as paddle blades, or they may be inclined to the 
 radius either forward in the direction of revolution, or backward. When 
 the blades are radial, the action of the fan is centrifugal only. The inclina- 
 tion of the blades backward from the direction of motion gives rise to an 
 action of propulsion, in addition to the centrifugal action of the fan. The 
 blades in this position may be either straight blades in an inclined position, 
 as in the original Guibal fan, or they may be curved backward in the form 
 of a spiral, as in the Schiele and Waddle fans. 
 
 Centrifugal fans may be (a) exhaust fans or (b) force fans or blowers. In 
 each, the action of the fan is essentially the same; i.e., to create a difference 
 of pressure between its intake or central opening, and its discharge at the 
 circumference. The centrifugal force developed by the revolution of the air 
 between the blades of the fan causes the air within the fan to crowd towards 
 the circumference; as a result, a rarification is caused at the center and a 
 compression at the circumference, giving rise to a difference of pressure 
 between the intake and the discharge of the fan. 
 
 Exhaust Fans. If the intake opening of the fan be placed in connection 
 with the mine airways, and the discharge be open to the atmosphere, the 
 fan will act to create rarefaction in the fan drift leading to the mine, which 
 will cause a flow of air through the mine airways and into and through the 
 fan. In this case, the fan^is exhausting, its position being ahead of the 
 current that it produces in the airway. The atmospheric pressure at 
 the intake of the mine forces the air or propels the current toward the 
 depression in pressure existing in the fan drift caused by the fan's action. 
 
 Force Fans and Blowers. If the discharge opening of the fan be placed in 
 connection with the mine airways, a compression will result in the fan drift 
 owing to the fan's action, and the air will flow from this point of compression 
 through the airways of the mine, and be discharged into the upcast, and 
 thence into the atmosphere. The ventilating pressure in the case of either 
 the exhaust fan or the force fan is equal to the difference of pressure created 
 by the fan's action. In the former case, when the fan is exhausting, the 
 absolute pressure in the fan drift is equal to the atmospheric pressure less 
 the ventilating pressure, while in the latter case, when a fan is forcing, the 
 absolute pressure in the fan drift is equal to the atmospheric pressure in- 
 creased by the ventilating pressure. This gives rise to two distinct systems 
 of ventilation, known as (a) vacuum system and (b) plenum system. 
 
 Vacuum System of Ventilation. In this system, the ventilation of the 
 mine is accomplished by creating a decrease of pressure in the return airway 
 of the mine. This decrease may be created by the action of an exhaust fan, 
 as just described, or by the action of a furnace. In either case, the absolute 
 pressure in the mine is below that of the atmosphere, or, we may say, the 
 mine is ventilated under a pressure below the atmospheric pressure. This 
 system has many points of advantage over the plenum system, and for years 
 was considered by many the only practicable system of ventilation. Its 
 application, however, is controlled by conditions in the mine with respect to 
 the gases liberated, the arrangement cf the haulage system, etc. 
 
 Plenum System of Ventilation. In this sytem, the air current is propelled 
 through the mine airways by means of the compression or ventilating 
 pressure created at the intake opening of the mine. This ventilating pres- 
 sure may be established by a fan, waterfall, wind cowl, or any other me- 
 chanical means at hand. In this system, the absolute pressure in the mine 
 is above that of the atmosphere; or, as we say, the mine is ventilated under 
 a pressure above the atmospheric pressure. 
 
 Comparison of Vacuum and Plenum Systems. No hard-and-fast rule can 
 be made to apply in every case, as each system has its particular advantages. 
 In case of a sudden stoppage of the ventilating motor at a mine, there is, 
 in the vacuum system, a rise of mine pressure, instead of a fall, and the 
 gases are driven back into the workings for a while, while, in the plenum 
 system, any stoppage of the ventilating motor is followed at once by a fall of 
 pressure in the mine, and mine gases expand more freely into the passage- 
 ways at the very moment when their presence is most dangerous. This 
 point must be carefully considered in the ventilation of deep workings. In 
 
VENTILATION OF MINES 
 
 931 
 
 shallow workings, the plenum system is often advantageous, especially if 
 there is a large area of abandoned workings that have a vent or opening to 
 the atmosphere, either through an old shaft or through crevices extending 
 to the surface. Every crevice or other vent becomes a discharge opening by 
 which the mine gases find their way to the surface, and the gases accumu- 
 lating in the old workings are driven back into the workings, and find their 
 way to the surface instead of being drawn into the mine airways, as would be 
 the case in an exhaust system. Any given fall of the barometer affects the 
 expansion of mine gases to a less extent in the plenum system than in the 
 vacuum system, but this small advantage would not give it considera- 
 tion in determining between the adoption of the one or the other of these 
 two systems; regard must be had, however, to other conditions more vital 
 than this. In the ventilation of gaseous seams, owing to the necessity of 
 making the intake airway the haulage road, the exhaust system has usually 
 been adopted, as the main road is thereby left unobstructed by doors. 
 
 TYPES OF CENTRIFUGAL FANS 
 
 We shall only mention the more prominent types of fans that have been 
 or are still in use, giving the characteristic features, as nearly as possible, 
 of each fan. Many fans have been built, however, combining many of the 
 features that originally characterized a single type of fan. 
 
 FIG. 10 
 
 FIG. 11 
 
 Nasmyth Fan. Fig. 10 is the original type of fan representing straight 
 paddle blades radiating from the center, which is its characteristic feature. 
 This was probably the earliest attempt to apply the centrifugal principle to 
 a mine ventilator, and although not recognized at the time, the fan embodied 
 some of the most essential principles in centrifugal ventilation. It possessed 
 certain disadvantages, however, chief of which was a contracted central 
 or intake opening. The blades, also, were straight throughout their entire 
 length, being normal both to 
 the inner and outer circles of 
 the fan, and thus did not pro- 
 vide for receiving the air 
 without shock at the throat 
 of the fan. The depth of 
 Nasmyth's blades equaled 
 one-half the radius of the fan, 
 which was, under ordinary 
 conditions of mine practice, 
 far too great, and gave the 
 fan a low efficiency. 
 
 B i r a m ' s Ventilator. 
 About 1850, Biram at- 
 tempted to improve upon the 
 Nasmyth ventilator by re- 
 ducing the depth of blade so p 12 
 that it was but one-tenth of Wmmma 
 the radius. The blades were 
 
 straight, as in Nasmyth's ventilator, but inclined backwards from the direc- 
 tion of motion at a considerable angle. A large number of these blades were 
 employed. This fan was run at a considerable speed, but proved very in- 
 efficient. It depended more on the effort of propulsion given to the air than 
 on the centrifugal principle, as the depth of the blade was as much too small 
 
932^ 
 
 VENTILATION OF MINES 
 
 as that of Nasmyth's was too great. The intake or central opening in this 
 fan was as contracted as in the former type. See Pig. 11. 
 
 Waddle Ventilator. In this fan, Fig. 12, the inventor attempted to reen- 
 force the discharge pressure at the circumference against the pressure of the 
 atmosphere. The discharge took place all around the entire circumference 
 of the fan, which was entirely opened to the atmosphere. The blades were 
 curved backward from the direction of motion in spiral form. The width 
 of the blade decreased from the throat toward the circumference, so as to 
 present an inverse ratio to the length of radius. Thus, the area of passage 
 between the fan blades was maintained constant from the throat to the cir- 
 cumference of the fan. The purpose of this was to maintain the velocity 
 of the air through the fan constant, and to fortify the pressure due to the fan 
 against the atmospheric pressure at the point of discharge. The essential 
 features of the Waddle ventilator were, therefore, curved blades tapered 
 towards the circumference, and a free discharge into the atmosphere all 
 around the circumference. This, type is the best type of the open-running 
 fans having no peripheral casing, and discharging air into the atmosphere all 
 around the circumference. 
 
 Schiele Ventilator. This ventilator, Fig. 13, was constructed on the same 
 principles as the Waddle ventilator just described, but differed from the 
 latter, as the discharge was made into a spiral chamber surrounding the 
 fan and leading to an expanding or eVase 1 chimney. There was some advan- 
 tage in this feature, as it protected the fan against the direct influence ofthe 
 atmosphere, and reduced the velocity of discharge; but, in each of these fans, 
 the intake opening was contracted, and the depth of blade was very great, 
 yielding a comparatively low efficiency. 
 
 FIG. 13 
 
 FIG. 14 
 
 Guibal Ventilator. The next important step in the improvement of cen- 
 trifugal ventilators was introduced by M. Guibal, who constructed a fan, 
 Fig. 14, embodying the features of the Nasmyth ventilator, with the addition 
 of a casing built over the fan to protect its circumference. This casing was, 
 however, a tight-fitting casing, and as such, differed very materially from the 
 Schiele casing. In the Guibal fan the blades were arranged upon a series of 
 parallel bars passing upon each side of the center and at some distance from 
 it. By this construction, the blades were not radial at their inner edge or 
 the throat of the fan. They were curved, however, as they approached the 
 circumference of the fan, sd as to be normal or radial at the circumference. 
 The advantage of this construction was to give a strong skeleton or frame- 
 work to the revolving parts, and, further, each blade was inclined to the 
 radius at its inner extremity, the effect of which was to receive the air upon 
 the blade with less shock than was the case in the Nasmyth ventilator. The 
 intake or central opening, however, was very contracted, and the tight-fitting 
 casing about the circumference prevented the effective action of the fan 
 during a considerable portion of its revolution. The fan was supplied 
 with an 6vas6 chimney, which was a feature of the Schiele fan, but vibra- 
 tion was so strong that a shutter was required at the cutoff below the chim- 
 ney, to prevent it. This shutter was made adjustable, and is known as 
 the Walker shutter, having been applied to the fan later. 
 
 The Guibal ventilator presents some important and valuable features 
 in the protecting cover, and in the blades meeting the outer circumference 
 radially, and in the air being received with less shock than before. On the 
 
VENTILATION OF MINES 
 
 933 
 
 whole, it has proved a very efficient ventilator, although much work is lost 
 by reason of its contracted central orifice and tight casing, where the same 
 is used. 
 
 Murphy Ventilator. Fig. 15 consists of twin fans supported on the same 
 shaft and set a few feet apart. Each fan receives its air on one side only, 
 the openings being turned towards each other. This ventilator is built with 
 a small diameter, and is run at a high speed. The blades are curved back- 
 wards from the direction of motion. The intake opening is considerably 
 enlarged; a spiral casing generally surrounds the fan, and in every respect 
 this fan makes an 
 efficient high-speed 
 ventilator. It has re- 
 ceived considerable 
 favor in the United 
 States, where it has 
 been introduced into 
 a large number of 
 mines. 
 
 Capell Ventilator. 
 Perhaps none of 
 the centrifugal venti- 
 lators have been as 
 little understood in 
 regard to their princi- 
 
 FlG. 15 
 
 pie of action as the Capell fan. The fan is constructed along the lines of the 
 Schiele ventilator, but differs from it in the manner of receiving its intake air 
 and delivering the same into the main body of the fan. Here, and revolving 
 with it, is a set of smaller supernumerary blades. These blades occupy a 
 cylindrical space within the main body of the fan, and are inclined to the 
 plane of revolution so as to assist in deflecting the entering air through small 
 ports or openings into the main body of the fan, where it is revolved and is 
 discharged at the circumference into a spiral space resembling that surround- 
 ing the Schiele fan. The larger blades of this fan are curved backwards as 
 the Schiele blades, but are not tapered toward the circumference. The fan 
 is capable of giving a high water gauge, and is efficient as a mine ventilator. 
 The space surrounding the fan is extended to form an expanding chimney. 
 The fan may be used either as an exhaust fan or a blower. The best results 
 in the United States have been obtained by blowers. In Germany, where 
 this fan is in general use, there are no blowers. 
 
 FIG. 16 
 
 FIG. 17 
 
 Sirocco Fan. This Fig. 17 is the original multi-blade fan, having forwardly 
 inclined blades. The blades, therefore, act upon air at rest, relatively to 
 their own path which is at right angles to that of the incoming stream. 
 
 Thomas Chester, chief engineer of the American Blower Co. gives num- 
 erous formulas for use in connection with these fans. These are given here 
 in detail. 
 
 Sirocco fan blades have a forward inclination; that is to say the outer 
 tips are in advance of the inner edges in the direction of rotation and in 
 consequence air is thrown off at a higher velocity than the peripheral speed. 
 This enhanced velocity is responsible for the remarkable volumetric and 
 
934 VENTILATION OF MINES 
 
 manometric efficiencies of the Sirocco fan, these values usually being around 
 250% and 100% respectively. 
 
 The high mechanical efficiency is due to the following features: 
 
 1. Large inlet area. 
 
 2. Uniform action over the whole periphery, due to the large number of 
 blades. 
 
 3. Absence of whirlpool or vortex motion of the entering air before reach- 
 ing the fan blades, thereby avoiding the expenditure of power on unnec- 
 essary work. 
 
 4. Better stream lines, as the air leaves blades tilted forwards in very 
 nearly the same path as that already given off by the impeller and 
 traveling towards the fan outlet, consequently minimizing the power- 
 absorbing eddies produced by conflicting streams. 
 
 Direct-connected Engines. For large volumes of air against ordinary 
 resistances when using fans direct connected to engines it is necessary to use 
 wheels of large diameters in order to obtain the peripheral speeds required. 
 This calls for fans of special proportions as the widths under these conditions 
 are usually less than standard. /'- 
 
 Other Drives. Sirocco mine fans driven by belt or ropes or directly con- 
 nected to motors can be made of standard proportions which means that in 
 the case of a single-inlet fan the peripheral width is equal to one-third the 
 wheel diameter and a double-inlet fan has a peripheral width two-thirds the 
 wheel diameter. 
 
 Method of Determining Fan Diameter. The following formulae are used 
 in designing these fans, the volume being in cubic feet per minute and W.G. 
 being the mine resistance in inches of water. 
 
 , .5"\volume 
 Single-inlet, diameter in inches equals 
 
 Qf\4 
 
 Double-inlet, diameter in inches equals 
 
 T 
 
 Taking as an example 200,000 cu. ft. per min. against 3-in. mine resistance, 
 a double inlet exhauster being required, the formula for a fan of this type 
 
 R'ves a diameter of 120 in. and the impeller would therefore be 120X80 in. 
 npeller diameters in inches are in multiples of 6 so that in event of either 
 formula giving an intermediate diameter such as 118 in., the nearest standard 
 size should be taken which in this case would be 120 in. 
 
 To Ascertain Fan Speed Required. Having determined the diameter of 
 wheel needed the rotative speed can be found as follows; 
 
 10,800-s/W.G. 
 
 Revolutions per minute *=-r-. = = r 
 
 diameter in inches 
 
 Horsepower Needed. The power consumption is arrived at in the ordi- 
 nary manner by calculating the theoretical horsepower or horsepower in the 
 air and dividing same by the mechanical efficiency. 
 
 In the example referred to previously the horsepower in the air would be 
 
 -r^ = 94.5. With a Sirocco fan of this capacity the mechanical 
 0,040 
 efficiency could safely be figured at 75 % so that the actual power consump- 
 
 04 *> 
 tion or brake horsepower would be =^- = 126. 
 
 . / o 
 
 Size of Motor. In selecting a motor for work of this character it should be 
 borne in mind that the actual mine resistance cannot be predetermined with 
 absolute accuracy. The resistance offered by a mine to the flow of the re- 
 quired quantity of air may be less than anticipated, with a consequent 
 increase in the volume handled by the fan and a correspondingly increased 
 power consumption, so that to provide a margin of safety the factor .6 should 
 
 Q4 5 
 be used. This would indicate that a motor capable of developing jr- = 
 
 say 158 B. H. P. should be installed. 
 
 Evase Stack. The foregoing is based on the supposition that the fan would 
 be equipped with an evase stack and the effective length in feet measured 
 along the stack axis from the cutoff should be 5 times the square root of 
 the water gauge in inches. In the example under consideration the effective 
 length would be 5^/3 or say 8 ft. 
 
VENTILATION OF MINES 
 
 935 
 
 = 60\/ 
 
 Maximum Inlet Velocity. The minimum inlet area of a Sirocco fan is at 
 the inner ends of the inlet cones, the diameter of each being .875 the wheel 
 diameter. In the case cited the minimum area would be 60.1 sq. ft. for 
 each inlet or a total of 120.2 sq. ft. The maximum inlet velocity would 
 therefore be 1 ,660 ft. per min. 
 
 Loss at Inlets. Due to the right-angle turn made by the air entering a 
 fan inlet the velocity energy at this point is almost entirely lost but as the 
 velocity head would only be .171-in. W.G. this could be considered satisfac- 
 tory and it would not pay to increase the size of fan to make a reduction of 
 this loss. 
 
 The velocity head is the height of a column of water that can be sup- 
 ported by a stream of air moving at any given velocity. This can readily 
 be calculated by using as a unit the air velocity required to sustain 1 in. 
 
 of water. This velocity can be figured from the formula 
 
 where g is 32.16 the acceleration due to gravity and h is the ratio between the 
 weight of a cubic foot of water at 62F. and the weight of a cubic foot of air 
 under the conditions respecting temperature, humidity and barometric 
 pressure prevailing. 
 
 Standard Air. United States Navy Department engineers figure on 
 standard air as 70F. and 70% relative humidity and in this condition at 
 sea level it weighs .07465 Ib. per cu. ft. Water at 62F. weighs 62.355 Ib. 
 per cu. ft. so that the constant K for standard air is 4,015 and an air velocity 
 of 4,015 ft. per min. would be equivalent to 1-in. W.G. 
 
 Inlet Velocities. Taking the case under consideration the velocity head or 
 
 equivalent water gauge of the air entering the fan inlets isf ' , -^ or .171-in 
 
 \4,015/ 
 
 W.G. as previously stated. The equivalent velocity head for any require- 
 ment can be worked out by using the constant K as shown and the fol- 
 lowing table gives the maximum inlet velocities of standard Sirocco fans 
 for various resistances with the impeller diameters figured as recommended. 
 
 Mine Resistance, 
 In. 
 
 Max. Inlet 
 Velocity, 
 Ft. per Min. 
 
 Mine Resistance, 
 In. 
 
 Max. Inlet 
 Velocity, 
 Ft. per Min. 
 
 1 
 
 960 
 
 4! 
 
 2,090 
 
 1} 
 
 1,070 
 
 5 
 
 2,140 
 
 H 
 
 1,175 
 
 5} 
 
 2,195 
 
 H 
 
 ,270 
 
 5i 
 
 2,250 
 
 2 
 
 ,355 
 
 5J 
 
 2,300 
 
 2* 
 
 ,440 
 
 6 
 
 2,350 
 
 2J 
 
 ,515 
 
 6i 
 
 2,400 
 
 2| 
 
 ,590 
 
 6J 
 
 2,445 
 
 3 
 
 ,660 
 
 6| 
 
 2,490 
 
 3} 
 
 ,730 
 
 7 
 
 2,535 
 
 3* 
 
 ,790 
 
 71 
 
 2,580 
 
 3| 
 
 ,855 
 
 7* 
 
 2,625 
 
 4 
 
 ,920 
 
 7J 
 
 2,670 
 
 4i 
 
 ,975 
 
 8 
 
 2,715 
 
 4* 
 
 2,030 
 
 8i 
 
 2,760 
 
 Special Fans. Fans of standard proportions can be used for all the mine 
 resistances given in the above table as the most severe duty stated requires 
 an inlet velocity of 2,760 ft. per min. which is equivalent to .47-in. velocity 
 head. When large volumes of air are to be handled against high resistances, 
 however, the power reduction which can be obtained by installing a larger and 
 more expensive fan than indicated by the formulae frequently justifies the 
 greater cost as each horsepower saved represents approximately $100 per 
 yr. Cases of this kind and those involving fans for high altitudes should be 
 submitted to mine fan specialists. 
 
 Equivalent Orifice. No mine should be equipped with any style of fan 
 having a minimum inlet area less than twice the equivalent -orifice, if any- 
 thing like good efficiency is desired. The equivalent orifice of a mine varies 
 
936 
 
 VENTILATION OF MINES 
 
 directly as the volume of air passed per minute and inversely as the square 
 root of the resistance, so that with the same mine conditions prevailing the 
 equivalent orifice remains the same even with the fan speed altered and 
 the volume increased or decreased. 
 
 Reverting to the requirement of 200,000 cu. ft. per min. against 3-in. mine 
 resistance previously considered, the equivalent orifice is found to be 46.2 
 sq. ft. by using the well-known formula 
 
 T^ 1 /= c nnn* ^ v l' cu - ft- P er rnin. 
 Equivalent orifice in square feet = .0004 X ._ 
 
 VW.G. 
 
 In other words a ventilator drawing air through an opening of 46.2 sq. ft. 
 in a thin plate would encounter just the same resistance as when exhausting 
 the same volume, 200,000 cu. ft. per min., from a mine offering a resistance 
 of 3-in. water gauge. 
 
 As already noted the fan selected for this requirement has a minimum 
 inlet area of 120.2 sq. ft. or 2.6 times the equivalent orifice of the mine. 
 
 Murgue's Formula. It will doubtless be instructive at this point to 
 examine the equivalent orifice equation developed by M. Daniel Murgue as 
 given above. Using the established value 62 % as representing the effective 
 area of an opening in a thin plate allowing for vena contracta, the equiva- 
 lent orifice of 46.2 sq. ft. is found to have an effective area of 28.6 sq. ft. 
 
 Dividing the volume, 200,000 cu. ft., by the effective area 28.6 the velocity 
 is found to be 7,000 ft. per min. Using K the constant for standard air as 
 per U. S. Navy practice namely 4,015 ft. per min., the equivalent water 
 gauge is found by dividing the square of the air velocity through the effective 
 area of the equivalent orifice by the square of the constant K 
 
 water gauge. 
 
 The small discrepancy indicates that Murgue used a constant slightly higher 
 than 4,015ft. per min. so that he evidently figured on air having a little less 
 weight than is considered standard by the Navy Department engineers. 
 This would readily be accounted for if he assumed a higher relative humidity 
 than 70%. 
 
 Sullivan Reversible Fans. The Sullivan fan is reversible. The opera- 
 tion of reversing is secured in a manner that is considered extraordinarily 
 simple and safe. It is by the use of a steel hood swing by a gear and pinion 
 controlled by a hand wheel. This has an advantage in that a smaller and 
 simpler housing is needed than is commonly the case. The fan itself is of 
 the multi-blade pattern with the double wheel, a double inlet and cone- 
 shaped deflectors for changing the direction of the air with minimum fric- 
 tion and loss in power. They are of relatively small diameter and of high 
 speed. 
 
 It must be noted that the action of the hopd is entirely independent of 
 that of the fan. It hangs in bearings concentric with those of the fan wheel 
 
 FIG. IS 
 
VENTILATION OF MINES 
 
 937 
 
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938 
 
 VENTILATION OF MINES 
 
 RATINGS. G-FT. AND 81-FT. PANS 
 
 6-ft. Fan 
 
 Capacity, 
 Cu. Ft. Air P.M. 
 
 Water Gauge, In. 
 
 i 
 
 * 
 
 I 
 
 1 
 
 li 
 
 U 
 
 1! 
 
 2 
 
 2^ 
 
 3 
 
 3* 
 
 4 
 
 4* 
 
 5 
 
 5* 
 
 6 
 
 10,000 
 20,000 
 
 R.P.M. 
 
 90 
 
 105 
 
 119 
 
 134 
 
 148 
 
 163 
 
 178 
 
 192 
 
 221 
 
 251 
 
 280 
 
 309 
 
 338 
 
 367 
 
 396 
 
 42,5 
 
 H.P. 
 R.P.M. 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 19 
 
 21 
 
 23 
 
 25 
 
 27 
 
 29 
 
 31 
 
 33 
 
 133 
 
 146 
 
 159 
 
 172 
 
 185 
 
 199 
 
 212 
 
 225 
 
 251 
 
 277 
 
 303 
 
 330 
 
 356 
 
 382 
 
 408 
 
 435 
 
 H.P. 
 
 13 
 
 15 
 
 16 
 
 17 
 
 19 
 
 20 
 
 22 
 
 23 
 
 26 
 
 29 
 
 32 
 
 34 
 
 37 
 
 40 
 
 42 
 
 45 
 
 30,000 
 
 R.P.M. 
 
 177 
 
 189 
 
 201 
 
 212 
 
 224 
 
 236 
 
 248 
 
 260 
 
 283 
 
 307 
 
 330 
 
 357 
 
 384 
 
 410 
 
 437 
 
 448 
 
 H.P. 
 
 17 
 
 18 
 
 20 
 
 22 
 
 24 
 
 25 
 
 27 
 
 29 
 
 33 
 
 36 
 
 40 
 
 43 
 
 47 
 
 50 
 
 53 
 
 57 
 
 40,000 
 
 R.P.M. 
 
 220 
 
 231 
 
 241 
 
 252 
 
 262 
 
 273 
 
 284 
 
 294 
 
 315 
 
 337 
 
 358 
 
 379 
 
 400 
 
 421 
 
 442 
 
 463 
 
 H.P. 
 
 20 
 
 22 
 
 24 
 
 26 
 
 29 
 
 31 
 
 33 
 
 35 
 
 39 
 
 44 
 
 48 
 
 52 
 
 56 
 
 61 
 
 66 
 
 69 
 
 50,000 
 
 R.P.M. 
 
 263 
 
 272 
 
 282 
 
 291 
 
 301 
 
 310 
 
 319 
 
 329 
 
 348 
 
 366 
 
 385 
 
 404 
 
 423 
 
 442 
 
 461 
 
 480 
 
 H.P. 
 
 23 
 
 26 
 
 28 
 
 31 
 
 34 
 
 36 
 
 38 
 
 41 
 
 46 
 
 31 
 
 56 
 
 61 
 
 66 
 
 71 
 
 76 
 
 81 
 
 60,000 
 
 R.P.M. 
 
 307 
 
 315 
 
 324 
 
 332 
 
 341 
 
 349 
 
 357 
 
 366 
 
 383 
 
 399 
 
 416 
 
 433 
 
 450 
 
 467 
 
 483 
 
 500 
 
 H.P. 
 
 27 
 
 29 
 
 32 
 
 35 
 
 38 
 
 41 
 
 43 
 
 47 
 
 53 
 
 59 
 
 64 
 
 70 
 
 76 
 
 82 
 
 87 
 
 93 
 
 70,000 
 
 R.P.M. 
 
 3.50 
 
 357 
 
 365 
 
 372 
 
 380 
 
 387 
 
 395 
 
 402 
 
 417 
 
 432 
 
 447 
 
 462 
 
 477 
 
 492 
 
 507 
 
 523 
 
 H.P. 
 
 30 
 
 33 
 
 36 
 
 40 
 
 43 
 
 46 
 
 49 
 
 53 
 
 60 
 
 66 
 
 72 
 
 79 
 
 86 
 
 92 
 
 99 
 
 105 
 
 80,000 
 
 R.P.M. 
 
 393 
 
 400 
 
 406 
 
 413 
 
 420 
 
 427 
 
 433 
 
 440 
 
 453 
 
 467 
 
 480 
 
 494 
 
 507 
 
 520 
 
 534 
 
 548 
 
 H.P. 
 
 33 
 
 37 
 
 40 
 
 44 
 
 48 
 
 51 
 
 54 
 
 59 
 
 66 
 
 74 
 
 80 
 
 88 
 
 96 
 
 103 
 
 110 
 
 117 
 
 90,000 
 
 R.P.M. 
 
 437 
 
 443 
 
 449 
 
 455 
 
 461 
 
 467 
 
 473 
 
 479 
 
 491 
 
 503 
 
 515 
 
 527 
 
 539 
 
 551 
 
 563 
 
 575 
 
 H.P. 
 
 37 
 
 40 
 
 44 
 
 49 
 
 53 
 
 57 
 
 60 
 
 65 
 
 73 
 
 81 
 
 89 
 
 97 
 
 105 
 
 113 
 
 121 
 
 129 
 
 100,000 
 
 R.P.M. 
 
 480 
 
 485 
 
 491 
 
 496 
 
 502 
 
 507 
 
 512 
 
 518 
 
 528 
 
 539 
 
 550 
 
 561 
 
 572 
 
 583 
 
 594 
 
 605 
 
 H.P. 
 
 40 
 
 44 
 
 49 
 
 53 
 
 58 
 
 62 
 
 66 
 
 71 
 
 80 
 
 88 
 
 97 
 
 106 
 
 115 
 
 124 
 
 132 141 
 
 H. P. tabulated are I. H. P. steam eng. dir. conn, or motor output belted. 
 NOTE. The power ratings are shown in their present form, rather than 
 as net H. P. delivered to the fan shaft, on account of the variation in efficiency 
 with each change in engine speed. 
 
VENTILATION OF MINES 
 
 8-ft. 6-in. Fan 
 
 Capacity, 
 Cu. Ft. Air P.M. 
 
 Water Gauge, In. 
 
 1 
 
 i 
 
 1 
 
 1 
 
 n 
 
 a 
 
 if 
 
 2 
 
 2* 
 
 3 
 
 3} 
 
 4 
 
 4| 
 
 5 
 
 5i 
 
 6 
 
 25,000 
 
 R.P.M. 
 
 56 
 
 65 
 
 74 
 
 83 
 
 91 
 
 100 
 
 109 
 
 118 
 
 136 
 
 153 
 
 171 
 
 189 
 
 207 
 
 224 
 
 242 
 
 260 
 
 H.P. 
 
 17 
 
 20 
 
 22 
 
 24 
 
 27 
 
 29 
 
 32 
 
 35 
 
 40 
 
 45 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 50,000 
 
 R.P.M. 
 
 80 
 
 88 
 
 97 
 
 105 
 
 114 
 
 122 
 
 131 
 
 139 
 
 156 
 
 173 
 
 190 
 
 206 
 
 223 
 
 240 
 
 257 
 
 274 
 
 H.P. 
 
 24 
 
 27 
 
 31 
 
 34 
 
 38 
 
 41 
 
 44 
 
 48 
 
 55 
 
 62 
 
 68 
 
 75 
 
 82 
 
 89 
 
 95 
 
 102 
 
 75,000 
 
 R.P.M. 
 
 104 
 
 112 
 
 119 
 
 127 
 
 134 
 
 142 
 
 150 
 
 157 
 
 172 
 
 188 
 
 203 
 
 218 
 
 233 
 
 248 
 
 264 
 
 279 
 
 H.P. 
 
 31 
 
 35 
 
 40* 
 
 44 
 
 48 
 
 52 
 
 57 
 
 62 
 
 71 
 
 79 
 
 87 
 
 96 
 
 104 
 
 113 
 
 121 
 
 129 
 
 100,000 
 
 R.P.M. 
 
 128 
 
 135 
 
 142 
 
 148 
 
 155 
 
 162 
 
 169 
 
 176 
 
 189 
 
 203 
 
 216 
 
 230 
 
 244 
 
 257 
 
 271 
 
 285 
 
 H.P. 
 
 38 
 
 43 
 
 48 
 
 53 
 
 58 
 
 64 
 
 69 
 
 74 
 
 84 
 
 94 
 
 104 
 
 115 
 
 125 
 
 135 
 
 145 
 
 156 
 
 125,000 
 
 R.P.M. 
 
 152 
 
 158 
 
 164 
 
 170 
 
 176 
 
 182 
 
 189 
 
 195 
 
 207 
 
 219 
 
 231 
 
 244 
 
 256 
 
 268 
 
 280 
 
 292 
 
 H.P. 
 
 45 
 
 51 
 
 57 
 
 63 
 
 69 
 
 75 
 
 81 
 
 87 
 
 99 
 
 111 
 
 123 
 
 135 
 
 147 
 
 159 
 
 171 
 
 183 
 
 150,000 
 
 R.P.M. 
 
 176 
 
 181 
 
 187 
 
 192 
 
 198 
 
 203 
 
 208 
 
 214 
 
 225 
 
 235 
 
 246 
 
 257 
 
 268 
 
 279 
 
 289 
 
 300 
 
 H.P. 
 
 52 
 
 59 
 
 66 
 
 73 
 
 80 
 
 87 
 
 93 
 
 100 
 
 114 
 
 128 
 
 142 
 
 156 
 
 169 
 
 183 
 
 197 
 
 210 
 
 175,000 
 
 R.P.M. 
 
 200 
 
 205 
 
 209 
 
 214 
 
 219 
 
 224 
 
 228 
 
 233 
 
 242 
 
 252 
 
 261 
 
 271 
 
 280 
 
 289 
 
 299 
 
 309 
 
 H.P. 
 
 59 
 
 67 
 
 75 
 
 82 
 
 90 
 
 98 
 
 106 
 
 113 
 
 129 
 
 144 
 
 160 
 
 175 
 
 191 
 
 206 
 
 222 
 
 237 
 319 
 264 
 320 
 
 200,000 
 
 R.P.M. 
 
 224 
 
 228 
 
 232 
 
 236 
 
 240 
 
 245 
 
 249 
 
 253 
 
 261 
 
 269 
 
 277 
 
 286 
 
 294 
 
 302 
 
 310 
 
 H.P. 
 
 66 
 
 75 
 
 83 
 
 92 
 
 100 
 
 109 
 
 118 
 
 126 
 
 143 
 
 161 
 
 178 
 
 195 
 
 212 
 
 229 
 
 247 
 
 225,000 
 250.000 
 
 R.P.M. 
 
 248 
 
 251 
 
 254 
 
 257 
 
 260 
 
 264 
 
 267 
 
 270 
 
 276 
 
 282 
 
 288 
 
 295 
 
 301 
 
 307 
 
 313 
 
 H.P. 
 
 73 
 
 83 
 
 92 
 
 102 
 
 111 
 
 121 
 
 130 
 
 140 
 
 159 
 
 178 
 
 197 
 
 216 
 
 235 
 
 254 
 
 273 
 
 291 
 
 R.P.M. 
 
 272 
 
 275 
 
 278 
 
 281 
 
 284 
 
 287 
 
 290 
 
 293 
 
 300 
 
 306 
 
 312 
 
 318 
 
 324 
 
 330 
 
 336 
 
 342 
 
 H.P. 
 
 80 
 
 90 
 
 101 
 
 111 
 
 121 
 
 132 
 
 142 
 
 152 
 
 173 
 
 193 
 
 214 
 
 235 
 
 255 
 
 276297 
 
 318 
 
 H. P. tabulated are I H.P. steam eng. dir. conn, or motor output belted. 
 
940 
 
 VENTILATION OF MINES 
 10- FT. PAN RATINGS 
 
 lO-'ft. Fan 
 
 Capacity, 
 Cu. ft. Air P.M. 
 
 Water Gauge, In. 
 
 i 
 
 ~J 
 
 1 
 
 1 
 
 11 
 
 l* 
 
 if 
 
 2 
 
 2i 
 
 3' 
 
 3} 
 
 4 
 
 *i 
 
 5 
 
 H 
 
 6 
 
 25,000 
 
 R.P.M. 
 
 46 
 
 63 
 
 78 
 
 90 
 
 100 
 
 no 
 
 119 
 
 126 
 
 141 
 
 154 
 
 167 
 
 178 
 
 189 
 
 199 
 
 209 
 
 218 
 
 H.P. 
 
 20 
 
 24 
 
 28 
 
 31 
 
 34 
 
 37 
 
 40 
 
 42 
 
 47 
 
 52 
 
 57 
 
 61 
 
 65 
 
 69 
 
 73 
 
 77 
 
 50,000 
 
 R.P.M. 
 
 52 
 
 69 
 
 82 
 
 93 
 
 103 
 
 112 
 
 121 
 
 128 
 
 144 
 
 157 
 
 169 
 
 180 
 
 192 
 
 202 
 
 212 
 
 221 
 
 H.P. 
 
 24 
 
 30 
 
 34 
 
 38 
 
 42 
 
 46 
 
 50 
 
 54 
 
 61 
 
 68 
 
 74 
 
 80 
 
 86 
 
 92 
 
 98 
 
 104 
 
 75,000 
 
 R.P.M. 
 
 62 
 
 75 
 
 87 
 
 98 
 
 107 
 
 116 
 
 124 
 
 132 
 
 147 
 
 159 
 
 172 
 
 183 
 
 194 
 
 204 
 
 214 
 
 223 
 
 H.P. 
 
 30 
 
 36 
 
 42 
 
 47 
 
 51 
 
 56 
 
 61 
 
 65 
 
 74 
 
 83 
 
 92 
 
 100 
 
 108 
 
 116 
 
 124 
 
 132 
 
 100,000 
 
 R.P.M. 
 
 74 
 
 84 
 
 94 
 
 104 
 
 113 
 
 121 
 
 129 
 
 137 
 
 150 
 
 163 
 
 174 
 
 186 
 
 197 
 
 207 
 
 216:225 
 
 H.P. 
 
 37 
 
 43 
 
 49 
 
 55 
 
 61 
 
 66 
 
 72 
 
 77 
 
 88 
 
 99 
 
 109 
 
 119 
 
 129 
 
 139 
 
 149 159 
 
 , 125,000 
 
 R.P.M. 
 
 90 
 44 
 
 97 
 50 
 
 103 
 
 113 
 
 121 
 
 129 
 
 136 
 
 143 
 
 156 
 
 167 
 
 178 
 
 190 
 
 200 
 
 210 
 
 219228 
 
 H.P. 
 
 57 
 
 64 
 
 70 
 
 77 
 
 83 
 
 90 
 
 102 
 
 114 
 
 126 
 
 138 
 
 151 
 
 163 
 
 175 188 
 
 150.000 
 
 R.P.M. 
 
 107 
 
 112 
 
 117 
 
 124 
 
 131 
 
 138 
 
 144 
 
 150 
 
 163 
 
 174 
 
 184 
 
 194 
 
 204 
 
 214 
 
 224 232 
 
 H.P. 
 
 51 
 
 58 
 
 65 
 
 73 
 
 80 
 
 88 
 
 95 
 
 102 
 
 117 
 
 131 
 
 45 
 
 159 
 
 173 
 
 187 
 
 201 
 
 214 
 
 175,000 
 
 R.P.M. 
 
 123 
 
 127 
 
 132 
 
 137 
 
 143 
 
 148 
 
 154 
 
 160 
 
 170 
 
 180 
 
 90 
 
 200 
 
 210 
 
 219 
 
 229 
 
 237 
 
 H.P. 
 
 59 
 
 67 
 
 74 
 
 82 
 
 91 
 
 99 
 
 107 
 
 115 
 
 131 
 
 147 
 
 63 
 
 79 
 
 95 
 
 211 
 
 227 
 
 242 
 
 200.000 
 
 R.P.M. 
 
 140 
 
 144 
 
 147 
 
 150 
 
 155 
 
 160 
 
 164 
 
 169 
 
 179 
 
 189 
 
 99 
 
 >08 
 
 217 
 
 226 
 
 235 
 
 243 
 
 H.P. 
 
 66 
 
 75 
 
 83 
 
 92 
 
 101 
 
 110 
 
 119 
 
 128 
 
 146 
 
 174 
 
 82 
 
 200 
 
 217 
 
 235 
 
 53 
 
 271 
 
 225,000 
 
 R.P.M. 
 
 158 
 
 160 
 
 163 
 
 166 
 
 169 
 
 173 
 
 177 
 
 181 
 
 189 
 
 199 
 
 08 
 
 17 
 
 ?25 
 
 >34 
 
 42 
 
 249 
 
 H.P. 
 
 73 
 
 83 
 
 93 
 
 102 
 
 112 
 
 121 
 
 131 
 
 141 
 
 161 
 
 81 
 
 01 
 
 20 
 
 240 
 
 60 
 
 79 
 
 299 
 
 250,000 
 
 R.P.M. 
 
 174 
 
 177 
 
 179 
 
 181 
 
 183 
 
 187 
 
 190 
 
 193 
 
 201 
 
 210 
 
 18 
 
 27 
 
 35 
 
 43 
 
 49 
 
 257 
 
 H.P. 
 
 81 
 
 91 
 
 102 
 
 112 
 
 123 
 
 133 
 
 144 
 
 155 
 
 176 
 
 98 
 
 20 
 
 41 
 
 63 
 
 85 
 
 06 
 
 327 
 
 275,000 
 
 R.P.M. 
 
 192 
 
 194 
 
 196 
 
 198 
 
 200 
 
 202 
 
 204 
 
 207 
 
 214 
 
 222 
 
 30 
 
 37 
 
 44 
 
 53 
 
 59265 
 
 H.P. 
 
 88 
 
 100 
 
 111 
 
 123 
 
 134 
 
 145 
 
 157 
 
 168 
 
 182 
 
 215 
 
 39 
 
 62 
 
 86 
 
 10 
 
 33 356 
 
 300,000 
 
 R.P.M. 
 
 209 
 
 211 
 
 212 
 
 213 
 
 215 
 
 217 
 
 219 
 
 223 
 
 228 
 
 235 
 
 40 
 
 47 
 
 55 
 
 262 
 
 68275 
 
 H.P. 
 
 96 
 
 108 
 
 120 
 
 132 
 
 145 
 
 157 
 
 170 
 
 183 
 
 208 
 
 233 
 
 58 
 
 83 
 
 09 
 
 334 
 
 60385 
 
 325,000 
 350,000 
 
 R.P.M. 
 
 227 
 
 228 
 
 229 
 
 230 
 
 231 
 
 233 
 
 235 
 
 237 
 
 242 
 
 248 
 
 54 
 
 61 
 
 67 
 
 273 
 
 79,285 
 
 H.P. 
 R.P.M. 
 
 103 
 
 117 
 
 130 
 
 143 
 
 156 
 
 170 
 
 183 
 
 96 
 
 223 
 
 251 
 
 79 
 
 05 
 
 32 
 
 360 
 
 87414 
 
 243 
 
 244 
 
 245 
 
 246 
 
 247 
 
 248 
 
 250 
 
 253 
 
 257 
 
 263 
 
 68 
 
 73 
 
 78 
 
 284 
 
 90296 
 
 H.P. 
 
 111 
 
 125 
 
 139 
 
 153 
 
 167 
 
 182 
 
 196 
 
 211 
 
 239 
 
 269 
 
 98 
 
 27 
 
 56 
 
 385 
 
 14443 
 
 H. P. tabulated are I. H. P. steam eng. dir. conn, or motor output belted. 
 
VENTILATION OF MINES 
 
 941 
 
 so that it may be easily revolved without stopping the fan. The operation 
 is so simple that anyone about a mine is enabled to reverse the current 
 instantly and to know positively that the operation is completed. 
 
 The foregoing types of fans are given to show the general designs that are 
 now in use. There are numerous makes now on the market, each with 
 one or more modifications of these general types. Most of these produce 
 results worthy of investigation. To describe them all in detail is impractical 
 in a pocketbook of this size. 
 
 The following table of capacities may b'e valuable to those having installa- 
 tions of the standard moderate- speed fan as manufactured by Crawford 
 and McCrimmon. 
 
 Diameter 
 of Fan, 
 . Ft. 
 
 Width 
 ofBlades, 
 In. 
 
 Size of 
 Driving 
 Engine 
 
 Revolutions 
 per Minute 
 
 Maximum Ca- 
 pacity, Cubic Feet 
 per Minute 
 
 8 
 
 32 
 
 5 X10 
 
 180 
 
 25,000 approx. 
 
 10 
 
 40 
 
 6JX12 
 
 150 
 
 40,000 approx. 
 
 12 
 
 48 
 
 8 X13 
 
 150 
 
 65,000 approx. 
 
 14 
 
 48 
 
 8 X16 
 
 150 
 
 75,000 approx. 
 
 15 
 
 60 
 
 10 X20 
 
 120 
 
 90,000 approx. 
 
 16 
 
 60 
 
 10 X20 
 
 120 
 
 100,000 approx. 
 
 18 
 
 72 
 
 10 X24 
 
 100 
 
 150,000 approx. 
 
 20 
 
 84 
 
 12 X24 
 
 100 
 
 200,000 approx. 
 
 The Position of Any Fan, Etc., whether used as an exhaust or blower, 
 should be sufficiently removed from the fan shaft or drift to avoid damage to 
 the fan in case of explosion in the mine. Even in non-gaseous mines, the fan 
 should be located a short distance back from the shaft mouth, to avoid 
 damage due to settlement. Con- 
 nection should be made with the 
 fan shaft by means of an ample 
 drift, which should be deflected 
 into the shaft so as to produce 
 as little shock to the current as 
 possible. In case of gaseous 
 seams, explosion doors should be 
 provided at the shaft mouth. 
 The ventilator at every large 
 mine should be arranged so that 
 it may be converted from an ex- 
 hausting to a blowing fan at short 
 notice. This is managed by 
 housing the central orifices or 
 intake of the fan in such a man- 
 ner as to connect them directly 
 with the fan drift. A large door 
 aft, Fig. 19, is arranged at the foot 
 of the expanding chimney, the 
 latter being placed between the 
 fan and the shaft. This door, 
 when the fan is exhausting, is in 
 the lower position aft, and then 
 forms a portion of the spiral 
 casing leading to the chimney. 
 
 When the fan is blowing, how- p IG . jg 
 
 ever, the door is swung upwards 
 
 so as to occupy the position ac, being tangent to the cutoff at c, thereby 
 closing the discharge into the chimney and causing it to enter the fan drift 
 behind the door. At the same time, the positions of the two doors, ed and 
 fd, in the fan drift, are changed to el and fs, respectively, to open the fan 
 drift to the discharge from the fan, and to close the openings leading from 
 the fan drift to the housing upon each side of the fan, while another set of 
 doors A A upon each side of the fan, in the housing, which were previously 
 closed tightly, are now set wide open to admit the outside air to the intake 
 
942 VENTILATION OF MINES 
 
 openings of the fan. The fan is thus made to draw its air from the atmos- 
 phere, and discharge it into the fan drift, instead of drawing its air from the 
 fan drift and discharging into the chimney, as before. 
 
 The manometrical efficiency of a fan is the ratio between its effective and 
 theoretical pressures. It has been assumed that the theoretical pressure due 
 
 M 2 M 2 X 1.2 X 12 
 
 to the fan's action is given by the equation h = , or * = ' , u being, 
 
 as before, the tangential speed (feet per second), and g the force of gravity 
 (32.16); h = head of air column in feet; i = water gauge in inches. 
 
 Mechanical efficiency is a term applied to the ratio between its effective 
 and theoretical powers. In estimating the efficiency of a ventilator, it is 
 customary, though incorrect, to estimate the theoretical power of the fan 
 from an engine card taken from the steam cylinder of the fan engine. The 
 efficiency of the steam engine is this confused with the efficiency of the 
 ventilator. Mr Beard gives the following formula for the theoretical work 
 
 of the fan per minute: U = . 001699^-^ -\/V R 3 bn 2 , in which ra = ratio 
 
 7W 3 
 
 between outer and inner diameters of fan (D md), and V = velocity (feet 
 per minute) of air in fan drift; R = outer radius of fan blades (feet); b = 
 breadth of fan blades (feet); n = number of revolutions of fan per minute. 
 If we divide the power upon the air, as determined by the expression qp, 
 by the theoretical work given in the last equation, we obtain the value of the 
 coefficient of efficiency. According to this formula the efficiency of the 
 ventilator changes with the speed, decreasing as the speed increases, but 
 not in the same ratio. An expression for the coefficient of efficiency of a 
 
 163,6002 
 ventilator is given by Beard as follows: K= X3 2 . 
 
 The factor c is a constant of design whose value may vary from 2 to 7, but 
 for an ordinary design, the value c = 4 may be taken. This factor has refer- 
 ence to the equipment of the machine with respect to its efficiency for pass- 
 ing an air current through itself with least resistance. Thus, where the 
 ventilator is to be equipped with intake blades for the deflection of the air cur 
 rent into the machine, and with straight radial blades having only a forward 
 curve at the lip of the blade to avoid the shock of the entering air against 
 the revolving blades, and the spiral casing starting a short distance upon the 
 cutoff and extending uniformly around the circumference of the fan, the 
 value of this constant may be 2 or 3. Where none of these accessories to 
 the efficiency of the fan is employed, the value of c may be as high as 7. 
 
 FAN CONSTRUCTION 
 
 Size of Central Orifice. The velocity of the intake should vary between 
 1,000 ft. and 1,500 ft. per min., while 1,200 ft. may be used for fan calcula- 
 tions. If d = diameter of opening, and q = quantity of air passing per 
 
 minute ' d= \UMOX.7854 f r sin e le - intake fans - and d = V 2 .400X.7S54 
 for double-intake fans. 
 
 Upon entering the fan the air travels in a radial direction; this change of 
 direction is accompanied by a slight reduction of the velocity, hence the 
 throat area of the fan must be slightly in excess of the intake area. The 
 throat is the surface of the imaginary cylinder that has for its two bases the 
 two intake openings of the fan, and for its length the width of the fan, = 
 trdb. [The throat area is commonly made 1.25 times the total area of the 
 intake orifices, which gives for breadth of blade b = %d for double-intake, 
 and b = f e d for single-intake. Beard.] 
 
 Diameter of Fan. Murgue assumes the tangential velocity of the blade 
 tips (w) to create a depression double that due to the velocity as expressed 
 
 by the equation H * , or if the manometrical efficiency = K, and the 
 
 effective head produced = h, h = KH = K~ t or u= A/^. From this equa . 
 
 & H K 
 
 tion, the tangential velocity (feet per second) may be calculated for any 
 given effective head h. This effective head h is the head of air column 
 effective in producing the circulation in the airway. To convert the 
 effective head of air column into inches of water gauge (t),.we have h = 
 
 1 2X12*' ** av * n S found the tangential speed required in feet per second 
 
VENTILATION OF MINES 943 
 
 this is multiplied by 60, to obtain the speed in feet per minute, and dividing 
 this result by the desired number of revolutions per minute, or the desired 
 speed of the ventilator, the outer circumference of the fan blades is obtained. 
 No reference is made in the equation to the quantity of air in circulation 
 which is determined from the equivalent orifice of the mine and of the fan 
 
 by the equation V = * - - - 12, in which V = volume of air (cubic feet per 
 
 second); a = equivalent orifice of the mine; o = the equivalent orifice of the 
 fan. M. Murgue also uses the equation h=> ~7~ and suggests that 
 
 <fe|ir) 
 
 the value of K for any particular type of machine should be first decided, 
 after which the tangential speed required to produce any given effective 
 
 head of air column (A) is easily calculated for the formula u = \~. The 
 
 breadth of the blade is left largely to judgment, while this method of cal- 
 culation gives the same size of fan for any given effective head desired, 
 regardless of the quantity of air to be circulated, which is the same as saying 
 that the ventilator will present the same efficiency when a large amount of 
 air is crowded through its orifice of passage as when a smaller amount of air 
 is necessary. 
 
 Mr. Beard uses the following formulas for determining the several dimen- 
 sions of a ventilating fan; 
 
 D~ m 3,770 V^. 
 
 xi-v' ^= 
 
 385.000.000^ . 
 
 (m*-l)n*K\/QV' * 170m p 
 
 in which m = -j, which is the ratio between the outer diameter of the fan 
 a 
 
 blades D and the inner diameter of the blade d, which equals the diameter of 
 the intake orifice; b = width of fan blade; e = expansion of spiral casing at 
 point of cutoff. 
 
 The other symbols stand for the same quantities as previously indicated. 
 
 Curvature of Blades. It was at one time supposed that the curvature of 
 the blades should be such that the radial passage of the air current would 
 be undisturbed by the revolution of the fan; but fans constructed on this 
 principle gave no adequate results, and the theoretical spiral thus developed 
 was entirely abandoned. A certain curvature of the blade backward, 
 however, is assumed by many to increase the efficiency of the fan. This 
 has not been proved in practice, but the effect of the backward curvature 
 appears simply to necessitate a higher speed of revolution in the fan, in 
 order to obtain the same results as are obtained with radial blades. 
 
 The Guibal blade, radial at its outer extremity, or normal to the outer 
 circumference, and curved forward in the direction of motion, at its inner 
 extremity, so that the lip of the blade approaches tangency to the throat 
 circle, seems to be an effective blade in centrifugal ventilation. 
 
 Tapered Blades. The object of the taper is to produce a constant area 
 of passage from the throat to the circumference of the fan, and thus prevent 
 the reduction of the velocity of the current in its passage through the fan. 
 This feature presents an attempt similar to that attempted by the curva- 
 ture of the blades, to hasten the passage of the air through the fan. It 
 has not been proved, however, to have produced any beneficial result, 
 except in the strengthening of the discharge pressure against the atmos- 
 pheric pressure, in open-running fans. On the other hand, the slowing up 
 of the air in its passage through a covered fan has by no means been proved 
 a detriment, but is assumed by many to be an advantage, inasmuch as the 
 air thus remains longer within the influence of the fan blades. 
 
 The number of blades depends on the size of the fan. An increased num- 
 ber strengthens the fan's action at the circumference, or supports the air at 
 that point, and thus prevents the backlash or the reentry of air into the fan, 
 due to the eddies occurring at the circumference when the blades are too far 
 apart. To a certain extent, the number of blades is modified by the speed 
 
944 VENTILATION OF MINES 
 
 of revolution, high-speed motors requiring a somewhat lesser number, 
 while low-speed motors require more. In any case, the number of blades 
 should not be so great as to abnormally increase the resistance to the air 
 current. In general, the distance upon the outer circumference from tip 
 to tip of the fan blades should be from 2 to 3 times the depth of the blade. 
 The spiral casing gradually reduces the velocity of the air and reduees the 
 shock incident to the discharge of the air into the atmosphere. The spiral 
 casing should be so proportioned that the velocity of the flow from the fan 
 blades will be maintained constant around the entire circumference, and 
 this should not be less than the velocity of the blade tips. The expansion e 
 of the casing at the cutoff should be such as to provide a velocity of the 
 air at this point equal to the velocity of the blade tips, according to the 
 
 equation e = =-r, in which D = diameter of fan; n = number revolutions 
 
 ^ iruno 
 per minute \b = breadth of fan blade. 
 
 The evase chimney reduces the velocity of the air, as it is discharged into 
 the atmosphere, to a minimum. The chimney should be sufficiently high 
 to protect the fan from the effect of high winds, but should not extend too 
 far above the fan casing, the point of cutoff being situated below this, at 
 about the level of a tangent to the throat circle at its lower side. - 
 
 High-speed and Low-speed Motors. The question of speed of the venti- 
 lating motor is largely an open one, inasmuch as the same work may be 
 performed by a small ventilator running at a high speed as is performed by 
 a large ventilator running at a low speed. 
 
 It is important to design a mine ventilator at a speed such as to admit of 
 its being increased in case of emergency. If the ventilator has been de- 
 signed at a high speed, a demand for an increase of speed cannot be met as 
 readily as when the ventilator is designed at a medium or low speed; in 
 other words, the exigencies of mine ventilation demand that a ventilator 
 shall be capable of greatly increased speed. 
 
 Fan Tests. A large number of fan tests have been made, from time to 
 time, on different types of fans and under different conditions, with respect 
 to the resistance against which the fan is operated, and the quantity of air 
 required, and the speed of the ventilator. The experiments have resulted, 
 to a large extent, in tabulating a mass of contradictory data. The condi- 
 tions that affect the yield of the centrifugal ventilator are so numerous, and 
 the tabulation of the necessary data has been so often neglected in these 
 experiments, as to render them practically useless for the purpose of scien- 
 tific investigation. In conducting a reliable fan test, the following points 
 should be observed: (1) Take the velocity, pressure, and temperature of 
 the air at the same point in the airway, as nearly as practicable. This 
 point should be selected near the foot of the downcast shaft, or in the fan 
 drift at a suitable distance from the fan, to avoid oscillations of pressure and 
 velocity. (2) The area of the fan drift should be uniform for a suitable 
 distance in each direction from the point of observation, and this area 
 should be carefully measured. (3) Take the velocity readings at different 
 positions in the airway, so as to obtain an average reading over the entire 
 sectional area. Do not interpose the body in this area so as to decrease the 
 sectional area of the airway. (4) Take outside temperature of the air and 
 the barometric pressure at the time of making the test. (5) The intake and 
 discharge openings of the fan should be protected against wind pressure. 
 (6) At least three observations should be made, at as many different speeds 
 of the ventilator, and the number of revolutions of the fan carefully observed 
 and recorded for each observation. 
 
 Mr. R. Van A. Norris (Trans. A. I. M. E., vol. XX, page 637) gives the 
 results of a large number of experiments performed upon different mine 
 ventilating fans. This table, like ajl other tabulated fan tests, shows a large 
 amount of contradictory data. The conclusions drawn by Mr. Norris from 
 these tests are interesting and would be given here excepting that they 
 might be misleading if considered apart from the description of the experi- 
 ments and the discussion leading up to the conclusions. 
 
 CONDUCTING AIR CURRENTS 
 
 Doors. A mine door is used for the purpose of deflecting the air current 
 from its course in one entry so as to cause it to traverse another entry, at the 
 same time permitting the passage of mine cars through the first entry. The 
 essential points in the construction of a mine door are that it shall be hung 
 from a strong door frame in such a manner as to close with the current. The 
 
MINE FIRES 945 
 
 door should be hung so as to have a slight fall. If necessary, canvas flaps 
 may be supplied to prevent leakage around the door, and particularly at the 
 bottom. Double doors are used on main entries at the shaft bottom, or at 
 any point where the opening of the door causes a stoppage of the entire cir- 
 culation of the mine. Such doors should be placed a sufficient distance 
 apart to allow'an entire trip of mine cars to stand between them, so that one 
 of the doors will always be closed while the other is open. 
 
 Stoppings. Stoppings are used to close breakthroughs that have been 
 made through two entries, or rooms, for the purpose of maintaining the cir- 
 culation as the workings advance; also to close or seal off abandoned rooms 
 or working places. ^Stoppings must be air-tight and substantially built. A 
 good form of stopping is constructed by laying up a double wall of slate, 
 having about 8 or 10 in. of space between the two walls. This space is filled, 
 as the building progresses, with dirt taken from the roadways, or other fine 
 material. A still better plan is to build the stopping of brick or concrete. 
 Hollow tile has been used as a material for stoppings and appears to be 
 admirably adapted to this purpose. 
 
 Air Bridges. An air bridge is a bridge constructed for the passage of air 
 across and over another airway, this being called an overcast; or, the cross- 
 ing may be made to pass under the airway, this being called an undercast. 
 In almost every instance, overcasts are preferable to undercasts for several 
 reasons. An undercast is liable to be filled with water accumulating from 
 mine drainage; it is also liable to fill with heavy damps from the mine, when 
 the ventilation is sluggish, and to offer considerable resistance to the free 
 passage of the air current. An undercast can never be maintained as air- 
 tight as an overcast, on account of the continual travel through the haul- 
 ageway or passageway leading over it. This continual passing over the 
 bridge causes a fine dust to sift into the airway and mingle with the air cur- 
 rent. All these objections are overcome in the construction of the overcast. 
 
 An air brattice is any partition erected in an airway for the purpose of 
 deflecting the current. A thin board stopping is sometimes spoken of as a 
 brattice; but the term applies more particularly to a thin board or canvas 
 partition running the length of an entry or room and dividing it into two 
 airways, so that the air will be obliged to pass up one side of the partition 
 and return on the other side of the partition, thus sweeping the face of the 
 heading or chamber. Such a temporary brattice _ is often constructed by 
 nailing brattice cloth or heavy duck canvas to upright posts set from 4 to 6 
 ft. apart along one side of the entry a short distance from the rib. 
 
 Curtains. These are sometimes called canvas doors. Heavy duck, or 
 canvas, is hung from the roof of the entry to divide the air or deflect a 
 portion of it into another chamber or entry. Curtains are thus used very 
 often previous to setting a permanent door frame. They are of much use 
 in long-wall work, or where there is a continued settlement .of the roof, 
 which would prevent the construction of a permanent door; also, in tempo- 
 rary openings where a door is not required. 
 
 MINE FIRES 
 
 Means Employed. There are two general methods of extinguishing mine 
 fires; namely, flooding and smothering. It is generally considered better 
 practice and cheaper to smother a fire than to drown it, since m the latter 
 case the water used for quenching must be pumped out of the mine after 
 the fire is extinguished. In cases, however, where sealing off cannot be 
 accomplished or where for any reason it is not effective, flooding may be the 
 only means of quenching the fire. 
 
 Isolating the Section. Where fire exists in a portion of a mine only and 
 it is expedient to keep the remainder of the mine in operation the section 
 involved may be isolated by means of a suitable dam or dams sufficiently 
 strong to withstand the greatest head of water that may possibly come upon 
 them. Such dams may be built of wood with clay or other filling of brick, 
 masonry, concrete or reinforced concrete. In most mines it will be found, 
 however, that the reinforced concrete will be the cheaper structure to build 
 if the head of water to be resisted is at all high. 
 
 When all necessary dams have been constructed water may be turned into 
 
 the portion of the mine affected and the fire thus effectually quenched, i he 
 
 water may be poured down a regular mine opening such as a slope or shaft 
 
 or one or more bore holes may be sunk from the surface for this purpose. 
 
 60 
 
946 
 
 MINE FIRES 
 
 In many instances a mixture of water and clay, mud, silt, culm or other mine 
 refuse may be used for quenching fires. Such a flush (often called slush) 
 has the advantage of baking into a more or less solid mass under the action 
 of the heat which it encounters and is consequently preferred by many 
 engineers. 
 
 Methods Employed in Sealing off Fires. In the majority of instances 
 it is not necessary to resort to flooding a mine, particularly if the fire is 
 promptly discovered and quick action is taken. Particularly in the more 
 
 easily inflamed bituminous 
 coals, fires often originate 
 in the process of shooting 
 down. These, if discovered 
 promptly, may be sealed off 
 without seriously endanger- 
 ing the rest of the mine or 
 any considerable loss in out- 
 put. Fig. 1 shows a fire of 
 this kind and the position of 
 the necessary stoppings for 
 sealing it off. 
 
 Mining men differ some- 
 what as to whether a fire of 
 this kind should be first 
 sealed on the intake or the 
 return. It'is probable, how- 
 ever, that in the majority of 
 instances it is preferable to 
 seal up first the intake. If, 
 however, there are several 
 openings to the fire all of 
 which must be closed and 
 through oversight or delay 
 the fire has gained consider- 
 able headway or if a strong 
 feeder of gas is the primary 
 cause of such a fire, or if the 
 sealing is to be undertaken a 
 considerable distance from 
 the fire, it might under cer- 
 tain circumstances be wise to 
 seal the return first. This 
 procedure should at least be 
 given careful consideration. 
 
 In fighting mine fires in 
 "c following points 
 
 general the 
 
 should be kept in mind: 
 Attack the fire as soon after 
 its origin as possible, extin- 
 guish it directly, that is, with 
 fire-hose and water if possi- 
 ble, and if it is safe to do so. 
 Never allow a gas feeder of 
 any magnitude discharging 
 
 in rear of the fire, that is, on the intake side to continue its discharge into 
 the air current reaching the fire, even though this gas discharge may be 
 diluted far below the explosive mixture. If possible conduct the gas from 
 such a feeder direct to the return. Erect all seals as close to the fire as 
 possible. No more air should be allowed to reach the sealing point than is 
 necessary while the work is being done. What air is carried to this point 
 should be directed by brattice and curtains close around the men. _ Men 
 erecting a seal should never raise their heads close to the roof and thus inhale 
 an overdose of smoke. 
 
 Stopping Materials. The materials employed in building a seal may be 
 the same as those used for ordinary stoppings, that is, rock packs covered 
 with cement, mortar or even clay, brick walls, concrete or reinforced con- 
 crete, hollow tile, etc. As a general rule, however, it will be found that a 
 double wooden partition with clay tamping between can be built up more 
 rapidly than any other type of stopping and speed is important. A good 
 
MINE FIRES 947 
 
 type of stopping of this nature is shown in Pig. 2. This should be set into 
 floor, ribs and roof, and the joint around the complete periphery made as 
 nearly air-tight as possible with clay tamping. It is frequently advisable on 
 discovering a fire to start a few men to preparing the places selected for the 
 various stoppings while others collect necessary material and as soon as 
 possible begin the erection of the first seal. The intake to the fire should 
 be short-circuited and a careful watch kept upon the smoke as a heavy fall 
 of rock may drive this smoke and the products of combustion back onto the 
 workers unless they receive warning in time to get away. The materials 
 will consist of the timber posts, which should be at least 6 in. square (10 in. 
 square is preferable), the necessary planking, brattice cloth to cover the entire 
 stopping and the clay or earth for the filling and for a daubing coat on the 
 outside if necessary. Both sides of the stopping should be carried up simul- 
 taneously together with the clay filling which should be carefully tamped in 
 place. 
 
 The last stopping is always the most difficult to build,. and it is frequently 
 advantageous to here erect a temporary brattice inside the stopping proper 
 to keep back as much as possible the smoke and gases from combustion. 
 
 FIG. 2 
 
 This brattice as well as the stopping itself should contain a section approxi- 
 mately 24X34 in. which may be afterwards easily removed, allowing the 
 entrance of a fire boss or other person to ascertain the condition of the 
 affected area. A pipe, say 4 in. in diameter, or more, and provided with a 
 valve, should be built into this last stopping to allow the escape of the heated 
 air in the fire area (see Fig. 3). Otherwise the expansion of this air may 
 push out one of the stoppings. Throughout the entire process of building 
 the last stopping extreme care should be exercised that no workman raise 
 his head into the dense smoke, thus inhaling gas. 
 
 When all passages leading to the fire have been sealed, the ventilation up 
 to the stopping should be restored, thus allowing the largest available amount 
 of air to circulate to all the working places in that portion of the mine, thus 
 sweeping out the smoke and gases which may have accumulated there while 
 the ventilation was restricted. A careful inspection should then be made to 
 see that such places are fit for operation. Near the seal containing the escape 
 pipe and valve a canvas brattice or tight curtain with suitable means of en- 
 trance should be constructed, so that the gas coming through the pipe may 
 be periodically tested. This test may be made each evening after the work- 
 men have left the mine. For the first few days the gas issuing from the pipe 
 will be afterdamp, after which firedamp will begin to appear. The showing 
 of this gas will get stronger from day to day and during the night or at such 
 times as no men are at work in the mines the valve may be left open. After 
 several days the gas issuing from the pipe will be sufficiently strong to give 
 a cap on the lamp when the latter is held some distance from the pipe. 
 From the indication of this gas it may be judged when it is advisable to 
 open the sealed area. This will probably not exceed 18 days to three weeks 
 from the time of sealing up, provided, of course, that the fire was promptly 
 discovered and that only a comparatively small volume of air exists in the 
 sealed area. 
 
 Unsealing after the Fire is Out. In unsealing a supposedly extinguished 
 fire, it is well to curtain off other districts of the mine so as to prevent the 
 escaping gases from reaching them; also to confine the return from the fire 
 to one air-course. The previously mentioned manhole opening in the last 
 seal is first broken open. During this process there should be no flame, not 
 even that of a safety lamp in line with the opening as the gas emitted will 
 be strongly inflammable. After this opening has been made in the return a 
 similar one may be opened in the intake and a current of fresh air thus 
 
948 
 
 MINE FIRES 
 
 passed through the heretofore sealed area. With the air current through 
 this fire area established, observers may be stationed at intervals along but 
 outside of the return at such points that a safety lamp may be pushed into 
 the return airway periodically to test the air. These tests should be made 
 at intervals. When no showing of gas appears in the return from the tire 
 area it is time enough to make a thorough inspection of the section which 
 has been sealed up. When this is found to be safe for working, all the stop- 
 pings may be removed, the place cleaned up if necessary, fallen or burned 
 timbering renewed and work resumed. 
 
 FIG. 3 
 
 Gob fires are due to the spontaneous ignition of coal, and are most likely 
 to occur in pack walls and gobs where there is an insufficiency of air. Ample 
 ventilation is the best preventive. 
 
 Spontaneous Combustion. According to Prof. Able, Dr. Percy, and Prof. 
 Lewes, the causes of the spontaneous ignition of coal are: First, and chiefly, 
 the condensation and absorption of oxygen from the air by the coal, which 
 of itself causes heating, and this promotes the chemical combination of the 
 volatile hydrocarbons in the coal and some of the carbon itself with the 
 condensed oxygen. This process may be described as self-stimulating, so 
 that, with conditions favorable, sufficient heat may be generated to cause 
 the ignition of portions of the coal. The favorable conditions are: A mod- 
 erately high external temperature; a broken condition of the coal, affording 
 the fresh surfaces for absorbing oxygen; a supply of air sufficient for the 
 purpose, but not in the nature of a strong current adequate to remove the 
 neat; a considerable percentage of volatile combustible matter or an ex- 
 
THE PREPARATION OF COAL 
 
 949 
 
 tremely divided condition. Second, moisture acting on sulphur in the form 
 of iron pyrites. The heating effect of this second cause is very small, and 
 it acts rather by breaking the coal and presenting fresh surfaces for the 
 absorption of oxygen. 
 
 Coal Storage. Prof. Lewes gives the following recommendations for the 
 storage of coal: "The coal store should be well roofed in, and have an iron 
 floor bedded in cement; all supports passing through and in contact with 
 the coal should be of iron or brick; if hollow iron supports are used, they 
 should be cast solid with cement. The coal must never be loaded or stored 
 during wet weather, and the depth of coal in the store should not exceed 
 8 ft., and should only be 6 ft. where possible. Under no condition must a 
 steam or exhaust pipe or flue be allowed in or near any wall of the store, 
 nor must the store be within 20 ft. of any boiler, furnace, or bench of retorts. 
 No coal should be stored or shipped to distant points until at least a month 
 has elapsed since it was brought to the surface. Every care should be taken 
 during loading or storing to prevent breaking or crushing of the coal, and 
 on no account must a large accumulation of small coal be allowed. These 
 precautions, if properly carried out, would amply suffice to entirely do 
 away with spontaneous ignition in stored coal on land." 
 
 When the coal pile has ignited, the best way to extinguish the fire is to 
 remove the coal, spread it out, and then use water on the burned part. The 
 incandescent portion is invariably in the interior, and when the fire has 
 gained any headway usually forms a crust that effectually prevents the 
 water from acting efficiently. ________ 
 
 THE PREPARATION OF COAL 
 
 CRUSHING MACHINERY 
 
 The object of crushing coal is usually to reduce it in size preliminary to 
 washing, a better separation of impurities being secured in the jig if the 
 particles are of nearly the same size. At the same time the coal is crushed 
 the larger pieces of slate, sulphur, etc., are separated by the action of the 
 machine from the lumps of 
 coal and are, also, more 
 effectively removed in the 
 subsequent washing. In 
 the case of anthracite coal 
 it is reduced in size to meet 
 the requirements of trade 
 which changes in its de- 
 mands from time to time, 
 requiring a maximum of 
 stove sizes today and a 
 maximum of nut sizes to- 
 morrow, and at no time 
 being able to consume the 
 lump as it comes from the 
 mines. 
 
 Jaw crushers, ball and 
 tube mills, stamps, etc., 
 commonly employed in 
 metallurgical operations do 
 not find a place in coal 
 preparation. Coal is 
 almost invariably broken 
 down in size by some form 
 of rolls, a few forms of which arei . 
 
 Cracking Rolls. This is a general name applied to rolls having t( 
 which are usually made separate and inserted. These rolls, Fig. 1, are ei 
 ployed for breaking the coal, the object being to break the material into 
 angular pieces with the smallest possible production of very fine materia 1. 
 The principal field for cracking rolls is in the preparation of anthracite coal, 
 and the exact style or design of the roll depends largely on the physical con- 
 dition of the coal under treatment. In most cases the rolls are constructs 
 with an iron cylinder having steel teeth inserted, the size, spacing, and form 
 of the teeth depending on the size and physical condition of the material to 
 be broken Cracking rolls vary from 12 to 48 in. in diameter and from 24 
 
 p IG _ 
 
950 
 
 THE PREPARATION OF COAL 
 
 to 36 in. in face width. The teeth of the larger sizes are from 3 to 3 in. 
 high, and of the smaller 1 in. or less. 
 
 The average practice in the anthracite regions of Pennsylvania is to give 
 the points of the teeth a speed of about 1,000 ft. per min., though the speed 
 in different cases varies from 750 to 1,200 ft. per min. One of the largest 
 anthracite companies has a standard roll speed of 97.5 R. P. M. for the main 
 rolls and 124.5 R. P. M. for the pony rolls. The harder the coal the faster 
 the rolls can be run. If run slow and overcrowded, the rolls will make more 
 culm than when driven at a proper speed. One advan- 
 tage of comparatively fast driven rolls is that the higher 
 speed has a tendency to free the rolls by throwing out, 
 by centrifugal force, any material lodged between the 
 teeth. In one test it was found that less fine coal was 
 produced at 800 ft. per min., but that the rolls blocked 
 at this speed and hence had to be driven 1,000 ft. per 
 min. 
 
 In one case a pair of main rolls 24 in. in diameter, 
 36 in. face, running at 1,000 ft. per min., handled 2,500 
 T. of coal in 24 hr. A pair of 19 in. X 24 in . main rolls run 
 at 1,000 ft. per min. handled 300 T. mine run in 10 hr. 
 A well-known maker of rolls for crushing bituminous 
 coal gives a speed of 100 to 150 R. P. M., according to 
 the output required, for rolls 24 in. in diameter and 33 
 in. long. . As a rule, cracking rolls are never run up to 
 their full capacity, as is the case with crushing rolls. 
 The form of the teeth varies greatly, but, as a rule, the larger rolls have 
 straight pointed teeth of the sparrow-bill or some similar form, Pig. 2a. 
 The old curved, or hawk-billed, teeth, Fig. 2&, have now gone almost wholly 
 out of use. 
 
 On small sized rolls, rectangular teeth with a height equal to one side of 
 the square base are" frequently employed, and these may be cast in segments 
 of manganese or chrome steel. 
 
 Corrugated rolls have teeth or corrugations extending their entire length. 
 They were first introduced by Mr. E. B. Coxe, at Drifton, Pa., but they 
 have not come into general use owing to the fact that, while they break some 
 coal fairly well, in most cases it has been found that a continuous edge causes 
 too much disintegration along its length, while a point splits the coal into 
 three or four pieces only, all the cracks 
 radiating from the place where the point 
 strikes, thus producing very much less 
 culm. Another advantage possessed by 
 the toothed rolls is that if anything hard 
 passes through the corrugated roll and 
 breaks out a piece of the corrugation, 
 the entire roll is ruined, while, in the 
 case of the toothed rolls, any one of the 
 teeth may be replaced. 
 
 Disintegrating rolls and pulverizers 
 are sometimes used to reduce coking coal 
 to the size of corn or rice before intro- 
 ducing it into the ovens. One roll is 
 driven at double the speed of the other, 
 the slower roll acting as a feed-roll, and 
 the other as a disintegrator. The slower 
 roll is commonly driven at from 1,800 to 
 2,000 ft. per min. peripheral speed, and 
 the faster roll at from 3,600 to 4,000 ft. 
 per min. The teeth are always fine, 
 rarely being over f in. high. In some cases, the inner roll is provided with 
 a series of saw teeth from J in. to | in. high and haying about f-in. pitch, 
 the individual teeth being set so as to form a slight spiral about the body of 
 the roll. The other roll is provided with teeth having their greatest dimen- 
 sion in the direction of rotation, so that they tend to cross the teeth on the 
 opposite roll. These teeth are also set so as to form a slight spiral, and thus 
 prevent blocking. In other cases, the teeth on both rolls are set in the form 
 of 
 
 FIG. 3 
 
 Lammers. For the reduction of coal, crushers employing hammers have 
 been used, Fig. 3. The crushing chamber is usually of a circular or barrel 
 
THE PREPARATION OF COAL 
 
 951 
 
 form, and the crushing is done by means of hammers pivoted about a central 
 shaft. These swing out by centrifugal force and strike blows upon the coal 
 to be broken. When it is reduced sufficiently fine, it is discharged through 
 bars or gratings at the lower portion of the machine. This style of machinery 
 is usually employed in preparing coal for coke ovens, thus occupying the same 
 field as the disintegrating rolls. A No. 3 pulverizer of this type will crush 
 50 to 75 T. per hr. run of mine, down to f in., or it will crush 100 T. per hr. of 
 slack. Such a machine occupies about 8 sq. ft. of floor space and requires 
 25 to 30 H. P. to run it. 
 
 Miscellaneous Forms of Crushers. Most crushers can be classed under 
 one of the previous heads, but there are some forms that depend on the 
 material itself to do the crushing. For instance, in the preparation of coal 
 for coke ovens, there has been a combined crusher and separator invented 
 that may be described as follows: A large horizontal drum or cylinder, 
 provided with screen openings around its periphery, is mounted in a hori- 
 zontal position. The coal to be separated is fed into one end and is caught 
 by shelves or plates projecting radially into the cylinder. These lift the 
 material to the upper side, from which it falls by gravity and strikes the 
 bottom, thus crushing the softer parts. The sulphur and slate, being harder 
 than the coal, are not crushed by the same height of fall, and hence, by a 
 proper adjustment of the diameter of the cylinder, the coal may be crushed 
 and discharged through the screen while the slate and sulphur will pass out 
 at the opposite end of the cylinder. 
 
 SIZING AND CLASSIFYING APPARATUS 
 Stationary Screens, Grizzlies, Head-Bars, or Platform Bars. These are 
 
 the various names given to an inclined screen employed for removing the 
 
 fine material from the run of mine so that only 
 
 the coarse portion will be passed to the crushers. 
 
 At concentrating works always and sometimes 
 
 at anthracite coal breakers, the term grizzly is 
 
 employed, and a common form is shown in Fig. 
 
 4. This is composed of flat bars held apart by 
 
 cast-iron washers through which the bar bolts 
 
 are passed to hold the entire frame together. 
 
 Grizzlies are usually placed at an angle of from 
 
 45 to 55, and ordinarily they are from 3 to 6 
 
 ft. wide and from 8 to 12 ft. long, the amount of 
 
 space between the bars depending on the size of FIG. 4 
 
 the run-of-mine material and on its subsequent 
 
 treatment. 
 
 In the anthracite coal breakers, the terms platform bars or head-bars are 
 
 usually employed, and these bars are made of H-in. to 2-in. round iron placed 
 at an inclination of 5 in. to 1 ft., the spacing depending on 
 the size of coal it is desired to make in the breaker. 
 
 A standard size for a bituminous lump screen (the bars 
 are called a screen) for Ohio, Pennsylvania, Indiana, and 
 Illinois is 12 ft. long and 6 ft. wide over the screen surface. 
 The screen consists of 6 bearing bars 4 in. by | in. of soft 
 steel and 39 steel screen bars, Fig. 5, with H m. clear space 
 between bars. In Iowa, the same sized bar is used, but the 
 space between the bars is If in. In the other Western and 
 Southern States there is apparently no standard. 
 
 Adjustable Bars. The top of the bar is cylindrical and 
 projects beyond the web which supports it, so that any 
 lump which passes through the upper part will fall freely 
 without jamming. The two ends of the bar are V-shaped 
 and fit into similarly shaped grooves, so that the bars can 
 be set at distances from each other varying with the sum 
 of the width of the bases of the triangles', the usual opening 
 being about 4 in. These bars are generally 4 ft. long, but 
 FIG. 5 they can be of any size. 
 
 Finger bars are screen bars that are fixed at one end only, 
 
 and the bars are narrower at the lower end than at the top, so that 
 
 spaces between them are wider at the bottom than at the top, thus giving 
 
 less tendency for pieces of material to become wedged between the bars. 
 Movable or oscillating bars are screen bars that are attached to eccentrics 
 
 at their lower ends, the eccentrics of adjoining bars being placed 180 apart. 
 
952 
 
 THE PREPARATION OF COAL 
 
 This movement throws the material forward and the bars do not, therefore 
 require nearly the same inclination as fixed bars. 
 
 Shaking screens have an advantage in that the entire area of the screen 
 is available for sizing, and hence a greater capacity can be obtained from a 
 given area of screening surface. They also occupy less vertical height than 
 a revolving screen. In coal breakers they are particularly applicable where 
 the coal is wet and has a tendency to stick together. The principal disad- 
 vantage of the shaking screen is that the reciprocating motion imparts a 
 vibration to the framing of the building. For anthracite coal, the screens 
 usually have an angle or pitch of from \ in. to 2 in. per ft., the average being 
 about | in. per ft. These screens are run at from 90 to 280 shakes per min., 
 the average being about 200 shakes per min. or 100 rev. per min. for the 
 camshaft. The throw of the eccentric or cam varies from 2 in. to 5 in. 
 
 The capacities of shaking screens operating n anthracite coal have been 
 given as follows. The parties giving these figures advise the use of 140 
 R. P. M. for the camshaft. 
 
 For broken and egg coal, i sq. ft. per T. for 10 hr. 
 
 For stove and chestnut coal, $ sq. ft. per T. for 10 hr. 
 
 For pea and buckwheat coal, i sq. ft. per T. for 10 hr. 
 
 For birdseye and rice, 1J sq. ft. per T. for 10 hr. 
 
 Size of Mesh. The following perforations have been adopted by two of 
 the largest anthracite coal companies as the dimensions for the holes in 
 shaking screens to produce sizes equivalent to those produced by revolving 
 screens : 
 
 MESH FOR SHAKING SCREENS 
 
 Kind of Coal 
 
 Lehigh Valley 
 Coal Co. 
 
 Phila. & Reading 
 Coal & Iron Co. 
 
 Kind of Coal 
 
 Round, 
 In. 
 
 Round, 
 In. 
 
 Square, 
 In. 
 
 Steamboat 
 
 
 4 
 3 
 2 
 1 
 
 .,'. ' 
 
 r 
 
 \ 
 
 5 
 4 
 2| 
 2 
 
 '! 
 
 Steamboat. 
 Large broken. 
 Small broken. 
 Egg. 
 Stove. 
 Chestnut. 
 Pea. 
 Buckwheat. 
 Rice. 
 
 Lump 
 Broken 
 
 4* 
 3J 
 
 I ,:::;; 
 
 Eecr 
 
 Stove 
 
 Chestnut 
 Pea 
 Buckwheat 
 Rice 
 
 
 Revolving Screens, or Trommels. The screen is placed about the pe- 
 riphery of a cylinder or frustum of a cone. The material to be sized is intro- 
 duced at one end; the small size passes through the screen, and the other 
 size is discharged from the other end. If the form is cylindrical, it is neces- 
 sary to place the supporting shaft on an incline so that the material will 
 advance towards the discharge end. The inclination of the shaft determines 
 the rapidity with which the material will be carried through the screen. 
 The advantage of the conical screen is that the shaft is horizontal and hence 
 the bearings are simpler. This is a very decided advantage in many plants 
 where the machinery must of necessity be crowded into a minimum space 
 and be hard to get at. 
 
 Revolving screens are frequently jacketed, that is, two or more screens 
 are placed concentrically about the same shaft, the inmost one being the 
 coarsest, and each succeeding screen serving to make additional separations. 
 This method reduces the space necessary for a given amount of sizing 
 machinery. In other cases, a long cylindrical screen has a coarse mesh near 
 its discharge end and finer mesh near the entrance end, thus making two or 
 more through products as well as the overproduct. The disadvantage of 
 jacketed screens is that the necessarily slow speed of the inmost screen 
 reduces the capacity of the entire combination, so that if rapid work is 
 essential, it is better to use fairly large-diameter screens placed one after the 
 other in place of jacketed screens. Another disadvantage is that, to renew 
 the inner jackets, it is often necessary to remove the outer ones. 
 
THE PREPARATION OF COAL 953 
 
 The disadvantages of having two or more sizes of wire cloth on one screen 
 are that the fine-meshed screen near the head is worn out rapidly, as all the 
 material both coarse and fine passes over it, while, when separate screens 
 are employed, each screen has to deal with its through or oversized prod- 
 uct, all coarser material having been removed. 
 
 Speed. The periphery of a revolving screen should travel about 200 ft. 
 per min. In the case of very fine material, screens are sometimes run 
 faster than this. 
 
 The following have been adopted as standard speeds for screens by one 
 of the largest anthracite coal companies: 
 
 SPEED OF SCREENS 
 Rev. per Min. Rev. per Min. 
 
 Mud screens 8.87 Big screens 8.52 
 
 Counter mud screens .... 15 . 49 Pony screens 10 . 87 
 
 Cast-iron screens 1 1 . 25 Buckwheat screens 15 . 30 
 
 Duty of Anthracite Screens. The following table gives the number of 
 square feet of screen surface required for a given duty in the case of revolv- 
 ing screens working upon anthracite coal: 
 
 Egg coal, 
 Stove coal, 
 Chestnut coal, 
 Pea coal, 
 Buckwheat coal, 
 Rice coal, 
 Culm, 
 
 T. per 1 sq. ft. per 10 hr. 
 T. per U sq. ft. per 10 hr. 
 T. per 1 sq. ft. per 10 hr. 
 T. per 2 sq. ft. per 10 hr. 
 T. per 2| sq. ft. per 10 hr. 
 T. per 3f sq. ft. per 10 hr. 
 T. per 5 sq. ft. per 10 hr. 
 
 These figures may be reduced from 20 % to 30 % for very dry or washed 
 coal. 
 
 Revolving Screen Mesh for Anthracite. A standard mesh for revolving 
 screens for sizing anthracite coal was adopted some years ago, but it is only 
 approximately adhered to and a considerable variation from the standard is 
 found throughout the anthracite region. 
 
 The following are probably as nearly standard meshes for revolving 
 screens for sizing anthracite coal as can be given: 
 
 MESH FOR SIZING COAL 
 Culm passes through &-in. mesh 
 
 Birdseye passes over 
 
 Buckwheat passes over 
 
 Pea passes over 
 
 Chestnut passes over 
 
 Stove passes over Ij 
 
 -in. mesh, and through f^-in. mesh, 
 -in. mesh, and through 5-in. mesh. 
 
 -in. mesh, and through f-in. mesh, 
 -in. mesh, and through If-in. mesh. 
 
 &-in- 
 5-in. 
 f-in. 
 
 if-in. 
 
 -in. mesh, and through 2 -in. mesh. 
 Egg passes over 2 -in. mesh, and through 2f-in. mesh. 
 
 * Grate passes over 2|-in. mesh, and out end of screen. 
 
 * Special grate passes over 3 -in. mesh; and out end of screen. 
 
 * Special steamboat passes over 3 -in. bars, and through 6-in. bars. 
 Hydraulic Classifiers. The separation of materials by this class of 
 
 machinery depends upon the law of equally falling bodies, which may be 
 stated as follows: Bodies falling free in a fluid, fall at a speed proportional 
 to their weight divided by the resistance. From this it will be seen that small 
 masses of a heavy mineral will fall as rapidly as large masses of a light 
 mineral, owing to the fact that the weight increases, as the volume and the 
 resistance only as the area, so that if a quantity of iron pyrites and coal of 
 various sizes were introduced into water, it would settle into approximate 
 layers, each composed of relatively large pieces of coal and relatively small 
 pieces of iron pyrites. This same action would be true in the case of any 
 minerals differing in specific gravity. 
 
 The Jeffrey-Robinson coal washer, Pig. 6, which operates on the principle 
 of the Spitzkasten, consists of a steel chamber B in the form of an inverted 
 cone, inside of which are projecting arms and stirring plates C, C revolved 
 by a driving gear A. The water supply enters at the bottom from the water 
 pipe P through perforations M. The coal is introduced through a chute 5 
 and is kept in a continual state of agitation by the current of water, and being 
 lighter than the impurities, it passes out through the overflow K onto the 
 conveyors E, F and through the chutes X, X, while the water and sludge 
 
 * These sizes and "lump" size are seldom made, and there is no uniformity 
 whatever in the sizes called by these names. 
 
954 
 
 THE PREPARATION OF COAL 
 
 drain through the hopper into the sludge tank G, whence, if necessary, the 
 same water can be again pumped by the pulsometer H back into the washer. 
 (As mentioned elsewhere, it is poor practice to use this water over again 
 when it is desired to decrease the percentage of sulphur in the washed 
 product as greatly as possible.) 
 
 The heavy impurities sink to the bottom into the chamber J and when 
 this is full the upper of the two valves shown is closed and the lower valve is 
 opened to discharge the refuse. 
 
 The following data in regard to one of these washers is given by Mr. 
 J. J. Ormsbee in the Transactions of the A. I. M E. These results were 
 obtained at the Pratt Mines, Alabama, with a plant having a nominal 
 
 capacity of 400 T. per day. 
 By washing slack that 
 passed between screen 
 bars placed \ in. in the 
 clear, the washed coal con- 
 tained 42 % less ash than 
 the unwashed coal, the re- 
 duction in sulphur was 
 15%, while ^ the volatile 
 matter was increased 4%, 
 and the fixed carbon 5%. 
 With coal passing overf-in. 
 perforations, the results 
 were a reduction of 48 % in 
 ash, 15 % in sulphur, and a 
 gain of 5 % in volatile mat- 
 ter and 6 % fixed carbon. 
 These results indicate that 
 the washer is better 
 adapted to large sizes than 
 to fines. The amount of 
 water used per ton of 
 washed coal was 35.1 gal. 
 FIG. 6. and the cost was 2.25 c. 
 
 per T. for washing 400 T., 
 
 itemized as follows: Labor at washer, $2.00; labor at boiler, fuel, -etc., $4.00; 
 repairs and supplies, $3.00; total, $9.00. 
 
 The Scaife trough washer consists of a semicircular iron trough 2 ft. 
 in diameter and 24 ft. long. Inside is a series of fixed dams or partitions 
 that can be made higher or lower, as required, by means of plates. A shaft 
 running the entire length of the trough and turning in babbitted journals 
 carries a number of stirring arms or forks and is given a reciprocating motion 
 by a connecting rod attached to a driving pulley at its center. The coal 
 is fed with water at the upper end of the trough, and by the action of the 
 flowing water and the agitation of the arms, the slate, pyrites, and other 
 impurities settle at the bottom and are caught behind the dams, while the 
 clean coal passes over the dams and out at the lower end of the trough. 
 When the spaces behind the dams are filled, feeding is stopped and the 
 refuse in the dams quickly dumped. This form of washer is particularly 
 successful with coal mixed with fireclay. One washer handles from 75 to 
 100 T. of coal per day, and one man can attend to six washers. Each 
 washer requires less than 1 H. P. to operate it. The larger the coal, the 
 greater must be the slope and the quantity of water used. 
 
 Jigs. This is a general term applied to that class of machines in which the 
 separation of the mineral from the impurities takes place on a screen or bed 
 of material and is effected by pulsating up-and-down currents of a fluid 
 medium. 
 
 There are a number of different methods in use for driving the pistons 
 that cause the pulsations of the water in jigs. Some of these use plain 
 eccentrics, giving the same time to both the up and the down strokes of the 
 pistons, while others employ special arrangements of parts, which give a 
 quick down stroke and a slow up stroke, thus allowing the water ample 
 time to work its way back through the bed without any sucking action 
 from the piston. This tends to make a better separation in some cases than 
 the use of the plain eccentrics. 
 
 Stationary Screen Jigs. This class is illustrated by Fig. 7, which shows a 
 3-compartment jig. The separation takes place on screens supported on 
 
THE PREPARATION OF COAL 
 
 955 
 
 wooden frames g, and is effected by moving the water in each compartment 
 so that it ascends through the screen, lifting the mineral and allowing it to 
 settle again, thus giving the material an opportunity to arrange itself accord- 
 ing to the law of equally falling particles. Each compartment is composed 
 of two separate parts, one containing the screen on the support g and the 
 other adjoining it and arranged so that the piston in it may impart the 
 necessary pulsations to the water. These pistons are equally loose fitting 
 
 and are operated by the eccentrics e on the shaft s. Jigs should be fed with 
 approximately sized material, when the impurities will accumulate near the 
 bottom on the screen and the coal will be carried over the discharge. 
 
 The Heberle gate, Fig. 8, acts as follows: a is a U-shaped shield fastened 
 against the inside of the jig and held in place by a band b, the ends of which 
 are drawn down into the form of bolts and pass through the sides of the jig, 
 where they are secured with suitable nuts. The shield a may be raised or 
 lowered by loosening the band 6. The dis- 
 charge takes place through the opening / in 
 the side of the jig, the size and position of 
 the opening being regulated by slides c. The 
 impurities k rest on the screen e supported by 
 a grating d, while the coal i occupies a higher 
 position. The shield a prevents the coal 
 from flowing out through the opening/, while 
 the impurities flow along the screen and rise 
 to a height somewhat lower than the top of 
 the coal in the jig, when they are discharged 
 through the opening / over the spout h, as 
 shown at p. The coal is usually discharged 
 over the dam at the end of the jig. 
 
 Theory of Jigging. By far the most ex- 
 haustive investigations on the theory of jig- 
 ging carried on in America are those of Prof. 
 Robert H. Richards, of the Massachusetts 
 Institute of Technology, and the greater part 
 of the following theoretical discussion is 
 based on his several papers published in the 
 Institute of Mining Engineers. 
 
 FIG. 8 
 Transactions of the American 
 
 Four laws of jigging are given by the several authorities: (1) The law of 
 equal settling particles, under free settling conditions; (2) the law of inter- 
 stitial currents, or settling under hindered settling conditions; (3) the law 
 of acceleration; (4) the law of suction. 
 
 The first of these is the most important, but the others are elements that 
 cannot be disregarded in connection with jigging. 
 
 Equal Settling Particles. Rittinger gives the following formulas to repre- 
 sent the relation between diameter of grains and rate of falling in water for 
 irregularly shaped grains: 
 
956 
 
 THE PREPARATION OF COAL 
 
 V = 2.73\/>(a 1), for roundish grains; 
 
 V = 2A4\fD(6 1). for average grains; 
 
 y = 2.37\/P(g-l). for long grains; 
 
 F = 1.92V#(-1), for flat grains, 
 
 in which V = velocity in meters per second; D = diameter of particles in 
 meters, and d = specific gravity of the minerals. 
 
 By means of these different formulas, the ratios of the diameters of 
 different particles that will be equal settling in water can be computed. 
 Professor Richards has not found these formulas to hold in all cases in prac- 
 tice, and, as the result of elaborate experiments, he gives the following table: 
 
 EQUAL SETTLING FACTORS OR MULTIPLIERS 
 
 Table of equal settling factors or multipliers for obtaining the diameter of 
 a quartz grain that will be equal settling under free settling conditions with 
 the mineral specified. 
 
 
 
 
 Velocity in Inches per Second 
 
 
 
 1 
 
 
 if 
 
 
 
 
 
 
 
 
 
 
 
 
 O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 id 
 
 
 
 
 
 
 
 
 
 
 4J """* 
 
 
 1 
 
 Author's Multipliers 
 
 1-4 3 
 
 Anthracite . . 
 
 1.473 
 
 .500 
 
 .352 
 
 .225 
 
 .213 
 
 
 
 
 
 
 .288 
 
 Epidote 
 
 3.380 
 
 1.57 
 
 1.35 
 
 .05 
 
 .13 
 
 1.50 
 
 1.61 
 
 1.56 
 
 1.56 
 
 1.47 
 
 1.45 
 
 Sphalerite. . . 
 Pyrrhotite.... 
 
 4.046 
 4.508 
 
 
 1.46 
 1.73 
 
 .05 
 .29 
 
 .17 
 
 .48 
 
 1.62 
 2.00 
 
 1.64 
 2.22 
 
 1.68 
 2.26 
 
 1.66 
 2.13 
 
 1.56 
 
 2.08 
 
 1.85 
 2.14 
 
 Chalcocite.... 
 
 5.334 
 
 
 1.90 
 
 .47 
 
 .62 
 
 2.07 
 
 2.28 
 
 2.41 
 
 2.44 
 
 2.17 
 
 2.64 
 
 Arsenopyrite 
 
 5.627 
 
 
 1.90 
 
 .57 
 
 .89 
 
 2.42 
 
 2.56 
 
 2.72 
 
 2.84 
 
 2.94 
 
 2.82 
 
 Cassiterite.. . 
 
 6.261 
 
 
 2.11 
 
 .79 
 
 2.00 
 
 2.73 
 
 2.93 
 
 3.03 
 
 3.05 
 
 3.12 
 
 3.32 
 
 Antimony. . . 
 
 6.706 
 
 
 2.71 
 
 .00 
 
 2.00 
 
 2.73 
 
 2.93 
 
 3.03 
 
 2.98 
 
 3.00 
 
 3.48 
 
 Wolframite. . 
 
 6.937 
 
 
 2.71 
 
 .83 
 
 2.07 
 
 2.86 
 
 3.04 
 
 3.21 
 
 3.28 
 
 3.26 
 
 3.64 
 
 Galena 
 
 7.856 
 
 
 2.71 
 
 .83 
 
 2.26 
 
 3.00 
 
 3.42 
 
 3.65 
 
 3.76 
 
 3.75 
 
 4.01 
 
 Copper 
 
 8.479 
 
 
 2.71 
 
 2.00 
 
 2.36 
 
 3.00 
 
 3.20 
 
 3.58 
 
 3.76 
 
 3.75 
 
 4.56 
 
 Quartz 
 
 2.640 
 
 
 
 
 
 
 
 
 
 
 
 The significance of the above table is as follows: If a piece of anthracite 
 of a certain size falls in water with a velocity of 4 in. per sec., a piece of quartz 
 .213 times the diameter of the anthracite will fall with the same velocity. 
 If a piece of copper of a certain size falls with a velocity of 7 in. per sec., a 
 piece of quartz 3.58 times as. large as the copper will fall with the same 
 velocity. 
 
 Interstitial Currents, or Law of Settling under Hindered Settling Condi- 
 tions. If d equals the diameter of a falling particle, and D that of the tube 
 
 in which it falls, the larger the fraction ^, the greater will be the retardation 
 
 / N. x~N or loss of a velocity by the particle. 
 
 ( J ( ) When this fraction equals 1, the parti- 
 
 V__/OV / s^-~^ cle stops. If, in Fig. 9 (a), the larger 
 
 circles represent say particles of quartz 
 and the smaller circles equal settling 
 particles of galena, then if these mixed 
 fb) particles are settling together or are 
 
 held in suspension by a rising current 
 of water, each particle may be consid- 
 ered to be falling in a tube, the walls of 
 which cpnsist of the surrounding particles. Substituting a circle in each case 
 for the imaginary tube, we have Fig. 9 (b) representing the conditions for 
 galena and quartz, the outer circle in each case representing the imaginary 
 
 tube. Evidently, r is much smaller for the galena than for the quartz, and 
 
 x 't s 
 
 QUO 
 OO 
 
 (a) 
 
 FIG. 9 
 
THE PREPARATION OF COAL 957 
 
 it will therefore be much less impeded in its fall than the quartz; hence, the 
 particles of galena found adjacent to the particles of quartz will be smaller 
 than the ratio that the law of equal settling particles under free settling con- 
 ditions would indicate. Application of this principle is found when a mass of 
 grains is subjected to a rising current of sufficient force to rearrange the 
 grains according to their settling power and the grains are said to be treated 
 under hindered settling conditions, as on the bed of a jig. 
 
 Interstitial factors, or multipliers for obtaining the diameter of the particle 
 of quartz that under hindered settling conditions will be found adjacent 
 to and in equilibrium with the particle of the mineral specified, are the 
 following: 
 
 Copper 8.598 Cassiterite . . . 4.698 Pyrrhotite. . 2.808 
 
 Galena 5.842 Arsenopyrite. 3.737 Sphalerite.... 2.127 
 
 Wolframite... 5.155 Chalcocite. . . 3.115 Epidote 1.628 
 
 Antimony 4.987 Magnetite... 2.808 Anthracite.. .1782 
 
 These signify that, after pulsion has done its work on a jig bed, for exam- 
 ple, where quartz and anthracite are being jigged, the grains will be so 
 arranged that the grains of quartz are .1782 times the diameter of the grains 
 of anthracite that are adjacent to and in equilibrium with them. 
 
 Acceleration. A particle of galena that is equal in settling to the particle of 
 quartz reaches its maximum velocity in perhaps one-tenth the time required 
 by the quartz. The oft-repeated pulsations of a jig, therefore, give the 
 galena particles a decided advantage over the quartz, placing beside the 
 quartz, when equilibrium is reached, a much smaller particle of galena than 
 we should expect according to the law of equal settling particles. 
 
 Suction acts to draw down through the screen small grains, mainly of the 
 heavier mineral, which are distributed among large grains. It increases as 
 the length of plunger stroke, with the difference in specific gravity of the two 
 minerals, and with the diminishing of the thickness of the bed on the sieve, 
 whether of the heavier mineral only or of both minerals. The law of suction 
 seems to be that jigging is greatly hindered by strong suction where the two 
 minerals are nearly of the same size, the quickest and best work then being 
 done with no suction; but when the two minerals differ much in size or 
 particles, the quartz being the larger, strong suction is not only a great advan- 
 tage, but may be necessary to get any separation at all. Experiments have 
 indicated an approximate boundary between grains that are helped and 
 those that are hindered by suction; namely, if the diameter of the quartz 
 particles is equal to or greater than 3.52 times the diameter of the other min- 
 eral particles, then separation is helped by suction; if less, separation is 
 hindered. This value 3.52 is approximate only, and it will differ with the 
 fracture of the quartz under consideration; if the quartz grains are much flat- 
 tened, it will have a large value. 
 
 Removal of Sulphur from Coal. The object of washing coal is to remove 
 the slate and pyrites, thus reducing the amount of ash and sulphur. Many 
 forms of washers easily and cheaply reduce the slate from 20 % in the coal to 
 8 % of ash in the coke, but it is much more difficult to reduce 4 % of sulphur in 
 the coal to 1 % or less of sulphur in the coke. Sulphur occurs in the coal in 
 three forms, as hydrogen sulphide, calcium sulphate, and pyrite. The 
 first is volatile and is removed in coking, the second cannot usually be re- 
 moved by preliminary treatment, and it is the removal of the third form with 
 which washing has to do. The presence of water in the coke ovens appar- 
 ently assists the removal of the sulphur; but wet coals require a longer time 
 for coking than dry, and, therefore, pyrite should be removed as far as prac- 
 ticable before charging the coal into the coke ovens. The pyrite in coal as 
 it comes from the mine seems to be in particles even finer than those of the 
 coal dust. This impalpable powder or flour pyrites floats in air or water. 
 This being the case, the common practice of using the water over and over 
 again in a washery cannot give the best results in the removal of sulphur, as 
 some flour pyrites will be carried back each time and remain with the washed 
 coal. Experiments made by Mr. C. C. Upham. of New York City, show that 
 the critical size at which an almost complete division of the coal and pyrites 
 takes place varies with coals from different districts and beds and in laying 
 out coal-washing plants, the proper fineness of crushing should be determim 
 beforehand by careful experiment. 
 
958 
 
 THE PREPARATION OF COAL 
 
 PREPARATION OF ANTHRACITE 
 
 Under* the well-known conditions of the anthracite field, the general 
 methods of preparation may be summarized under three classes: namely, 
 (I) dry "preparation; (II) dry and wet preparation; and (III) wet prepara- 
 tion; of which the one to be adopted depends on the quality of coal to be 
 mined. 
 
 Class I (Fig. 10) is employed when the seams of coal mined are dry, or 
 are practically free from impurities, or where the benches of slate occurring 
 in the seams cleave free from the coal, and may be removed during hand 
 loading, and the run-of-mine contains generally _ not over 7 or 8% of rock 
 or slate, which may be removed by hand-picking or by dry mechanical 
 separators. 
 
 Lump to Pocket 
 Crusher Rolls-Break Lump 
 to St. Boat or Broken 
 
 FIG. 10. 
 
 Class II (Fig. 11) is employed when the run-of-mine contains a high per- 
 centage of impurities, including rock, slate, and bone. This percentage 
 may be as high as 55%, but the run-of-mine must contain large lumps of 
 pure coal, which can be handled as a separate product, as in the first class. 
 The sizes smaller than lump are sized and cleaned, using water to wash the 
 product,, to improve its appearance, and to remove the impurities by jigging. 
 
 Class III (Fig. 12) is adopted when the run-of-mine is high in impurities 
 and shows a discoloration, as is the case near the outcrop of the vein, or 
 when the entire product comes from wet, dirty seams, requiring a thorough 
 washing to remove the dirt and discoloration. 
 
 Class I presents the ideal breaker, with the advantages of low costs of 
 installation, operation, and maintenance. Moreover, shipments of dry coal 
 
 * The Preparation of Anthracite, Paul Stirling, E. M. in Trans., Amer. 
 Inst. Ming. Engrs., vol. XLII (1911). 
 
THE PREPARATION OF COAL 959 
 
 are very desirable to the trade, as they are free from the risk of the freezing 
 of coal in cars, and the subsequent trouble of unloading it. 
 
 Class II retains to some extent the advantage of dry coal-shipments, but 
 is higher in first-cost, operation, and maintenance than Class I or III. 
 
 Class III permits no dry shipments, and is higher in first-cost, operation, 
 and maintenance than Class I. 
 
 CRY PREPARATION-. 
 
 Pure Coal 
 
 IG. 11. 
 
 PREPARATION OF BITUMINOUS COAL 
 
 Sizes. Bituminous coal is not, as a rule, prepared with as great care as is 
 anthracite. In some regions where the coal is used mainly as a domestic 
 fuel and where competition is strong the coal is carefully sized and in many 
 instances the smaller grades are washed before being sent to market. Un- 
 like anthracite soft coal ignites with ease but has a tendency to spaul off 
 small pieces during the process of burning. It is therefore in most cases 
 unnecessary to carry sizing to as fine a point as with hard coal. The grade 
 of bituminous which brings the highest price is the lump. There appears to 
 be no fixed rule or even well-established custom concerning the sizes .into 
 which the run-of-mine is prepared. In general outside of southern Illinois 
 not more than four or five grades are made. These and their approximate 
 sizes are shown on the following table: 
 
 Through Over 
 
 Grade Circular Circular 
 
 Perforation Perforation 
 
 Slack f in. 
 
 Nut 1 5 in. in. 
 
 Egg 4 in. lj in. 
 
 Lump 4 in. 
 
 Another grade which has made its' appearance recently is called cobble 
 and is intermediate between the egg and the lump, passing through a 6-m. 
 to 7-in. circular opening and over (say) a 3-in. to 4-in. circular opening. 
 
960 
 
 THE PREPARATION OF COAL 
 
 Many other grades such as li-in. lump, 2-in. lump, etc., are prepared in 
 certain fields. These are produced either by passing the coal over bar 
 screens or perforated shaking screens. The coal which passes over being 
 known as the lump and that which passes through as slack. 
 
 Method of Preparation. Bituminous coal is usually sized on some type 
 of shaking screen, two general varieties being in use: the inclined shaking 
 
 le~.fi 
 
 FIG. 12. 
 
 screen and the horizontal screen. The horizontal screen has only one 
 representative. This is patented and is known as the Marcus. The motion 
 imparted to the screen by means of a special driving head is a reciprocation 
 back and forth with a non-uniform rapidity, that is, one stroke being made 
 more quickly than the other. The coal is thus caused to travel along the 
 screen and over the perforations unaided by gravity. This type of screen 
 may be readily used as a picking table and possesses some other advantages. 
 The inclined shaking screen which has a uniform rapidity of oscillation in 
 both directions is either hung from above or supported from below. If hung 
 
THE PREPARATION OF COAL 96i 
 
 from above, it may be suspended either by links or cpnnecting rods which 
 pivot upon pins at either end or may be hung by flexible wooden supports 
 rigidly attached at both top and bottom. If supported from below it is 
 usually either placed on rollers or carried by flexible wooden supports 
 similar to those used for suspension. Large screens sizing run-of-mine coal 
 into three or four grades are usually given a stroke of 5 to 6 in., the latter 
 being the more common. The speed usually varies from 90 to 120 R. P. M. 
 of the driving shaft and the inclination of the screen is usually about 15 
 but this varies somewhat with the district where the coal is produced on 
 account of the means employed in mining and the fracture of the coal. 
 Frequently the screening plate is not made flat but in a series of steps, each 
 one tending to turn over the lumps of coal and dislodge any fines which may 
 be riding thereon. Such screens are known as lip screens and the perfora- 
 tions are frequently slots instead of circular openings. The following table 
 shows the inclination of various fixed screens and other apparatus over which 
 the coal may slide in a tipple: 
 
 Inclination, 
 
 Degrees 
 
 Fixed lip chute screens for 6-in. egg (slot f X H in. tapered) 30 
 Fixed lip chute screen for 3-in. nut (slot \ X I in. tapered) 32 
 
 Dump chute 30 
 
 Standard bar screens 28 
 
 Weigh pan 38 
 
 Mine-run chute 40 in. diam. (circular) 28 
 
 Slack hopper and chute 45 
 
 Screening Area. The area of a shaking screen should be sufficient to 
 size the coal but not so large that the material is needlessly handled. The 
 area of the various perforated plates does not vary directly with the output 
 of the mine. There is no means of calculating the area necessary but ex- 
 perience has proved that the following sizes of plates are ordinarily well 
 adapted to a tipple handling 1,000 T. of coal per 8-hr, day where this coal 
 is passed over a bar screen or grizzly before reaching the shaking screens: 
 
 lj-in. round perforations 96 sq. ft. 
 
 2J- to 3-;n. perforations 96 sq. ft. 
 
 5- to 6-in. circular perforations 24 sq. ft. 
 
 If no bar screen is employed the areas above given should be increased about 
 30%. 
 
 Any screen designed to prepare 2,500 T. or more of run-in-mine run coal 
 in 8 hr. should be equipped with a feeder. The areas of the screens of a 2,500- 
 T. mine would be as follows: 
 
 l^-in. circular perforations 160 sq. ft. 
 
 2?- to 3-in. circular perforations 160 sq. ft. 
 
 5- to 6-in. circular perforations 40 sq. ft. 
 
 The areas of a screen plate for a capacity of 4,000 T. in 8 hr. would be as 
 follows: 
 
 1 J-in. circular perforations 190 sq. ft. 
 
 2|- to 3-in. circular perforations 190 sq. ft. 
 
 5- to 6-in. circular perforations 40 sq. ft. 
 
 Shaker Screens for Small Sizes. It is sometimes advantageous when 
 handling large capacities to make a double separation, that is, screen out 
 of the run-of-mine the egg coal and smaller in one operation and then size 
 this material into the egg, nut, slack and other grades in a secondary process. 
 The chief difference in the design of shaker screens for handling run-of-mine 
 and those making smaller sizes is in the pitch and speed of the screen. Small 
 coal screens need not be given a pitch in excess of H m. in a foot. The speed 
 of such a screen should be about 120 R. P. M. of the driving shaft and the 
 throw of the eccentric or crank should be about 3 in. Such screens are 
 frequently used for preparing material which will pass through a 2-in. 
 circular opening; that which passes over this opening being known as 2-in. 
 lump. In such a case the following grades are made: 
 
 Through Over 
 
 Name of Grade Circular Circular 
 
 Perforation Perforation 
 
 No. 2 nut 2 in. If in. 
 
 No. 3 nut H m. i m. 
 
 No. 4 pea I m. rs m. 
 
 Duff & in. . 
 
 61 
 
962 THE PREPARATION OF COAL 
 
 Screen Feeders. Two types of screen feeders are in general use, the 
 reciprocating and the continuous feed. The reciprocating feeder always 
 leaves a cushion of coal in the hopper for the succeeding dump to strike, 
 With this type of feeder, however, coal from two or three dumps is mixed 
 in the hopper and it is often impossible to dock for impurities. The recipro- 
 cating pan of such a feeder oscillates longitudinally at a speed about 60 
 R. P. M. of the driving shaft while the stroke is usually about 8 in. This 
 type of feeder subjects the coal to a more or less pronounced grinding action, 
 frequently causing unnecessary degradation. 
 
 The continuous feeder is a heavy steel-plate apron, the plates being 
 usually beaded. It is provided with a dump chute and hopper at one end 
 receiving the coal from the weigh pan while the sides are from 2 to 4 ft. 
 high to prevent spillage. With this type of feeder it is possible to thoroughly 
 inspect, each carload of coal as it leaves the weigh pan and docking is made 
 easy without delaying hoisting. 
 
 Tipple Design. The efficiency, capacity and cost of sizing coal depends in 
 large measure upon the design of the tipple and sizing apparatus. As 
 reliability is .of greater importance than extreme efficiency, simplicity should 
 always be sought in the design of a bituminous preparation plant. The 
 arrangement of such plants differs somewhat in different localities and with 
 the wage agreement with the miners' organization if any exists. Taking the 
 most complicated case of a shaft mine, the process and equipment is some- 
 what as follows: 
 
 The coal is delivered by self-dumping cages to bar screens if the mine is 
 operated on a lump basis or to the weigh pan if operated on a run-of-mine 
 basis. In the former instance the bar screens discharge to the weigh pan and 
 in the latter instance the weigh pan discharges to the bar screens. If 
 these screens discharge to the weigh pan the screenings pass through and are 
 delivered by chute to the shaking screens thus preceding the lump coal. 
 This is the better process so far as the shakers are concerned as a less screen- 
 ing area will be required. After passing the shaking screens the lump, 
 cobble if any, egg and frequently nut coal are picked on separate picking 
 tables. The egg and lump are, however, frequently picked together before 
 final separation is made. The larger sizes are delivered to railroad cars on 
 separate tracks either by telescoping chutes, side shaking chutes or hinged 
 loading booms of either the apron or belt conveyor type, frequently the 
 loading boom, or rather the horizontal portion of it, is utilized as a picking 
 table. Side shaking chutes for the delivery of the larger sizes often contain 
 degradation screens which deliver to a conveyor, which in turn discharges 
 the coal to the head of the sizing screen or to the slack car. 
 
 Washing Bituminous Coal. In many localities bituminous coal, particu- 
 larly the smaller sizes, is washed in order to remove the sulphur, fire clay, 
 slate and other detrimental material. While differing somewhat in detail, 
 the process as well as the machinery employed is similar to that employed 
 with anthracite. 
 
 HANDLING OF MATERIAL 
 
 Anthracite Coal. The following may be taken as average figures for the 
 angle or grade of chutes for anthracite coal, to be used where the chutes are 
 lined with sheet steel: For broken or egg coal, 2j in. per ft.; for stove or 
 chestnut coal, 3$ in. per ft.; for pea coal, 4i in. per ft.; for buckwheat coal, 
 6 in. per ft.; for rice coal, 7 in. per ft.; for culm, 8 in. per ft. 
 
 If the coal is to start on the chute, 1 in. per ft. should be added to each of 
 the above figures; while if the chutes are lined with manganese bronze in 
 place of steel, the above figures can be reduced 1 in. per ft. for coal in mo- 
 tion, or would remain as stated to start the coal. When the run-of- 
 mine is to be handled, as in the main chute, at the head of the breaker, the 
 angle should be not less than 5 in. per ft., or practically 22 J from the hori- 
 zontal. If chutes for hard coal are lined with glass, the angle can be re- 
 duced from 30% to 50%, depending somewhat on the nature of the coal. 
 In all cases, the flatter the coal, the steeper the angle must be, on account of 
 the large fric^n surfaces exp9sed, compared with the weight of the piece. 
 If chutes are lined with cast iron, the angle should be about the same as 
 that employed for steel, though sometimes a slightly greater angle is allowed. 
 
 The following tables are printed through the courtesy of the Link-Belt 
 Engineering Co., Philadelphia, Pa.; 
 
THE PREPARATION OF COAL 
 WEIGHTS AND CAPACITIES OF STANDARD STEEL BUCKETS 
 
 
 
 Weight 
 
 Capacity 
 
 Capacity of Elevator. 
 100 Ft. per Min. 
 
 Number 
 
 Chain 
 
 Size of 
 Bucket, In. 
 
 of 
 Bucket, 
 
 of 
 Bucket, 
 
 
 of 
 Draw- 
 
 
 
 
 
 Lb. 
 
 Lb. 
 
 Lb. per 
 
 Net Tons 
 
 ing 
 
 
 
 
 
 Min. 
 
 per Hr. 
 
 
 ! In. 
 Dodge | 
 
 12X 9X1H 
 14X 9X1H 
 18X 9X11J 
 24X 9X1H 
 
 &i 
 
 22 i 
 27 
 36 
 
 11 
 12* 
 Id} 
 
 22 
 
 1,100 
 1,250 
 1,650 
 2,200 
 
 33.0 
 37.5 
 49.5 
 66.0 
 
 5,357 
 5,357 
 5,357 
 5.357 
 
 
 12X10X16J 
 18X10X16* 
 
 20 
 29 
 
 19 
 
 28* 
 
 1,380 
 2,072 
 
 41.4 
 62.2 
 
 5,357 
 5,357 
 
 
 24X10X161 
 
 38 
 
 38 
 
 2,760 
 
 82.8 
 
 5,357 
 
 8 in. 
 Dodge 
 
 30X10X161 
 18X12X16* 
 
 46* 
 31 
 
 47* 
 33 
 
 3,450 
 2,400 
 
 103.5 
 72.0 
 
 5.357 
 5,357 
 
 
 24X12X161 
 |30X12X16; 
 
 40 
 
 48 
 
 44 
 55 
 
 3,200 
 4,000 
 
 96.0 
 120.0 
 
 5,357 
 5,357 
 
 Buckets taken f full. Buckets continuous. 1 Ib. of coal = 34 cu. in. 
 
 ELEVATING CAPACITIES OF MALLEABLE IRON BUCKETS 
 Table gives tons (2,000 Ib.) of pea coal per hour at 100 ft. per min. 
 
 Buckets 
 
 Ca- 
 pacities 
 
 Distance between Buckets in In. 
 
 Size, 
 In. 
 
 Wt., 
 Lb. 
 
 Cu. 
 In. 
 
 Lb. 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 2fX4 
 3X 5 
 4X6 
 4J-X 7 
 5X8 
 6 XIO 
 7 X12 
 7 X14 
 10 X18 
 
 0.75 
 1.50 
 2.00 
 2.56 
 3.56 
 5.47 
 8.97 
 11.41 
 
 15 
 
 31 
 51 
 
 75 
 102 
 185 
 287 
 295 
 
 0.48 
 0.97 
 1.57 
 2.33 
 3.15 
 5.73 
 8.90 
 9.14 
 
 2.16 
 4.36 
 
 7.06 
 10.38 
 
 1.73 
 3.49 
 5.65 
 8.39 
 11.34 
 
 1.44 
 2.91 
 4.71 
 6.99 
 9.45 
 17.19 
 
 1.23 
 
 2.49 
 4.04 
 5.99 
 8.10 
 14.73 
 22.88 
 
 1.08 
 
 2.18 
 3.53 
 5.19 
 7.09 
 12.88 
 20.02 
 20.56 
 
 1.94 
 3.14 
 4.66 
 6.30 
 11.46 
 17.80 
 18.28 
 
 2.83 
 4.19 
 5.67 
 10.31 
 16.02 
 16.45 
 
 3.81 
 5.15 
 9.38 
 14.56 
 14.95 
 
 4.72 
 8.59 
 13.35 
 13.71 
 
 
 
 
 
 
 
 
 
 
 Weight of 1 cu. ft. of pea coal = 53.5 Ib. 32.3 cu. in., or .0187 cu. ft. = 1 Ib. 
 
 CONVEYING CAPACITIES OF PLIGHTS AT 100 FT. PER MIN. 
 
 (Tons of Pea Coal per Hour) 
 
 Size of 
 Flight, In. 
 
 Horizontal 
 
 Inclined 
 
 10 
 
 20 
 
 30 
 
 Every 
 16 In. 
 
 Every 
 18 In. 
 
 Every 
 24 In. 
 
 Lb. Coal 
 per Flight 
 
 Every 
 24 In. 
 
 Every 
 24 In. 
 
 Every 
 24 In. 
 
 4X10 
 4X12 
 5X12 
 5X15 
 6X18 
 8X18 
 8X20 
 8X24 
 10X24 
 
 33.75 
 42.75 
 51.75 
 69.75 
 
 30 
 38 
 46 
 62 
 80 
 120 
 
 22.5 
 28.5 
 34.5 
 46.5 
 60.0 
 90.0 
 105.0 
 135.0 
 172.5 
 
 15 
 19 
 23 
 31 
 40 
 60 
 70 
 90 
 115 
 
 18.0 
 24.0 
 28.5 
 40.5 
 49.5 
 72.0 
 84.0 
 120.0 
 150.0 
 
 14.25 
 18.00 
 22 . 50 
 31.50 
 40.50 
 57.00 
 66.50 
 96.00 
 120.00 
 
 10.5 
 13.5 
 16.5 
 22.5 
 31.5 
 48.0 
 56.0 
 72.0 
 90. Q 
 
 
 
 NOTE. These ratings are for continuous feed. 2,000 Ib. = 1 T. 
 
964 
 
 THE PREPARATION OF COAL 
 
 HORSEPOWER FOR BUCKET ELEVATORS 
 
 N = number taken from table;' 
 fif = height of elevator in feet; 
 w = weight of material in one bucket ; 
 distance apart of buckets, in inches. 
 
 Revolutions 
 
 Diameter of Head-wheels 
 
 Revolu- 
 tions 
 
 per 
 
 Minute 
 
 22 In. 
 
 24 In. 
 
 26 In. 
 
 28 In. 
 
 30 In. 
 
 32 In. 
 
 per 
 
 Minute 
 
 10 
 
 .064 
 
 .070 
 
 .075 
 
 .080 
 
 .087 
 
 .093 
 
 10 
 
 12 
 
 .077 
 
 .083 
 
 .090 
 
 .097 
 
 .104 
 
 .111 
 
 12 
 
 14 
 
 .089 
 
 .096 
 
 .106 
 
 .114 
 
 .121 
 
 .130 
 
 14 
 
 16 
 
 .102 
 
 .111 
 
 .121 
 
 .130 
 
 .140 
 
 .148 
 
 16 
 
 18 
 
 .115 
 
 .125 
 
 .136 
 
 .146 
 
 .157 
 
 .167 
 
 18 
 
 20 
 
 .128 
 
 .139 
 
 .151 
 
 .162 
 
 .174 
 
 .186 
 
 20 
 
 22 
 
 .140 
 
 .153 
 
 .166 
 
 .179 
 
 .191 
 
 .204 
 
 22 
 
 24 
 
 .153 
 
 .167 
 
 .181 
 
 .195 
 
 .209 
 
 .223 
 
 24 
 
 26 
 
 .166 
 
 .181 
 
 .196 
 
 .211 
 
 .226 
 
 .242 
 
 26 
 
 28 
 
 .179 
 
 .195 
 
 .211 
 
 .227 
 
 .244 
 
 .260 
 
 28 
 
 30 
 
 .191 
 
 .209 
 
 .226 
 
 .244 
 
 .261 
 
 .279 
 
 30 
 
 32 
 
 .204 
 
 .223 
 
 .241 
 
 .260 
 
 .278 
 
 .297 
 
 32 
 
 34 
 
 .217 
 
 .237 
 
 .256 
 
 .276 
 
 .296 
 
 .316 
 
 34 
 
 36 
 
 .230 
 
 .251 
 
 .271 
 
 .292 
 
 .313 
 
 .334 
 
 36 
 
 38 
 
 .242 
 
 .265 
 
 .287 
 
 .309 
 
 .331 
 
 .353 
 
 38 
 
 40 
 
 .255 
 
 .279 
 
 .302 
 
 .325 
 
 .348 
 
 .372 
 
 40 
 
 PITCH AT WHICH ANTHRACITE COAL WILL RUN, IN INCHES PER FOOT 
 
 
 Sheet Iron 
 
 Cast 
 Iron 
 
 Glass 
 
 Glass 
 
 Kind of Coal 
 
 Start 
 on 
 
 Con- 
 tinue 
 
 Start 
 on 
 
 Start 
 on 
 
 Con- 
 tinue 
 
 Start 
 on 
 
 Con- 
 tinue 
 
 
 
 
 
 
 
 
 
 
 
 Dry 
 
 Wet 
 
 Broken slate 
 
 5 
 
 4 
 
 
 5 
 
 3 
 
 3 
 
 
 
 
 Dry egg slate 
 Dry stove slate 
 
 5 
 5 
 
 
 4 
 4 
 
 
 5 
 5 
 
 
 3 
 3 
 
 
 3 
 3 
 
 
 
 
 Dry chestnut slate 5 
 
 4 
 
 
 5 
 
 
 3 J 
 
 
 3 
 
 
 
 
 Broken coal 
 
 
 
 
 fr 
 
 
 ?- 
 
 
 
 
 
 Egg coal 3 
 Stove coal 4 
 
 
 3 
 41 
 
 3 
 
 4 
 
 
 2j 
 3 
 
 
 2\ 
 21 
 
 
 2f 
 
 2* 
 
 If 
 
 2J 
 
 Chestnut coal . /. 
 
 4 
 
 
 41 
 
 h 
 
 4. 
 
 
 3 
 
 Bl 
 
 
 8 
 
 
 2* 
 
 Pea coal 
 
 5 
 
 
 5 
 
 j 
 
 
 3 
 3 
 
 
 2\ 
 3^ 
 
 
 3 
 3 
 
 
 If 
 
 Buckwheat No. 1 
 
 Buckwheat No. 2 
 
 
 
 
 3 
 
 
 3 J 
 
 
 3 
 
 
 3i 
 
 Buckwheat No. 3 
 
 
 
 
 4 
 
 
 Si 
 
 
 7 
 
 
 *4 
 
 Buckwheat No. 4 | ... 
 
 
 4 
 
 
 4 
 
 
 4 
 
 
 4? 
 
THE PREPARATION OF COAL 
 
 965 
 
 HORSEPOWERS FOR COAL CONVEYORS (COAL INCLUDED) 
 Speed, 1C i ft. per min. Conveyors, 100 ft. long. Standard steel troughs. 
 
 s 
 s 
 
 CO 
 
 Size of 
 
 Flights," 
 In. 
 
 Horizontal 
 
 In- 
 clined 
 
 d 
 
 'rt 
 J3 
 
 
 i 
 
 CO 
 
 Size of 
 Flights, 
 In. 
 
 Horizontal 
 
 In- 
 clined 
 
 JM 
 atf 
 
 sjt 
 
 i 
 
 16 In. 
 between 
 Flights 
 
 1-1 j be 
 
 sji 
 
 a 
 " *" 
 
 o"o 
 
 4X10 
 4X12 
 5X12 
 5X15 
 6X18 
 
 O h^OOOO K5 
 
 2 
 3* 
 4f 
 
 05 mi** oo oo 
 
 s, 
 g 
 
 q 
 
 d 
 
 5X15 
 6X18 
 8X18 
 8X20 
 8X24 
 10X24 
 
 4 
 5 
 
 7 
 8 
 
 3* 
 
 5 
 6 
 
 7 
 8 
 
 10 
 111 
 
 14 
 
 HORIZONTAL PRESSURE EXERTED BY BITUMINOUS COAL AGAINST VERTICAL 
 RETAINING WALLS PER FOOT OF LENGTH 
 
 I 
 
 Surface horizontal 
 r . 
 Surface sloping ' 
 
 Angle of repose 
 
 d = height of wall in feet or ab 
 
 35 
 
 BITUMINOUS 
 
 49 
 
 Horizontal 
 Surface, 
 
 Sloping 
 Surface, 
 
 
 Horizontal 
 Surface, 
 
 Sloping 
 Surface, 
 
 fc-t 
 
 bm 
 
 be 
 
 P^H 
 
 bm 
 
 be 
 
 d 
 
 
 c 
 
 
 
 J 
 
 
 ^j 
 
 
 - 
 
 Q 
 
 .O 
 
 
 ^ 
 
 
 j 
 
 X 
 
 - S 
 
 &H 
 
 ~ $ 
 
 fo 
 
 ^ 
 
 i 
 
 gfe 
 
 ~ 
 
 plH 
 
 a 
 
 CTj 3 
 
 3 
 
 rt 3 
 
 3 ^ 
 
 o. 
 
 rt 3 
 
 ^ +^ 
 
 d d 
 
 ^ 4_T 
 
 Q 
 
 *l 
 
 W "1 
 
 If 
 
 ^1 
 
 8 
 
 
 
 Q 
 
 
 
 || 
 
 O w 
 
 r 0) 
 
 
 * 
 
 
 
 -> 
 
 
 H 
 
 
 
 -) 
 
 
 H-J 
 
 1 
 
 6.4 
 
 6.4 
 
 10 
 
 10 
 
 26 
 
 4,305 
 
 325 
 
 6,760 
 
 510 
 
 2 
 
 25.0 
 
 19.0 
 
 40 
 
 30 
 
 27 
 
 4,641 
 
 338 
 
 7,290 
 
 530 
 
 3 
 
 57.0 
 
 32.0 
 
 90 
 
 50 
 
 28 
 
 4.993 
 
 350 
 
 7,840 
 
 550 
 
 4 
 
 102.0 
 
 45.0 
 
 160 
 
 70 
 
 29 
 
 5,358 
 
 363 
 
 8,410 
 
 570 
 
 5 
 
 159.0 
 
 57.0 
 
 250 
 
 90 
 
 30 
 
 5,733 
 
 376 
 
 9,000 
 
 590 
 
 6 
 
 229.0 
 
 70.0 
 
 360 
 
 110 
 
 31 
 
 6,122 
 
 389 
 
 9,610 
 
 610 
 
 7 
 
 312.0 
 
 83.0 
 
 490 
 
 130 
 
 32 
 
 6,523 
 
 401 
 
 10,240 
 
 630 
 
 8 
 
 407.0 
 
 96.0 
 
 640 
 
 150 
 
 33 
 
 6.935 
 
 414 
 
 10,890 
 
 650 
 
 9 
 
 516.0 
 
 108.0 
 
 810 
 
 170 
 
 34 
 
 7,362 
 
 427 
 
 11,560 
 
 670 
 
 10 
 
 637.0 
 
 121.0 
 
 1,000 
 
 190 
 
 35 
 
 7,778 
 
 440 
 
 12.250 
 
 690 
 
 11 
 
 770.0 
 
 134.0 
 
 1,210 
 
 210 
 
 36 
 
 8,253 
 
 452 
 
 12.960 
 
 710 
 
 12 
 
 917.0 
 
 146.0 
 
 1,440 
 
 230 
 
 37 
 
 8,754 
 
 465 
 
 13.690 
 
 730 
 
 13 
 
 1,076.0 
 
 159.0 
 
 1,690 
 
 250 
 
 38 
 
 9,193 
 
 478 
 
 14,440 
 
 750 
 
 14 
 
 1,248.0 
 
 172.0 
 
 1,960 
 
 270 
 
 39 
 
 9,682 
 
 490 
 
 15,210 
 
 770 
 
 15 
 
 1,433.0 
 
 185.0 
 
 2,250 
 
 290 
 
 40 
 
 10,192 
 
 503 
 
 16,000 
 
 790 
 
 16 
 
 1,630.0 
 
 197.0 
 
 2,560 
 
 310 
 
 41 
 
 10,669 
 
 516 
 
 16,810 
 
 810 
 
 17 
 
 1,840.0 
 
 210.0 
 
 2,890 
 
 330 
 
 42 
 
 11.236 
 
 529 
 
 17,640 
 
 830 
 
 18 
 
 2,063.0 
 
 223.0 
 
 3,240 
 
 350 
 
 43 
 
 11,797 
 
 541 
 
 18,490 
 
 850 
 
 19 
 
 2,298.0 
 
 236.0 
 
 3,610 
 
 370 
 
 44 
 
 12,331 
 
 554 
 
 19,360 
 
 870 
 
 20 
 
 2,548.0 
 
 248.0 
 
 4,000 
 
 390 
 
 45 
 
 12,968 
 
 567 
 
 20,250 
 
 890 
 
 21 
 
 2,809.0 
 
 261.0 
 
 4,410 
 
 410 
 
 46 
 
 13,478 
 
 580 
 
 21.160 
 
 910 
 
 22 
 
 3,083.0 
 
 274.0 
 
 4,840 
 
 430 
 
 47 
 
 14,100 
 
 592 
 
 22,090 
 
 930 
 
 23 
 
 3,369.0 
 
 287.0 
 
 5,290 
 
 450 
 
 48 
 
 14,679 
 
 605 
 
 23,040 
 
 950 
 
 24 
 
 3,669.0 
 
 299.0 
 
 5,760 
 
 470 
 
 49 
 
 15,275 
 
 618 
 
 24,010 
 
 970 
 
 25 
 
 3,981.0 
 
 312.0 
 
 6,250 
 
 490 
 
 50 
 
 15,925 
 
 631 
 
 25,000 
 
 990 
 
 Wp.it/ht of coal = 47 Ib. ner cu. ft. 
 
966 
 
 THE PREPARATION OF COAL 
 
 HORIZONTAL PRESSURE EXERTED BY ANTHRACITE COAL AGAINST VERTICAL 
 RETAINING WALLS PER FOOT OF LENGTH 
 
 9.78<f2 
 = 9.78(2d-l) 
 
 Surface horizontal 
 
 Surface sloping < 
 
 Angle of repose 
 
 d = height of wall in feet. 
 
 14.22 (2d-l) 
 27 
 
 ANTHRACITE 
 
 
 Horizontal 
 
 Sloping 
 
 
 Horizontal 
 
 Sloping 
 
 
 
 Surface, 
 
 Surface, 
 
 
 
 Surface, 
 
 Surface, 
 
 P-I 
 
 bm 
 
 be 
 
 PH 
 
 bm 
 
 be 
 
 a 
 
 
 
 C 
 
 
 
 
 
 
 
 j> 
 
 D 
 
 -M 
 
 'i 
 
 
 
 
 
 
 Oj ry 
 
 *& 
 
 *t 3 
 
 
 "oj 3 
 
 W ** 
 
 ^ 
 
 *c3 a 
 
 a ^ 
 
 32 
 
 *S+r 
 
 I 
 
 l l 
 
 II 
 
 *! 
 
 l| 
 
 c 
 
 11 
 
 IJ 
 
 el. 
 
 PH 
 
 <() 4) 
 C^ O 
 
 2 
 
 9.78 
 39.12 
 
 9.78 
 29.34 
 
 14.22 
 56.88 
 
 14.22>26 
 42.66[27 
 
 6,611.1 
 7,129.5 
 
 498.78 
 518.35 
 
 9,612.8 
 10,366.0 
 
 725.21 
 753 . 67 
 
 3 
 
 88.02 
 
 48.90 
 
 127.98 
 
 71.1028 
 
 7,667.6 
 
 537.90 
 
 11,149.0 
 
 782.10 
 
 4 
 
 156.48 
 
 68.46 
 
 227 . 52 
 
 99.54 
 
 29 
 
 8,225.0 
 
 557.46 
 
 11,988.0 
 
 810.54 
 
 5 
 
 244 . 50 
 
 88.02 
 
 355.50 
 
 127.98 
 
 30 
 
 8,802.0 
 
 577.01 
 
 12,797.0 
 
 839 . 00 
 
 6 
 
 352.08 
 
 107.58 
 
 511.92 
 
 156.4231 
 
 9,398.5 
 
 596.59 
 
 13,655.0 
 
 867.41 
 
 7 
 
 479.22 
 
 127.14 
 
 696.78 
 
 184.86 
 
 32 
 
 10,015.0 
 
 616.14 
 
 14,561.0 
 
 895.86 
 
 8 
 
 625.92 
 
 146.70 
 
 910.08 
 
 213.30 
 
 33 
 
 10,650.0 
 
 635.70 
 
 15,486.0 
 
 924 . 30 
 
 9 
 
 792.18 
 
 166.26 
 
 1,151.82 
 
 241.74 
 
 34 
 
 11,306.0 
 
 655.26 
 
 16,439.0 
 
 952.70 
 
 10 
 
 978.00 
 
 185.82 
 
 1,422.00 
 
 270.18 
 
 35 
 
 11,980.0 
 
 674.81 
 
 17,420.0 
 
 981.19 
 
 11 
 
 1,183.38 
 
 205.38 
 
 1,720.62 
 
 298.62 
 
 36 
 
 12,675.0 
 
 694.39 
 
 18,429.0 
 
 1,009.60 
 
 12 
 
 1,408.32 
 
 224.94 
 
 2,047.68 
 
 327.06 
 
 37 
 
 13,389.0 
 
 713.94 
 
 19,467.0 
 
 1,038.10 
 
 13 
 
 1,652.82 
 
 244.50 
 
 2,403.18 
 
 355.50 
 
 38 
 
 14,123.0 
 
 733.50 
 
 20,533.0 
 
 1,066.50 
 
 14 
 
 1,916.88 
 
 264.06 
 
 2,787.12 
 
 383.94 
 
 39 
 
 14,875.0 
 
 753.07 
 
 21,629.0 
 
 1,095.00 
 
 15 
 
 2,200.50 
 
 283.62 
 
 3,199.50 
 
 412.38 
 
 40 
 
 15,648.0 
 
 772.63 
 
 22,752.0 
 
 1,123.40 
 
 16 
 
 2,503.68 
 
 303.18 
 
 3,640.32 
 
 440.82 
 
 41 
 
 16,440.0 
 
 792.20 
 
 23,904.0 
 
 1,151.80 
 
 17 
 
 2,826.42 
 
 322.74 
 
 4,109.56 
 
 469.26 
 
 42 
 
 17,252.0 
 
 811.74 
 
 25,084.0 
 
 1,180.30 
 
 18 
 
 3,168.72 
 
 342.30 
 
 4,607.28 
 
 497.70 
 
 43 
 
 18,083.0 
 
 830.73 
 
 26,293.0 
 
 1,208.70 
 
 19 
 
 3,530.58 
 
 361.86 
 
 5,133.42 
 
 526.14 
 
 44 
 
 18,934.0 
 
 850.86 
 
 27,530.0 
 
 1,237.20 
 
 20 
 
 3,912.00 
 
 381.42 
 
 5,688.00 
 
 554 . 58 
 
 45 
 
 19,804.0 
 
 870.41 
 
 28,793.0 
 
 1,265.60 
 
 21 
 
 4,313.00 
 
 400.98 
 
 6,271.00 
 
 583 . 26 
 
 46 
 
 20,695.0 
 
 889.99 
 
 30,090.0 
 
 1,294.00 
 
 22 
 
 4,733.50 
 
 420.54 
 
 6,882 . 50 
 
 611.46 
 
 47 
 
 21,605.0 
 
 909 . 54 
 
 31,412.0 
 
 1,322.30 
 
 23 
 
 5,173.70 
 
 440.10 
 
 7,522.50 
 
 639.90J48 
 
 22,533.0 
 
 929.10 
 
 32,763.0 
 
 1,350.90 
 
 24 
 
 5.633.30 
 
 459.67 
 
 8,190.70 
 
 668.35 
 
 49 
 
 23,482.0 
 
 948.66 
 
 34,143.0 
 
 1,379.40 
 
 25!6ill2.60 
 
 479.22 
 
 8,887.50 
 
 696.7950 
 
 24,450.0 
 
 968.21 
 
 35,550.0 
 
 1,407.90 
 
 COST OF UNLOADING COAL 
 
 Coal is generally unloaded from railroad cars into the hold of a vessel by 
 some form of unloader, which usually raises the car bodily and dumps it 
 directly into the hold of the vessel. In this way the cost of unloading has 
 been reduced to a very small figure, and the speed of unloading greatly 
 increased. The cost of unloading is given by the makers of the Brownhoist 
 as varying from 2j c. per T. up to 4 c. per T.; deducting in each case 2 c. for 
 
THE PREPARATION OF COAL 
 
 967 
 
 trimming the coal in the vessel, the actual cost of loading varies from i c. to 
 2j c. per T., depending on the conditions. Along the Lakes it is customary 
 to pay a premium of | c. per T. to all connected with the loading, for all coal 
 loaded in excess of 2,500 T. per day and 1,800 T. per night. The Brownhoist 
 has a guaranteed capacity of at least 300 T. per hr., but this has been greatly 
 exceeded in practice. The McMyler end dump has a record of 4.65 T. per 
 min., and the McMyler side dump of 8.41 T. per min. These figures apply to 
 the lake cities of the U. S. 
 
 The C. W. Hunt Co., West New Brighton, N. Y., gives the following 
 figures for handling coal along the Atlantic seaboard: The cost of shoveling 
 coal by hand in the hold of the vessel into ordinary iron buckets is about 6 to 
 7 c. per T. of 2,000 lb.; the cost for iron ore, phosphate rock, or sand, about 
 10 % less. The cost of shoveling coal and hoisting it out of vessel to the 
 wharf with an ordinary hoist with manila rope is 12 to 13 c. per T., so that 
 the hoisting costs about the same as the shoveling. The cost for both 
 shoveling and hoisting with a steam engine is 10 to 11 c. per T. The cost 
 when using a steam shovel or grab bucket for taking up coal out of the vessel 
 varies greatly in different classes of vessels, but usually runs from about 1 $ to 
 5 c. per T., averaging about 3 c. After the coal is hoisted, it can be carried 
 into storage with an automatic railway or other efficient plant, at a cost of 
 about 1 to 1 c. per T. For great distances, a cable railway or a conveyor can 
 be used, which handles the material about as cheaply as for short distances, 
 but the cost of plant is greatly increased. 
 
 In unloading anthracite from cars on a trestle into pockets or on the 
 ground, the loss on all sizes is 2 to 3 % when the coal is not resized; when it is 
 resized the loss is 8 to 9%. 
 
 The cost of stocking and unloading anthracite by the Dodge system is 
 given by Mr. Piez, as follows: 
 
 Year 
 
 fj 
 
 xpense, 
 n. Cents. 
 
 0> o3 to 
 M P,t! 
 * - <U 
 
 15U 
 
 h 
 
 'ftO<_w 
 
 C t cj 
 
 3 .S k 
 
 per Ton. 
 
 1 
 
 
 
 
 Ia4?! 
 
 Wo 
 
 fiS 
 
 3 
 
 Bj 
 
 .2 to 
 
 .* 
 
 
 ^ O "* "H 
 
 Q; " 
 
 H -4 
 
 O TTH d 
 
 a C! 
 
 3.0 
 
 a| 
 
 
 jCtfiJU 
 
 ,1 
 
 l 3 ^ 
 
 3 
 
 S 
 
 ^ 
 
 ft ^ 
 
 CO 
 
 $ 
 
 1895... 
 1896 
 1897 
 
 .87 
 .78 
 .69 
 
 .29 
 .30 
 .32 
 
 .97 
 
 .82 
 .62 
 
 2.67 
 2.19 
 1.88 
 
 .78 
 .90 
 .97 
 
 .25 
 .27 
 .16 
 
 5.83 
 5.26 
 4.64 
 
 BRIQUETING 
 
 Machines Employed. Fuel, fuel dust, and other products may be bri- 
 queted by a number of different styles of machines, but all these may be 
 divided into two classes, briquet and eggette machines. The eggette ma- 
 chines have a pair of rollers, the faces of which are provided with semisphencal 
 or semiovoid depressions. The material that is fed between these rolls 
 crowds into the openings of the two rolls, thus forming small nodules. In 
 material is mixed with a suitable binder before being fed to the rolls, and the 
 eggsttes are received on any suitable form of traveling belt or chute and 
 removed for drying or storage. This style of machine has not been used 
 
 J.I1LU WlUCil l/IIC IllctLClldl 10 v^i w vv uvu.* j. j-j.^ **.i -w* -v*-. ^- j 
 
 being fed into the mold or subsequently by some form of plunger. For some 
 materials, common brick machines, such as are used in the manufacture ol 
 building brick, are employed, while in others special f9rms are necessary. 
 
 Briqueting of Fuel. Fuel briquets have not come into general use in the 
 United States for two reasons: (1) on account of the great amount of cheap 
 fuel available, which has prevented the utilization of culm, coal dust etc.; 
 and (2) on account of the lack of or high price of suitable bonding material. 
 This latter condition is now being removed by the introduction of byproduc 
 coke ovens, from which supplies of coal tar can be obtained. Aside from peat 
 and certain kinds of brown coal, and possibly some caking coals, it is neces- 
 
968 
 
 THE PREPARATION OF COAL 
 
 sary to employ a binder in the making of any fuel briquets. This is especially 
 true in the case of anthracite coal. The present tendency is to employ no 
 in9rganic bonding materials, as they increase the ash. The material to be 
 briqueted should be as clean and free from dirt or slate as possible, and the 
 particles should be of practically uniform size, the most satisfactory product 
 being from coal crushed to about | in. cube size. The coal must be thor- 
 oughly mixed with bonding material and then subjected to a heavy pressure. 
 One advantage claimed for briquets is that they can be made of such a form 
 as to occupy less space than the original fuel. The French navy has found 
 it possible to store 10% more briquets than coal in a given space, and also 
 that the loss by breakage and pulverization is very much less. Under favora- 
 ble conditions, fuel can be briqueted for 20 c. per T., and the following 
 are some of the advantages claimed for these briquets: They are sound 
 throughout and will not decrepitate while burning, thus reducing the loss by 
 fine material working through the grates. The binder if properly selected, 
 renders the briquets practically waterproof, so that they are not injured if 
 kept in storage, do not evolve combustible gases, nor ignite from spontaneous 
 combustion. There is no fine material mixed with the briquets, and hence a 
 more uniform fire can be maintained with them. 
 
 Briqueting of Flue Dust. Flue dust from iron blast furnaces has been suc- 
 cessfully briqueted in a number of instances. One firm employs a common 
 brick machine, making bricks 2? in. X4 in. X9 in. With this machine, 
 they mix the flue dust with 3 % of lime and 3 % of cement, the lime acting as 
 a flux in the furnace. These machines work with comparatively light pres- 
 sure. When regular briqueting machines, producing round bricks and 
 employing high pressures are employed, no cement need be used, the flue dust 
 being mixed with 4 % to 6 % of lime. The flue dust is first carefully screened 
 from hard lumps and then mixed warm with milk of lime in a mixer, after 
 which it is put through the press, and the briquets are then placed in drying 
 ovens and subjected to heat from the gases of a boiler or furnace plant, 
 the temperature not to exceed 300F. For moderate sized briquets, about 
 6 hours' drying is sufficient. Just before the briquets are quite dry, they 
 are loaded into barrels and taken direct to the blast furnace, with as little 
 handling as possible. The results have been very satisfactorily compared 
 with the ore replaced. The flue dust itself frequently contains 30 % to 40 % 
 metallic iron and more or less carbonaceous matter. It is also stated that at 
 a large furnace plant the cost of making and handling should not exceed 
 $1 per T. 
 
 Another firm, figuring on a basis of 130 T. per 24 hr., and using 3% lime 
 in the solution, gave the following figures: 
 
 4 T. lime, $3.00 per T $12 . 00 
 
 2 machine tenders (day and night), 12 hr. at $2.50. 5.00 
 
 2 laborers (day and night), 12 hr. at $1.75 3 . 50 
 
 Oil and waste 2 . 00 
 
 Wear on machinery 1 . 50 
 
 Interest on cost of plant 1 . 00 $25 . 00 
 
 This is less than 20 c. per T. This estimate does not take into considera- 
 tion the cost of power, which would be about 35 H.P., nor does it take into 
 consideration hauling of material to plant and removing of briquets. 
 CUBIC FEET OCCUPIED BY 2,000 POUNDS OF VARIOUS COALS 
 (Link-Belt Engineering Co., Philadelphia, Pa.} 
 
 Varieties 
 
 Broken | Egg | Stove | Chestnut | Pea 
 
 Lackawanna, anthracite 
 
 37.10 
 37.30 
 37.55 
 38.05 
 34.90 
 34.95 
 33.30 
 34.65 
 35.35 
 35.45 
 
 36.65 
 36.95 
 37.25 
 37.70 
 34.85 
 34.35 
 33.80 
 34.20 
 35.20 
 34.95 
 
 34.90 
 36.35 
 37.55 
 37.25 
 34.75 
 33.75 
 33.55 
 33.80 
 34.60 
 34.35 
 
 34.35 
 36.35 
 37.25 
 37.25 
 34.70 
 34.00 
 32.55 
 33.55 
 33.30 
 33.70 
 
 37.25 
 37.50 
 38.50 
 38.50 
 36.90 
 36.90 
 33.05 
 35.20 
 34.95 
 35.50 
 
 Garfield red ash, anthracite 
 Lykens Valley, anthracite.. 
 
 Shamokin, anthracite 
 
 Plymouth red ash, anthracite 
 Wilkes-Barre, anthracite 
 Lehigh, anthracite 
 Lorberry anthracite 
 
 Scranton, anthracite 
 Pittston, anthracite 
 
 Cumberland, bituminous 136.65 
 Clearfield, bituminous 33.55 
 
 Pocahontas, bituminous 
 American cannel, bituminous . . 
 English cannel, bituminous 
 
 34.00 
 41.50 
 42.30 
 
 New River, bituminous 40. 15 
 
SAFETY AND FIRST AID 
 
 SAFETY AND FIRST AID 
 
 The following directions for first aid to the injured were prepared by Dr. 
 George H. Halberstadt of Pottsville, Pa., Surgeon for the Philadelphia & 
 Reading Coal and Iron Co. They cover in a concise manner the principles 
 of the excellent detailed instructions that have resulted in the great efficiency 
 of the P. & R. G. and I. Co.'s first-aid corps. 
 
 RULES FOR FIRST-AID CORPS 
 
 1. The work is limited to first aid. 
 
 2. In all serious cases summon a doctor. On his arrival, if requested, give 
 him all possible assistance. 
 
 3. Keep your presence of mind and do not, by your manner, indicate to the 
 patient the seriousness of the injury. 
 
 4. Examine the mouth and remove any foreign substance. 
 
 5. In all serious injuries cut off the clothing to properly inspect and dress 
 wounds. For slight injuries begin removal of the clothing from the sound 
 side, and tp replace it begin on the injured side. 
 
 6. Place the patient in a comfortable position, preferably on his back. 
 
 7. When vomiting occurs turn the patient on his side, neck extended and 
 head low, so that the vomited material will not enter the wind pipe. 
 
 8. Never attempt to wash or cleanse a wound; do not touch ft with the 
 fingers; cover up quickly every wound with sterile dressing and secure this 
 with a clean bandage. This will prevent infection and blood poisoning. The 
 old common practice of applying a chew of tobacco to stop bleed- 
 ing, and the use of handkerchiefs or pieces torn from clothing in 
 binding up open wounds is a source of serious danger. 
 
 9. Do not handle the part of the dressing that will come into 
 contact with the wound. 
 
 10. Stop severe hemorrhage from arms and 
 legs with a tourniquet applied above the 
 wound, then apply sterile dressings securely* 
 held with bandage. If the dressings control 
 the hemorrhage, loosen tourniquet but leave 
 it in position to be retightened if necessary; 
 always watch for secondary hemorrhage. 
 
 A tourniquet may be made of the material 
 contained in a first-aid cabinet or a handker- 
 chief can be used. Lay a firm and even com- 
 press or pad over the artery if you can readily 
 locate it. The artery in the thigh runs along 
 the inner side of the muscle in front near the p i 
 
 bone, as shown by a dotted line on Fig. 1. A 
 little above the knee it passes to the back of the bone. In case of injuries at 
 or above the knee, apply the compress higher up, on the_inner side of the 
 thigh, along the line of the artery, as for instance, at the point P. When the 
 leg is injured below apply the compress at the back of the thigh just above 
 the knee at P, Fig. 2. The artery in the arm runs down the inner side of 
 the large muscle in front, quite close to the bone as shown in Fig. 3. Lower 
 down it is further forward, towards the bend of the elbow. It is most easily 
 
 compressed a little above the middle at P. 
 
 In all cases apply the tourniquet as close above 
 
 the wound as possible. 
 
 Tie the cloth or the handkerchief around 
 
 the limb, covering the compress, put a bit of 
 
 stick between the bandage and the limb and 
 twist it as in Fig. 4. until it is just tight enough 
 
 to stop the bleeding, then put one end of the 
 
 stick under the handkerchief as shown in Fig. 
 
 5 to prevent untwisting. 
 FlG. 3 11. Check bleeding from all parts of the 
 
 body by dressings and bandages. Both roller 
 
 and triangular bandages are used in first-aid work. The roller bandages are 
 made of various widths, and 5 yd. long. Triangular bandages as furnished 
 in first-aid equipments are triangular pieces of cotton cloth, measuring 4 
 ft. 2 in. on the base, and 2 ft. 9 in. on the sides. Similar bandages can be 
 made by cutting a yard of muslin diagonally. The advantages of triangular 
 
 FIG. 2 
 
970 SAFETY AND FIRST AID 
 
 bandages are: they can be folded to make bandages of any desired width, and 
 can also be used as slings. Triangular bandages furnished in first-aid outfits 
 have illustrations printed on them showing their application to different 
 parts of the body. 
 
 12. Cover up every injured person with blankets, regardless of the weather. 
 Use hot-water bottles and an ambulance stove, when necessity requires 
 them. When hot-water bottles are used always have clothing or woolen 
 blankets between them and the patient. 
 
 13. Do not, under any circumstances, use the so-called antiseptic lotions, 
 
 salves, balsams, or any material that is likely to 
 infect the wound. 
 
 14. Splint every injury from toe to hip and 
 from fingers to shoulders. Always support fore- 
 arm with sling. 
 
 15. Notify at once the patient's family or the 
 hospital of the character of the injury and prob- 
 able time of arrival at destination. 
 
 Shock. Shock accompanies all serious acci- 
 dents. The skin is cold and clammy; the pulse 
 is weak, rapid and often intermittent; the breath- 
 ing irregular; vomiting and retching are common; 
 eyelids naif open; pupils dilated; and there may 
 be any degree of insensibility. Check hemorrhage 
 at once. Cover patient with blankets and sur- 
 round him with hot-water bottles. The hot-water 
 bottles must not come into contact with the skin, 
 FIG. 4 FIG. 5 have a layer of blanket or clothing intervene. 
 
 When able to swallow give hot black coffee or a 
 
 half teaspoqnful of aromatic spirits of ammonia in a half tumbler of water. 
 Alcoholic stimulants should not be given unless ordered by the doctor. If 
 vomiting occurs, turn patient on his side and see that no vomited material 
 is left in the mouth. When the injury is to the skull give no stimulants. 
 
 Burns and Scalds. Remove clothing with knife or scissors. Do not 
 break the blisters. Cover with picric acid gauze; this with a layer of cotton 
 and secure with bandage. A solution of baking soda, one tablespoonful to 
 a quart of boiled water, may be applied on gauze, if picric acid gauze is not 
 at nand. 
 
 Heat Prostration and Heat Exhaustion. In heat prostration, the face is 
 flushed, the skin dry and hot, pulse may be rapid or slow, and the heat of the 
 body excessive; and patient may be unconscious. Remove patient to a cool 
 place, loosen the clothing, lessen the heat of the body and head by cold 
 applications. 
 
 In heat exhaustion, the face is pale, the skin cold and clammy, breathing 
 shallow, pulse weak and rapid. Loosen the clothing, apply heat to the 
 surface of the body, and when able to swallow, give hot black coffee or tea. 
 Convulsions. Lay patient on back, loosen clothing, place blanket or 
 coat under his head. Do not attempt to resist the convulsive efforts ; 
 stand by and protect him from doing injury to himself. If he is biting his 
 tongue, force a stick between his back teeth and release it. 
 
 Artificial Respiration. This is administered for drowning, for electric 
 shocks, suffocation by smoke, illuminating gas or any mine gas. 
 
 The Schaefer Method. Lay the subject on his belly, with arms extended 
 as straight forward as possible, as shown in Fig. 6, and with face to one side 
 so that the nose and mouth are free for breathing. Let an assistant draw 
 forward the subject's tongue. If possible, avoid so laying the subject that 
 any burned or injured places are pressed upon. Do not permit bystanders to 
 crowd around and shut off the fresh air. 
 
 Kneel straddling the subject's thighs and facing his head; rest the palms 
 of your hands on his loins (on the muscles of the small of the back), with 
 thumbs nearly touching each other (Fig. 6) and with fingers spread over the 
 lowest ribs. 
 
 With arms held straight (Fig. 7), swing forward slowly so that the weight 
 of your body is gradually brought to bear upon the subject. This operation, 
 which should take from 2 to 3 sec., must not be violent or internal organs 
 may be injured. The lower part of the chest and also the abdomen are 
 thus compressed, and the air is forced out of the lungs. 
 
 Now immediately swing backward so as to remove the pressure, but 
 leave your hands in place, thus returning to the position shown in Fig. 6. 
 
SAFETY AND FIRST AID 
 
 971 
 
 Through their elasticity, the chest walls expand and the lungs are thus 
 supplied with fresh air. 
 
 After 2 sec. swing forward again. Thus repeat deliberately 12 to 15 times 
 a minute the double movement of compression and release; a complete 
 respiration in 4 or 5 sec. If a watch or clock is not visible, follow the natural 
 rate of your own deep breathing; swing forward with each expiration, and 
 backward with each inspiration. While this is being done, an assistant 
 should loosen any tight clothing about the subject's neck, chest, or waist. 
 
 FIG. 
 
 Continue artificial respiration, if necessary, 2 hr. or longer without inter- 
 ruption until natural breathing is restored, or until a physician arrives. 
 Even after natural breathing begins carefully watch that it continues. If 
 it stops, start artificial respiration again. During the period of operation, 
 keep the subject warm by applying a proper covering and by laying beside 
 his body bottles or rubber bags filled with warm (not hot) water. The atten- 
 tion to keeping the subject warm should be given by an assistant or assistants. 
 
 FIG. 7 
 
 The Sylvester Method. Loosen clothing. Place the patient on his back 
 with folded coat under the shoulders to extend the neck. Kneel at his head. 
 Grasp the forearms "just below the elbows with each hand. To expand the 
 chest, draw the arms outwards and upwards to the sides of the head, as in Fig. 
 8. To expel the air from the chest, bring patient's arms to sides and front 
 of chest as in Fig. 9, and exert firm compression on lower border of ribs. 
 This should be done 15 times a minute. The tongue, when the patient is in 
 this condition, may drop back. The mouth can be pried open with a stick, 
 and the tongue drawn forwards with the fingers covered with a handkerchief. 
 
972 
 
 SAFETY AND FIRST AID 
 
 With either method of artificial respiration the administration of oxygen 
 can be given at the same time. The tube, preferably, is placed in the nose. 
 If the Draeger pulmotor is at hand, the mask can be adjusted to the face and 
 used synchronously with artificial respiration, or the pulmotor may be used 
 alone. 
 
 Treatment for Electrical Shock. An accidental electric shock usually 
 does not kill at once, but may only stun the victim and for a while stop his 
 breathing. The shock is not likely to be immediately fatal, because: 
 
 FIG. 8 
 
 (A) The conductors may make only a brief and imperfect contact with 
 the body. . 
 
 (B) The skin, unless it is wet, offers high resistance to the current. 
 Hope of restoring the victim lies in prompt and continued use of artificial 
 
 respiration. The reasons for this statement are: 
 
 (A) The body continuously depends on an exchange of air, as shown by 
 the fact that we must breath in and out about 15 times a minute. 
 
 FIG. 9 
 
 (B) If the body is not thus repeatedly supplied with air, suffocation occurs. 
 
 (C) Persons whose breathing has been stopped by electric shock have been 
 restored after artificial respiration has been continued for approximately 
 2 hr. 
 
 Rescue from Electrical Contact. Break the circuit immediately. 
 
 1. With a single quick motion separate the victim from the live conductor. 
 In so doing avoid receiving a shock yourself. Many have, by their care- 
 lessness, received injury in trying to disconnect victims of shock from live 
 conductors. 
 
SAFETY AND FIRST AID 973 
 
 Observe the following precautions: 
 
 (A) Use a dry coat, a dry rope, a dry stick or board, or any other dry non- 
 conductor to move either the victim or the wire, so as to break the electrical 
 contact. Beware of using metal or any moist material. The victim's 
 loose clothing, if dry, may be used to pull him away; do not touch the sole 
 or heels of his shoes while he remains in contact; the nails are dangerous. 
 
 (B) If the body must be touched by your hands, be sure to cover them with 
 rubber gloves, mackintosh, rubber sheeting or dry cloth; or stand on a dry 
 board or on some other insulating surface. If possible, use only one hand. 
 
 If the victim is conducting the current to the ground, and is convulsively 
 clutching the live_conductor, it may be easier to shut off the current by lifting 
 him than by leaving him on the ground and trying to break his grasp. 
 
 2. Open the nearest switch, if that is the quickest way to break the circuit. 
 
 3. If necessary to cut a live wire, use an ax or a hatchet with a dry wooden 
 handle, or properly insulated pliers. 
 
 After release from contact get patient's face or hand in contact with 
 ground, so as to discharge any retained current. Summon a doctor at once. 
 Immediately begin artificial respiration by the Schaeferpr Sylvester methods. 
 
 Fractures. Fractures of bones can be divided into simple and compound. 
 The simple fracture is a break of the bone without an opening to the surface 
 of the skin. A compound fracture is a break of the bone with an opening to 
 the surface of the skin. Fractures of the bones of the arms and legs can 
 usually be detected by the position the limb assumes, and the loss of power 
 and control over the limb. The limb should be straightened gently by pulling 
 on the foot or hand firmly, and fixed in position by padded splints, securely 
 fastened with bandages. 
 
 In compound fractures do not attempt to replace a protruding bone. Cover 
 the wound with sterile dressings and then apply splints. Fractures of the 
 bones of the head and body should be fastened with dressings and bandages. 
 
 In the absence of regular splints, straight pieces of wood of proper length, 
 well padded can be used in emergencies. 
 
 Dislocations. Dress all dislocations of joints in the position they assume 
 with bandages drawn only sufficiently tight to render the transportation of 
 the patient less painful. 
 
 Drowning. After removal from the water, elevate patient's hips, shake 
 him gently and press on chest as in Shafer method for about 2 min. to 
 allow the water to run out of chest. The mouth should be cleansed and arti- 
 ficial respiration continued for an hour or more. The patient's body should 
 be warmed by the application of hot-water bottles. 
 
 Foreign Body in Eye. Have patient face the light. Examine the eye, 
 when the foreign body is not imbedded, remove it with a clean handkerchief 
 or gauze. Evert the upper lid by taking hold of the lashes, have patient 
 look down and apply pressure with stick to skin of upper lid. The under 
 surface of the upper lid is where most loose foreign bodies are found. Do not 
 try to scrape off imbedded foreign bodies. If a foreign body cannot be 
 removed without scraping wait for a physician. Do not use cocaine. 
 
 Foreign Bodies in Throat. Stand patient on his feet and head and a few 
 smart blows on back will usually dislodge foreign body. 
 
 Foreign Body in Nose. If it cannot be blown out by patient, summon a 
 
 Foreign Body in Ear, Insects, Etc. A teaspoonful of water or olive oil 
 will drown an insect. Hardened wax better be removed by a doctor. 
 
 METHOD OF MOVING INJURED PERSONS 
 
 One Bearer. To lift patient erect: Turn patient on his face. The 
 bearer steps astride body, facing towards head, with hands in arm pits, he 
 lifts the patient to his knees, then clasping hands over abdomen he lifts 
 him to his feet. He then with left hand seizes patient's left wrist (Fig. 10), 
 drawing left arm about his (the bearer's) neck holds it against his lett chest, 
 the patient's left side resting against his body and supports him with his 
 right arm about the waist. 
 
 To Place Patient Across the Back. The bearer with his left hand seizes 
 the right wrist of the patient (Fig. 11) and draws the arm over his head 
 and down upon his left shoulder, then shifting himself in front, stoops and 
 clasps the right thigh with his right arm placed between the legs, his right 
 hand seizing the patient's right wrist; lastly, he, with the left hand grasps the 
 patient's left hand and steadies it against his side, when he rises. 
 
 To place patient across shoulder: The bearer clasps his hands about the 
 
974 
 
 SAFETY AND FIRST AID 
 
 patient's waist, shifts himself to the front, facing him, and stooping places his 
 right shoulder against the abdomen; he passes his right hand and arm be- 
 tween the thighs (Fig 12), securing the right thigh, and with his left grasps 
 
 FIG. 12 
 
 FIG. 13 
 
 the patient's right hand, bringing it from behind under his (bearer's) left 
 armpit, when, the wrist being firmly grasped by his right hand he rises. This 
 position leaves the left hand free. 
 
 In lowering patient from these positions the motions are reversed. Should 
 a patient be injured in such a manner as to require these motions to be 
 
SAFETY AND FIRST AID 975 
 
 conducted from his right side, instead of left, as laid down, the change is 
 simply one of hands, the motions proceed as directed, substituting right for 
 left, and vice versa. 
 
 By Two Bearers. Bearers face each other on right and left of patient 
 Raise patient to sitting posture, clasp hands behind patient's back, while the 
 other hands are passed under patient's thighs and fingers interlocked as in 
 Fig. 13. Athird bearer can support the legs. 
 
 By Three Bearers. Lay patient on back; the bearers kneel on knees 
 nearest the patient's feet. Pass arms under shoulders, hips and knees 
 Raise patient to bearers' knees; bearers rise and carry patient facing them 
 in elbows. To lower patient to litter, reverse movements. 
 
 Emergency Supplies. Accidents very commonly happen where supplies 
 are not available for proper treatment of injuries. In such cases make- 
 shifts may be devised from material at hand. Splints may be made from 
 
 FIG. 14 
 
 strips of bark removed from a post; by splitting a post or cap; from the 
 staves of nail or spike kegs; from powder kegs cut in strips with an ax, and 
 even thin and long pieces of slate, sprags, etc. Bandages for holding splints 
 in place may be improvised from clothing torn into strips. 
 
 A very common form of emergency stretcher is made from two coats as 
 shown in Fig. 14. The sleeves of two coats are turned inside out and the 
 coats placed on the ground with their lower edges touching. A pole or long 
 drill is placed through the sleeves on each side, the coats are buttoned up and 
 the buttoned side turned down. This stretcher is commonly made by one 
 man grasping a drill in either hand, and his companion pulling his coat off 
 over his head. Stretchers may be made from doors, plank nailed together, 
 etc., but the coat-stretcher described above is probably the easiest and 
 quickest to make and the most comfortable for the injured person. 
 
 MINE SAFETY 
 
 Safety First. Although the motto of "safety first" has been generally 
 adopted by many American' coal mining firms it may or 1 may not have a real 
 significance. Unless this or a similar motto is to be strictly lived up to it is 
 better not adopted. The chief cause of mining accidents is of course falls of 
 roof and coal. These can be guarded against only by vigilance, care and an 
 adequate amount of carefully placed timber. 
 
 Systematic Timbering. The roofs of mines differ widely from one field to 
 another and even frequently in different mines of the same field or even in 
 different portions of the same mine. Experience has demonstrated that it 
 is often safer to set an excess of timbers, that is, more than is deemed neces- 
 sary under the existing conditions than to trust to the judgment of even 
 experienced men. The spacing of such timbering will vary considerably 
 throughout different fields but will in the main bear a considerable resem- 
 blance to Fig. 1 which has proved eminently successful in the prevention 
 of accidents in the Pocahontas field of West Virginia. No props or timbers 
 as a general rule should ever be set without cap pieces. 
 
 Adequate Supervision. Experience has proved that to attain the greatest 
 measure of safety to the mine workers adequate supervision must be given to 
 each working face. For this purpose one assistant mine foreman (sometimes 
 called face foreman or roof inspector) should be employed for each 20 to 40 
 men, this number varying somewhat with natural conditions and with the 
 area over which the miners are scattered. The fundamental idea of employ- 
 ing the assistant mine foreman is that he shall be able to visit each working 
 face within the territory intrusted to his care at least twice during each 
 shift. It is his duty whenever he sees a dangerous condition of any kind, 
 
976 
 
 MINE SAFETY 
 
 whether from loose coal, loose roof, inadequate timbering or what not, not 
 only to instruct the workmen in that place to rectify the condition at once 
 but to himself remain until the dangerous condition has been rendered 
 absolutely safe. 
 
 The Premium System and Company Rules. In order to encourage the 
 foremen and assistant foremen to be constantly on the alert for danger and 
 dangerous practices and to see to it that the laws of the state and the rules of 
 the company are implicitly obeyed, one plan which has been adopted is a 
 premium system arranged on a merit and demerit basis so that the official 
 
 who has a clean record, that 
 is, one without a serious or 
 fatal accident, is paid a bonus 
 at the end of the month. If 
 this record is clean for six 
 months a special bonusis paid 
 which continues monthly as 
 long as the record is clean. 
 The United States Coal & 
 Coke Co., with works in Mc- 
 Dowell County W. Va., which 
 js has adopted this system with 
 " marked success, furnishes 
 each foreman and assistant 
 foreman with a book of in- 
 structions which he is sup- 
 posed to carry at all times 
 and which contains the rules 
 of the company which he is 
 expected to see obeyed. 
 Although many of these rules 
 may be considered as being 
 applicable only to the field in 
 question several of the more 
 important ones are here 
 given. Doubtless many 
 others will suggest them- 
 selves to wide awake officials 
 operating in other localities. 
 The last breakthrough of 
 every pair of headings, 
 whether working or not, 
 must have at least 12,000 
 cu. ft. of air per min. passing 
 through it. 
 
 Assistant foremen must 
 examine each working place 
 in their district, and mark 
 each place visited with date 
 of month before allowing men 
 
 Where cars nlder 
 this one are used: 
 clearances must be kept- 
 the same. 
 
 Where necessary, fempora 
 posts must be Set to 
 protect loaders rrftite 
 ^loading out 
 ^-. If any additional 
 % posts arereauired 
 
 FIG. 1 
 
 to enter them. Each idle place must also be examined each day and a record 
 of the examination must be made daily in the book provided for this purpose. 
 
 When the fan has been stopped for 1 hr. or more for any reason, all places 
 must be thoroughly examined by assistant foremen before allowing men to 
 enter them and a record of the examination must be made in the record book. 
 All permanent brattices must be built of incombustible material, con- 
 crete preferred. 
 
 _ Air measurements must be made weekly and be recorded in the book pro- 
 vided for that purpose. 
 
 Assistant foremen must carry Pieler testing lamps when making examina- 
 tions, and all final tests for gas must be made with this lamp. When an 
 ordinary safety lamp will not detect gas, try the Pieler lamp. 
 
 The presence of dust, as well as gas, must be noted in the record book. 
 
 Dust must not be allowed to accumulate in working places nor anywhere 
 in the mine. 
 
 All dusty places on haulage roads must be sprinkled daily. 
 
 No charge of any explosive in any hole shall exceed 2 Ib. 
 
 Assistant foremen must not fire any shot that is improperly drilled, 
 drilled on the solid, or improperly tamped. 
 
MINE SAFETY 
 
 977 
 
 An assistant foreman must not fire any shot within 3 hr. after detecting gas 
 in any place in his district. 
 
 Where more than one shot is to be fired in any place, one shot only shall be 
 charged, tamped and fired, and an examination of the place must be made 
 before firing the second or following shots. Only one shot shall be fired at a 
 time. Assistant foremen must carefully examine working places after shoot- 
 ing before allowing work to begin. 
 
 Ail trolley frogs are to be placed directly aboys 
 point where, irjside of .curvzd rait, /s &rrom 
 inside of main line rait. 
 
 FIG. 2 
 
 No explosives except flameless explosives approved by the U. S. Bureau of 
 Mines shall be used. 
 
 If necessary, water dust at working face before shooting. 
 
 Shots must be fired by battery and not from machine or trolley wire. 
 
 All haulage roads on which more than one car is hauled per trip shall be 
 at least 5 ft. high above the rail, and there shall be at least 2$ ft. clearance 
 between any part of a car, and the side of the heading at all places. 
 
 ?C --.. 
 
 t. X' 
 
 300 Ft. Radius, Hangers 6'F'rom Track 
 
 250 ft. Radius, Hangers 6'Frotn Track 
 
 J50 Ft. Rad'ius , Hangers 6From Trac 
 
 100 F+. Radius, Hangers 6 From Track 
 FIG. 3 
 
 All rash, slate, etc., is to be kept cleaned off haulage roads. 
 
 Permanent track must be bonded as it is laid. 
 
 Where any dangerous slate is found, an assistant foreman must take it 
 down at once before work is done near it or anyone or any trip allowed to 
 pass under it. 
 
 Loaders must post their working places. Proper arrangement and placing 
 of caps, posts, etc., is shown on standard plan which must be strictly followed. 
 Posts must be set in straight lines and be vertical. Cap pieces must be 
 wedged tightly against roof with wedge between post and cap. 
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 ^:?^?is^^^^$S5$ 
 
 MINE SAFETY 
 
 Assistant foremen must 
 not O. K. nor allow any 
 place to be cut where 
 posts are more than 6 it. 
 from the face at the bot- 
 tom. 
 
 No permanent timber- 
 ing will be allowed on 
 haulage roads ^ unless 
 under special instruc- 
 tions from the general 
 superintendent. 
 
 Loaders must clean up 
 slate falls in their work- 
 ing places, and must be 
 paid extra for this work. 
 The general arrange- 
 ment of hangers, etc., 
 for trolley wire is shown 
 on accompanying plans 
 (see Figs. 2, 3, 4 and 5) 
 which must be strictly 
 followed. 
 
 ^ . Trolley wire must be 
 ^g hung 6 in. outside of rail 
 ^iu,o and must be as nearly 
 1 5 parallel to it, both hori- 
 zontally and vertically as 
 it can be. 
 
 Feeder cables must be 
 supported at intervals of 
 20 ft. on barn hangers 
 and special " Gem " insu- 
 lators. Cables are to be 
 . placed 12 in. outside of trolley lines, 
 ** and must be connected to them at in- 
 tervals of 200 ft. Cables must be 
 properly dead ended with cable clamps 
 and insulated turn buckles. 
 
 All insulated cables and wires must 
 be kept free from grounds, same as 
 bare wires. 
 
 All men must be checked in and out 
 of the mine each day. 
 
 All work excepting such repairs as 
 cannot be done while operating or at 
 night must be suspended on Sundays. 
 No machinery of any kind must be 
 allowed to operate unless all gears and 
 dangerous portions are fully guarded. 
 Safeguarding Machinery. The 
 second greatest cause of accidents in 
 & i coal mines results directly or indi- 
 ^S>5 rectly from machinery, mechanical 
 PJJ devices, electrical conductors, etc. 
 ;^ Although there are many exceptions, 
 ;5z accidents with machinery generally 
 ;5 arise from one or more of five causes: 
 g (o) Falls from ladders, platforms, 
 !<*< runways, etc., around machines. 
 '= = (6) Coming into contact with mov- 
 * =. ing machine parts. 
 zo (c) Electric shocks. 
 r 5 W The failure of a machine part. 
 (e) Mismanipulation of hand-oper- 
 zo ated controlling devices (valves, levers, 
 0:= switches, etc.). 
 << The remedy for the[class of accidents 
 
MINE SAFETY 
 
 979 
 
 under (a) is simple and if 
 carefully executed, quite 
 effective. Ladders, stag- 
 ings, platforms, runways, 
 etc., should be made 
 abundantly strong to 
 carry any weight which 
 may be placed upon 
 them; ample railings 
 should be provided on all 
 platforms, stairways, 
 etc., and non-slipping 
 feet on movable ladders. 
 Coming into contact 
 with moving elements of 
 machines is a prolific 
 source of mining acci- 
 dent. When buying new 
 machinery it is wise to 
 specify that such ma- 
 chines should be properly 
 safeguarded before deliv- 
 ery. Particularly danger- 
 ous are explosed gear 
 trains, revolving l)olt 
 heads, set screws, splines, 
 open keyways and the 
 like. Such machine parts 
 should be eliminated so 
 far as possible, e.g., 
 ordinary square-head set 
 screws should be replaced 
 with hollow flush-head 
 set screws. In addition, 
 revolving or moving dan- 
 gerous machine parts 
 should be thoroughly 
 guarded. Guards for 
 machine parts or ma- 
 chines in general may be 
 of many materials and 
 many types of construc- 
 tion. Wooden guards 
 are vastly better than 
 none. Pipe or structural 
 shape railings _ have a 
 legitimate application in 
 safeguarding belts, silent 
 chains and the like. 
 Probably the most satis- 
 factory guards are, how- 
 ever, constructed of a 
 structural shape frame- 
 work over which heavy 
 woven wire or expanded 
 metal is placed. _ Such 
 guards are shown in Figs. 
 6, 7, 8, 9 and 10. Some 
 firms have constructed 
 quite efficient guards as 
 well as some presenting a 
 respectable appearance 
 from worn-out perforated 
 plates used on shaker 
 screens. For this pur- 
 pose, however, the per- 
 forations should not ex- 
 ceed about 2 5 in. in diam- 
 
980 
 
 MINE SAFETY 
 
 Experience has proved 
 o which access is neces- 
 
 eter as a larger opening may admit a man's hand. 
 
 that it is better to make the guarding of machinery to wnicn access is neces- 
 sary for oiling, etc., a little difficult of removal rather than extremely easy 
 to take apart. If it is too easily removed, it may not be replaced. 
 
 Protecting from Electricity. Generally speaking an air gap of sufficient 
 width is a sure protection against electric shocks. The only safe way in 
 which to treat an electrical conductor, regardless of insulation or the voltage 
 carried, is to consider it as if it carried a high potential and was devoid of all 
 insulation. Trolley wires may be portected from accidental contact by 
 trolley guard boards, a good type of which is shown in Fig. 5. In all locations 
 where men may pass under such wires during the day's work, as at turnouts, 
 such boards should always be placed. 
 
 The failure of machine parts is an accident which it is difficult to antici- 
 pate. There is practically no means of determining the existence of a flaw in 
 a welded pipe or a cold shut in a cast fitting. The danger from the failure of 
 
 FIGS. 6 TO 8 
 
 such parts is in many instances quite as much from the release of the fluid 
 carried (steam, air, hot water, etc.), as from flying fragments. In certain 
 instances breaking parts, dangerous in themselves, may be rendered harmless 
 by the installation of proper shields or retainers. Probably the best known 
 of such devices are water glass protectors on boilers and safety collars on 
 emery wheels. 
 
 Preventing Mismanipulation of Controlling Devices. Many machines, 
 machine parts and electrical equipment cause accidents through mismanipu- 
 lation. Among these might be mentioned overwinds, the closing of electric 
 circuits while men are repairing parts thereof; the unintentional opening of 
 valves allowing steam or hot water to enter boilers in which repair men are at 
 work, and the like. Overwinds may be prevented by reliable overwind pre- 
 ventors or regulating devices attached to the engine which will not allow a 
 safe speed to be exceeded or the landing to be passed. Many such devices 
 are on the market. Switches controlling electric circuits should be provided 
 with means for locking them open, the key being carried by the chief repair 
 man. In the case of such circuits as trolleys or the cables feeding them an 
 additional precaution consists in placing an intentional temporary short 
 circuit, e.g., a crowbar, mine drill, piece of wire, etc., between the trolley and 
 the rail a few yards away from the repair men in the direction of the power 
 supply. Valves leading to the interior of boilers, feed-water heaters and the 
 like wherein repairs are being made should either be locked in the closed posi- 
 tion by means of a chain and padlock or some other means should be taken 
 
Tfghfener Pulle 
 ttotor Pulley -- 
 
 981 
 
 DETAILS OF6UARD 
 FIG. 10 
 
982 MINE SAFETY 
 
 which will render it impossible for either steam or hot water to be turned in 
 upon them. 
 
 The foregoing are only a few suggestions of the many means which may be 
 employed to insure the safety of workers around coal mines. Many others 
 will doubtless suggest themselves and be found advisable to install under 
 specific circumstances. 
 
 Safety Practices of the H. C. Frick Coke Co. In the proceedings of the 
 American Institute of Mining Engineers, vol. 51, page 345, Thomas W. 
 Dawson gives the following r6sum6 of the safety practices employed by the 
 H. C. Frick Coke Co. These are all well worthy of careful consideration by 
 the official who really wishes to make his mines as safe as possible. 
 
 Every official and foreman of the company is continually impressed with 
 the fact that "safety" should be the first consideration, and all officials and 
 their subordinates are brought together as one great committee on safety. 
 Pamphlets showing the duties of the miner and the manner in which he may 
 protect himself from danger and giving safety regulations for those working 
 around machinery have been printed and generally distributed. Permanent 
 danger signs are placed wherever there is the least possibility of an accident. 
 When men are working in shafts, the " Men in Shaft" sign is placed so that 
 no accident can be caused by mistake in moving cages. A similar sign is 
 placed on hoisting engines and other machinery when it is being repaired. 
 When workmen are cleaning or making repairs to the inside of a boiler, a 
 "Man in the Boiler" sign is displayed outside and the steam valve for this 
 boiler is locked and the key carried by one of the men until the work is 
 completed. When coke-drawing machines are being repaired or cleaned, the 
 "Do Not Move" sign is placed on the controller and the trolley wheel is 
 locked and the key carried by one of the repair men until the work is finished. 
 "No Clearance" signs are conspicuously displayed at all points about the 
 plants where there is no clearance for a man between moving cars and ob- 
 structions of any character. Bridge guards and overhead warning signs are 
 placed wherever needed. 
 
 In the mines, guide signs in various languages are posted at road junctions 
 and on traveling ways, indicating the safest way out of the mine. 
 
 All machinery is safely guarded. These guards include locking devices 
 for handwheels of valves, safety locks for electric switches, guards for water 
 gauges; safety gaskets to be inserted in steam blow-off and feed- water con- 
 nections when cleaning and repairing boilers; safety locking device for self- 
 dumping cages; soap lubrication for air compressors; wagon guard and 
 dumping platform for swing-gate mine cars; spooling device for tail ropes on 
 haulages; stiles or protected crossings over rope and sheaves where necessary 
 for men to pass; improved safety catch for cages; device for positively 
 rectifying wagon catches on car hauls; self-closing hinges for shaft gates ; steel 
 galleries for runways over boilers, and safety platforms for operating electric 
 larries. "Do Not Touch " signs are used about electric wires, indicating vol- 
 tage of ^current; and "Do Not Pass Under" signs are used where there is 
 danger in passing underneath structures. Steel doors are provided to drop 
 over shafts which have wooden head frames or coal bins above them, should 
 these wooden structures catch fire. The company has originated a device 
 for automatically controlling high-pressure air compressors. When the tem- 
 perature of the discharge air in the pipe reaches a predetermined point, 
 showing that the pressure is excessively high, it acts on the thermometer and 
 recording device, thus closing an electric circuit and energizing a solenoid. 
 This moves over a tripping device, which opens the pilot valve, releasing the 
 steam pressure on one side of the regulating piston. Thereby the valve on 
 the steam feed pipe is automatically closed, shutting off the steam and 
 stopping the compressor. 
 
 All hoisting engines are equipped with an automatic overwinding device, 
 which acts directly on the engine, cutting off the steam and applying the 
 brakes. 
 
 When it is necessary to clean the sump at the bottom of the shaft, the 
 cages are hoisted to a clearance height and secured by iron pins, through holes 
 in the guides; these pins are attached to the guides by chains, which prevent 
 their removal when not in use. 
 
 At the surface landings of all shaft mines, a device is installed which pre- 
 vents the gates from being opened when the cage is not in position at the 
 landing. All hoisting compartments of shafts are lined at the cage ends. 
 All cages and safety catches are periodically inspected, tested, and a written 
 report made of the inspection. In no case is a hoisting rope kept in service 
 
MINE SAFETY 983 
 
 longer than 2\ yr., even though apparently safe and in good condition. Fre- 
 quent inspection of air shafts must be made to keep them open and free at 
 all times from ice and other obstructions. A fire boss must make this exami- 
 nation and travel either up or down such shaft once each day, the mine fore- 
 men once each two weeks, and the superintendent once a month. 
 
 The company's rules require that in mines generating explosive gas not less 
 than 500 cu. ft. of air per min. per person employed in the mine shall be 
 provided at the intake and this must be so distributed that there will not be 
 less than 300 cu. ft. per min. per person employed in each split at the working 
 faces. No mine shall have at the intake less than 300 cu. ft. of air per min. 
 per person employed, and at the working places at least 150 cu. ft. per min. 
 per person employed. Measurements of air supplied are carefully made and 
 reported to the general office once each week. Local officials at mines gen- 
 erating gas are required to keep air up to the working faces and to such other 
 places where explosive gas might be encountered. At a number of the larger 
 and more recent plants, the ventilating fan is operated by two engines, one 
 on each end, and either of them powerful enough to operate the fan in case of 
 failure of the other. All ventilating systems in the mines are ascensional. 
 
 The Clowes hydrogen test lamp is used in all mines generating gas, for 
 testing purposes. Samples of air are taken in gaseous mines and sent in 
 copper cans to the company's laboratory, where they are analyzed. The 
 results of the analyses are reported to the general office and to the mine. If 
 these show a percentage of explosive gas which might have been detected by 
 the Clowes lamp, the party making the test and reporting no gas is required 
 to make an explanation. 
 
 Boreholes are frequently drilled from the surface to release any dangerous 
 accumulations of explosive gas in the gob, where these cannot be remoyed by 
 the mine ventilation. Shot firers have been employed to do all blasting by 
 battery, and inspect all places where shots have been fired to see that there is 
 no fire or other danger thereafter. Only the safest permissible explosives are 
 used, and all tamping is done with clay. 
 
 All safety-lamp mines are examined on Sundays, holidays and lay-off days, 
 and all mines which have been idle for more than two consecutive days are 
 examined before operations are renewed. In the larger mines, wherever 
 safety lamps are used, auxiliary escapeways are provided. In some instances 
 these are stair shafts from the surface to the mine, placed in the active work- 
 ing sections, and used also for additional ventilation. In other cases, means 
 of escape are provided by having connections between mines, which are closed 
 by double iron doors. Frequent examinations are made to see that these 
 doors are always in condition for use. Where coal dust occurs, a system of 
 pipes and a supply of water under sufficient head and all necessary appliances 
 are provided to dampen thoroughly the floor, sides, and roof of all parts of 
 dry mines. 
 
 On rope haulage, a device is provided for disengaging the rope from the trip 
 as soon as it is given slack. Brakes are provided for all mine cars and 2^ ft. 
 clearance is provided on all haulageways on one side; this side being indicated 
 by a wide whitewashed strip on the rib. _ 
 
 Systematic timbering systems are demised and strictly followed. Printed 
 regulations cover the system of timbering in rooms, headings, and in rib and 
 pillar drawing; these are worked out to suit conditions at the various mines. 
 Timbering is not set without caps or cross-bars. 
 
 All mines have complete mine-telephone systems. Stables, pump rooms, 
 haulage-engine rooms, shaft bottoms, underground offices and all such places 
 where men might congregate are of fireproof construction and are kept clean 
 and neat. No open lights are allowed in any building. Cans are provided 
 for the reception of oily waste, grease, small quantities of oil, etc. All 
 electric wiring is carefully inspected twice each year. All bare power lines 
 underground and on the surface are properly guarded for their entire length 
 by a neat wooden guard, so as to prevent the workman or his tools from com- 
 ing in contact with the same. For the same reason, trolley wires for coke- 
 drawing machines are placed at a sufficient height to make contact with tools 
 unlikely. A system of checking men in and out of the workings is maintained 
 at all of the mines. All abandoned places in the mines are fenced off. 
 
 The company employs four mine inspectors, one of them acting as cruet. 
 It is the duty of these men to visit each mine and thoroughly inspect it at 
 least once every 60 days. When an accident occurs in or about any mine, 
 the chief mine inspector promptly visits the scene of the" accident, gathers all 
 of the data he can relative thereto and makes a sketch of the surroundings. 
 
984 MINE SAFETY 
 
 This sketch is put into permanent form, blueprinted and sent to each mine 
 with a circular letter, giving a full account of the accident and making sug- 
 gestions for the prevention of similar ones. This is discussed at the meeting 
 of the local officials at each plant. Once each week, the superintendent of 
 each plant and his subordinates meet and discuss mine conditions and opera- 
 tions in general and especially matters pertaining to the safety of their 
 employees. The discussions of these meetings are reported to the General 
 Superintendent each week. General meetings are held at stated intervals at 
 the general office, which are attended by the superintendent of each plant and 
 .heads of departments. 
 
 Projections for mine workings are made far in advance of the actual work, 
 and the haulage and ventilating problems are planned so that when the mine 
 is developed the best system is in use. Specifications are written for each 
 mine, stating where and how the mining is to be done. The officials of the 
 company make detailed inspections at intervals, insuring that their instruc- 
 tions and the best methods are actually followed. 
 
 A safety committee of three or four men is appointed at each mine, which 
 inspects periodically the working places, roadways, ventilation and any other 
 things which in its opinion might be the cause of an accident. The com- 
 mittee reports in writing to the superintendent of the mine, who forwards the 
 same to the general office. These suggestions are immediately acted upon 
 and all dangers reported, should there be any, are removed as quickly as 
 possible. . Three rescue and first-aid stations are maintained at the different 
 plants of the company, which are fully" equipped with the best apparatus and 
 accessories obtainable. About 400 men have been thoroughly trained and 
 qualified in both rescue and first-aid work, local contests being held by the 
 different teams at various times. 
 
 Emergency hospitals, fully equipped, have been provided at a number of 
 the largest mines. 
 
 Tests are made frequently for gas above roof falls in gobs. Work is 
 prohibited in any place in which gas is found, until after it has been removed. 
 Mine inspectors instruct all new employees about the dangers of their work. 
 
 MINE-RESCUE WORK 
 
 Mine-rescue work is usually understood to mean the rescue of men or the 
 recovery of bodies after a mine explosion, mine fire or other disaster. In the 
 case of explosions or fires it implies the use of so-called rescue apparatus 
 consisting of oxygen helmets, mouth-breathing apparatus, etc. 
 
 Organization. The organization for mine-rescue work will differ so 
 widely with local conditions that but little may be said on the subject in a 
 book of this kind. Careful preparation and training of a rescue crew here 
 means everything. While rescue work may be undertaken by untrained 
 men it is necessarily much slower and more dangerous than where a well- 
 trained, well-disciplined and thoroughly reliable team of helmet men are at 
 hand. As to the selection, organization and training of a helmet crew the U. 
 S. Bureau of Mines has done much valuable work along this line, and every 
 mine or group of mines under one management should avail itself of the in- 
 struction, training and advice of the mine-rescue experts on the various 
 mine-rescue cars maintained by the government. At least four helmets and 
 preferably six should be available at all times for immediate use, and the 
 organization of the team should be such that not more than half its members 
 should be underground at any one time, that is, with a rescue team contain- 
 ing 12 men, 6 should at all times be available for instant call to service, and 
 at least 4 of these should be thoroughly familiar with the underground work- 
 ings. All should be men of good physique, sound heart and of known re- 
 liability, nerve and coolness. 
 
 First Steps after a Disaster. It is extremely important that immediately 
 upon the occurrence of a mine disaster, such as an explosion, that the proper 
 steps toward rescue be taken promptly. Here again much will depend upon 
 circumstances and local conditions, but in a general sense the following is 
 necessary. Call the helmet men together, summon aid from nearby mines, 
 summon the nearest government mine-rescue car. It is important that 
 exploration work start as promptly as possible. Consequently the helmet 
 men should precede all others into the mine. There are two other important 
 considerations which require careful attention; the ventilation must be 
 restored as quickly as possible and the means of communicating with the 
 underground workings must be kept intact or repaired immediately. If the 
 mine is a shaft operation the hoisting cages if damaged should be repaired as 
 
MINE SAFETY 935 
 
 quickly as possible or if this is out of the question a temporary means of rais- 
 ing and lowering men and material must be had. For this purpose some 
 mines keep on hand an emergency cage so that if the regular cages are put 
 out of commission, men at least may still be raised and lowered by the 
 emergency apparatus. 
 
 Reversing the Air Current. An explosion usually causes more or less 
 havoc with the underground ventilating system, that is, brattices are fre- 
 quently destroyed, stoppings broken down, etc. There is a wide diversity of 
 opinion among engineers and mine men in general concerning the advisability 
 of reversing the air current, that is, changing a blowing fan to an exhauster and 
 vice versa after a mine disaster. This is a question, the expediency of which 
 had better be thought out before the explosion occurs, or in any instance the 
 current should not be reversed without due and careful consideration. Men 
 attempting to find their way out of the mine after a disaster are apt to be 
 guided largely by the air current flowing. They are in utter darkness unless 
 of course they be provided with safety lamps or electric lamps and will 
 naturally move against the air current. If this current is reversed it will in 
 many instances drive the foul and poisonous gases resulting from the explo- 
 sion directly upon them. There may however be instances wherein it would 
 be advisable to reverse the current. 
 
 The Work of Recovery. Mine-rescue and recovery work requires above 
 all else a strong and careful leader. This leader should if possible be known 
 at least by reputation to all the men engaged in the work. He should be a 
 man whom all- can respect and trust. 
 
 After it has been ascertained that the fan is in working order and at work 
 (an auxiliary fan may be used if necessary), and a means of access to the 
 mine is established, the helmet men with their mice, canaries or qther means of 
 testing the gas may enter the mine. These men are to the main body of the 
 rescuers what the scouts are to an army inlarge measure at least they con- 
 stitute the department of security and information. Their work will be to 
 explore the mine, ascertain the presence of dangerous gas and bring to a 
 point of safety any living men that may be found. Unhelmeted men should 
 follow them, restoring the ventilation as they go. This usually requires t the 
 building of a considerable amount of temporary bratticework and stoppings 
 and material therefor (boards, plank, posts, canvass, nails, spikes, etc.) 
 must be provided. No one should be allowed to enter the mine merely 
 through curiosity. Whoever enters should be immediately put to work. 
 The person directing recovery work may do so either from the surface, the 
 foot of the shaft or some other convenient point, communicating with his 
 various lieutenants either by word of mouth, by telephone if possible or in 
 some instances by messenger at frequent intervals. 
 
 The person directing rescue and recovery work should be careful in his 
 selection of lieutenants. The ventilation apparatus is perhaps the most 
 important of all machinery. It must be kept going, or if a shutdown is 
 absolutely necessary, this must be anticipated, a sufficient amount of time to 
 allow all men, helmeted as well as unhelmeted to be withdrawn, from the mine 
 before the air current is actually stopped. It is well therefore to place an 
 experienced man at the fan, whose sole duty it shall be to keep it in opera- 
 tion. If necessary, this man should have all the helpers he may require. 
 The hoisting apparatus is also important, but if possible the regular hoist man 
 should stick to his post. There should be appointed a gang whose duty 
 should be to secure and bring to the mouth of the mine the materials neces- 
 sary for bratticing. If the mine is electrically lighted a competent electrician 
 with a requisite number of helpers should be put to work repairing or estab- 
 lishing lighting conditions. The brattice men fol^wing the helmet crew 
 should be under an experienced brattice builder who is competent to see that 
 the work is done properly and rapidly; in many instances also a man with 
 such assistance as he may need may be employed to transport the various 
 materials from the mine entrance to the point where they are needed. 
 Furthermore, since mine rescue work usually lasts for several hours or even 
 days a commissary department should be established so that food such as 
 sandwiches, hot soup and particularly hot coffee may be served to the men 
 at work at regular intervals and the coffee whenever they desire it. Men 
 skilled in first aid as well as physicians should also be on hand to give prompt 
 and efficient treatment to any men that may be found alive. The helmet 
 men will of course remove few if any dead bodies so long as there is even hope 
 of finding living people in the mine. Once a man is found alive he should be 
 promptly taken to a point where at least reasonably pure air is available. 
 
986 
 
 MINE SAFETY 
 
 In selecting his lieutenants heading the various gangs or groups of men 
 above mentioned, the" man in charge should use careful discretion and dele- 
 
 ate to each subordinate the work with which that particular man is most 
 familiar. Thus a mine official of even high standing such as a superintendent 
 might be given a job of caging at the ground landing if he were known to 
 have had successful previous experience at that kind of work. The man in 
 charge of the transporting of material from the shaft bottom to the point of 
 use might be a mine superintendent or he might be a motor boss, depending 
 on his previous experience in the transportation department. The main idea 
 is that every man in charge of a gang should know the work which he is 
 called upon to do, know it well and be a person that can be depended upon. 
 The success of mine-rescue work, that is, the recovery of living men, will often 
 depend much upon the coolness, good judgment and persistence of the man 
 or men in charge of this work. The careful mine official will therefore think 
 out and decide many possible mine-rescue problems before the actual time of 
 disaster arrives. _ 
 
 MINE-RESCUE APPARATUS 
 
 Mine-rescue apparatus, so-called, is of two general types: (a) breathing 
 apparatus, used by the rescue crew, and (b) resuscitation apparatus used by 
 or rather on the people. recovered. 
 
 Breathing Apparatus. There are two types of breathing apparatus in 
 general use in the United States. These are known respectively as helmet 
 apparatus and mouth-breathing apparatus. The helmet apparatus consists 
 or a metal helmet which may be strapped over the face and be rendered air- 
 tight by an inflatable gasket which fits under the chin and extends upwards 
 completely encircling the front portion of the head or by other means. 
 
 PIG. 1 
 
 The rear portion of the head is protected by a leather apron. The mouth- 
 breathing apparatus is exactly similar except that in place of the helmet a 
 mouthpiece which is provided with a device to close the nostrils of the nose 
 is strapped onto the head. The oxygen containers, pipes, breathing bag and 
 regenerator are at least similar if not identical in the two types and sometimes 
 are made interchangeable. 
 
 The operation of the instrument is simple and may be readily understood 
 from the diagrammatic drawing Fig. 1. The oxygen tanks A A are connected 
 together and the flow of oxygen is regulated by the valve B. Opening this 
 valve allows the compressed oxygen in the tanks to flow to the pressure 
 gauge C and to the reducing valve D, which is fitted with a safety valve E. 
 The oxygen is reduced to a predetermined pressure in the regulating valve 
 and next passes to the injector F. It then flows through the pipe G to the 
 inhalation compartment of breathing bag H and from thence to the mouth- 
 piece or helmet. After being exhaled from the lungs the gas passes to a 
 
MINE SAFETY 
 
 987 
 
 second compartment or exhalation bag / which is part and parcel of the 
 inhalation bag but separated therefrom by a partition. From here it passes 
 through the pipe J to the regenerator. This is provided with potash in a 
 granular form which is arranged in wire gauze trays around which the exhaled 
 oxygen passes and from which the carbon dioxide is absorbed by the chem- 
 ical. It then passes through the pipe K to the injector where it is reoxygen- 
 ated and again passed to the breathing bag // to be inhaled. Under ordinary 
 conditions the oxygen tanks contain sufficient compressed oxygen for 2 hr. 
 of hard work. A smaller regenerator is sometimes employed for practice 
 work in the smoke. room, thus reducing the cost of each practice. When the 
 mouth-breathing apparatus is used, it is advisable to supply the wearer with 
 smoke goggles to protect the eyes in case work is being done in any gas which 
 would tend to irritate them. 
 
 The operation of the helmet is practically the same as that of the mouth- 
 breathing apparatus above described except that the helmet is substituted 
 in place of the mouthpiece. The mouth-breathing . - 
 
 apparatus is somewhat lighter and simpler 'both in 
 construction and operation than is the helmet. The 
 helmet, however, possesses the advantage of allowing 
 the wearer to talk with his companions which is diffi- 
 cult, if not impossible, with the mouth-breathing 
 apparatus. 
 
 Oxygen for use with mine-rescue apparatus may be 
 purchased in large cylinders from whence it may be 
 transferred to the small cartridges of the breathing 
 apparatus by means of a suitable hand pump. Such 
 pumps are usually made double-acting and will com- 
 press the oxygen in the small tanks to approximately 
 120 atmospheres. 
 
 Self Rescuer. A small type of breathing apparatus 
 for use in noxious or poisonous gases and holding a 
 charge of oxygen sufficient for 30 min. work is known 
 as ^ the self rescuer. This apparatus is compact, 
 weighs about 6J. lb., can be quickly adjusted to the 
 wearer and does not require previous training. This 
 apparatus is shown diagramatically in Fig. 2. Here 
 5 represents the oxygen cylinder, U the closing valve, 
 P the potash or regenerating cartridge, A the breath- 
 ing bag, L the respiration pipe which is provided with 
 the rubber mouthpiece M. The apparatus is sus- 
 pended by a strap around the neck while a canvas 
 apron fastened around the waist holds the apparatus 
 in place. The exhaled air flows through the respira- 
 tion pipe L into the regenerator P where it is subjected to the action of 
 the carbon-dioxide-absorbihg chemicals. Freed from the products of respira- 
 tion the air enters the breathing bag A where a fresh oxygen supply is pro- 
 vided from the cylinder S. The regenerated air is again drawn through 
 the potash cartridge where it is once more subjected to purification and 
 is inhaled through the pipe L. Care must be taken with any of these instru- 
 ments to provide fresh potash cartridges for regenerating the air. Fresh 
 cartridges when shaken will rattle, spent ones will not. 
 
 Resuscitation Apparatus. In cases of partial asphyxiation from poisonous 
 gas or drowning, severe electric shock, etc., a means of compelling the patient 
 to breathe is necessary. This may be supplied either by artificial respiration 
 according to the Schaefer or Sylvester method or by some variety of re- 
 suscitation apparatus. One of the simplest of resuscitation apparatuses is 
 shown in Fig. 3 and is known as the lungmotor. This may be arranged to 
 administer either atmospheric air only or atmospheric air enriched with oxy- 
 gen either from a charged tank or an oxygen generator, or pure 9xygen from 
 the same source. The lungmotor consists of two-air pumps which are oper- 
 ated simultaneously but which are connected together only by the two flexi- 
 ble tubes leading to the face mask. After the face mask has been adjusted 
 and strapped in place and the adjustment for the size of the patient made 
 by turning the pin A so as to give the proper length of stroke to the two 
 pumps the handle of the machine is simply worked up and down at the normal 
 rapidity of breathing; the operator may judge this from his own respiration. 
 Air is thus gently but positively forced into and withdrawn from the patient's 
 lungs, the lungs meanwhile being maintained at their normal inflation. In 
 
 FIG. 2 
 
MINE SAFETY 
 
 FIG. 4 
 
NATURAL SINES AND COSINES 989 
 
 case it is desired to administer to the patient an atmosphere richer in oxygen 
 than atmospheric air a charged tank of oxygen or an oxygen generator may 
 be connected to the nipple C which forms the oxygen inlet. An adjustment 
 of the mixing valve B renders it possible to administer all air, all oxygen, or 
 any desired mixture^of the two. This apparatus is light, positive in action, 
 easily portable and is not dependent for operation upon a supply of oxygen 
 either compressed in tanks or generated as required. 
 
 Another type of apparatus which has been used to a considerable extent 
 is known as the pulmotor. The motive power for this machine is the oxygen 
 compressed in the cylinder C (see Fig. 4). When the valve V is opened the 
 full pressure of the oxygen in the tank is exerted upon valve D. _ It is here 
 reduced to 75 Ib. per sq. in. and at this pressure passes to the injector 5. 
 Here the oxygen is fed at the rate of cu. ft. per min. through the tube L. 
 The injector is so arranged, 'however, that while accomplishing this function 
 it will create a suction through a line connected to the outside air, thus 
 drawing in a large volume of atmospheric air, mixing it with the oxygen and 
 forcing it through tube E to the lungs, which are represented by the bag at 
 the bottom of the figure. This action continues until the lungs are inflated 
 to a measured amount. There being no valve or other obstruction to 
 prevent, this increase of pressure acts through the tube A which leads to the 
 bellows B. As soon as the pressure attains .29 Ib. per sq. in. this pressure 
 forces the head of the bellows outward reversing the pulmotor valve L 
 through the medium of a tension spring. The suction action of the nozzle 
 5 is now cut off from the outside circuit and is carried through the return air 
 tube A which is connected through the face mask to the lungs. Air from the 
 lungs is thus exhausted to the outside air until a proper vacuum amounting 
 to .37 Ib. per sq. in. is developed in the lungs, when the bellows contracts 
 under the action of the vacuum throwing the valve back to its original posi- 
 tion and starting the cycle of operations over again. This action proceeds at 
 the rate of from 14 to 18 strokes per min. 
 
 The entire equipment, including^ several sizes of face masks, is packed in a 
 wooden carrying case for convenience in transportation. This apparatus 
 has the advantage of being automatic in action but is somewhat complicated. 
 It has, however, been used to a wide extent and with considerable success. 
 
 TABLE OF NATURAL SINES, COSINES, 
 TANGENTS, AND COTANGENTS 
 
 EXPLANATION 
 
 Given an angle, to find its sine, cosine, tangent, and cotangent 
 
 To find the sine, cosine, tangent, and cotangent of 37 24', look in the table 
 of natural sines along the tops of the pages, and find 37. Glancing down the 
 left-hand column marked ('), until 24 is found, find opposite this 24 in the 
 column marked sine and headed 37, the number .60738; then .60738 = 
 sin 37 24'. Similarly, find in the column marked cosine and headed 37, 
 the number .79441, which corresponds to cos 37 24'. So, also, find in the 
 column marked tangent and headed 37, and opposite 24', the number 
 .76456; and in the column marked cotangent and headed 37, and opposite 
 24', the number 1.30795. 
 
 In most of the tables published, the angles run only from to 45 at the 
 heads of the columns; to find an angle greater than 45, look at the bottom oj 
 the. page and glance upwards, using the extreme right-hand column to find 
 minutes, which begin with at the bottom and run upwards, 1, 2, 3, etc., 
 
 To find the sine of 77 43', look along the bottom of the tables until the 
 column marked sine and marked 77 is found. Glancing up the column of 
 minutes on the right until 43' is found, find opposite 43' in the column marked 
 sine at the bottom and marked 77, the number .97711; this is the sine of 
 77 43'. Similarly, the cosine, tangent, and cotangent may be found. 
 
 To find the sine, cosine, tangent, or cotangent of an angle whose exact 
 value is not given in the table: 
 
f 
 
 990 NATURAL SINES AND COSINES 
 
 Rule. Find in the table the sine, cosine, tangent, or cotangent corresponding 
 to the degrees and minutes of the angle. For the seconds, find the difference of 
 the values of the sine, cosine, tangent, or cotangent taken from the table between 
 which the seconds of the angle fall; multiply this difference by a fraction whose 
 numerator is the number of seconds in the given angle and whose denominator 
 is 60. 
 
 // sine or tangent, add this correction to the value first found; if cosine or 
 cotangent, subtract the correction. 
 
 EXAMPLE. Find the sine, cosine, tangent, and cotangent of 56 43' 17". 
 
 SOLUTION. Sin 56 43' = .83597. Sin 56 44' = .83613. As 56 43' 17" 
 is greater than 56 43' and less than 56 44', the value of the sine of the angle 
 lies between .83597 and .83613; the difference equals .83613 - .83597 = 
 .00016; multiplying this by the fraction JJ, .00016 X H = .00005, nearly, 
 which is to be added to .83597, the value first found, or .83597 + .00005 = 
 .83602. Hence, sin 56 43' 17" = .83602. 
 
 Cos 56 43' = .54878; cos 56 44' = .54854; the difference equals .54878 
 .54854 = .00024, and .00024 X II = .00007, nearly. Now, as the cosine 
 is desired, this correction must be subtracted from cos 56 43', or .54878; 
 subtraction, .54878 - .00007 = .54871. Hence, cos 56 43' 17" = .54871. 
 Given the sine, cosine, tangent, or cotangent, to find the angle corresponding 
 
 If the sine of an angle is .47486; what is the angle? Consulting the table 
 of natural sines, glance down the columns marked sine until .47486 is found, 
 opposite 21' in the left-hand column and under the column headed 28. 
 Therefore, the angle whose sine = .47486 is 28 21', or sin 28 21' = .47486. 
 
 To find the angle corresponding to a given sine, cosine, tangent, or co- 
 tangent whose exact value is not contained in the table: 
 
 Rule. Find the difference of the two numbers in the table between which the 
 given sine, cosine, tangent, or cotangent falls, and use the number of parts in 
 this difference as the denominator of a fraction. 
 
 Find the difference between the number belonging to the smaller angle and the 
 given sine, cosine, tangent, or cotangent, and use the number of parts in the dif- 
 ference just found as the numerator of the ftaction just mentioned. Multiply 
 this fraction by 60, and the result will be the number of seconds to be added to the 
 smaller angle. 
 
 EXAMPLE. Find the angle whose sine equals .57698. 
 
 SOLUTION. Looking in the table of natural sines, in the column marked 
 sine, it is found between .57691 = sin 35 14' and .57715 = 35 15'. The 
 difference between them is .57715 - .57691 = .00024, or 24 parts. The 
 difference between the sine of the smaller angle, or sine 35 14' = .57691, 
 and the given sine, or .57698, is .57698 .57691 = .00007, or 7 parts. 
 
 Then, / 4 X 60 = 17.5", and the angle = 35 14' 17.5", or sin 35 14' 17.5" 
 = .57698. 
 
 The cosecant of an angle is equal to the reciprocal of its sine, and the 
 secant is equal to the reciprocal of its cosine. Hence, to multiply a quantity 
 
 by the cosecant, divide it by the sine; or, to divide it by the cosecant, multi- 
 ply it by the sine. Similarly, to multiply a quantity by the secant of an 
 angle, divide it by the cosine; or, to divide it by the secant, multiply it by 
 
NATURAL SINES AND COSINES 
 
 991 
 
 / 
 
 fl 
 
 P 
 
 1 
 
 
 
 2 
 
 
 
 5 
 
 
 
 4 
 
 
 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .00000 
 
 1. 
 
 .01745 
 
 .99985 
 
 .03490 
 
 .99939 
 
 .05234 
 
 .99863 
 
 .06976 
 
 .99756 
 
 60 
 
 1 
 
 .00029 
 
 1. 
 
 .01774 
 
 .99984 
 
 .03519 
 
 .99938 
 
 .05263 
 
 .99861 
 
 .07005 
 
 .99754 
 
 59 
 
 2 
 
 .00058 
 
 
 .01803 
 
 .99984 
 
 .03548 
 
 .99937 
 
 .05292 
 
 .99860 
 
 .07034 
 
 .99752 
 
 58 
 
 3 
 
 .00087 
 
 
 .01832 
 
 .99983 
 
 .03577 
 
 .99936 
 
 .05321 
 
 .99858 
 
 .07063 
 
 .99750 
 
 57 
 
 4 
 
 .00116 
 
 
 .01862 
 
 .99983 " 
 
 .03606 
 
 .99935 
 
 .05350 
 
 .99857 
 
 .07092 
 
 .99748 
 
 56 
 
 5 
 
 .00145 
 
 
 .01891 
 
 .99982 
 
 .03635 
 
 .99934 
 
 .05379 
 
 .99855 
 
 .07121 
 
 .99746 
 
 55 
 
 6 
 
 .00175 
 
 
 .01920 
 
 .99982 
 
 .03664 
 
 .99933 
 
 .05408 
 
 .99854 
 
 .07150 
 
 .99744 
 
 54 
 
 7 
 
 .00204 
 
 
 .01949 
 
 .99981 
 
 .03693 
 
 .99932 
 
 .05437 
 
 .99852 
 
 .07179 
 
 .99742 
 
 53 
 
 8 
 
 .00233 
 
 
 .01978 
 
 .99980 
 
 .03723 
 
 .99931 
 
 .05466 
 
 .99851 
 
 .07208 
 
 .99740 
 
 52 
 
 9 
 
 .00262 
 
 
 .02007 
 
 .99980 
 
 .03752 
 
 .99930 
 
 .05495 
 
 .99849 
 
 .07237 
 
 .99738 
 
 51 
 
 10 
 
 .00291 
 
 
 .02036 
 
 .99979 
 
 .03781 
 
 .99929 
 
 .05524 
 
 .99847 
 
 .07266 
 
 .99736 
 
 50 
 
 11 
 
 .00320 
 
 .99999 
 
 .02065 
 
 .99979 
 
 .03810 
 
 .99927 
 
 .05553 
 
 .99846 
 
 .07295 
 
 .99734 
 
 49 
 
 12 
 
 .00349 
 
 .99999 
 
 .02094 
 
 .99978 
 
 .03839 
 
 .99926 
 
 .05582 
 
 .99844 
 
 .07324 
 
 .99731 
 
 48 
 
 13 
 
 .00378 
 
 .99999 
 
 .02123 
 
 .99977 
 
 .03868 
 
 .99925 
 
 .05611 
 
 .99842 
 
 .07353 
 
 .99729 
 
 47 
 
 14 
 
 .00407 
 
 .99999 
 
 .02152 
 
 .99977 
 
 .03897 
 
 .99924 
 
 .05640 
 
 .99841 
 
 .07382 
 
 .99727 
 
 46 
 
 15 
 
 .00436 
 
 .99999 
 
 .02181 
 
 .99976 
 
 .03926 
 
 .99923 
 
 .05669 
 
 .99839 
 
 .07411 
 
 .99725 
 
 45 
 
 16 
 
 .00465 
 
 .99999 
 
 .02211 
 
 .99976 
 
 .03955 
 
 .99922 
 
 .05698 
 
 99838 
 
 .07440 
 
 .99723 
 
 44 
 
 17 
 
 .00495 
 
 .99999 
 
 .02240 
 
 .99975 
 
 .03984 
 
 .99921 
 
 .05727 
 
 .99836 
 
 .07469 
 
 .99721 
 
 43 
 
 18 
 
 .00524 
 
 .99999 
 
 .02269 
 
 .99974 
 
 .04013 
 
 .99919 
 
 .05756 
 
 .99834 
 
 .07498 
 
 .99719 
 
 42 
 
 19 
 
 .00553 
 
 .99998 
 
 .02298 
 
 .99974 
 
 .04042 
 
 .99918 
 
 .05785 
 
 .99833 
 
 .07527 
 
 .99716 
 
 41 
 
 20 
 
 .00582 
 
 .99998 
 
 .02327 
 
 .99973 
 
 .04071 
 
 .99917 
 
 .05814 
 
 .99831 
 
 .07556 
 
 .99714 
 
 40 
 
 21 
 
 .00611 
 
 .99998 
 
 .02356 
 
 .99972 
 
 .04100 
 
 .99916 
 
 .05844 
 
 .99829 
 
 .07585 
 
 .99712 
 
 39 
 
 22 
 
 .00640 
 
 .99998 
 
 .02385 
 
 .99972 
 
 .04129 
 
 .99915 
 
 .05873 
 
 .99827 
 
 .07614 
 
 .99710 
 
 38 
 
 23 
 
 .00669 
 
 .99998 
 
 .02414 
 
 .99971 
 
 .04159 
 
 .99913 
 
 .05902 
 
 .99826 
 
 .07643 
 
 .99708 
 
 37 
 
 24 
 
 .00698 
 
 .99998 
 
 .02443 
 
 .99970 
 
 .04188 
 
 .99912 
 
 .05931 
 
 .99824 
 
 .07672 
 
 .99705 
 
 36 
 
 25 
 
 .00727 
 
 .99997 
 
 .02472 
 
 .99969 
 
 .04217 
 
 .99911 
 
 .05960 
 
 .99822 
 
 .07701 
 
 .99703 
 
 35 
 
 26 
 
 .00756 
 
 .99997 
 
 .02501 
 
 .99969 
 
 .04246 
 
 .99910 
 
 .05989 
 
 .99821 
 
 .07730 
 
 .99701 
 
 34 
 
 27 
 
 .00785 
 
 .99997 
 
 .02530 
 
 .99968 
 
 .04275 
 
 .99909 
 
 .06018 
 
 .99819 
 
 .07759 
 
 
 33 
 
 28 
 
 .00814 
 
 .99997 
 
 .02560 
 
 .99967 
 
 .04304 
 
 .99907 
 
 .06047 
 
 .99817 
 
 .07788 
 
 [99696 
 
 32 
 
 29 
 
 .00844 
 
 .99996 
 
 .02589 
 
 .99966 
 
 .04333 
 
 .99906 
 
 .06076 
 
 .99815 
 
 .07817 
 
 .99694 
 
 31 
 
 30 
 
 .00873 
 
 .99996 
 
 .02618 
 
 .99966 
 
 .04362 
 
 .99905 
 
 .06105 
 
 .99813 
 
 .07846 
 
 .99692 
 
 30 
 
 31 
 
 .00902 
 
 .99996 
 
 .02647 
 
 .99965 
 
 .04391 
 
 .99904 
 
 .06134 
 
 .99812 
 
 .07875 
 
 .99689 
 
 29 
 
 32 
 
 .00931 
 
 .99996 
 
 .02676 
 
 .99964 
 
 .04420 
 
 .99902 
 
 .06163 
 
 .99810 
 
 .07904 
 
 .99687 
 
 28 
 
 33 
 
 .00960 
 
 .99995 
 
 .02705 
 
 .99963 
 
 .04449 
 
 .99901 
 
 .06192 
 
 .99808 
 
 .07933 
 
 .99685 
 
 27 
 
 34 
 
 .00989 
 
 .99995 
 
 .02734 
 
 .99963 
 
 .04478 
 
 .99900 
 
 .06221 
 
 .99806 
 
 .07962 
 
 .99683 
 
 26 
 
 35 
 
 .01018 
 
 .99995 
 
 .02763 
 
 .99962 
 
 .04507 
 
 .99898 
 
 .06250 
 
 .99804 
 
 .07991 
 
 .99680 
 
 25 
 
 36 
 
 .01047 
 
 .99995 
 
 .02792 
 
 .99961 
 
 .04536 
 
 .99897 
 
 .06279 
 
 .99803 
 
 .08020 
 
 .99678 
 
 24 
 
 37 
 
 .01076 
 
 .99994 
 
 .02821 
 
 .99960 
 
 .04565 
 
 .99896 
 
 .06308 
 
 .99801 
 
 .08049 
 
 .99676 
 
 23 
 
 38 
 
 .01105 
 
 .99994 
 
 .02850 
 
 .99959 
 
 .04594 
 
 .99894 
 
 .06337 
 
 .99799 
 
 .08078 
 
 .99673 
 
 22 
 
 39 
 
 .01134 
 
 .99994 
 
 .02879 
 
 .99959 
 
 .04623 
 
 .99893 
 
 .06366 
 
 .99797 
 
 .08107 
 
 .99671 
 
 21 
 
 40 
 
 .01164 
 
 .99993 
 
 .02908 
 
 .99958 
 
 .04653 
 
 .99892 
 
 .06395 
 
 .99795 
 
 .08136 
 
 .99668 
 
 20 
 
 41 
 
 .01193 
 
 .99993 
 
 .02938 
 
 .99957 
 
 .04682 
 
 .99890 
 
 .06424 
 
 .99793 
 
 .08165 
 
 .99666 
 
 19 
 
 42 
 
 .01222 
 
 .99993 
 
 .02967 
 
 .99956 
 
 .04711 
 
 .99889 
 
 .06453 
 
 .99792 
 
 .08194 
 
 .99664 
 
 18 
 
 43 
 
 .01251 
 
 .99992 
 
 .02996 
 
 
 .04740 
 
 .99888 
 
 .06482 
 
 .99790 
 
 .08223 
 
 .99661 
 
 17 
 
 44 
 
 .01280 
 
 .99992 
 
 .03025 
 
 ;99954 
 
 .04769 
 
 .99886 
 
 .06511 
 
 .99788 
 
 .08252 
 
 .99659 
 
 16 
 
 45 
 
 .01309 
 
 .99991 
 
 .03054 
 
 .99953 
 
 .04798 
 
 .99885 
 
 .06540 
 
 .99786 
 
 .08281 
 
 .99657 
 
 15 
 
 46 
 
 .01338 
 
 .99991 
 
 .03083 
 
 .99952 
 
 .04827 
 
 .99883 
 
 .06569 
 
 .99784 
 
 .08310 
 
 .99654 
 
 14 
 
 47 
 
 .01367 
 
 .99991 
 
 .03112 
 
 .99952 
 
 .04856 
 
 [99882 
 
 .06598 
 
 .99782 
 
 .08339 
 
 .99652 
 
 13 
 
 48 
 
 .01396 
 
 .99990 
 
 .03141 
 
 .99951 
 
 .04885 
 
 
 .06627 
 
 .99780 
 
 .08368 
 
 .99649 
 
 12 
 
 49 
 
 .01425 
 
 .99990 
 
 .03170 
 
 .99950 
 
 .04914 
 
 [99879 
 
 .06656 
 
 .99778 
 
 .08397 
 
 .99647 
 
 11 
 
 50 
 
 .01454 
 
 .99989 
 
 .03199 
 
 .99949 
 
 .04943 
 
 .99878 
 
 .06685 
 
 .99776 
 
 .08426 
 
 .99644 
 
 10 
 
 51 
 
 .01483 
 
 .99989 
 
 .03228 
 
 .99948 
 
 .04972 
 
 .99876 
 
 .06714 
 
 .99774 
 
 .08455 
 
 .99642 
 
 
 52 
 
 .01513 
 
 .99989 
 
 .03257 
 
 .99947 
 
 .05001 
 
 .99875 
 
 .06743 
 
 .99772 
 
 .08484 
 
 .99639 
 
 
 53 
 
 .01542 
 
 .99988 
 
 .03286 
 
 .99946 
 
 .05030 
 
 .99873 
 
 .06773 
 
 .99770- 
 
 .08513 
 
 .99637 
 
 
 54 
 
 .01571 
 
 .99988 
 
 .03316 
 
 .99945 
 
 .05059 
 
 .99872 
 
 .06802 
 
 .99768 
 
 .08542 
 
 .99635 
 
 
 55 
 
 .01600 
 
 .99987 
 
 .03345 
 
 .99944 
 
 .05088 
 
 .99870 
 
 .06831 
 
 .99766 
 
 .08571 
 
 .99632 
 
 
 56 
 
 .01629 
 
 .99987 
 
 .03374 
 
 .99943 
 
 .05117 
 
 .99869 
 
 .06860 
 
 .99764 
 
 .08600 
 
 .99630 
 
 
 57 
 
 .01658 
 
 .99986 
 
 .03403 
 
 .99942 
 
 .05146 
 
 .99867 
 
 .06889 
 
 .99762 
 
 .08629 
 
 .99627 
 
 
 58 
 
 .01687 
 
 .99986 
 
 .03432 
 
 .99941 
 
 .05175 
 
 .99866 
 
 .06918 
 
 .99760 
 
 .08658 
 
 .99625 
 
 
 59 
 
 .01716 
 
 .99985 
 
 .03461 
 
 
 .05205 
 
 .99864 
 
 .06947 
 
 .99758 
 
 .08687 
 
 .99622 
 
 
 60 
 
 .01745 
 
 .99985 
 
 .03490 
 
 !99939 
 
 .05234 
 
 .99863 
 
 .06976 
 
 .99756 
 
 .08716 
 
 .99619 
 
 
 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 81 
 
 > 
 
 
 
 ; 
 
 8 1 ; 
 
 
 
 8( 
 
 ) 
 
 8 
 
 
 
 
992 
 
 NATURAL SINES AND COSINES 
 
 
 5 
 
 6 
 
 70 
 
 8 
 
 9 
 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .08716 
 
 .99619 
 
 .10453 
 
 .99452 
 
 .12187 
 
 .99255 
 
 .13917 
 
 .99027 
 
 .15643 
 
 .98769 
 
 60 
 
 1 
 
 .08745 
 
 .99617 
 
 .10482 
 
 .99449 
 
 .12216 
 
 .99251 
 
 .13946 
 
 .99023 
 
 .15672 
 
 .98764 
 
 59 
 
 2 
 
 .08774 
 
 .99614 
 
 .10511 
 
 .99446 
 
 .12245 
 
 .99248 
 
 .13975 
 
 .99019 
 
 .15701 
 
 .98760 
 
 58 
 
 3 
 
 .08803 
 
 .99612 
 
 .10540 
 
 .99443 
 
 .12274 
 
 .99244 
 
 .14004 
 
 .99015 
 
 .15730 
 
 .98755 
 
 57 
 
 4 
 
 .08831 
 
 .99609 
 
 .10569 
 
 .99440 
 
 .12302 
 
 .99240 
 
 .14033 
 
 .99011 
 
 .15758 
 
 .98751 
 
 56 
 
 5 
 
 .08860 
 
 .99607 
 
 .10597 
 
 .99437 
 
 .12331 
 
 .99237 
 
 .14061 
 
 .99006 
 
 .15787 
 
 .98746 
 
 55 
 
 6 
 
 .08889 
 
 .99604 
 
 .10626 
 
 .99434 
 
 .12360 
 
 .99233 
 
 .14090 
 
 .99002 
 
 .15816 
 
 .98741 
 
 54 
 
 7 
 
 .08918 
 
 .99602 
 
 .10655 
 
 .99431 
 
 .12389 
 
 .99230 
 
 .14119 
 
 .98998 
 
 .15845 
 
 .98737 
 
 53 
 
 8 
 
 .08947 
 
 .99599 
 
 .10684 
 
 .99428 
 
 .12418 
 
 .99226 
 
 .14148 
 
 .98994 
 
 .15873 
 
 .98732 
 
 52 
 
 9 
 
 .08976 
 
 .99596 
 
 .10713 
 
 .99424 
 
 .12447 
 
 .99222 
 
 .14177 
 
 .98990 
 
 .15902 
 
 .98728 
 
 51 
 
 10 
 
 .09005 
 
 .99594 
 
 .10742 
 
 .99421 
 
 .12476 
 
 .99219 
 
 .14205 
 
 .98986 
 
 .15931 
 
 .98723 
 
 50 
 
 11 
 
 .09034 
 
 .99591 
 
 .10771 
 
 .99418 
 
 .12504 
 
 .99215 
 
 .14234 
 
 .98982 
 
 .15959 
 
 .98718 
 
 49 
 
 12 
 
 .09063 
 
 .99588 
 
 .10800 
 
 .99415 
 
 .12533 
 
 .99211 
 
 .14263 
 
 .98978 
 
 .15988 
 
 98714 
 
 48 
 
 13 
 
 .09092 
 
 .99586 
 
 .10829 
 
 .99412 
 
 .12562 
 
 .99208 
 
 .14292 
 
 .98973 
 
 .16017 
 
 .98709 
 
 47 
 
 14 
 
 .09121 
 
 .99583 
 
 .10858 
 
 .99409 
 
 .12591 
 
 .99204 
 
 .14320 
 
 .98969 
 
 .16046 
 
 .98704 
 
 46 
 
 15 
 
 .09150 
 
 .99580 
 
 .10887 
 
 .99406 
 
 .12620 
 
 .99200 
 
 .14349 
 
 .98965 
 
 .16074 
 
 .98700 
 
 45 
 
 16 
 
 .09179 
 
 .99578 
 
 .10916 
 
 .99402 
 
 .12649 
 
 .99197 
 
 .14378 
 
 .98961 
 
 .16103 
 
 .98695 
 
 44 
 
 17 
 
 .09208 
 
 .99575 
 
 .10945 
 
 .99399 
 
 .12678 
 
 .99193 
 
 .14407 
 
 .98957 
 
 .16132 
 
 .98690 
 
 43 
 
 18 
 
 .09237 
 
 .99572 
 
 .10973 
 
 .99396 
 
 .12706 
 
 .99189 
 
 .14436 
 
 .98953 
 
 .16160 
 
 .98686 
 
 42 
 
 19 
 
 .09266 
 
 .99570 
 
 .11002 
 
 .99393 
 
 .12735 
 
 .99186 
 
 .14464 
 
 .98948 
 
 .16189 
 
 .98681 
 
 41 
 
 20 
 
 .09295 
 
 .99567 
 
 .11031 
 
 .99390 
 
 .12764 
 
 .99182 
 
 .14493 
 
 .98944 
 
 .16218 
 
 .98676 
 
 40 
 
 21 
 
 .09324 
 
 .99564 
 
 .11060 
 
 .99386 
 
 .12793 
 
 .99178 
 
 .14522 
 
 .98940 
 
 .16246 
 
 .98671 
 
 39 
 
 22 
 
 .09353 
 
 .99562 
 
 .11089 
 
 .99383 
 
 .12822 
 
 .99175 
 
 .14551 
 
 .98936 
 
 .16275 
 
 .98667 
 
 38 
 
 23 
 
 .09382 
 
 .99559 
 
 .11118 
 
 .99380 
 
 .12851 
 
 .99171 
 
 .14580 
 
 .98931 
 
 .16304 
 
 .98662 
 
 37 
 
 24 
 
 .09411 
 
 .99556 
 
 .11147 
 
 .99377 
 
 .12880 
 
 .99167 
 
 .14608 
 
 .98927 
 
 .16333 
 
 .98657 
 
 36 
 
 26 
 
 .09440 
 
 .99553 
 
 .11176 
 
 .99374 
 
 .12908 
 
 .99163 
 
 .14637 
 
 .98923 
 
 .16361 
 
 .98652 
 
 35 
 
 26 
 
 .09469 
 
 .99551 
 
 .11205 
 
 .99370 
 
 .12937 
 
 .99160 
 
 .14666 
 
 .98919 
 
 .16390 
 
 .98648 
 
 34 
 
 2T 
 
 .09498 
 
 .99548 
 
 .11234 
 
 .99367 
 
 .12966 
 
 .99156 
 
 .14695 
 
 .98914 
 
 .16419 
 
 .98643 
 
 33 
 
 28 
 
 .09527 
 
 .99545 
 
 .11263 
 
 .99364 
 
 .12995 
 
 .99152 
 
 .14723 
 
 .98910 
 
 .16447 
 
 .98638 
 
 32 
 
 29 
 
 .09556 
 
 .99542 
 
 .11291 
 
 .99360 
 
 .13024 
 
 .99148 
 
 .14752 
 
 .98906 
 
 .16476 
 
 .98633 
 
 31 
 
 30 
 
 .09585 
 
 .99540 
 
 .11320 
 
 .99357 
 
 .13053 
 
 .99144 
 
 .14781 
 
 .98902 
 
 .16505 
 
 .98629 
 
 30 
 
 31 
 
 .09614 
 
 .99537 
 
 .11349 
 
 .99354 
 
 .13081 
 
 .99141 
 
 .14810 
 
 .98897 
 
 .16533 
 
 .98624 
 
 29 
 
 32 
 
 .09642 
 
 .99534 
 
 .11378 
 
 .99351 
 
 .13110 
 
 .99137 
 
 .14838 
 
 .98893 
 
 .16562 
 
 .98619 
 
 S8 
 
 33 
 
 .09671 
 
 .99531 
 
 .11407 
 
 .99347 
 
 .13139 
 
 .99133 
 
 .14867 
 
 .98889 
 
 .16591 
 
 .98614 
 
 27 
 
 34 
 
 .09700 
 
 .99528 
 
 .11436 
 
 .99344 
 
 .13168 
 
 .99129 
 
 .14896 
 
 .98884 
 
 .16620 
 
 .98609 
 
 26 
 
 35 
 
 .09729 
 
 .99526 
 
 .11465 
 
 .99341 
 
 .13197 
 
 .99125 
 
 .14925 
 
 .98880 
 
 .16648 
 
 .98604 
 
 25 
 
 36 
 
 .09758 
 
 .99523 
 
 .11494 
 
 .99337 
 
 .13226 
 
 .99122 
 
 .14954 
 
 .98876 
 
 .16677 
 
 .98600 
 
 24 
 
 37 
 
 .09787 
 
 .99520 
 
 .11523 
 
 .99334 
 
 .13254 
 
 .99118 
 
 .14982 
 
 .98871 
 
 .16706 
 
 .98595 
 
 23 
 
 33 
 
 .09816 
 
 .99517 
 
 .11552 
 
 .99331 
 
 .13283 
 
 .99114 
 
 .15011 
 
 .98867 
 
 .16734 
 
 .98590 
 
 22 
 
 39 
 
 .09845 
 
 .99514 
 
 .11580 
 
 .99327 
 
 .13312 
 
 .99110 
 
 .15040 
 
 .98863 
 
 .16763 
 
 .98585 
 
 21 
 
 40 
 
 .09874 
 
 .99511 
 
 .11609 
 
 .99324 
 
 .13341 
 
 .99106 
 
 .15069 
 
 .98858 
 
 .16792 
 
 .98580 
 
 20 
 
 41 
 
 .09903 
 
 .99508 
 
 .11638 
 
 .99320 
 
 .13370 
 
 .99102 
 
 .15097 
 
 .98854 
 
 .16820 
 
 .98575 
 
 19 
 
 42 
 
 .09932 
 
 .99506 
 
 .11667 
 
 .99317 
 
 .18399 
 
 .99098 
 
 .15126 
 
 .98849 
 
 .16849 
 
 .98570 
 
 18 
 
 43 
 
 .09961 
 
 .99503 
 
 .11696 
 
 .99314 
 
 .13427 
 
 .99094 
 
 .15155 
 
 .98845 
 
 .16878 
 
 .98565 
 
 17 
 
 44 
 
 .09990 
 
 .99500 
 
 .11725 
 
 .99310 
 
 .13456 
 
 .99091 
 
 .15184 
 
 .98841 
 
 .16906 
 
 .98561 
 
 16 
 
 15 
 
 .10019 
 
 .99497 
 
 .11754 
 
 .99307 
 
 .13485 . 
 
 .99087 
 
 .15212 
 
 .98836 
 
 .16935 
 
 .98556 
 
 15 
 
 46 
 
 .10048 
 
 .99494 
 
 .11783 
 
 .99303 
 
 .13514 
 
 .99083 
 
 .15241 
 
 .98832 
 
 .16964 
 
 .98551 
 
 14 
 
 47 
 
 .10077 
 
 .99491 
 
 .11812 
 
 .99300 
 
 .13543 
 
 .99079 
 
 .15270 
 
 .98827 
 
 .16992 
 
 .98546 
 
 13 
 
 48 
 
 .10106 
 
 .99488 
 
 .11840 
 
 .99297 
 
 .13572 
 
 .99075 
 
 .15299 
 
 .98823 
 
 .17021 
 
 .98541 
 
 12 
 
 49 
 
 .10135 
 
 .99485 
 
 .11869 
 
 .99293 
 
 .13600 
 
 .99071 
 
 .15327 
 
 .98818 
 
 .17050 
 
 .98536 
 
 11 
 
 50 
 
 .10164 
 
 .99482 
 
 .11898 
 
 .99290 
 
 .13629 
 
 .99067 
 
 .15356 
 
 .98814 
 
 .17078 
 
 .98531 
 
 10 
 
 51 
 
 .10192 
 
 .99479 
 
 .11927 
 
 .99286 
 
 .13658 
 
 .99063 
 
 .15385 
 
 .98809 
 
 .17107 
 
 .98526 
 
 9 
 
 52 
 
 .10221 
 
 .99476 
 
 .11956 
 
 .99283 
 
 .13687 
 
 .99059 
 
 .15414 
 
 .98805 
 
 .17136 
 
 .98521 
 
 8 
 
 53 
 
 .10250 
 
 .99473 
 
 .11985 
 
 .99279 
 
 .13716 
 
 .99055 
 
 .15442 
 
 .98800 
 
 .17164 
 
 .98516 
 
 7 
 
 54 
 
 .10279 
 
 .99470 
 
 .12014 
 
 .99276 
 
 .13744 
 
 .99051 
 
 .15471 
 
 .98796 
 
 .17193 
 
 .98511 
 
 6 
 
 55 
 
 .10308 
 
 .99467 
 
 .12043 
 
 .99272 
 
 .13773 
 
 .99047 
 
 .15500 
 
 .98791 
 
 .17222 
 
 .98506 
 
 5 
 
 56 
 
 .10337 
 
 .99464 
 
 .12071 
 
 .99269 
 
 .13802 
 
 .99043 
 
 .15529 
 
 .98787 
 
 .17250 
 
 .98501 
 
 4 
 
 57 
 
 .10366 
 
 .99461 
 
 .12100 
 
 .99265 
 
 .13831 
 
 .99039 
 
 .15557 
 
 .98782 
 
 .17279 
 
 .984% 
 
 3 
 
 58 
 
 .10395 
 
 .99458 
 
 .12129 
 
 .99262 
 
 .13860 
 
 .99035 
 
 .15586 
 
 .98778 
 
 .17308 
 
 .98491 
 
 2 
 
 59 
 
 .10424 
 
 .99455 
 
 .12158 
 
 .99258 
 
 .13889 
 
 .99031 
 
 .15615 
 
 .98773 
 
 .17336 
 
 .98486 
 
 
 60 
 
 .10453 
 
 .99452 
 
 .12187 
 
 .99255 
 
 .13917 
 
 .99027 
 
 .15643 
 
 .98769 
 
 .17365 
 
 .98481 
 
 
 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 84 
 
 83 
 
 82 
 
 81 
 
 80 
 
 
NATURAL SINES AND COSINES 
 
 993 
 
 / 
 
 1 
 
 [) 
 
 1 
 
 1 
 
 1 
 
 2 
 
 1 
 
 3 
 
 1 
 
 4 
 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .17365 
 
 .98481 
 
 .19081 
 
 .98163 
 
 .20791 
 
 .97815 
 
 .22495 
 
 .97437 
 
 .24192 
 
 .97030 
 
 60 
 
 1 
 
 .17393 
 
 .98476 
 
 .19109 
 
 .98157 
 
 .20820 
 
 .97809 
 
 .22523 
 
 .97430 
 
 .24220 
 
 .97023 
 
 59 
 
 2 
 
 .17422 
 
 .98471 
 
 .19138 
 
 .98152 
 
 .20848 
 
 .97803 
 
 .22552 
 
 .97424 
 
 .24249 
 
 .97015 
 
 58 
 
 3 
 
 .17451 
 
 .98466 
 
 .19167 
 
 .98146 
 
 .20877 
 
 .97797 
 
 .22580 
 
 .97417 
 
 .24277 
 
 .97008 
 
 57 
 
 4 
 
 .17479 
 
 .98461 
 
 .19195 
 
 .98140 
 
 .20905 
 
 .97791 
 
 .22608 
 
 .97411 
 
 .24305 
 
 .97001 
 
 56 
 
 5 
 
 .17508 
 
 .98455 
 
 .19224 
 
 .98135 
 
 .20933 
 
 .97784 
 
 .22637 
 
 .97404 
 
 .24333 
 
 .96994 
 
 55 
 
 6 
 
 .17537 
 
 .98450 
 
 .19252 
 
 .98129 
 
 .20962 
 
 .97778 
 
 .22665 
 
 .97398 
 
 .24362 
 
 .96987 
 
 54 
 
 7 
 
 .17565 
 
 .98445 
 
 .19281 
 
 .98124 
 
 .20990 
 
 .97772 
 
 .22693 
 
 .97391 
 
 .24390 
 
 .96980 
 
 53 
 
 8 
 
 .17594 
 
 .98440 
 
 .19309 
 
 .98118 
 
 .21019 
 
 .97766 
 
 .22722 
 
 .97384 
 
 .24418 
 
 .96973 
 
 52 
 
 9 
 
 .17623 
 
 .98435 
 
 .19338 
 
 .98112 
 
 .21047 
 
 .97760 
 
 .22750 
 
 .97378 
 
 .24446 
 
 .96966 
 
 51 
 
 10 
 
 .17651 
 
 .98430 
 
 .19366 
 
 .98107 
 
 .21076 
 
 .97754 
 
 .22778 
 
 .97371 
 
 .24474 
 
 .96959 
 
 50 
 
 11 
 
 .17680 
 
 .98425 
 
 .19395 
 
 .98101 
 
 .21104 
 
 .97748 
 
 .22807 
 
 .97365 
 
 .24503 
 
 .96952 
 
 49 
 
 12 
 
 .17708 
 
 .98420 
 
 .19423 
 
 .98096 
 
 .21132 
 
 .97742 
 
 .22835 
 
 .97358 
 
 .24531 
 
 .96945 
 
 48 
 
 13 
 
 .17737 
 
 .98414 
 
 .19452 
 
 .98090 
 
 .21161 
 
 .97735 
 
 .22863 
 
 .97351 
 
 .24559 
 
 .96937 
 
 47 
 
 14 
 
 .17766 
 
 .98409 
 
 .19481 
 
 .98084 
 
 .21189 
 
 .97729 
 
 .22892 
 
 .97345 
 
 .24587 
 
 .96930 
 
 46 
 
 15 
 
 .17794 
 
 .98404 
 
 .19509 
 
 .98079 
 
 .21218 
 
 .97723 
 
 .22920 
 
 .97338 
 
 .24615 
 
 .96923 
 
 45 
 
 16 
 
 .17823 
 
 .98399 
 
 .19538 
 
 .98073 
 
 .21246 
 
 .97717 
 
 .22948 
 
 .97331 
 
 .24644 
 
 .96916 
 
 44 
 
 17 
 
 .17852 
 
 .98394 
 
 .19566 
 
 .98067 
 
 .21275 
 
 .97711 
 
 .22977 
 
 .97325 
 
 .24672 
 
 .96909 
 
 43 
 
 18 
 
 .17880 
 
 .98389 
 
 .19595 
 
 .98061 
 
 .21303 
 
 .97705 
 
 .23005 
 
 .97318 
 
 .24700 
 
 .96902 
 
 42 
 
 19 
 
 .17909 
 
 .98383 
 
 .19623 
 
 .98056 
 
 .21331 
 
 .97698 
 
 .23033 
 
 .97311 
 
 .24728 
 
 .96894 
 
 41 
 
 20 
 
 .17937 
 
 .98378 
 
 .19652 
 
 .98050 
 
 .21360 
 
 .97692 
 
 .23062 
 
 .97304 
 
 .24756 
 
 .96887 
 
 40 
 
 21 
 
 .17966 
 
 .98373 
 
 .19680 
 
 .98044 
 
 .21388 
 
 .97686 
 
 .23090 
 
 .97298 
 
 .24784 
 
 .96880 
 
 39 
 
 22 
 
 .17995 
 
 .98368 
 
 .19709 
 
 .98039 
 
 .21417 
 
 .97680 
 
 .23118 
 
 .97291 
 
 .24813 
 
 .96873 
 
 38 
 
 23 
 
 .18023 
 
 .98362 
 
 .19737 
 
 .98033 
 
 .21445 
 
 .97673 
 
 .23146 
 
 .97284 
 
 .24841 
 
 .96866 
 
 87 
 
 24 
 
 .18052 
 
 .98357 
 
 .19766 
 
 .98027 
 
 .21474 
 
 .97667 
 
 .23175 
 
 .97278 
 
 .24869 
 
 .96858 
 
 36 
 
 25 
 
 .18081 
 
 .98352 
 
 .19794 
 
 .98021 
 
 .21502 
 
 .97661 
 
 .23203 
 
 .97271 
 
 .24897 
 
 .96851 
 
 35 
 
 26 
 
 .18109 
 
 .98347 
 
 .19823 
 
 .98016 
 
 .21530 
 
 .97655 
 
 .23231 
 
 .97264 
 
 .24925 
 
 .96844 
 
 34 
 
 27 
 
 .18138 
 
 .98341 
 
 .19851 
 
 .98010 
 
 .21559 
 
 .97648 
 
 .23260 
 
 .97257 
 
 .24954 
 
 .96837 
 
 33 
 
 28 
 
 .18166 
 
 .98336 
 
 .19880 
 
 .98004 
 
 .21587 
 
 .97642 
 
 .23288 
 
 .97251 
 
 .24982 
 
 .96829 
 
 32 
 
 29 
 
 .18195 
 
 .98331 
 
 .19908 
 
 .97998 
 
 .21616 
 
 .97636 
 
 .23316 
 
 .97244 
 
 .25010 
 
 .96822 
 
 31 
 
 30 
 
 .18224 
 
 .98325 
 
 .19937 
 
 .97992 
 
 .21644 
 
 .97630 
 
 .23345 
 
 .97237 
 
 .25038 
 
 .96815 
 
 30 
 
 31 
 
 .18252 
 
 .98320 
 
 .19965 
 
 .97987 
 
 .21672 
 
 .97623 
 
 .23373 
 
 .97230 
 
 .25066 
 
 .96807 
 
 29 
 
 32 
 
 .18281 
 
 .98315 
 
 .19994 
 
 .97981 
 
 .21701 
 
 .97617 
 
 .23401 
 
 .97223 
 
 .25094 
 
 .96800 
 
 28 
 
 33 
 
 .18309 
 
 .98310 
 
 .20022 
 
 .97975 
 
 .21729 
 
 .97611 
 
 .23429 
 
 .97217 
 
 .25122 
 
 .96793 
 
 27 
 
 34 
 
 .18338 
 
 .98304 
 
 .20051 
 
 .97969 
 
 .21758 
 
 .97604 
 
 .23458 
 
 .97210 
 
 .25151 
 
 .96786 
 
 26 
 
 35 
 
 .18367 
 
 .98299 
 
 .20079 
 
 .97963 
 
 .21786 
 
 .97598 
 
 .23486 
 
 .97203 
 
 .25179 
 
 .96778 
 
 25 
 
 36 
 
 .18395 
 
 .98294 
 
 .20108 
 
 .97958 
 
 .21814 
 
 .97592 
 
 .23514 
 
 .97196 
 
 .25207 
 
 .96771 
 
 24 
 
 37 
 
 .18424 
 
 .98288 
 
 .20136 
 
 .97952 
 
 .21843 
 
 .97585 
 
 .23542 
 
 .97189 
 
 .25235 
 
 .96764 
 
 23 
 
 38 
 
 .18452 
 
 .98283 
 
 .20165 
 
 .97946 
 
 .21871 
 
 .97579 
 
 .23571 
 
 .97182 
 
 .25263 
 
 .96756 
 
 22 
 
 39 
 
 .18481 
 
 .98277 
 
 .20193 
 
 .97940 
 
 .21899 
 
 .97573 
 
 .23599 
 
 .97176 
 
 .25291 
 
 .96749 
 
 21 
 
 40 
 
 .18509 
 
 .98272 
 
 .20222 
 
 .97934 
 
 .21928 
 
 .97566 
 
 .23627 
 
 .97169 
 
 .25320 
 
 .96742 
 
 20 
 
 41 
 
 .18538 
 
 .98267 
 
 .20250 
 
 .97928 
 
 .21956 
 
 .97560 
 
 .23656 
 
 .97162 
 
 .25348 
 
 .96734 
 
 19 
 
 42 
 
 .18567 
 
 .98261 
 
 .20279 
 
 .97922 
 
 .21985 
 
 .97553 
 
 .23684 
 
 .97155 
 
 .25376 
 
 .96727 
 
 18 
 
 43 
 
 .18595 
 
 .98256 
 
 .20307 
 
 .97916 
 
 .22013 
 
 .97547 
 
 .23712 
 
 .97148 
 
 .25404 
 
 .96719 
 
 17 
 
 44 
 
 .18624 
 
 .98250 
 
 .20336 
 
 .97910 
 
 .22041 
 
 .97541 
 
 .23740 
 
 .97141 
 
 .25432 
 
 .96712 
 
 16 
 
 45 
 
 .18652 
 
 .98245 
 
 .20364 
 
 .97905 
 
 .22070 
 
 .97534 
 
 .23769 
 
 .97134 
 
 .25460 
 
 .96705 
 
 15 
 
 46 
 
 .18681 
 
 .98240 
 
 .20393 
 
 .97899 
 
 .22098 
 
 .97528 
 
 .23797 
 
 .97127 
 
 .25488 
 
 .96697 
 
 14 
 
 47 
 
 .18710 
 
 .98234 
 
 .20421 
 
 .97893 
 
 .22126 
 
 .97521 
 
 .23825 
 
 .97120 
 
 .25516 
 
 .96690 
 
 13 
 
 48 
 
 .18738 
 
 .93229 
 
 .20450 
 
 .97887 
 
 .22155 
 
 .97515 
 
 .23853 
 
 .97113 
 
 .25545 
 
 .96682 
 
 12 
 
 49 
 50 
 
 .18767 
 .18795 
 
 .98223 
 .98218 
 
 .20478 
 .20507 
 
 .97881 
 .97875 
 
 .22183 
 .22212 
 
 .97508 
 .97502 
 
 .23882 
 .23910 
 
 .97106 
 .97100 
 
 .25573 
 .25601 
 
 .96675 
 .96667 
 
 11 
 10 
 
 51 
 62 
 53 
 
 .18824 
 
 .18852 
 .18881 
 
 .98212 
 .98207 
 .98201 
 
 .20535 
 .20563 
 .20592 
 
 .97869 
 .97863 
 .97857 
 
 .22240 
 .22268 
 .22297 
 
 .97496 
 .97489 
 .97483 
 
 .23938 
 .23966 
 .23995 
 
 .97093 
 .97086 
 .97079 
 
 .25629 
 .25657 
 .25685 
 
 .96660 
 .96653 
 .96645 
 
 9 
 
 54 
 
 .18910 
 
 .98196 
 
 .20620 
 
 .97851 
 
 .22325 
 
 .97476 
 
 .24023 
 
 .97072 
 
 .25713 
 
 .96638 
 
 
 55 
 
 .18938 
 
 .98190 
 
 .20649 
 
 .97845 
 
 .22353 
 
 .97470 
 
 .24051 
 
 .97065 
 
 .25741 
 
 .96630 
 
 
 56 
 
 .18967 
 
 .98185 
 
 .20677 
 
 .97839 
 
 .22382 
 
 .97463 
 
 .24079 
 
 .97058 
 
 .25769 
 
 .96623 
 
 
 57 
 
 18995 
 
 .98179 
 
 .20706 
 
 .97833 
 
 .22410 
 
 .97457 
 
 .24108 
 
 .97051 
 
 .25798 
 
 .96615 
 
 
 58 
 69 
 
 .19024 
 19052 
 
 .98174 
 .98168 
 
 .20734 
 .20763 
 
 .97827 
 .97821 
 
 .22438 
 .22467 
 
 .97450 
 .97444 
 
 .24136 
 .24164 
 
 .97044 
 .97037 
 
 .25826 
 .25854 
 
 .96608 
 .96600 
 
 
 60 
 
 .19081 
 
 .98163 
 
 .20791 
 
 .97815 
 
 .22495 
 
 .97437 
 
 .24192 
 
 .97030 
 
 .25882 
 
 .96593 
 
 
 
 Oosia* 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 
 l 
 
 7t 
 
 P 
 
 11 
 
 i 
 
 77 
 
 o 
 
 76 
 
 o 
 
 75 
 
 3 
 
 
 63 
 
994 
 
 NATURAL SINUS AND COSINES 
 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .25882 
 
 .96593 
 
 .27564 
 
 .96126 
 
 .29237 
 
 .95630 
 
 .30902 
 
 .95106 
 
 .32557 
 
 .94552 
 
 60 
 
 1 
 
 .25910 
 
 .96585 
 
 .27592 
 
 .96118 
 
 .29265 
 
 .95622 
 
 .30929 
 
 .95097 
 
 .32584 
 
 .94542 
 
 59 
 
 2 
 
 .25938 
 
 .96578 
 
 .27620 
 
 .96110 
 
 .29293 
 
 .95613 
 
 .30957 
 
 .95088 
 
 .32612 
 
 .94533 
 
 58 
 
 3 
 
 .25966 
 
 .96570 
 
 .27648 
 
 .96102 
 
 .29321 
 
 .95605 
 
 .30985 
 
 .95079 
 
 .32639 
 
 .94523 
 
 57 
 
 4 
 
 .25994 
 
 .96562 
 
 .27676 
 
 .96094 
 
 .29348 
 
 .95596 
 
 .31012 
 
 .95070 
 
 .32667 
 
 .94514 
 
 56 
 
 5 
 
 .26022 
 
 .96555 
 
 .27704 
 
 .96086 
 
 .29376 
 
 .95588 
 
 .81040 
 
 .95061 
 
 .32694 
 
 .94504 
 
 55 
 
 6 
 
 .26050 
 
 .96547 
 
 .27731 
 
 .96078 
 
 .29404 
 
 .95579 
 
 .31068 
 
 .95052 
 
 .32722 
 
 .94495 
 
 54 
 
 7 
 
 .26079 
 
 .96540 
 
 .27759 
 
 .96070 
 
 .29432 
 
 .95571 
 
 .31095 
 
 .95043 
 
 .32749 
 
 .94485 
 
 53 
 
 8 
 
 .26107 
 
 .96532 
 
 .27787 
 
 .96062 
 
 .29460 
 
 .95562 
 
 .31123 
 
 .95033 
 
 .32777 
 
 .94476 
 
 52 
 
 9 
 
 .26135 
 
 .96524 
 
 .27815 
 
 .96054 
 
 .29487 
 
 .95554 
 
 .31151 
 
 .95024 
 
 .32804 
 
 .94466 
 
 51 
 
 10 
 
 .26163 
 
 .96517 
 
 .27843 
 
 .96046 
 
 .29515 
 
 .95545 
 
 .31178 
 
 .95015 
 
 .32832 
 
 .94457 
 
 50 
 
 11 
 
 .26191 
 
 .96509 
 
 .27871 
 
 .96037 
 
 .29543 
 
 .96536 
 
 .31206 
 
 .95006 
 
 .32859 
 
 .94447 
 
 49 
 
 12 
 
 .26219 
 
 .96502 
 
 .27899 
 
 .96029 
 
 .29571 
 
 .95528 
 
 .31233 
 
 .94997 
 
 .32887 
 
 .94438 
 
 48 
 
 13- 
 
 .26247 
 
 .96494 
 
 .27927 
 
 .96021 
 
 .29599 
 
 .95519 
 
 .31261 
 
 .94988 
 
 .32914 
 
 .94428 
 
 47 
 
 14 
 
 .26275 
 
 .96486 
 
 .27955 
 
 .96013 
 
 .29626 
 
 .95511 
 
 .31289 
 
 .94979 
 
 .32942 
 
 .94418 
 
 46 
 
 15 
 
 .26303 
 
 .96479 
 
 .27983 
 
 .96005 
 
 .29654 
 
 .95502 
 
 .31316 
 
 .94970 
 
 .32969 
 
 .94409 
 
 45 
 
 16 
 
 .26331 
 
 .96471 
 
 .28011 
 
 .95997 
 
 .29682 
 
 .95493 
 
 .31344 
 
 .94961 
 
 .32997 
 
 .94399 
 
 44 
 
 17 
 
 .26359 
 
 .96463 
 
 .28039 
 
 .95989 
 
 .29710 
 
 .95485 
 
 .31372 
 
 .94952 
 
 .33024 
 
 .94390 
 
 43 
 
 18 
 
 .26387 
 
 .96456 
 
 .28067 
 
 .95981 
 
 .29737 
 
 .95476 
 
 .81399 
 
 .94943 
 
 .33051 
 
 .94380 
 
 42 
 
 19 
 
 .26415 
 
 .96448 
 
 .28095 
 
 .95972 
 
 .29765 
 
 .95467 
 
 .81427 
 
 .94933 
 
 .33079 
 
 .94370 
 
 41 
 
 20 
 
 .26443 
 
 .96440 
 
 .28123 
 
 .95964 
 
 .29793 
 
 .95459 
 
 .31454 
 
 .94924 
 
 .33106 
 
 .94361 
 
 40 
 
 21 
 
 .26471 
 
 .96433 
 
 .28150 
 
 .95956 
 
 .29821 
 
 .95450 
 
 .31482 
 
 .94915 
 
 .83134 
 
 .94351 
 
 39 
 
 22 
 
 .26500 
 
 .96425 
 
 .28178 
 
 .95948 
 
 .29849 
 
 .95441 
 
 .31510 
 
 .94906 
 
 .33161 
 
 .94342 
 
 38 
 
 23 
 
 .26528 
 
 .96417 
 
 .28206 
 
 .95940 
 
 .29876 
 
 .95433 
 
 .31537 
 
 .94897 
 
 .33189 
 
 .94332 
 
 37 
 
 24 
 
 .26556 
 
 .96410 
 
 .28234 
 
 .95931 
 
 .29904 
 
 .95424 
 
 .31565 
 
 .94888 
 
 .33216 
 
 .94322 
 
 36 
 
 25 
 
 .26584 
 
 .96402 
 
 .28262 
 
 .95923 
 
 .29932 
 
 .95415 
 
 .31593 
 
 .94878 
 
 .33244 
 
 .94313 
 
 35 
 
 26 
 
 .26612 
 
 .96394 
 
 .28290 
 
 .95915 
 
 .29960 
 
 .95407 
 
 .31620 
 
 .94869 
 
 .33271 
 
 .94303 
 
 34 
 
 27 
 
 .26640 
 
 .96386 
 
 .28318 
 
 .95907 
 
 .29987 
 
 .95398 
 
 .31648 
 
 .94860 
 
 .33298 
 
 .94293 
 
 33 
 
 28 
 
 .26668 
 
 .96379 
 
 .28346 
 
 .95898 
 
 .30015 
 
 .95389 
 
 .31675 
 
 .94851 
 
 .33326 
 
 .94284 
 
 32 
 
 29 
 
 .26696 
 
 .96371 
 
 .28374 
 
 .95890 
 
 .30043 
 
 .95380 
 
 .31703 
 
 .94842 
 
 .33353 
 
 .94274 
 
 31 
 
 30 
 
 .26724 
 
 .96363 
 
 .28402 
 
 .95882 
 
 .30071 
 
 .95372 
 
 .31730 
 
 .94832 
 
 .33381 
 
 .94264 
 
 30 
 
 31 
 
 .26752 
 
 .96355 
 
 .28429 
 
 .95874 
 
 .30098 
 
 .95363 
 
 .31758 
 
 .94823 
 
 .33408 
 
 .94254 
 
 29 
 
 32 
 
 .26780 
 
 .96347 
 
 .28457 
 
 .95865 
 
 .30126 
 
 .95354 
 
 .31786 
 
 .94814 
 
 .33436 
 
 .94245 
 
 28 
 
 33 
 
 .26808 
 
 .96340 
 
 .28485 
 
 .95857 
 
 .30154 
 
 .95345 
 
 .31813 
 
 .94805 
 
 .33463 
 
 .94235 
 
 27 
 
 34 
 
 .26836 
 
 .96332 
 
 .28513 
 
 .95849 
 
 .30182 
 
 .95337 
 
 .31841 
 
 .94795 
 
 .33490 
 
 .94225 
 
 26 
 
 35 
 
 .26864 
 
 .96324 
 
 .28541 
 
 .95841 
 
 .30209 
 
 .95328 
 
 .31868 
 
 .94786 
 
 .33518 
 
 .94215 
 
 25 
 
 36 
 
 .26892 
 
 .96316 
 
 .28569 
 
 .95832 
 
 .30237 
 
 .95319 
 
 .31896 
 
 .94777 
 
 .33545 
 
 .94206 
 
 24 
 
 37 
 
 .26920 
 
 .96308 
 
 !28597 
 
 .95824 
 
 .30265 
 
 .95310 
 
 .31923 
 
 .94768 
 
 .33573 
 
 .94196 
 
 23 
 
 38 
 
 .26948 
 
 .96301 
 
 .28625 
 
 .95816 
 
 .30292 
 
 .95301 
 
 .31951 
 
 .94758 
 
 .33600 
 
 .94186 
 
 22 
 
 39 
 
 .26976 
 
 .96293 
 
 .28652 
 
 .95807 
 
 .30320 
 
 .95293 
 
 .31979 
 
 .94749 
 
 .33627 
 
 .94176 
 
 21 
 
 40 
 
 .27004 
 
 .96285 
 
 .28680 
 
 .95799 
 
 .30348 
 
 .95284 
 
 .32006 
 
 .94740 
 
 .33655 
 
 .94167 
 
 20 
 
 41 
 
 .27032 
 
 .96277 
 
 .28708 
 
 .95791 
 
 .30376 
 
 .95275 
 
 .32034 
 
 .94730 
 
 .33682 
 
 .94157 
 
 19 
 
 42 
 
 .27060 
 
 .96269 
 
 .28736 
 
 .95782 
 
 .30403 
 
 .95266 
 
 .32061 
 
 .94721 
 
 .33710 
 
 .94147 
 
 18 
 
 43 
 
 .27088 
 
 .96261 
 
 .28764 
 
 .95774 
 
 .30431 
 
 .95257 
 
 .32089 
 
 .94712 
 
 .33737 
 
 .94137 
 
 17 
 
 44 
 
 .27116 
 
 .96253 
 
 .28792 
 
 .95766 
 
 .30459 
 
 .95248 
 
 .32116 
 
 .94702 
 
 .33764 
 
 .94127 
 
 16 
 
 45 
 
 .27144 
 
 .96246 
 
 .28820 
 
 .95757 
 
 .30486 
 
 .95240 
 
 .82144 
 
 .94693 
 
 .33792 
 
 .94118 
 
 15 
 
 46 
 
 .27172 
 
 .96238 
 
 .28847 
 
 .95749 
 
 .30514 
 
 .95231 
 
 .32171 
 
 .94684 
 
 .33819 
 
 .94108 
 
 14 
 
 47 
 
 .27200 
 
 .96230 
 
 .28875 
 
 .95740 
 
 .30542 
 
 .95222 
 
 .32199 
 
 .94674 
 
 .33846 
 
 .94098 
 
 13 
 
 48 
 
 .27228 
 
 .96222 
 
 .28903 
 
 .95732 
 
 .30570 
 
 .95213 
 
 .32227 
 
 .94665 
 
 .33874 
 
 .94088 
 
 12 
 
 49 
 
 .27256 
 
 .96214 
 
 .28931 
 
 .95724 
 
 .30597 
 
 .95204 
 
 .32254 
 
 .94656 
 
 .33901 
 
 .94078 
 
 11 
 
 50 
 
 .27284 
 
 .96206 
 
 .28959 
 
 .95715 
 
 .30625 
 
 .95195 
 
 .32282 
 
 .94646 
 
 .33929 
 
 .94068 
 
 10 
 
 51 
 
 .27312 
 
 .96198 
 
 .28987 
 
 .95707 
 
 .30653 
 
 .95186 
 
 .32309 
 
 .94637 
 
 .33956 
 
 .94058 
 
 9 
 
 52 
 
 .27340 
 
 .96190 
 
 .29015 
 
 .95698 
 
 .30680 
 
 .95177 
 
 .32337 
 
 .94627 
 
 .33983 
 
 .94049 
 
 8 
 
 53 
 
 .27368 
 
 .96182 
 
 .29042 
 
 .95690 
 
 .30708 
 
 .95168 
 
 .32364 
 
 .94618 
 
 .34011 
 
 .94039 
 
 7 
 
 54 
 
 .27396 
 
 .96174 
 
 .29070 
 
 .95681 
 
 .30736 
 
 .95159 
 
 .32392 
 
 .94609 
 
 .34038 
 
 .94029 
 
 6 
 
 55 
 
 .27424 
 
 .96166 
 
 .29098 
 
 .95673 
 
 .30763 
 
 .95150 
 
 .82419 
 
 .94599 
 
 .34065 
 
 .94019 
 
 5 
 
 56 
 
 .27452 
 
 .96158 
 
 .29126 
 
 .95664 
 
 .30791 
 
 .95142 
 
 .32447 
 
 .94590 
 
 .34093 
 
 .94009 
 
 4 
 
 57 
 
 .27480 
 
 .96150 
 
 .29154 
 
 .95656 
 
 .30819 
 
 .95133 
 
 .82474 
 
 .94580 
 
 .34120 
 
 .93999 
 
 3 
 
 58 
 
 .27508 
 
 .96142 
 
 .29182 
 
 .95647 
 
 .30846 
 
 .95124 
 
 .32502 
 
 .94571 
 
 .34147 
 
 .93989 
 
 2 
 
 59 
 
 .27536 
 
 .96134 
 
 .29209 
 
 .95639 
 
 .30874 
 
 .95115 
 
 .32529 
 
 .94561 
 
 .34175 
 
 .93979 
 
 1 
 
 60 
 
 .27564 
 
 .96126 
 
 .29237 
 
 .95630 
 
 .30902 
 
 .95106 
 
 .32557 
 
 .94552 
 
 .34202 
 
 .93969 
 
 
 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 
 / 
 
 74 
 
 73 
 
 72 
 
 71 
 
 70 
 
 / 
 
NATURAL SINES AND COSINES 
 
 995 
 
 / 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .34202 
 
 .93969 
 
 .35837 
 
 .93358 
 
 .37461 
 
 .92718 
 
 .39073 
 
 .92050 
 
 .40674 
 
 .91355 
 
 60 
 
 1 
 
 .34229 
 
 .93959 
 
 .35864 
 
 .93348 
 
 .37488 
 
 .92707 
 
 .39100 
 
 .92039 
 
 .40700 
 
 .91843 
 
 59 
 
 2 
 
 .34257 
 
 .93949 
 
 .35891 
 
 .93337 
 
 .37515 
 
 .92697 
 
 .39127 
 
 .92028 
 
 .40727 
 
 .91331 
 
 58 
 
 3 
 
 .34284 
 
 .93939 
 
 .35918 
 
 .93327 
 
 .37542 
 
 .92686 
 
 .39153 
 
 .92016 
 
 .40753 
 
 .91319 
 
 57 
 
 4 
 
 .34311 
 
 .93929 
 
 .35945 
 
 .93316 
 
 .37569 
 
 .92675 
 
 .39180 
 
 .92005 
 
 .40780 
 
 .91307 
 
 56 
 
 5 
 
 .34339 
 
 .93919 
 
 .35973 
 
 .93306 
 
 .37595 
 
 .92664 
 
 .39207 
 
 .91994 
 
 .40806 
 
 .91295 
 
 55 
 
 6 
 
 .34366 
 
 .93909 
 
 .36000 
 
 .93295 
 
 .37622 
 
 .92653 
 
 .39234 
 
 .91982 
 
 .40833 
 
 .91283 
 
 54 
 
 7 
 
 .34393 
 
 .93899 
 
 .36027 
 
 .93285 
 
 .37649 
 
 .92642 
 
 .39260 
 
 .91971 
 
 .40860 
 
 .91272 
 
 53 
 
 8 
 
 .34421 
 
 .93889 
 
 .36054 
 
 .93274 
 
 .37676 
 
 .92631 
 
 .39287 
 
 .91959 
 
 .40886 
 
 .91260 
 
 52 
 
 9 
 
 .34448 
 
 .93879 
 
 .36081 
 
 .93264 
 
 .37703 
 
 .92620 
 
 .39314 
 
 .91948 
 
 .40913 
 
 .91248 
 
 51 
 
 10 
 
 .34475 
 
 .93869 
 
 .36108 
 
 .93253 
 
 .37730 
 
 .92609 
 
 .39341 
 
 .91936 
 
 .40939 
 
 .91236 
 
 50 
 
 11 
 
 .34503 
 
 .93859 
 
 .36135 
 
 .93243 
 
 .37757 
 
 .92598 
 
 .39367 
 
 .91925 
 
 .40966 
 
 .91224 
 
 49 
 
 12 
 
 .34530 
 
 .93849 
 
 .36162 
 
 .93232 
 
 .37784 
 
 .92587 
 
 .39394 
 
 .91914 
 
 .40992 
 
 .91212 
 
 48 
 
 13 
 
 .34557 
 
 .93839 
 
 .36190 
 
 .93222 
 
 .37811 
 
 .92576 
 
 .39421 
 
 .91902 
 
 .41019 
 
 .91200 
 
 47 
 
 14 
 
 .34584 
 
 .93829 
 
 .36217 
 
 .93211 
 
 .37838 
 
 .92565 
 
 .39448 
 
 .91891 
 
 .41045 
 
 .91188 
 
 46 
 
 15 
 
 .34612 
 
 .93819 
 
 .36244 
 
 .93201 
 
 .37865 
 
 .92554 
 
 .39474 
 
 .91879 
 
 .41072 
 
 .91176 
 
 45 
 
 16 
 
 .34639 
 
 .93809 
 
 .36271 
 
 .93190 
 
 .37892 
 
 .92543 
 
 .39501 
 
 .91868 
 
 .41098 
 
 .91164 
 
 44 
 
 17 
 
 .34666 
 
 .93799 
 
 .36298 
 
 .93180 
 
 .37919 
 
 .92532 
 
 .39528 
 
 .91856 
 
 .41125 
 
 .91152 
 
 43 
 
 18 
 
 .34694 
 
 .93789 
 
 .36325 
 
 .93169 
 
 .37946 
 
 .92521 
 
 .39555 
 
 .91845 
 
 .41151 
 
 .91140 
 
 42 
 
 19 
 
 .34721 
 
 .93779 
 
 .36352 
 
 .93159 
 
 .37973 
 
 .92510 
 
 .39581 
 
 .91833 
 
 .41178 
 
 .91128 
 
 41 
 
 20 
 
 .34748 
 
 .93769 
 
 .36379 
 
 .93148 
 
 .37999 
 
 .92499 
 
 .39608 
 
 .91822 
 
 .41204 
 
 .91116 
 
 40 
 
 21 
 
 .34775 
 
 .93759 
 
 .36406 
 
 .93137 
 
 .38026 
 
 .92488 
 
 .39635 
 
 .91810 
 
 .41231 
 
 .91104 
 
 39 
 
 22 
 
 .34803 
 
 .93748 
 
 .36434 
 
 .93127 
 
 .38053 
 
 .92477 
 
 .39661 
 
 .91799 
 
 .41257 
 
 .91092 
 
 38 
 
 23 
 
 .84830 
 
 .93738 
 
 .36461 
 
 .93116 
 
 .38080 
 
 .92466 
 
 .39688 
 
 .91787 
 
 .41284 
 
 .91080 
 
 37 
 
 24 
 
 .34857 
 
 .93728 
 
 .36488 
 
 .93106 
 
 .38107 
 
 .92455 
 
 .39715 
 
 .91775 
 
 .41310 
 
 .91068 
 
 36 
 
 25 
 
 .34884 
 
 .93718 
 
 .36515 
 
 .93095 
 
 .38134 
 
 .92444 
 
 .39741 
 
 .91764 
 
 .41337 
 
 .91056 
 
 35 
 
 26 
 
 .34912 
 
 .93708 
 
 .36542 
 
 .93084 
 
 .38161 
 
 .92432 
 
 .39768 
 
 .91752 
 
 .41363 
 
 .91044 
 
 34 
 
 27 
 
 .34939 
 
 .93698 
 
 .36569 
 
 .93074 
 
 .38188 
 
 .92421 
 
 .39795 
 
 .91741 
 
 .41390 
 
 .91032 
 
 33 
 
 28 
 
 .34966 
 
 193688 
 
 .36596 
 
 .93063 
 
 .38215 
 
 .92410 
 
 .39822 
 
 .91729 
 
 .41416 
 
 .91020 
 
 32 
 
 29 
 
 .34993 
 
 .93677 
 
 .36623 
 
 .93052 
 
 .38241 
 
 .92399 
 
 .39848 
 
 .91718 
 
 .41443 
 
 .91008 
 
 31 
 
 30 
 
 .35021 
 
 .93667 
 
 .36650 
 
 .93042 
 
 .38268 
 
 .92388 
 
 .39875 
 
 .91706 
 
 .41469 
 
 .90996 
 
 30 
 
 31 
 
 .35048 
 
 .93657 
 
 .36677 
 
 .93031 
 
 .38295 
 
 .92377 
 
 .39902 
 
 .91694 
 
 .41496 
 
 .90984 
 
 29 
 
 32 
 
 .35075 
 
 .93647 
 
 .36704 
 
 .93020 
 
 .38322 
 
 .92366 
 
 .39928 
 
 .91683 
 
 .41*22 
 
 .90972 
 
 28 
 
 33 
 
 .35102 
 
 .93637 
 
 .36731 
 
 .93010 
 
 .38349 
 
 .92355 
 
 .39955 
 
 .91671 
 
 .41549 
 
 .90960 
 
 27 
 
 34 
 
 .35130 
 
 .93626 
 
 .36758 
 
 .92999 
 
 .38376 
 
 .92343 
 
 .39982 
 
 .91660 
 
 .41575 
 
 .90948 
 
 26 
 
 35 
 
 .35157 
 
 .93616 
 
 .36785 
 
 .92988 
 
 .38403 
 
 .92332 
 
 .40008 
 
 .91648 
 
 .41602 
 
 .90936 
 
 25 
 
 36- 
 
 .35184 
 
 .93606 
 
 .36812 
 
 .92978 
 
 .38430 
 
 .92321 
 
 .40035 
 
 .91636 
 
 .41628 
 
 .90924 
 
 24 
 
 37 
 
 .35211 
 
 .93596 
 
 .36839 
 
 .92967 
 
 .38456 
 
 .92310 
 
 .40062 
 
 .91625 
 
 .41655 
 
 .90911 
 
 23 
 
 38 
 
 .35239 
 
 .93585 
 
 .36867 
 
 .92956 
 
 .38483 
 
 .92299 
 
 .40088 
 
 .91613 
 
 .41681 
 
 .90899 
 
 22 
 
 39 
 
 .35266 
 
 .93575 
 
 .36894 
 
 .92945 
 
 .38510 
 
 .92287 
 
 .40115 
 
 .91601 
 
 .41707 
 
 .90887 
 
 21 
 
 40 
 
 .35293 
 
 .93565 
 
 .36921 
 
 .92935 
 
 .38537 
 
 .92276 
 
 .40141 
 
 .91590 
 
 .41734 
 
 .90875 
 
 20 
 
 41 
 
 .35320 
 
 .93555 
 
 .36948 
 
 .92924 
 
 .38564 
 
 .92265 
 
 .40168 
 
 .91578 
 
 .41760 
 
 .90863 
 
 19 
 
 42 
 
 .35347 
 
 .93544 
 
 .36975 
 
 .92913 
 
 .38591 
 
 .92254 
 
 .40195 
 
 .91566 
 
 .41787 
 
 .90851 
 
 18 
 
 43 
 
 .35375 
 
 .93534 
 
 .37002 
 
 .92902 
 
 .38617 
 
 .92243 
 
 .40221 
 
 .91555 
 
 .41813 
 
 .90839 
 
 17 
 
 44 
 
 .35402 
 
 .93524 
 
 .37029 
 
 .92892 
 
 .38644 
 
 .92231 
 
 .40248 
 
 .91543 
 
 .41840 
 
 .90826 
 
 16 
 
 45 
 
 .35429 
 
 .93514 
 
 .37056 
 
 .92881 
 
 .38671 
 
 .92220 
 
 .40275 
 
 .91531 
 
 .41866 
 
 .90814 
 
 15 
 
 46 
 
 .35456 
 
 .93502 
 
 .37083 
 
 .92870 
 
 
 .92209 
 
 .40301 
 
 .91519 
 
 .41892 
 
 .90802 
 
 14 
 
 47 
 
 .35484 
 
 .93493 
 
 .37110 
 
 .92859 
 
 138725 
 
 .92198 
 
 .40328 
 
 .91508 
 
 .41919 
 
 .90790 
 
 13 
 
 48 
 
 .35511 
 
 .93483 
 
 .37137 
 
 .92849 
 
 .38752 
 
 .92186 
 
 .40355 
 
 .91496 
 
 .41945 
 
 .90778 
 
 12 
 
 49 
 
 .35538 
 
 .93472 
 
 .37164 
 
 .92838 
 
 .38778 
 
 .92175 
 
 .40381 
 
 .91484 
 
 .41972 
 
 .90766 
 
 11 
 
 50 
 
 .35565 
 
 .93462 
 
 .37191 
 
 .92827 
 
 .38805 
 
 .92164 
 
 .40408 
 
 .91472 
 
 .41998 
 
 .90753 
 
 10 
 
 51 
 
 .35592 
 
 .93452 
 
 .87218 
 
 .92816 
 
 .38832 
 
 .92152 
 
 .40434 
 
 .91461 
 
 .42024 
 
 .90741 
 
 9 
 
 52 
 
 .35619 
 
 .93441 
 
 .37245 
 
 .92805 
 
 
 .92141 
 
 .40461 
 
 .91449 
 
 .42051 
 
 .90729 
 
 8 
 
 53 
 
 .35647 
 
 .93431 
 
 .37272 
 
 .92794 
 
 .38886 
 
 .92130 
 
 .40488 
 
 .91437 
 
 .42077 
 
 .90717 
 
 7 
 
 54 
 
 .35674 
 
 .93420 
 
 .87299 
 
 .92784 
 
 [38912 
 
 .92119 
 
 .40514 
 
 .91425 
 
 .42104 
 
 .90704 
 
 6 
 
 55 
 
 .35701 
 
 .93410 
 
 .37326 
 
 .92773 
 
 .38939 
 
 .92107 
 
 .40541 
 
 .91414 
 
 .42130 
 
 .90692 
 
 5 
 
 56 
 
 .35728 
 
 .93400 
 
 .37353 
 
 .92762 
 
 .38966 
 
 .92096 
 
 .40567 
 
 .91402 
 
 .42156 
 
 .90680 
 
 4 
 
 57 
 
 .35755 
 
 .93389 
 
 .37380 
 
 .92751 
 
 .38993 
 
 .92085 
 
 .40594 
 
 .91390 
 
 .42183 
 
 .90668 
 
 3 
 
 58 
 
 35782 
 
 .93379 
 
 .37407 
 
 .92740 
 
 .39020 
 
 .92073 
 
 .40621 
 
 .91378 
 
 .42209 
 
 .90655 
 
 2 
 
 59 
 60 
 
 .35810 
 .35837 
 
 .93368 
 .93358 
 
 .37434 
 .37461 
 
 .92729 
 .92718 
 
 .39046 
 .39073 
 
 .92062 
 .92050 
 
 .40647 
 .40674 
 
 .91366 
 .91355 
 
 .42235 
 .42262 
 
 .90643 
 .90631 
 
 1 
 
 
 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 
 t 
 
 69 
 
 68 
 
 67 
 
 66 
 
 65 
 
 
NATURAL SINES AND COSINES 
 
 / 
 
 2 
 
 3 
 
 2 
 
 6 
 
 2 
 
 7 
 
 2 
 
 8 
 
 2 
 
 9 
 
 f 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .42262 
 
 .90631 
 
 .43837 
 
 .89879 
 
 .45399 
 
 .89101 
 
 .46947 
 
 .88295 
 
 .48481 
 
 .87462 
 
 60 
 
 1 
 
 .42288 
 
 .90618 
 
 .43863 
 
 .89867 
 
 .45425 
 
 .89087 
 
 .46973 
 
 .88281 
 
 .48506 
 
 .87448 
 
 59 
 
 2 
 
 .42315 
 
 .90606 
 
 .43889 
 
 .89854 
 
 .45451 
 
 .89074 
 
 .46999 
 
 .88267 
 
 -.-48532 
 
 .87434 
 
 58 
 
 
 .42341 
 
 .90594 
 
 .43916 
 
 .89841 
 
 .45477 
 
 .89061 
 
 .47024 
 
 .88254 
 
 .48557 
 
 .87420 
 
 57 
 
 
 .42367 
 
 .90582 
 
 .43942 
 
 .89828 
 
 .45503 
 
 .89048 
 
 .47050 
 
 .88240 
 
 .48583 
 
 .87406 
 
 56 
 
 
 .42394 
 
 .90569 
 
 .43968 
 
 .89816 
 
 .45529 
 
 .89035 
 
 .47076 
 
 .88226 
 
 .48608 
 
 .87391 
 
 55 
 
 
 .42420 
 
 .90557 
 
 .43994 
 
 .89803 
 
 .45554 
 
 .89021 
 
 .47101 
 
 .88213 
 
 .48634 
 
 .87377 
 
 54 
 
 
 .42446 
 
 .90545 
 
 .44020 
 
 .89790 
 
 .45580 
 
 .89008 
 
 .47127 
 
 .88199 
 
 .48659 
 
 .87363 
 
 53 
 
 8 
 
 .42473 
 
 .90532 
 
 .44046 
 
 .89777 
 
 .45606 
 
 .88995 
 
 .47153 
 
 .88185 
 
 .48684 
 
 .87349 
 
 52 
 
 9 
 
 .42499 
 
 .90520 
 
 .44072 
 
 .89764 
 
 .45632 
 
 .88981 
 
 .47178 
 
 .88172 
 
 .48710 
 
 .87335 
 
 51 
 
 10 
 
 .42525 
 
 .90507 
 
 .44098 
 
 .89752 
 
 .45658 
 
 .88968 
 
 .47204 
 
 .88158 
 
 .48735 
 
 .87321 
 
 50 
 
 11 
 
 .42552 
 
 .90495 
 
 .44124 
 
 .89739 
 
 .45684 
 
 .88955 
 
 .47229 
 
 .88144 
 
 .48761 
 
 .87306 
 
 49 
 
 12 
 
 .42578 
 
 .90483 
 
 .44151 
 
 .89726 
 
 .45710 
 
 .88942 
 
 .47255 
 
 .88130 
 
 .48786 
 
 .87292 
 
 48 
 
 13 
 
 .42604 
 
 .90470 
 
 .44177 
 
 .89713 
 
 .45736 
 
 .88928 
 
 .47281 
 
 .88117 
 
 .48811 
 
 .87278 
 
 47 
 
 14 
 
 .42631 
 
 .90458 
 
 .44203 
 
 .89700 
 
 .45762 
 
 .88915 
 
 .47306 
 
 .88103 
 
 .48837 
 
 .87264 
 
 46 
 
 15 
 
 .42657 
 
 .90446 
 
 .44229 
 
 .89687 
 
 .45787 
 
 .88902 
 
 .47332 
 
 .88089 
 
 .48862 
 
 .87250 
 
 45 
 
 16 
 
 .42683 
 
 .90433 
 
 .44255 
 
 .89674 
 
 .45813 
 
 
 .47358 
 
 .88075 
 
 .48888 
 
 .87235 
 
 44 
 
 17 
 
 .42709 
 
 .90421 
 
 .44281 
 
 .89662 
 
 .45839 
 
 !88875 
 
 .47383 
 
 .88062 
 
 .48913 
 
 .87221 
 
 43 
 
 18 
 
 .42736 
 
 .90408 
 
 .44307 
 
 .89649 
 
 .45865 
 
 .88862 
 
 .47409 
 
 .88048 
 
 .48938 
 
 .87207 
 
 42 
 
 19 
 
 .42762 
 
 .90396 
 
 .44333 
 
 .89636 
 
 .45891 
 
 
 .47434 
 
 .88034 
 
 .48964 
 
 .87193 
 
 41 
 
 20 
 
 .42788 
 
 .90383 
 
 .44359 
 
 .89623 
 
 .45917 
 
 !88835 
 
 .47460 
 
 .88020 
 
 .48989 
 
 .87178 
 
 40 
 
 21 
 
 .42815 
 
 .90371 
 
 .44385 
 
 .89610 
 
 .45942 
 
 .88822 
 
 .47486 
 
 .88006 
 
 .49014 
 
 .87164 
 
 39 
 
 22 
 
 .42841 
 
 .90358 
 
 .44411 
 
 .89597 
 
 .45968 
 
 .88808 
 
 .47511 
 
 .87993 
 
 .49040 
 
 .87150 
 
 38 
 
 23 
 
 .42867 
 
 .90346 
 
 .44437 
 
 .89584 
 
 .45994 
 
 .88795 
 
 .47537 
 
 .87979 
 
 .49065 
 
 .87136 
 
 37 
 
 24 
 
 .42894 
 
 .90334 
 
 .44464 
 
 .89571 
 
 .46020 
 
 .88782 
 
 .47562 
 
 .87965 
 
 .49090 
 
 .87121 
 
 36 
 
 25 
 
 .42920 
 
 .90321 
 
 .44490 
 
 .89558 
 
 .46046 
 
 .88768 
 
 .47588 
 
 .87951 
 
 .49116 
 
 .87107 
 
 35 
 
 26 
 
 .42946 
 
 .90309 
 
 .44516 
 
 .89545 
 
 .46072 
 
 .88755 
 
 .47614 
 
 .87937 
 
 .49141 
 
 .87093 
 
 34 
 
 27 
 
 .42972 
 
 .90296 
 
 .44542 
 
 .89532 
 
 .46097 
 
 .88741 
 
 .47639 
 
 .87923 
 
 .49166 
 
 .87079 
 
 .33 
 
 28 
 
 .42999 
 
 .90284 
 
 .44568 
 
 .89519 
 
 .46123 
 
 .88728 
 
 .47665 
 
 .87908 
 
 .49192 
 
 .87064 
 
 32 
 
 29 
 
 .43025 
 
 .90271 
 
 .44594 
 
 .89506 
 
 .46149 
 
 .88715 
 
 .47690 
 
 .87896 
 
 .49217 
 
 .87050 
 
 31 
 
 30 
 
 .43051 
 
 .90259 
 
 .44620 
 
 .89493 
 
 .46175 
 
 .88701 
 
 .47716 
 
 .87882 
 
 .49242 
 
 .87036 
 
 30 
 
 31 
 
 .43077 
 
 .90246 
 
 .44646 
 
 .89480 
 
 .46201 
 
 .88688 
 
 .47741 
 
 .87868 
 
 .49268 
 
 .87021 
 
 29 
 
 82 
 
 .43104 
 
 .90133 
 
 .44672 
 
 .89467 
 
 .46226 
 
 .88674 
 
 .47767 
 
 .87854 
 
 .49293 
 
 .87007 
 
 28 
 
 33 
 
 .43130 
 
 .90221 
 
 .44698 
 
 .89454 
 
 .46252 
 
 .88661 
 
 .47793 
 
 .87840 
 
 .49318 
 
 .86993 
 
 27 
 
 34 
 
 .43156 
 
 .90208 
 
 .44724 
 
 .89441 
 
 .46278 
 
 .88647 
 
 .47818 
 
 .87826 
 
 .49344 
 
 .86978 
 
 26 
 
 35 
 
 .43182 
 
 .90196 
 
 .44750 
 
 .89428 
 
 .46304 
 
 .88634 
 
 .47844 
 
 .87812 
 
 
 .86964 
 
 25 
 
 36 
 
 .43209 
 
 .90183 
 
 .44776 
 
 .8941-5 
 
 .46330 
 
 .88620 
 
 .47869 
 
 .87798 
 
 .49394 
 
 .86949 
 
 24 
 
 87 
 
 .43235 
 
 .90171 
 
 .44802 
 
 .89402 
 
 .46355 
 
 .88607 
 
 .47895 
 
 .87784 
 
 .49419 
 
 .86935 
 
 23 
 
 38 
 
 .43261 
 
 .90158 
 
 .44828 
 
 .89389 
 
 .46381 
 
 .88593 
 
 .47920 
 
 .87770 
 
 .49445 
 
 .86921 
 
 22 
 
 39 
 
 .43287 
 
 .90146 
 
 .44854 
 
 :89376 
 
 .46407 
 
 .88580 
 
 .47946 
 
 .87756 
 
 .49470 
 
 .86906 
 
 21 
 
 40 
 
 .43313 
 
 .90133 
 
 .44880 
 
 .89363 
 
 .46433 
 
 .88566 
 
 .47971 
 
 .87743 
 
 .49495 
 
 .86892 
 
 20 
 
 41 
 
 .43340 
 
 .90120 
 
 .44906 
 
 .89350 
 
 .46458 
 
 .88553 
 
 .47997 
 
 .87729 
 
 .49521 
 
 .86878 
 
 19 
 
 42 
 
 .43366 
 
 .90108 
 
 .44932 
 
 .89337 
 
 .46484 
 
 .88539 
 
 .48022 
 
 .87715 
 
 .49546 
 
 .86863 
 
 18 
 
 43 
 
 .43392 
 
 .90095 
 
 .44958 
 
 .89324 
 
 .46510 
 
 .88526 
 
 .48048 
 
 .87701 
 
 .49571 
 
 .86849 
 
 17 
 
 44 
 
 .43418 
 
 .90082 
 
 .44984 
 
 .89311 
 
 .46536 
 
 .88512 
 
 .48073 
 
 .87687 
 
 .49596 
 
 .86834 
 
 16 
 
 45 
 
 .43445 
 
 .90070 
 
 .45010 
 
 .89298 
 
 .46561 
 
 .88499 
 
 .48099 
 
 .87673 
 
 .49622 
 
 .86820 
 
 15 
 
 46 
 
 .43471 
 
 .90057 
 
 .45036 
 
 .89285 
 
 .46587 
 
 .88485 
 
 .48124 
 
 .87659 
 
 .49647 
 
 .86805 
 
 14 
 
 47 
 
 .43497 
 
 .90045 
 
 .45062 
 
 .89272 
 
 .46613 
 
 .88472 
 
 .48150 
 
 .87645 
 
 .49672 
 
 .86791 
 
 13 
 
 48 
 
 .43523 
 
 .90032 
 
 .45088 
 
 .89259 
 
 .46639 
 
 .88458 
 
 .48175 
 
 .87631 
 
 .49697 
 
 .86777 
 
 12 
 
 49 
 
 .43549 
 
 .90019 
 
 .45114 
 
 .89245 
 
 .46664 
 
 .88445 
 
 .48201 
 
 .87617 
 
 .49723 
 
 .86762 
 
 11 
 
 50 
 
 .43575 
 
 .90007 
 
 .45140 
 
 .89232 
 
 .46690 
 
 .88431 
 
 .48226 
 
 .87603 
 
 .49748 
 
 .86748 
 
 10 
 
 51 
 
 .43602 
 
 .89994 
 
 .45166 
 
 .89219 
 
 .46716 
 
 .88417 
 
 .48252 
 
 .87589 
 
 .49773 
 
 .86733 
 
 9 
 
 52 
 
 .43628 
 
 .89981 
 
 .45192 
 
 .89206 
 
 .46742 
 
 .88404 
 
 .48277 
 
 .87575 
 
 .49798 
 
 .86719 
 
 8 
 
 53 
 
 .43654 
 
 .89968 
 
 .45218 
 
 .89193 
 
 .46767 
 
 .88390 
 
 .48303 
 
 .87561 
 
 .49824 
 
 .86704 
 
 7 
 
 54 
 
 .43680 
 
 .89956 
 
 .45243 
 
 .89180 
 
 .46793 
 
 .88377 
 
 .48328 
 
 .87546 
 
 .49849 
 
 .86690 
 
 6 
 
 55 
 
 .43706 
 
 .89943 
 
 .45269 
 
 .89167 
 
 .46819 
 
 .88363 
 
 .48354 
 
 .87532 
 
 .49874 
 
 .86675 
 
 5 
 
 56 
 
 .43733 
 
 .89930 
 
 .45295 
 
 .89153 
 
 .46844 
 
 .88349 
 
 .48379 
 
 .87518 
 
 .49899 
 
 .86661 
 
 4 
 
 67 
 
 .43759 
 
 .89918 
 
 .45321 
 
 .89140 
 
 .46870 
 
 .88336 
 
 .48405 
 
 .87504 
 
 .49924 
 
 .86646 
 
 8 
 
 58 
 
 .43785 
 
 .89905 
 
 .45347 
 
 .89127 
 
 .46896 
 
 .88322 
 
 .48430 
 
 .87490 
 
 .49950 
 
 .86632 
 
 2 
 
 59 
 
 .43811 
 
 .89892 
 
 .45373 
 
 .89114 
 
 .46921 
 
 .88308 
 
 .48456 
 
 .87476 
 
 .49975 
 
 .86617 
 
 1 
 
 60 
 
 .43837 
 
 .89879 
 
 .45399 
 
 .89101 
 
 .46947 
 
 .88295 
 
 .48481 
 
 .87462 
 
 .50000 
 
 86603 
 
 
 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 
 9 
 
 64 
 
 
 
 63 
 
 
 
 62 
 
 
 
 61 
 
 
 
 60 
 
 
 
 / 
 
NATURAL SINES AND COSINES 
 
 
 30 
 
 31 
 
 32 
 
 33 
 
 34 
 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .50000 
 
 .86603 
 
 .51504 
 
 .85717 
 
 .52992 
 
 .84805 
 
 .54464 
 
 .83867 
 
 .55919 
 
 .82904 
 
 60 
 
 1 
 
 .50025 
 
 .86588 
 
 .51529 
 
 .85702 
 
 .53017 
 
 .84789 
 
 .54488 
 
 .83851 
 
 .55943 
 
 .82887 
 
 59 
 
 2 
 
 .50050 
 
 .86573 
 
 .51554 
 
 .85687 
 
 .53041 
 
 .84774 
 
 .54513 
 
 .83835 
 
 .55968 
 
 .82871 
 
 58 
 
 3 
 
 .50076 
 
 .86559 
 
 .51579 
 
 .85672 
 
 .53066 
 
 .84759 
 
 .54537 
 
 .83819 
 
 .55992 
 
 .82855 
 
 57 
 
 4 
 
 .50101 
 
 .86544 
 
 .51604 
 
 .85657 
 
 .53091 
 
 .84743 
 
 .54561 
 
 .83804 
 
 .56016 
 
 .82839 
 
 56 
 
 5 
 
 .50126 
 
 .86530 
 
 .51628 
 
 .85642 
 
 .53115 
 
 .84728 
 
 .54586 
 
 .83788 
 
 .56040 
 
 .82822 
 
 55 
 
 6 
 
 .50151 
 
 .86515 
 
 .51653 
 
 .85627 
 
 .53140 
 
 .84712 
 
 .54610 
 
 .83772 
 
 .56064 
 
 .82806 
 
 54' 
 
 7 
 
 .50176 
 
 .86501 
 
 .51678 
 
 .85612 
 
 .53164 
 
 .84697 
 
 .54635 
 
 .83756 
 
 .56088 
 
 .82790 
 
 53 
 
 8 
 
 .50201 
 
 .86486 
 
 .51703 
 
 .85597 
 
 .53189 
 
 .84681 
 
 .54659 
 
 .83740 
 
 .56112 
 
 .82773 
 
 52 
 
 9 
 
 .50227 
 
 .86471 
 
 .51728 
 
 .85582 
 
 .53214 
 
 .84666 
 
 .54683 
 
 .83724 
 
 .56136 
 
 .82757 
 
 51 
 
 10 
 
 .50252 
 
 .86457 
 
 .51753 
 
 .85567 
 
 .53238 
 
 .84650 
 
 .54708 
 
 .83708 
 
 .56160 
 
 .82741 
 
 50 
 
 11 
 
 .50277 
 
 .86442 
 
 .51778 
 
 .85551 
 
 .53263 
 
 .84635 
 
 .54732 
 
 .83692 
 
 .56184 
 
 .82724 
 
 49 
 
 12 
 
 .50302 
 
 .86427 
 
 .51803 
 
 .85536 
 
 .53288 
 
 .84619 
 
 .54756 
 
 .83676 
 
 .56208 
 
 .82708 
 
 48 
 
 13 
 
 .50327 
 
 .86413 
 
 .51828 
 
 .85521 
 
 .53312 
 
 .84604 
 
 .54781 
 
 .83660 
 
 .56232 
 
 .82692 
 
 47 
 
 14 
 
 .50352 
 
 .86398 
 
 .51852 
 
 .85506 
 
 .53337 
 
 .84588 
 
 .64805 
 
 .83645 
 
 .56256 
 
 .82675 
 
 46 
 
 15 
 
 .50377 
 
 .86384 
 
 .51877 
 
 .85491 
 
 .53361 
 
 .84573 
 
 .54829 
 
 .83629 
 
 .56280 
 
 .82659 
 
 45 
 
 16 
 
 .50403 
 
 .86369 
 
 .51902 
 
 .85476 
 
 .53386 
 
 .84557 
 
 .54854 
 
 .83613 
 
 .56305 
 
 .82643 
 
 44 
 
 17 
 
 .50428 
 
 .86354 
 
 .51927 
 
 .85461 
 
 .53411 
 
 .84542 
 
 .54878 
 
 .83597 
 
 .56329 
 
 .82626 
 
 43 
 
 18 
 
 .50453 
 
 .86340 
 
 .51952 
 
 .85446 
 
 .53435 
 
 .84526 
 
 .54902 
 
 .83581 
 
 .56353 
 
 .82610 
 
 42 
 
 19 
 
 .50478 
 
 .86325 
 
 .51977 
 
 .85431 
 
 .53460 
 
 .84511 
 
 .54927 
 
 .83565 
 
 .56377 
 
 .82593 
 
 41 
 
 20 
 
 .50503 
 
 .86310 
 
 .52002 
 
 .85416 
 
 .53484 
 
 .84495 
 
 .54951 
 
 .83549 
 
 .56401 
 
 .82577 
 
 40 
 
 21 
 
 .50528 
 
 .86295 
 
 .52026 
 
 .85401 
 
 .53509 
 
 .84480 
 
 .54975 
 
 .83533 
 
 .56425 
 
 .82561 
 
 89 
 
 22 
 
 .50553 
 
 .86281 
 
 .52051 
 
 .85385 
 
 .53534 
 
 .84464 
 
 .54999 
 
 .83517 
 
 .56449 
 
 .82544 
 
 88 
 
 23 
 
 .50578 
 
 .86266 
 
 .52076 
 
 .85370 
 
 .53558 
 
 .84448 
 
 .55024 
 
 .83501 
 
 .56473 
 
 .82528 
 
 37 
 
 24 
 
 .50603 
 
 .86251 
 
 .52101 
 
 .85355 
 
 .53583 
 
 .84433 
 
 .55048 
 
 .83485 
 
 .66497 
 
 .82511 
 
 36 
 
 25 
 
 .50628 
 
 .86237 
 
 .52126 
 
 .85340 
 
 .53607 
 
 .84417 
 
 .55072 
 
 .83469 
 
 .56521 
 
 .82495 
 
 35 
 
 26 
 
 .50654 
 
 .86222 
 
 .52151 
 
 .85325 
 
 .53632 
 
 .84402 
 
 .55097 
 
 .83453 
 
 .56545 
 
 .82478 
 
 34 
 
 27 
 
 .50679 
 
 .86207 
 
 .52175 
 
 .85310 
 
 .53656 
 
 .84386 
 
 .55121 
 
 .83437 
 
 .56569 
 
 .82462 
 
 33 
 
 28 
 
 .50704 
 
 .86192 
 
 .52200 
 
 .85294 
 
 .53681 
 
 .84370 
 
 .55145 
 
 .83421 
 
 .56593 
 
 .82446 
 
 32 
 
 29 
 
 .50729 
 
 .86178 
 
 .52225 
 
 .85279 
 
 .53705 
 
 .84355 
 
 .55169 
 
 .83405 
 
 .66617 
 
 .82429 
 
 31 
 
 30 
 
 .50754 
 
 .86163 
 
 .52250 
 
 .85264 
 
 .53730 
 
 .84339 
 
 .65194 
 
 .83389 
 
 .56641 
 
 .82413 
 
 SO 
 
 31 
 
 .50779 
 
 .86148 
 
 .52275 
 
 .85249 
 
 .53754 
 
 .84324 
 
 .55218 
 
 .83373 
 
 .56665 
 
 .82396 
 
 29 
 
 32 
 
 .50804 
 
 .86133 
 
 .52299 
 
 .85234 
 
 .53779 
 
 .84308 
 
 .65242 
 
 .83356 
 
 .56689 
 
 .82380 
 
 28 
 
 33 
 
 .50829 
 
 .86119 
 
 .52324 
 
 .85218 
 
 .53804 
 
 .84292 
 
 .55266 
 
 .83340 
 
 .56713 
 
 .82363 
 
 27 
 
 34 
 
 .50854 
 
 .86104 
 
 .52349 
 
 .85203 
 
 .53828 
 
 .84277 ' 
 
 .55291 
 
 .83324 
 
 .56736 
 
 .82347 
 
 26 
 
 35 
 
 .50879 
 
 .86089 
 
 .52374 
 
 .85188 
 
 .53853 
 
 .84261 
 
 .55315 
 
 .83308 
 
 .56760 
 
 .82330 
 
 25 
 
 36 
 
 .50904 
 
 .86074 
 
 .52399 
 
 .85173 
 
 .53877 
 
 .84245 
 
 .55389 
 
 .83292 
 
 .56784 
 
 .82314 
 
 24 
 
 37 
 
 .50929 
 
 .86059 
 
 .52423 
 
 .85157 
 
 .53902 
 
 .84230 
 
 .55363 
 
 .83276 
 
 .56808 
 
 .82297 
 
 23 
 
 38 
 
 .50954 
 
 .86045 
 
 .52448 
 
 .85142 
 
 .53926 
 
 .84214 
 
 .55388 
 
 .83260 
 
 .56832 
 
 .82281 
 
 22 
 
 39 
 
 .50979 
 
 .86030 
 
 .52473 
 
 .85127 
 
 .53951 
 
 ..84198 
 
 .55412 
 
 .83244 
 
 .56856 
 
 .82264 
 
 21 
 
 40 
 
 .51004 
 
 .86015 
 
 .52498 
 
 .85112 
 
 .53975 
 
 .84182 
 
 .65436 
 
 .83228 
 
 .56880 
 
 .82248 
 
 20 
 
 41 
 
 .51029 
 
 .86000 
 
 .52522 
 
 .85096 
 
 .54000 
 
 .84167 
 
 .55460 
 
 .83212 
 
 .56904 
 
 .82231 
 
 19 
 
 42 
 
 .51054 
 
 .85985 
 
 .52547 
 
 .85081 
 
 .54024 
 
 .84151 
 
 .55484 
 
 .83195 
 
 .56928 
 
 .82214 
 
 18 
 
 43 
 
 .51079 
 
 .85970 
 
 .52572 
 
 .85066 
 
 .54049 
 
 .84135 
 
 .55509 
 
 .83179 
 
 .56952 
 
 .82198 
 
 17 
 
 44 
 
 .51104 
 
 .85956 
 
 .52597 
 
 .85051 
 
 .54073 
 
 .84120 
 
 .55533 
 
 .83163 
 
 .56976 
 
 .82181 
 
 16 
 
 45 
 
 .51129 
 
 .85941 
 
 .52621 
 
 .85035 
 
 .54097 
 
 .84104 
 
 .55557 
 
 .83147 
 
 .57000 
 
 .82165 
 
 15 
 
 46 
 
 .51154 
 
 .85926 
 
 .52646 
 
 .85020 
 
 .54122 
 
 .84088 
 
 .55581 
 
 .83131 
 
 .57024 
 
 .82148 
 
 14 
 
 47 
 
 .51179 
 
 .85911 
 
 .52671 
 
 .85005 
 
 .54146 
 
 .84072 
 
 .55605 
 
 .83115 
 
 .57047 
 
 .82132 
 
 13 
 
 48 
 
 .51204 
 
 .85896 
 
 .52696 
 
 .84989 
 
 .54171 
 
 .84057 
 
 .55630 
 
 .83098 
 
 .57071 
 
 .82115 
 
 12 
 
 49 
 
 .51229 
 
 .85881 
 
 .52720 
 
 .84974 
 
 .54195 
 
 .84041 
 
 .55654 
 
 .83082 
 
 .57095 
 
 .82098 
 
 11 
 
 50 
 
 .51254 
 
 .85866 
 
 .52745 
 
 .84959 
 
 .54220 
 
 .84025 
 
 .55678 
 
 .83066 
 
 .57119 
 
 .82082 
 
 10 
 
 51 
 
 .51279 
 
 .85851 
 
 .52770 
 
 .84943 
 
 .54244 
 
 .84009 
 
 .65702 
 
 .83050 
 
 .57143 
 
 .82065 
 
 9 
 
 52 
 
 .51304 
 
 .85836 
 
 .52794 
 
 .84928 
 
 .54269 
 
 .83994 
 
 .55726 
 
 .83034 
 
 .57167 
 
 .82048 
 
 8 
 
 53 
 
 .51329 
 
 .85821 
 
 .52819 
 
 .84913 
 
 .54293 
 
 .83978 
 
 .55750 
 
 .83017 
 
 .57191 
 
 .82032 
 
 7 
 
 54 
 
 .51354 
 
 .85806 
 
 .52844 
 
 .84897 
 
 .54317 
 
 .83962 
 
 .55775 
 
 .83001 
 
 .57215 
 
 .82015 
 
 6 
 
 55 
 
 .51379 
 
 .85792 
 
 .52869 
 
 .84882 
 
 .54342 
 
 .83946 
 
 .55799 
 
 .82985 
 
 .57238 
 
 .81999 
 
 5 
 
 56 
 
 .51404 
 
 .85777 
 
 .52893 
 
 .84866 
 
 .54366 
 
 .83930 
 
 .55823 
 
 .82969 
 
 .57262 
 
 .81982 
 
 4 
 
 57 
 
 .61429 
 
 .85762 
 
 .52918 
 
 .84851 
 
 .54391 
 
 .83915 
 
 .55847 
 
 .82953 
 
 .57286 
 
 .81965 
 
 8 
 
 58 
 
 .51454 
 .51479 
 
 .85747 
 .85732 
 
 .52943 
 .62967 
 
 .84836 
 .84820 
 
 .54415 
 .54440 
 
 .83899 
 .83883 
 
 .55871 
 .65895 
 
 .82936 
 .82920 
 
 .57310 
 .57334 
 
 .81949 
 .81932 
 
 2 
 
 60 
 
 .51504 
 
 .85717 
 
 .52992 
 
 .84805 
 
 .54464 
 
 .83867 
 
 .55919 
 
 .82904 
 
 .57358 
 
 31915 
 
 
 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 
 
 59 
 
 58 
 
 57 
 
 56 
 
 65 
 
 
998 
 
 NATURAL SINES AND COSINES 
 
 f 
 
 35 
 
 36 
 
 37 
 
 38 
 
 39 
 
 / 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .57358 
 
 .81915 
 
 .58779 
 
 .80902 
 
 .60182 
 
 .79864 
 
 .61566 
 
 .78801 
 
 .62932 
 
 T 
 
 .77715 
 
 60 
 
 1 
 
 .57381 
 
 .81899 
 
 .58802 
 
 .80885 
 
 .60205 
 
 .79846 
 
 .61589 
 
 .78783 
 
 .62955 
 
 .77696 
 
 59 
 
 2 
 
 .57405 
 
 .81882 
 
 .58826 
 
 .80867 
 
 .60228 
 
 .79829 
 
 .61612 
 
 .78765 
 
 .62977 
 
 .77678 
 
 58 
 
 3 
 
 .57429 
 
 .81865 
 
 .58849 
 
 .80850 
 
 .60251 
 
 .79811 
 
 .61635 
 
 .78747 
 
 .63000 
 
 .77660 
 
 57 
 
 4 
 
 .57453 
 
 .81848 
 
 .58873 
 
 .80833 
 
 .60274 
 
 .79793 
 
 .61658 
 
 .78729 
 
 .63022 
 
 .77641 
 
 56 
 
 5 
 
 .57477 
 
 .81832 
 
 .58896 
 
 .80816 
 
 .60298 
 
 .79776 
 
 .61681 
 
 .78711 
 
 .63045 
 
 .77623 
 
 55 
 
 6 
 
 .57501 
 
 .81815 
 
 .58920 
 
 .80799 
 
 .60321 
 
 .79758 
 
 .61704 
 
 .78694 
 
 .63068 
 
 .77605 
 
 54 
 
 1 
 
 .57524 
 
 .81798 
 
 .58943 
 
 .80782 
 
 .60344 
 
 .,79741 
 
 .61726 
 
 .78676 
 
 .63090 
 
 .77586 
 
 53 
 
 8 
 
 .57548 
 
 .81782 
 
 .58967 
 
 .80765 
 
 .60367 
 
 .79723 
 
 .61749 
 
 .78658 
 
 .63113 
 
 .77568 
 
 52 
 
 9 
 
 .57572 
 
 .81765 
 
 .58990 
 
 .80748 
 
 .60390 
 
 .79706 
 
 .61772 
 
 .78640 
 
 .63135 
 
 .77550 
 
 51 
 
 10 
 
 .57596 
 
 .81748 
 
 .59014 
 
 .80730 
 
 .60414 
 
 .79688 
 
 .61795 
 
 .78622 
 
 .63158 
 
 .77531 
 
 60 
 
 11 
 
 .57619 
 
 .81731 
 
 .59037 
 
 .80713 
 
 .60437 
 
 .79671 
 
 .61818 
 
 .78604 
 
 .63180 
 
 .77513 J 
 
 49 
 
 12 
 
 .67643 
 
 .81714 
 
 .59061 
 
 .80696 
 
 .60460 
 
 .79653 
 
 .61841 
 
 .78586 
 
 .63203 
 
 .77494 
 
 48 
 
 13 
 
 .67667 
 
 .81698 
 
 .59084 
 
 .80679 
 
 .60483 
 
 .79635 
 
 .61864 
 
 .78568 
 
 .63225 
 
 .77476 
 
 47 
 
 14 
 
 .57691 
 
 .81681 
 
 .59108 
 
 .80662 
 
 .60506 
 
 .79618 
 
 .61887 
 
 .78550 
 
 .63248 
 
 .77458 
 
 46 
 
 15 
 
 .57715 
 
 .81664 
 
 .59131 
 
 .80644 
 
 .60529 
 
 .79600 
 
 .61909 
 
 .78532 
 
 .63271 
 
 .77439 
 
 45 
 
 16 
 
 .67738 
 
 .81647 
 
 .59154 
 
 .80627 
 
 .60553 
 
 .79583 
 
 .61932 
 
 .78514 
 
 .63293 
 
 .77421 
 
 44 
 
 17 
 
 .57762 
 
 .81631 
 
 .59178 
 
 .80610 
 
 .60576 
 
 .79565 
 
 .61955 
 
 .784*96 
 
 .63316 
 
 .77402 
 
 43 
 
 18 
 
 .57786 
 
 .81614 
 
 .59201 
 
 .80593 
 
 .60599 
 
 .79547 
 
 .61978 
 
 .78478 
 
 .63338 
 
 .77384 
 
 42 
 
 19 
 
 .57810 
 
 .81597 
 
 .59225 
 
 .80576 
 
 .60622x 
 
 .79530 
 
 .62001 
 
 .78460 
 
 .63361 
 
 .77366 
 
 41 
 
 20 
 
 .57833 
 
 .81580 
 
 .59248 
 
 .80558 
 
 .60645 
 
 .79512 
 
 .62024 
 
 .78442 
 
 .63383 
 
 .77347 
 
 40 
 
 21 
 
 .57857 
 
 .81563 
 
 .59272 
 
 .80541 
 
 .60668 
 
 .79494 
 
 .62046 
 
 .78424 
 
 .63406 
 
 .77329 
 
 39 
 
 22 
 
 .57881 
 
 .81546 
 
 .59295 
 
 .80524 
 
 .60691 
 
 .79477 
 
 .62069 
 
 .78405 
 
 .63428 
 
 .77310 
 
 38 
 
 23 
 
 .57904 
 
 .81530 
 
 .59318 
 
 .80507 
 
 .60714 
 
 .79459 
 
 .62092 
 
 .78387 
 
 .63451 
 
 .77292 
 
 37 
 
 24 
 
 .57928 
 
 .81513 
 
 .59342 
 
 .80489 
 
 .60738 
 
 .79441 
 
 .62115 
 
 .78369 
 
 .63473 
 
 .77273 
 
 36 
 
 25 
 
 .67952 
 
 .81496 
 
 .59365 
 
 .80472 
 
 .60761 
 
 .79424 
 
 .62138 
 
 .78351 
 
 .63496 
 
 .77255 
 
 35 
 
 26 
 
 .57976 
 
 .81479 
 
 .59389 
 
 .80455 
 
 .60784 
 
 .79406 
 
 .62160 
 
 .78333 
 
 .63518 
 
 .77236 
 
 34 
 
 27 
 
 .57999 
 
 .81462 
 
 .69412 
 
 .80438 
 
 .60807 
 
 .79388 
 
 .62183 
 
 .78315 
 
 .63540 
 
 .77218 
 
 33 
 
 28 
 
 .68023 
 
 .81445 
 
 .59436 
 
 .80420 
 
 .60830 
 
 .79371 
 
 .62206 
 
 .78297 
 
 .63563 
 
 .77199 
 
 32 
 
 29 
 
 .58047 
 
 .81428 
 
 .59459 
 
 .80403 
 
 .60853 
 
 .79353 
 
 .62229 
 
 .78279 
 
 .63585 
 
 .77181 
 
 31 
 
 30 
 
 .58070 
 
 .81412 
 
 .59482 
 
 .80386 
 
 .60876 
 
 .79335 
 
 .62251 
 
 .78261 
 
 .63608 
 
 .77162 
 
 30 
 
 31 
 
 .58094 
 
 .81395 
 
 .59506 
 
 .80368 
 
 .60899 
 
 .79318 
 
 .62274 
 
 .78243 
 
 .63630 
 
 .77144 
 
 29 
 
 32 
 
 .58118 
 
 .81378 
 
 .59529 
 
 .80351 
 
 .60922 
 
 .79300 
 
 .62297 
 
 .78225 
 
 .63653 
 
 .77125 
 
 28 
 
 33 
 
 .58141 
 
 .81361 
 
 .59552 
 
 .80334 
 
 .60945 
 
 .79282 
 
 .62320 
 
 .78206 
 
 .63675 
 
 .77107 
 
 27 
 
 34 
 
 .58165 
 
 .81344 
 
 .59576 
 
 .80316 
 
 .60968 
 
 .79264 
 
 .62342 
 
 -.78188 
 
 .63698 
 
 .77088 
 
 26 
 
 35 
 
 .58189 
 
 .81327 
 
 .59599 
 
 .80299 
 
 .60991 
 
 .79247 
 
 .62365 
 
 .78170 
 
 .63720 
 
 .77070 
 
 25 
 
 36 
 
 .58212 
 
 .81310 
 
 .59622 
 
 .80282 
 
 .61015 
 
 .79229 
 
 .62388 
 
 .78152 
 
 .63742 
 
 .77051 
 
 24 
 
 37 
 
 .58236 
 
 .81293 
 
 .59646 
 
 .80264 
 
 .61038 
 
 .79211 
 
 .62411 
 
 .78134 
 
 .63765 
 
 .77033 
 
 23 
 
 38 
 
 .68260 
 
 .81276 
 
 .59669 
 
 .80247 
 
 .61061 
 
 .79193 
 
 .62433 
 
 .78116 
 
 .63787 
 
 .77014 
 
 22 
 
 39 
 
 .58283 
 
 .81259 
 
 .59693 
 
 .80230 
 
 .61084 
 
 .79176 
 
 .62456 
 
 .78098 
 
 .63810 
 
 .76996 
 
 21 
 
 40 
 
 .58307 
 
 .81242 
 
 .59716 
 
 .80212 
 
 .61107 
 
 .79158 
 
 .62479 
 
 .78079 
 
 .63832 
 
 .76977 
 
 20 
 
 41 
 
 .58330 
 
 .81225 
 
 .59739 
 
 .80195 
 
 .61130 
 
 .79140 
 
 .62502 
 
 .78061 
 
 .63854 
 
 .76959 
 
 19 
 
 42 
 
 .58354 
 
 .81208 
 
 .59763 
 
 .80178 
 
 .61153 
 
 .79122 
 
 .62524 
 
 .78043 
 
 .63877 
 
 .76940 
 
 18 
 
 43 
 
 .58378 
 
 .81191 
 
 .59786 
 
 .80160 
 
 .61176 
 
 .79105 
 
 .62547 
 
 .78025 
 
 .63899 
 
 .76921 
 
 17 
 
 44 
 
 .58401 
 
 .81174 
 
 .59809 
 
 .80143 
 
 .61199 
 
 .79087 
 
 .62570 
 
 .78007 
 
 .63922 
 
 .76903 
 
 16 
 
 45 
 
 .58425 
 
 .81157 
 
 .59832 
 
 .80125 
 
 .61222 
 
 .79069 
 
 .62592 
 
 .77988 
 
 .63944 
 
 .76884 
 
 15 
 
 46 
 
 .58449 
 
 .81140 
 
 .59856 
 
 .80108 
 
 .61245 
 
 .79051 
 
 .62615 
 
 .77970 
 
 .63966 
 
 .76866 
 
 14 
 
 47 
 
 .68472 
 
 .81123 
 
 .59879 
 
 .80091 
 
 .61268 
 
 .79033 
 
 .62638 
 
 .77952 
 
 .63989 
 
 .76847 
 
 13 
 
 48 
 
 .68496 
 
 .81106 
 
 .59902 
 
 .80073 
 
 .61291 
 
 .79016 
 
 .62660 
 
 .77934 
 
 .64011 
 
 .76828 
 
 12 
 
 49 
 
 .58519 
 
 .81089 
 
 .59926 
 
 .80056 
 
 .61314 
 
 .78998 
 
 .62683 
 
 .77916 
 
 .64033 
 
 .76810 
 
 11 
 
 50 
 
 .58543 
 
 .81072 
 
 .59949 
 
 .80038 
 
 .61337 
 
 .78980 
 
 .62706 
 
 .77897 
 
 .64056 
 
 .76791 
 
 10 
 
 51 
 
 .58567 
 
 .81055 
 
 .59972 
 
 .80021 
 
 .61360 
 
 .78962 
 
 .62728 
 
 .77879 
 
 .64078 
 
 .76772 
 
 9 
 
 52 
 
 .58590 
 
 .81038 
 
 .59995 
 
 .80003 
 
 .61383 
 
 .78944 
 
 .62751 
 
 .77861 
 
 .64100 
 
 .76754 
 
 8 
 
 53 
 
 .58614 
 
 .81021 
 
 .60019 
 
 .79986 
 
 .61406 
 
 .78926 
 
 .62774 
 
 .77843 
 
 .64123 
 
 .76735 
 
 7 
 
 54 
 
 .58637 
 
 .81004 
 
 .60042 
 
 .79968 
 
 .61429 
 
 .78908 
 
 .62796 
 
 .77824 
 
 .64145 
 
 .76717 
 
 6 
 
 55 
 
 .58661 
 
 .80987 
 
 .60065 
 
 .79951 
 
 .61451 
 
 .78891 
 
 .62819 
 
 .77806 
 
 .64167 
 
 .76698 
 
 5 
 
 56 
 
 .58684 
 
 .80970 
 
 .60089 
 
 .79934 
 
 .61474 
 
 .78873 
 
 .62842 
 
 .77788 
 
 .64190 
 
 .76679 
 
 4 
 
 57 
 
 .58708 
 
 .80953 
 
 .60112 
 
 .79916 
 
 .61497 
 
 .78855 
 
 .62864 
 
 .77769 
 
 .64212 
 
 .76661 
 
 3 
 
 68 
 
 .58731 
 
 .80936 
 
 .60135 
 
 .79899 
 
 .61520 
 
 .78837 
 
 .62887 
 
 .77751 
 
 .64234 
 
 .76642 
 
 2 
 
 59 
 
 .58755 
 
 .80919 
 
 .60158 
 
 .79881 
 
 .61543 
 
 .78819 
 
 .62909 
 
 .77733 
 
 .64256 
 
 .76623 
 
 1 
 
 60 
 
 .58779 
 
 .80902 
 
 .60182 
 
 .79864 
 
 .61566 
 
 .78801 
 
 .62932 
 
 .77715 
 
 .64279 
 
 .76604 
 
 
 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 
 / 
 
 64 
 
 53 
 
 52 
 
 51 
 
 50 
 
 / 
 
NATURAL SINES AND COSINES 
 
 1 
 
 40 
 
 41 
 
 42 
 
 43 
 
 44 
 
 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 
 
 
 .64279 
 
 .76604 
 
 .65606 
 
 .75471 
 
 .66913 
 
 .74314 
 
 .68200 
 
 .73135 
 
 .69466 
 
 .71934 
 
 60 
 
 1 
 
 .64301 
 
 .76586 
 
 .65628 
 
 .75452 
 
 .66935 
 
 .74295 
 
 .68221 
 
 .73116 
 
 .69487 
 
 .71914 
 
 59 
 
 2 
 
 .64323 
 
 .76567 
 
 .65650 
 
 .75433 
 
 .66956 
 
 .74276 
 
 .68242 
 
 .73096 
 
 .69508 
 
 .71894 
 
 58 
 
 3 
 
 .64346 
 
 .76548 
 
 .65672 
 
 .75414 
 
 .66978 
 
 .74256 
 
 .68264 
 
 .73076 
 
 .69529 
 
 .71873 
 
 57 
 
 4 
 
 .64368 
 
 .76530 
 
 .65694 
 
 .75395 
 
 .66999 
 
 .74237 
 
 .68285 
 
 .73056 
 
 .69549 
 
 .71853 
 
 56 
 
 5 
 
 .64390 
 
 .76511 
 
 .65716 
 
 .75375 
 
 .67021 
 
 .74217 
 
 .68306 
 
 .73036 
 
 .69570 
 
 .71833 
 
 55 
 
 6 
 
 .64412 
 
 .76492 
 
 .65738 
 
 .75356 
 
 .67043 
 
 .74198 
 
 .68327 
 
 .73016 
 
 .69591 
 
 .71813 
 
 54 
 
 7 
 
 .64435 
 
 .76473 
 
 .65759 
 
 .75337 
 
 .67064 
 
 .74178 
 
 .68349 
 
 .72996 
 
 .69612 
 
 .71792 
 
 53 
 
 8 
 
 .64457 
 
 .76455 
 
 .65781 
 
 .75318 
 
 .67086 
 
 .74159 
 
 .68370 
 
 .72976 
 
 .69633 
 
 .71772 
 
 52 
 
 9 
 
 .64479 
 
 .76436 
 
 .65803 
 
 .75299 
 
 .67107 
 
 .74139 
 
 .68391 
 
 .72957 
 
 .69654 
 
 .71752 
 
 51 
 
 10 
 
 .64501 
 
 .76417 
 
 .65825 
 
 .75280 
 
 .67129 
 
 .74120 
 
 .68412 
 
 .72937 
 
 .69675 
 
 .71732 
 
 50 
 
 11 
 
 .64524 
 
 .76398 
 
 .65847 
 
 .75261 
 
 .67151 
 
 .74100 
 
 .68434 
 
 .72917 
 
 .69696 
 
 .71711 
 
 49 
 
 12 
 
 .64546 
 
 .76380 
 
 .65869 
 
 .75241 
 
 .67172 
 
 .74080 
 
 .68455 
 
 .72897 
 
 .69717 
 
 .71691 
 
 48 
 
 13 
 
 .64568 
 
 .76361 
 
 .65891 
 
 .75222 
 
 .67194 
 
 .74061 
 
 .68476 
 
 .72877 
 
 .69737 
 
 .71671 
 
 47 
 
 [4 
 
 .64590 
 
 .76342 
 
 .65913 
 
 .75203 
 
 .67215 
 
 .74041 
 
 .68497 
 
 .72857 
 
 .69758 
 
 .71650 
 
 46 
 
 15 
 
 .64612 
 
 .76323 
 
 .65935 
 
 .75184 
 
 .67237 
 
 .74022 
 
 .68518 
 
 .72837 
 
 .69779 
 
 .71630 
 
 45 
 
 16 
 
 .64635 
 
 .76304 
 
 .65956 
 
 .75165 
 
 .67258 
 
 .74002 
 
 .68539 
 
 .72817 
 
 .69800 
 
 .71610 
 
 44 
 
 17 
 
 .64657 
 
 .76286 
 
 .65978 
 
 .75146 
 
 .67280 
 
 .73983 
 
 .68561 
 
 .72797 
 
 .69821 
 
 .71590 
 
 43 
 
 18 
 
 .64679 
 
 .76267 
 
 .66000 
 
 .75126 
 
 .67301 
 
 .73963 
 
 .68582 
 
 .72777 
 
 .69842 
 
 .71569 
 
 42 
 
 19 
 
 .64701 
 
 .76248 
 
 .66022 
 
 .75107 
 
 .67323 
 
 .73944 
 
 .68603 
 
 .72757 
 
 .69862 
 
 .71549 
 
 41 
 
 20 
 
 .64723 
 
 .76229 
 
 .66044 
 
 .75088 
 
 .67344 
 
 .73924 
 
 .68624 
 
 .72737 
 
 .69883 
 
 .71529 
 
 40 
 
 21 
 
 .64746 
 
 .76210 
 
 .66066 
 
 .75069 
 
 .67366 
 
 .73904 
 
 .68645 
 
 .72717 
 
 .69904 
 
 .71508 
 
 39 
 
 22 
 
 .64768 
 
 .76192 
 
 .66088 
 
 .75050 
 
 .67387 
 
 .73885 
 
 .68666 
 
 .72697 
 
 .69925 
 
 .71488 
 
 38 
 
 23 
 
 .64790 
 
 .76173 
 
 .66109 
 
 .75030 
 
 .67409 
 
 .73865 
 
 .68688 
 
 .72677 
 
 .69946 
 
 .71468 
 
 37 
 
 24 
 
 .64812 
 
 .76154 
 
 .66131 
 
 .75011 
 
 .67430 
 
 .73846 
 
 .68709 
 
 .72657 
 
 .69966 
 
 .71447 
 
 36 
 
 25 
 
 .64834 
 
 .76135 
 
 .66153 
 
 .74992 
 
 .67452 
 
 .73826 
 
 .68730 
 
 .72637 
 
 .69987 
 
 .71427 
 
 35 
 
 26 
 
 .64856 
 
 .76116 
 
 .66175 
 
 .74973 
 
 .67473 
 
 .73806 
 
 .68751 
 
 .72617 
 
 .70008 
 
 .71407 
 
 34 
 
 27 
 
 .64878 
 
 .76097 
 
 .66197 
 
 .74953 
 
 .67495 1 
 
 .73787 
 
 .68772 
 
 .72597 
 
 .70029 
 
 .71386 
 
 33 
 
 28 
 
 .64901 
 
 .76078 
 
 .66218 
 
 .74934 
 
 .67516 
 
 .73767 
 
 .68793 
 
 .72577 
 
 .70049 
 
 .71366 
 
 32 
 
 29 
 
 .64923 
 
 .76059 
 
 .66240 
 
 .74915 
 
 .67538 
 
 .73747 
 
 .68814 
 
 .72557 
 
 .70070 
 
 .71345 
 
 31 
 
 30 
 
 .64945 
 
 .76041 
 
 .66262 
 
 .74896 
 
 .67559 
 
 .73728 
 
 .68835 
 
 .72537 
 
 .70091 
 
 .71325 
 
 30 
 
 31 
 
 .64967 
 
 .76022 
 
 .66284 
 
 .74876 
 
 .67580 
 
 .73708 
 
 .68857 
 
 .72517 
 
 .70112 
 
 .71305 
 
 29 
 
 32 
 
 .64989 
 
 .76003 
 
 .66306 
 
 .74857 
 
 .67602 
 
 .73688 
 
 .68878 
 
 .72497 
 
 .70132 
 
 .71284 
 
 28 
 
 33 
 
 .65011 
 
 .75984 
 
 .66327 
 
 .74838 
 
 .67623 
 
 .73669 
 
 .68899 
 
 .72477 
 
 .70153 
 
 .71264 
 
 27 
 
 34 
 
 .65033 
 
 .75965 
 
 .66349 
 
 .74818 
 
 .67645 
 
 .73649 
 
 .68920 
 
 .72457 
 
 .70174 
 
 .71243 
 
 26 
 
 35 
 
 .65055 
 
 .75946 
 
 .66371 
 
 .74799 
 
 .67666 
 
 .73629 
 
 .68941 
 
 .72437 
 
 .70195 
 
 .71223 
 
 25 
 
 36 
 
 .65077 
 
 .75927 
 
 .66393 
 
 .74780 
 
 .67688 
 
 .73610 
 
 .68962 
 
 .72417 
 
 .70215 
 
 .71203 
 
 24 
 
 37 
 
 .65100 
 
 .75908 
 
 .66414 
 
 .74760 
 
 .67709 
 
 .73590 
 
 .68983 
 
 .72397 
 
 .70236 
 
 .71182 
 
 23 
 
 38 
 
 .65122 
 
 .75889 
 
 .66436 
 
 .74741 
 
 .67730 
 
 .73570 
 
 .69004 
 
 .72377 
 
 .70257 
 
 .71162 
 
 22 
 
 39 
 
 .65144 
 
 .75870 
 
 .66458 
 
 .74722 
 
 .67752 
 
 .73551 
 
 .69025 
 
 .72357 
 
 .70277 
 
 .71141 
 
 21 
 
 40 
 
 .65166 
 
 .75851 
 
 .66480 
 
 .74703 
 
 .67773 
 
 .73531 
 
 .69046 
 
 .72337 
 
 .70298 
 
 .71121 
 
 20 
 
 41 
 
 42 
 
 .65188 
 .65210 
 
 .75832 
 
 .75813 
 
 .66501 
 .66523 
 
 .74683 
 .74664 
 
 .67795 
 .67816 
 
 .73511 
 .73491 
 
 .69067 
 .69088 
 
 .72317 
 
 .72297 
 
 .70319 
 .70339 
 
 .71100 
 .71080 
 
 19 
 
 18 
 
 43 
 44 
 
 45 
 
 .65232 
 .65254 
 .65276 
 
 .75794 
 .75775 
 .75756 
 
 .66545 
 .66566 
 
 .66588 
 
 .74644 
 .74625 
 .74606 
 
 .67837 
 .67859 
 .67880 
 
 .73472 
 .73452 
 .73432 
 
 .69109 
 .69130 
 .69151 
 
 .72277 
 .72257 
 .72236 
 
 .70360 
 .70381 
 .70401 
 
 .71059 
 .71039 
 .71019 
 
 17 
 16 
 
 15 
 
 46 
 47 
 48 
 49 
 50 
 
 .65298 
 .65320 
 .65342 
 .65364 
 .65386 
 
 .75738 
 .75719 
 .75700 
 .75680 
 .75661 
 
 .66610 
 .66632 
 .66653 
 .66675 
 .66697 
 
 .74586 
 .74567 
 .74548 
 .74528 
 .74509 
 
 .67901 
 .67923 
 .67944 
 .67965 
 .67987 
 
 .73413 
 .73393 
 .73373 
 .73353 
 .73333 
 
 .69172 
 .69193 
 .69214 
 .69235 
 .69256 
 
 .72216 
 .72196 
 .72176 
 .72156 
 .72136 
 
 .70422 .70998 
 .70443 .70978 
 .70463 .70957 
 .70484 .70937 
 .70505 .70916 
 
 14 
 13 
 12 
 11 
 10 
 
 51 
 52 
 53 
 54 
 55 
 56 
 57 
 58 
 59 
 60 
 
 .65408 
 .65430 
 .65452 
 .65474 
 .65496 
 .65518 
 .65540 
 .65562 
 .65584 
 .65606 
 
 .75642 
 .75623 
 .75604 
 .75585 
 .75566 
 .75547 
 .75528 
 .75509 
 .75490 
 .75471 
 
 .66718 
 .66740 
 .66762 
 .66783 
 .66805 
 .66827 
 .66848 
 .66870 
 .66891 
 .66913 
 
 .74489 
 .74470 
 .74451 
 .74431 
 .74412 
 .74392 
 .74373 
 .74353 
 .74334 
 .74314 
 
 .68008 
 .68029 
 .68051 
 .68072 
 .68093 
 .68115 
 .68136 
 .68157 
 .68179 
 .68200 
 
 .73314 
 .73294 
 .73274 
 .73254 
 .73234 
 .73215 
 .73195 
 .73175 
 .73155 
 .73135 
 
 .69277 
 .69298 
 .69319 
 .69340 
 .69361 
 .69382 
 .69403 
 .69424 
 .69445 
 .69466 
 
 .72116 
 .72095 
 .72075 
 .72055 
 .72035 
 .72015 
 .71995 
 .71974 
 .71954 
 .71934 
 
 .70525 
 .70546 
 .70567 
 .70587 
 .70608 
 .70628 
 .70649 
 .70670 
 .70690 
 .70711 
 
 .70896 
 .70875 
 .70855 
 .70834 
 .70813 
 .70793 
 .70772 
 .70752 
 .70731 
 .70711 
 
 
 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 Cosine 
 
 Sine 
 
 
 t 
 
 49 
 
 48 
 
 47 
 
 46 
 
 45 
 
 
1000 
 
 NATURAL TANGENTS AND COTANGENTS 
 
 f 
 
 
 
 > 
 
 V 
 
 > 
 
 2 
 
 J 
 
 3 
 
 9 
 
 '1 
 
 9 
 
 f 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .00000 
 
 Infln. 
 
 .01746 
 
 57.2900 
 
 .03492 
 
 28.6363 
 
 .05241 
 
 19.0811 
 
 .06993 
 
 14.3007 
 
 60 
 
 1 
 
 .00029 
 
 3437.75 
 
 .01775 
 
 56.3506 
 
 .03521 
 
 28.3994 
 
 .05270 
 
 18.9755 
 
 .07022 
 
 14.2411 
 
 59 
 
 2 
 
 .00058 
 
 1718.87 
 
 .01804 
 
 55.4415 
 
 .03550 
 
 28.1664 
 
 .05299 
 
 18.8711 
 
 .07051 
 
 14.1821 
 
 58 
 
 3 
 
 .00087 
 
 1145.92 
 
 .01833 
 
 54.5613 
 
 .03579 
 
 27.9372 
 
 .05328 
 
 18.7678 
 
 .07080 
 
 14.1235 
 
 57 
 
 4 
 
 .00116 
 
 859.436 
 
 .01862 
 
 53.7086 
 
 .03609 
 
 27.7117 
 
 .05357 
 
 18.6656 
 
 .07110 
 
 14.0655 
 
 56 
 
 5 
 
 .00145 
 
 687.549 
 
 .01891 
 
 52.8821 
 
 .03638 
 
 27.4899 
 
 .05387 
 
 18.5645 
 
 .07139 
 
 14.0079 
 
 55 
 
 6 
 
 .00175 
 
 572.957 
 
 .01920 
 
 52.0807 
 
 .03667 
 
 27.2715 
 
 .05416 
 
 18.4645 
 
 .07168 
 
 13.9507 
 
 54 
 
 7 
 
 .00204 
 
 491.106 
 
 .01949 
 
 51.3032 
 
 .03696 
 
 27.0566 
 
 .05445 
 
 18.3655 
 
 .07197 
 
 13.8940 
 
 53 
 
 8 
 
 .00233 
 
 429.718 
 
 .01978 
 
 50.5485 
 
 .03725 
 
 26.8450 
 
 .05474 
 
 18.2677 
 
 .07227 
 
 13.8378 
 
 52 
 
 9 
 
 .00262 
 
 381.971 
 
 .02007 
 
 49.8157 
 
 .03754 
 
 26.6367 
 
 .05503 
 
 18.1708 
 
 .07256 
 
 13.7821 
 
 51 
 
 10 
 
 .00291 
 
 343.774 
 
 .02036 
 
 49.1039 
 
 .03783 
 
 26.4316 
 
 .05533 
 
 18.0750 
 
 .07285 
 
 13.7267 
 
 50 
 
 11 
 
 .00320 
 
 312.521 
 
 .02066 
 
 48.4121 
 
 .03812 
 
 26.2296 
 
 .05562 
 
 17.9802 
 
 .07314 
 
 13.6719 
 
 49 
 
 12 
 
 .00349 
 
 286.478 
 
 .02095 
 
 47.7395 
 
 .03842 
 
 26.0307 
 
 .05591 
 
 17.8863 
 
 .07344 
 
 13.6174 
 
 48 
 
 13 
 
 .00378 
 
 264.441 
 
 .02124 
 
 47.0853 
 
 .03871 
 
 25.8348 
 
 .05620 
 
 17.7934 
 
 .07373 
 
 13.5634 
 
 47 
 
 14 
 
 .00407 
 
 245.552 
 
 .02153 
 
 46.4489 
 
 .03900 
 
 25.6418 
 
 .05649 
 
 17.7015 
 
 .07402 
 
 13.5098 
 
 46 
 
 15 
 
 .00436 
 
 229.182 
 
 .02182 
 
 45.8294 
 
 .03929 
 
 25.4517 
 
 .05678 
 
 17.6106 
 
 .07431 
 
 13.4566 
 
 45 
 
 16 
 
 .00465 
 
 214.858 
 
 .02211 
 
 45.2261 
 
 .03958 
 
 25.2644 
 
 .05708 
 
 17.5205 
 
 .07461 
 
 13.4039 
 
 44 
 
 17 
 
 .00495 
 
 202.219 
 
 .02240 
 
 44.6386 
 
 .03987 
 
 25.0798 
 
 .05737 
 
 17.4314 
 
 .07490 
 
 13.3515 
 
 43 
 
 18 
 
 .00524 
 
 190.984 
 
 .02269 
 
 44.0661 
 
 .04016 
 
 24.8978 
 
 .05766 
 
 17.3432 
 
 .07519 
 
 13.2996 
 
 42 
 
 19 
 
 .00553 
 
 180.932 
 
 .02298 
 
 43.5081 
 
 .04046 
 
 24.7185 
 
 .05795 
 
 17.2558 
 
 .07548 
 
 13.2480 
 
 41 
 
 20 
 
 .00682 
 
 171.885 
 
 .02328 
 
 42.9641 
 
 .04075 
 
 24.5418 
 
 .05824 
 
 17.1693 
 
 .07578 
 
 13.1969 
 
 40 
 
 21 
 
 .00611 
 
 163.700 
 
 .02357 
 
 42.4335 
 
 .04104 
 
 24.3675 
 
 .05854 
 
 17.0837 
 
 .07607 
 
 13.1461 
 
 39 
 
 22 
 
 .00640 
 
 156.259 
 
 .02386 
 
 41.9158 
 
 .04133 
 
 24.1957 
 
 .05883 
 
 16.9990 
 
 .07636 
 
 13.0958 
 
 38 
 
 23 
 
 .00669 
 
 149.465 
 
 .02415 
 
 41.4106 
 
 .04162 
 
 24.0263 
 
 .05912 
 
 16.9150 
 
 .07665 
 
 13.0458 
 
 37 
 
 24 
 
 .00698 
 
 143.237 
 
 .02444 
 
 40.9174 
 
 .04191 
 
 23.8593 
 
 .05941 
 
 16.8319 
 
 .07695 
 
 12.9962 
 
 36 
 
 25 
 
 .00727 
 
 137.507 
 
 .02473 
 
 40.4358 
 
 .04220 
 
 23.6945 
 
 .05970 
 
 16.7496 
 
 .07724 
 
 12.9469 
 
 35 
 
 26 
 
 .00756 
 
 132.219 
 
 .02502 
 
 39.9655 
 
 .04250 
 
 23.5321 
 
 .05999 
 
 16.6681 
 
 .07753 
 
 12.8981 
 
 34 
 
 27 
 
 .00785 
 
 127.321 
 
 .02531 
 
 39.5059 
 
 .04279 
 
 23.3718 
 
 .06029 
 
 16.5874 
 
 .07782 
 
 12.8496 
 
 33 
 
 28 
 
 .00815 
 
 122.774 
 
 .02560 
 
 39.0568 
 
 .04308 
 
 23.2137 
 
 .06058 
 
 16.5075 
 
 .07812 
 
 12.8014 
 
 32 
 
 29 
 
 .00844 
 
 118.540 
 
 .02589 
 
 38.6177 
 
 .04337 
 
 23.0577 
 
 .06087 
 
 16.4283 
 
 .07841 
 
 12.7536 
 
 31 
 
 30 
 
 .00873 
 
 114.589 
 
 .02619 
 
 38.1885 
 
 .04366 
 
 22.9038 
 
 .06116 
 
 16.3499 
 
 .07870 
 
 12.7062 
 
 30 
 
 31 
 
 .00902 
 
 110.892 
 
 .0?648 
 
 37.7686 
 
 .04395 
 
 22.7519 
 
 .06145 
 
 16.2722 
 
 .07899 
 
 12.6591 
 
 29 
 
 32 
 
 .00931 
 
 107.426 
 
 .02677 
 
 37.3579 
 
 .04424 
 
 22.6020 
 
 .06175 
 
 16.1952 
 
 .07929 
 
 12.6124 
 
 28 
 
 33 
 
 .00960 
 
 104.171 
 
 .02706 
 
 36.9560 
 
 .04454 
 
 22.4541 
 
 .06204 
 
 16.1190 
 
 .07958 
 
 12.5660 
 
 27 
 
 34 
 
 .00989 
 
 101.107 
 
 .02735 
 
 36.5627 
 
 .04483 
 
 22.3081 
 
 .06233 
 
 16.0435 
 
 .07987 
 
 12.5199 
 
 26 
 
 35 
 
 .01018 
 
 98.2179 
 
 .02764 
 
 36.1776 
 
 .04512 
 
 22.1640 
 
 .06262 
 
 15.9687 
 
 .08017 
 
 12.4742 
 
 25 
 
 36 
 
 .01047 
 
 95.4895 
 
 .02793 
 
 35.8006 
 
 .04541 
 
 22.0217 
 
 .06291 
 
 15.8945 
 
 .08046 
 
 12.4288 
 
 24 
 
 37 
 
 .01076 
 
 92.9085 
 
 .02822 
 
 35.4313 
 
 .04570 
 
 21.8813 
 
 .06321 
 
 15.8211 
 
 .08075 
 
 12.3838 
 
 23 
 
 38 
 
 .01105 
 
 90.4633 
 
 .02851 
 
 35.0695 
 
 .04599 
 
 21.7426 
 
 .06350 
 
 15.7483 
 
 .08104 
 
 12.3390 
 
 22 
 
 39 
 
 .01135 
 
 88.1436 
 
 .02881 
 
 34.7151 
 
 .04628 
 
 21.6056 
 
 .06379 
 
 15.6762 
 
 .08134 
 
 12.2946 
 
 21 
 
 40 
 
 .01164 
 
 85.9398 
 
 .02910 
 
 34.3678 
 
 .04658 
 
 21.4704 
 
 .06408 
 
 15.6048 
 
 .08163 
 
 12.2505 
 
 20 
 
 41 
 
 .01193 
 
 83.8435 
 
 .02939 
 
 34.0273 
 
 .04687 
 
 21.3369 
 
 .06437 
 
 15.5340 
 
 .08192 
 
 12.2067 
 
 19 
 
 42 
 
 .01222 
 
 81.8470 
 
 .02968 
 
 33.6935 
 
 .04716 
 
 21.2049 
 
 .06467 
 
 15.4638 
 
 .08221 
 
 12.1632 
 
 18 
 
 43 
 
 .01251 
 
 79.9434 
 
 .02997 
 
 33.3662 
 
 .04745 
 
 21.0747 
 
 .06496 
 
 15.3943 
 
 .08251 
 
 12.1201 
 
 17 
 
 44 
 
 .01280 
 
 78.1263 
 
 .03026 
 
 33.0452 
 
 .04774 
 
 20.9460 
 
 .06525 
 
 15.3254 
 
 .08280 
 
 12.0772 
 
 16 
 
 45 
 
 .01309 
 
 76.3900 
 
 .03055 
 
 32.7303 
 
 .04803 
 
 20.8188 
 
 .06554 
 
 15.2571 
 
 .08309 
 
 12.0346 
 
 15 
 
 46 
 
 .01338 
 
 74.7292 
 
 .03084 
 
 32.4213 
 
 .04833 
 
 20.6932 
 
 .06584 
 
 15.1893 
 
 .08339 
 
 11.9923 
 
 14 
 
 47 
 
 .01367 
 
 73.1390 
 
 .03114 
 
 32.1181 
 
 .04862 
 
 20.5691 
 
 .06613 
 
 15.1222 
 
 .08368 
 
 11.9504 
 
 13 
 
 48 
 
 .01396 
 
 71.6151 
 
 .03143 
 
 31.8205 
 
 .04891 
 
 20.4465 
 
 .06642 
 
 15.0557 
 
 .08397 
 
 11.9087 
 
 12 
 
 49 
 
 .01425 
 
 70.1533 
 
 .03172 
 
 31.5284 
 
 .04920 
 
 20.3253 
 
 .06671 
 
 14.9898 
 
 .08427 
 
 11.8673 
 
 11 
 
 50 
 
 .01455 
 
 68.7501 
 
 .03201 
 
 31.2416 
 
 .04949 
 
 20.2056 
 
 .06700 
 
 14.9244 
 
 .08456 
 
 11.8262 
 
 10 
 
 51 
 
 .01484 
 
 67.4019 
 
 .03230 
 
 30.9599 
 
 .04978 
 
 20.0872 
 
 .06730 
 
 14.8596 
 
 .08485 
 
 11.7853 
 
 9 
 
 52 
 
 .01513 
 
 66.1055 
 
 .03259 
 
 30.6833 
 
 .05007 
 
 19.9702 
 
 .06759 
 
 14.7954 
 
 .08514 
 
 11.7448 
 
 8 
 
 53 
 
 .01542 
 
 64.8580 
 
 .03288 
 
 30.4116 
 
 .05037 
 
 19.8546 
 
 .06788 
 
 14.7317 
 
 .08544 
 
 11.7045 
 
 
 54 
 
 .01571 
 
 63.6567 
 
 .03317 
 
 30.1446 
 
 .05066 
 
 19.7403 
 
 .06817 
 
 14.6685 
 
 .08573 
 
 11.6645 
 
 
 55 
 
 .01600 
 
 62.4992 
 
 .03346 
 
 29.8823 
 
 .05095 
 
 19.6273 
 
 .06847 
 
 14.6059 
 
 .08602 
 
 11.6248 
 
 
 56 
 
 .01629 
 
 61.3829 
 
 .03376 
 
 29.6245 
 
 .05124 
 
 19.5156 
 
 .06876 
 
 14.5438 
 
 .08632 
 
 11.5853 
 
 
 57 
 
 .01658 
 
 60.3058 
 
 .03405 
 
 29.3711 
 
 .05153 
 
 19.4051 
 
 .06905 
 
 14.4823 
 
 .08661 
 
 11.5461 
 
 
 58 
 
 .01687 
 
 59.2659 
 
 .03434 
 
 29.1220 
 
 .05182 
 
 19.2959 
 
 .06934 
 
 14.4212 
 
 .08690 
 
 11.5072 
 
 
 59 
 
 .01716 
 
 58.2612 
 
 .03463 
 
 28.8771 
 
 .05212 
 
 19.1879 
 
 .06963 
 
 14.3607 
 
 .08720 
 
 11.4685 
 
 
 60 
 
 .01746 
 
 57.2900 
 
 .03492 
 
 28.6363 
 
 .05241 
 
 19.0811 
 
 .06993 
 
 14.3007 
 
 .08749 
 
 11.4301 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 / 
 
 8 
 
 9 
 
 8! 
 
 3 
 
 8 
 
 7 
 
 8 
 
 5 
 
 8 
 
 5 
 
 
NATURAL TANGENTS AND COTANGENTS 
 
 1001 
 
 
 5 
 
 
 
 6 
 
 o 
 
 7 
 
 
 
 8 
 
 Q 
 
 9 
 
 o 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 .08749 
 
 11.4301 
 
 .10510 
 
 9.51436 
 
 .12278 
 
 8.14435 
 
 .14054 
 
 7.11537 
 
 .15838 
 
 6.31375 
 
 60 
 
 
 .08778 
 
 11.3919 
 
 .10540 
 
 9.48781 
 
 .12308 
 
 8.12481 
 
 .14084 
 
 7.10038 
 
 .15868 
 
 6.30189 
 
 59 
 
 
 .08807 
 
 11.3540 
 
 .10569 
 
 9.46141 
 
 .12338 
 
 8.10536 
 
 .14113 
 
 7.08546 
 
 .15898 
 
 6.29007 
 
 58 
 
 
 .08837 
 
 11.3163 
 
 .10599 
 
 9.43515 
 
 .12367 
 
 8.08600 
 
 .14143 
 
 7.07059 
 
 .15928 
 
 6.27829 
 
 57 
 
 
 .08866 
 
 11.2789 
 
 .10628 
 
 9.40904 
 
 .12397 
 
 8.06674 
 
 .14173 
 
 7.05579 
 
 .15958 
 
 6.26655 
 
 56 
 
 
 .08895 
 
 11.2417 
 
 .10657 
 
 9.38307 
 
 .12426 
 
 8.04756 
 
 .14202 
 
 7.04105 
 
 .15988 
 
 6.25486 
 
 55 
 
 
 .08925 
 
 11.2048 
 
 .10687 
 
 9.35724 
 
 .12456 
 
 8.02848 
 
 .14232 
 
 7.02637 
 
 .16017 
 
 6.24321 
 
 54 
 
 
 .08954 
 
 11.1681 
 
 .10716 
 
 9.33155 
 
 .12485 
 
 8.00948 
 
 .14262 
 
 7.01174 
 
 .16047 
 
 6.23160 
 
 53 
 
 
 .08983 
 
 11.1316 
 
 .10746 
 
 9.30599 
 
 .12515 
 
 7.99058 
 
 .14291 
 
 6.99718 
 
 .16077 
 
 6.22003 
 
 52 
 
 
 .09013 
 
 11.0954 
 
 .10775 
 
 9.28058 
 
 .12544 
 
 7.97176 
 
 .14321 
 
 6.98268 
 
 .16107 
 
 6.20851 
 
 51 
 
 10 
 
 .09042 
 
 11.0594 
 
 .10805 
 
 9.25530 
 
 .12574 
 
 7.95302 
 
 .14351 
 
 6.96823 
 
 .16137 
 
 6.19703 
 
 50 
 
 11 
 
 .09071 
 
 11.0237 
 
 .10834 
 
 9.23016 
 
 .12603 
 
 7.93438 
 
 .14381 
 
 6.95385 
 
 .16167 
 
 6.18559 
 
 49 
 
 12 
 
 .09101 
 
 10.9882 
 
 .10863 
 
 9.20516 
 
 .12633 
 
 7.91582 
 
 .14410 
 
 6.93952 
 
 .16196 
 
 6.17419 
 
 48 
 
 13 
 
 .09130 
 
 10.9529 
 
 .10893 
 
 9.18028 
 
 .12662 
 
 7.89734 
 
 .14440 
 
 6.92525 
 
 .16226 
 
 6.16283 
 
 47 
 
 14 
 
 .09159 
 
 10.9178 
 
 .10922 
 
 9.15554 
 
 .12692 
 
 7.87895 
 
 .14470 
 
 6.91104 
 
 .16256 
 
 6.15151 
 
 46 
 
 15 
 
 .09189 
 
 10.8829 
 
 .10952 
 
 9.13093 
 
 .12722 
 
 7.86064 
 
 .14499 
 
 6.89688 
 
 .16286 
 
 6.14023 
 
 45 
 
 16 
 
 .09218 
 
 10.8483 
 
 .10981 
 
 9.10646 
 
 .12751 
 
 7.84242 
 
 .14529 
 
 6.88278 
 
 .16316 
 
 6.12899 
 
 44 
 
 17 
 
 .09247 
 
 10.8139 
 
 .11011 
 
 9.08211 
 
 .12781 
 
 7.82428 
 
 .14559 
 
 6.86874 
 
 .16346 
 
 6.11779 
 
 43 
 
 18 
 
 .09277 
 
 10.7797 
 
 .11040 
 
 9.05789 
 
 .12810 
 
 7.80622 
 
 .14588 
 
 6.85475 
 
 .16376 
 
 6.10664 
 
 42 
 
 19 
 
 .09306 
 
 10.7457 
 
 .11070 
 
 9.03379 
 
 .12840 
 
 7.78825 
 
 .14618 
 
 6.84082 
 
 .16405 
 
 6.09552 
 
 41 
 
 20 
 
 .09335 
 
 10.7119 
 
 .11099 
 
 9.00983 
 
 .12869 
 
 7.77035 
 
 .14648 
 
 6.82694 
 
 .16435 
 
 6.08444 
 
 40 
 
 21 
 
 .09365 
 
 10.6783 
 
 .11128 
 
 8.98598 
 
 .12899 
 
 7.75254 
 
 .14678 
 
 6.81312 
 
 .16465 
 
 6.07340 
 
 39 
 
 22 
 
 .09394 
 
 10.6450 
 
 .11158 
 
 8.96227 
 
 .12929 
 
 7.73480 
 
 .14707 
 
 6.79936 
 
 .16495 
 
 6.06240 
 
 38 
 
 23 
 
 .09423 
 
 10.6118 
 
 .11187 
 
 8.93867 
 
 .12958 
 
 7.71715 
 
 .14737 
 
 6.78564 
 
 .16525 
 
 6.05143 
 
 37 
 
 24 
 
 .09453 
 
 10.5789 
 
 .11217 
 
 8.91520 
 
 .12988 
 
 7.69957 
 
 .14767 
 
 6.77199 
 
 .16555 
 
 6.04051 
 
 36 
 
 25 
 
 .09482 
 
 10.5462 
 
 .11246 
 
 8.89185 
 
 .13017 
 
 7.68208 
 
 .14796 
 
 6.75838 
 
 .16585 
 
 6.02962 
 
 35 
 
 26 
 
 .09511 
 
 10.5136 
 
 .11276 
 
 8.86862 
 
 .13047 
 
 7.66466 
 
 .14826 
 
 6.74483 
 
 .16615 
 
 6.01878 
 
 34 
 
 27 
 
 .09541 
 
 10.4813 
 
 .11305 
 
 8.84551 
 
 .13076 
 
 7.64732 
 
 .14856 
 
 6.73133 
 
 .16645 
 
 6.00797 
 
 33 
 
 28 
 
 .09570 
 
 10.4491 
 
 .11335 
 
 8.82252 
 
 .13106 
 
 7.63005 
 
 .14886 
 
 6.71789 
 
 .16674 
 
 5.99720 
 
 32 
 
 29 
 
 .09600 
 
 10.4.172 
 
 .11364 
 
 8.79964 
 
 .13136 
 
 7.61287 
 
 .14915 
 
 6.70450 
 
 .16704 
 
 5.98646 
 
 31 
 
 30 
 
 .09629 
 
 10.3854 
 
 .11394 
 
 8.77689 
 
 .13165 
 
 7.59575 
 
 .14945 
 
 6.69116 
 
 .16734 
 
 5.97576 
 
 30 
 
 31 
 
 .09658 
 
 10.3538 
 
 .11423 
 
 8.75425 
 
 .13195 
 
 7.57872 
 
 .14975 
 
 6.67787 
 
 .16764 
 
 5.96510 
 
 29 
 
 32 
 
 .09688 
 
 10.3224 
 
 .11452 
 
 8.73172 
 
 .13224 
 
 7.56176 
 
 .15005 
 
 6.66463 
 
 .16794 
 
 5.95448 
 
 28 
 
 33 
 
 .09717 
 
 10.2913 
 
 .11482 
 
 8.70931 
 
 .13254 
 
 7.54487 
 
 .15034 
 
 6.65144 
 
 .16824 
 
 5.94390 
 
 27 
 
 34 
 
 .09746 
 
 10.2602 
 
 .11511 
 
 8.68701 
 
 .13284 
 
 7.52806 
 
 .15064 
 
 6.63831 
 
 .16854 
 
 5.93335 
 
 26 
 
 35 
 
 .09776 
 
 10.2294 
 
 .11541 
 
 8.66482 
 
 .13313 
 
 7.51132 
 
 .15094 
 
 6.62523 
 
 .16884 
 
 5.92283 
 
 25 
 
 36 
 
 .09805 
 
 10.1988 
 
 .11570 
 
 8.64275 
 
 .13343 
 
 7.49465 
 
 .15124 
 
 6.61219 
 
 .16914 
 
 5.91236 
 
 24 
 
 37 
 
 .09834 
 
 10.1683 
 
 .11600 
 
 8.62078 
 
 .13372 
 
 7.47806 
 
 .15153 
 
 6.59921 
 
 .16944 
 
 5.90191 
 
 23 
 
 38 
 
 .09864 
 
 10.1381 
 
 .11629 
 
 8.59893 
 
 .13402 
 
 7.46154 
 
 .15183 
 
 6.58627 
 
 .16974 
 
 5.89151 
 
 22 
 
 39 
 
 .09893 
 
 10.1080 
 
 .11659 
 
 8.57718 
 
 .13432 
 
 7.44509 
 
 .15213 
 
 6.57339 
 
 .17004 
 
 5.88114 
 
 21 
 
 40 
 
 .09923 
 
 10.0780 
 
 .11688 
 
 8.55555 
 
 .13461 
 
 7.42871 
 
 .15243 
 
 6.56055 
 
 .17033 
 
 5.87080 
 
 20 
 
 41 
 
 .09952 
 
 10.0483 
 
 .11718 
 
 8.53402 
 
 .13491 
 
 7.41240 
 
 .15272 
 
 6.54777 
 
 .17063 
 
 5.86051 
 
 19 
 
 42 
 
 .09981 
 
 10.0187 
 
 .11747 
 
 8.51259 
 
 .13521 
 
 V. 39616 
 
 .15302 
 
 6.53503 
 
 .17093 
 
 5.85024 
 
 18 
 
 43 
 
 .10011 
 
 9.98931 
 
 .11777 
 
 8.49128 
 
 .13550 
 
 7.37999 
 
 .15332 
 
 6.52234 
 
 .17123 
 
 5.84001 
 
 17 
 
 44 
 
 .10040 
 
 9.96007 
 
 .11806 
 
 8.47007 
 
 .13580 
 
 7.36389 
 
 .15362 
 
 6.50970 
 
 .17153 
 
 5.82982 
 
 16 
 
 45 
 
 .10069 
 
 9.93101 
 
 .11836 
 
 8.44896 
 
 .13609 
 
 7.34786 
 
 .15391 
 
 6.49710 
 
 .17183 
 
 5.81966 
 
 15 
 
 46 
 
 .10099 
 
 9.90211 
 
 .11865 
 
 8.42795 
 
 .13639 
 
 7.33190 
 
 .15421 
 
 6.48456 
 
 .17213 
 
 5.80953 
 
 14 
 
 47 
 
 .10128 
 
 9.87338 
 
 .11895 
 
 8.40705 
 
 .13669 
 
 7.31600 
 
 .15451 
 
 6.47206 
 
 .17243 
 
 5.79944 
 
 13 
 
 48 
 
 .10158 
 
 9.84482 
 
 .11924 
 
 8.38625 
 
 .13698 
 
 7.30018 
 
 .15481 
 
 6.45961 
 
 .17273 
 
 5.78938 
 
 12 
 
 49 
 
 .10187 
 
 9.81641 
 
 .11954 
 
 8.36555 
 
 .13728 
 
 7.28442 
 
 .15511 
 
 6.44720 
 
 .17303 
 
 5.77936 
 
 11 
 
 50 
 
 .10216 
 
 9.78817 
 
 .11983 
 
 8.34496 
 
 .13758 
 
 7.26873 
 
 .15540 
 
 6.43484 
 
 .17333 
 
 5.76937 
 
 10 
 
 51 
 
 .10246 
 
 9.76009 
 
 .12013 
 
 8.32446 
 
 .13787 
 
 7.25310 
 
 .15570 
 
 6.42253 
 
 .17363 
 
 5.75941 
 
 9 
 
 52 
 
 .10275 
 
 9.73217 
 
 .12042 
 
 8.30406 
 
 .13817 
 
 7.23754 
 
 .15600 
 
 6.41026 
 
 .17393 
 
 5.74949 
 
 8 
 
 53 
 
 .10305 
 
 9.70441 
 
 .12072 
 
 8.28376 
 
 .13846 
 
 7.22204 
 
 .15630 
 
 6.39804 
 
 .17423 
 
 5.73960 
 
 7 
 
 54 
 
 .10334 
 
 9.67680 
 
 .12101 
 
 8.26355 
 
 .13876 
 
 7.20661 
 
 .15660 
 
 6.88587 
 
 .17453 
 
 5.72974 
 
 
 55 
 
 .10363 
 
 9.64935 
 
 .12131 
 
 8.24345 
 
 .13906 
 
 7.19125 
 
 .15689 
 
 6.37374 
 
 .17483 
 
 5.71992 
 
 
 56 
 
 .10393 
 
 9.62205 
 
 .12160 
 
 8.22344 
 
 .13935 
 
 7.17594 
 
 .15719 
 
 6.36165 
 
 .17513 
 
 5.71013 
 
 
 57 
 
 .10422 
 
 9.59490 
 
 .12190 
 
 8.20352 
 
 .13965 
 
 7.16071 
 
 .15749 
 
 6.34961 
 
 .17543 
 
 5.70037 
 
 
 58 
 
 .10452 
 
 9.56791 
 
 .12219 
 
 8.18370 
 
 .13995 
 
 7.14553 
 
 .15779 
 
 6.33761 
 
 .17573 
 
 5.69064 
 
 
 59 
 
 .10481 
 
 9.54106 
 
 .12249 
 
 8.16398 
 
 .14024 
 
 7.13042 
 
 .15809 
 
 6.32566 
 
 .17603 
 
 5.68094 
 
 
 60 
 
 .10510 
 
 9.51436 
 
 .12278 
 
 8.14435 
 
 .14054 
 
 7.11537 
 
 .15838 
 
 6.31375 
 
 .17633 
 
 5.67128 
 
 
 
 
 
 
 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 o ang 
 
 
 
 
 
 f 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 8 
 
 4 
 
 & 
 
 J 
 
 8 
 
 2 
 
 8 
 
 L 
 
 8 
 
 
 
 
1002 
 
 NATURAL TANGENTS AND COTANGENTS 
 
 t 
 
 1( 
 
 ) 
 
 1 
 
 L 
 
 1 
 
 y> 
 
 1, 
 
 5 
 
 3 
 
 40 
 
 / 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .17633 
 
 5.67128 
 
 .19438 
 
 5.14455 
 
 .21256 
 
 4.70463 
 
 .23087 
 
 4.33148 
 
 .24933 
 
 4.01078 
 
 60 
 
 
 .17663 
 
 5.66165 
 
 .19468 
 
 5.13658 
 
 .21286 
 
 4.69791 
 
 .23117 
 
 4.32573 
 
 .24964 
 
 4.00582 
 
 59 
 
 
 .17693 
 
 5.65205 
 
 .19498 
 
 5.12862 
 
 .21316 
 
 4.69121 
 
 .23148 
 
 4.32001 
 
 .24995 
 
 4.00086 
 
 58 
 
 
 .17723 
 
 5.64248 
 
 .19529 
 
 5.12069 
 
 .21347 
 
 4.68452 
 
 .23179 
 
 4.31430 
 
 .25026 
 
 3.99592 
 
 57 
 
 
 .17753 
 
 5.63295 
 
 .19559 
 
 5.11279 
 
 .21377 
 
 4.67786 
 
 .23209 
 
 4.30860 
 
 .25056 
 
 3.99099 
 
 56 
 
 
 .17783 
 
 5.62344 
 
 .19589 
 
 5.10490 
 
 .21408 
 
 4.67121 
 
 .23240 
 
 4.80291 
 
 .25087 
 
 3.98607 
 
 55 
 
 
 .17813 
 
 5.61397 
 
 .19619 
 
 5.09704 
 
 .21438 
 
 4.66458 
 
 .23271 
 
 4.29724 
 
 .25118 
 
 3.98117 
 
 54 
 
 
 .17843 
 
 5.60452 
 
 .19649 
 
 5.08921 
 
 .21469 
 
 4.65797 
 
 .23301 
 
 4.29159 
 
 .25149 
 
 3.97627 
 
 53 
 
 8 
 
 .17873 
 
 5.59511 
 
 .19680 
 
 5.08139 
 
 .21499 
 
 4.65138 
 
 .23332 
 
 4.28595 
 
 .25180 
 
 3.97139 
 
 52 
 
 9 
 
 .17903 
 
 5.58573 
 
 .19710 
 
 5.07360 
 
 .21529 
 
 4.64480 
 
 .23363 
 
 4.28032 
 
 .25211 
 
 3.96651 
 
 51 
 
 10 
 
 .17933 
 
 5.57638 
 
 .19740 
 
 5.06584 
 
 .21560 
 
 4.63825 
 
 .23393 
 
 4.27471 
 
 .25242 
 
 3.96165 
 
 50 
 
 11 
 
 .17963 
 
 5.56706 
 
 .19770 
 
 5.05809 
 
 .21590 
 
 4.63171 
 
 .23424 
 
 4.26911 
 
 .25273 
 
 3.95680 
 
 49 
 
 12 
 
 .17993 
 
 5.55777 
 
 .19801 
 
 5.05037 
 
 .21621 
 
 4.62518 
 
 .23455 
 
 4.26352 
 
 .25304 
 
 3.95196 
 
 48 
 
 13 
 
 .18023 
 
 5.54851 
 
 .19831 
 
 5.04267 
 
 .21651 
 
 4.61868 
 
 .23485 
 
 4.25795 
 
 .25335 
 
 3.94713 
 
 47 
 
 14 
 
 .18053 
 
 5.53927 
 
 .19861 
 
 5.03499 
 
 .21682 
 
 4.61219 
 
 .23516 
 
 4.25239 
 
 .25366 
 
 3.94232 
 
 46 
 
 15 
 
 .18083 
 
 5.53007 
 
 .19891 
 
 5.02734 
 
 .21712 
 
 4.60572 
 
 .23547 
 
 4.24685 
 
 .25397 
 
 3.93751 
 
 45 
 
 16 
 
 .18113 
 
 5.52090 
 
 .19921 
 
 5.01971 
 
 .21743 
 
 4.59927 
 
 .23578 
 
 4.24132 
 
 .25428 
 
 3.93271 
 
 44 
 
 17 
 
 .18143 
 
 5.51176 
 
 .19952 
 
 5.01210 
 
 .21773 
 
 4.59283 
 
 .23608 
 
 4.23580 
 
 .25459 
 
 3.92793 
 
 43 
 
 18 
 
 .18173 
 
 5.50264 
 
 .19982 
 
 5.00451 
 
 .21804 
 
 4.58641 
 
 .23639 
 
 4.23030 
 
 .25490 
 
 3.92316 
 
 42 
 
 19 
 
 .18203 
 
 5.49356 
 
 .20012 
 
 4.99695 
 
 .21834 
 
 4.58001 
 
 .23670 
 
 4.22481 
 
 .25521 
 
 3.91839 
 
 41 
 
 20 
 
 .18233 
 
 5.48451 
 
 .20042 
 
 4.98940 
 
 .21864 
 
 4.57363 
 
 .23TOO 
 
 4.21933 
 
 .25552 
 
 3.91364 
 
 40 
 
 21 
 
 .18263 
 
 5.47548 
 
 .20073 
 
 4.98188 
 
 .21895 
 
 4.56726 
 
 .23731 
 
 4.21387 
 
 .25583 
 
 3.90890 
 
 39 
 
 22 
 
 .18293 
 
 5.46648 
 
 .20103 
 
 4.97438 
 
 .21925 
 
 4.56091 
 
 .23762 
 
 4.20842 
 
 .25614 
 
 3.90417 
 
 38 
 
 23 
 
 .18523 
 
 5.45751 
 
 .20133 
 
 4.96690 
 
 .21956 
 
 4.55458 
 
 .23793 
 
 4.20298 
 
 .25645 
 
 3.89945 
 
 37 
 
 24 
 
 .18353 
 
 5.44857 
 
 .20164 
 
 4.95945 
 
 .21986 
 
 4.54826 
 
 .23823 
 
 4.19756 
 
 .25676 
 
 3.89474 
 
 36 
 
 25 
 
 .18384 
 
 5.43966 
 
 .20194 
 
 4.95201 
 
 .22017 
 
 4.54196 
 
 .23854 
 
 4.19215 
 
 .25707 
 
 3.89004 
 
 35 
 
 26 
 
 .18414 
 
 5.43077 
 
 .20224 
 
 4.94460 
 
 .22047 
 
 4.53568 
 
 .23885 
 
 4.18675 
 
 .25738 
 
 3.88536 
 
 34 
 
 27 
 
 .18444 
 
 5.42192 
 
 .20254 
 
 4.93721 
 
 .22078 
 
 4.52941 
 
 .23916 
 
 4.18137 
 
 .25769 
 
 3.88068 
 
 33 
 
 28 
 
 .18474 
 
 5.41309 
 
 .20285 
 
 4.92984 
 
 .22108 
 
 4.52316 
 
 .23946 
 
 4.17600 
 
 .25800 
 
 3.87601 
 
 32 
 
 29 
 
 .18504 
 
 6.40429 
 
 .20315 
 
 4.92249 
 
 .22139 
 
 4.51693 
 
 .23977 
 
 4.17064 
 
 .25831 
 
 3.87136 
 
 31 
 
 30 
 
 .18534 
 
 5.39552 
 
 .20345 
 
 4.91516 
 
 .22169 
 
 4.51071 
 
 .24008 
 
 4.16530 
 
 .25862 
 
 3.86671 
 
 30 
 
 31 
 
 .18564 
 
 5.38677 
 
 .20376 
 
 4.90785 
 
 .22200 
 
 4.50451 
 
 .24039 
 
 4.15997 
 
 .25893 
 
 3.86208 
 
 29 
 
 32 
 
 .18594 
 
 5.37805 
 
 .20406 
 
 4.90056 
 
 .22231 
 
 4.49832 
 
 .24069 
 
 4.15465 
 
 .25924 
 
 3.85745 
 
 28 
 
 33 
 
 .18624 
 
 5.36936 
 
 .20436 
 
 4.89330 
 
 .22261 
 
 4.49215 
 
 .24100 
 
 4.14934 
 
 .25955 
 
 3.85284 
 
 27 
 
 34 
 
 .18654 
 
 5.36070 
 
 .20466 
 
 4.88605 
 
 .22292 
 
 4.48600 
 
 .24131 
 
 4.14405 
 
 .25986 
 
 3.84824 
 
 26 
 
 35 
 
 .18684 
 
 5.35206 
 
 .20497 
 
 4.87882 
 
 .22322 
 
 4.47986 
 
 .24162 
 
 4.13877 
 
 .26017 
 
 3.84364 
 
 25 
 
 36 
 
 .18714 
 
 5.34345 
 
 .20527 
 
 4.87162 
 
 .22353 
 
 4.47374 
 
 .24193 
 
 4.13350 
 
 .26048 
 
 3.83906 
 
 24 
 
 37 
 
 .18745 
 
 5.33487 
 
 .20557 
 
 4.86444 
 
 .22383 
 
 4.46764 
 
 .24223 
 
 4.12825 
 
 .26079 
 
 3.83449 
 
 23 
 
 38 
 
 .18775 
 
 5.32631 
 
 .20588 
 
 4.85727 
 
 .22414 
 
 4.46155 
 
 .24254 
 
 4.12301 
 
 .26110 
 
 3.82992 
 
 22 
 
 39 
 
 .18805 
 
 5.31778 
 
 .20618 
 
 4.85013 
 
 .22444 
 
 4.45548 
 
 .24285 
 
 4.11778 
 
 .26141 
 
 3.82537 
 
 21 
 
 40 
 
 .18835 
 
 5.30928 
 
 .20648 
 
 4.84300 
 
 .22475 
 
 4.44942 
 
 .24316 
 
 4.11256 
 
 .26172 
 
 3.82083 
 
 20 
 
 41 
 
 .18865 
 
 5.30080 
 
 .20679 
 
 4.83590 
 
 .22505 
 
 4.44338 
 
 .24347 
 
 4.10736 
 
 .26203 
 
 3.81630 
 
 19 
 
 42 
 
 .18895 
 
 5.29235 
 
 .20709 
 
 
 .22536 
 
 4.43735 
 
 .24377 
 
 4.10216 
 
 .26235 
 
 3.81177 
 
 18 
 
 43 
 
 .18925 
 
 5.28393 
 
 .20739 
 
 4182175 
 
 .22567 
 
 4.43134 
 
 .24408 
 
 4.09699 
 
 .26266 
 
 3.80726 
 
 17 
 
 44 
 
 .18955 
 
 5.27553 
 
 .20770 
 
 4.81471 
 
 .22597 
 
 4.42534 
 
 .24439 
 
 4.09182 
 
 .26297 
 
 3.80276 
 
 16 
 
 45 
 
 .18986 
 
 5.26715 
 
 .20800 
 
 4.80769 
 
 .22628 
 
 4.41936 
 
 .24470 
 
 4.08666 
 
 .26328 
 
 3.79827 
 
 15 
 
 46 
 
 .19016 
 
 5.25880 
 
 .20830 
 
 4.80068 
 
 .22658 
 
 4.41340 
 
 .24501 
 
 4.08152 
 
 .26359 
 
 3.79378 
 
 14 
 
 47 
 
 .19046 
 
 5.25048 
 
 .20861 
 
 4.79370 
 
 .22689 
 
 4.40745 
 
 .24532 
 
 4.07639 
 
 .26390 
 
 3.78931 
 
 13 
 
 48" 
 
 .19076 
 
 5.24218 
 
 .20891 
 
 4.78673 
 
 .22719 
 
 4.40152 
 
 .24562 
 
 4.07127 
 
 .26421 
 
 3.78485 
 
 12 
 
 49 
 
 .19106 
 
 5.23391 
 
 .20921 
 
 4.77978 
 
 .22750 
 
 4.39560 
 
 .24593 
 
 406616 
 
 .26452 
 
 3.78040 
 
 11 
 
 50 
 
 .19186 
 
 5.22566 
 
 .20952 
 
 4.77286 
 
 .22781 
 
 4.38969 
 
 .24624 
 
 4.06107 
 
 .26483 
 
 3.77595 
 
 10 
 
 51 
 
 .19166 
 
 5.21744 
 
 .20982 
 
 4.76595 
 
 .22811 
 
 4.38381 
 
 .24655 
 
 4.05599 
 
 .26515 
 
 3.77152 
 
 9 
 
 52 
 
 .19197 
 
 5.20925 
 
 .21013 
 
 4.75906 
 
 .22842 
 
 4.37793 
 
 .24686 
 
 4.05092 
 
 .26546 
 
 3.76709 
 
 8 
 
 53 
 
 .19227 
 
 5.20107 
 
 .21043 
 
 4.75219 
 
 .22872 
 
 4.37207 
 
 .24717 
 
 4.04586 
 
 .26577 
 
 3.76268 
 
 7 
 
 54 
 
 .19257 
 
 5.19293 
 
 .21073 
 
 4.74534 
 
 .22903 
 
 4.36623 
 
 .24747 
 
 4.04081 
 
 .26608 
 
 3.75828 
 
 6 
 
 55 
 
 .19287 
 
 5.18480 
 
 .21104 
 
 4.73851 
 
 .22934 
 
 4.36040 
 
 .24778 
 
 4.03578 
 
 .26639 
 
 3.75388 
 
 5 
 
 56 
 
 .19317 
 
 5.17671 
 
 .21134 
 
 4.73170 
 
 .22964 
 
 4.35459 
 
 .24809 
 
 4.03076 
 
 .26670 
 
 3.74950 
 
 4 
 
 57 
 
 .19347 
 
 5.16863 
 
 .21164 
 
 4.72490 
 
 .22995 
 
 4.34879 
 
 .24840 
 
 4.02574 
 
 .26701 
 
 3.74512 
 
 3 
 
 58 
 
 .19378 
 
 5.16058 
 
 .21195 
 
 4.71813 
 
 .23026 
 
 4.34300 
 
 .24871 
 
 4.02074 
 
 .26733 
 
 3.74075 
 
 2 
 
 59 
 
 .19408 
 
 5.15256 
 
 .21225 
 
 4.71137 
 
 .23056 
 
 4.33723 
 
 .24902 
 
 4.01576 
 
 .26764 
 
 3.73640 
 
 1 
 
 60 
 
 .19438 
 
 5.14455 
 
 .21256 
 
 4.70463 
 
 .23087 
 
 4.33148 
 
 .24933 
 
 4.01078 
 
 .26795 
 
 3.73205 
 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 1 
 
 7< 
 
 19 
 
 7! 
 
 5 
 
 T 
 
 r 
 
 H 
 
 ) 
 
 7 
 
 5 
 
 t 
 
NATURAL TANGENTS AND COTANGENTS 
 
 1003 
 
 
 11 
 
 > 
 
 If 
 
 > 
 
 H 
 
 o 
 
 1* 
 
 * 
 
 1 
 
 9 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .S6795 
 
 3.73205 
 
 .28675 
 
 3.48741 
 
 .30573 
 
 3.27085 
 
 .32492 
 
 3.07768 
 
 .34433 
 
 2.90421 
 
 60 
 
 1 
 
 .26826 
 
 3.72771 
 
 .28706 
 
 3.48359 
 
 .30605 
 
 3.26745 
 
 .32524 
 
 3.07464 
 
 .34465 
 
 2.90147 
 
 59 
 
 2 
 
 26857 
 
 3.72338 
 
 .28738 
 
 3.47977 
 
 .30637 
 
 3.26406 
 
 .32556 
 
 3.07160 
 
 .34498 
 
 2.89873 
 
 58 
 
 3 
 
 .26888 
 
 3.71907 
 
 .28769 
 
 3.47596 
 
 .30669 
 
 3.26067 
 
 .32588 
 
 3.06857 
 
 .34530 
 
 2.89600 
 
 57 
 
 4 
 
 .26920 
 
 3.71476 
 
 .28800 
 
 3.47216 
 
 .30700 
 
 3.25729 
 
 .32621 
 
 3.06554 
 
 .34563 
 
 2.89327 
 
 56 
 
 5 
 
 .26951 
 
 3.71046 
 
 .28832 
 
 3.46837 
 
 .30732 
 
 3.25392 
 
 .32653 
 
 3.06252 
 
 .34596 
 
 2.89055 
 
 55 
 
 
 .26982 
 
 3.70616 
 
 .28864 
 
 3.46458 
 
 .30764 
 
 3.25055 
 
 .32685 
 
 3.05950 
 
 .34628 
 
 2.88783 
 
 54 
 
 7 
 
 .27013 
 
 3.70188 
 
 .28895 
 
 3.46080 
 
 .30796 
 
 3.24719 
 
 .32717 
 
 3.05649 
 
 .34661 
 
 2.88511 
 
 53 
 
 8 
 
 .27044 
 
 3.69761 
 
 .28927 
 
 3.45703 
 
 .30828 
 
 3.24383 
 
 .32749 
 
 3.05349 
 
 .34693 
 
 2.88240 
 
 52 
 
 9 
 
 .27076 
 
 3.69335 
 
 .28958 
 
 3.45327 
 
 .30860 
 
 3.24049 
 
 .32782 
 
 3.05049 
 
 .34726 
 
 2.87970 
 
 51 
 
 10 
 
 .27107 
 
 3.68909 
 
 .28990 
 
 3.44951 
 
 .30891 
 
 3.23714 
 
 .32814 
 
 3.04749 
 
 .34758 
 
 2.87700 
 
 50 
 
 11 
 
 .27138 
 
 3.68485 
 
 .29021 
 
 3.44576 
 
 .30923 
 
 3.23381 
 
 .32846 
 
 3.04450 
 
 .34791 
 
 2.87430 
 
 49 
 
 12 
 
 .27169 
 
 3.68061 
 
 .29053 
 
 3.44202 
 
 .30955 
 
 3.23048 
 
 .32878 
 
 3.04152 
 
 .34824 
 
 2.87161 
 
 48 
 
 13 
 
 .27201 
 
 3.67638 
 
 .29084 
 
 3.43829 
 
 .30987 
 
 3.22715 
 
 .32911 
 
 3.03854 
 
 .34856 
 
 2.86892 
 
 47 
 
 14 
 
 .27232 
 
 3.67217 
 
 .29116 
 
 3.43456 
 
 .31019 
 
 3.22384 
 
 .32943 
 
 3.03556 
 
 .34889 
 
 2.86624 
 
 46 
 
 15 
 
 .27263 
 
 3.66796 
 
 .29147 
 
 3.43084 
 
 .31051 
 
 3.22053 
 
 .32975 
 
 3.03260 
 
 .34922 
 
 2.86356 
 
 45 
 
 16 
 
 .27294 
 
 3.66376 
 
 .29179 
 
 3.42713 
 
 .31083 
 
 3.21722 
 
 .33007 
 
 3.02963 
 
 .34954 
 
 2.86089 
 
 44 
 
 17 
 
 .27326 
 
 3.65957 
 
 .29210 
 
 3.42343 
 
 .31115 
 
 3.21392 
 
 .33<T40 
 
 3.02667 
 
 .34987 
 
 2.85822 
 
 43 
 
 18 
 
 .27357 
 
 3.65538 
 
 .29242 
 
 3.41973 
 
 .31147 
 
 3.21063 
 
 .33072 
 
 3.02372 
 
 .35020 
 
 2.85555 
 
 42 
 
 19 
 
 .27388 
 
 3.65121 
 
 .29274 
 
 3.41604 
 
 .31178 
 
 3.20734 
 
 .33104 
 
 3.02077 
 
 .35052 
 
 2.85289 
 
 41 
 
 20 
 
 .27419 
 
 3.64705 
 
 .29305 
 
 3.41236 
 
 .31210 
 
 3.20406 
 
 .33136 
 
 3.01783 
 
 .35085 
 
 2.85023 
 
 40 
 
 21 
 
 .27451 
 
 3.64289 
 
 .29337 
 
 3.40869 
 
 .31242 
 
 3.20079 
 
 .33169 
 
 3.01489 
 
 .35118 
 
 2.84758 
 
 39 
 
 22 
 
 .27482 
 
 3.63874 
 
 .29368 
 
 3.40502 
 
 .31274 
 
 3.19752 
 
 .33201 
 
 3.01196 
 
 .35150 
 
 2.84494 
 
 38 
 
 23 
 
 .27513 
 
 3.63461 
 
 .29400 
 
 3.40136 
 
 .31306 
 
 3.19426 
 
 .33233 
 
 3.00903 
 
 .35183 
 
 2.84229 
 
 37 
 
 24 
 
 .27545 
 
 3.63048 
 
 .29432 
 
 3.39771 
 
 .31338 
 
 3.19100 
 
 .33266 
 
 3.00611 
 
 .35216 
 
 2.83965 
 
 36 
 
 25 
 
 .27576 
 
 3.62636 
 
 .29463 
 
 3.39406 
 
 .31370 
 
 3.18775 
 
 .33298 
 
 3.00319 
 
 .35248 
 
 2.83702 
 
 35 
 
 26 
 
 .27607 
 
 3.62224 
 
 .29495 
 
 3.39042 
 
 .31402 
 
 3 18451 
 
 .33330 
 
 3.00028 
 
 .35281 
 
 2.83439 
 
 34 
 
 27 
 
 .27638 
 
 3.61814 
 
 .29526 
 
 3.38679 
 
 .31434 
 
 3.18127 
 
 .33363 
 
 2.99738 
 
 .35314 
 
 2.83176 
 
 33 
 
 28 
 
 .27670 
 
 3.61405 
 
 .29558 
 
 3.38317 
 
 .31466 
 
 3.17804 
 
 .33395 
 
 2.99447 
 
 .35346 
 
 2.82914 
 
 32 
 
 29 
 
 .27701 
 
 3.60996 
 
 .29590 
 
 3.37955 
 
 .31498 
 
 3.17481 
 
 .33427 
 
 2.99158 
 
 .35379 
 
 2.82653 
 
 31 
 
 80 
 
 .27732 
 
 3.60588 
 
 .29621 
 
 3.37594 
 
 .31530 
 
 3.17159 
 
 .33460 
 
 2.98868 
 
 .35412 
 
 2.82391 
 
 30 
 
 31 
 
 .27764 
 
 3.60181 
 
 .29653 
 
 3.37234 
 
 .31562 
 
 3.16838 
 
 .33492 
 
 2.98580 
 
 .35445 
 
 2.82130 
 
 29 
 
 82 
 
 .27795 
 
 3.59775 
 
 .29685 
 
 3.36875 
 
 31594 
 
 3.16517 
 
 .33524 
 
 2.98292 
 
 .35477 
 
 2.81870 
 
 28 
 
 33 
 
 .27826 
 
 3.59370 
 
 .29716 
 
 3.36516 
 
 .31626 
 
 3.16197 
 
 .33557 
 
 2.98004 
 
 .35510 
 
 2.81610 
 
 27 
 
 84 
 
 .27858 
 
 3.58966 
 
 .29748 
 
 3.36158 
 
 .31658 
 
 3.15877 
 
 .33589 
 
 2.97717 
 
 .35543 
 
 2.81350 
 
 26 
 
 35 
 
 .27889 
 
 3.58562 
 
 .29780 
 
 3.35800 
 
 .31690 
 
 3.15558 
 
 .33621 
 
 2.97430 
 
 .35576 
 
 2.81091 
 
 25 
 
 36 
 
 .27921 
 
 3.58160 
 
 .29811 
 
 3.35443 
 
 .31722 
 
 3.15240 
 
 .33654 
 
 2.97144 
 
 .35608 
 
 2.80833 
 
 24 
 
 37 
 
 .27952 
 
 3.57758 
 
 .29843 
 
 3.35087 
 
 .31754 
 
 3.14922 
 
 .33686 
 
 2.96858 
 
 .35641 
 
 2.80574 
 
 23 
 
 38 
 
 .27983 
 
 3.57357 
 
 .29875 
 
 3.34732 
 
 .31786 
 
 3.14605 
 
 .33718 
 
 2.96573 
 
 .35674 
 
 2.80316 
 
 29 
 
 89 
 
 .28015 
 
 3.56957 
 
 .29906 
 
 3.34377 
 
 .31818 
 
 3.14288 
 
 .33751 
 
 2.96288 
 
 .35707 
 
 2.80059 
 
 21 
 
 40 
 
 .28046 
 
 3.56557 
 
 .29938 
 
 3.34023 
 
 .31850 
 
 3.13972 
 
 .33783 
 
 2.96004 
 
 .35740 
 
 2.79802 
 
 20 
 
 41 
 
 .28077 
 
 3.56159 
 
 .29970 
 
 3.33670 
 
 .31882 
 
 3.13656 
 
 .33816 
 
 2.95721 
 
 .35772 
 
 2.79545 
 
 19 
 
 42 
 
 .28109 
 
 3.55761 
 
 .30001 
 
 3.33317 
 
 .31914 
 
 3.13341 
 
 .33848 
 
 2.95437 
 
 .35805 
 
 2.79289 
 
 18 
 
 43 
 
 .28140 
 
 3.55364 
 
 .30033 
 
 3.32965 
 
 .31946 
 
 3.13027 
 
 .33881 
 
 2.95155 
 
 .35838 
 
 2.79033 
 
 17 
 
 44 
 
 .28172 
 
 3.54968 
 
 .30065 
 
 3.32614 
 
 .31978 
 
 3.12713 
 
 .33913 
 
 2.94872 
 
 .35871 
 
 2.78778 
 
 16 
 
 45 
 
 .28203 
 
 3.54573 
 
 .30097 
 
 3.32264 
 
 .32010 
 
 3.12400 
 
 .33945 
 
 2.94591 
 
 .35904 
 
 2.78523 
 
 15 
 
 46 
 
 .28234 
 
 3.54179 
 
 .30128 
 
 3.31914 
 
 .32042 
 
 3.12087 
 
 .33978 
 
 2.94309 
 
 .35937 
 
 2.78269 
 
 14 
 
 47 
 
 .28266 
 
 3.53785 
 
 .30160 
 
 3.31565 
 
 .32074 
 
 3.11775 
 
 .34010 
 
 2.94028 
 
 .35969 
 
 2.78014 
 
 n 
 
 48 
 
 .28297 
 
 3.53393 
 
 .30192 
 
 3.31216 
 
 .32106 
 
 3.11464 
 
 .34043 
 
 2.93748 
 
 .36002 
 
 2.77761 
 
 12 
 
 49 
 
 .28329 
 
 3.53001 
 
 .30224 
 
 3.30868 
 
 .32139 
 
 3.11153 
 
 .34075 
 
 2.93468 
 
 .36035 
 
 2.77507 
 
 11 
 
 50 
 
 .28360 
 
 3.52609 
 
 .30255 
 
 3.30521 
 
 .32171 
 
 3.10842 
 
 .34108 
 
 2.93189 
 
 .36068 
 
 2.77254 
 
 10 
 
 51 
 
 52 
 
 .28391 
 28423 
 
 3.52219 
 3 51829 
 
 .30287 
 .30319 
 
 3.30174 
 3.29829 
 
 .32203 
 .32235 
 
 3.10532 
 3.10223 
 
 .34140 
 .34173 
 
 2.92910 
 2.92632 
 
 .36101 
 .36134 
 
 2.77002 
 2.76750 
 
 9 
 
 8 
 
 53 
 54 
 
 .28454 
 .28486 
 
 3.51441 
 3 51053 
 
 .30351 
 .30382 
 
 3.29483 
 3.29139 
 
 .32267 
 .32299 
 
 3.09914 
 3.09606 
 
 .34205 
 .34238 
 
 2.92354 
 2.92076 
 
 .36167 
 .36199 
 
 2.76498 
 2.76247 
 
 
 55 
 56 
 
 .28517 
 .28549 
 
 3.50666 
 3 50279 
 
 .30414 
 .30446 
 
 3.28795 
 3.28452 
 
 .32331 
 .32363 
 
 3.09298 
 3.08991 
 
 .34270 
 .34303 
 
 2.91799 
 2.91523 
 
 .36232 
 .36265 
 
 2.75996 
 2.75746 
 
 
 57 
 58 
 
 .28580 
 .28612 
 
 3.49894 
 3 49509 
 
 .30478 
 .30509 
 
 3.28109 
 3.27767 
 
 .32396 
 .32428 
 
 3.08685 
 3.08379 
 
 .34335 
 .34368 
 
 2.91246 
 2.90971 
 
 .36298 
 .36331 
 
 2.75496 
 2.75246 
 
 
 59 
 60 
 
 !28643 
 .28675 
 
 3.49125 
 3.48741 
 
 .30541 
 .30573 
 
 3.27426 
 3.27085 
 
 .32460 
 .32492 
 
 3.08073 
 3.07768 
 
 .34400 
 .34433 
 
 2.90696 
 2.90421 
 
 .86364 
 .36397 
 
 2.74997 
 2.74748 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 
 7 
 
 40 
 
 7 
 
 3 
 
 7 
 
 2 
 
 7 
 
 1 
 
 7 
 
 [) 
 
 
1004 
 
 NATURAL TANGENTS AND COTANGENTS 
 
 f 
 
 2( 
 
 ) 
 
 2] 
 
 L 
 
 2 
 
 J 
 
 2 
 
 J 
 
 2 
 
 40 
 
 f 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 .36397 
 
 2.74748 
 
 .38386 
 
 2.60509 
 
 .40403 
 
 2.47509 
 
 .42447 
 
 2.35585 
 
 .44523 
 
 2.24604 
 
 60 
 
 
 .36430 
 
 2.74499 
 
 .38420 
 
 2.60283 
 
 .40436 
 
 2.47302 
 
 .42482 
 
 2.35395 
 
 .44558 
 
 2.24428 
 
 59 
 
 
 .36463 
 
 2.74251 
 
 .38453 
 
 2.60057 
 
 .40470 
 
 2.47095 
 
 .42516 
 
 2.35205 
 
 .44593 
 
 2.24252 
 
 58 
 
 
 .364% 
 
 2.74004 
 
 .38487 
 
 2.59831 
 
 .40504 
 
 2.46888 
 
 .42551 
 
 2.35015 
 
 .44627 
 
 2.24077 
 
 57 
 
 
 .36529 
 
 2.73756 
 
 .38520 
 
 2.59606 
 
 .40538 
 
 2.46682 
 
 .42585 
 
 2.34825 
 
 .44662 
 
 2.23902 
 
 56 
 
 
 .36562 
 
 2.73509 
 
 .38553 
 
 2.59381 
 
 .40572 
 
 2.46476 
 
 .42619 
 
 2.34636 
 
 .44697 
 
 2.23727 
 
 55 
 
 
 .36595 
 
 2.73263 
 
 .38587 
 
 2.59156 
 
 .40606 
 
 2.46270 
 
 .42654 
 
 2.34447 
 
 .44732 
 
 2.23553 
 
 54 
 
 7 
 
 .36628 
 
 2.73017 
 
 .38620 
 
 2.58932 
 
 .40640 
 
 2.46065 
 
 .42688 
 
 2.34258 
 
 .44767 
 
 2.23378 
 
 53 
 
 8 
 
 .36661 
 
 2.72771 
 
 .38654 
 
 2.58708 
 
 .40674 
 
 2.45860 
 
 .42722 
 
 2.34069 
 
 .44802 
 
 2.23204 
 
 52 
 
 9 
 
 .36694 
 
 2.72526 
 
 .38687 
 
 2.58484 
 
 .40707 
 
 2.45655 
 
 .42757 
 
 2.33881 
 
 .44837 
 
 2.23030 
 
 51 
 
 10 
 
 .36727 
 
 2.72281 
 
 .38721 
 
 2.58261 
 
 .40741 
 
 2.45451 
 
 .42791 
 
 2.33693 
 
 .44872 
 
 2.22857 
 
 50 
 
 11 
 
 .36760 
 
 2.72036 
 
 .38754 
 
 2.58038 
 
 .40775 
 
 2.45246 
 
 .42826 
 
 2.33505 
 
 .44907 
 
 2.22683 
 
 49 
 
 12 
 
 .36793 
 
 2.71792 
 
 .38787 
 
 2.57815 
 
 .40809 
 
 2.45043 
 
 .42860 
 
 2.33317 
 
 .44942 
 
 2.22510 
 
 48 
 
 13 
 
 .36826 
 
 2.71548 
 
 .38821 
 
 2.57593 
 
 .40843 
 
 2.44839 
 
 .42894 
 
 2.83130 
 
 .44977 
 
 2.22337 
 
 47 
 
 14 
 
 .36859 
 
 2.71305 
 
 .38854 
 
 2.57371 
 
 .40877 
 
 2.44636 
 
 .42929 
 
 2.32943 
 
 .45012 
 
 2.22164 
 
 46 
 
 15 
 
 .36892 
 
 2.71062 
 
 .38888 
 
 2.57150 
 
 .40911 
 
 2.44433 
 
 .42963 
 
 2.32756 
 
 .45047 
 
 2.21992 
 
 45 
 
 16 
 
 .36925 
 
 2.70819 
 
 .38921 
 
 2.56928 
 
 .40945 
 
 2.44230 
 
 .42998 
 
 2.32570 
 
 .45082 
 
 2.21819 
 
 44 
 
 17 
 
 .36958 
 
 2.70577 
 
 .38955 
 
 2.56707 
 
 .40979 
 
 2.44027 
 
 .43032 
 
 2.32383 
 
 .45117 
 
 2.21647 
 
 43 
 
 18 
 
 .86991 
 
 2.70335 
 
 .38988 
 
 2.56487 
 
 .41013 
 
 2.43825 
 
 .43067 
 
 2.32197 
 
 .45152 
 
 2.21475 
 
 42 
 
 19 
 
 .37024 
 
 2.70094 
 
 .39022 
 
 2.56266 
 
 .41047 
 
 2.43623 
 
 .43101 
 
 2.32012 
 
 .45187 
 
 2.21804 
 
 41 
 
 20 
 
 .37057 
 
 2.69853 
 
 .39055 
 
 2.56046 
 
 .41081 
 
 2.43422 
 
 .43136 
 
 2.31826 
 
 .45222 
 
 2.21132 
 
 40 
 
 21 
 
 .37090 
 
 2.69612 
 
 .39089 
 
 2.55827 
 
 .41115 
 
 2.43220 
 
 .43170 
 
 2.31641 
 
 .45257 
 
 2.20961 
 
 39 
 
 22 
 
 .37123 
 
 2.69371 
 
 .39122 
 
 2.55608 
 
 .41149 
 
 2.43019 
 
 43205 
 
 2.31456 
 
 .45292 
 
 2.20790 
 
 38 
 
 23 
 
 .37157 
 
 2.69131 
 
 .39156 
 
 2:55389 
 
 .41183 
 
 2.42819 
 
 .43239 
 
 2.31271 
 
 .45327 
 
 2.20619 
 
 37 
 
 24 
 
 .37190 
 
 2.68892 
 
 .39190 
 
 2.55170 
 
 .41217 
 
 2.42618 
 
 .43274 
 
 2.31086 
 
 .45362 
 
 2.20449 
 
 36 
 
 25 
 
 .37223 
 
 2.68653 
 
 .39223 
 
 2.54952 
 
 .41251 
 
 2.42418 
 
 .43308 
 
 2.30902 
 
 .45397 
 
 2.20278 
 
 35 
 
 26 
 
 .37256 
 
 2.68414 
 
 .39257 
 
 2.54734 
 
 .41285 
 
 2.42218 
 
 .43343 
 
 2.30718 
 
 .45432 
 
 2.20108 
 
 34 
 
 27 
 
 .37289 
 
 2.68175 
 
 .39290 
 
 2.54516 
 
 .41319 
 
 2.42019 
 
 .43378 
 
 2.30534 
 
 .45467 
 
 2.19938 
 
 33 
 
 28 
 
 .37322 
 
 2.67937 
 
 .39324 
 
 2.54299 
 
 .41353 
 
 2.41819 
 
 .43412 
 
 2.30351 
 
 .45502 
 
 2.19769 
 
 32 
 
 29 
 
 .37355 
 
 2.67700 
 
 .39357 
 
 2.54082 
 
 .41387 
 
 2.41620 
 
 .43447 
 
 2.30167 
 
 .45538 
 
 2.19599 
 
 31 
 
 30 
 
 .37388 
 
 2.67462 
 
 .39391 
 
 2.53865 
 
 .41421 
 
 2.41421 
 
 .43481 
 
 2.29984 
 
 .45573 
 
 2.19430 
 
 30 
 
 31 
 
 .37422 
 
 2.67225 
 
 .39425 
 
 2.53648 
 
 .41455 
 
 2.41223 
 
 .43516 
 
 2.29801 
 
 .45608 
 
 2.19261 
 
 29 
 
 32 
 
 .37455 
 
 2.66989 
 
 .39458 
 
 2.53432 
 
 .41490 
 
 2.41025 
 
 .43550 
 
 2.29619 
 
 .45643 
 
 2.19092 
 
 28 
 
 33 
 
 .37488 
 
 2.66752 
 
 .39492 
 
 2.53217 
 
 .41524 
 
 2.40827 
 
 .43585 
 
 2.29437 
 
 .45678 
 
 2.18923 
 
 27 
 
 34 
 
 .37521 
 
 2.66516 
 
 .39526 
 
 2.53001 
 
 .41558 
 
 2.40629 
 
 .43620 
 
 2.29254 
 
 .45713 
 
 2.18755 
 
 26 
 
 35 
 
 .37554 
 
 2.66281 
 
 .39559 
 
 2.52786 
 
 .41592 
 
 2.40432 
 
 .43654 
 
 2.29073 
 
 .45748 
 
 2.18587 
 
 25 
 
 36 
 
 .37588 
 
 2.66046 
 
 .39593 
 
 2.52571 
 
 .41626 
 
 2.40235 
 
 .43689 
 
 2.28891 
 
 .45784 
 
 2.18419 
 
 24 
 
 37 
 
 .37621 
 
 2.65811 
 
 .39626 
 
 2.52357 
 
 .41660 
 
 2.40038 
 
 .43724 
 
 2.28710 
 
 .45819 
 
 2.18251 
 
 23 
 
 38 
 
 .37654 
 
 2.65576 
 
 .39660 
 
 2.52142 
 
 .41694 
 
 2.39841 
 
 .43758 
 
 2.28528 
 
 .45854 
 
 2.18084 
 
 22 
 
 39 
 
 .37687 
 
 2.65342 
 
 .39694 
 
 2.51929 
 
 .41728 
 
 2.39645 
 
 .43793 
 
 2.28348 
 
 .45889 
 
 2.17916 
 
 21 
 
 40 
 
 .37720 
 
 2.65109 
 
 .39727 
 
 2.51715 
 
 .41763 
 
 2.39449 
 
 .43828 
 
 2.28167 
 
 .45924 
 
 2.17749 
 
 20 
 
 41 
 
 .37754 
 
 2.64875 
 
 .39761 
 
 2.51502 
 
 .41797 
 
 2.39253 
 
 .43862 
 
 2.27987 
 
 .45960 
 
 2.17582 
 
 19 
 
 42 
 
 .37787 
 
 2.64642 
 
 .39795 
 
 2.51289 
 
 .41831 
 
 2.39058 
 
 .43897 
 
 2.27806 
 
 .45995 
 
 2.17416 
 
 18 
 
 43 
 
 .37820 
 
 2.64410 
 
 .39829 
 
 2.51076 
 
 .41865 
 
 2.38863 
 
 .43932 
 
 2.27626 
 
 .46030 
 
 2.17249 
 
 17 
 
 44 
 
 .37853 
 
 2.64177 
 
 .39862 
 
 2.50864 
 
 .41899 
 
 2.38668 
 
 .43966 
 
 2.27447 
 
 .46065 
 
 2.17083 
 
 16 
 
 45 
 
 .37887 
 
 2.63945 
 
 .398% 
 
 2.50652 
 
 .41933 
 
 2.38473 
 
 .44001 
 
 2.27267 
 
 .46101 
 
 2.16917 
 
 15 
 
 46 
 
 .37920 
 
 2.63714 
 
 .39930 
 
 2.50440 
 
 .41968 
 
 2.38279 
 
 .44036 
 
 2.27088 
 
 .46136 
 
 2.16751 
 
 14 
 
 47 
 
 .37953 
 
 2.63483 
 
 .39%3 
 
 2.50229 
 
 .42002 
 
 2.38084 
 
 .44071 
 
 2.26909 
 
 .46171 
 
 2.16585 
 
 13 
 
 48 
 
 .37986 
 
 2.63252 
 
 .39997 
 
 2.50018 
 
 .42036 
 
 2.37891 
 
 .44105 
 
 2.26730 
 
 .46206 
 
 2.16420 
 
 12 
 
 49 
 
 .38020 
 
 2.63021 
 
 .40031 
 
 2.49807 
 
 .42070 
 
 2.37697 
 
 .44140 
 
 2.26552 
 
 .46242 
 
 2.16255 
 
 11 
 
 50 
 
 .38053 
 
 2.62791 
 
 .40065 
 
 2.49597 
 
 .42105 
 
 2.37504 
 
 .44175 
 
 2.26374 
 
 .46277 
 
 2.16090 
 
 10 
 
 51 
 
 .38086 
 
 2.62561 
 
 .40098 
 
 2.49386 
 
 .42139 
 
 2.37311 
 
 .44210 
 
 2.26196 
 
 .46312 
 
 2.15925 
 
 9 
 
 52 
 
 .38120 
 
 2.62332 
 
 .40132 
 
 2.49177 
 
 .42173 
 
 2.37118 
 
 .44244 
 
 2.26018 
 
 .46348 
 
 2.15760 
 
 8 
 
 53 
 
 .38153 
 
 2.62103 
 
 .40166 
 
 2.48967 
 
 .42207 
 
 2.36925 
 
 .44279 
 
 2.25840 
 
 .46383 
 
 2.155% 
 
 
 54 
 
 .38186 
 
 2.61874 
 
 .40200 
 
 2.48758 
 
 .42242 
 
 2.36733 
 
 .44314 
 
 2.25663 
 
 .46418 
 
 2.15432 
 
 
 55 
 
 .38220 
 
 2.61646 
 
 .40234 
 
 2.48549 
 
 .42276 
 
 2.36541 
 
 .44349 
 
 2.25486 
 
 .46454 
 
 2.15268 
 
 
 56 
 
 .38253 
 
 2.61418 
 
 .40267 
 
 2.48340 
 
 .42310 
 
 2.36349 
 
 .44384 
 
 2.25309 
 
 .46489 
 
 2.15104 
 
 
 57 
 
 .38286 
 
 2.61190 
 
 .40301 
 
 2.48132 
 
 .42345 
 
 2.36158 
 
 .44418 
 
 2.25132 
 
 .46525 
 
 2.14940 
 
 
 58 
 
 .38320 
 
 2.60963 
 
 .40335 
 
 2.47924 
 
 .42379 
 
 2.35967 
 
 .44453 
 
 2.24956 
 
 .46560 
 
 2.14777 
 
 
 9 
 
 .38353 
 
 2.60736 
 
 .40369 
 
 2.47716 
 
 .42413 
 
 2.35776 
 
 .44488 
 
 2.24780 
 
 .46595 
 
 2.14614 
 
 1 
 
 60 
 
 .38386 
 
 2.60509 
 
 .40403 
 
 2.47509 
 
 .42447 
 
 2.35585 
 
 .44523 
 
 2.24604 
 
 .46631 
 
 2.14451 
 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 
 6< 
 
 ) 
 
 61 
 
 $ 
 
 6' 
 
 70 
 
 6( 
 
 ) 
 
 6 
 
 5 
 
 / 
 
NATURAL TANGENTS AND COTANGENTS 
 
 1005 
 
 
 2J 
 
 ) 
 
 2 
 
 5 
 
 2 
 
 7 
 
 2. 
 
 3 
 
 2 
 
 9 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .46631 
 
 2.14451 
 
 .48773 
 
 2.05030 
 
 .50953 
 
 1.96261 
 
 .53171 
 
 1.88073 
 
 .55431 
 
 1.80405 
 
 60 
 
 
 .46666 
 
 2.14288 
 
 .48809 
 
 2.04879 
 
 .50989 
 
 1.96120 
 
 .53208 
 
 1.87941 
 
 .55469 
 
 1.80281 
 
 59 
 
 
 .46702 
 
 2.14125 
 
 .48845 
 
 2.04728 
 
 .51026 
 
 1.95979 
 
 .53246 
 
 1.87809 
 
 .55507 
 
 1.80158 
 
 58 
 
 
 .46737 
 
 2.13963 
 
 .48881 
 
 2.04577 
 
 .51063 
 
 1.95838 
 
 .53283 
 
 1.87677 
 
 .55545 
 
 1.80034 
 
 57 
 
 
 .46772 
 
 2.13801 
 
 .48917 
 
 2.04426 
 
 .51099 
 
 1.95698 
 
 .53320 
 
 1.87546 
 
 .55583 
 
 1.79911 
 
 56 
 
 
 .46808 
 
 2.13639 
 
 .48953 
 
 2.04276 
 
 .51136 
 
 1.95557 
 
 .53358 
 
 1.87415 
 
 .55621 
 
 1.79788 
 
 55 
 
 
 .46843 
 
 2.13477 
 
 .48989 
 
 2.04125 
 
 .51173 
 
 1.95417 
 
 .53395 
 
 1.87283 
 
 .55659 
 
 1.79665 
 
 54 
 
 
 .46879 
 
 2.13316 
 
 .49026 
 
 2.03975 
 
 .51209 
 
 1.95277 
 
 .53432 
 
 1.87152 
 
 .55697 
 
 1.79542 
 
 53 
 
 
 .46914 
 
 2.13154 
 
 .49062 
 
 2.03825 
 
 .51246 
 
 1.95137 
 
 .53470 
 
 1.87021 
 
 .55736 
 
 1.79419 
 
 52 
 
 
 .46950 
 
 2.12993 
 
 .49098 
 
 2.03675 
 
 .51283 
 
 1.94997 
 
 .53507 
 
 1.86891 
 
 .55774 
 
 1.79296 
 
 51 
 
 10 
 
 .46985 
 
 2.12832 
 
 .49134 
 
 2.03526 
 
 .51319 
 
 1.94858 
 
 .53545 
 
 1.86760 
 
 .55812 
 
 1.79174 
 
 50 
 
 11 
 
 .47021 
 
 2.12671 
 
 .49170 
 
 2.03376 
 
 .51356 
 
 1.94718 
 
 .53582 
 
 1.86630 
 
 .55850 
 
 1.79051 
 
 49 
 
 12 
 
 .47056 
 
 2.12511 
 
 .49206 
 
 2.03227 
 
 .51393 
 
 1.94579 
 
 .53620 
 
 1.86499 
 
 .55888 
 
 1.78929 
 
 48 
 
 13 
 
 .47092 
 
 2.12350 
 
 .49242 
 
 2.03078 
 
 .51430 
 
 1.94440 
 
 .53657 
 
 1.86369 
 
 .55926 
 
 1.78807 
 
 47 
 
 14 
 
 .47128 
 
 2.12190 
 
 .49278 
 
 2.02929 
 
 .51467 
 
 1.94301 
 
 .53694 
 
 1.86239 
 
 .55964 
 
 1.78685 
 
 46 
 
 15 
 
 .47163 
 
 2.12030 
 
 .49315 
 
 2.02780 
 
 .51503 
 
 1.94162 
 
 .53732 
 
 1.86109 
 
 .56003 
 
 1.78563 
 
 45 
 
 16 
 
 .47199 
 
 2.11871 
 
 .49351 
 
 2.02631 
 
 .51540 
 
 1.94023 
 
 .53769 
 
 1.85979 
 
 .56041 
 
 1.78441 
 
 44 
 
 17 
 
 .47234 
 
 2.11711 
 
 .49387 
 
 2.02483 
 
 .51577 
 
 1.93885 
 
 .53807 
 
 1.85850 
 
 .56079 
 
 1.78319 
 
 43 
 
 18 
 
 .47270 
 
 2.11552 
 
 .49423 
 
 2.02335 
 
 .51614 
 
 1.93746 
 
 .53844 
 
 1.85720 
 
 .56117 
 
 1.78198 
 
 42 
 
 19 
 
 .47305 
 
 2.11392 
 
 .49459 
 
 2.02187 
 
 .51651 
 
 1.93608 
 
 .53882 
 
 1.85591 
 
 .56156 
 
 1.78077 
 
 41 
 
 20 
 
 .47341 
 
 2.11233 
 
 .49495 
 
 2.02039 
 
 .51688 
 
 1.93470 
 
 .53920 
 
 1.85462 
 
 .56194 
 
 1.77955 
 
 40 
 
 21 
 
 .47377 
 
 2.11075 
 
 .49532 
 
 2.01891 
 
 .51724 
 
 1.93332 
 
 .53957 
 
 1.85333 
 
 .56232 
 
 1.77834 
 
 39 
 
 22 
 
 .47412 
 
 2.10916 
 
 .49568 
 
 2.01743 
 
 .51761 
 
 1.93195 
 
 .53995 
 
 1.85204 
 
 .56270 
 
 1.77713 
 
 38 
 
 23 
 
 .47448 
 
 2.10758 
 
 .49604 
 
 2.01596 
 
 .51798 
 
 1.93057 
 
 .54032 
 
 1.85075 
 
 .56309 
 
 1.77592 
 
 37 
 
 24 
 
 .47483 
 
 2.10600 
 
 .49640 
 
 2.01449 
 
 .51835 
 
 1.92920 
 
 .54070 
 
 1.84946 
 
 .56347 
 
 1.774U 
 
 36 
 
 25 
 
 .47519 
 
 2.10442 
 
 .49677 
 
 2.01302 
 
 .51872 
 
 1.92782 
 
 .54107 
 
 1.84818 
 
 .56385 
 
 1.77351 
 
 35 
 
 26 
 
 .47555 
 
 2.10284 
 
 .49713 
 
 2.01155 
 
 .51909 
 
 1.92645 
 
 .54145 
 
 1.84689 
 
 .56424 
 
 1.77230 
 
 34 
 
 27 
 
 .47590 
 
 2.10126 
 
 .49749 
 
 2.01008 
 
 .51946 
 
 1.92508 
 
 .54183 
 
 1.84561 
 
 .56462 
 
 1.77110 
 
 33 
 
 28 
 
 .47626 
 
 2.09969 
 
 .49786 
 
 2.00862 
 
 .51983 
 
 1.92371 
 
 .54220 
 
 1.84433 
 
 .56501 
 
 1.76990 
 
 32 
 
 29 
 
 .47662 
 
 2.09811 
 
 .49822 
 
 2.00715 
 
 .52020 
 
 1.92235 
 
 .54258 
 
 1.84305 
 
 .56539 
 
 1.76869 
 
 31 
 
 30 
 
 .47698 
 
 2.09654 
 
 .49858 
 
 2.00569 
 
 .52057 - 
 
 1.92098 
 
 .54296 
 
 1.84177 
 
 .56577 
 
 1.76749 
 
 30 
 
 31 
 
 .47733 
 
 2.09498 
 
 .49894 
 
 2.00423 
 
 .52094 
 
 1.91962 
 
 .54333 
 
 1.84049 
 
 .56616 
 
 1.76629 
 
 29 
 
 32 
 
 .47769 
 
 2.09341 
 
 .49931 
 
 2.00277 
 
 .52131 
 
 1.91826 
 
 .54371 
 
 1.83922 
 
 .56654 
 
 1.76510 
 
 28 
 
 33 
 
 .47805 
 
 2.09184 
 
 .49967 
 
 2.00131 
 
 .52168 
 
 1.91690 
 
 .54409 
 
 1.83794 
 
 .56693 
 
 1.76390 
 
 27 
 
 34 
 
 .47840 
 
 2.09028 
 
 .50004 
 
 1.99986 
 
 .52205 
 
 1.91554 
 
 .54446 
 
 1.83667 
 
 .56731 
 
 1.76271 
 
 26 
 
 35 
 
 .47876 
 
 2.08872 
 
 .50040 
 
 1.99841 
 
 .52242 
 
 1.91418 
 
 .54484 
 
 1.83540 
 
 .56769 
 
 1.76151 
 
 25 
 
 36 
 
 .47912 
 
 2.08716 
 
 .50076 
 
 1.99695 
 
 .52279 
 
 1.91282 
 
 .54522 
 
 1.83413 
 
 .56808 
 
 1.76032 
 
 24 
 
 37 
 
 .47948 
 
 2.08560 
 
 .50113 
 
 1.99550 
 
 .52316 
 
 1.91147 
 
 .54560 
 
 1.83286 
 
 .56846 
 
 1.75913 
 
 23 
 
 38 
 
 .47984 
 
 2.08405 
 
 .50149 
 
 1.99406 
 
 .52353 
 
 1.9101-2 
 
 .54597 
 
 1.83159 
 
 .56885 
 
 1.75794 
 
 22 
 
 39 
 
 .48019 
 
 2.08250 
 
 .50185 
 
 1.99261 
 
 .52390 
 
 1.90876 
 
 .54635 
 
 1.83033 
 
 .56923 
 
 1.75675 
 
 21 
 
 40 
 
 .48055 
 
 2.08094 
 
 .50222 
 
 1.99116 
 
 .52427 
 
 1.90741 
 
 .54673 
 
 1.82906 
 
 .56962 
 
 1.75556 
 
 20 
 
 41 
 
 .48091 
 
 2.07939 
 
 .50258 
 
 1.98972 
 
 .52464 
 
 1.90607 
 
 .54711 
 
 1.82780 
 
 .57000 
 
 1.75437 
 
 19 
 
 42 
 
 .48127 
 
 2.07785 
 
 .50295 
 
 1.98828 
 
 .52501 
 
 1.90472 
 
 .54748 
 
 1.82654 
 
 .57039 
 
 1.75319 
 
 18 
 
 43 
 
 .48163 
 
 2.07630 
 
 .50331 
 
 1.98684 
 
 .52538 
 
 1.90337 
 
 .54786 
 
 1 .82528 
 
 .57078 
 
 1.75200 
 
 17 
 
 44 
 
 .48198 
 
 2.07476 
 
 .50368 
 
 1.98540 
 
 .52575 
 
 1.90203 
 
 .54824 
 
 1.82402 
 
 .57116 
 
 1.75082 
 
 16 
 
 45 
 
 .48234 
 
 2.07321 
 
 .50404 
 
 1.98396 
 
 .52613 
 
 1.90069 
 
 .54862 
 
 1.82276 
 
 .57155 
 
 1.74964 
 
 15 
 
 46 
 
 .48270 
 
 2.07167 
 
 .50441 
 
 1.98253 
 
 .52650 
 
 1.89935 
 
 .54900 
 
 1.82150 
 
 .57193 
 
 1.74846 
 
 14 
 
 47 
 
 .48306 
 
 2.07014 
 
 .50477 
 
 1.98110 
 
 .52687 
 
 1.89801 
 
 .54938 
 
 1.82025 
 
 .57232 
 
 1.74728 
 
 13 
 
 48 
 
 .48342 
 
 2.06860 
 
 .50514 
 
 1.97966 
 
 .52724 
 
 1.89667 
 
 .54975 
 
 1.81899 
 
 .57271 
 
 1.74610 
 
 12 
 
 49 
 
 .48378 
 
 2.06706 
 
 .50550 
 
 1.97823 
 
 .52761 
 
 1.89533 
 
 .55013 
 
 1.81774 
 
 .57309 
 
 1.74492 
 
 11 
 
 50 
 
 .48414 
 
 2.06553 
 
 .50587 
 
 1.97681 
 
 .52798 
 
 1.89400 
 
 .55051 
 
 1.81649 
 
 .57348 
 
 1.74375 
 
 10 
 
 51 
 
 .48450 
 
 2.06400 
 
 .50623 
 
 1.97538 
 
 .52836 
 
 1.89266 
 
 .55089 
 
 1.81524 
 
 .57386 
 
 1.74257 
 
 
 52 
 
 .48486 
 
 2.06247 
 
 .50660 
 
 1.97395 
 
 .52873 
 
 1.89133 
 
 .55127 
 
 1.81399 
 
 .57425 
 
 1.74140 
 
 
 53 
 
 .48521 
 
 2.06094 
 
 .50696 
 
 1.97253 
 
 .52910 
 
 1.89000 
 
 .55165 
 
 1.81274 
 
 .57464 
 
 1.74022 
 
 
 54 
 
 .48557 
 
 2.05942 
 
 .50733 
 
 1.97111 
 
 .52947 
 
 1.88867 
 
 .55203 
 
 1.81150 
 
 .57503 
 
 1.73905 
 
 
 55 
 
 .48593 
 
 2.05790 
 
 .50769 
 
 1.96969 
 
 .52985 
 
 1.88734 
 
 .55241 
 
 1.81025 
 
 .57541 
 
 1.73788 
 
 
 56 
 
 .48629 
 
 2.05637 
 
 .50806 
 
 1.96827 
 
 .53022 
 
 1.88602 
 
 .55279 
 
 1.80901 
 
 .57580 
 
 1.73671 
 
 
 57 
 
 .48665 
 
 2.05485 
 
 .50843 
 
 1 .96685 
 
 .53059 
 
 1.88469 
 
 .55317 
 
 1.80777 
 
 .57619 
 
 1.73555 
 
 
 58 
 
 .48701 
 
 2.05333 
 
 .50879 
 
 1.96544 
 
 .53096 
 
 1.88337 
 
 .55355 
 
 1.80653 
 
 .57657 
 
 1.73438 
 
 
 59 
 
 .48737 
 
 2.05182 
 
 .50916 
 
 1.96402 
 
 .53134 
 
 1.88205 
 
 .55393 
 
 1.80529 
 
 .57696 
 
 1.73321 
 
 
 60 
 
 .48773 
 
 2.05030 
 
 .50953 
 
 1.96261 
 
 .53171 
 
 1.88073 
 
 .55431 
 
 1.80405 
 
 .57735 
 
 1.73205 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 1 
 
 64 
 
 
 
 K 
 
 \ 
 
 6S 
 
 O 
 
 61 
 
 
 
 
 
 ) 
 
 t 
 
1006 
 
 NATURAL TANGENTS AND COTANGENTS 
 
 
 30 
 
 31 
 
 32 
 
 33 
 
 34 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .57735 
 
 1.73205 
 
 .60086 
 
 1.66428 
 
 .62487 
 
 1.60033 
 
 .64941 
 
 1.53986 
 
 .67451 
 
 1.48256 
 
 60 
 
 1 
 
 .57774 
 
 1.73089 
 
 .60126 
 
 1.66318 
 
 .62527 
 
 1.59930 
 
 .64982 
 
 1.53888 
 
 .67493 
 
 1.48163 
 
 59 
 
 2 
 
 .57813 
 
 1.72973 
 
 .60165 
 
 1.66209 
 
 .62568 
 
 1.59826 
 
 .65024 
 
 1.53791 
 
 .67536 
 
 1.48070 
 
 58 
 
 3 
 
 .57851 
 
 1.72857 
 
 .60205 
 
 1.66099 
 
 .62608 
 
 1.59723 
 
 .65065 
 
 1.53693 
 
 .67578 
 
 1.47977 
 
 57 
 
 4 
 
 .57890 
 
 1.72741 
 
 .60245 
 
 1.65990 
 
 .62649 
 
 1.59620 
 
 .65106 
 
 1.53595 
 
 .67620 
 
 1.47885 
 
 56 
 
 5 
 
 .57929 
 
 1.72625 
 
 .60284 
 
 1.65881 
 
 .62689 
 
 1.59517 
 
 .65148 
 
 1.53497 
 
 .67663 
 
 1.47792 
 
 55 
 
 6 
 
 .57968 
 
 1.72509 
 
 .60324 
 
 1.65772 
 
 .62730 
 
 1.59414 
 
 .65189 
 
 1.53400 
 
 .67705 
 
 1.47699 
 
 54 
 
 7 
 
 .58007 
 
 1.72393 
 
 .60364 
 
 1.65663 
 
 .62770 
 
 1.59311 
 
 .65231 
 
 1.53302 
 
 .67748 
 
 1.47607 
 
 53 
 
 8 
 
 .58046 
 
 1.72278 
 
 .60403 
 
 1.65554 
 
 .62811 
 
 1.59208 
 
 .65272 
 
 1.53205 
 
 .67790 
 
 1.47514 
 
 52 
 
 9 
 
 .58085 
 
 1.72163 
 
 .60443 
 
 1.65445 
 
 .62852 
 
 1.59105 
 
 .65314 
 
 1.53107 
 
 .67832 
 
 1.47422 
 
 51 
 
 10 
 
 .58124 
 
 1.72047 
 
 .60483 
 
 1.65337 
 
 .62892 
 
 1.59002 
 
 .65355 
 
 1.53010 
 
 .67875 
 
 1.47330 
 
 50 
 
 11 
 
 .58162 
 
 1.71932 
 
 .60522 
 
 1.65228 
 
 .62933 
 
 1.58900 
 
 .65397 
 
 1.52913 
 
 .67917 
 
 1.47238 
 
 49 
 
 12 
 
 .58201 
 
 1.71817 
 
 .60562 
 
 1.65120 
 
 .62973 
 
 1.58797 
 
 .65438 
 
 1.52816 
 
 .67960 
 
 1.47146 
 
 48 
 
 13 
 
 -.58240 
 
 1.71702 
 
 .60602 
 
 1.65011 
 
 .63014 
 
 1.58695 
 
 .65480 
 
 1.52719 
 
 .68002 
 
 1.47053 
 
 47 
 
 14 
 
 .58279 
 
 1.71588 
 
 .60642 
 
 1.64903 
 
 .63055 
 
 1.58593 
 
 .65521 
 
 1.52622 
 
 .68045 
 
 1.46962 
 
 46 
 
 15 
 
 .58318 
 
 1.71473 
 
 .60681 
 
 1.64795 
 
 .63095 
 
 1.58490 
 
 .65563 
 
 1.52525 
 
 .68088 
 
 1.46870 
 
 45 
 
 16 
 
 .58357 
 
 1.71358 
 
 .60721 
 
 1.64687 
 
 .63136 
 
 1.58388 
 
 .65604 
 
 1.52429 
 
 .68130 
 
 1.46778 
 
 44 
 
 17 
 
 .58396 
 
 1.71244 
 
 .60761 
 
 1.64579 
 
 .63177 
 
 1.58286 
 
 .65646 
 
 1.52332 
 
 .68173 
 
 1.46686 
 
 43 
 
 18 
 
 .58435 
 
 1.71129 
 
 .60801 
 
 1.64471 
 
 .63217 
 
 1.58184 
 
 .65688 
 
 1.52235 
 
 .68215 
 
 1.46595 
 
 42 
 
 19 
 
 .58474 
 
 1.71015 
 
 .60841 
 
 1.64363 
 
 .63258 
 
 1.58083 
 
 .65729 
 
 1.52139 
 
 .68258 
 
 1.46503 
 
 41 
 
 20 
 
 .58513 
 
 1.70901 
 
 .60881 
 
 1.64256 
 
 .63299 
 
 1.57981 
 
 .65771 
 
 1.52043 
 
 .68301 
 
 1.46411 
 
 40 
 
 21 
 
 .58552 
 
 1.70787 
 
 .60921 
 
 1.64148 
 
 .63340 
 
 1.5787J9 
 
 .65813 
 
 1.51946 
 
 .68343 
 
 1.46320 
 
 39 
 
 22 
 
 .58591 
 
 1.70673 
 
 .60960 
 
 1.64041 
 
 .63380 
 
 1.57778 
 
 .65854 
 
 1.51850 
 
 .68386 
 
 1.46229 
 
 38 
 
 23 
 
 .58631 
 
 1.70560 
 
 .61000 
 
 1.63934 
 
 .63421 
 
 1.57676 
 
 .65896 
 
 1.51754 
 
 .68429 
 
 1.46137 
 
 37 
 
 24 
 
 .58670 
 
 1.70446 
 
 .61040 
 
 1.63826 
 
 .63462 
 
 1.57575 
 
 .65938 
 
 1.51658 
 
 .68471 
 
 1.46046 
 
 36 
 
 25 
 
 .58709 
 
 1.70332 
 
 .61080 
 
 1.63719 
 
 .63503 
 
 1.57474 
 
 .65980 
 
 1.51562 
 
 .68514 
 
 1.45955 
 
 35 
 
 26 
 
 .58748 
 
 1.70219 
 
 .61120 
 
 1.63612 
 
 .63544 
 
 1.57372 
 
 .66021 
 
 1.51466 
 
 .68557 
 
 1.45864 
 
 34 
 
 27 
 
 .58787 
 
 1.70106 
 
 .61160 
 
 1.63505 
 
 .63584 
 
 1.57271 
 
 .66063 
 
 1.51370 
 
 .68600 
 
 1.45773 
 
 33 
 
 28 
 
 .58826 
 
 1.69992 
 
 .61200 
 
 1.63398 
 
 .63625 
 
 1.57170 
 
 .66105 
 
 1.51275 
 
 .68642 
 
 1.45682 
 
 32 
 
 29 
 
 .58865 
 
 1.69879 
 
 .61240 
 
 1.63292 
 
 .63666 
 
 1.57069 
 
 .66147 
 
 1.51179 
 
 .68685 
 
 1.45592 
 
 31 
 
 30 
 
 .58905 
 
 1.69766 
 
 .61280 
 
 1.63185 
 
 .63707 
 
 1.56969 
 
 .66189 
 
 1.51084 
 
 .68728 
 
 1.45501 
 
 30 
 
 31 
 
 .58944 
 
 1.69653 
 
 .61320 
 
 1.63079 
 
 .63748 
 
 1.56868 
 
 .66230 
 
 1.50988 
 
 .68771 
 
 1.45410 
 
 29 
 
 32 
 
 
 1.69541 
 
 .61360 
 
 1.62972 
 
 .63789 
 
 1.56767 
 
 .66272 
 
 1.50893 
 
 .68814 
 
 1.45320 
 
 28 
 
 33 
 
 .'59022 
 
 1.69428 
 
 .61400 
 
 1.62866 
 
 .63830 
 
 1.56667 
 
 .66314 
 
 1.50797 
 
 .68857 
 
 1.45229 
 
 27 
 
 34 
 
 .59061 
 
 1.69316 
 
 .61440 
 
 1.62760 
 
 .63871 
 
 1.56566 
 
 .66356 
 
 1.50702 
 
 .68900 
 
 1.45139 
 
 26 
 
 35 
 
 .59101 
 
 1.69203 
 
 .61480 
 
 1.62654 
 
 .63912 
 
 1.56466 
 
 .66398 
 
 1.50607 
 
 .68942 
 
 1.45049 
 
 25 
 
 36 
 
 .WHO 
 
 1.69091 
 
 .61520 
 
 1.62548 
 
 .63953 
 
 1.56366 
 
 .66440 
 
 1.50512 
 
 .68985 
 
 1.44958 
 
 24 
 
 37 
 
 .59179 
 
 1.68979 
 
 .61561 
 
 1.62442 
 
 .63994 
 
 1.56265 
 
 .66482 
 
 1.50417 
 
 .69028 
 
 1.44868 
 
 23 
 
 88 
 
 .59218 
 
 1.68866 
 
 .61601 
 
 1.62336 
 
 .64035 
 
 1.56165 
 
 .66524 
 
 1.50322 
 
 .69071 
 
 1.44778 
 
 22 
 
 39 
 
 .59258 
 
 1.68754 
 
 .61641 
 
 1.62230 
 
 .64076 
 
 1.56065 
 
 .66566 
 
 1.50228 
 
 .69114 
 
 1.44688 
 
 21 
 
 40 
 
 .59297 
 
 1.68643 
 
 .61681 
 
 1.62125 
 
 .64117 
 
 1.55966 
 
 .66608 
 
 1.50133 
 
 .69157 
 
 1.44598 
 
 20 
 
 41 
 
 .59336 
 
 1.68531 
 
 .61721 
 
 1.62019 
 
 .64158 
 
 1.55866 
 
 .66650 
 
 1.50038 
 
 .69200 
 
 1.44508 
 
 19 
 
 42 
 
 .59376 
 
 1.68419 
 
 .61761 
 
 1.61914 
 
 .64199 
 
 1.55766 
 
 .66692 
 
 1.49944 
 
 .69243 
 
 1.44418 
 
 18 
 
 43 
 
 .59415 
 
 1.68308 
 
 .61801 
 
 1.61808 
 
 .64240 
 
 1.55666 
 
 .66734 
 
 1.49849 
 
 .69286 
 
 1.44329 
 
 17 
 
 44 
 
 .59454 
 
 1.68196 
 
 .61842 
 
 1.61703 
 
 .64281 
 
 1.55567 
 
 .66776 
 
 1.49755 
 
 .69329 
 
 1.44239 
 
 16 
 
 45 
 
 .59494 
 
 1.68085 
 
 .61882 
 
 1.61598 
 
 .64322 
 
 1.55467 
 
 .66818 
 
 1.49661 
 
 .69372 
 
 1.44149 
 
 15 
 
 46 
 
 .59533 
 
 1.67974 
 
 .61922 
 
 1.61493 
 
 .64363 
 
 1.55368 
 
 .66860 
 
 1.49566 
 
 .69416 
 
 1.44060 
 
 14 
 
 47 
 
 .59573 
 
 1.67863 
 
 .61962 
 
 1.61388 
 
 .64404 
 
 1.55269 
 
 .66902 
 
 1.49472 
 
 .69459 
 
 1.43970 
 
 13 
 
 48 
 
 .59612 
 
 1.67752 
 
 .62003 
 
 1.61283 
 
 .64446 
 
 1.55170 
 
 .66944 
 
 1.49378 
 
 .69502 
 
 1.43881 
 
 12 
 
 49 
 
 .59651 
 
 1.67641 
 
 .62043 
 
 1.61179 
 
 .64487 
 
 1.55071 
 
 .66986 
 
 1.49284 
 
 .69545 
 
 1.43792 
 
 11 
 
 50 
 
 .59691 
 
 1.67530 
 
 .62083 
 
 1.61074 
 
 .64528 
 
 1.54972 
 
 .67028 
 
 1.49190 
 
 .69588 
 
 1.43703 
 
 10 
 
 51 
 
 .59730 
 
 1.67419 
 
 .62124 
 
 1.60970 
 
 .64569 
 
 1.54873 
 
 .67071 
 
 1.49097 
 
 .69631 
 
 1.43614 
 
 9 
 
 52 
 
 .59770 
 
 1.67309 
 
 .62164 
 
 1.60865 
 
 .64610 
 
 1.54774 
 
 .67113 
 
 1.49003 
 
 .69675 
 
 1.43525 
 
 8 
 
 53 
 
 .59803 
 
 1.67198 
 
 .62204 
 
 1.60761 
 
 .64652 
 
 1.54675 
 
 .67155 
 
 1.48909 
 
 .69718 
 
 1.43436 
 
 7 
 
 54 
 
 .59849 
 
 1.67088 
 
 .62245 
 
 1.60657 
 
 .64693 
 
 1.54576 
 
 .67197 
 
 1.48816 
 
 .69761 
 
 1.43347 
 
 6 
 
 55 
 
 .59888 
 
 1.66978 
 
 .62285 
 
 1.60553 
 
 .64734 
 
 1.54478 
 
 .67239 
 
 1.48722 
 
 .69804 
 
 1.43258 
 
 5 
 
 56 
 
 .59928 
 
 1.66867 
 
 .62325 
 
 1.60449 
 
 .64775 
 
 1.54379 
 
 .67282 
 
 1.48629 
 
 .69847 
 
 1.43169 
 
 4 
 
 57 
 
 .59967 
 
 1.66757 
 
 .62366 
 
 1.60345 
 
 .64817 
 
 1.54281 
 
 .67324 
 
 1.48536 
 
 .69891 
 
 1.43080 
 
 3 
 
 58 
 
 .60007 
 
 1.66647 
 
 .62406 
 
 1.60241 
 
 .64858 
 
 1.54183 
 
 .67366 
 
 1.48442 
 
 .69934 
 
 1.42992 
 
 2 
 
 59 
 
 .60046 
 
 1.66538 
 
 .62446 
 
 1.60137 
 
 .64899 
 
 1.54085 
 
 .67409 
 
 1.48349 
 
 .69977 
 
 1.42903 
 
 1 
 
 60 
 
 .60086 
 
 1.66428 
 
 .62487 
 
 1.60033 
 
 .64941 
 
 1.53986 
 
 .67451 
 
 1.48256 
 
 .70021 
 
 1.42815 
 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 t 
 
 59 
 
 58 
 
 57 
 
 5b 
 
 55 
 
 t 
 
NATURAL TANGENTS AND COTANGENTS 
 
 1007 
 
 
 * 
 
 o 
 
 36 
 
 o 
 
 37 
 
 
 
 38 
 
 o 
 
 3 
 
 3 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .70021 
 
 1.42815 
 
 .72654 
 
 1.37638 
 
 .75355 
 
 1.32704 
 
 .78129 
 
 1.27994 
 
 .80978 
 
 1.23490 
 
 60 
 
 1 
 
 .70064 
 
 1.42726 
 
 .72699 
 
 1.37554 
 
 .75401 
 
 1.32624 
 
 .78175 
 
 1.27917 
 
 .81027 
 
 1.23416 
 
 59 
 
 2 
 
 .70107 
 
 1.42638 
 
 .72743 
 
 1.37470 
 
 .75447 
 
 1.32544 
 
 .78222 
 
 1.27841 
 
 .81075 
 
 1.23343 
 
 58 
 
 3 
 
 .70151 
 
 1.42550 
 
 .72788 
 
 1.37386 
 
 .75492 
 
 1.32464 
 
 .78269 
 
 1.27764 
 
 .81123 
 
 1.23270 
 
 57 
 
 4 
 
 .70194 
 
 1.42462 
 
 .72832 
 
 1.37302 
 
 .75538 
 
 1.32384 
 
 .78316 
 
 1.27688 
 
 .81171 
 
 1.23196 
 
 56 
 
 5 
 
 .70238 
 
 1.42374 
 
 .72877 
 
 1.37218 
 
 .75584 
 
 1.32304 
 
 .78363 
 
 1.27611 
 
 .81220 
 
 1.23123 
 
 55 
 
 6 
 
 .70281 
 
 1.42286 
 
 .72921 
 
 1.37134 
 
 .75629 
 
 1.32224 
 
 .78410 
 
 1.27535 
 
 .81268 
 
 1.23050 
 
 54 
 
 7 
 
 .70325 
 
 1.42198 
 
 .72966 
 
 1.37050 
 
 .75675 
 
 1.32144 
 
 .78457 
 
 1.27458 
 
 .81316 
 
 1.22977 
 
 53 
 
 8 
 
 .70368 
 
 1.42110 
 
 .73010 
 
 1.36967 
 
 .75721 
 
 1.32064 
 
 .78504. 
 
 1.27382 
 
 .81364 
 
 1.22904 
 
 52 
 
 9 
 
 .70412 
 
 1.42022 
 
 .73055 
 
 1.36883 
 
 .75767 
 
 1.31984 
 
 .78551 
 
 1.27306 
 
 .81413 
 
 1.22831 
 
 51 
 
 10 
 
 .70455 
 
 1.41934 
 
 .73100 
 
 1.36800 
 
 .75812 
 
 1.31904 
 
 .78598 
 
 1.27230 
 
 .81461 
 
 1.22758 
 
 50 
 
 11 
 
 .70499 
 
 1.41847 
 
 .73144 
 
 1.36716 
 
 .75858 
 
 1.31825 
 
 .78645 
 
 1.27153 
 
 .81510 
 
 1.22685 
 
 49 
 
 12 
 
 .70542 
 
 1.41759 
 
 .73189 
 
 1.36633 
 
 .75904 
 
 1.31745 
 
 .78692 
 
 1.27077 
 
 .81558 
 
 1.22612 
 
 48 
 
 13 
 
 .70586 
 
 1.41672 
 
 .73234 
 
 1.36549 
 
 .75950 
 
 1.31666 
 
 .78739 
 
 1.27001 
 
 .81606 
 
 1.22539 
 
 47 
 
 14 
 
 .70629 
 
 1.41584 
 
 .73278 
 
 1.36466 
 
 .75996 
 
 1.31586 
 
 .78786 
 
 1.26925 
 
 .81655 
 
 1.22467 
 
 46 
 
 15 
 
 .70673 
 
 1.41497 
 
 .73323 
 
 1.36383 
 
 .76042 
 
 1.31507 
 
 .78834 
 
 1.26849 
 
 .81703 
 
 1.22394 
 
 45 
 
 16 
 
 .70717 
 
 1.41409 
 
 .73368 
 
 1.36300 
 
 .76088 ' 
 
 1.31427 
 
 .78881 
 
 1.26774 
 
 .81752 
 
 1.22321 
 
 44 
 
 17 
 
 .70760 
 
 1.41322 
 
 .73413 
 
 1.36217 
 
 .76134 
 
 1.31348 
 
 .78928 
 
 1.26698 
 
 .81800 
 
 1.22249 
 
 43 
 
 18 
 
 .70804 
 
 1.41235 
 
 .73457 
 
 1.36134 
 
 .76180 
 
 1.31269 
 
 .78975 
 
 1.26622 
 
 .81849 
 
 1.22176 
 
 42 
 
 19 
 
 .70848 
 
 1.41148 
 
 .73502 
 
 1.36051 
 
 .76226 
 
 1.31190 
 
 .79022 
 
 1.26546 
 
 .81898 
 
 1.22104 
 
 41 
 
 20 
 
 .70891 
 
 1.41061 
 
 .73547 
 
 1 35968 
 
 .76272 
 
 1.31110 
 
 .79070 
 
 1.26471 
 
 .81946 
 
 1.22031 
 
 40 
 
 21 
 
 .70935 
 
 1.40974 
 
 .73592 
 
 1.35885 
 
 .76318 
 
 1.31031 
 
 .79117 
 
 1.26395 
 
 .81995 
 
 1.21959 
 
 39 
 
 22 
 
 .70979 
 
 1.40887 
 
 .73637 
 
 1.35802 
 
 .76364 
 
 1.30952 
 
 .79164 
 
 1.26319 
 
 .82044 
 
 1.21886 
 
 38 
 
 23 
 
 .71023 
 
 1.40800 
 
 .73681 
 
 1.35719 
 
 .76410 
 
 1.30873 
 
 .79212 
 
 1.26244 
 
 .82092 
 
 1.21814 
 
 37 
 
 24 
 
 .71066 
 
 1.40714 
 
 .73726 
 
 1.35637 
 
 .76456 
 
 1.30795 
 
 .79259 
 
 1 .26169 
 
 .82141 
 
 1.21742 
 
 36 
 
 25 
 
 .71110 
 
 1.40627 
 
 .73771 
 
 1.35554 
 
 .76502 
 
 1.30716 
 
 .79306 
 
 1.26093 
 
 .82190 
 
 1.21670 
 
 35 
 
 26 
 
 .71154 
 
 1.40540 
 
 .73816 
 
 1.35472 
 
 .76548 
 
 1.30637 
 
 .79354 
 
 1 .26018 
 
 .82238 
 
 1.21598 
 
 34 
 
 27 
 
 .71198 
 
 1.40454 
 
 .73861 
 
 1.35389 
 
 .76594 
 
 1.30558 
 
 .79401 
 
 1.25943 
 
 .82287 
 
 1.21526 
 
 33 
 
 28 
 
 .71242 
 
 1.40367 
 
 .73906 
 
 1.35307 
 
 .76640 
 
 1.30480 
 
 .79449 
 
 1.25867 
 
 .82336 
 
 1.21454 
 
 32 
 
 29 
 
 .71285 
 
 1.40281 
 
 .73951 
 
 1.35224 
 
 .76686 
 
 1.30401 
 
 .79496 
 
 1.25792 
 
 .82385 
 
 1.21382 
 
 31 
 
 30 
 
 .71329 
 
 1.40195 
 
 .73996 
 
 1.35142 
 
 .76733 
 
 1.30323 
 
 .79544 
 
 1.25717 
 
 .82434 
 
 1.21310 
 
 80 
 
 31 
 
 .71373 
 
 1.40109 
 
 .74041 
 
 1.35060 
 
 .76779 
 
 1.30244 
 
 .79591 
 
 1.25642 
 
 .82483 
 
 1.21238 
 
 29 
 
 32 
 
 .71417 
 
 1.40022 
 
 .7-40*6 
 
 1.34978 
 
 .76825 
 
 1.30166 
 
 .79639 
 
 1.25567 
 
 .82531 
 
 1.21166 
 
 28 
 
 33 
 
 .71461 
 
 1.39936 
 
 .74181 
 
 1.34896 
 
 .76871 
 
 1.30087 
 
 .79686 
 
 1.25492 
 
 .82580 
 
 1.21094 
 
 27 
 
 34 
 
 .71505 
 
 1.39850 
 
 .74176 
 
 1.34814 
 
 .76918 
 
 1 .30009 
 
 .79734 
 
 1.25417 
 
 .82629 
 
 1.21023 
 
 26 
 
 35 
 
 .71549 
 
 1.39764 
 
 .74221 
 
 1.34732 
 
 . .76964 
 
 1.29931 
 
 .79781 
 
 1.25343 
 
 .82678 
 
 1.20951 
 
 25 
 
 36 
 
 .71593 
 
 1.39679 
 
 .74267 
 
 1.34650 
 
 .77010 
 
 1.29853 
 
 .79829 
 
 1.25268 
 
 .82727 
 
 1.20879 
 
 24 
 
 37 
 
 .71637 
 
 1.39593 
 
 .74312 
 
 1 .84568 
 
 .77057 
 
 1.29775 
 
 .79877 
 
 1.25193 
 
 .82776 
 
 1 .20808 
 
 23 
 
 38 
 
 .71681 
 
 1.39507 
 
 .74357 
 
 1.34487 
 
 .77103 
 
 1.29696 
 
 .79924 
 
 1.25118 
 
 .82825 
 
 1.20736 
 
 22 
 
 39 
 
 .71725 
 
 1.39421 
 
 .74402 
 
 1.34405 
 
 .77149 
 
 1.29618 
 
 .79972 
 
 1.25044 
 
 .82874 
 
 1.20665 
 
 21 
 
 40 
 
 .71769 
 
 1.39336 
 
 .74447 
 
 1.34323 
 
 .77196 
 
 1.29541 
 
 .80020 
 
 1.24969 
 
 .82923 
 
 1.20593 
 
 20 
 
 41 
 
 .71813 
 
 1.39250 
 
 .74492 
 
 1.34242 
 
 .77242 
 
 1.29463 
 
 .80067 
 
 1.24895 
 
 .82972 
 
 1.20522 
 
 19 
 
 42 
 
 .71857 
 
 1.39165 
 
 .74538 
 
 1.34160 
 
 .77289 
 
 1.29385 
 
 .80115 
 
 1.24820 
 
 .83022 
 
 1.20451 
 
 18 
 
 43 
 
 .71901 
 
 1.39079 
 
 .74583 
 
 1.34079 
 
 .77335 
 
 1.29307 
 
 .80163 
 
 1.24746 
 
 .83071 
 
 1.20379 
 
 17 
 
 44 
 
 .71946 
 
 1.38994 
 
 .74628 
 
 1.33998 
 
 .77382 
 
 1.29229 
 
 .80211 
 
 1.24672 
 
 .83120 
 
 1.20308 
 
 16 
 
 45 
 
 .71990 
 
 1.38909 
 
 .74674 
 
 1.33916 
 
 .77428 
 
 1.29152 
 
 .80258 
 
 1.24597 
 
 .83169 
 
 1.20237 
 
 15 
 
 46 
 
 .72034 
 
 1.38824 
 
 .74719 
 
 1.33835 
 
 .77475 
 
 1.29074 
 
 .80306 
 
 1.24523 
 
 .83218 
 
 1.20166 
 
 14 
 
 47 
 
 .72078 
 
 1.38738 
 
 .74764 
 
 1.33754 
 
 .77521 
 
 1.28997 
 
 .80354 
 
 1.24449 
 
 .83268 
 
 1.20095 
 
 13 
 
 48 
 
 .72122 
 
 1.38653 
 
 .74810 
 
 1.33673 
 
 .77568 
 
 1.28919 
 
 .80402 
 
 1.24375 
 
 .83317 
 
 1.20024 
 
 12 
 
 49 
 
 .72167 
 
 1.38568 
 
 .74855 
 
 1.33592 
 
 .77615 
 
 1.28842 
 
 .80450 
 
 1.24301 
 
 .83366 
 
 1.19953 
 
 11 
 
 50 
 
 .72211 
 
 1.38484 
 
 .74900 
 
 1.33511 
 
 .77661 
 
 1.28764 
 
 .80498 
 
 1.24227 
 
 .83415 
 
 1.19882 
 
 10 
 
 51 
 
 .72255 
 
 1.38399 
 
 .74946 
 
 1.33430 
 
 .77708 
 
 1.28687 
 
 .80546 
 
 1.24153 
 
 .83465 
 
 1.19811 
 
 9 
 
 52 
 
 .72299 
 
 1.38314 
 
 .74991 
 
 1.33349 
 
 .77754 
 
 1.28610 
 
 .80594 
 
 1.24079 
 
 .83514 
 
 1.19740 
 
 8 
 
 53 
 
 .72344 
 
 1.38229 
 
 .75037 
 
 1.33268 
 
 .77801 
 
 1.28533 
 
 .80642 
 
 1.24005 
 
 .83564 
 
 .19669 
 
 1 
 
 54 
 
 .72388 
 
 1.38145 
 
 .75082 
 
 1.33187 
 
 .77848 
 
 1.28456 
 
 .80690 
 
 1.23931 
 
 .83613 
 
 .19599 
 
 6 
 
 55 
 
 .72432 
 
 1.38060 
 
 .75128 
 
 1.33107 
 
 .77895 
 
 1.28379 
 
 .80738 
 
 1.23858 
 
 .83662 
 
 .19528 
 
 5 
 
 56 
 
 .72477 
 
 1.37976 
 
 .75173 
 
 1.33026 
 
 .77941 
 
 1.28302 
 
 .80786 
 
 1.23784 
 
 .83712 
 
 .19457 
 
 4 
 
 57 
 
 .72521 
 
 1.37891 
 
 .75219 
 
 1.32946 
 
 .77988 
 
 1.28225 
 
 .80834 
 
 1.23710 
 
 .83761 
 
 .19387 
 
 3 
 
 58 
 
 .72565 
 
 1.37807 
 
 .75264 
 
 1.32865 
 
 .78035 
 
 1.28148 
 
 .80882 
 
 1.23637 
 
 .83811 
 
 .19316 
 
 2 
 
 59 
 
 .72610 
 
 1.37722 
 
 .75310 
 
 1.32786 
 
 .78082 
 
 1.28071 
 
 .80930 
 
 1.23563 
 
 .83860 
 
 .19246 
 
 1 
 
 60 
 
 .72654 
 
 1.37638 
 
 .75355 
 
 1.32704 
 
 .78129 
 
 1.27994 
 
 .80978 
 
 1.23490 
 
 .83910 
 
 1.19175 
 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 t 
 
 5 
 
 4 
 
 5 
 
 J 
 
 5 
 
 > 
 
 51 
 
 L 
 
 5 
 
 
 
 f 
 
1008 
 
 NATURAL TANGENTS AND COTANGENTS 
 
 
 4C 
 
 o 
 
 41 
 
 
 
 ti 
 
 JO 
 
 42 
 
 o 
 
 4 
 
 1 
 
 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 
 
 
 .83910 
 
 1.19175 
 
 .86929 
 
 1.15037 
 
 .90040 
 
 1.11061 
 
 .93252 
 
 1.07237 
 
 .96569 
 
 1.03553 
 
 60 
 
 
 .83960 
 
 1.19105 
 
 .86980 
 
 1.14969 
 
 .90093 
 
 .10996 
 
 .93306 
 
 1.07174 
 
 .96625 
 
 1 .03493 
 
 59 
 
 
 .84009 
 
 1.19035 
 
 .87031 
 
 1.14902 
 
 .90146 
 
 .10931 
 
 .93360 
 
 1.07112 
 
 .96681 
 
 1.03433 
 
 58 
 
 
 .84059 
 
 1.18964 
 
 .87082 
 
 1.14834 
 
 .90199 
 
 1.10867 
 
 .93415 
 
 1.07049 
 
 .96738 
 
 1.03372 
 
 57 
 
 
 .84108 
 
 1.18894 
 
 .87133 
 
 1.14767 
 
 .90251 
 
 .10802 
 
 .93469 
 
 1.06987 
 
 .96794 
 
 1.03312 
 
 56 
 
 
 .84158 
 
 1.18824 
 
 .87184 
 
 1.14699 
 
 .90304 
 
 1.10737 
 
 .93524 
 
 1.06925 
 
 .96850 
 
 1.03252 
 
 55 
 
 
 .84208 
 
 1.18754 
 
 .87236 
 
 1.14632 
 
 .90357 
 
 1.10672 
 
 .93578 
 
 1.06862 
 
 .96907 
 
 1.03192 
 
 54 
 
 
 .84258 
 
 1.18684 
 
 .87287 
 
 1.14565 
 
 .90410 
 
 1.10607 
 
 .93633 
 
 1.06800 
 
 .96963 
 
 1.03132 
 
 53 
 
 
 .84307 
 
 1.18614 
 
 .87338 
 
 1.14498 
 
 .90463 
 
 .10543 
 
 .93688 
 
 1.06738 
 
 .97020 
 
 1.03072 
 
 52 
 
 
 .84357 
 
 1.18544 
 
 .87389 
 
 1.14430 
 
 .90516 
 
 .10478 
 
 .93742 
 
 1.06676 
 
 .97076 
 
 1.03012 
 
 51 
 
 10 
 
 .84407 
 
 1.18474 
 
 .87441 
 
 1.14363 
 
 .90569 
 
 .10414 
 
 .93797 
 
 1.06613 
 
 .97133 
 
 1.02952 
 
 50 
 
 11 
 
 .84457 
 
 1.18404 
 
 .87492 
 
 1.14296 
 
 .90621 
 
 .10349 
 
 .93852 
 
 1.06551 
 
 .97189 
 
 1.02892 
 
 49 
 
 12 
 
 .84507 
 
 1.18334 
 
 .87543 
 
 1.14229 
 
 .90674 
 
 .10285 
 
 .93906 
 
 1.06489 
 
 .97246 
 
 1.02832 
 
 48 
 
 13 
 
 .84556 
 
 1.18264 
 
 .87595 
 
 1.14162 
 
 .90727 
 
 .10220 
 
 .93961 
 
 1.06427 
 
 .97302 
 
 1.02772 
 
 47 
 
 14 
 
 .84606 
 
 1.18194 
 
 .87646 
 
 1.14095 
 
 .90781 
 
 .10156 
 
 .94016 
 
 1.06365 
 
 .97359 
 
 1.02713 
 
 46 
 
 15 
 
 .84656 
 
 1.18125 
 
 .87698 
 
 1.14028 
 
 .90834, 
 
 .10091 
 
 .94071 
 
 1.06303 
 
 .97416 
 
 1.02653 
 
 45 
 
 16 
 
 .84706 
 
 1.18055 
 
 .87749 
 
 1.13961 
 
 .90887 
 
 .10027 
 
 .94125 
 
 1.06241 
 
 .97472 
 
 1.02593 
 
 44 
 
 17 
 
 .84756 
 
 1.17986 
 
 .87801 
 
 1.13894 
 
 .90940 
 
 1.09963 
 
 .94180 
 
 1.06179 
 
 .07529 
 
 1.02533 
 
 43 
 
 18 
 
 .84806 
 
 1.17916 
 
 .87852 
 
 1.13828 
 
 .90993 
 
 1.09899 
 
 .94235 
 
 1.06117 
 
 .97586 
 
 1.02474 
 
 42 
 
 19 
 
 .84856 
 
 1.17846 
 
 .87904 
 
 1.13761 
 
 .91046 
 
 1.09834 
 
 .94290 
 
 1.06056 
 
 .97643 
 
 1.02414 
 
 41 
 
 20 
 
 .84906 
 
 1.17777 
 
 .87955 
 
 1.13694 
 
 .91099 
 
 1.09770 
 
 .94345 
 
 1.05994 
 
 .97700 
 
 1.02355 
 
 40 
 
 21 
 
 .84956 
 
 1.17708 
 
 .88007 
 
 1.13627 
 
 .91153 
 
 1.09706 
 
 .94400 
 
 1.05932 
 
 .97756 
 
 1.02295 
 
 39 
 
 22 
 
 .85006 
 
 1.17638 
 
 .88059 
 
 1.13561 
 
 .91206 
 
 1.09642 
 
 .94455 
 
 1.05870 
 
 .97813 
 
 1.02236 
 
 38 
 
 23 
 
 .85057 
 
 1.17569 
 
 .88110 
 
 1.13494 
 
 .91259 
 
 1.09578 
 
 .94510 
 
 1.05809 
 
 .97870 
 
 1.02176 
 
 37 
 
 24 
 
 .85107 
 
 1.17500 
 
 .88162 
 
 1.13428 
 
 .91313 
 
 1.09514 
 
 .94565 
 
 1.05747 
 
 .97927 
 
 1.02117 
 
 36 
 
 25 
 
 .85157 
 
 1.17430 
 
 .88214 
 
 1.13361 
 
 .91366 
 
 1.09450 
 
 .94620 
 
 1.05685 
 
 .97984 
 
 1.02057 
 
 35 
 
 26 
 
 .85207 
 
 1.17361 
 
 .88265 
 
 1.13295 
 
 .91419 
 
 1.09386 
 
 .94676 
 
 1.05624 
 
 .98041 
 
 1.01998 
 
 34 
 
 27 
 
 .85257 
 
 1.17292 
 
 .88317 
 
 1.13228 
 
 .91473 
 
 1.09322 
 
 .94731 
 
 1.05562 
 
 .98098 
 
 1.01939 
 
 33 
 
 28 
 
 .85308 
 
 1.17223 
 
 .88369 
 
 1.13162 
 
 .91526 
 
 1.09258 
 
 .94786 
 
 1.05501 
 
 .98155 
 
 1.01879 
 
 32 
 
 29 
 
 .85358 
 
 1.17154 
 
 .88421 
 
 1.13096 
 
 .91580 
 
 1.09195 
 
 .94841 
 
 1 .05439 
 
 .98213 
 
 1.01820 
 
 31 
 
 30 
 
 .85408 
 
 1.17085 
 
 .88473 
 
 1.13029 
 
 .91633 
 
 1.09131 
 
 .94896 
 
 1.05378 
 
 .98270 
 
 1.01761 
 
 30 
 
 31 
 
 .85458 
 
 1.17016 
 
 .88524 
 
 1.12963 
 
 .91687 
 
 1.09067 
 
 .94952 
 
 1.05317 
 
 .98327 
 
 1.01702 
 
 29 
 
 32 
 
 .85509 
 
 1.16947 
 
 .88576 
 
 1.12897 
 
 .91740 
 
 1.09003 
 
 .95007 
 
 1.05255 
 
 .98384 
 
 1.01642 
 
 28 
 
 33 
 
 .85559 
 
 1.16878 
 
 .88628 
 
 1.12831 
 
 .91794 
 
 1.08940 
 
 .95062 
 
 1.05194 
 
 .98441 
 
 1.01583 
 
 27 
 
 34 
 
 .85609 
 
 1.16809 
 
 .88680 
 
 1.12765 
 
 .91847 
 
 1.08876 
 
 .95118 
 
 1.05133 
 
 .98499 
 
 1.01524 
 
 26 
 
 35 
 
 .85660 
 
 1.16741 
 
 .88732 
 
 1.12699 
 
 .91901 
 
 1.08813 
 
 .95173 
 
 1.05072 
 
 .98556 
 
 1.01465 
 
 25 
 
 36 
 
 .85710 
 
 1.16672 
 
 .88784 
 
 1.12633 
 
 .91955 
 
 1.08749 
 
 .95229 
 
 1.05010 
 
 .98613 
 
 1.01406 
 
 24 
 
 37 
 
 .85761 
 
 1.16603 
 
 .88836 
 
 1.12567 
 
 .92008 
 
 1.08686 
 
 .95284 
 
 1.04949 
 
 .98671 
 
 1.01347 
 
 23 
 
 38 
 
 .85811 
 
 1.16535 
 
 .88888 
 
 1.12501 
 
 .92062 
 
 1.08622 
 
 .95340 
 
 1.04888 
 
 .98728 
 
 1.01288 
 
 22 
 
 39 
 
 .85862 
 
 1.16466 
 
 .88940 
 
 1.12435 
 
 .92116 
 
 1.08559 
 
 .95395 
 
 1.04827 
 
 .98786 
 
 1.01229 
 
 21 
 
 40 
 
 .85912 
 
 1.16398 
 
 .88992 
 
 1.12369 
 
 .92170 
 
 1.08496 
 
 .95451 
 
 1.04766 
 
 .98843 
 
 1.01170 
 
 20 
 
 41 
 
 .85963 
 
 1.16329 
 
 .89045 
 
 1.12303 
 
 .92224 
 
 1.08432 
 
 .95506 
 
 1.04705 
 
 .98901 
 
 1.01112 
 
 19 
 
 42 
 
 .86014 
 
 1.16261 
 
 .89097 
 
 1.12238 
 
 .92277 
 
 1.08369 
 
 .95562 
 
 1.04644 
 
 .98958 
 
 1.01053 
 
 18 
 
 43 
 
 .86064 
 
 1.16192 
 
 .89149 
 
 1.12172 
 
 .92331 
 
 1.08306 
 
 .95618 
 
 1.04583 
 
 .99016 
 
 1.00994 
 
 17 
 
 44 
 
 .86115 
 
 1.16124 
 
 .89201 
 
 1.12106 
 
 .92385 
 
 1.08243 
 
 .95673 
 
 1.04522 
 
 .99073 
 
 1.00935 
 
 16 
 
 45 
 
 .86166 
 
 1.16056 
 
 .89253 
 
 1.12041 
 
 .92439 
 
 1.08179 
 
 .95729 
 
 1.04461 
 
 .99131 
 
 1.00876 
 
 15 
 
 46 
 
 .86216 
 
 1.15987 
 
 .89306 
 
 1.11975 
 
 .92493 
 
 1.08116 
 
 .95785 
 
 1.04401 
 
 .99189 
 
 1.00818 
 
 14 
 
 47 
 
 .86267 
 
 1.15919 
 
 .89358 
 
 1.11909 
 
 .92547 
 
 1.08053 
 
 .95841 
 
 1.04340 
 
 .99247 
 
 1.00759 
 
 13 
 
 48 
 
 .86318 
 
 1.15851 
 
 .89410 
 
 1.11844 
 
 .92601 
 
 1.07990 
 
 .95897 
 
 1.04279 
 
 .99304 
 
 1.00701 
 
 12 
 
 49 
 
 .86368 
 
 1.15783 
 
 .89463 
 
 1.11778 
 
 .92655 
 
 1.07927 
 
 .95952 
 
 1.04218 
 
 .99362 
 
 1.00642 
 
 11 
 
 50 
 
 .86419 
 
 1.15715 
 
 .89515 
 
 1.11713 
 
 .92709 
 
 1.07864 
 
 .96008 
 
 1.04158 
 
 .99420 
 
 1.00583 
 
 10 
 
 51 
 
 .86470 
 
 1.15647 
 
 .89567 
 
 1.11648 
 
 .92763 
 
 1.07801 
 
 .96064 
 
 1.04097 
 
 .99478 
 
 1.00525 
 
 9 
 
 52 
 
 .86521 
 
 1.15579 
 
 .89620 
 
 1.11582 
 
 .92817 
 
 1.07738 
 
 .96120 
 
 1.04036 
 
 .99536 
 
 1.00467 
 
 8 
 
 53 
 
 -86572 
 
 1.15511 
 
 .89672 
 
 1.11517 
 
 .92872 
 
 1.07676 
 
 .96176 
 
 1.03976 
 
 .99594 
 
 1.00408 
 
 7 
 
 54 
 
 86623 
 
 1.15443 
 
 .89725 
 
 1.11452 
 
 .92926 
 
 1.07613 
 
 .96232 
 
 1.03915 
 
 .99652 
 
 1.00350 
 
 6 
 
 55 
 
 86674 
 
 1.15375 
 
 .89777 
 
 1.11387 
 
 .92980 
 
 1.07550 
 
 .96288 
 
 1.03855 
 
 .99710 
 
 1.00291 
 
 5 
 
 56 
 
 86725 
 
 1.15308 
 
 .89830 
 
 1.11321 
 
 .93034 
 
 1.07487 
 
 .96344 
 
 1.03794 
 
 .99768 
 
 1.00233 
 
 4 
 
 57 
 
 .86776 
 
 1.15240 
 
 .89883 
 
 1.11256 
 
 .93088 
 
 1.07425 
 
 .96400 
 
 1.03734 
 
 .99826 
 
 1.00175 
 
 3 
 
 58 
 
 .86827 
 
 1.15172 
 
 .89935 
 
 1.11191 
 
 .93143 
 
 1.07362 
 
 .96457 
 
 1.03674 
 
 .99884 
 
 1.00116 
 
 2 
 
 59 
 
 .86878 
 
 1.15104 
 
 .89988 
 
 1.11126 
 
 .93197 
 
 1.07299 
 
 .96513 
 
 1.03613 
 
 .99942 
 
 1.00058 
 
 1 
 
 60 
 
 .86929 
 
 1.15037 
 
 .90040 
 
 1.11061 
 
 .93252 
 
 1.07237 
 
 .96569 
 
 1.03553 
 
 1.00000 
 
 1.00000 
 
 
 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 Cotang 
 
 Tang 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 t 
 
 
 4< 
 
 > 
 
 4$ 
 
 * 
 
 4' 
 
 1 
 
 4( 
 
 o 
 
 4 
 
 5 
 
 
LOGARITHMIC TABLES 
 
 1009 
 
 LOGARITHMIC TABLES 
 
 To Find the Logarithmic Sine, Cosine, Tangent, or Cotangent of an Angle 
 From to 45. In the table entitled Logarithms of Trigonometric Functions, 
 find the number of degrees at the top of the page, and the number of^minutes 
 in the left-hand column headed (') ; opposite the latter, and under the proper 
 head, find the desired logarithmic sine, cosine, tangent, or cotangent. 
 
 To Find the Logarithmic Sine, Cosine, Tangent, or Cotangent of an Angle 
 From 45 to 90. In the table entitled Logarithms of Trigonometric Func- 
 tions, find the number of degrees at the bottom of the page, and the number 
 of minutes in the right-hand column headed (') ; opposite the latter, and 
 above the proper head, find the desired logarithmic sine, cosine, tangent, or 
 cotangent. 
 
 To Find the Logarithmic Functions for an Angle Containing Degrees, Min- 
 utes, and Seconds. Find the logarithm for the degrees and minutes in the 
 manner just given, then from the column headed d. take the number next 
 below the logarithm thus found; under the heading P.P., find a column 
 headed by this number, and find in this column the number opposite the given 
 number of seconds; add it to the logarithm already found for the degrees 
 and minutes. If the exact number of seconds is not given under P.P., the 
 proper values may be found by interpolating between the values given. 
 As the differences in the column headed d. represent differences correspond- 
 ing to 60 sec., the amount to be added after the logarithm of the degrees 
 and minutes has been found may be obtained by multiplying the difference 
 by the number of seconds, and dividing the result by 60. 
 
 The columns headed Cpl. S. and Cpl. T. on pages 1028 to 1030 can be used 
 to find logarithms of angles including seconds less than 3 and greater than 86. 
 Reduce the degrees, minutes, and seconds to seconds, and use the following 
 formulas, substituting for Cpl. S and Cpl. T. the values given in the table, 
 and for S. and T., the difference between 10 and Cpl. S. and Cpl. T. as given. 
 
 For angles less than 4, log sin a = log a" + S.; log tang a = log a" 
 + T.; log cotg a = Cpl. log a" + Cpl. T. = Cpl. log tang ; log a" = log 
 sin a + Cpl. S. = log tang a + Cpl. T. = Cpl. log cotg a + Cpl. T. 
 
 For angles greater than 86, log cos a = log (90 a") + S.: log c6tg a 
 = log (90 - a") + T.; log tang a = Cpl. log (90 - a") + Cpl. T. = Cpl. 
 log cotg a; log (90 - a") = log cos a + Cpl. S. = log cotg a + Cpl. T. 
 = Cpl. log tang a + Cpl. T. 
 
 COMMON LOGARITHMS OF NUMBERS 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 
 
 
 20 
 
 30 103 
 
 40 
 
 60 206 
 
 60 
 
 77 815 
 
 80 
 
 90 309 
 
 
 no nno 
 
 21 
 
 32 222 
 
 41 
 
 61 278 
 
 61 
 
 78 533 
 
 81 
 
 90849 
 
 o an im 
 
 22 
 
 34 242 
 
 4?, 
 
 62 325 
 
 62 
 
 79 239 
 
 82 
 
 91 381 
 
 3 
 4 
 
 5 
 
 47 712 
 60 206 
 69 897 
 
 23 
 24 
 25 
 
 36 173 
 38021 
 39 794 
 
 43 
 44 
 45 
 
 63 347 
 64 345 
 65 321 
 
 63 
 64 
 65 
 
 79 934 
 80 618 
 81 291 
 
 83 
 84 
 85 
 
 91 908 
 92 428 
 92 942 
 
 
 77 815 
 84 510 
 
 26 
 
 27 
 
 41 497 
 43 136 
 
 46 
 47 
 
 66 276 
 67 210 
 
 66 
 67 
 
 81 954 
 82 607 
 
 86 
 87 
 
 93 450 
 93 952 
 
 9 
 
 90 309 
 95424 
 
 28 
 29 
 
 44 716 
 46 240 
 
 48 
 49 
 
 68 124 
 69020 
 
 68 
 69 
 
 83 251 
 83 885 
 
 88 
 89 
 
 94 448 
 94 939 
 
 in 
 
 00 000 
 
 30 
 
 47 712 
 
 50 
 
 69 897 
 
 70 
 
 84510 
 
 90 
 
 95424 
 
 11 
 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 
 04 139 
 07 918 
 11 394 
 14 613 
 17 609 
 20 412 
 23 045 
 25 527 
 27 875 
 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 
 49136 
 50 515 
 51 851 
 53148 
 54407 
 55 630 
 56820 
 57 978 
 59 106 
 
 51 
 52 
 53 
 54 
 55 
 56 
 57 
 58 
 59 
 
 70 757 
 71 600 
 72 428 
 73 239 
 74 036 
 74 819 
 75 587 
 76 343 
 77085 
 
 71 
 72 
 73 
 74 
 75 
 76 
 77 
 78 
 79 
 
 85 126 
 85 733 
 86 332 
 86 923 
 87 506 
 88081 
 88649 
 89 209 
 89 763 
 
 91 
 92 
 93 
 94 
 95 
 96 
 97 
 98 
 99 
 
 95 904 
 96 379 
 96 848 
 97 313 
 97772 
 98 227 
 98 677 
 99 123 
 99564 
 
 20 
 
 30103 
 
 40 
 
 60 206 
 
 60 
 
 77815 
 
 80 
 
 90309 
 
 100 
 
 00000 
 
1010 
 
 LOGARITHMS 
 
 N. 
 
 L. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 too 
 
 101 
 102 
 103 
 104 
 105 
 106 
 107 
 108 
 109 
 
 110 
 
 111 
 
 112 
 113 
 114 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 121 
 122 
 123 
 124 
 125 
 126 
 127 
 128 
 129 
 
 130 
 
 131 
 132 
 133 
 134 
 135 
 136 
 137 
 138 
 139 
 
 140 
 
 141 
 142 
 143 
 144 
 145 
 146 
 147 
 148 
 149 
 
 150 
 
 00 000 
 
 043 
 
 087 
 
 130 
 
 173 
 
 217 
 
 260 
 
 303 
 
 346 
 
 389 
 
 8 
 9 
 
 a 
 i 
 
 i 
 
 2 
 3 
 4 
 5 
 I 
 7 
 8 
 1 
 
 1 
 > 
 1 
 4 
 8 
 6 
 7 
 8 
 9 
 
 1 
 2 
 3 
 4 
 5 
 i 
 
 7 
 8 
 9 
 
 44 
 
 4.4 
 
 8.8 
 13.2 
 17.6 
 22.0 
 26.4 
 30.8 
 35.2 
 39.6 
 
 41 
 
 4.1 
 
 8.2 
 12.3 
 16.4 
 20.5 
 24.6 
 28.7 
 32.8 
 36.9 
 
 38 
 
 3.8 
 7.6 
 11.4 
 15.2 
 19.0 
 22.8 
 26.6 
 80.4 
 34.2 
 
 35 
 
 3.5 
 7.0 
 10.5 
 14.0 
 17,5 
 21.0 
 24.5 
 28.0 
 31.5 
 
 32 
 
 3.2 
 6.4 
 9.6 
 
 12.8 
 16.0 
 19.2 
 22.4 
 25.6 
 28.8 
 
 43| 
 
 4.3 
 
 8.6 
 12.9 
 17.2 
 21.5 
 25.8 
 30.1 
 34.4 
 38.7 
 
 40 
 
 4.0 
 8.0 
 12.0 
 16.0 
 20.0 
 24.0 
 28.0 
 82.0 
 36.0 
 
 37 
 
 3.7 
 
 7.4 
 11.1 
 14.8 
 18.5 
 22.2 
 25.9 
 296 
 33.3 
 
 34 
 
 3.4 
 
 6.8 
 10.2 
 13.6 
 17.0 
 20.4 
 23.8 
 27.2 
 30.6 
 
 31 
 
 3.1 
 
 6.2 
 9.3 
 12.4 
 15.5 
 18.6 
 21.7 
 24.8 
 27.9 
 
 42 
 
 4.2 
 
 8.4 
 12.6 
 16.8 
 21.0 
 25.2 
 29.4 
 33.6 
 37.8 
 
 39 
 
 3.9 
 7.8 
 11.7 
 15.6 
 19.5 
 23.4 
 27.3 
 31.2 
 35.1 
 
 36 
 
 3.6 
 
 7.2 
 10.8 
 14.4 
 18.0 
 21.6 
 25.2 
 28.8 
 32.4 
 
 33 
 
 3.3 
 
 6.6 
 9.9 
 13.2 
 16.5 
 19.8 
 23.1 
 26.4 
 29.7 
 
 30 
 
 3.0 
 6.0 
 9.0 
 12.0 
 15.0 
 18.0 
 21.0 
 24.0 
 27.0 
 
 432 
 860 
 01 284 
 703 
 02 119 
 531 
 938 
 03 342 
 743 
 
 475 
 903 
 326 
 745 
 160 
 572 
 979 
 383 
 782 
 
 518 
 945 
 
 368 
 787 
 202 
 612 
 *019 
 423 
 822 
 
 561 
 988 
 410 
 828 
 243 
 653 
 *060 
 463 
 862 
 
 258 
 
 604 
 *030 
 452 
 870 
 284 
 694 
 *100 
 503 
 902 
 
 297 
 
 647 
 *072 
 494 
 912 
 325 
 735 
 *141 
 543 
 941 
 
 336 
 
 689 
 *115 
 536 
 953 
 366 
 776 
 *181 
 583 
 981 
 
 376 
 
 732 
 *157 
 578 
 995 
 407 
 816 
 *222 
 623 
 *021 
 
 415 
 
 775 
 *199 
 620 
 *036 
 449 
 857 
 *262 
 663 
 *060 
 
 817 
 *242 
 662 
 *078 
 490 
 898 
 *302 
 703 
 *100 
 
 04139* 
 
 179 
 
 218 
 
 454 
 
 ->493 
 
 532 
 922 
 05308 
 690 
 06070 
 446 
 819 
 07 188 
 555 
 
 571 
 961 
 346 
 729 
 108 
 483 
 856 
 225 
 591 
 
 954 
 
 610 
 999 
 385 
 767 
 145 
 521 
 893 
 262 
 628 
 
 650 
 *038 
 423 
 805 
 183 
 558 
 930 
 298 
 664 
 
 689 
 *077 
 461 
 843 
 221 
 595 
 967 
 335 
 700 
 
 727 
 *115 
 500 
 881 
 258 
 633 
 *004 
 372 
 737 
 
 766 
 *154 
 538 
 918 
 296 
 670 
 *041 
 408 
 773 
 
 805 
 *192 
 576 
 956 
 333 
 707 
 *078 
 445 
 809 
 
 844 
 *231 
 614 
 994 
 371 
 744 
 *115 
 482 
 846 
 
 883 
 *269 
 652 
 *032 
 408 
 781 
 *151 
 518 
 882 
 
 918 
 
 990 
 
 350 
 707 
 *061 
 412 
 760 
 106 
 449 
 789 
 126 
 
 *027 
 
 *063 
 
 422 
 
 778 
 *132 
 482 
 830 
 175 
 517 
 857 
 193 
 
 528 
 
 *099 
 
 458 
 814 
 *167 
 517 
 864 
 209 
 551 
 890 
 227 
 
 *135 
 
 493 
 849 
 *202 
 552 
 899 
 243 
 585 
 924 
 261 
 
 *171 
 
 529 
 884 
 *237 
 587 
 934 
 278 
 619 
 958 
 294 
 
 628 
 
 *207 
 
 *243 
 
 08 279 
 636 
 991 
 09 342 
 691 
 10037 
 380 
 721 
 11 059 
 
 314 
 672 
 *026 
 377 
 726 
 072 
 415 
 755 
 093 
 
 386 
 743 
 *096 
 447 
 795 
 140 
 483 
 823 
 160 
 
 565 
 920 
 *272 
 621 
 968 
 312 
 653 
 992 
 327 
 
 661 
 
 600 
 955 
 *307 
 656 
 *003 
 346 
 687 
 *025 
 361 
 
 394 
 
 428 
 
 461 
 
 494 
 
 561 
 
 594 
 
 694 
 
 727 
 12 057 
 385 
 710 
 13033 
 354 
 672 
 988 
 14 301 
 
 760 
 090 
 418 
 743 
 066 
 386 
 704 
 *019 
 333 
 
 793 
 123 
 450 
 775 
 098 
 418 
 735 
 *051 
 364 
 
 675 
 
 983 
 290 
 594 
 897 
 197 
 495 
 791 
 085 
 377 
 
 826 
 156 
 483 
 808 
 130 
 450 
 767 
 *082 
 395 
 
 860 
 189 
 516 
 840 
 162 
 481 
 799 
 *114 
 426 
 
 737 
 
 893 
 222 
 548 
 872 
 194 
 513 
 830 
 *145 
 457 
 
 768 
 
 926 
 
 254 
 581 
 905 
 226 
 545 
 862 
 *176 
 489 
 
 959 
 
 287 
 613 
 937 
 258 
 577 
 
 *208 
 520 
 
 992 
 320 
 646 
 969 
 290 
 609 
 925 
 *239 
 551 
 
 *024 
 352 
 678 
 *001 
 322 
 640 
 956 
 *270 
 582 
 
 613 
 
 644 
 
 706 
 
 *014 
 320 
 625 
 927 
 227 
 524 
 820 
 114 
 406 
 
 799 
 
 *106 
 412 
 715 
 *017 
 316 
 613 
 909 
 202 
 493 
 
 829 
 
 *137 
 442 
 746 
 *047 
 346 
 643 
 938 
 231 
 522 
 
 860 
 
 891 
 
 *198 
 503 
 806 
 *107 
 406 
 702 
 997 
 289 
 580 
 
 922 
 15 229 
 534 
 836 
 16 137 
 435 
 732 
 17 026 
 319 
 
 953 
 259 
 564 
 866 
 167 
 465 
 761 
 056 
 348 
 
 *045 
 351 
 655 
 957 
 256 
 554 
 850 
 143 
 435 
 
 *076 
 381 
 685 
 987 
 2S6 
 584 
 879 
 173 
 464 
 
 *168 
 473 
 776 
 *077 
 376 
 673 
 967 
 260 
 551 
 
 609 
 
 638 
 
 667 
 
 696 
 
 725 
 
 754 
 
 782 
 
 811 
 
 840 
 
 869 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
LOGARITHMS 
 
 1011 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 F 
 
 .] 
 
 P. 
 
 ISO 
 
 17 609 
 
 638 
 
 667 
 
 696 
 
 725 
 
 754 
 
 782 
 
 811 
 
 840 
 
 869 
 
 
 
 
 
 151 
 152 
 153 
 154 
 155 
 156 
 157 
 158 
 159 
 
 898 
 18 184 
 469 
 752 
 19 033 
 312 
 590 
 866 
 20 140 
 
 926 
 213 
 498 
 780 
 061 
 340 
 618 
 893 
 167 
 
 955 
 241 
 526 
 808 
 089 
 368 
 645 
 921 
 194 
 
 984 
 270 
 554 
 837 
 117 
 396 
 673 
 948 
 222 
 
 *013 
 298 
 583 
 865 
 145 
 424 
 700 
 976 
 249 
 
 *041 
 327 
 611 
 893 
 173 
 451 
 728 
 *003 
 276 
 
 *070 
 355 
 639 
 921 
 201 
 479 
 756 
 *030 
 303 
 
 *099 
 384 
 667 
 949 
 229 
 507 
 783 
 *058 
 330 
 
 *127 
 412 
 696 
 977 
 257 
 535 
 811 
 *085 
 358 
 
 *156 
 441 
 724 
 *005 
 285 
 562 
 838 
 *112 
 385 
 
 8 
 9 
 
 2 
 
 2 
 5 
 8 
 11 
 14 
 17 
 20 
 28 
 26 
 
 9 
 
 .9 
 .8 
 .7 
 .6 
 .5 
 .4 
 .3 
 .2 
 .1 
 
 28 
 
 2.8 
 5.6 
 8.4 
 11.2 
 14.0 
 16.8 
 19.6 
 22.4 
 25.2 
 
 160 
 
 412 
 
 439 
 
 466 
 
 493 
 
 520 
 
 548 
 
 575 
 
 602 
 
 629 
 
 656 
 
 
 
 
 
 161 
 162 
 163 
 164 
 165 
 166 
 167 
 168 
 169 
 
 683 
 952 
 21 219 
 484 
 748 
 22 Oil 
 272 
 531 
 789 
 
 710 
 978 
 245 
 511 
 775 
 037 
 298 
 557 
 ,814 
 
 737 
 *005 
 272 
 537 
 801 
 063 
 324 
 583 
 840 
 
 763 
 *032 
 299 
 564 
 827 
 089 
 350 
 608 
 866 
 
 790 
 *059 
 325 
 590 
 854 
 115 
 376 
 634 
 891 
 
 817 
 *085 
 352 
 617 
 880 
 141 
 401 
 660 
 917 
 
 844 
 *112 
 378 
 643 
 906 
 167 
 427 
 686 
 943 
 
 871 
 *139 
 405 
 669 
 932 
 194 
 453 
 712 
 968 
 
 898 
 *165 
 431 
 696 
 958 
 220 
 479 
 737 
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 13 
 16 
 18 
 21 
 24 
 
 7 
 
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 4 
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 8 
 5 
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 26 
 
 2.6 
 5.2 
 7.8 
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 15.6 
 18.2 
 20.8 
 23.4 
 
 170 
 
 23 045 
 
 070 
 
 096 
 
 121 
 
 147 
 
 172 
 
 198 
 
 223 
 
 249 
 
 274 
 
 
 
 
 
 171 
 172 
 173 
 174 
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 177 
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 300 
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 376 
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 502 
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 254 
 502 
 748 
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 528 
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 279 
 527 
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 181 
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 184 
 185 
 186 
 187 
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 768 
 26 007 
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 4 
 7 
 9 
 12 
 14 
 16 
 19 
 21 
 
 4 
 
 4 
 
 8 
 2 
 6 
 
 4 
 8 
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 6 
 
 23 
 
 2.3 
 4.6 
 6.9 
 9.2 
 11.5 
 13.8 
 16.1 
 18.4 
 20.7 
 
 190 
 
 875 
 
 898 
 
 921 
 
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 967 
 
 989 
 
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 191 
 192 
 193 
 194 
 195 
 196 
 197 
 198 
 199 
 
 28 103 
 330 
 556 
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 226 
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 126 
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 149 
 
 375 
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 171 
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 194 
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 217 
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 240 
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 6 
 8 
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 13 
 15 
 17 
 19 
 
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 2 
 4 
 
 6 
 8 
 
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 4 
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 21 
 
 2.1 
 
 4.2 
 6.3 
 8.4 
 10.5 
 12.6 
 14.7 
 16.8 
 18.9 
 
 200 
 
 30103 
 
 125 
 
 146 
 
 168 
 
 190 
 
 211 
 
 233 
 
 255 
 
 276 
 
 298 
 
 
 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 P 
 
 I 
 
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1012 
 
 LOGARITHMS 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 200 
 
 201 
 202 
 203 
 204 
 205 
 206 
 207 
 208 
 209 
 
 210 
 
 211 
 212 
 213 
 214 
 215 
 216 
 217 
 '218 
 219 
 
 220 
 
 221 
 222 
 223 
 224 
 225 
 226 
 227 
 228 
 229 
 
 230 
 
 231 
 
 232 
 233 
 234 
 235 
 236 
 237 
 238 
 239 
 
 240 
 
 241 
 242 
 243 
 244 
 245 
 246 
 247 
 248 
 249 
 
 250 
 
 30 103 
 
 125 
 
 146 
 
 168 
 
 190 
 
 211 
 
 233 
 
 255 
 
 276 
 
 298 
 
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 2 4 
 3 6 
 4 8 
 5 11 
 6 13 
 7 15 
 8 17 
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 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 1 
 
 2 
 3 
 4 
 
 5 
 6 
 7 
 8 
 9 
 
 7 
 8 
 9 
 
 2 21 
 
 .2 2.1 
 .4 4.2 
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 .8 8.4 
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 .2 12.6 
 .4 14.7 
 .8 16.8 
 .8 18.9 
 
 20 
 
 2.0 
 4.0 
 6.0 
 8.0 
 10.0 
 12.0 
 14.0 
 16.0 
 18.0 
 
 19 
 
 1.9 
 3.8 
 5.7 
 7.6 
 9.5 
 11.4 
 13.3 
 15.2 
 17.1 
 
 18 
 
 1.8 
 3.6 
 5.4 
 7.2 
 9.0 
 10.8 
 12.6 
 14.4 
 16.2 
 
 17 
 
 1.7 
 34 
 5.1 
 6.8 
 8.5 
 10.2 
 11.9 
 13.6 
 15.3 
 
 320 
 535 
 750 
 963 
 31 175 
 387 
 597 
 806 
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 341 
 557 
 771 
 984 
 197 
 408 
 618 
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 363 
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 218 
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 384 
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 239 
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 660 
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 406 
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 835 
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 260 
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 428 
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 281 
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 118 
 
 449 
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 302 
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 323 
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 492 
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 514 
 
 728 
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 366 
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 201 
 
 222 
 
 243 
 
 263 
 
 284 
 
 305 
 
 325 
 
 346 
 
 366 
 
 387 
 
 408 
 
 428 
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 449 
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 666 
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 469 
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 284 
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 490 
 695 
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 102 
 304 
 506 
 706 
 905 
 104 
 
 510 
 715 
 919 
 122 
 325 
 526 
 726 
 925 
 124 
 
 531 
 736 
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 143 
 345 
 546 
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 143 
 
 552 
 756 
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 163 
 365 
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 572 
 777 
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 385 
 586 
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 593 
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 203 
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 613 
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 626 
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 223 
 
 242 
 
 262 
 
 459 
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 282 
 
 479 
 
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 301 
 
 321 
 
 341 
 
 537 
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 380 
 
 400 
 
 420 
 
 439 
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 498 
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 596 
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 180 
 372 
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 324 
 
 511 
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 254 
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 36 173 
 
 192 
 
 380 
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 211 
 
 399 
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 229 
 
 248 
 
 267 
 
 286 
 
 305 
 
 361 
 549 
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 37 107 
 291 
 475 
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 418 
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 977 
 162 
 346 
 530 
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 436 
 624 
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 181 
 365 
 548 
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 455 
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 383 
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 474 
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 401 
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 493 
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 236 
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 530 
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 903 
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 273 
 457 
 639 
 822 
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 38 021 
 
 039 
 
 057 
 
 075 
 
 093 
 
 112 
 
 130 
 
 148 
 
 166 
 
 184 
 
 202 
 382 
 561 
 739 
 917 
 39 094 
 270 
 445 
 620 
 
 220 
 399 
 578 
 757 
 934 
 111 
 287 
 463 
 637 
 
 238 
 417 
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 775 
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 129 
 305 
 480 
 655 
 
 829 
 
 256 
 435 
 614 
 792 
 970 
 146 
 322 
 498 
 672 
 
 846 
 
 3 
 
 274 
 453 
 632 
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 164 
 340 
 515 
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 292 
 471 
 650 
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 358 
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 310 
 489 
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 199 
 375 
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 328 
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 915 
 
 346 
 525 
 703 
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 235 
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 585 
 759 
 
 364 
 543 
 
 721 
 899 
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 252 
 
 428 
 602 
 
 777 
 
 950 
 
 794 
 
 811 
 
 863 
 
 881 
 
 898 
 
 933 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
- LOGARITHMS 
 
 1013 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 250 
 
 251 
 
 252 
 253 
 254 
 255 
 256 
 257 
 258 
 259 
 
 260 
 
 261 
 262 
 263 
 264 
 265 
 266 
 267 
 268 
 269 
 
 270 
 
 271 
 272 
 273 
 274 
 275 
 276 
 277 
 278 
 279 
 
 280 
 
 281 
 282 
 283 
 284 
 285 
 286 
 287 
 288 
 289 
 
 290 
 
 291 
 292 
 293 
 294 
 295 
 296 
 297 
 298 
 299 
 
 300 
 
 39 794 
 
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 829 
 
 846 
 
 863 
 
 *037 
 209 
 381 
 552 
 722 
 892 
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 229 
 397 
 
 564 
 
 881 
 
 898 
 
 915 
 
 933 
 
 950 
 
 8 
 9 
 
 7 
 8 
 9 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 18 
 
 1.8 
 3.6 
 
 5.4 
 7.2 
 9.0 
 10.8 
 12.6 
 14.4 
 16.2 
 
 17 
 
 1.7 
 3.4 
 5.1 
 6.8 
 8.5 
 10.2 
 11.9 
 13.6 
 15.3 
 
 16 
 
 1.6 
 3.2 
 4.8 
 6.4 
 8.0 
 9.6 
 11.2 
 12.8 
 14.4 
 
 15 
 
 1.5 
 3.0 
 4.5 
 6.0 
 7,5 
 9.0 
 10.5 
 12.0 
 13.5 
 
 14 
 
 1.4 
 2 8 
 4.2 
 5.6 
 7.0 
 8.4 
 9.8 
 11.2 
 12.6 
 
 967 
 40 140 
 312 
 483 
 654 
 824 
 993 
 41 162 
 330 
 
 985 
 157 
 329 
 500 
 671 
 841 
 *010 
 179 
 347 
 
 *002 
 175 
 346 
 518 
 688 
 858 
 *027 
 196 
 363 
 
 *019 
 192 
 364 
 535 
 705 
 875 
 *044 
 212 
 380 
 
 *054 
 226 
 398 
 569 
 739 
 909 
 *078 
 246 
 414 
 
 *071 
 243 
 415 
 586 
 756 
 926 
 *095 
 263 
 430 
 
 597 
 
 *088 
 261 
 432 
 603 
 773 
 943 
 *111 
 280 
 447 
 
 614 
 
 *106 
 278 
 449 
 620 
 790 
 960 
 *128 
 296 
 464 
 
 *123 
 295 
 466 
 637 
 807 
 976 
 *145 
 313 
 481 
 
 647 
 
 497 
 
 514 
 
 531 
 
 697 
 863 
 *029 
 193 
 357 
 521 
 684 
 846 
 *008 
 
 169 
 
 547 
 
 714 
 880 
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 210 
 374 
 537 
 700 
 862 
 *024 
 
 581 
 
 631 
 
 664 
 830 
 996 
 42 160 
 325 
 488 
 651 
 813 
 975 
 
 681 
 847 
 *012 
 177 
 341 
 504 
 667 
 830 
 991 
 
 731 
 896 
 *062 
 226 
 390 
 553 
 716 
 878 
 *010 
 
 747 
 913 
 *078 
 243 
 406 
 570 
 732 
 894 
 *056 
 
 217 
 
 377 
 537 
 696 
 854 
 *012 
 170 
 326 
 483 
 638 
 
 764 
 929 
 *095 
 259 
 423 
 586 
 749 
 911 
 *072 
 
 780 
 946 
 *111 
 275 
 439 
 602 
 765 
 927 
 *088 
 
 797 
 963 
 *127 
 292 
 455 
 619 
 781 
 943 
 *104 
 
 265 
 
 814 
 979 
 *144 
 308 
 472 
 635 
 797 
 959 
 *120 
 
 281 
 
 43 136 
 
 152 
 
 185 
 
 201 
 
 233 
 
 393 
 553 
 712 
 870 
 *028 
 185 
 342 
 498 
 654 
 
 249 
 
 297 
 457 
 616 
 775 
 933 
 44091 
 248 
 404 
 560 
 
 313 
 473 
 632 
 791 
 949 
 107 
 264 
 420 
 576 
 
 731 
 
 329 
 489 
 648 
 807 
 965 
 122 
 279 
 436 
 592 
 
 747 
 
 345 
 505 
 664 
 823 
 981 
 138 
 295 
 451 
 607 
 
 361 
 521 
 680 
 838 
 996 
 154 
 311 
 467 
 623 
 
 409 
 569 
 727 
 886 
 *044 
 
 201 
 358 
 514 
 669 
 
 425 
 584 
 743 
 902 
 *059 
 217 
 373 
 529 
 685 
 
 441 
 600 
 759 
 917 
 *075 
 232 
 389 
 545 
 700 
 
 855 
 
 716 
 
 762 
 
 917 
 071 
 225 
 378 
 530 
 682 
 834 
 984 
 135 
 
 285 
 
 778 
 
 932 
 086 
 240 
 393 
 545 
 697 
 849 
 *000 
 150 
 
 300 
 
 793 
 
 809 
 
 824 
 
 840 
 
 871 
 45 025 
 179 
 332 
 484 
 637 
 788 
 939 
 46090 
 
 886 
 040 
 194 
 347 
 500 
 652 
 803 
 954 
 105 
 
 902 
 056 
 209 
 362 
 515 
 667 
 818 
 969 
 120 
 
 948 
 102 
 255 
 408 
 561 
 712 
 864 
 *015 
 165 
 
 963 
 117 
 271 
 423 
 576 
 728 
 879 
 *030 
 180 
 
 979 
 133 
 286 
 439 
 591 
 743 
 894 
 *045 
 195 
 
 994 
 148 
 301 
 454 
 606 
 758 
 909 
 *060 
 210 
 
 *010 
 163 
 317 
 469 
 621 
 773 
 924 
 *075 
 225 
 
 240 
 
 255 
 
 404 
 553 
 702 
 850 
 997 
 144 
 290 
 436 
 582 
 
 270 
 
 315 
 
 464 
 613 
 761 
 909 
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 202 
 349 
 494 
 640 
 
 330 
 
 345 
 
 359 
 
 374 
 
 389 
 538 
 687 
 835 
 982 
 47 129 
 276 
 422 
 567 
 
 419 
 568 
 716 
 864 
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 159 
 305 
 451 
 596 
 
 434 
 583 
 731 
 879 
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 173 
 319 
 465 
 611 
 
 756 
 
 449 
 
 598 
 746 
 894 
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 188 
 334 
 480 
 625 
 
 479 
 627 
 776 
 923 
 *070 
 217 
 363 
 509 
 654 
 
 494 
 642 
 790 
 938 
 *085 
 232 
 378 
 524 
 669 
 
 813 
 
 509 
 657 
 805 
 953 
 *100 
 246 
 392 
 538 
 683 
 
 523 
 672 
 820 
 967 
 *114 
 261 
 407 
 553 
 698 
 
 712 
 
 727 
 
 741 
 
 770 
 
 784 
 
 799 
 
 828 
 
 842 
 
 9 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 P.P. 
 
1014 
 
 LOGARITHMS 
 
 N. 
 
 L.O 
 
 1 
 
 727 
 
 871 
 015 
 159 
 302 
 444 
 586 
 728 
 869 
 *010 
 
 2 
 
 741 
 
 3 
 
 756 
 
 4 
 770 
 
 5 
 
 784 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 300 
 
 301 
 302 
 303 
 304 
 305 
 306 
 307 
 308 
 309 
 
 310 
 
 311 
 312 
 313 
 314 
 315 
 316 
 317 
 318 
 319 
 
 320 
 
 321 
 322 
 323 
 324 
 325 
 326 
 327 
 328 
 329 
 
 330 
 
 331 
 332 
 333 
 334 
 335 
 336 
 337 
 338 
 339 
 
 340 
 
 341 
 342 
 343 
 344 
 345 
 346 
 347 
 348 
 349 
 
 350 
 
 47 712 
 
 799 
 
 813 
 
 828 
 
 842 
 
 986 
 130 
 273 
 416 
 
 558 
 700 
 841 
 982 
 *122 
 
 8 
 9 
 
 1 
 2 
 
 8 
 9 
 
 1 
 2 
 3 
 4 
 
 5 
 6 
 
 7 
 8 
 9 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 15 
 
 1.5 
 3.0 
 4.5 
 6.0 
 7.5 
 9.0 
 10.5 
 12.0 
 13.5 
 
 14 
 
 1.4 
 
 2.8 
 4.2 
 5.6 
 7.0 
 8.4 
 9.8 
 11.2 
 12.6 
 
 13 
 
 1.3 
 2.6 
 3.9 
 5 2 
 6.5 
 7.8 
 9,1 
 10.4 
 11,7 
 
 12 
 
 1.2 
 2.4 
 3.6 
 4.8 
 6.0 
 7.2 
 8.4 
 9.6 
 10.8 
 
 857 
 48 001 
 144 
 287 
 430 
 572 
 714 
 855 
 9% 
 
 885 
 029 
 173 
 316 
 458 
 601 
 742 
 883 
 *024 
 
 900 
 044 
 187 
 330 
 473 
 615 
 756 
 897 
 *038 
 
 914 
 058 
 202 
 344 
 487 
 629 
 770 
 911 
 *052 
 
 929 
 073 
 216 
 359 
 501 
 643 
 785 
 926 
 *066 
 
 943 
 087 
 230 
 373 
 515 
 657 
 799 
 940 
 *080 
 
 958 
 101 
 244 
 387 
 530 
 671 
 813 
 954 
 *094 
 
 972 
 116 
 259 
 401 
 544 
 686 
 827 
 968 
 *108 
 
 49 136 
 
 150 
 
 164 
 
 178 
 
 192 
 
 206 
 
 220 
 
 234 
 
 374 
 513 
 651 
 790 
 927 
 *065 
 202 
 338 
 474 
 
 610 
 
 248 
 
 388 
 527 
 665 
 803 
 941 
 *079 
 215 
 352 
 488 
 
 262 
 
 276 
 415 
 554 
 693 
 831 
 969 
 50 106 
 243 
 379 
 
 290 
 429 
 568 
 707 
 845 
 982 
 120 
 256 
 393 
 
 304 
 443 
 582 
 721 
 859 
 996 
 133 
 270 
 406 
 
 542 
 
 318 
 457 
 596 
 734 
 872 
 *010 
 147 
 284 
 420 
 
 332 
 471 
 610 
 
 748 
 886 
 *024 
 161 
 297 
 433 
 
 569 
 
 346 
 
 485 
 624 
 762 
 900 
 *037 
 174 
 311 
 447 
 
 360 
 499 
 638 
 776 
 914 
 *051 
 188 
 325 
 461 
 
 596 
 
 402 
 541 
 679 
 817 
 955 
 *092 
 229 
 365 
 501 
 
 637 
 
 515 
 
 529 
 
 556 
 
 583 
 
 623 
 
 651 
 786 
 920 
 51 055 
 188 
 322 
 455 
 587 
 720 
 
 664 
 799 
 934 
 068 
 202 
 335 
 468 
 601 
 733 
 
 678 
 813 
 947 
 081 
 215 
 348 
 481 
 614 
 746 
 
 691 
 826 
 961 
 095 
 228 
 362 
 495 
 627 
 759 
 
 705 
 840 
 974 
 108 
 242 
 375 
 508 
 640 
 772 
 
 718 
 853 
 987 
 121 
 255 
 388 
 521 
 654 
 786 
 
 732 
 866 
 *001 
 135 
 268 
 402 
 534 
 667 
 799 
 
 745 
 880 
 *014 
 148 
 282 
 415 
 548 
 680 
 812 
 
 759 
 893 
 *028 
 162 
 295 
 428 
 561 
 693 
 825 
 
 772 
 907 
 *041 
 175 
 308 
 441 
 574 
 706 
 838 
 
 851 
 
 865 
 
 878 
 
 891 
 
 904 
 
 917 
 
 930 
 
 943 
 
 957 
 
 970 
 
 983 
 52 114 
 244 
 375 
 504 
 634 
 763 
 892 
 53 020 
 
 996 
 127 
 257 
 388 
 517 
 647 
 776 
 905 
 033 
 
 *009 
 140 
 270 
 401 
 530 
 660 
 789 
 917 
 046 
 
 *022 
 153 
 284 
 414 
 543 
 673 
 802 
 930 
 058 
 
 *035 
 166 
 297 
 427 
 556 
 686 
 815 
 943 
 071 
 
 *048 
 179 
 310 
 440 
 569 
 699 
 827 
 956 
 084 
 
 *061 
 192 
 323 
 453 
 
 582 
 711 
 840 
 969 
 097 
 
 *075 
 205 
 336 
 466 
 595 
 724 
 853 
 982 
 110 
 
 *088 
 218 
 349 
 479 
 608 
 737 
 866 
 994 
 122 
 
 *101 
 231 
 362 
 492 
 621 
 750 
 879 
 *007 
 135 
 
 148 
 
 161 
 
 173 
 
 186 
 
 199 
 
 212 
 
 224 
 
 237 
 
 250 
 
 263 
 
 275 
 403 
 529 
 656 
 782 
 908 
 54 033 
 158 
 283 
 
 288 
 415 
 542 
 668 
 794 
 920 
 045 
 170 
 295 
 
 301 
 428 
 555 
 681 
 807 
 933 
 058 
 183 
 307 
 
 314 
 441 
 567 
 694 
 820 
 945 
 070 
 195 
 320 
 
 444 
 
 326 
 453 
 580 
 706 
 832 
 958 
 083 
 208 
 332 
 
 456 
 
 339 
 
 466 
 593 
 719 
 845 
 970 
 095 
 220 
 345 
 
 469 
 
 352 
 479 
 605 
 732 
 857 
 983 
 108 
 233 
 357 
 
 481 
 
 364 
 491 
 618 
 744 
 870 
 995 
 120 
 245 
 370 
 
 494 
 
 377 
 504 
 631 
 757 
 882 
 *008 
 133 
 258 
 382 
 
 390 
 517 
 643 
 769 
 895 
 *020 
 145 
 270 
 394 
 
 407 
 
 419 
 
 432 
 
 506 
 
 518 
 
 V N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
LOGARITHMS 
 
 1015 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 350 
 
 351 
 352 
 353 
 354 
 355 
 356 
 357 
 358 
 359 
 
 360 
 
 361 
 362 
 363 
 364 
 365 
 366 
 367 
 368 
 369 
 
 370 
 
 54 407 
 
 419 
 
 432 
 
 555 
 679 
 802 
 925 
 047 
 169 
 291 
 413 
 534 
 
 444 
 
 456 
 
 469 
 
 481 
 
 494 
 
 506 
 
 518 
 
 i 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 8 
 9 
 
 1 
 
 2 
 
 13 
 
 1.3 
 2.6 
 3.9 
 5.2 
 6.5 
 7.8 
 9.1 
 10.4 
 11.7 
 
 12 
 
 1.2 
 2.4 
 3.6 
 4.8 
 6.0 
 7.2 
 8.4 
 9.6 
 10.8 
 
 II 
 
 1.1 
 
 2.2 
 3.3 
 4.4 
 5.5 
 6.6 
 7.7 
 8.8 
 9.9 
 
 10 
 
 1.0 
 2,0 
 3.0 
 4.0 
 5.0 
 6.0 
 7.0 
 8.0 
 9,0 
 
 531 
 654 
 
 777 
 900 
 55 023 
 145 
 267 
 388 
 509 
 
 543 
 
 667 
 790 
 913 
 035 
 157 
 279 
 400 
 522 
 
 568 
 691 
 814 
 937 
 060 
 182 
 303 
 425 
 546 
 
 580 
 704 
 827 
 949 
 072 
 194 
 315 
 437 
 558 
 
 593 
 716 
 839 
 962 
 084 
 206 
 328 
 449 
 570 
 
 605 
 728 
 851 
 974 
 096 
 218 
 340 
 461 
 582 
 
 703 
 
 617 
 741 
 864 
 986 
 108 
 230 
 352 
 473 
 594 
 
 630 
 753 
 876 
 998 
 121 
 242 
 364 
 485 
 606 
 
 727 
 
 642 
 765 
 888 
 *011 
 133 
 255 
 376 
 497 
 618 
 
 630 
 
 642 
 
 654 
 
 666 
 
 678 
 
 691 
 
 715 
 
 739 
 
 751 
 871 
 991 
 56 110 
 229 
 348 
 467 
 585 
 703 
 
 763 
 883 
 *003 
 122 
 241 
 360 
 478 
 597 
 714 
 
 775 
 
 895 
 *015 
 134 
 253 
 372 
 490 
 608 
 726 
 
 844 
 
 787 
 907 
 *027 
 146 
 265 
 384 
 502 
 620 
 738 
 
 855 
 
 799 
 919 
 *038 
 158 
 277 
 396 
 514 
 632 
 750 
 
 867 
 
 811 
 931 
 *050 
 170 
 289 
 407 
 526 
 644 
 761 
 
 823 
 943 
 *062 
 182 
 301 
 419 
 538 
 656 
 773 
 
 835 
 955 
 *074 
 194 
 312 
 431 
 549 
 667 
 785 
 
 847 
 967 
 *086 
 205 
 324 
 443 
 561 
 679 
 797 
 
 914 
 
 859 
 979 
 *098 
 217 
 336 
 455 
 573 
 691 
 808 
 
 926 
 
 *043 
 159 
 276 
 392 
 507 
 623 
 738 
 852 
 967 
 
 820 
 
 832 
 
 879 
 
 891 
 
 902 
 
 371 
 372 
 373 
 374 
 375 
 376 
 377 
 378 
 379 
 
 380 
 
 381 
 382 
 383 
 384 
 385 
 386 
 387 
 388 
 389 
 
 390 
 
 391 
 392 
 393 
 394 
 395 
 396 
 397 
 398 
 399 
 
 400 
 
 937 
 57 054 
 171 
 287 
 403 
 519 
 634 
 749 
 864 
 
 949 
 066 
 183 
 299 
 415 
 530 
 646 
 761 
 875 
 
 961 
 078 
 194 
 310 
 426 
 542 
 657 
 772 
 887 
 
 972 
 089 
 206 
 322 
 438 
 553 
 669 
 784 
 898 
 
 *013 
 
 984 
 101 
 217 
 334 
 449 
 565 
 680 
 795 
 910 
 
 *024 
 
 996 
 113 
 229 
 345 
 461 
 576 
 692 
 807 
 921 
 
 *008 
 124 
 241 
 357 
 473 
 588 
 703 
 818 
 933 
 
 *019 
 136 
 252 
 368 
 484 
 600 
 715 
 830 
 944 
 
 *031 
 148 
 264 
 380 
 496 
 611 
 726 
 841 
 955 
 
 978 
 
 990 
 
 104 
 218 
 331 
 444 
 557 
 670 
 782 
 894 
 *006 
 
 *001 
 
 *035 
 
 *047 
 
 *058 
 
 *070 
 
 184 
 297 
 410 
 524 
 636 
 749 
 861 
 973 
 *084 
 
 *081 
 
 58092 
 206 
 320 
 433 
 546 
 659 
 771 
 883 
 995 
 
 115 
 229 
 343 
 456 
 569 
 681 
 794 
 906 
 *017 
 
 127 
 240 
 354 
 467 
 580 
 692 
 805 
 917 
 *028 
 
 138 
 252 
 365 
 478 
 591 
 704 
 816 
 928 
 *040 
 
 151 
 
 149 
 263 
 377 
 490 
 602 
 715 
 827 
 939 
 *051 
 
 161 
 
 274 
 388 
 501 
 614 
 
 726 
 838 
 950 
 *062 
 
 172 
 
 286 
 399 
 512 
 625 
 737 
 850 
 961 
 *073 
 
 195 
 309 
 422 
 535 
 647 
 760 
 872 
 984 
 *095 
 
 59 106 
 
 118 
 
 129 
 
 140 
 
 162 
 
 173 
 
 284 
 395 
 506 
 616 
 726 
 835 
 945 
 *054 
 163 
 
 184 
 
 195 
 
 306 
 417 
 528 
 638 
 748 
 857 
 966 
 *076 
 184 
 
 207 
 
 218 
 329 
 439 
 550 
 660 
 770 
 879 
 988 
 60 097 
 
 229 
 340 
 450 
 561 
 671 
 780 
 890 
 999 
 108 
 
 240 
 351 
 461 
 572 
 682 
 791 
 901 
 *010 
 119 
 
 228 
 
 251 
 362 
 
 472 
 583 
 693 
 802 
 912 
 *021 
 130 
 
 262 
 373 
 483 
 594 
 704 
 813 
 923 
 *032 
 141 
 
 273 
 384 
 494 
 605 
 715 
 824 
 934 
 *043 
 152 
 
 295 
 406 
 517 
 627 
 737 
 846 
 956 
 *065 
 173 
 
 318 
 428 
 539 
 649 
 759 
 868 
 977 
 *086 
 195 
 
 304 
 
 206 
 
 217 
 
 239 
 
 249 
 
 260 
 
 5 
 
 271 
 
 282 
 
 293 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
1016 
 
 LOGARITHMS 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P 
 
 .P. 
 
 400 
 
 60 206 
 
 217 
 
 228 
 
 239 
 
 249 
 
 260 
 
 271 
 
 282 
 
 293 
 
 304 
 
 
 
 401 
 402 
 403 
 404 
 405 
 406 
 407 
 408 
 409 
 
 314 
 423 
 531 
 638 
 746 
 853 
 959 
 61 066 
 172 
 
 325 
 433 
 541 
 649 
 756 
 863 
 970 
 077 
 183 
 
 336 
 444 
 552 
 660 
 767 
 874 
 981 
 087 
 194 
 
 347 
 
 455 
 563 
 670 
 778 
 885 
 991 
 098 
 204 
 
 358 
 466 
 574 
 681 
 788 
 895 
 *002 
 109 
 215 
 
 369 
 477 
 584 
 692 
 799 
 906 
 *013 
 119 
 225 
 
 379 
 487 
 595 
 703 
 810 
 917 
 *023 
 130 
 236 
 
 390 
 498 
 606 
 713 
 821 
 927 
 *034 
 140 
 247 
 
 401 
 509 
 617 
 724 
 831 
 938 
 *045 
 151 
 257 
 
 412 
 520 
 627 
 735 
 842 
 949 
 *055 
 162 
 268 
 
 l 
 
 2 
 
 II 
 
 1.1 
 2.2 
 
 410 
 
 278 
 
 289 
 
 300 
 
 310 
 
 321 
 
 331 
 
 342 
 
 352 
 
 363 
 
 374 
 
 4 
 
 4.4 
 
 411 
 412 
 413 
 414 
 415 
 416 
 417 
 418 
 419 
 
 384 
 490 
 595 
 700 
 805 
 909 
 62014 
 118 
 221 
 
 395 
 500 
 606 
 711 
 815 
 920 
 024 
 128 
 232 
 
 405 
 511 
 616 
 721 
 826 
 930 
 034 
 138 
 242 
 
 416 
 521 
 627 
 731 
 836 
 941 
 045 
 149 
 252 
 
 426 
 532 
 637 
 742 
 847 
 951 
 055 
 159 
 263 
 
 437 
 542 
 648 
 752 
 857 
 962 
 066 
 170 
 273 
 
 448 
 553 
 658 
 763 
 868 
 972 
 076 
 180 
 284 
 
 458 
 563 
 669 
 773 
 878 
 982 
 086 
 190 
 294 
 
 469 
 574 
 679 
 784 
 888 
 993 
 097 
 201 
 304 
 
 479 
 584 
 690 
 794 
 899 
 *003 
 107 
 211 
 315 
 
 6 
 
 7 
 8 
 9 
 
 M 
 
 7.7 
 8.8 
 9.9 
 
 420 
 
 325 
 
 335 
 
 346 
 
 356 
 
 366 
 
 377 
 
 387 
 
 397 
 
 408 
 
 418 
 
 
 
 421 
 
 422 
 423 
 424 
 425 
 
 426 
 427 
 428 
 429 
 
 428 
 531 
 634 
 737 
 839 
 941 
 63 043 
 144 
 246 
 
 439 
 542 
 644 
 747 
 849 
 951 
 053 
 155 
 256 
 
 449 
 552 
 655 
 757 
 859 
 961 
 063 
 165 
 266 
 
 459 
 562 
 665 
 767 
 870 
 972 
 073 
 175 
 276 
 
 469 
 572 
 675 
 
 778 
 880 
 982 
 083 
 185 
 286 
 
 480 
 583 
 685 
 788 
 890 
 992 
 094 
 195 
 296 
 
 490 
 593 
 696 
 798 
 900 
 *002 
 104 
 205 
 306 
 
 500 
 603 
 706 
 808 
 910 
 *012 
 114 
 215 
 317 
 
 511 
 613 
 716 
 818 
 921 
 *022 
 124 
 225 
 327 
 
 521 
 624 
 726 
 829 
 931 
 *033 
 134 
 236 
 337 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 1.0 
 2.0 
 3.0 
 4.0 
 5.0 
 6.0 
 70 
 8.0 
 9.0 
 
 430 
 
 347 
 
 357 
 
 367 
 
 377 
 
 387 
 
 397 
 
 407 
 
 417 
 
 428 
 
 438 
 
 
 
 431 
 432 
 433 
 434 
 435 
 436 
 437 
 438 
 439 
 
 448 
 548 
 649 
 749 
 849 
 949 
 64 048 
 147 
 246 
 
 458 
 558 
 659 
 759 
 859 
 959 
 058 
 157 
 256 
 
 468 
 568 
 669 
 769 
 869 
 969 
 068 
 167 
 266 
 
 478 
 579 
 679 
 779 
 879 
 979 
 078 
 177 
 276 
 
 488 
 589 
 689 
 789 
 889 
 
 088 
 187 
 286 
 
 498 
 599 
 699 
 799 
 899 
 998 
 098 
 197 
 296 
 
 508 
 609 
 709 
 809 
 909 
 *008 
 108 
 207 
 306 
 
 518 
 619 
 719 
 819 
 919 
 *018 
 118 
 217 
 316 
 
 528 
 629 
 729 
 829 
 929 
 *028 
 128 
 227 
 326 
 
 538 
 639 
 739 
 839 
 939 
 *038 
 137 
 237 
 335 
 
 1 
 
 2 
 3 
 
 9 
 
 0.9 
 1,8 
 
 2.7 
 
 440 
 
 345 
 
 355 
 
 365 
 
 375 
 
 385 
 
 395 
 
 404 
 
 414 
 
 424 
 
 434 
 
 5 
 
 4.5 
 
 441 
 442 
 443 
 444 
 445 
 446 
 447 
 448 
 449 
 
 444 
 542 
 640 
 738 
 836 
 933 
 65 031 
 128 
 225 
 
 454 
 552 
 650 
 748 
 846 
 943 
 040 
 137 
 234 
 
 464 
 562 
 660 
 758 
 856 
 953 
 050 
 147 
 244 
 
 473 
 
 572 
 670 
 768 
 865 
 963 
 060 
 157 
 254 
 
 483 
 582 
 680 
 777 
 875 
 972 
 070 
 167 
 263 
 
 493 
 591 
 689 
 787 
 885 
 982 
 079 
 176 
 273 
 
 503 
 601 
 699 
 797 
 895 
 992 
 089 
 186 
 283 
 
 513 
 611 
 
 709 
 807 
 904 
 *002 
 099 
 196 
 292 
 
 523 
 621 
 719 
 816 
 914 
 *011 
 108 
 205 
 302 
 
 532 
 631 
 729 
 826 
 924 
 *021 
 118 
 215 
 312 
 
 7 
 8 
 9 
 
 6.3 
 7.2 
 8.1 
 
 450 
 
 321 
 
 331 
 
 341 
 
 350 
 
 360 
 
 369 
 
 379 
 
 389 
 
 398 
 
 408 
 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P 
 
 P. 
 
LOGARITHMS 
 
 1017 
 
 N. 
 
 L.O 
 
 1 
 
 331 
 
 427 
 523 
 619 
 715 
 811 
 906 
 *001 
 096 
 191 
 
 2 
 
 341 
 
 3 
 
 4 
 
 5 
 
 6 
 
 379 
 
 475 
 571 
 667 
 763 
 858 
 954 
 *049 
 143 
 238 
 
 7 
 
 8 
 
 ^9 
 
 408 
 
 P.P. 
 
 450 
 
 451 
 452 
 453 
 454 
 455 
 456 
 457 
 458 
 459 
 
 460 
 
 461 
 462 
 463 
 464 
 465 
 466 
 467 
 468 
 469 
 
 470 
 
 471 
 472 
 473 
 474 
 
 475 
 476 
 477 
 478 
 479 
 
 480 
 
 481 
 
 482 
 483 
 484 
 485 
 486 
 487 
 488 
 489 
 
 490 
 
 491 
 492 
 493 
 494 
 495 
 496 
 497 
 498 
 499 
 
 500 
 
 65 321 
 
 350 
 
 360 
 
 369 
 
 389 
 
 398 
 
 i 
 
 2 
 3 
 4 
 
 5 
 6 
 
 7 
 8 
 9 
 
 1 
 
 2 
 3 
 4 
 
 I 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 10 
 
 1.0 
 
 2.0 
 3.0 
 4.0 
 5.0 
 6.0 
 7.0 
 8.0 
 9.0 
 
 9 
 
 0.9 
 
 
 
 3.6 
 4.5 
 
 5.4 
 6.3 
 7.2 
 8.1 
 
 8 
 
 0.8 
 1.6 
 2.4 
 3.2 
 4.0 
 4.8 
 5.6 
 6.4 
 7.2 ' 
 
 418 
 514 
 610 
 706 
 801 
 896 
 992 
 66 087 
 181 
 
 437 
 533 
 629 
 725 
 820 
 916 
 *011 
 106 
 200 
 
 447 
 543 
 639 
 734 
 830 
 925 
 *020 
 115 
 210 
 
 456 
 552 
 648 
 744 
 839 
 935 
 *030 
 124 
 219 
 
 466 
 562 
 658 
 753 
 849 
 944 
 *039 
 134 
 229 
 
 323 
 
 485 
 581 
 677 
 772 
 -868 
 963 
 *058 
 153 
 247 
 
 495 
 591 
 686 
 782 
 877 
 973 
 *068 
 162 
 257 
 
 504 
 600 
 696 
 792 
 887 
 982 
 *077 
 172 
 266 
 
 361 
 
 276 
 
 285 
 
 295 
 
 389 
 483 
 577 
 671 
 764 
 857 
 950 
 043 
 136 
 
 304 
 
 398 
 492 
 586 
 680 
 773 
 867 
 960 
 052 
 145 
 
 314 
 
 332 
 
 342 
 
 351 
 
 370 
 464 
 558 
 652 
 745 
 839 
 932 
 67 025 
 117 
 
 380 
 474 
 567 
 661 
 755 
 848 
 941 
 034 
 12? 
 
 408 
 502 
 596 
 689 
 783 
 876 
 969 
 062 
 154 
 
 417 
 511 
 605 
 699 
 792 
 885 
 978 
 071 
 164 
 
 427 
 521 
 614 
 
 708 
 801 
 894 
 987 
 080 
 173 
 
 265 
 
 436 
 530 
 624 
 717 
 811 
 904 
 997 
 089 
 182 
 
 445 
 539 
 633 
 727 
 820 
 913 
 *006 
 099 
 191 
 
 455 
 549 
 642 
 736 
 829 
 922 
 *015 
 108 
 201 
 
 210 
 
 219 
 
 228 
 
 321 
 413 
 
 504 
 596 
 688 
 779 
 870 
 961 
 052 
 
 142 
 
 237 
 
 330 
 422 
 514 
 605 
 697 
 788 
 879 
 970 
 061 
 
 247 
 
 256 
 
 274 
 
 284 
 
 293 
 
 385 
 477 
 569 
 660 
 752 
 843 
 934 
 *024 
 115 
 
 302 
 394 
 486 
 578 
 669 
 761 
 852 
 943 
 68 034 
 
 311 
 
 403 
 495 
 587 
 679 
 770 
 861 
 952 
 043 
 
 339 
 431 
 523 
 614 
 706 
 797 
 888 
 979 
 070 
 
 348 
 440 
 532 
 624 
 715 
 806 
 897 
 988 
 079 
 
 357 
 449 
 541 
 633 
 
 724 
 815 
 906 
 997 
 088 
 
 367 
 459 
 550 
 642 
 733 
 825 
 916 
 *006 
 097 
 
 376 
 
 468 
 560 
 651 
 742 
 834 
 925 
 *015 
 106 
 
 124 
 
 133 
 
 151 
 
 160 
 
 169 
 
 178 
 
 187 
 
 196 
 
 205 
 
 215 
 305 
 395 
 485 
 574 
 664 
 753 
 842 
 931 
 
 224 
 314 
 404 
 494 
 583 
 673 
 762 
 851 
 940 
 
 233 
 323 
 413 
 502 
 592 
 681 
 771 
 860 
 949 
 
 242 
 332 
 422 
 511 
 601 
 690 
 780 
 869 
 958 
 
 251 
 341 
 431 
 520 
 610 
 699 
 789 
 878 
 966 
 
 260 
 350 
 440 
 529 
 619 
 708 
 797 
 886 
 975 
 
 269 
 359 
 449 
 538 
 628 
 717 
 806 
 895 
 984 
 
 278 
 368 
 458 
 547 
 637 
 726 
 815 
 904 
 993 
 
 287 
 377 
 467 
 556 
 646 
 735 
 824 
 913 
 *002 
 
 296 
 386 
 476 
 565 
 655 
 744 
 833 
 922 
 *011 
 
 69 020 
 
 028 
 
 037 
 
 046 
 
 055 
 
 064 
 
 073 
 
 082 
 
 090 
 
 099 
 
 108 
 197 
 285 
 373 
 461 
 548 
 636 
 723 
 810 
 
 117 
 
 205 
 294 
 381 
 469 
 557 
 644 
 732 
 819 
 
 126 
 214 
 302 
 390 
 478 
 566 
 653 
 740 
 827 
 
 135 
 
 223 
 311 
 399 
 487 
 574 
 662 
 749 
 836 
 
 144 
 
 232 
 320 
 408 
 496 
 583 
 671 
 758 
 845 
 
 152 
 241 
 329 
 417 
 504 
 592 
 679 
 767 
 854 
 
 940 
 
 161 
 249 
 338 
 425 
 513 
 601 
 688 
 775 
 862 
 
 949 
 
 170 
 258 
 346 
 434 
 522 
 609 
 697 
 784 
 871 
 
 179 
 267 
 355 
 443 
 531 
 618 
 705 
 793 
 880 
 
 188 
 276 
 364 
 452 
 539 
 627 
 714 
 801 
 888 
 
 897 
 
 906 
 
 914 
 
 923 
 
 932 
 
 958 
 
 966 
 
 975 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
1018 
 
 'LOGARITHMS 
 
 N. 
 
 L.O 
 
 1 
 
 . 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 500 
 
 501 
 
 502 
 503 
 504 
 505 
 506 
 507 
 508 
 509 
 
 510 
 
 511 
 512 
 513 
 514 
 515 
 516 
 517 
 518 
 519 
 
 520 
 
 521 
 522 
 523 
 524 
 525 
 526 
 527 
 528 
 529 
 
 530 
 
 531 
 532 
 533 
 534 
 535 
 536 
 537 
 538 
 539 
 
 540 
 
 541 
 
 542 
 543 
 544 
 545 
 546 
 547 
 548 
 549 
 
 550 
 
 69 897 
 
 906 
 
 914 
 
 *001 
 088 
 174 
 260 
 346 
 432 
 518 
 603 
 689 
 
 923 
 
 *010 
 096 
 183 
 269 
 355 
 441 
 526 
 612 
 697 
 
 932 
 
 *018 
 105 
 191 
 278 
 364 
 449 
 535 
 621 
 706 
 
 940 
 
 949 
 
 *036 
 122 
 209 
 295 
 381 
 467 
 552 
 638 
 723 
 
 958 
 
 *044 
 131 
 217 
 303 
 389 
 475 
 561 
 646 
 731 
 
 966 
 
 975 
 
 l 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 9 
 
 0.9 
 1.8 
 2.7 
 3.6 
 4.5 
 5.4 
 6.3 
 7.2 
 8.1 
 
 - 
 
 0.8 
 1.6 
 2.4 
 3.2 
 4.0 
 4.8 
 5.6 
 6.4 
 7.2 
 
 7 
 
 0.7 
 1.4 
 2.1 
 2.8 
 3.5 
 4.2 
 4.9 
 56 
 6.3 
 
 984 
 70 070 
 157 
 243 
 329 
 415 
 501 
 586 
 672 
 
 992 
 079 
 165 
 252 
 338 
 424 
 509 
 595 
 680 
 
 *027 
 114 
 200 
 286 
 372 
 458 
 544 
 629 
 714 
 
 *053 
 140 
 226 
 312 
 398 
 484 
 569 
 655 
 740 
 
 *062 
 148 
 234 
 321 
 406 
 492 
 578 
 663 
 749 
 
 757 
 
 766 
 
 774 
 
 783 
 
 868 
 952 
 037 
 122 
 206 
 290 
 374 
 458 
 542 
 
 791 
 
 876 
 961 
 046 
 130 
 214 
 299 
 383 
 466 
 550 
 
 634 
 
 717 
 800 
 883 
 966 
 049 
 132 
 214 
 296 
 378 
 
 460 
 
 542 
 624 
 705 
 787 
 868 
 949 
 *030 
 111 
 191 
 
 272 
 
 800 
 
 885 
 969 
 054 
 139 
 223 
 307 
 391 
 475 
 559 
 
 808 
 
 893 
 978 
 063 
 147 
 231 
 315 
 399 
 483 
 567 
 
 817 
 
 902 
 986 
 071 
 155 
 240 
 324 
 408 
 492 
 575, 
 
 825 
 
 910 
 995 
 079 
 164 
 248 
 332 
 416 
 500 
 584 
 
 834 
 
 842 
 927 
 71 012 
 096 
 181 
 265 
 349 
 433 
 517 
 
 600 
 
 851 
 935 
 020 
 105 
 189 
 273 
 357 
 441 
 525 
 
 859 
 944 
 029 
 113 
 198 
 282 
 366 
 450 
 533 
 
 919 
 *003 
 088 
 172 
 257 
 341 
 425 
 508 
 592 
 
 609 
 
 692 
 775 
 858 
 941 
 024 
 107 
 189 
 272 
 354 
 
 617 
 
 700 
 784 
 867 
 950 
 032 
 115 
 198 
 280 
 362 
 
 625 
 
 709 
 792 
 875 
 958 
 041 
 123 
 206 
 288 
 370 
 
 642 
 
 650 
 
 659 
 
 667 
 
 675 
 
 759 
 842 
 925 
 *008 
 090 
 173 
 255 
 337 
 419 
 
 684 
 767 
 850 
 933 
 72 016 
 099 
 181 
 263 
 346 
 
 725 
 809 
 892 
 975 
 057 
 140 
 222 
 304 
 387 
 
 734 
 817 
 900 
 983 
 066 
 148 
 230 
 313 
 395 
 
 742 
 825 
 908 
 991 
 074 
 156 
 239 
 321 
 403 
 
 750 
 834 
 917 
 999 
 082 
 165 
 247 
 329 
 411 
 
 428 
 
 436 
 
 518 
 599 
 681 
 762 
 843 
 925 
 *006 
 086 
 167 
 
 247 
 
 444 
 
 452 
 
 469 
 
 477 
 
 558 
 640 
 722 
 803 
 884 
 965 
 *046 
 127 
 207 
 
 485 
 
 493 
 
 501 
 
 509 
 591 
 673 
 754 
 835 
 916 
 997 
 73 078 
 159 
 
 239 
 
 526 
 607 
 689 
 770 
 852 
 933 
 *014 
 094 
 175 
 
 534 
 616 
 697 
 779 
 860 
 941 
 *022 
 102 
 183 
 
 550 
 632 
 713 
 795 
 876 
 957; 
 *038 
 119 
 199 
 
 567 
 648 
 730 
 811 
 892 
 973 
 *054 
 135 
 215 
 
 575 
 656 
 738 
 819 
 900 
 981 
 *062 
 143 
 223 
 
 583 
 665 
 746 
 827 
 908 
 989 
 *070 
 151 
 231 
 
 312 
 
 255 
 
 263 
 
 280 
 
 288 
 
 296 
 
 304 
 
 320 
 400 
 480 
 560 
 640 
 719 
 799 
 878 
 957 
 
 328 
 408 
 488 
 568 
 648 
 727 
 807 
 886 
 965 
 
 336 
 416 
 496 
 576 
 656 
 735 
 815 
 894 
 973 
 
 344 
 424 
 504 
 584 
 664 
 743 
 823 
 902 
 981 
 
 352 
 432 
 512 
 592 
 672 
 751 
 830 
 910 
 989 
 
 360 
 440 
 520 
 600 
 679 
 759 
 838 
 918 
 997 
 
 368 
 448 
 528 
 608 
 687 
 767 
 846 
 926 
 *005 
 
 376 
 456 
 536 
 616 
 695 
 775 
 854 
 
 *013 
 
 384 
 464 
 544 
 624 
 703 
 783 
 862 
 941 
 *020 
 
 099 
 
 392 
 472 
 552 
 632 
 711 
 791 
 870 
 949 
 *028 
 
 74 036 
 
 044 
 
 052 
 
 060 
 
 3 
 
 068 
 
 076 
 
 084 
 
 092 
 
 107 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
LOGARITHMS 
 
 1019 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 550 
 
 74 036 
 
 044 
 
 052 
 
 060 
 
 068 
 
 076 
 
 084 
 
 092 
 
 099 
 
 107 
 
 
 551 
 
 552 
 553 
 554 
 555 
 556 
 557 
 558 
 559 
 
 115 
 194 
 273 
 351 
 429 
 507 
 586 
 663 
 741 
 
 123 
 202 
 280 
 359 
 437 
 515 
 593 
 671 
 749 
 
 131 
 
 210 
 288 
 367 
 445 
 523 
 601 
 679 
 757 
 
 139 
 
 218 
 296 
 374 
 453 
 531 
 609 
 687 
 764 
 
 147 
 225 
 304 
 382 
 461 
 539 
 617 
 695 
 772 
 
 155 
 233 
 312 
 390 
 468 
 547 
 624 
 702 
 780 
 
 162 
 241 
 320 
 398 
 476 
 554 
 632 
 710 
 788 
 
 170 
 
 249 
 327 
 406 
 484 
 562 
 640 
 718 
 796 
 
 178 
 257 
 335 
 414 
 492 
 570 
 648 
 726 
 803 
 
 186 
 265 
 343 
 421 
 500 
 578 
 656 
 733 
 811 
 
 
 560 
 
 819 
 
 827 
 
 834 
 
 842 
 
 850 
 
 858 
 
 865 
 
 873. 
 
 881 
 
 889 
 
 
 561 
 562 
 563 
 564 
 565 
 566 
 567 
 568 
 569 
 
 896 
 974 
 75 051 
 128 
 205 
 282 
 358 
 435 
 511 
 
 904 
 981 
 059 
 136 
 213 
 289 
 366 
 442 
 519 
 
 912 
 989 
 066 
 143 
 220 
 297 
 374 
 450 
 526 
 
 920 
 
 997 
 074 
 151 
 228 
 305 
 381 
 458 
 534 
 
 927 
 *005 
 082 
 159 
 236 
 312 
 389 
 465 
 542 
 
 935 
 *012 
 089 
 166 
 243 
 320 
 397 
 473 
 549 
 
 943 
 
 *020 
 097 
 174 
 251 
 328 
 404 
 481 
 557 
 
 950 
 *028 
 105 
 182 
 259 
 335 
 412 
 488 
 565 
 
 958 
 *035 
 113 
 189 
 266 
 343 
 420 
 496 
 572 
 
 966 
 *043 
 120 
 197 
 274 
 351 
 427 
 504 
 580 
 
 0.8 
 1.6 
 2.4 
 3.2 
 4.0 
 4.8 
 5.6 
 6.4 
 7.2 
 
 570 
 
 587 
 
 595 
 
 603 
 
 610 
 
 618 
 
 626 
 
 633 
 
 641 
 
 648 
 
 656 
 
 
 571 
 572 
 573 
 574 
 575 
 576 
 577 
 578 
 579 
 
 664 
 740 
 815 
 891 
 967 
 76 042 
 118 
 193 
 268 
 
 671 
 747 
 823 
 899 
 974 
 050 
 125 
 200 
 275 
 
 679 
 75-5 
 831 
 906 
 982 
 057 
 133 
 208 
 283 
 
 686 
 762 
 838 
 914 
 989 
 065 
 140 
 215 
 290 
 
 694 
 770 
 846 
 921 
 997 
 072 
 148 
 223 
 298 
 
 702 
 778 
 853 
 929 
 *005 
 080 
 155 
 230 
 305 
 
 709 
 785 
 861 
 937 
 *012 
 087 
 163 
 238 
 313 
 
 717 
 793 
 868 
 944 
 *020 
 095 
 170 
 245 
 320 
 
 724 
 800 
 876 
 952 
 *027 
 103 
 178 
 253 
 328 
 
 732 
 808 
 884 
 959 
 *035 
 110 
 185 
 260 
 335 
 
 
 580 
 
 343 
 
 350 
 
 358 
 
 365 
 
 373 
 
 380 
 
 388 
 
 395 
 
 403 
 
 410 
 
 7 
 
 581 
 
 582 
 583 
 584 
 585 
 586 
 587 
 588 
 589 
 
 418 
 492 
 567 
 641 
 716 
 790 
 864 
 938 
 77 012 
 
 425 
 500 
 574 
 649 
 723 
 797 
 871 
 945 
 019 
 
 433 
 
 507 
 582 
 656 
 730 
 805 
 879 
 953 
 026 
 
 440 
 515 
 
 589 
 664 
 738 
 812 
 886 
 960 
 034 
 
 448 
 522 
 597 
 671 
 745 
 819 
 893 
 967 
 041 
 
 455 
 530 
 604 
 678 
 753 
 827 
 901 
 975 
 048 
 
 462 
 537 
 612 
 686 
 760 
 834 
 908 
 982 
 056 
 
 470 
 545 
 619 
 693 
 768 
 842 
 916 
 989 
 063 
 
 477 
 552 
 626 
 701 
 775 
 849 
 923 
 997 
 070 
 
 485 
 559 
 634 
 708 
 782 
 856 
 930 
 *004 
 078 
 
 0.7 
 1.4 
 2.1 
 2.8 
 3.5 
 4.2 
 4.9 
 8 5.6 
 9 6.3 
 
 590 
 
 085 
 
 093 
 
 100 
 
 107 
 
 115 
 
 122 
 
 129 
 
 137 
 
 144 
 
 151 
 
 
 591 
 592 
 593 
 594 
 595 
 596 
 597 
 598 
 599 
 
 159 
 232 
 305 
 379 
 452 
 525 
 597 
 670 
 743 
 
 166 
 240 
 313 
 386 
 459 
 532 
 605 
 677 
 750 
 
 173 
 247 
 320 
 393 
 466 
 539 
 612 
 685 
 757 
 
 181 
 254 
 327 
 401 
 474 
 546 
 619 
 692 
 764 
 
 188 
 262 
 335 
 408 
 481 
 554 
 627 
 699 
 772 
 
 195 
 269 
 342 
 415 
 488 
 561 
 634 
 706 
 779 
 
 203 
 276 
 349 
 422 
 495 
 568 
 641 
 714 
 786 
 
 210 
 283 
 357 
 430 
 503 
 576 
 648 
 721 
 793 
 
 217 
 291 
 364 
 437 
 510 
 583 
 656 
 728 
 801 
 
 225 
 298 
 371 
 444 
 517 
 590 
 663 
 735 
 808 
 
 
 600 
 
 815 
 
 822 
 
 830 
 
 837 
 
 844 
 
 851 
 
 859 
 
 866 
 
 873 
 
 880 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
1020 
 
 LOGARITHMS 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 r 
 
 .P. 
 
 600 
 
 77 815 
 
 822 
 
 830 
 
 837 
 
 844 
 
 851 
 
 859 
 
 866 
 
 873 
 
 880 
 
 
 
 601 
 602 
 603 
 604 
 605 
 606 
 607 
 608 
 609 
 
 887 
 960 
 78 032 
 104 
 176 
 247 
 319 
 390 
 462 
 
 895 
 967 
 039 
 111 
 183 
 254 
 326 
 398 
 469 
 
 902 
 974 
 046 
 118 
 190 
 262 
 333 
 405 
 476 
 
 909 
 981 
 053 
 125 
 197 
 269 
 340 
 412 
 483 
 
 916 
 988 
 061 
 132 
 204 
 276 
 347 
 419 
 490 
 
 924 
 996 
 068 
 140 
 211 
 283 
 355 
 426 
 497 
 
 931 
 *003 
 075 
 147 
 219 
 290 
 362 
 433 
 504 
 
 938 
 *010 
 082 
 154 
 226 
 297 
 369 
 440 
 512 
 
 945 
 *017 
 089 
 161 
 233 
 305 
 376 
 447 
 519 
 
 952 
 *025 
 097 
 168 
 240 
 312 
 383 
 455 
 526 
 
 i 
 
 2 
 
 8 
 
 0.8 
 1.6 
 
 610 
 
 533 
 
 540 
 
 547 
 
 554 
 
 561 
 
 569 
 
 576 
 
 583 
 
 590 
 
 597 
 
 4 
 
 3.2 
 
 611 
 612 
 613 
 614 
 615 
 616 
 617 
 618 
 619 
 
 604 
 675 
 746 
 817 
 888 
 958 
 79 029 
 099 
 169 
 
 611 
 
 682 
 753 
 824 
 895 
 965 
 036 
 106 
 176 
 
 618 
 689 
 760 
 831 
 902 
 972 
 043 
 113 
 183 
 
 625 
 696 
 767 
 838 
 909 
 979 
 050 
 120 
 190 
 
 633 
 704 
 774 
 S45 
 916 
 986 
 057 
 127 
 197 
 
 640 
 711 
 781 
 852 
 923 
 993 
 064 
 134 
 204 
 
 647 
 718 
 789 
 859 
 930 
 *000 
 071 
 141 
 211 
 
 654 
 725 
 796 
 866 
 937 
 *007 
 078 
 148 
 218 
 
 661 
 732 
 803 
 873 
 944 
 *014 
 085 
 155 
 225 
 
 668 
 739 
 810 
 880 
 951 
 *021 
 092 
 162 
 232 
 
 6 
 7 
 8 
 9 
 
 4.8 
 5.6 
 6.4 
 7.2 
 
 620 
 
 239 
 
 246 
 
 253 
 
 260 
 
 267 
 
 274 
 
 281 
 
 288 
 
 295 
 
 302 
 
 
 
 621 
 622 
 623 
 624 
 625 
 626 
 627 
 628 
 629 
 
 309 
 379 
 449 
 518 
 588 
 657 
 727 
 796 
 865 
 
 316 
 386. 
 456 
 525 
 595 
 664 
 734 
 803 
 872 
 
 323 
 393 
 463 
 532 
 602 
 671 
 741 
 810 
 879 
 
 330 
 400 
 470 
 539 
 609 
 678 
 748 
 817 
 886 
 
 337 
 407 
 477 
 546 
 616 
 685 
 754 
 824 
 893 
 
 344 
 414 
 
 484 
 553 
 623 
 692 
 761 
 831 
 900 
 
 351 
 421 
 491 
 560 
 630 
 699 
 768 
 837 
 906 
 
 358 
 428 
 498 
 567 
 637 
 706 
 775 
 844 
 913 
 
 365 
 435 
 505 
 574 
 644 
 713 
 782 
 851 
 920 
 
 372 
 442 
 511 
 581 
 650 
 720 
 789 
 858 
 927 
 
 9 
 
 7 
 
 0.7 
 1.4 
 2.1 
 2.8 
 3.5 
 4.2 
 4.9 
 5.6 
 6.3 
 
 630 
 
 934 
 
 941 
 
 948 
 
 955 
 
 962 
 
 969 
 
 975 
 
 982 
 
 989 
 
 996 
 
 
 
 631 
 632 
 633 
 634 
 635 
 636 
 637 
 638 
 639 
 
 80 003 
 072 
 140 
 209 
 277 
 346 
 414 
 482 
 550 
 
 010 
 079 
 147 
 216 
 284 
 353 
 421 
 489 
 557 
 
 017 
 085 
 154 
 223 
 291 
 359 
 428 
 496 
 564 
 
 024 
 092 
 161 
 229 
 298 
 366 
 434 
 502 
 570 
 
 030 
 099 
 168 
 236 
 305 
 373 
 441 
 509 
 577 
 
 037 
 106 
 175 
 243 
 312 
 380 
 448 
 516 
 584 
 
 044 
 113 
 182 
 250 
 318 
 387 
 
 591 
 
 051 
 120 
 
 188 
 257 
 325 
 393 
 462 
 530 
 598 
 
 058 
 127 
 195 
 264 
 332 
 400 
 468 
 536 
 604 
 
 065 
 134 
 202 
 271 
 339 
 407 
 475 
 543 
 611 
 
 1 
 2 
 3 
 
 6 
 
 0.6 
 1.2 
 
 1.8 
 
 640 
 
 618 
 
 625 
 
 632 
 
 638 
 
 645 
 
 652 
 
 659 
 
 665 
 
 672 
 
 679 
 
 5 
 
 3.0 
 
 641 
 642 
 643 
 644 
 645 
 646 
 647 
 648 
 649 
 
 686 
 754 
 821 
 889 
 956 
 81 023 
 090 
 158 
 224 
 
 693 
 760 
 828 
 895 
 963 
 030 
 097 
 164 
 231 
 
 699 
 767 
 835 
 902 
 969 
 037 
 104 
 171 
 238 
 
 706 
 774 
 841 
 909 
 976 
 043 
 111 
 178 
 245 
 
 713 
 781 
 848 
 916 
 983 
 050 
 117 
 184 
 251 
 
 720 
 787 
 855 
 922 
 990 
 057 
 124 
 191 
 258 
 
 726 
 794 
 862 
 929 
 996 
 064 
 131 
 198 
 265 
 
 733 
 801 
 868 
 936 
 003 
 070 
 137 
 204 
 271 
 
 740 
 808 
 875 
 943 
 010 
 077 
 144 
 211 
 278 
 
 747 
 814 
 882 
 949 
 *017 
 084 
 151 
 218 
 285 
 
 7 
 8 
 9 
 
 4.2 
 4.8 
 5.4 
 
 650 
 
 291 
 
 298 
 
 305 
 
 311 
 
 318 
 
 325 
 
 331 
 
 338 
 
 345 
 
 351 
 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P. 
 
 P. 
 
LOGARITHMS 
 
 1021 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 650 
 
 81 291 
 
 298 
 
 305 
 
 311 
 
 318 
 
 325 
 
 331 
 
 338 
 
 345 
 
 351 
 
 
 651 
 652 
 653 
 654 
 655 
 656 
 657 
 658 
 659 
 
 358 
 425 
 491 
 558 
 624 
 690 
 757 
 823 
 889 
 
 365 
 431 
 498 
 564 
 631 
 697 
 763 
 829 
 895 
 
 371 
 438 
 505 
 571 
 637 
 704 
 770 
 836 
 902 
 
 378 
 445 
 511 
 578 
 644 
 710 
 776 
 842 
 908 
 
 385 
 451 
 518 
 
 584 
 651 
 717 
 783 
 849 
 915 
 
 391 
 458 
 525 
 591 
 657 
 723 
 790 
 856 
 921 
 
 398 
 465 
 531 
 598 
 664 
 730 
 796 
 862 
 928 
 
 405 
 471 
 538 
 604 
 671 
 737 
 803 
 869 
 935 
 
 411 
 478 
 544 
 611 
 677 
 743 
 809 
 875 
 941 
 
 418 
 485 
 551 
 617 
 684 
 750 
 816 
 882 
 948 
 
 
 660 
 
 954 
 
 961 
 
 968 
 
 974 
 
 981 
 
 987 
 
 994 
 
 *000 
 
 *007 
 
 *014 
 
 
 661 
 662 
 663 
 664 
 665 
 666 
 667 
 668 
 669 
 
 82 020 
 086 
 151 
 217 
 282 
 347 
 413 
 478 
 543 
 
 027 
 092 
 158 
 223 
 289 
 354 
 419 
 484 
 549 
 
 033 
 099 
 164 
 230 
 295 
 360 
 426 
 491 
 556 
 
 040 
 105 
 171 
 236 
 302 
 367 
 432 
 497 
 562 
 
 046 
 112 
 178 
 243 
 308 
 373 
 439 
 504 
 569 
 
 053 
 119 
 184 
 249 
 315 
 380 
 445 
 510 
 575 
 
 060 
 125 
 191 
 256 
 321 
 387 
 452 
 517 
 582 
 
 066 
 132 
 197 
 263 
 328 
 393 
 458 
 523 
 588 
 
 073 
 138 
 204 
 269 
 334 
 400 
 465 
 530 
 595 
 
 079 
 145 
 210 
 276 
 341 
 406 
 471 
 536 
 601 
 
 1 0.7 
 2 1.4 
 3 2.1 
 4 2.8 
 5 3.5 
 6 4.2 
 7 4.9 
 8 5.6 
 9 6.3 
 
 670 
 
 607 
 
 614 
 
 620 
 
 627 
 
 633 
 
 640 
 
 646 
 
 653 
 
 659 
 
 666 
 
 
 671 
 672 
 673 
 674 
 675 
 676 
 677 
 678 
 679 
 
 672 
 737 
 802 
 866 
 930 
 995 
 83 059 
 123 
 187 
 
 679 
 743 
 808 
 872 
 937 
 *001 
 065 
 129 
 193 
 
 685 
 750 
 814 
 879 
 943 
 *008 
 072 
 136 
 200 
 
 692 
 756 
 821 
 885 
 950 
 *014 
 078 
 142 
 206 
 
 698 
 763 
 827 
 892 
 956 
 *020 
 085 
 149 
 213 
 
 705 
 769 
 834 
 898 
 963 
 *027 
 091 
 155 
 219 
 
 711 
 776 
 840 
 905 
 969 
 *033 
 097 
 161 
 225 
 
 718 
 782 
 847 
 911 
 975 
 *040 
 104 
 168 
 232 
 
 724 
 789 
 853 
 918 
 982 
 *046 
 110 
 174 
 238 
 
 730 
 795 
 860 
 924 
 988 
 *052 
 117 
 181 
 245 
 
 
 680 
 
 251 
 
 257 
 
 264 
 
 270 
 
 276 
 
 283 
 
 289 
 
 296 
 
 302 
 
 308 
 
 6 
 
 681 
 682 
 683 
 684 
 685 
 686 
 687 
 688 
 689 
 
 315 
 378 
 442 
 506 
 569 
 632 
 696 
 759 
 822 
 
 321 
 
 385 
 448 
 512 
 575 
 639 
 702 
 765 
 828 
 
 327 
 391 
 455 
 518 
 582 
 645 
 708 
 771 
 835 
 
 334 
 398 
 461 
 525 
 588 
 651 
 715 
 77 
 841 
 
 340 
 404 
 467 
 531 
 594 
 658 
 721 
 784 
 847 
 
 347 
 410 
 474 
 537 
 601 
 664 
 727 
 790 
 853 
 
 353 
 417 
 480 
 544 
 607 
 670 
 734 
 797 
 860 
 
 359 
 423 
 487 
 550 
 613 
 677 
 740 
 803 
 866 
 
 366 
 429 
 493 
 556 
 620 
 683 
 746 
 809 
 872 
 
 372 
 436 
 499 
 563 
 626 
 689 
 753 
 816 
 879 
 
 1 0.6 
 2 1.2 
 3 1.8 
 4 2.4 
 5 3.0 
 6 3.6 
 7 4.2 
 8 4.8 
 9 5.4 
 
 690 
 
 885 
 
 891 
 
 897 
 
 904 
 
 910 
 
 916 
 
 923 
 
 929 
 
 935 
 
 942 
 
 
 691 
 692 
 693 
 694 
 695 
 696 
 697 
 698 
 699 
 
 948 
 84 Oil 
 073 
 136 
 198 
 261 
 323 
 386 
 448 
 
 954 
 
 017 
 080 
 142 
 205 
 267 
 330 
 392 
 454 
 
 960 
 023 
 086' 
 148 
 211 
 273 
 336 
 398 
 460 
 
 967 
 029 
 092 
 155 
 217 
 280 
 342 
 404 
 466 
 
 973 
 
 036 
 098 
 161 
 223 
 286 
 348 
 410 
 473 
 
 979 
 042 
 105 
 167 
 230 
 292 
 354 
 417 
 479 
 
 985 
 048 
 111 
 173 
 236 
 298 
 361 
 423 
 485 
 
 992 
 055 
 117 
 180 
 242 
 305 
 367 
 429 
 491 
 
 998 
 061 
 123 
 186 
 248 
 311 
 373 
 435 
 497 
 
 004 
 067 
 130 
 192 
 255 
 317 
 379 
 442 
 504 
 
 
 700 
 
 510 
 
 516 
 
 522 
 
 528 
 
 535 
 
 541 
 
 547 
 
 553 
 
 559 
 
 566 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
1022 
 
 LOGARITHMS 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P 
 
 .P. 
 
 700 
 
 84 510 
 
 516 
 
 522 
 
 528 
 
 535 
 
 541 
 
 547 
 
 553 
 
 559 
 
 566 
 
 
 
 701 
 702 
 703 
 704 
 705 
 706 
 707 
 708 
 709 
 
 572 
 634 
 696 
 757 
 819 
 880 
 942 
 85 003 
 065 
 
 578 
 640 
 702 
 763 
 825 
 887 
 948 
 009 
 071 
 
 584 
 646 
 708 
 770 
 831 
 893 
 954 
 016 
 077 
 
 590 
 652 
 714 
 776 
 837 
 899 
 960 
 022 
 083 
 
 597 
 658 
 720 
 782 
 844 
 905 
 967 
 028 
 089 
 
 603 
 665 
 726 
 788 
 850 
 911 
 973 
 034 
 095 
 
 609 
 671 
 733 
 794 
 856 
 917 
 979 
 040 
 101 
 
 615 
 677 
 739 
 800 
 862 
 924 
 985 
 046 
 107 
 
 621 
 683 
 745 
 807 
 868 
 930 
 991 
 052 
 114 
 
 628 
 689 
 751 
 813 
 874 
 936 
 997 
 058 
 120 
 
 i 
 
 2 
 
 7 
 
 0.7 
 1.4 
 
 710 
 
 126 
 
 132 
 
 138 
 
 144 
 
 150 
 
 156 
 
 163 
 
 169 
 
 175 
 
 181 
 
 3 
 4 
 
 2.1 
 
 2.8 
 
 711 
 712 
 713 
 714 
 715 
 716 
 717 
 718 
 719 
 
 187 
 248 
 309 
 370 
 431 
 491 
 552 
 612 
 673 
 
 193 
 254 
 315 
 376 
 437 
 497 
 558 
 618 
 679 
 
 199 
 260 
 321 
 382 
 443 
 503 
 564 
 625 
 685 
 
 205 
 266 
 327 
 388 
 449 
 509 
 570 
 631 
 691 
 
 211 
 272 
 333 
 394 
 455 
 516 
 576 
 637 
 697 
 
 217 
 278 
 339 
 400 
 461 
 522 
 582 
 643 
 703 
 
 224 
 285 
 345 
 406 
 467 
 528 
 588 
 649 
 709 
 
 230 
 291 
 352 
 412 
 473 
 534 
 594 
 655 
 715 
 
 236 
 297 
 358 
 418 
 479 
 540 
 600 
 .661 
 721 
 
 242 
 303 
 364 
 425 
 485 
 546 
 606 
 667 
 727 
 
 5 
 6 
 7 
 8 
 9 
 
 3.5 
 4.2 
 4.9 
 5.6 
 6.3 
 
 720 
 
 733 
 
 739 
 
 745 
 
 751 
 
 757 
 
 763 
 
 769 
 
 775 
 
 781 
 
 788 
 
 
 
 721 
 722 
 723 
 724 
 725 
 726 
 727 
 728 
 729 
 
 794 
 854 
 914 
 974 
 86 034 
 094 
 153 
 213 
 273 
 
 800 
 860 
 920 
 980 
 040 
 100 
 159 
 219 
 279 
 
 806 
 866 
 926 
 986 
 046 
 106 
 165 
 225 
 285 
 
 812 
 872 
 932 
 992 
 052 
 112 
 171 
 231 
 291 
 
 818 
 878 
 938 
 998 
 058 
 118 
 177 
 237 
 297 
 
 824 
 884 
 944 
 *004 
 064 
 124 
 183 
 243 
 303 
 
 830 
 890 
 950 
 *010 
 070 
 130 
 189 
 249 
 308 
 
 836 
 896 
 956 
 *016 
 076 
 136 
 195 
 255 
 314 
 
 842 
 902 
 962 
 *022 
 082 
 141 
 201 
 261 
 320 
 
 848 
 908 
 968 
 *028 
 088 
 147 
 207 
 267 
 326 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 6 
 
 0.6 
 1.2 
 1.8 
 2.4 
 3.0 
 3.6 
 4.2 
 4.8 
 5.4 
 
 730 
 
 332 
 
 338 
 
 344 
 
 350 
 
 356 
 
 362 
 
 368 
 
 374 
 
 380 
 
 386 
 
 
 
 731 
 732 
 733 
 734 
 735 
 736 
 737 
 738 
 739 
 
 392 
 451 
 510 
 570 
 629 
 688 
 747 
 806 
 864 
 
 398 
 457 
 516 
 576 
 635 
 694 
 753 
 812 
 870 
 
 404 
 463 
 522 
 581 
 641 
 700 
 759 
 817 
 876 
 
 410 ' 
 469 
 528 
 587 
 646 
 705 
 764 
 823 
 882 
 
 415 
 475 
 534 
 593 
 652 
 711 
 770 
 829 
 888 
 
 421 
 481 
 540 
 599 
 658 
 717 
 776 
 835 
 894 
 
 427 
 487 
 546 
 605 
 664 
 723 
 782 
 841 
 900 
 
 433 
 493 
 552 
 611 
 670 
 729 
 788 
 847 
 906 
 
 439 
 499 
 558 
 617 
 676 
 735 
 794 
 853 
 911 
 
 445 
 504 
 564 
 623 
 
 682 
 741 
 800 
 859 
 917 
 
 1 
 2 
 3 
 
 5 
 
 0.5 
 1.0 
 1.5 
 
 740 
 
 923 
 
 929 
 
 935 
 
 941 
 
 947 
 
 953 
 
 958 
 
 964 
 
 970 
 
 976 
 
 4 
 
 5 
 
 2.0 
 2.5 
 
 741 
 742 
 743 
 744 
 745 
 746 
 747 
 748 
 749 
 
 982 
 87 040 
 099 
 157 
 216 
 274 
 332 
 390 
 448 
 
 988 
 046 
 105 
 163 
 221 
 280 
 338 
 396 
 454 
 
 994 
 052 
 111 
 169 
 227 
 286 
 344 
 402 
 460 
 
 999 
 058 
 116 
 175 
 233 
 291 
 349 
 408 
 466 
 
 *005 
 064 
 122 
 181 
 239 
 297 
 355 
 413 
 471 
 
 *011 
 070 
 128 
 186 
 245 
 303 
 361 
 419 
 477 
 
 *017 
 075 
 134 
 192 
 251 
 309 
 367 
 425 
 483 
 
 *023 
 081 
 140 
 198 
 256 
 315 
 373 
 431 
 489 
 
 *029 
 087 
 146 
 204 
 262 
 320 
 379 
 437 
 495 
 
 *035 
 093 
 151 
 210 
 268 
 326 
 384 
 442 
 500 
 
 6 
 7 
 8 
 9 
 
 3.5 
 4.0 
 45 
 
 750 
 
 506 
 
 512 
 
 518 
 
 523 
 
 529 
 
 535 
 
 541 
 
 547 
 
 552 
 
 558 
 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P. 
 
 P. 
 
LOGARITHMS 
 
 1023 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 750 
 
 87 50 
 
 512 
 
 518 
 
 523 
 
 529 
 
 535 
 
 541 
 
 547 
 
 552 
 
 558 
 
 
 751 
 752 
 753 
 754 
 755 
 756 
 757 
 758 
 759 
 
 564 
 622 
 67 
 737 
 795 
 852 
 910 
 967 
 88024 
 
 570 
 628 
 685 
 743 
 800 
 858 
 915 
 973 
 030 
 
 576 
 633 
 691 
 749 
 806 
 864 
 921 
 978 
 036 
 
 581 
 639 
 697 
 754 
 812 
 869 
 927 
 984 
 041 
 
 587 
 645 
 703 
 760 
 818 
 875 
 933 
 990 
 047 
 
 593 
 651 
 708 
 766 
 823 
 881 
 938 
 996 
 053 
 
 599 
 656 
 714 
 772 
 829 
 887 
 944 
 *001 
 058 
 
 604 
 662 
 720 
 777 
 835 
 892 
 950 
 *007 
 064 
 
 610 
 668 
 726 
 783 
 841 
 898 
 955 
 *013 
 070 
 
 616 
 674 
 731 
 789 
 846 
 904 
 961 
 *018 
 076 
 
 
 760 
 
 081 
 
 087 
 
 093 
 
 098 
 
 104 
 
 110 
 
 116 
 
 121 
 
 127 
 
 133 
 
 
 761 
 
 762 
 763 
 764 
 765 
 766 
 767 
 788 
 769 
 
 138 
 195 
 252 
 309 
 366 
 423 
 480 
 536 
 593 
 
 144 
 
 201 
 258 
 315 
 372 
 429 
 485 
 542 
 598 
 
 150 
 207 
 264 
 321 
 377 
 434 
 491 
 647 
 604 
 
 156 
 213 
 270 
 326 
 383 
 440 
 497 
 553 
 610 
 
 161 
 218 
 275 
 332 
 389 
 446 
 502 
 559 
 615 
 
 167 
 224 
 281 
 338 
 395 
 451 
 508 
 564 
 621 
 
 173 
 230 
 287 
 343 
 400 
 457 
 513 
 570 
 627 
 
 178 
 235 
 292 
 349 
 406 
 463 
 519 
 576 
 632 
 
 184 
 241 
 298 
 355 
 412 
 468 
 525 
 581 
 638 
 
 190 
 247 
 304 
 360 
 417 
 474 
 530 
 587 
 643 
 
 6 
 
 1 0.6 
 
 2 1.2 
 3 1.8 
 4 2.4 
 5 3.0 
 6 3.6 
 7 4.2 
 8 4.8 
 9 5.4 
 
 770 
 
 649 
 
 655 
 
 660 
 
 666 
 
 672 
 
 677 
 
 683 
 
 689 
 
 694 
 
 700 
 
 
 771 
 Til 
 773 
 774 
 775 
 776 
 777 
 778 
 779 
 
 705 
 762 
 818 
 874 
 930 
 986 
 89 042 
 098 
 154 
 
 711 
 767 
 824 
 880 
 936 
 992 
 048 
 104 
 159 
 
 717 
 773 
 829 
 885 
 941 
 997 
 053 
 109 
 165 
 
 722 
 779 
 835 
 891 
 947 
 *003 
 059 
 115 
 170 
 
 728 
 784 
 840 
 897 
 953 
 *009 
 064 
 120 
 176 
 
 734 
 790 
 846 
 902 
 958 
 *014 
 070 
 126 
 182 
 
 739 
 795 
 852 
 908 
 964 
 *020 
 076 
 131 
 187 
 
 745 
 801 
 857 
 913 
 969 
 *025 
 081 
 137 
 193 
 
 750 
 807 
 863 
 919 
 975 
 *031 
 087 
 143 
 198 
 
 756 
 812 
 868 
 925 
 981 
 *037 
 092 
 148 
 204 
 
 
 780 
 
 209 
 
 215 
 
 221 
 
 226 
 
 232 
 
 237 
 
 243 
 
 248 
 
 254 
 
 260 
 
 5 
 
 781 
 782 
 783 
 784 
 785 
 786 
 787 
 788 
 789 
 
 265 
 321 
 376 
 432 
 487 
 542 
 597 
 653 
 708 
 
 271 
 
 326 
 382 
 437 
 492 
 548 
 603 
 658 
 713 
 
 276 
 332 
 387 
 443 
 498 
 553 
 609 
 664 
 719 
 
 282 
 337 
 393 
 448 
 504 
 559 
 614 
 669 
 724 
 
 287 
 343 
 398 
 454 
 509 
 564 
 620 
 675 
 730 
 
 293 
 348 
 404 
 459 
 515 
 570 
 625 
 680 
 735 
 
 298 
 354 
 409 
 465 
 520 
 575 
 631 
 686 
 741 
 
 304 
 360 
 415 
 470 
 526 
 581 
 636 
 691 
 746 
 
 310 
 365 
 421 
 476 
 531 
 586 
 642 
 697 
 752 
 
 315 
 371 
 426 
 481 
 537 
 592 
 647 
 702 
 757 
 
 1 0.5 
 2 1.0 
 3 1.5 
 4 2.0 
 5 2.5 
 6 3.0 
 7 3.5 
 8 4.0 
 9 j 4.5 
 
 790 
 
 763 
 
 768 
 
 774 
 
 779 
 
 785 
 
 790 
 
 796 
 
 801 
 
 807 
 
 812 
 
 
 791 
 
 792 
 793 
 794 
 795 
 7% 
 797 
 798 
 799 
 
 818 
 873 
 927 
 982 
 90 037 
 091 
 146 
 200 
 255 
 
 823 
 878 
 933 
 988 
 042 
 097 
 151 
 206 
 260 
 
 829 
 883 
 938 
 993 
 048 
 102 
 157 
 211 
 266 
 
 834 
 889 
 944 
 998 
 053 
 108 
 162 
 217 
 271 
 
 840 
 894 
 949 
 *004 
 059 
 113 
 168 
 222 
 276 
 
 845 
 900 
 955 
 *009 
 064 
 119 
 173 
 227 
 282 
 
 851 
 905 
 960 
 *015 
 069 
 124 
 179 
 233 
 287 
 
 856 
 911 
 966 
 020 
 075 
 129 
 184 
 238 
 293 
 
 862 
 916 
 971 
 026 
 080 
 135 
 189 
 244 
 298 
 
 867 
 922 
 977 
 *031 
 086 
 140 
 195 
 249 
 304 
 
 
 800 
 
 309 
 
 314 
 
 320 
 
 325 
 
 331 
 
 336 
 
 342 
 
 347 
 
 352 
 
 358 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
1024 
 
 LOGARITHMS 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 347 
 
 8 
 
 352 
 
 9 
 
 P.P. 
 
 800 
 
 801 
 
 802 
 803 
 804 
 805 
 806 
 807 
 808 
 809 
 
 810 
 
 811 
 812 
 813 
 814 
 815 
 816 
 817 
 818 
 819 
 
 820 
 
 821 
 822 
 823 
 824 
 825 
 826 
 827 
 828 
 829 
 
 830 
 
 831 
 832 
 833 
 834 
 835 
 836 
 837 
 838 
 839 
 
 840 
 
 841 
 
 842 
 843 
 844 
 845 
 846 
 847 
 848 
 849 
 
 850 
 
 90 309 
 
 314 
 
 320 
 
 325 
 
 331 
 
 336 
 
 342 
 
 358 
 
 6 
 
 1 0.6 
 2 1.2 
 3 1.8 
 4 2.4 
 5 3.0 
 6 3.6 
 7 4.2 
 8 4.8 
 9 5.4 
 
 5 
 
 1 0.5 
 2 1.0 
 3 1.5 
 4 2.0 
 5 2.5 
 6 3.0 
 7 3.5 
 8 4.0 
 9 4.6 
 
 363 
 417 
 472 
 526 
 580 
 634 
 687 
 741 
 795 
 
 369 
 423 
 477 
 531 
 585 
 639 
 693 
 747 
 800 
 
 374 
 
 428 
 482 
 536 
 590 
 644 
 698 
 752 
 806 
 
 488 
 542 
 596 
 650 
 703 
 757 
 811 
 
 385 
 439 
 493 
 547 
 601 
 655 
 709 
 763 
 816 
 
 390 
 445 
 499 
 553 
 607 
 660 
 714 
 768 
 822 
 
 396 
 450 
 504 
 558 
 612 
 666 
 720 
 773 
 827 
 
 881 
 
 401 
 455 
 509 
 563 
 617 
 671 
 725 
 779 
 832 
 
 407 
 461 
 515 
 569 
 623 
 677 
 730 
 784 
 838 
 
 412 
 466 
 520 
 574 
 628 
 682 
 736 
 789 
 843 
 
 897 
 
 849 
 
 854 
 
 907 
 961 
 014 
 068 
 121 
 174 
 228 
 281 
 334 
 
 859 
 
 913 
 966 
 020 
 073 
 126 
 180 
 233 
 286 
 339 
 
 865 
 
 918 
 972 
 025 
 078 
 132 
 185 
 238 
 291 
 344 
 
 870 
 
 875 
 
 929 
 982 
 036 
 089 
 142 
 196 
 249 
 302 
 355 
 
 886 
 
 891 
 
 902 
 956 
 91 009 
 062 
 116 
 169 
 222 
 275 
 328 
 
 924 
 977 
 030 
 084 
 137 
 190 
 243 
 297 
 350 
 
 934 
 988 
 041 
 094 
 148 
 201 
 254 
 307 
 360 
 
 940 
 993 
 046 
 100 
 153 
 206 
 259 
 312 
 365 
 
 945 
 
 998 
 052 
 105 
 158 
 212 
 265 
 318 
 371 
 
 950 
 *004 
 057 
 110 
 164 
 217 
 270 
 323 
 376 
 
 429 
 
 381 
 
 387 
 
 392 
 
 397 
 
 403 
 
 408 
 
 413 
 
 418 
 
 424 
 
 434 
 487 
 540 
 593 
 645 
 698 
 751 
 803 
 855 
 
 440 
 492 
 545 
 598 
 651 
 703 
 756 
 808 
 861 
 
 445 
 498 
 551 
 603 
 656 
 709 
 761 
 814 
 866 
 
 450 
 503 
 556 
 609 
 661 
 714 
 766 
 819 
 871 
 
 455 
 508 
 561 
 614 
 666 
 719 
 772 
 824 
 876 
 
 461 
 514 
 
 566 
 619 
 672 
 
 724 
 777 
 829 
 882 
 
 466 
 519 
 
 572 
 624 
 677 
 730 
 
 782 
 834 
 887 
 
 471 
 
 524 
 577 
 630 
 682 
 735 
 787 
 840 
 892 
 
 477 
 529 
 582 
 635 
 687 
 740 
 793 
 845 
 897 
 
 482 
 535 
 587 
 640 
 693 
 745 
 798 
 850 
 903 
 
 908 
 
 913 
 
 918 
 
 924 
 
 976 
 028 
 080 
 132 
 184 
 236 
 288 
 340 
 392 
 
 929 
 
 981 
 033 
 085 
 137 
 189 
 241 
 293 
 345 
 397 
 
 934 
 
 939 
 
 944 
 
 950 
 
 955 
 
 960 
 92 012 
 065 
 117 
 169 
 221 
 273 
 324 
 376 
 
 965 
 018 
 070 
 122 
 174 
 226 
 278 
 330 
 381 
 
 433 
 
 971 
 023 
 075 
 127 
 179 
 231 
 283 
 335 
 387 
 
 438 
 
 986 
 038 
 091 
 143 
 195 
 247 
 298 
 350 
 402 
 
 991 
 044 
 096 
 148 
 200 
 252 
 304 
 355 
 407 
 
 459 
 
 997 
 049 
 101 
 153 
 205 
 257 
 309 
 361 
 412 
 
 464 
 
 *002 
 054 
 106 
 158 
 210 
 262 
 314 
 366 
 418 
 
 469 
 
 *007 
 059 
 111 
 163 
 215 
 267 
 319 
 371 
 423 
 
 428 
 
 443 
 
 449 
 
 454 
 
 474 
 
 480 
 531 
 583 
 634 
 686 
 737 
 788 
 840 
 891 
 
 485 
 536 
 588 
 639 
 691 
 742 
 793 
 845 
 896 
 
 947 
 
 490 
 542 
 593 
 645 
 696 
 747 
 799 
 850 
 901 
 
 495 
 
 547 
 598 
 650 
 701 
 752 
 804 
 855 
 906 
 
 957 
 
 500 
 552 
 603 
 655 
 706 
 758 
 809 
 860 
 911 
 
 962 
 
 505 
 557 
 609 
 660 
 711 
 763 
 814 
 865 
 916 
 
 511 
 
 562 
 614 
 665 
 716 
 768 
 819 
 870 
 921 
 
 973 
 
 516 
 567 
 619 
 670 
 722 
 773 
 824 
 875 
 927 
 
 978 
 
 521 
 
 572 
 624 
 675 
 727 
 778 
 829 
 881 
 932 
 
 526 
 578 
 629 
 681 
 732 
 783 
 834 
 886 
 937 
 
 942 
 
 952 
 
 967 
 
 983 
 
 988 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
LOGARITHMS 
 
 1025 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P 
 
 '.P. 
 
 850 
 
 92 942 
 
 947 
 
 952 
 
 957 
 
 962 
 
 967 
 
 973 
 
 978 
 
 983 
 
 988 
 
 
 
 851 
 852 
 853 
 854 
 855 
 856 
 857 
 858 
 859 
 
 993 
 93 044 
 095 
 146 
 197 
 247 
 298 
 349 
 399 
 
 998 
 049 
 100 
 151 
 202 
 252 
 303 
 354 
 404 
 
 *003 
 054 
 105 
 156 
 207 
 258 
 308 
 359 
 409 
 
 *008 
 059 
 110 
 161 
 212 
 263 
 313 
 364 
 414 
 
 *013 
 064 
 115 
 166 
 217 
 268 
 318 
 369 
 420 
 
 *018 
 069 
 120 
 171 
 222 
 273 
 323 
 374 
 425 
 
 *024 
 075 
 125 
 176 
 227 
 278 
 328 
 379 
 430 
 
 *029 
 080 
 131 
 181 
 232 
 283 
 334 
 384 
 435 
 
 *034 
 085 
 136 
 186 
 237 
 288 
 339 
 389 
 440 
 
 *039 
 090 
 141 
 192 
 242 
 293 
 344 
 394 
 445 
 
 i 
 
 2 
 
 6 
 
 0.6 
 1.2 
 
 860 
 
 450 
 
 455 
 
 460 
 
 465 
 
 470 
 
 475 
 
 480 
 
 485 
 
 490 
 
 495 
 
 4 
 
 2.4 
 
 861 
 
 862 
 863 
 864 
 865 
 866 
 867 
 868 
 869 
 
 500 
 551 
 601 
 651 
 702 
 752 
 802 
 852 
 902 
 
 505 
 556 
 606 
 656 
 707 
 757 
 807 
 857 
 907 
 
 510 
 561 
 611 
 661 
 712 
 762 
 812 
 862 
 912 
 
 515 
 
 566 
 616 
 666 
 717 
 767 
 817 
 867 
 917 
 
 520 
 571 
 621 
 671 
 
 722 
 772 
 822 
 872 
 922 
 
 526 
 576 
 626 
 676 
 727 
 777 
 827 
 877 
 927 
 
 531 
 581 
 631 
 682 
 732 
 782 
 832 
 882 
 932 
 
 536 
 586 
 636 
 
 687 
 737 
 787 
 837 
 887 
 937 
 
 541 
 591 
 641 
 692 
 742 
 792 
 842 
 892 
 942 
 
 546 
 596 
 646 
 697 
 747 
 797 
 847 
 897 
 947 
 
 6 
 
 7 
 
 9 
 
 3.6 
 
 4.2 
 
 4.8 
 5.4 
 
 870 
 
 952 
 
 957 
 
 962 
 
 967 
 
 972 
 
 977 
 
 982 
 
 987 
 
 992 
 
 997 
 
 
 
 871 
 872 
 873 
 874 
 875 
 876 
 877 
 878 
 879 
 
 94 002 
 052 
 101 
 151 
 201 
 250 
 300 
 349 
 399 
 
 007 
 057 
 106 
 156 
 206 
 255 
 305 
 354 
 404 
 
 012 
 062 
 111 
 161 
 211 
 260 
 310 
 359 
 409 
 
 017 
 067 
 116 
 166 
 216 
 265 
 315 
 364 
 414 
 
 022 
 072 
 121 
 171 
 221 
 270 
 320 
 369 
 419 
 
 027 
 077 
 126 
 176 
 226 
 275 
 325 
 374 
 424 
 
 032 
 082 
 131 
 181 
 231 
 280 
 330 
 379 
 429 
 
 037 
 086 
 136 
 186 
 236 
 285 
 335 
 384 
 433 
 
 042 
 091 
 141 
 191 
 240 
 290 
 340 
 389 
 438 
 
 047 
 096 
 146 
 196 
 245 
 295 
 345 
 394 
 443 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 0.5 
 1.0 
 1.5 
 2.0 
 2.5 
 3.0 
 3.5 
 4.0 
 4.5 
 
 880 
 
 448 
 
 453 
 
 458 
 
 463 
 
 468 
 
 473 
 
 478 
 
 483 
 
 488 
 
 493 
 
 
 
 881 
 882 
 883 
 884 
 885 
 886 
 887 
 888 
 889 
 
 498 
 547 
 596 
 645 
 694 
 743 
 792 
 841 
 890 
 
 503 
 552 
 601 
 650 
 699 
 748 
 797 
 846 
 895 
 
 507 
 557 
 606 
 655 
 704 
 753 
 802 
 851 
 900 
 
 512 
 562 
 611 
 660 
 709 
 758 
 807 
 856 
 905 
 
 517 
 567 
 616 
 665 
 714 
 763 
 812 
 861 
 910 
 
 522 
 571 
 621 
 670 
 719 
 768 
 817 
 866 
 915 
 
 527 
 576 
 626 
 675 
 724 
 773 
 822 
 871 
 919 
 
 532 
 581 
 630 
 680 
 729 
 778 
 827 
 876 
 924 
 
 537 
 586 
 635 
 685 
 734 
 783 
 832 
 880 
 929 
 
 542 
 591 
 640 
 689 
 738 
 787 
 836 
 885 
 934 
 
 1 
 2 
 3 
 
 4 
 
 0.4 
 0.8 
 1.2 
 
 890 
 
 939 
 
 944 
 
 949 
 
 954 
 
 959 
 
 963 
 
 968 
 
 973 
 
 978 
 
 983 
 
 5 
 
 2.0 
 
 891 
 892 
 893 
 894 
 895 
 896 
 897 
 898 
 899 
 
 988 
 95 036 
 085 
 134 
 182 
 231 
 279 
 328 
 376 
 
 993 
 041 
 090 
 139 
 187 
 236 
 284 
 332 
 381 
 
 998 
 046 
 095 
 143 
 192 
 240 
 289 
 337 
 386 
 
 *002 
 051 
 100 
 148 
 197 
 245 
 294 
 342 
 390 
 
 *007 
 056 
 105 
 153 
 202 
 250 
 299 
 347 
 395 
 
 *012 
 061 
 109 
 158 
 207 
 255 
 303 
 352 
 400 
 
 *017 
 066 
 114 
 163 
 211 
 260 
 308 
 357 
 405 
 
 *022 
 071 
 119 
 168 
 216 
 265 
 313 
 361 
 410 
 
 *027 
 075 
 124 
 173 
 221 
 270 
 318 
 366 
 415 
 
 *032 
 080 
 129 
 177 
 226 
 274 
 323 
 371 
 419 
 
 7 
 8 
 9 
 
 2.8 
 3.2 
 3.6 
 
 900 
 
 424 
 
 429 
 
 434 
 
 439 
 
 444 
 
 448 
 
 453 
 
 458 
 
 463 
 
 468 
 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P 
 
 P. 
 
 05 
 
1026 
 
 LOGARITHMS 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 900 
 
 901 
 
 902 
 903 
 904 
 905 
 906 
 907 
 908 
 909 
 
 910 
 
 911 
 912 
 913 
 914 
 915 
 916 
 917 
 918 
 919 
 
 920 
 
 . 921 
 
 922 
 923 
 924 
 925 
 926 
 927 
 928 
 929 
 
 930 
 
 931 
 932 
 933 
 934 
 935 
 936 
 937 
 938 
 939 
 
 940 
 
 941 
 942 
 943 
 944 
 945 
 946 
 947 
 948 
 949 
 
 950 
 
 95 424 
 
 429 
 
 434 
 
 439 
 
 444 
 
 448 
 
 453 
 
 501 
 550 
 598 
 646 
 694 
 742 
 789 
 837 
 885 
 
 458 
 
 463 
 
 468 
 
 5 
 
 1 0.5 
 2 1.0 
 3 1.5 
 4 2.0 
 5 2.5 
 6 3.0 
 7 3.5 
 8 4.0 
 9 4.5 
 
 4 
 
 1 0.4 
 2 0.8 
 3 1.2 
 4 1.6 
 5 2.0 
 6 2.4 
 7 2.8 
 8 3.2 
 9 3.6 
 
 472 
 521 
 569 
 617 
 665 
 713 
 761 
 809 
 856 
 
 904 
 
 477 
 525 
 574 
 622 
 670 
 718 
 766 
 813 
 861 
 
 482 
 530 
 578 
 626 
 674 
 722 
 770 
 818 
 866 
 
 487 
 535 
 583 
 631 
 679 
 727 
 775 
 823 
 871 
 
 492 
 540 
 
 588 
 636 
 684 
 732 
 780 
 828 
 875 
 
 923 
 
 497 
 545 
 593 
 641 
 689 
 737 
 785 
 832 
 880 
 
 506 
 554 
 602 
 650 
 698 
 746 
 794 
 842 
 890 
 
 511 
 559 
 607 
 655 
 703 
 751 
 799 
 847 
 895 
 
 516 
 564 
 612 
 660 
 708 
 756 
 804 
 852 
 899 
 
 909 
 
 957 
 *004 
 052 
 099 
 147 
 194 
 242 
 289 
 336 
 
 914 
 
 961 
 *009 
 057 
 104 
 152 
 199 
 246 
 294 
 341 
 
 918 
 
 966 
 *014 
 061 
 109 
 156 
 204 
 251 
 298 
 346 
 
 928 
 
 933 
 
 938 
 
 985 
 *033 
 080 
 128 
 175 
 223 
 270 
 317 
 365 
 
 942 
 
 947 
 
 995 
 *042 
 090 
 137 
 185 
 232 
 280 
 327 
 374 
 
 421 
 
 952 
 999 
 96 047 
 095 
 142 
 190 
 237 
 284 
 332 
 
 971 
 *019 
 066 
 114 
 161 
 209 
 256 
 303 
 350 
 
 976 
 *023 
 071 
 118 
 166 
 213 
 261 
 308 
 355 
 
 980 
 *028 
 076 
 123 
 171 
 218 
 265 
 313 
 360 
 
 990 
 *038 
 085 
 133 
 180 
 227 
 275 
 322 
 369 
 
 379 
 
 384 
 
 431 
 478 
 525 
 572 
 619 
 666 
 713 
 759 
 806 
 
 388 
 
 393 
 
 398 
 
 445 
 492 
 539 
 
 586 
 633 
 680 
 
 727 
 774 
 820 
 
 402 
 
 450 
 497 
 544 
 591 
 638 
 685 
 731 
 778 
 825 
 
 407 
 
 454 
 
 501 
 548 
 595 
 642 
 689 
 736 
 783 
 830 
 
 412 
 
 459 
 506 
 553 
 600 
 647 
 694 
 741 
 788 
 834 
 
 881 
 
 417 
 
 464 
 511 
 558 
 605 
 652 
 699 
 745 
 792 
 839 
 
 886 
 
 426 
 473 
 520 
 567 
 614 
 661 
 708 
 755 
 802 
 
 435 
 483 
 530 
 577 
 624 
 670 
 717 
 764 
 811 
 
 440 
 487 
 534 
 581 
 628 
 675 
 722 
 769 
 816 
 
 468 
 515 
 562 
 609 
 656 
 703 
 750 
 797 
 844 
 
 848 
 
 853 
 
 858 
 
 862 
 
 867 
 
 872 
 
 876 
 
 890 
 
 895 
 942 
 988 
 97 035 
 081 
 128 
 174 
 220 
 267 
 
 900 
 946 
 993 
 039 
 086 
 132 
 179 
 225 
 271 
 
 904 
 951 
 997 
 044 
 090 
 137 
 183 
 230 
 276 
 
 909 
 956 
 *002 
 049 
 095 
 142 
 188 
 234 
 280 
 
 327 
 
 914 
 960 
 *007 
 053 
 100 
 146 
 192 
 239 
 285 
 
 918 
 965 
 *011 
 058 
 104 
 151 
 197 
 243 
 290 
 
 923 
 970 
 *016 
 063 
 109 
 155 
 202 
 248 
 294 
 
 928 
 974 
 *021 
 067 
 114 
 160 
 206 
 253 
 299 
 
 932 
 979 
 *025 
 072 
 118 
 165 
 211 
 257 
 304 
 
 937 
 984 
 *030 
 077 
 123 
 169 
 216 
 262 
 308 
 
 313 
 
 317 
 
 322 
 
 331 
 
 336 
 
 340 
 
 345 
 
 350 
 
 354 
 
 359 
 405 
 451 
 497 
 543 
 589 
 635 
 681 
 727 
 
 364 
 410 
 456 
 502 
 548 
 594 
 640 
 685 
 731 
 
 777 
 
 368 
 414 
 460 
 506 
 552 
 598 
 644 
 690 
 736 
 
 782 
 
 373 
 419 
 465 
 511 
 557 
 603 
 649 
 695 
 740 
 
 377 
 
 424 
 470 
 516 
 562 
 607 
 653 
 699 
 745 
 
 382 
 428 
 474 
 520 
 566 
 612 
 658 
 704 
 749 
 
 387 
 433 
 479 
 525 
 571 
 617 
 663 
 708 
 754 
 
 391 
 437 
 483 
 529 
 575 
 621 
 667 
 713 
 759 
 
 396 
 442 
 488 
 534 
 580 
 626 
 672 
 717 
 763 
 
 400 
 447 
 493 
 539 
 585 
 630 
 676 
 722 
 768 
 
 772 
 
 786 
 
 791 
 
 4 
 
 795 
 
 800 
 
 6 
 
 804 
 
 809 
 
 813 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 5 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
LOGARITHMS 
 
 1027 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 950 
 
 7 772 
 
 777 
 
 782 
 
 786 
 
 791 
 
 795 
 
 800 
 
 804 
 
 809 
 
 813 
 
 
 951 
 952 
 953 
 954 
 955 
 956 
 957 
 958 
 959 
 
 818 
 864 
 909 
 955 
 98 000 
 046 
 091 
 137 
 182 
 
 823 
 868 
 914 
 959 
 005 
 050 
 096 
 141 
 186 
 
 827 
 873 
 918 
 964 
 009 
 055 
 100 
 146 
 191 
 
 832 
 877 
 923 
 968 
 014 
 059 
 105 
 150 
 195 
 
 836 
 882 
 928 
 973 
 019 
 064 
 109 
 155 
 200 
 
 841 
 886 
 932 
 978 
 023 
 068 
 114 
 159 
 204 
 
 845 
 891 
 937 
 982 
 028 
 073 
 118 
 164 
 209 
 
 850 
 896 
 941 
 987 
 032 
 078 
 123 
 168 
 214 
 
 855 
 900 
 946 
 991 
 037 
 082 
 127 
 173 
 218 
 
 859 
 905 
 950 
 996 
 041 
 087 
 132 
 177 
 223 
 
 
 960" 
 
 227 
 
 232 
 
 236 
 
 241 
 
 245 
 
 250 
 
 254 
 
 259 
 
 263 
 
 268 
 
 5 
 
 961 
 962 
 963 
 964 
 965 
 966 
 967 
 968 
 969 
 
 272 
 318 
 363 
 408 
 453 
 498 
 543 
 588 
 632 
 
 277 
 322 
 367 
 412 
 457 
 502 
 547 
 592 
 637 
 
 281 
 327 
 372 
 417 
 462 
 507 
 552 
 597 
 641 
 
 286 
 331 
 376 
 421 
 466 
 511 
 556 
 601 
 646 
 
 290 
 336 
 381 
 426 
 471 
 516 
 561 
 605 
 650 
 
 295 
 340 
 385 
 430 
 475 
 520 
 565 
 610 
 655 
 
 299 
 345 
 390 
 435 
 480 
 525 
 570 
 614 
 659 
 
 304 
 349 
 394 
 439 
 484 
 529 
 574 
 619 
 664 
 
 308 
 354 
 399 
 444 
 489 
 534 
 579 
 623 
 668 
 
 313 
 
 358 
 403 
 448 
 493 
 538 
 583 
 628 
 673 
 
 1 0.5 
 2 1.0 
 3 1.5 
 4 2.0 
 5 2.5 
 6 3.0 
 7 3.5 
 8 4.0 
 9 4.5 
 
 970 
 
 677 
 
 682 
 
 686 
 
 691 
 
 695 
 
 700 
 
 704 
 
 709 
 
 713 
 
 717 
 
 
 971 
 972 
 973 
 974 
 975 
 976 
 977 
 978 
 979 
 
 722 
 767 
 811 
 856 
 900 
 945 
 989 
 99034 
 078 
 
 726 
 771 
 816 
 860 
 905 
 949 
 994 
 038 
 083 
 
 731 
 776 
 820 
 865 
 909 
 954 
 998 
 043 
 087 
 
 735 
 780 
 825 
 869 
 914 
 958 
 *003 
 047 
 092 
 
 740 
 784 
 829 
 874 
 918 
 963 
 *007 
 052 
 096 
 
 744 
 789 
 834 
 878 
 923 
 967 
 *012 
 056 
 100 
 
 749 
 793 
 838 
 883 
 927 
 972 
 *016 
 061 
 105 
 
 753 
 
 798 
 843 
 887 
 932 
 976 
 *021 
 065 
 109 
 
 758 
 802 
 847 
 892 
 936 
 981 
 *025 
 069 
 114 
 
 762 
 807 
 851 
 896 
 941 
 985 
 *029 
 074 
 118 
 
 
 980 
 
 123 
 
 127 
 
 131 
 
 136 
 
 140 
 
 145 
 
 149 
 
 154 
 
 158 
 
 162 
 
 4 
 
 981 
 982 
 983 
 984 
 985 
 986 
 987 
 988 
 989 
 
 167 
 211 
 255 
 300 
 344 
 388 
 432 
 476 
 520 
 
 171 
 
 216 
 260 
 304 
 348 
 392 
 436 
 480 
 524 
 
 176 
 220 
 264 
 308 
 352 
 396 
 441 
 484 
 528 
 
 180 
 224 
 269 
 313 
 357 
 401 
 445 
 489 
 533 
 
 185 
 229 
 273 
 317 
 361 
 405 
 449 
 493 
 537 
 
 189 
 233 
 277 
 322 
 366 
 410 
 454 
 498 
 542 
 
 193 
 238 
 282 
 326 
 370 
 414 
 458 
 502 
 546 
 
 198 
 242 
 286 
 330 
 374 
 419 
 463 
 506 
 550 
 
 202 
 247 
 291 
 335 
 379 
 423 
 467 
 511 
 555 
 
 207 
 251 
 295 
 339 
 383 
 427 
 471 
 515 
 559 
 
 2 0.8 
 3 1.2 
 4 1.6 
 5 2.0 
 6 2.4 
 7 2.8 
 8 8.2 
 9 3.6 
 
 990 
 
 564 
 
 568 
 
 572 
 
 577 
 
 581 
 
 585 
 
 590 
 
 594 
 
 599 
 
 603 
 
 
 991 
 992 
 993 
 994 
 995 
 996 
 997 
 998 
 999 
 
 607 
 651 
 695 
 739 
 782 
 826 
 870 
 913 
 957 
 
 612 
 656 
 699 
 743 
 787 
 830 
 874 
 917 
 961 
 
 616 
 660 
 704 
 747 
 791 
 835 
 878 
 922 
 965 
 
 621 
 664 
 708 
 752 
 795 
 839 
 883 
 926 
 970 
 
 625 
 669 
 712 
 756 
 800 
 843 
 887 
 930 
 974 
 
 629 
 673 
 717 
 760 
 804 
 848 
 891 
 935 
 978 
 
 634 
 677 
 721 
 765 
 808 
 852 
 896 
 939 
 983 
 
 638 
 682 
 726 
 769 
 813 
 856 
 900 
 944 
 987 
 
 642 
 686 
 730 
 774 
 817 
 861 
 904 
 948 
 991 
 
 647 
 691 
 734 
 778 
 822 
 865 
 909 
 952 
 996 
 
 
 1000 
 
 00 000 
 
 004 
 
 009 
 
 013 
 
 017 
 
 022 
 
 026 
 
 030 
 
 035 
 
 039 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
1028 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 
 
 It 
 
 / 
 
 L. Sin. 
 
 d. 
 
 Cpl. S. 
 
 Cpl. T. 
 
 L. Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L.Cos. 
 
 
 o 
 60 
 120 
 180 
 240 
 
 
 1 
 2 
 3 
 4 
 
 6.46373 
 6.76476 
 6.94085 
 7.06579 
 
 30103 
 17609 
 12494 
 QfiQI 
 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 
 5.31443 
 5.31443 
 5.31443 
 5.31442 
 
 6.46373 
 6.76476 
 6.94085 
 7.06579 
 
 30103 
 17609 
 12494 
 
 QfiQI 
 
 3.53627 
 3.23524 
 3.05915 
 2.93421 
 
 0.00000 
 0.00000 
 0.00000 
 0.00000 
 0.00000 
 
 60 
 
 59 
 58 
 57 
 56 
 
 300 
 360 
 420 
 480 
 540 
 
 5 
 6 
 7 
 8 
 9 
 
 7.16270 
 
 7.24188 
 7.30882 
 7.36682 
 7.41797 
 
 7918 
 6694 
 5800 
 5115 
 4576 
 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 
 5.31442 
 5.31442 
 5.31442 
 5.31442 
 5.31442 
 
 7.16270 
 7.24188 
 7.30882 
 7.36682 
 7.41797 
 
 7918 
 6694 
 5800 
 5115 
 4576 
 
 2.83730 
 2.75812 
 2.69118 
 2.63318 
 2.58203 
 
 0.00000 
 0.00000 
 0.00000 
 0.00000 
 0.00000 
 
 55 
 54 
 53 
 52 
 51 
 
 600 
 660 
 720 
 780 
 840 
 
 10 
 
 11 
 12 
 13 
 14 
 
 7.46373 
 7.50512 
 7.54291 
 7.57767 
 7.60985 
 
 4139 
 3779 
 3476 
 3218 
 2997 
 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 
 5.31442 
 5.31442 
 5.31442 
 5.31442 
 5.31442 
 
 7.46373 
 7.50512 
 7.54291 
 7.57767 
 7.60986 
 
 4139 
 3779 
 3476 
 3219 
 2996 
 
 2.53627 
 2.49488 
 2.45709 
 2.42233 
 2.39014 
 
 0.00000 
 0.00000 
 0.00000 
 0.00000" 
 0.00000 
 
 50 
 
 49 
 48 
 47 
 46 
 
 900 
 960 
 1020 
 1080 
 1140 
 
 15 
 16 
 17 
 18 
 19 
 
 7.63982 
 7.66784 
 7.69417 
 7.71900 
 7.74248 
 
 2802 
 2633 
 2483 
 2348 
 9997 
 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 
 5.31442 
 5.31442 
 5.31442 
 5.31442 
 5.31442 
 
 7.63982 
 7.66785 
 7.69418 
 7.71900 
 7.74248 
 
 2803 
 2633 
 2482 
 2348 
 
 OOOQ 
 
 2.36018 
 2.33215 
 2.30582 
 2.28100 
 2.25752 
 
 0.00000 
 0.00000 
 9.99999 
 9.99999 
 9.99999 
 
 45 
 44 
 43 
 42 
 41 
 
 1200 
 1260 
 1320 
 1380 
 1440 
 
 20 
 
 21 
 22 
 23 
 24 
 
 7.76475 
 7.78594 
 7.80615 
 7.82545 
 7.84393 
 
 2119 
 2021 
 1930 
 1848 
 1773 
 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 
 5.31442 
 5.31442 
 5.31442 
 5.31442 
 5.31442 
 
 7.76476 
 7.78595 
 7.80615 
 7.82546 
 7.84394 
 
 2119 
 2020 
 1931 
 1848 
 1773 
 
 2.23524 
 2.21405 
 2.19385 
 2.17454 
 2.15606 
 
 9.99999 
 9.99999 
 9.99999 
 9.99999 
 9.99999 
 
 40 
 
 39 
 38 
 37 
 36 
 
 1500 
 
 1560 
 1620 
 1680 
 1740 
 
 25 
 26 
 27 
 28 
 29 
 
 7.86166 
 7.87870 
 7.89509 
 7.91088 
 7.92612 
 
 1704 
 1639 
 1579 
 1524 
 1472 
 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 
 5.31442 
 5.31442 
 5.31442 
 5.31442 
 5.31441 
 
 7.86167 
 7.87871 
 7.89510 
 7.91089 
 7.92613 
 
 1704 
 1639 
 1579 
 1524 
 1473 
 
 2.13833 
 2.12129 
 2.10490 
 2.08911 
 2.07387 
 
 9.99999 
 9.99999 
 9.99999 
 9.99999 
 9.99998 
 
 35 
 34 
 33 
 32 
 31 
 
 1800 
 1860 
 1920 
 1980 
 2040 
 
 30 
 
 31 
 32 
 33 
 34 
 
 7.94084 
 7.95508 
 7.96887 
 7.98223 
 7.99520 
 
 1424 
 1379 
 1336 
 1297 
 
 -lOKQ 
 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 
 5.31441 
 5.31441 
 5.31441 
 5.31441 
 5.31441 
 
 7.94086 
 7.95510 
 7.96889 
 7.98225 
 7.99522 
 
 1424 
 1379 
 1336 
 1297 
 
 IOCQ 
 
 2.05914 
 2.04490 
 2.03111 
 2.01775 
 2.00478 
 
 9.99998 
 9.99998 
 9.99998 
 9.99998 
 9.99998 
 
 30 
 
 29 
 28 
 27 
 26 
 
 2100 
 2160 
 2220 
 2280 
 2340 
 
 35 
 36 
 37 
 38 
 39 
 
 8.00779 
 8.02002 
 8.03192 
 8.04350 
 8.05478 
 
 1223 
 1190 
 1158 
 1128 
 1100 
 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 5.31443 
 
 5.31441 
 5.31441 
 5.31441 
 5.31441 
 5.31441 
 
 8.00781 
 8.02004 
 8.03194 
 8.04353 
 8.05481 
 
 1223 
 1190 
 1159 
 1128 
 110ft 
 
 1.99219 
 1.97996 
 1.96806 
 1.95647 
 1.94519 
 
 9.99998 
 9.99998 
 9.99997 
 9.99997 
 9.99997 
 
 25 
 24 
 23 
 22 
 21 
 
 2400 
 2460 
 2520 
 2580 
 2640 
 
 40 
 
 41 
 42 
 43 
 
 44 
 
 8.06578 
 8.07650 
 8.08696 
 8.09718 
 8.10717 
 
 1072 
 1046 
 1022 
 999 
 Q7fi 
 
 5.31443 
 5.31444 
 5.31444 
 5.31444 
 5.31444 
 
 5.31441 
 5.31440 
 5.31440 
 5.31440 
 5.31440 
 
 8.06581 
 8.07653 
 8.08700 
 8.09722 
 8.10720 
 
 1072 
 1047 
 1022 
 998 
 
 1.93419 
 1.92347 
 1.91300 
 1.90278 
 1.89280 
 
 9.99997 
 9.99997 
 9.99997 
 9.99997 
 9.999% 
 
 20 
 
 19 
 18 
 17 
 16 
 
 2700 
 2760 
 2820 
 2880 
 2940 
 
 45 
 46 
 
 47 
 48 
 49 
 
 8.11693 
 8.12647 
 8.13581 
 8.14495 
 8.15391 
 
 954 
 934 
 914 
 
 896 
 877 
 
 5.31444 
 5.31444 
 5.31444 
 5.31444 
 5.31444 
 
 5.31440 
 5.31440 
 5.31440 
 5.31440 
 5.31440 
 
 8.11696 
 8.12651 
 8.13585 
 8.14500 
 8.15395 
 
 955 
 934 
 915 
 
 895 
 
 070 
 
 1.88304 
 1.87349 
 1.86415 
 1.85500 
 1.84605 
 
 9.99996 
 9.99996 
 9.99996 
 9.999% 
 9.999% 
 
 15 
 14 
 13 
 12 
 11 
 
 3000 
 3060 
 3120 
 3180 
 3240 
 
 50 
 
 51 
 52 
 53 
 
 54 
 
 8.16268 
 8.17128 
 8.17971 
 8.18798 
 8.19610 
 
 860 
 843 
 827 
 812 
 7Q7 
 
 5.31444 
 5.31444 
 5.31444 
 5.31444 
 5.31444 
 
 5.31439 
 5.31439 
 5.31439 
 5.31439 
 5.31439 
 
 8.16273 
 8.17133 
 8.17976 
 8.18804 
 8.19616 
 
 860 
 843 
 828 
 812 
 
 1.83727 
 1.82867 
 1.82024 
 1.81196 
 1.80384 
 
 9.99995 
 9.99995 
 9.99995 
 9.99995 
 9.99995 
 
 10 
 
 9 
 8 
 7 
 6 
 
 3300 
 3360 
 3420 
 3480 
 3540 
 
 55 
 56 
 57 
 58 
 59 
 
 8.20407 
 8.21189 
 8.21958 
 8.22713 
 8.23456 
 
 782 
 769 
 755 
 743 
 730 
 
 5.31444 
 5.31444 
 5.31445 
 5.31445 
 5.31445 
 
 5.31439 
 5.31439 
 5.31439 
 5.31438 
 5.31438 
 
 8.20413 
 8.21195 
 8.21964 
 8.22720 
 8.23462 
 
 782 
 769 
 756 
 742 
 
 70A 
 
 1.79587 
 1.78805 
 1.78036 
 1 77280 
 1.76538 
 
 9.99994 
 9.99994 
 9.99994 
 9.99994 
 9.99994 
 
 5 
 4 
 3 
 2 
 1 
 
 3600 
 
 60 
 
 8.24186 
 
 
 5.31445 
 
 5.31438 
 
 8.24192 
 
 
 1.75808 
 
 9.99993 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 
 
 L.cotg. 
 
 d.c. 
 
 L. Tang. 
 
 L. Sin. 
 
 i 
 
 89 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 1 
 
 1029 
 
 II 
 
 ' 
 
 L. Sin. 
 
 d. 
 
 Cpl. S. 
 
 Cpl. T. 
 
 L. Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 
 3600 
 3660 
 3720 
 3780 
 3840 
 
 
 
 1 
 2 
 3 
 4 
 
 8.24186 
 8.24903 
 8.25609 
 8.26304 
 8.26988 
 
 717 
 706 
 695 
 684 
 673 
 
 5.31445 
 5.31445 
 5.31445 
 5.31445 
 5.31445 
 
 5.31438 
 5.31438 
 5.31438 
 5.31438 
 5.31437 
 
 8.24192 
 8.24910 
 8.25616 
 8.26312 
 8.269% 
 
 718 
 706 
 696 
 684 
 673 
 
 1.75808 
 1.75090 
 1.74384 
 1.73688 
 1.73004 
 
 9.99993 
 9.99993 
 9.99993 
 9.99993 
 9.99992 
 
 60 
 
 59 
 58 
 57 
 56 
 
 3900 
 3960 
 4020 
 4080 
 4140 
 
 5 
 6 
 7 
 8 
 9 
 
 8.27661 
 8.28324 
 8.28977 
 8.29621 
 8.30255 
 
 663 
 653 
 644 
 634 
 fi24 
 
 5.31445 
 5.31445 
 5.31445 
 5.31445 
 5.31445 
 
 5.31437 
 5.31437 
 5.31437 
 5.31437 
 5.31437 
 
 8.27669 
 8.28332 
 8.28986 
 8.29629 
 8.30263 
 
 663 
 654 
 643 
 634 
 625 
 
 1.72331 
 1.71668 
 1.71014 
 1.70371 
 1.69737 
 
 9.99992 
 9.99992 
 9.99992 
 9.99992 
 9.99991 
 
 55 
 54 
 53 
 52 
 51 
 
 4200 
 4260 
 4320 
 4380 
 4440 
 
 10 
 
 11 
 12 
 13 
 14 
 
 8.30879 
 8.31495 
 8.32103 
 8.32702 
 8.33292 
 
 616 
 608 
 599 
 590 
 
 5.31446 
 5.31446 
 5.31446 
 5.31446 
 5.31446 
 
 5.31437 
 5.31436 
 5.31436 
 5.31436 
 5.31436 
 
 8.30888 
 8.31505 
 8.32112 
 8.32711 
 8.33302 
 
 617 
 607 
 599 
 591 
 
 KOt 
 
 1.69112 
 1.68495 
 1.67888 
 1.67289 
 1.66698 
 
 9.99991 
 9.99991 
 9.99990 
 9.99990 
 9.99990 
 
 50 
 
 49 
 
 48 
 47 
 46 
 
 4500 
 4560 
 4620 
 4680 
 4740 
 
 15 
 16 
 17 
 18 
 19 
 
 8.33875 
 8.34450 
 8.35018 
 8.35578 
 8.36131 
 
 575 
 568 
 560 
 553 
 
 vt? 
 
 5.3144& 
 5.31446 
 531446 
 5.31446 
 5.31446 
 
 5.31436 
 5.31435 
 5.31435 
 5.31435 
 5.31435 
 
 8.33886 
 8.34461 
 8.35029 
 8.35590 
 8.36143 
 
 575 
 568 
 561 
 553 
 546 
 
 1.66114 
 1.65539 
 1.64971 
 1.64410 
 1.63857 
 
 9.99990 
 9.99989 
 9.99989 
 9.99989 
 9.99989 
 
 45 
 44 
 43 
 42 
 41 
 
 4800 
 4860 
 4920 
 4980 
 5040 
 
 20 
 
 21 
 22 
 23 
 24 
 
 8.36678 
 8.37217 
 8.37750 
 8.38276 
 8.38796 
 
 539 
 533 
 526 
 520 
 
 5.31446 
 5.31447 
 5.31447 
 5.31447 
 5.31447 
 
 5.31435 
 5.31434 
 5.31434 
 5.31434 
 5.31434 
 
 8.36689 
 8.37229 
 8.37762 
 8.38289 
 8.38809 
 
 540 
 533 
 527 
 520 
 
 r-M 
 
 1.63311 
 1.62771 
 1.62238 
 1.61711 
 1.61191 
 
 9.99988 
 9.99988 
 9.99988 
 9.99987 
 9.99987 
 
 40 
 
 39 
 38 
 37 
 36 
 
 5100 
 5160 
 5220 
 5280 
 5340 
 
 25 
 26 
 
 27 
 28 
 29 
 
 8.39310 
 8.39818 
 8.40320 
 8.40816 
 8.41307 
 
 508 
 502 
 496 
 491 
 
 5.31447 
 5.31447 
 5.31447 
 5.31447 
 5.31447 
 
 5.31434 
 5.31433 
 5.31433 
 5.31433 
 5.31433 
 
 8.39323 
 8.39832 
 8.40334 
 8.40830 
 8.41321 
 
 509 
 502 
 496 
 491 
 486 
 
 1.60677 
 1.60168 
 1.59666 
 1.59170 
 1.58679 
 
 9.99987 
 9.99986 
 9.99986 
 9.99986 
 9.99985 
 
 35 
 34 
 33 
 32 
 31 
 
 5400 
 5460 
 5520 
 5580 
 5640 
 
 30 
 
 31 
 32 
 33 
 34 
 
 8.41792 
 8.42272 
 8.42746 
 8.43216 
 8.43680 
 
 480 
 474 
 470 
 464 
 
 5.31447 
 5.31448 
 5.31448 
 5.31448 
 5.31448 
 
 5.31433 
 5.31432 
 5.31432 
 5.31432 
 5.31432 
 
 8.41807 
 8.42287 
 8.42762 
 8.43232 
 8.43696 
 
 480 
 475 
 470 
 464 
 460 
 
 1.58193 
 1.57713 
 1.57238 
 1.56768 
 1.56304 
 
 9.99985 
 9.99985 
 9.99984 
 9.99984 
 9.99984 
 
 30 
 
 29 
 28 
 27 
 26 
 
 5700 
 5760 
 5820 
 5880 
 5940 
 
 35 
 36 
 37 
 38 
 39 
 
 8.44139 
 8.44594 
 8.45044 
 8.45489 
 8.45930 
 
 455 
 450 
 445 
 441 
 
 AQC 
 
 5.31448 
 5.31448 
 5.31448 
 5.31448 
 5.31449 
 
 5.31431 
 5.31431 
 5.31431 
 5.31431 
 5.31431 
 
 8.44156 
 8.44611 
 8.45061 
 8.45507 
 8.45948 
 
 455 
 450 
 446 
 441 
 437 
 
 1.55844 
 1.55389 
 1.54939 
 1.54493 
 1.54052 
 
 9.99983 
 9.99983 
 9.99983 
 9.99982 
 9.99982 
 
 25 
 24 
 23 
 22 
 21 
 
 6000 
 6060 
 6120 
 6180 
 6240 
 
 40 
 
 41 
 42 
 43 
 44 
 
 8.46366 
 8.46799 
 8.47226 
 8.47650 
 8.48069 
 
 433 
 427 
 424 
 419 
 
 5.31449 
 5.31449 
 5.31449 
 5.31449 
 5.31449 
 
 5.31430 
 5.31430 
 5.31430 
 5.31430 
 5.31429 
 
 8.46385 
 8.46817 
 8.47245 
 8.47669 
 8.48089 
 
 432 
 428 
 424 
 420 
 416 
 
 1.53615 
 1.53183 
 1.52755 
 1.52331 
 1.51911 
 
 9.99982 
 9.99981 
 9.99981 
 9.99981 
 9.99980 
 
 20 
 
 19 
 18 
 17 
 16 
 
 6300 
 6360 
 6420 
 6480 
 6540 
 
 45 
 
 46 
 47 
 48 
 49 
 
 8.48485 
 8.48896 
 8.49304 
 8.49708 
 8.50108 
 
 411 
 
 408 
 404 
 400 
 
 5.31449 
 5.31449 
 5.31450 
 5.31450 
 5.31450 
 
 5.31429 
 5.31429 
 5.31428 
 5.31428 
 5.31428 
 
 8.48505 
 8.48917 
 8.49325 
 8.49729 
 8.50130 
 
 412 
 408 
 404 
 401 
 397 
 
 1.51495 
 1.51083 
 1.50675 
 1.50271 
 1.49870 
 
 9.99980 
 9.99979 
 9.99979 
 9.99979 
 9.99978 
 
 15 
 14 
 13 
 12 
 11 
 
 6600 
 6660 
 6720 
 6780 
 6840 
 
 50 
 
 51 
 
 52 
 53 
 
 54 
 
 8.50504 
 8.50897 
 8.51287 
 8.51673 
 8.52055 
 
 393 
 390 
 386 
 
 382 
 
 5.31450 
 5.31450 
 5.31450 
 5.31450 
 5.31450 
 
 5.31428 
 5.31427 
 5.81427 
 5.31427 
 5.31427 
 
 8.50527 
 8.50920 
 8.51310 
 8.51696 
 8.52079 
 
 393 
 390 
 386 
 383 
 380 
 
 1.49473 
 
 1.49080 
 1.48690 
 1.48304 
 1.47921 
 
 9.99978 
 9.99977 
 9.99977 
 9.99977 
 9.99976 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6900 
 6960 
 7020 
 7080 
 7140 
 
 55 
 56 
 57 
 58 
 59 
 
 8.52434 
 8.52810 
 8.53183 
 8.53552 
 8.53919 
 
 376 
 373 
 369 
 367 
 
 5.31451 
 5.31451 
 5.31451 
 5.31451 
 5.31451 
 
 5.31426 
 5.31426 
 5.31426 
 5.31425 
 5.31425 
 
 8.52459 
 8.52835 
 8.53208 
 8.53578 
 8.53945 
 
 376 
 373 
 370 
 367 
 363 
 
 1.47541 
 1.47165 
 1.46792 
 1.46422 
 1.46055 
 
 9.99976 
 9.99975 
 9.99975 
 9.99974 
 9.99974 
 
 5 
 4 
 3 
 2 
 1 
 
 7200 
 
 60 
 
 8.54282 
 
 
 5.31451 
 
 5.31425 
 
 8.54308 
 
 
 1.45692 
 
 9.99974 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 
 
 L.Cotg. 
 
 d.c. 
 
 L. Tang. 
 
 L. Sin. 
 
 
 88 
 
1030 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 2 
 
 If 
 
 / 
 
 L. Sin. 
 
 d. 
 
 Cpl. S. 
 
 Cpl. T. 
 
 L. Tang. 
 
 d.c. 
 
 L. Cotg 
 
 L. Cos. 
 
 
 7200 
 7260 
 7320 
 7380 
 7440 
 
 
 
 1 
 2 
 3 
 4 
 
 8.54282 
 8.54642 
 8.54999 
 8.55354 
 8.55705 
 
 360 
 357 
 355 
 351 
 349 
 
 5.31451 
 5.31451 
 5.31452 
 5.31452 
 5.31452 
 
 5.31425 
 5.31425 
 5.31424 
 5.31424 
 5.31424 
 
 8.54308 
 8.54669 
 8.55027 
 8.55382 
 8.55734 
 
 361 
 358 
 355 
 352 
 040 
 
 1.45692 
 1.45331 
 1.44973 
 1.44618 
 1.44266 
 
 9.99974 
 9.99973 
 9.99973 
 9.99972 
 9.99972 
 
 60 
 
 59 
 58 
 57 
 56 
 
 7500 
 7560 
 7620 
 7680 
 7740 
 
 5 
 6 
 
 7 
 8 
 9 
 
 8.56054 
 8.56400 
 8.56743 
 8.57084 
 8.57421 
 
 346 
 343 
 341 
 337 
 336 
 
 5.31452 
 5.31452 
 5.31452 
 5.31453 
 5.31453 
 
 5.31423 
 5.31423 
 5.31423 
 5.31422 
 5.31422 
 
 8.56083 
 8.56429 
 8.56773 
 8.57114 
 8.57452 
 
 346 
 344 
 341 
 
 338 
 
 qofi 
 
 1.43917 
 1.43571 
 1.43227 
 1.42886 
 1.42548 
 
 9.99971 
 9.99971 
 9.99970 
 9.99970 
 9.99969 
 
 55 
 54 
 53 
 52 
 51 
 
 7800 
 7860 
 7920 
 7980 
 8040 
 
 10 
 
 11 
 12 
 13 
 14 
 
 8.57757 
 8.58089 
 8.58419 
 8.58747 
 8.59072 
 
 332 
 330 
 328 
 325 
 323 
 
 5.31453 
 5.31453 
 5.31453 
 5.31453 
 5.31454 
 
 5.31422 
 5.31421 
 5.31421 
 5.31421 
 5.31421 
 
 8.57788 
 8.58121 
 8.58451 
 8.58779 
 8.59105 
 
 333 
 330 
 328 
 326 
 323 
 
 1.42212 
 1.41879 
 1.41549 
 1.41221 
 1.40895 
 
 9.99969 
 9.99968 
 9.99968 
 9.99967 
 9.99967 
 
 50 
 
 49 
 48 
 47 
 46 
 
 8100 
 8160 
 8220 
 8280 
 8340 
 
 15 
 16 
 17 
 18 
 19 
 
 8.59395 
 8.59715 
 8.60033 
 8.60349 
 8.60662 
 
 320 
 318 
 316 
 313 
 311 
 
 5.31454 
 5.31454 
 5.31454 
 5.31454 
 5.31454 
 
 5.31420 
 5.31420 
 5.31420 
 5.31419 
 5.31419 
 
 8.59428 
 8.59749 
 8.60068 
 8.60384 
 8.60698 
 
 321 
 319 
 316 
 314 
 
 1.40572 
 1.40251 
 1.39932 
 1.39616 
 1.39302 
 
 9.99967 
 9.99966 
 9.99966 
 9.99965 
 9.99964 
 
 45 
 44 
 43 
 42 
 41 
 
 8400 
 8460 
 8520 
 8580 
 8640 
 
 20 
 
 21 
 22 
 23 
 24 
 
 8.60973 
 8.61282 
 8.61589 
 8.61894 
 8.62196 
 
 309 
 307 
 305 
 302 
 301 
 
 5.31455 
 5.31455 
 5.31455 
 5.31455 
 5.31455 
 
 5.31418 
 5.31418 
 5.31418 
 5.31417 
 5.31417 
 
 8.61009 
 8.61319 
 8.61626 
 8.61931 
 8.62234 
 
 310 
 307 
 305 
 303 
 qni 
 
 1.38991 
 1.38681 
 1.38374 
 1.38069 
 1.37766 
 
 9.99964 
 9.99963 
 9.99963 
 9.99962 
 9.99962 
 
 40 
 
 39 
 38 
 37 
 36 
 
 8700 
 8760 
 8820 
 8880 
 8940 
 
 25 
 
 26 
 
 27 
 28 
 29 
 
 8.62497 
 8.62795 
 8.63091 
 8.63385 
 8.63678 
 
 298 
 296 
 294 
 293 
 290 
 
 5.31455 
 5.31456 
 5.31456 
 5.31456 
 5.31456 
 
 5.31417 
 5.31416 
 5.31416 
 5.31416 
 5.31415 
 
 8.62535 
 8.62834 
 8.63131 
 8.63426 
 8.63718 
 
 299 
 297 
 295 
 292 
 291 
 
 1.37465 
 1.37166 
 1.36869 
 1.36574 
 1.36282 
 
 9.99961 
 9.99961 
 9.99960 
 9.99960 
 9.99959 
 
 35 
 34 
 33 
 32 
 31 
 
 9000 
 9060 
 9120 
 9180 
 9240 
 
 30 
 
 31 
 32 
 33 
 34 
 
 8.63968 
 8.64256 
 8.64543 
 8.64827 
 8.65110 
 
 288 
 287 
 284 
 283 
 281 
 
 5.31456 
 5.31456 
 5.31457 
 5.31457 
 5.31457 
 
 5.31415 
 5.31415 
 5.31414 
 5.31414 
 5.31413 
 
 8.64009 
 8.64298 
 8.64585 
 8.64870 
 8.65154 
 
 289 
 287 
 285 
 284 
 
 001 
 
 1.35991 
 1.35702 
 1.35415 
 1.35130 
 1.34846 
 
 9.99959 
 9.99958 
 9.99958 
 9.99957- 
 9.99956 
 
 30 
 
 29 
 28 
 27 
 26 
 
 9300 
 9360 
 9420 
 9480 
 9540 
 
 35 
 36 
 37 
 38 
 39 
 
 8.65391 
 8.65670 
 8.65947 
 8.66223 
 8.66497 
 
 279 
 277 
 276 
 274 
 272 
 
 5.31457 
 5.31457 
 5.31458 
 5.31458 
 5.31458 
 
 5.31413 
 5.31413 
 5.31412 
 5.31412 
 5.31412 
 
 8.65435 
 8.65715 
 8.65993 
 8.66269 
 8.66543 
 
 280 
 278 
 276 
 274 
 273 
 
 1.34565 
 1.34285 
 1.34007 
 1.33731 
 1.33457 
 
 9.99956 
 9.99955 
 9.99955 
 9.99954 
 9.99954 
 
 25 
 24 
 23 
 22 
 21 
 
 9600 
 9660 
 9720 
 9780 
 9840 
 
 40 
 
 41 
 42 
 43 
 44 
 
 8.66769 
 8.67039 
 8.67308 
 8.67575 
 8.67841 
 
 270 
 269 
 267 
 266 
 
 oco 
 
 5.31458 
 5.31458 
 5.31459 
 5.31459 
 5.31459 
 
 5.31411 
 5.31411 
 5.31410 
 5.31410 
 5.31410 
 
 8.66816 
 8.67087 
 8.67356 
 8.67624 
 8.67890 
 
 271 
 269 
 268 
 266 
 
 net 
 
 1.33184 
 1.32913 
 1.32644 
 1.32376 
 1.32110 
 
 9.99953 
 9.99952 
 9.99952 
 9.99951 
 9.99951 
 
 20 
 
 19 
 18 
 17 
 16 
 
 9900 
 9960 
 10020 
 10080 
 10140 
 
 45 
 46 
 47 
 48 
 49 
 
 8.68104 
 8.68367 
 8.68627 
 8.68886 
 8.69144 
 
 263 
 260 
 259 
 258 
 256 
 
 5.31459 
 5.31459 
 5.31460 
 5.31460 
 5.31460 
 
 5.31409 
 5.31409 
 5.31408 
 5.31408 
 5.31408 
 
 8.68154 
 8.68417 
 8.68678 
 8.68938 
 8.69196 
 
 263 
 261 
 260 
 258 
 57 
 
 1.31846 
 1.31583 
 1.31322 
 1.31062 
 1.30804 
 
 9.99950 
 9.99949 
 9.99949 
 9.99948 
 9.99948 
 
 15 
 14 
 13 
 12 
 11 
 
 10200 
 10260 
 10320 
 10380 
 10440 
 
 SO 
 
 51 
 52 
 53 
 54 
 
 8.69400 
 8.69654 
 8.69907 
 8.70159 
 8.70409 
 
 254 
 253 
 252 
 250 
 249 
 
 5.31460 
 5.31460 
 5.31461 
 5.31461 
 5.31461 
 
 5.31407 
 5.31407 
 5.31406 
 5.31406 
 5.31405 
 
 8.69453 
 8.69708 
 8.69962 
 8.70214 
 8.70465 
 
 255 
 254 
 252 
 251 
 
 1.30547 
 1.30292 
 1.30038 
 1.29786 
 1.29535 
 
 9.99947 
 9.99946 
 9.99946 
 9.99945 
 9.99944 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 10500 
 10560 
 10620 
 10680 
 10740 
 
 55 
 56 
 57 
 58 
 59 
 
 8.70658 
 8.70905 
 8.71151 
 8.71395 
 8.71638 
 
 247 
 246 
 244 
 243 
 242 
 
 5.31461 
 5.31461 
 5.31462 
 5.31462 
 5.31462 
 
 5.31405 
 5.31405 
 5.31404 
 5.31404 
 5.31403 
 
 8.70714 
 8.70962 
 8.71208 
 8.71453 
 8.71697 
 
 248 
 246 
 245 
 244 
 
 1.29286 
 1.29038 
 1.28792 
 1.28547 
 1.28303 
 
 9.99944 
 9.99943 
 9.99942 
 9.99942 
 9.99941 
 
 5 
 4 
 3 
 2 
 1 
 
 10800 
 
 60 
 
 8.71880 
 
 
 5.31462 
 
 5.31403 
 
 8.71940 
 
 
 1.28060 
 
 9.99940 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 
 
 L. Cotg. 
 
 d.C. 
 
 L. Tang. 
 
 L. Sin. 
 
 ' 
 
 87 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 1031 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 
 
 I 
 
 >. P. 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 8.71880 
 8.72120 
 8.72359 
 8.72597 
 8.72834 
 
 240 
 239 
 238 
 237 
 235 
 
 8.71940 
 
 8.72181 
 8.72420 
 8.72659 
 8.72896 
 
 241 
 
 239 
 239 
 237 
 oqc 
 
 1.28060 
 1.27819 
 1.27580 
 1.27341 
 1.27104 
 
 9.99940 
 9.99940 
 9.99939 
 9.99938 
 9.99938 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 7 
 8 
 9 
 
 238 
 
 23.8 
 27.8 
 31.7 
 35.7 
 
 234 
 
 23.4 
 27.3 
 31.2 
 35.1 
 
 229 
 
 22.9 
 26.7 
 30.5 
 34.4 
 
 5 
 6 
 
 7 
 8 
 9 
 
 8.73069 
 8.73303 
 8.73535 
 8.73767 
 8.73997 
 
 234 
 232 
 232 
 230 
 229 
 
 8.73132 
 8.73366 
 8.73600 
 8.73832 
 8.74063 
 
 234 
 234 
 232 
 231 
 
 OOQ 
 
 1.26868 
 1.26634 
 1.26400 
 1.26168 
 1.25937 
 
 9.99937 
 9.99936 
 9.99936 
 9.99935 
 9.99934 
 
 55 
 54 
 53 
 52 
 51 
 
 10 
 20 
 30 
 40 
 50 
 
 39.7 
 79.3 
 119.0 
 158.7 
 198.3 
 
 39.0 
 78.0 
 117.0 
 156.0 
 195.0 
 
 38.2 
 76.3 
 114.5 
 152.7 
 190.8 
 
 10 
 11 
 
 12 
 13 
 14 
 
 8.74226 
 8.74454 
 8.74680 
 8.74906 
 8.75130 
 
 228 
 226 
 226 
 224 
 223 
 
 8.74292 
 8.74521 
 8.74748 
 8.74974 
 8.75199 
 
 229 
 227 
 226 
 225 
 224 
 
 1.25708 
 1.25479 
 1.25252 
 1.25026 
 1.24801 
 
 9.99934 
 9.99933 
 9.99932 
 9.99932 
 9.99931 
 
 50 
 
 49 
 48 
 47 
 46 
 
 6 
 7 
 8 
 q 
 
 225 
 
 22.5 
 26.3 
 30.0 
 338 
 
 220 
 
 22.0 
 25.7 
 29.3 
 33 
 
 216 
 21.6 
 25.2 
 28.8 
 324 
 
 15 
 16 
 17 
 18 
 19 
 
 8.75353 
 8.75575 
 8.75795 
 8.76015 
 8.76234 
 
 222 
 220 
 220 
 219 
 217 
 
 8.75423 
 8.75645 
 8.75867 
 8.76087 
 8.76306 
 
 222 
 222 
 220 
 219 
 21 Q 
 
 1.24577 
 1.24355 
 1.24133 
 1.23913 
 1.23694 
 
 9.99930 
 9.99929 
 9.99929 
 9.99928 
 9.99927 
 
 45 
 44 
 43 
 42 
 41 
 
 10 
 20 
 30 
 40 
 50 
 
 37.5 
 75.0 
 112.5 
 150.0 
 
 187.5 
 
 36.7 
 73.3 
 110.0 
 146.7 
 183.3 
 
 36.0 
 72.0 
 108.0 
 144.0 
 180.0 
 
 20 
 
 21 
 22 
 23 
 24 
 
 8.76451 
 8.76667 
 8.76883 
 8.77097 
 8.77310 
 
 216 
 216 
 214 
 213 
 212 
 
 8.76525 
 8.76742 
 8.76958 
 8.77173 
 
 8.77387 
 
 217 
 216 
 215 
 214 
 
 010 
 
 1.23475 
 1.23258 
 1.23042 
 1.22827 
 1.22613 
 
 9.99926 
 9.99926 
 9.99925 
 9.99924 
 9.99923 
 
 40 
 
 39 
 38 
 37 
 36 
 
 6 
 7 
 8 
 Q 
 
 212 
 
 21.2 
 24.7 
 28.3 
 31 8 
 
 208 
 
 20.8 
 24.3 
 27.7 
 31 2 
 
 204 
 
 20.4 
 23.8 
 
 27.2 
 30 6 
 
 25 
 26 
 27 
 28 
 29 
 
 8.77522 
 8.77733 
 8.77943 
 8.78152 
 8.78360 
 
 211 
 
 210 
 209 
 208 
 208 
 
 8.77600 
 8.77811 
 8.78022 
 8.78232 
 8.78441 
 
 211 
 211 
 210 
 209 
 
 OAQ 
 
 1.22400 
 1.22189 
 1.21978 
 1.21768 
 1.21559 
 
 9.99923 
 9.99922 
 9.99921 
 9.99920 
 9.99920 
 
 35 
 34 
 33 
 32 
 31 
 
 10 
 20 
 30 
 40 
 50 
 
 35.3 
 70.7 
 106.0 
 141.3 
 176.7 
 
 34.7 
 69.3 
 104.0 
 138.7 
 173.3 
 
 34.0 
 68.0 
 102.0 
 136.0 
 170.0 
 
 30 
 
 31 
 32 
 33 
 34 
 
 8.78568 
 8.78774 
 8.78979 
 8.79183 
 8.79386 
 
 206 
 205 
 204 
 203 
 
 909 
 
 8.78649 
 8.78855 
 8.79061 
 8.79266 
 8.79470 
 
 206 
 206 
 205 
 204 
 
 1.21351 
 1.21145 
 
 1.20939 
 1.20734 
 1.20530 
 
 9.99919 
 9.99918 
 9.99917 
 9.99917 
 9.99916 
 
 30 
 
 29 
 28 
 27 
 26 
 
 6 
 7 
 8 
 
 201 
 
 20.1 
 23.5 
 26.8 
 
 197 
 
 19.7 
 23.0 
 26.3 
 
 193 
 
 19.3 
 22.5 
 25.7 
 
 35 
 36 
 37 
 38 
 39 
 
 8.79588 
 8.79789 
 8.79990 
 8.80189 
 8.80388 
 
 201 
 201 
 199 
 199 
 
 8.79673 
 8.79875 
 8.80076 
 8.80277 
 8.80476 
 
 202 
 201 
 201 
 199 
 
 1.20327 
 1.20125 
 1.19924 
 1.19723 
 1.19524 
 
 9.99915 
 9.99914 
 9.99913 
 9.99913 
 9.99912 
 
 25 
 24 
 23 
 22 
 21 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 33.5 
 67.0 
 100.5 
 134.0 
 167 5 
 
 32.8 
 65.7 
 98.5 
 131.3 
 164 2 
 
 32.2 
 64.3 
 96.5 
 128.7 
 160.8 
 
 40 
 
 41 
 42 
 43 
 44 
 
 8.80585 
 8.80782 
 8.80978 
 8.81173 
 8.81367 
 
 197 
 196 
 195 
 194 
 
 1QO 
 
 8.80674 
 8.80872 
 8.81068 
 8.81264 
 8.81459 
 
 198 
 196 
 196 
 195 
 194 
 
 1.19326 
 1.19128 
 1.18932 
 1.18736 
 1.18541 
 
 9.99911 
 9.99910 
 9.99909 
 9.99909 
 9.99908 
 
 20 
 
 19 
 18 
 17 
 16 
 
 6 
 
 7 
 8 
 
 189 
 
 18.9 
 22.1 
 25.2 
 
 185 
 
 18.5 
 21.6 
 24.7 
 
 181 
 
 18.1 
 21.1 
 
 24.1 
 
 45 
 46 
 47 
 48 
 49 
 
 8.81560 
 8.81752 
 8.81944 
 8.82134 
 8.82324 
 
 192 
 192 
 190 
 190 
 IRQ 
 
 8.81653 
 8.81846 
 8.82038 
 8.82230 
 8.82420 
 
 193 
 192 
 192 
 190 
 190 
 
 1.18347 
 1.18154 
 1.17962 
 1.17770 
 1.17580 
 
 9.99907 
 9.99906 
 9.99905 
 9.99904 
 9.99904 
 
 15 
 14 
 13 
 12 
 11 
 
 9 
 
 10 
 20 
 30 
 40 
 50 
 
 28.4 
 31.5 
 63.0 
 94.5 
 126.0 
 157 5 
 
 27.8 
 30.8 
 61.7 
 92.5 
 123.3 
 154 2 
 
 27.2 
 30.2 
 60.3 
 90.5 
 120.7 
 150.8 
 
 50 
 
 51 
 52 
 53 
 54 
 
 8.82513 
 8.82701 
 8.82888 
 8.83075 
 8.83261 
 
 188 
 187 
 187 
 186 
 
 -IQC 
 
 8.82610 
 8.82799 
 8.82987 
 8.83175 
 8.83361 
 
 189 
 188 
 188 
 186 
 186 
 
 1.17390 
 1.17201 
 1.17013 
 1.16825 
 1.16639 
 
 9.99903 
 9.99902 
 9.99901 
 9.99900 
 9.99899 
 
 10 
 
 9 
 8 
 
 7 
 6 
 
 6 
 
 7 
 8 
 
 4 
 
 0.4 
 0.5 
 0.5 
 
 3 2 
 
 3.3 0.2 
 0.4 0.2 
 3.4 0.3 
 
 1 
 
 0.1 
 0.1 
 
 0.1 
 
 55 
 56 
 57 
 58 
 59 
 
 8.83446 
 8.83630 
 8.83813 
 8.83996 
 8.84177 
 
 184 
 183 
 183 
 181 
 
 8.83547 
 8.83732 
 8.83916 
 8.84100 
 8.84282 
 
 185 
 184 
 184 
 182 
 182 
 
 1.16453 
 1.16268 
 1.16084 
 1.15900 
 1.15718 
 
 9.99898 
 9.99898 
 9.99897 
 9.99896 
 9.99895 
 
 5 
 4 
 3 
 2 
 1 
 
 9 
 
 10 
 20 
 30 
 40 
 
 0.6 
 0.7 
 1.3 
 2.0 
 
 2.7 
 
 3.5 0.3 
 3.5 0.3 
 1.0 0.7 
 1.5 1.0 
 2.0 1.3 
 j K. 17 
 
 0.2 
 0.2 
 0.3 
 0.5 
 0.7 
 8 
 
 60 
 
 8.84358 
 
 
 8.84464 
 
 
 1.15536 
 
 9.99894 
 
 
 
 
 
 
 
 
 
 i 
 
 L. Cotg. 
 
 d,c. 
 
 L.Tang. 
 
 L. Sin. 
 
 ' 
 
 
 1 
 
 . P. 
 
 
 
 
 
 
 
 86 
 
 
 
 
 
 
 
1032 
 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 1 
 
 L. Sin. 
 
 d. 
 
 L.Tang 
 
 d.c 
 
 L. Cotg 
 
 L. Cos. 
 
 
 
 1 
 
 >. P. 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 8.84358 
 8.84539 
 8.84718 
 8.84897 
 8.85075 
 
 181 
 179 
 
 179 
 178 
 177 
 
 8.84464 
 8.84646 
 8.84826 
 8.85006 
 8.85185 
 
 182 
 180 
 180 
 179 
 178 
 
 1.15536 
 1.15354 
 1.15174 
 1.14994 
 1.14815 
 
 9.99894 
 9.99893 
 9.99892 
 9.99891 
 9.99891 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 8 
 9 
 
 181 
 
 18.1 
 21.1 
 24.1 
 27.2 
 
 179 
 
 17.9 
 20.9 
 23.9 
 26.9 
 
 177 
 
 17.7 
 20.7 
 23.6 
 26.6 
 
 5 
 6 
 
 7 
 8 
 9 
 
 8.85252 
 8.85429 
 8.85605 
 8.85780 
 8.85955 
 
 177 
 176 
 175 
 175 
 170 
 
 8.85363 
 8.85540 
 8.85717 
 8.85893 
 8.86069 
 
 177 
 177 
 176 
 176 
 
 1.14637 
 1.14460 
 1.14283 
 1.14107 
 1.13931 
 
 9.99890 
 9.99889 
 9.99888 
 9.99887 
 9.99886 
 
 55 
 54 
 53 
 52 
 51 
 
 10 
 20 
 30 
 40 
 50 
 
 30.2 
 60.3 
 90.5 
 120.7 
 150.8 
 
 29.8 
 59.7 
 89.5 
 119.3 
 149.2 
 
 29.5 
 59.0 
 88.5 
 118.0 
 147.5 
 
 10 
 
 11 
 12 
 13 
 14 
 
 8.86128 
 8.86301 
 8.86474 
 8.86645 
 8.86816 
 
 173 
 173 
 171 
 171 
 171 
 
 8.86243 
 8.86417 
 8.86591 
 8.86763 
 8.86935 
 
 174 
 174 
 172 
 172 
 171 
 
 1.13757 
 1.13583 
 1.13409 
 1.13237 
 1.13065 
 
 9.99885 
 9.99884 
 9.99883 
 9.99882 
 9.99881 
 
 SO 
 
 49 
 48 
 47 
 46 
 
 6 
 
 7 
 8 
 q 
 
 175 
 
 17.5 
 20.4 
 23.3 
 26.3 
 
 173 
 
 17.3 
 20.2 
 23.1 
 260 
 
 171 
 
 17.1 
 20.0 
 22.8 
 257 
 
 15 
 16 
 17 
 18 
 19 
 
 8.86987 
 8.87156 
 8.87325 
 8.87494 
 8.87661 
 
 169 
 169 
 169 
 167 
 168 
 
 8.87106 
 8.87277 
 8.87447 
 8.87616 
 8.87785 
 
 171 
 170 
 169 
 169 
 168 
 
 1.12894 
 1.12723 
 1.12553 
 1.12384 
 1.12215 
 
 9.99880 
 9.99879 
 9 99879 
 9.99878 
 9.99877 
 
 45 
 44 
 43 
 42 
 41 
 
 10 
 20 
 30 
 40 
 50 
 
 29.2 
 58.3 
 87.5 
 116.7 
 145.8 
 
 28.8 
 57.7 
 86.5 
 115.3 
 144.2 
 
 28.5 
 57.0 
 85.5 
 114.0 
 142.5 
 
 20 
 
 21 
 22 
 23 
 24 
 
 8.87829 
 8.87995 
 8.88161 
 8.88326 
 8.88490 
 
 166 
 166 
 165 
 164 
 1fi4 
 
 8.87953 
 8.88120 
 8.88287 
 8.88453 
 8.88618 
 
 167 
 167 
 166 
 165 
 165 
 
 1.12047 
 1.11880 
 1.11713 
 1.11547 
 1.11382 
 
 9.99876 
 9.99875 
 9.99874 
 9.99873 
 9.99872 
 
 40 
 
 39 
 38 
 37 
 36 
 
 6 
 
 7 
 8 
 
 i) 
 
 168 
 
 16.8 
 19.6 
 22.4 
 25 2 
 
 166 
 
 16.6 
 19.4 
 22.1 
 24 Q 
 
 164 
 
 16.4 
 19.1 
 21.9 
 24 fi 
 
 25 
 26 
 27 
 28 
 29 
 
 8.88654 
 8.88817 
 8.88980 
 8.89142 
 8.89304 
 
 163 
 163 
 162 
 162 
 160 
 
 8.88783 
 8.88948 
 8.89111 
 8.89274 
 8.89437 
 
 165 
 163 
 163 
 163 
 161 
 
 1.11217 
 1.11052 
 1.10889 
 1.10726 
 1.10563 
 
 9.99871 
 9.99870 
 9.99869 
 9.99868 
 9.99867 
 
 35 
 34 
 33 
 32 
 31 
 
 10 
 20 
 30 
 40 
 50 
 
 28.0 
 56.0 
 84.0 
 112.0 
 140.0 
 
 27.7 
 55.3 
 83.0 
 110.7 
 138.3 
 
 27.3 
 54.7 
 82.0 
 109.3 
 136.7 
 
 30 
 
 31 
 32 
 33 
 34 
 
 8.89464 
 8.89625 
 8.89784 
 8.89943 
 8.90102 
 
 161 
 159 
 159 
 159 
 158 
 
 8.89598 
 8.89760 
 8.89920 
 8.90080 
 8.90240 
 
 162 
 160 
 160 
 160 
 159 
 
 1.10402 
 1.10240 
 1.10080 
 1.09920 
 1.09760 
 
 9.99866 
 9.99865 
 9.99864 
 9.99863 
 9.99862 
 
 30 
 
 29 
 28 
 27 
 26 
 
 6 
 
 7 
 8 
 
 162 
 
 16.2 
 18.9 
 21.6 
 
 159 
 
 15.9 
 18.6 
 21.2 
 
 157 
 
 15.7 
 18.3 
 20.9 
 
 35 
 36 
 37 
 38 
 39 
 
 8.90260 
 8.90417 
 8.90574 
 8.90730 
 8.90885 
 
 157 
 157 
 156 
 155 
 
 IKK 
 
 8.90399 
 8.90557 
 8.90715 
 8.90872 
 8.91029 
 
 158 
 158 
 157 
 157 
 156 
 
 1.09601 
 1.09443 
 1.09285 
 1.09128 
 1.08971 
 
 9.99861 
 9.99860 
 9.99859 
 9.99858 
 9.99857 
 
 25 
 24 
 23 
 22 
 21 
 
 10 
 20 
 30 
 40 
 fiO 
 
 27.0 
 54.0 
 81.0 
 108.0 
 135.0 
 
 26.5 
 53.0 
 79.5 
 106.0 
 1325 
 
 26.2 
 52.3 
 78.5 
 104.7 
 1308 
 
 40 
 
 41 
 42 
 43 
 44 
 
 8.91040 
 8.91195 
 8.91349 
 8.91502 
 8.91655 
 
 155 
 154 
 153 
 153 
 152 
 
 8.91185 
 8.91340 
 8.91495 
 8.91650 
 8.91803 
 
 155 
 155 
 155 
 153 
 154 
 
 1.08815 
 1.08660 
 1.08505 
 1.08350 
 1.08197 
 
 9.99856 
 9.99855 
 9.99854 
 9.99853 
 9.99852 
 
 20 
 
 19 
 18 
 17 
 16 
 
 6 
 
 7 
 8 
 
 155 
 
 15.5 
 18.1 
 20.7 
 
 153 
 
 15.3 
 17.9 
 20.4 
 
 151 
 
 15.1 
 17.6 
 20.1 
 
 45 
 
 46 
 47 
 48 
 49 
 
 8.91807 
 8.91959 
 8.92110 
 8.92261 
 8.92411 
 
 152 
 151 
 151 
 150 
 
 -icjrv 
 
 8.91957 
 8.92110 
 8.92262 
 8.92414 
 8.92565 
 
 153 
 
 152 
 152 
 151 
 
 1.08043 
 1.07890 
 1.07738 
 1.07586 
 1.07435 
 
 9.99851 
 9.99850 
 9.99848 
 9.99847 
 9.99846 
 
 15 
 14 
 13 
 12 
 11 
 
 9 
 10 
 20 
 30 
 40 
 rn 
 
 23.3 
 25.8 
 51.7 
 77.5 
 103.3 
 129 2 
 
 23.0 
 25.5 
 51.0 
 76.5 
 102.0 
 127 5 
 
 22.7 
 25.2 
 50.3 
 75.5 
 100.7 
 125 8 
 
 50 
 
 51 
 52 
 53 
 54 
 
 8.92561 
 8.92710 
 8.92859 
 8.93007 
 8.93154 
 
 149 
 149 
 148 
 147 
 147 
 
 8.92716 
 8.92866 
 8.93016 
 8.93165 
 8.93313 
 
 150 
 150 
 149 
 148 
 149 
 
 1.07284 
 1.07134 
 1.06984 
 1.06835 
 1.06687 
 
 9.99845 
 9.99844 
 9.99843 
 9.99842 
 9.99841 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 6 
 7 
 8 
 
 149 
 
 14.9 
 17.4 
 19.9 
 
 147 
 
 14.7 
 17.2 
 19.6 
 
 1 
 0.1 
 0.1 
 0.1 
 
 55 
 56 
 57 
 58 
 59 
 
 8.93301 
 8.93448 
 8.93594 
 8.93740 
 8.93885 
 
 147 
 146 
 146 
 145 
 145 
 
 8.93462 
 3.93609 
 8.93756 
 8.93903 
 8.94049 
 
 147 
 147 
 147 
 146 
 146 
 
 1.06538 
 1.06391 
 1.06244 
 1.06097 
 1.05951 
 
 9.99840 
 9.99839 
 9.99838 
 9.99837 
 9.99836 
 
 5 
 4 
 3 
 2 
 1 
 
 9 
 10 
 20 
 30 
 40 
 
 22.4 
 24.8 
 49.7 
 74.5 
 99.3 
 
 22.1 
 24.5 
 49.0 
 73.5 
 
 98.0 
 
 0.2 
 0.2 
 0.3 
 0.5 
 0.7 
 
 60 
 
 8.94030 
 
 
 8.94195 
 
 
 1.05805 
 
 9.99834 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 ' 
 
 
 P 
 
 P. 
 
 
 85 C 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 1033 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 
 
 F 
 
 .P. 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 8.94030 
 8.94174 
 8.94317 
 8.94461 
 8.94603 
 
 144 
 143 
 144 
 142 
 143 
 
 8.94195 
 8.94340 
 8.94485 
 8.94630 
 8.94773 
 
 145 
 145 
 145 
 143 
 144 
 
 1.05805 
 1.05660 
 1.05515 
 1.05370 
 1.05227 
 
 9.99834 
 9.99833 
 9.99832 
 9.99831 
 9.99830 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 8 
 9 
 
 145 
 
 14.5 
 16.9 
 19.3 
 21.8 
 
 143 
 14.3 
 16.7 
 19.1 
 21.5 
 
 141 
 14.1 
 16.5 
 
 18.8 
 21.2 
 
 5 
 6 
 7 
 8 
 9 
 
 8.94746 
 8.94887 
 8.95029 
 8.95170 
 8.95310 
 
 141 
 142 
 141 
 140 
 140 
 
 8.94917 
 
 8.95060 
 8.95202 
 8.95344 
 8.95486 
 
 143 
 142 
 142 
 142 
 141 
 
 1.05083 
 1.04940 
 1.04798 
 1.04656 
 1.04514 
 
 9.99829 
 9.99828 
 9.99827 
 9.99825 
 9.99824 
 
 55 
 54 
 53 
 52 
 51 
 
 10 
 20 
 30 
 40 
 50 
 
 24.2 
 48.3 
 72.5 
 96.7 
 120.8 
 
 23.8 
 47.7 
 71.5 
 95.3 
 119.2 
 
 23.5 
 47.0 
 70.5 
 94.0 
 117.5 
 
 10 
 
 11 
 12 
 13 
 14 
 
 8.95450 
 8.95589 
 8.95728 
 8.95867 
 8.96005 
 
 139 
 139 
 139 
 138 
 -100 
 
 8.95627 
 8.95767 
 8.95908 
 8.96047 
 8.96187 
 
 140 
 141 
 139 
 140 
 138 
 
 1.04373 
 1.04233 
 1.04092 
 1.03953 
 1.03813 
 
 9.99823 
 9.99822 
 9.99821 
 9.99820 
 9.99819 
 
 50 
 
 49 
 48 
 47 
 46 
 
 6 
 7 
 8 
 9 
 
 139 
 
 13.9 
 16.2 
 18.5 
 20.9 
 
 138 
 
 13.8 
 16.1 
 18.4 
 20.7 
 
 136 
 13.6 
 15.9 
 18.1 
 20.4 
 
 15 
 16 
 17 
 18 
 19 
 
 8.96143 
 8.96280 
 8.96417 
 8.96553 
 8.96689 
 
 137 
 137 
 136 
 136 
 
 8.96325 
 8.96464 
 8.96602 
 8.96739 
 8.96877 
 
 139 
 138 
 137 
 138 
 136 
 
 1.03675 
 1.03536 
 1.03398 
 1.03261 
 1.03123 
 
 9.99817 
 9.99816 
 9.99815 
 9.99814 
 9.99813 
 
 45 
 44 
 43 
 42 
 41 
 
 10 
 20 
 30 
 40 
 50 
 
 23.2 
 46.3 
 69.5 
 92.7 
 115.8 
 
 23.0 
 46.0 
 69.0 
 92.0 
 115.0 
 
 22.7 
 45.3 
 68.0 
 90.7 
 113.3 
 
 20 
 
 21 
 22 
 23 
 24 
 
 8.96825 
 8.96960 
 8.97095 
 8.97229 
 8.97363 
 
 135 
 135 
 134 
 134 
 
 8.97013 
 8.97150 
 8.97285 
 8.97421 
 8.97556 
 
 137 
 135 
 136 
 135 
 135 
 
 1.02987 
 1 02850 
 1.02715 
 1.02579 
 1.02444 
 
 9.99812 
 9.99810 
 9.99809 
 9.99808 
 9.99807 
 
 40 
 
 39 
 38 
 37 
 36 
 
 6 
 7 
 8 
 q 
 
 135 
 
 13.5 
 15.8 
 18.0 
 203 
 
 133 
 
 13.3 
 15.5 
 17.7 
 20.0 
 
 131 
 
 13.1 
 15.3 
 17.5 
 19.7 
 
 25 
 26 
 27 
 28 
 29 
 
 8.97496 
 8.97629 
 8.97762 
 8.97894 
 8.98026 
 
 133 
 133 
 132 
 132 
 
 8.97691 
 8.97825 
 8.97959 
 8.98092 
 8.98225 
 
 134 
 134 
 133 
 133 
 
 100 
 
 1.02309 
 1.02175 
 1.02041 
 1.01908 
 1.01775 
 
 9.99806 
 9.99804 
 9.99803 
 9.99802 
 9.99801 
 
 35 
 34 
 33 
 32 
 31 
 
 10 
 20 
 30 
 40 
 50 
 
 22.5 
 45.0 
 67.5 
 90.0 
 112.5 
 
 22.2 
 44.3 
 66.5 
 88.7 
 110.8 
 
 21.8 
 43.7 
 65.5 
 87.3 
 109.2 
 
 30 
 
 31 
 32 
 33 
 34 
 
 8.98157 
 8.98288 
 8.98419 
 8.98549 
 8.98679 
 
 131 
 131 
 130 
 130 
 
 8.98358 
 8.98490 
 8.98622 
 8.98753 
 8.98884 
 
 132 
 132 
 131 
 131 
 131 
 
 1.01642 
 1.01510 
 1.01378 
 1.01247 
 1.01116 
 
 9.99800 
 9.99798 
 9.99797 
 9.99796 
 9.99795 
 
 30 
 
 29 
 28 
 27 
 26 
 
 6 
 
 7 
 8 
 9 
 
 129 
 
 129 
 15.1 
 17.2 
 19 4 
 
 128 
 
 12.8 
 14.9 
 17.1 
 19 2 
 
 126 
 
 12.6 
 14.7 
 16.8 
 18 9 
 
 35 
 36 
 37 
 38 
 39 
 
 8.98808 
 8.98937 
 8.99066 
 8.99194 
 8.99322 
 
 129 
 129 
 
 128 
 '128 
 
 8.99015 
 8.99145 
 8.99275 
 8.99405 
 8.99534 
 
 130 
 130 
 130 
 129 
 
 128 
 
 1.00985 
 1.00855 
 1.00725 
 1.00595 
 1.00466 
 
 9.99793 
 9.99792 
 9.99791 
 9.99790 
 9.99788 
 
 25 
 24 
 23 
 22 
 21 
 
 10 
 20 
 30 
 40 
 50 
 
 21.5 
 43.0 
 64.5 
 86.0 
 107.5 
 
 21.3 
 42.7 
 64.0 
 85.3 
 106.7 
 
 21.0 
 42.0 
 63.0 
 84.0 
 105.0 
 
 40 
 
 41 
 42 
 43 
 44 
 
 8.99450 
 8.99577 
 8.99704 
 8.99830 
 8.99956 
 
 127 
 127 
 126 
 126 
 
 8.99662 
 8.99791 
 8.99919 
 9.00046 
 9.00174 
 
 129 
 
 128 
 127 
 128 
 197 
 
 1.00338 
 1.00209 
 1.00081 
 0.99954 
 0.99826 
 
 9.99787 
 9.99786 
 9.99785 
 9.99783 
 9.99782 
 
 20 
 
 19 
 18 
 17 
 16 
 
 6 
 
 7 
 8 
 
 125 
 
 12.5 
 14.6 
 16.7 
 18 8 
 
 123 
 
 12.3 
 14.4 
 16.4 
 18 5 
 
 122 
 
 12.2 
 14.2 
 16.3 
 18 3 
 
 45 
 
 46 
 47 
 48 
 49 
 
 9.00082 
 9.00207 
 9.00332 
 9.00456 
 9.00581 
 
 125 
 125 
 124 
 125 
 
 9.00301 
 9.00427 
 9.00553 
 9.00679 
 9.00805 
 
 126 
 126 
 126 
 126 
 
 0.99699 
 0.99573 
 0.99447 
 0.99321 
 0.99195 
 
 9.99781 
 9.99780 
 9.99778 
 9.99777 
 9.99776 
 
 15 
 14 
 13 
 12 
 11 
 
 10 
 20 
 30 
 40 
 50 
 
 20.8 
 41.7 
 62.5 
 83.3 
 104.2 
 
 20.5 
 41.0 
 61.5 
 82.0 
 102.5 
 
 20.3 
 40.7 
 61.0 
 81.3 
 101.7 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.00704 
 9.00828 
 9.00951 
 9.01074 
 9.01196 
 
 124 
 123 
 123 
 122 
 
 9.00930 
 9.01055 
 9.01179 
 9.01303 
 9.01427 
 
 125 
 124 
 124 
 124 
 
 -IrtO 
 
 0.99070 
 0.98945 
 0.98821 
 0.98697 
 0.98573 
 
 9.99775 
 9.99773 
 9.99772 
 9.99771 
 9.99769 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 
 
 7 
 8 
 
 121 
 
 12.1 
 14.1 
 16.1 
 
 120 
 
 12.0 
 14.0 
 16.0 
 
 1 
 
 0.1 
 0.1 
 0.1 
 
 55 
 56 
 57 
 58 
 59 
 
 w 
 
 9.01318 
 9.01440 
 9.01561 
 9.01682 
 9.01803 
 9.01923 
 
 122 
 121 
 121 
 121 
 120 
 
 9.01550 
 9.01673 
 9.01796 
 9.01918 
 9.02040 
 9.02162 
 
 123 
 123 
 122 
 122 
 122 
 
 0.98450 
 0.98327 
 0.98204 
 0.98082 
 0.97960 
 0.97838 
 
 9.99768 
 9.99767 
 9.99765 
 9.99764 
 9.99763 
 9.99761 
 
 5 
 4 
 3 
 2 
 1 
 
 
 10 
 20 
 3C 
 40 
 5C 
 
 20.2 
 40.3 
 60.E 
 80. 1 / 
 100.8 
 
 
 
 20.C 
 40.C 
 60.C 
 80.( 
 100.( 
 
 r-p 
 
 0.2 
 0.3 
 0.5 
 0.7 
 ) 0.8 
 
 
 L. COS. 
 
 rt 
 
 L. Cotg 
 
 (1,0 
 
 L.Tang 
 
 L. Sin. 
 
 
 
 
 
 
1034 
 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 I 
 
 L. Sin. 
 
 d. 
 
 L.Tang 
 
 d.c. 
 
 L. Cotg 
 
 L. Cos. 
 
 
 
 P 
 
 P. 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.01923 
 9.02043 
 9.02163 
 9.02283 
 9.02402 
 
 120 
 120 
 120 
 119 
 
 9.02162 
 9.02283 
 9.02404 
 9.02525 
 9.02645 
 
 121 
 121 
 121 
 120 
 
 0.97838 
 0.97717 
 0.97596 
 0.97475 
 0.97355 
 
 9.99761 
 9.99760 
 9.99759 
 9.99757 
 9.99756 
 
 60 
 
 59 
 
 58 
 57 
 56 
 
 6 
 
 7 
 8 
 9 
 
 121 
 
 12.1 
 14.1 
 16.1 
 18.2 
 
 120 
 
 12.0 
 14.0 
 16.0 
 18.0 
 
 113 
 11.9 
 13.9 
 15.9 
 17.9 
 
 5 
 6 
 7 
 8 
 9 
 
 9.02520 
 9.02639 
 9.02757 
 9.02874 
 9.02992 
 
 119 
 118 
 117 
 118 
 
 9.02766 
 9.02885 
 9.03005 
 9.03124 
 9.03242 
 
 119 
 120 
 119 
 118 
 
 0.97234 
 0.97115 
 0.96995 
 0.96876 
 0.96758 
 
 9.99755 
 9.99753 
 9.99752 
 9.99751 
 9.99749 
 
 55 
 54 
 53 
 52 
 61 
 
 10 
 20 
 30 
 40 
 50 
 
 20.2 
 40.3 
 60.5 
 80.7 
 100.8 
 
 20.0 
 40.0 
 60.0 
 80.0 
 100.0 
 
 19.8 
 39.7 
 59.5 
 79.3 
 99.2 
 
 10 
 11 
 12 
 13 
 14 
 
 9.03109 
 9.03226 
 9.03342 
 9.03458 
 9.03574 
 
 117 
 116 
 116 
 116 
 
 9.03361 
 9.03479 
 9.03597 
 9.03714 
 9.03832 
 
 118 
 118 
 117 
 118 
 
 0.96639 
 0.96521 
 0.96403 
 0.96286 
 0.96168 
 
 9.99748 
 9.99747 
 9.99745 
 9.99744 
 9.99742 
 
 60 
 
 49 
 48 
 47 
 46 
 
 6 
 
 7 
 8 
 
 118 
 
 11.8 
 13.8 
 15.7 
 
 117 
 
 11.7 
 13.7 
 16.6 
 
 116 
 11.6 
 13.5 
 15.5 
 
 15 
 16 
 17 
 18 
 19 
 
 9.03690 
 9.03805 
 9.03920 
 9.04034 
 9.04149 
 
 115 
 115 
 114 
 115 
 
 9.03948 
 9.04065 
 9.04181 
 9.04297 
 9.04413 
 
 117 
 116 
 116 
 116 
 
 0.96052 
 0.95935 
 0.95819 
 0.95703 
 0.95587 
 
 9.99741 
 9.99740 
 9.99738 
 9.99737 
 9.99736 
 
 45 
 44 
 43 
 42 
 41 
 
 10 
 20 
 30 
 40 
 50 
 
 19.7 
 39.3 
 59.0 
 78.7 
 98.3 
 
 19.5 
 39.0 
 58.5 
 78.0 
 97.5 
 
 19.3 
 38.7 
 58.0 
 77.3 
 96.7 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.04262 
 9.04376 
 9.04490 
 9.04603 
 9.04715 
 
 114 
 114 
 113 
 112 
 
 9.04528 
 9.04643 
 9.04758 
 9.04873 
 9.04987 
 
 115 
 115 
 115 
 114 
 
 0.95472 
 0.95357 
 0.95242 
 0.95127 
 0.95013 
 
 9.99734 
 9.99733 
 9.99731 
 9.99730 
 9.99728 
 
 40 
 39 
 38 
 37 
 36 
 
 6 
 
 7 
 8 
 
 115 
 
 11.5 
 13.4 
 15.3 
 
 114 
 11.4 
 13.3 
 15.2 
 
 113 
 11.3 
 13.2 
 15.1 
 
 25 
 26 
 27 
 28 
 29 
 
 9.04828 
 9.04940 
 9.05052 
 9.05164 
 9.05275 
 
 112 
 112 
 112 
 111 
 
 9.05101 
 9.05214 
 9.05328 
 9.05441 
 9.05553 
 
 113 
 114 
 113 
 112 
 
 0.94899 
 0.94786 
 0.94672 
 0.94559 
 0.94447 
 
 9.99727 
 9.99726 
 9.99724 
 9.99723 
 9.99721 
 
 35 
 34 
 33 
 32 
 31 
 
 9 
 10 
 
 20 
 30 
 40 
 50 
 
 17.3 
 19.2 
 38.3 
 57.5 
 76.7 
 958 
 
 17.1 
 19.0 
 38.0 
 57.0 
 76.0 
 950 
 
 17.0 
 18.8 
 37.7 
 56.5 
 75.3 
 942 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.05386 
 9.05497 
 9.05607 
 9.05717 
 9.05827 
 
 111 
 110 
 110 
 110 
 no 
 
 9.05666 
 9.05778 
 9.05890 
 9.06002 
 9.06113 
 
 112 
 112 
 112 
 111 
 
 0.94334 
 0.94222 
 0.94110 
 0.93998 
 0.93887 
 
 9.99720 
 9.99718 
 9.99717 
 9.99716 
 9.99714 
 
 30 
 
 29 
 28 
 27 
 26 
 
 6 
 7 
 8 
 
 112 
 
 11.2 
 13.1 
 14.9 
 
 III 
 
 11.1 
 13.0 
 14.8 
 
 110 
 11.0 
 
 12.8 
 14.7 
 
 35 
 36 
 37 
 38 
 39 
 
 9.05937 
 9.06046 
 9.06155 
 9.06264 
 9.06372 
 
 109 
 109 
 109 
 108 
 
 9.06224 
 9.06335 
 9.06445 
 9.06556 
 9.06666 
 
 111 
 110 
 111 
 110 
 
 0.93776 
 0.93665 
 0.93555 
 0.93444 
 0.93334 
 
 9.99713 
 9.99711 
 9.99710 
 9.99708 
 9.99707 
 
 25 
 24 
 23 
 22 
 
 21 
 
 9 
 10 
 20 
 30 
 40 
 
 16.8 
 18.7 
 37.3 
 56.0 
 
 74.7 
 
 16.7 
 18.5 
 37.0 
 55.5 
 74.0 
 
 16.5 
 18.3 
 36.7 
 55.0 
 73.3 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.06481 
 9.06589 
 9.06696 
 9.06804 
 9.06911 
 
 108 
 107 
 108 
 107 
 
 9.06775 
 9.06885 
 9.06994 
 9.07103 
 9.07211 
 
 110 
 109 
 109 
 108 
 
 -IAQ 
 
 0.93225 
 0.93115 
 0.93006 
 0.92897 
 0.92789 
 
 9.99705 
 9.99704 
 9.99702 
 9.99701 
 9.99699 
 
 20 
 
 19 
 18 
 17 
 16 
 
 6 
 7 
 8 
 
 109 
 
 10.9 
 12.7 
 14.5 
 
 108 
 
 10.8 
 12.6 
 14.4 
 
 107 
 
 10.7 
 12.5 
 14.3 
 
 45 
 46 
 
 47 
 48 
 49 
 
 9.07018 
 9.07124 
 9.07231 
 9.07337 
 9.07442 
 
 106 
 107 
 106 
 105 
 Iftfi 
 
 9.07320 
 9.07428 
 9.07536 
 9.07643 
 9.07751 
 
 108 
 108 
 107 
 108 
 1O7 
 
 0.92680 
 0.92572 
 0.92464 
 0.92357 
 0.92249 
 
 9.99698 
 9.99696 
 9.99695 
 9.99693 
 9.99692 
 
 15 
 14 
 13 
 12 
 11 
 
 9 
 10 
 20 
 30 
 40 
 
 16.4 
 18.2 
 36.3 
 54.5 
 72.7 
 
 16.2 
 18.0 
 36.0 
 54.0 
 72.0 
 
 16.1 
 17.8 
 35.7 
 53.5 
 71.3 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.07548 
 9.07653 
 9.07758 
 9.07863 
 9.07968 
 
 105 
 105 
 105 
 105 
 104 
 
 9.07858 
 9.07964 
 9.08071 
 9.08177 
 9.08283 
 
 106 
 107 
 106 
 106 
 106 
 
 0.92142 
 0.92036 
 0.91929 
 0.91823 
 0.91717 
 
 9.99690 
 9.99689 
 9.99687 
 9.99686 
 9.99684 
 
 10 
 
 9 
 8 
 
 7 
 6 
 
 50 
 
 6 
 
 7 
 8 
 
 90.8 
 
 106 
 
 10.6 
 12.4 
 14.1 
 
 90.0 
 
 105 
 
 10.5 
 12.3 
 14.0 
 
 89.2 
 
 104 
 
 10.4 
 12.1 
 13.9 
 
 55 
 56 
 57 
 
 58 
 59 
 
 9.08072 
 9.08176 
 9.08280 
 9.08383 
 9.08486 
 
 104 
 104 
 103 
 103 
 103 
 
 9.08389 
 9.08495 
 9.08600 
 9.08705 
 9.08810 
 
 106 
 105 
 105 
 105 
 104 
 
 0.91611 
 0.91505 
 0.91400 
 0.91295 
 0.91190 
 
 9.99683 
 9.99681 
 9.99680 
 9.99678 
 9.99677 
 
 5 
 4 
 3 
 2 
 1 
 
 9 
 
 10 
 20 
 30 
 40 
 
 15.9 
 17.7 
 35.3 
 53.0 
 70.7 
 
 15.8 
 17.5 
 35.0 
 52.5 
 70.0 
 
 15.6 
 17.3 
 34.7 
 52.0 
 69.3 
 
 60 
 
 9.08589 
 
 
 9.08914 
 
 
 0.91086 
 
 9.99675 
 
 
 
 50 
 
 88.3 
 
 87.5 
 
 86.7 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 / 
 
 
 P. 
 
 P. 
 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 7 
 
 1035 
 
 1 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 
 
 P. 
 
 P. 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.08589 
 9.08692 
 9.08795 
 9.08897 
 9.08999 
 
 103 
 103 
 102 
 102 
 102 
 
 9.08914 
 9.09019 
 9.09123 
 9.09227 
 9.09330 
 
 105 
 104 
 104 
 103 
 104 
 
 0.91086 
 0.90981 
 0.90877 
 0.90773 
 0.90670 
 
 9.99675 
 9.99674 
 9.99672 
 9.99670 
 9.99669 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 8 
 g 
 
 105 
 
 10.5 
 12.3 
 14.0 
 15 8 
 
 104 
 
 10.4 
 12.1 
 13.9 
 15 6 
 
 103 
 
 10.3 
 12.0 
 13.7 
 15 5 
 
 5 
 
 6 
 7 
 8 
 9 
 
 9.09101 
 9.09202 
 9.09304 
 9.09405 
 9.09506 
 
 101 
 102 
 101 
 101 
 100 
 
 9.09434 
 9.09537 
 9.09640 
 9.09742 
 9.09845 
 
 103 
 103 
 102 
 103 
 102 
 
 0.90566 
 0.90463 
 0.90360 
 0.90258 
 0.90155 
 
 9.99667 
 9.99666 
 9.99664 
 9.99663 
 9.99661 
 
 55 
 54 
 53 
 52 
 51 
 
 10 
 20 
 30 
 40 
 50 
 
 17.5 
 35.0 
 52.5 
 70.0 
 87.5 
 
 17.3 
 34.7 
 52.0 
 69.3 
 86.7 
 
 17.2 
 34.3 
 51.5 
 68.7 
 85.8 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.09606 
 9.09707 
 9.09807 
 9.09907 
 9.10006 
 
 101 
 100 
 100 
 99 
 100 
 
 9.09947 
 9.10049 
 9.10150 
 9.10252 
 9.10353 
 
 102 
 101 
 102 
 101 
 101 
 
 0.90053 
 0.89951 
 0.89850 
 0.89748 
 0.89647 
 
 9.99659 
 9.99658 
 9.99656 
 9.99655 
 9.99653 
 
 50 
 
 49 
 48 
 47 
 46 
 
 6 
 7 
 8 
 g. 
 
 102 
 
 10.2 
 11.9 
 13.6 
 15 3 
 
 101 
 
 10.1 
 11.8 
 13.5 
 
 -ico 
 
 100 
 
 10.0 
 11.7 
 13.3 
 15 
 
 15 
 16 
 
 17 
 18 
 19 
 
 9.10106 
 9.10205 
 9.10304 
 9.10402 
 9.10501 
 
 99 
 99 
 98 
 99 
 
 QQ 
 
 9.10454 
 9.10555 
 9.10656 
 9.10756 
 9.10856 
 
 101 
 101 
 100 
 100 
 
 100 
 
 0.89546 
 0.89445 
 0.89344 
 0.89244 
 0.89144 
 
 9.99651 
 9.99650 
 9.99648 
 9.99647 
 9.99645 
 
 45 
 44 
 43 
 42 
 41 
 
 10 
 
 20 
 30 
 40 
 50 
 
 17.0 
 34.0 
 51.0 
 68.0 
 85,0 
 
 16.8 
 33.7 
 50.5 
 67.3 
 
 84,?, 
 
 16.7 
 33.3 
 50.0 
 66.7 
 83.3 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.10599 
 9.10697 
 9.10795 
 9.10893 
 9.10990 
 
 98 
 98 
 98 
 97 
 97 
 
 9.10956 
 9.11056 
 9.11155 
 9.11254 
 9.11353 
 
 100 
 99 
 99 
 99 
 99 
 
 0.89044 
 0.88944 
 0.88845 
 0.88746 
 0.88647 
 
 9.99643 
 9.99642 
 9.99640 
 9.99638 
 9.99637 
 
 40 
 
 39 
 38 
 37 
 36 
 
 
 9 
 
 6 9 
 7 11 
 8 13 
 
 ) 9 
 
 9 9 
 6 11 
 2 13 
 
 J 
 
 8 
 4 
 
 1 
 
 25 
 26 
 27 
 28 
 29 
 
 9.11087 
 9-11184 
 S.11281 
 9.11377 
 9.11474 
 
 97 
 97 
 96 
 
 97 
 
 9.11452 
 9.11551 
 9.11649 
 9.11747 
 9.11845 
 
 99 
 98 
 98 
 98 
 
 0.88548 
 0.88449 
 0.88351 
 0.88253 
 0.88155 
 
 9.99635 
 9.99633 
 9.99632 
 9.99630 
 9.99629 
 
 35 
 34 
 33 
 32 
 31 
 
 : 
 4 
 
 1 
 
 16 
 !0 33 
 10 49 
 LO 66 
 )0 82 
 
 5 16 
 32 
 5 49 
 65 
 5 81 
 
 3 
 
 7 
 
 3 
 
 7 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.11570 
 9.11666 
 9.11761 
 9.11857 
 9.11952 
 
 96 
 95 
 96 
 95 
 
 9.11943 
 9.12040 
 9.12138 
 9.12235 
 9.12332 
 
 97 
 98 
 97 
 97 
 
 0.88057 
 0.87960 
 0.87862 
 0.87765 
 0.87668 
 
 9.99627 
 9.99625 
 9.99624 
 9.99622 
 9.99620 
 
 30 
 
 29 
 28 
 27 
 26 
 
 6 
 7 
 8 
 
 97 
 
 9.7 
 11.3 
 12.9 
 
 96 
 
 9.6 
 11.2 
 12.8 
 
 95 
 
 9.5 
 11.1 
 
 12.7 
 
 35 
 36 
 37 
 38 
 39 
 
 9.12047 
 9.12142 
 9.12236 
 9.12331 
 9.12425 
 
 95 
 94 
 95 
 94 
 Q4 
 
 9.12428 
 9.12525 
 9.12621 
 9.12717 
 9.12813 
 
 97 
 96 
 96 
 96 
 96 
 
 0.87572 
 0.87475 
 0.87379 
 0.87283 
 0.87187 
 
 9.99618 
 9.99617 
 9.99615 
 9.99613 
 9.99612 
 
 25 
 24 
 23 
 22 
 21 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 14.6 
 16.2 
 32.3 
 
 48.5 
 64.7 
 808 
 
 14.4 
 16.0 
 32.0 
 48.0 
 64.0 
 800 
 
 14.3 
 15.8 
 31.7 
 47.5 
 63.3 
 79.2 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.12519 
 9.12612 
 9.12706 
 9.12799 
 9.12892 
 
 93 
 94 
 93 
 93 
 
 9.12909 
 9.13004 
 9.13099 
 9.13194 
 9.13289 
 
 95 
 95 
 95 
 95 
 
 QT 
 
 0.87091 
 0.86996 
 0.86901 
 0.86806 
 0.86711 
 
 9.99610 
 9.99608 
 9.99607 
 9.99605 
 9.99603 
 
 20 
 
 19 
 18 
 17 
 16 
 
 6 
 
 7 
 8 
 
 94 
 
 9.4 
 11.0 
 12.5 
 
 93 
 
 9.3 
 10.9 
 12.4 
 
 92 
 
 9.2 
 10.7 
 12.3 
 
 45 
 46 
 47 
 
 48 
 49 
 
 9.12985 
 9.13078 
 9.13171 
 9.13263 
 9.13355 
 
 93 
 93 
 92 
 92 
 
 9.13384 
 9.13478 
 9.13573 
 9.13667 
 9.13761 
 
 94 
 
 95 
 94 
 94 
 
 QO 
 
 0.86616 
 0.86522 
 0.86427 
 0.86333 
 0.86239 
 
 9.99601 
 9.99600 
 9.99598 
 9.99596 
 9.99595 
 
 15 
 14 
 13 
 12 
 11 
 
 9 
 
 10 
 20 
 30 
 40 
 
 14.1 
 15.7 
 31.3 
 47.0 
 62.7 
 
 70 
 
 14.0 
 15.5 
 31.0 
 46.5 
 62.0 
 77 5 
 
 13.8 
 15.3 
 30.7 
 46.0 
 61.3 
 76 7 
 
 50 
 
 51 
 52 
 53 
 
 54 
 
 9.13447 
 9.13539 
 9.13630 
 9.13722 
 9.13813 
 
 92 
 91 
 92 
 91 
 Q1 
 
 9.13854 
 9.13948 
 9.14041 
 9.14134 
 9.14227 
 
 94 
 93 
 93 
 93 
 93 
 
 0.86146 
 0.86052 
 0.85959 
 0.85866 
 0.85773 
 
 9.99593 
 9.99591 
 9.99589 
 9.99588 
 9.99586 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 
 
 7 
 8 
 
 91 
 
 9.1 
 10.6 
 12.1 
 
 90 
 
 9.0 
 10.5 
 12.0 
 
 2 
 
 0.2 
 0.2 
 0.3 
 
 55 
 56 
 57 
 58 
 59 
 
 9.13904 
 9.13994 
 9.14085 
 9.14175 
 9.14266 
 
 90 
 91 
 90 
 91 
 
 9.14320 
 9.14412 
 9.14504 
 9.14597 
 9.14688 
 
 92 
 92 
 93 
 91 
 92 
 
 0.85680 
 0.85588 
 0.85496 
 0.85403 
 0.85312 
 
 9.99584 
 9.99582 
 9.99581 
 9.99579 
 9.99577 
 
 5 
 4 
 3 
 2 
 1 
 
 9 
 10 
 20 
 30 
 40 
 
 13.V 
 15.2 
 30.3 
 45.5 
 60.7 
 
 13.5 
 15.0 
 30.0 
 45.0 
 60.0 
 
 0.3 
 0.3 
 0.7 
 1.0 
 1.3 
 1 7 
 
 60 
 
 9.14356 
 
 
 9.14780 
 
 
 0.8522C 
 
 9.99575 
 
 
 
 
 
 
 
 
 L. Cos 
 
 d. 
 
 L. Cotg 
 
 d.c 
 
 L.Tang 
 
 L. Sin 
 
 r 
 
 
 i 
 
 '. P. 
 
 
 
 
 
 
 
 82 
 
 
 
 
 
 
 
1036 
 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 8 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 
 
 
 P. 
 
 P. 
 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.14356 
 9.14445 
 9.14535 
 9.14624 
 9.14714 
 
 89 
 90 
 89 
 90 
 
 9.14780 
 9.14872 
 9.14963 
 9.15054 
 9.15145 
 
 92 
 91 
 91 
 91 
 
 Q-l 
 
 0.85220 
 0.85128 
 0.85037 
 0.84946 
 0.84855 
 
 9.99575 
 9.99574 
 9.99572 
 9.99570 
 9.99568 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 8 
 9 
 
 9 
 
 9 
 10 
 VI 
 Y\ 
 
 2 
 
 .2 
 .7 
 .3 
 
 H 
 
 9 
 
 9 
 10 
 12 
 IS* 
 
 1 
 .1 
 .6 
 
 .1 
 
 7 
 
 90 
 
 9.0 
 10.5 
 12.0 
 13 5 
 
 5 
 
 6 
 7 
 8 
 9 
 
 9.14803 
 9.14891 
 9.14980 
 9.15069 
 9.15157 
 
 88 
 89 
 89 
 88 
 
 88 
 
 9.15236 
 9.15327 
 9.15417 
 9.15508 
 9.15598 
 
 91 
 90 
 91 
 90 
 90 
 
 0.84764 
 0.84673 
 0.84583 
 0.84492 
 0.84402 
 
 9.99566 
 9.99565 
 9.99563 
 9.99561 
 9.99559 
 
 55 
 54 
 53 
 52 
 51 
 
 10 
 20 
 30 
 40 
 50 
 
 u 
 
 30 
 4(j 
 61 
 
 7C 
 
 & 
 
 .1 
 .0 
 .3 
 *.? 
 
 15 
 
 30 
 45 
 GO 
 
 75 
 
 .2 
 .3 
 .5 
 .7 
 
 .8 
 
 15.0 
 30.0 
 45.0 
 60.0 
 75.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.15245 
 9.15333 
 9.15421 
 9.15508 
 9.15596 
 
 88 
 88 
 87 
 88 
 
 9.15688 
 9.15777 
 9.15867 
 9.15956 
 9.16046 
 
 89 
 90 
 89 
 90 
 
 CQ 
 
 0.84312 
 0.84223 
 0.84133 
 0.84044 
 0.83954 
 
 9.99557 
 9.99556 
 9.99554 
 9.99552 
 9.99550 
 
 50 
 
 49 
 48 
 47 
 46 
 
 
 6 
 
 7 
 8 
 
 8 
 8 
 
 10 
 11 
 V 
 
 9 
 
 .9 
 .4 
 .9 
 
 8 
 
 8 
 10 
 11 
 1 
 
 8 
 
 .8 
 .3 
 .7 
 2 
 
 15 
 16 
 17 
 18 
 19 
 
 9.15683 
 9.15770 
 9.15857 
 9.15944 
 9.16030 
 
 87 
 87 
 87 
 86 
 
 oa 
 
 9.16135 
 9.16224 
 9.16312 
 9.16401 
 9.16489 
 
 89 
 88 
 89 
 88 
 
 CO 
 
 0.83865 
 0.83776 
 0.83688 
 0.83599 
 0.83511 
 
 9.99548 
 9.99546 
 9.99545 
 9.99543 
 9.99541 
 
 45 
 44 
 43 
 42 
 41 
 
 '* ' 
 
 ' 
 
 
 >0 
 50 
 10 
 >0 
 
 14 
 20 
 44 
 
 59 
 74 
 
 .8 
 .7 
 .5 
 .3 
 .2 
 
 14 
 
 21 
 44 
 
 f)S 
 
 73 
 
 .7 
 .3 
 .0 
 .7 
 .3 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.16116 
 9.16203 
 9.16289 
 9.16374 
 9.16460 
 
 87 
 86 
 85 
 86 
 
 85 
 
 9.16577 
 9.16665 
 9.16753 
 9.16841 
 9.16928 
 
 88 
 88 
 88 
 87 
 88 
 
 0.83423 
 0.83335 
 0.83247 
 0.83159 
 0.83072 
 
 9.99539 
 9.99537 
 9.99535 
 9.99533 
 9.99532 
 
 40 
 
 39 
 38 
 37 
 36 
 
 
 6 
 
 7 
 8 
 
 Q 
 
 8 
 8 
 
 10 
 11 
 1 
 
 7 
 
 .7 
 .2 
 .0 
 
 8 
 
 8 
 10 
 11 
 -it 
 
 6 
 
 .6 
 .0 
 .5 
 q 
 
 25 
 26 
 27 
 28 
 29 
 
 9.16545 
 9.16631 
 9.16716 
 9.16801 
 9.16886 
 
 86 
 85 
 85 
 85 
 84 
 
 9.17016 
 9.17103 
 9.17190 
 9.17277 
 9.17363 
 
 87 
 87 
 87 
 86 
 87 
 
 0.82984 
 0.82897 
 0.82810 
 0.82723 
 0.82637 
 
 9.99530 
 9.99528 
 9.99526 
 9.99524 
 9.99522 
 
 35 
 34 
 33 
 32 
 31 
 
 \ 
 
 10 
 
 20 
 W 
 40 
 V) 
 
 14 
 21 
 43 
 58 
 72 
 
 .5 
 .0 
 .5 
 .0 
 
 5 
 
 14 
 
 2J- 
 
 43 
 57 
 71 
 
 .3 
 .7 
 .0 
 .3 
 
 .7 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.16970 
 9.17055 
 9.17139 
 9.17223 
 9.17307 
 
 85 
 84 
 84 
 84 
 
 84 
 
 9.17450 
 9.17536 
 9.17622 
 9.17708 
 9.17794 
 
 86 
 86 
 86 
 86 
 86 
 
 0.82550 
 0.82464 
 0.82378 
 0.82292 
 0.82206 
 
 9.99520 
 9.99518 
 9.99517 
 9.99515 
 9.99513 
 
 30 
 
 29 
 28 
 27 
 26 
 
 
 G 
 
 7 
 8 
 
 8 
 8 
 
 1 
 11 
 
 5 
 
 .5 
 .9 
 .3 
 
 8 
 1 
 
 S 
 11 
 
 4 
 .4 
 
 .8 
 .2 
 
 35 
 36 
 37 
 38 
 39 
 
 9.17391 
 9.17474 
 9.17558 
 9.17641 
 9.17724 
 
 83 
 84 
 83 
 83 
 83 
 
 9.17880 
 9.17965 
 9.18051 
 9.18136 
 9.18221 
 
 85 
 86 
 85 
 85 
 85 
 
 0.82120 
 0.82035 
 0.81949 
 0.81864 
 0.81779 
 
 9.99511 
 9.99509 
 9.99507 
 9.99505 
 9.99503 
 
 25 
 24 
 23 
 22 
 21 
 
 
 y 
 
 10 
 20 
 *) 
 40 
 "i() 
 
 J^ 
 14 
 2^ 
 42 
 5t 
 9) 
 
 .8 
 .2 
 .3 
 .5 
 .7 
 g 
 
 1. 
 14 
 '2k 
 
 41 
 
 5e 
 
 7f 
 
 .6 
 .0 
 .0 
 .0 
 .0 
 
 o 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.17807 
 9.17890 
 9.17973 
 9.18055 
 9.18137 
 
 83 
 83 
 82 
 82 
 83 
 
 9.18306 
 9.18391 
 9.18475 
 9.18560 
 9.18644 
 
 85 
 84 
 85 
 
 84 
 84 
 
 0.81694 
 0.81609 
 0.81525 
 0.81440 
 0.81356 
 
 9.99501 
 9.99409 
 9.99497 
 9.99495 
 9.99494 
 
 20 
 
 19 
 
 18 
 17 
 16 
 
 
 6 
 
 7 
 8 
 
 8 
 1 
 1 
 
 11 
 
 3 
 
 .3 
 
 .7 
 .1 
 
 8 
 8 
 
 8 
 
 K 
 
 2 
 
 .2 
 .6 
 .9 
 
 45 
 
 46 
 47 
 48 
 49 
 
 9.18220 
 9.18302 
 9.18383 
 9.18465 
 9.18547 
 
 82 
 81 
 82 
 82 
 81 
 
 9.18728 
 9.18812 
 9.18896 
 9.18979 
 9.19063 
 
 84 
 84 
 83 
 84 
 83 
 
 0.81272 
 0.81188 
 0.81104 
 0.81021 
 0.80937 
 
 9.99492 
 9.99490 
 9.99488 
 9.99486 
 9.99484 
 
 15 
 14 
 13 
 12 
 11 
 
 
 y 
 
 10 
 20 
 30 
 10 
 jO 
 
 n 
 i: 
 
 27 
 41 
 
 55 
 6 
 
 .0 
 
 .8 
 .7 
 .5 
 .3 
 
 
 
 11 
 
 i! 
 
 27 
 41 
 54 
 
 fi< 
 
 .3 
 .7 
 .3 
 .0 
 
 .7 
 
 q 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.18628 
 9.18709 
 9.18790 
 9.18871 
 9.18952 
 
 81 
 81 
 81 
 81 
 81 
 
 9.19146 
 9.19229 
 9.19312 
 9.19395 
 9.19478 
 
 83 
 83 
 83 
 83 
 
 CO 
 
 0.80854 
 0.80771 
 0.80688 
 0.80605 
 0.80522 
 
 9.99482 
 9.99480 
 9.99478 
 9.99476 
 9.99474 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 6 
 
 7 
 8 
 
 8 
 i 
 
 c 
 
 K 
 
 1 
 LI 
 
 .5 
 
 .8 
 
 8 
 
 i 
 
 ! 
 
 If 
 
 
 
 .0 
 .3 
 
 .7 
 
 2 
 
 0.2 
 0.2 
 0.3 
 
 55 
 56 
 57 
 58 
 59 
 
 9.19033 
 9.19113 
 9.19193 
 9.19273 
 9.19353 
 
 80 
 80 
 80 
 80 
 80 
 
 9.19561 
 9.19643 
 9.19725 
 9.19807 
 9.19889 
 
 82 
 82 
 82 
 82 
 
 CO 
 
 0.80439 
 0.80357 
 0.80275 
 0.80193 
 0.80111 
 
 9.99472 
 9.99470 
 9.99468 
 9.99466 
 9.99464 
 
 5 
 4 
 3 
 
 2 
 
 1 
 
 9 
 
 10 
 20 
 30 
 40 
 
 r_ 
 
 lc 
 27 
 4( 
 
 5^ 
 
 .2 
 .5 
 .0 
 .5 
 .0 
 
 11 
 
 i; 
 
 2f 
 4C 
 53 
 
 .0 
 .3 
 
 .7 
 .0 
 .3 
 
 0.3 
 0.3 
 0.7 
 1.0 
 1.3 
 
 60 
 
 9.19433 
 
 
 9.19971 
 
 
 0.80029 
 
 9.99462 
 
 
 
 50 
 
 6/ 
 
 .0 
 
 6f 
 
 ./ 
 
 1.7 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 i 
 
 
 
 P. 
 
 P. 
 
 
 
 81 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 1037 
 9 
 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 
 
 
 P. 
 
 P 
 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.19433 
 9.19513 
 9.19592 
 9.19672 
 9.19751 
 
 80 
 79 
 80 
 79 
 7Q 
 
 9.19971 
 9.20053 
 9.20134 
 9.20216 
 9.20297 
 
 82 
 81 
 82 
 81 
 
 0.80029 
 0.79947 
 0.79866 
 0.79784 
 0.79703 
 
 9.99462 
 9.99460 
 9.99458 
 9.99456 
 9.99454 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 8 
 
 8 
 
 I 
 r 
 
 1C 
 
 2 
 
 .2 
 
 .6 
 .9 
 
 8 
 I 
 
 c 
 
 1C 
 
 1 
 
 .1 
 .5 
 .8 
 
 80 
 
 8.0 
 9.3 
 10.7 
 
 5 
 6 
 7 
 8 
 9 
 
 9.19830 
 9.19909 
 9.19988 
 9.20067 
 9.20145 
 
 79 
 79 
 79 
 
 78 
 78 
 
 9.20378 
 9.20459 
 9.20540 
 9.20621 
 9.20701 
 
 81 
 81 
 81 
 80 
 
 0.79622 
 0.79541 
 0.79460 
 0.79379 
 0.79299 
 
 9.99452 
 9.99450 
 9.99448 
 9.99446 
 9.99444 
 
 55 
 54 
 53 
 52 
 51 
 
 10 
 20 
 30 
 40 
 50 
 
 IS 
 
 27 
 41 
 54 
 
 
 .7 
 .3 
 
 .0 
 
 .7 
 3 
 
 IS 
 27 
 4C 
 54 
 6' 
 
 .5 
 .0 
 .5 
 .0 
 5 
 
 13.3 
 26.7 
 40.0 
 53.3 
 66.7 
 
 10 
 11 
 12 
 13 
 
 14 
 
 9.20223 
 9.20302 
 9.20380 
 9.20458 
 9.20535 
 
 79 
 
 78 
 78 
 77 
 78 
 
 9.20782 
 9.20862 
 9.20942 
 9.21022 
 9.21102 
 
 80 
 80 
 80 
 80 
 
 0.79218 
 0.79138 
 0.79058 
 0.78978 
 0.78898 
 
 9.99442 
 9.99440 
 9.99438 
 9.99436 
 9.99434 
 
 50 
 
 49 
 48 
 47 
 46 
 
 
 6 
 
 7 
 8 
 
 7 
 
 Q 
 
 10 
 
 J 
 9 
 2 
 5 
 
 7 
 
 7 
 9 
 10 
 
 8 
 .8 
 .1 
 .4 
 
 15 
 16 
 17 
 
 18 
 19 
 
 9.20613 
 9.20691 
 9.20768 
 9.20845 
 9.20922 
 
 78 
 77 
 
 77 
 77 
 77 
 
 9.21182 
 9.21261 
 9.21341 
 9.21420 
 9.21499 
 
 79 
 80 
 79 
 79 
 
 0.78818 
 0.78739 
 0.78659 
 0.78580 
 0.78501 
 
 9.99432 
 9.99429 
 9.99427 
 9.99425 
 9.99423 
 
 45 
 44 
 43 
 42 
 41 
 
 ] 
 I 
 | 
 
 4 
 
 
 
 
 
 
 iO 
 
 13 
 26 
 39 
 52 
 fi r > 
 
 2 
 3 
 
 5 
 
 7 
 
 s 
 
 13 
 2f 
 39 
 52 
 6 r i 
 
 .7 
 .0 
 .0 
 .0 
 .0 
 
 o 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.20999 
 9.21076 
 9.21153 
 9.21229 
 9.21306 
 
 77 
 77 
 76 
 77 
 76 
 
 9.21578 
 9.21657 
 9.21736 
 9.21814 
 9.21893 
 
 79 
 79 
 78 
 79 
 
 0.78422 
 0.78343 
 0.78264 
 0.78186 
 0.78107 
 
 9.99421 
 9.99419 
 9.99417 
 9.99415 
 9.99413 
 
 40 
 
 39 
 38 
 37 
 36 
 
 
 6 
 
 7 
 8 
 
 7 
 
 7 
 9 
 10 
 
 1 
 
 1 
 
 3 
 
 7 
 
 7 
 8 
 10 
 
 6 
 .6 
 .9 
 .1 
 
 25 
 26 
 27 
 28 
 29 
 
 9.21382 
 9.21458 
 9.21534 
 9.21610 
 9.21685 
 
 76 
 76 
 76 
 
 75 
 7fi 
 
 9.21971 
 9.22049 
 9.22127 
 9.22205 
 9.22283 
 
 78 
 78 
 78 
 78 
 
 0.78029 
 0.77951 
 0.77873 
 0.77795 
 0.77717 
 
 9.99411 
 9.99409 
 9.99407 
 9.99404 
 9.99402 
 
 35 
 34 
 33 
 32 
 31 
 
 ] 
 
 ! 
 S 
 
 I 
 
 f 
 
 9 
 
 
 
 
 
 Q 
 
 11 
 12 
 
 25 
 38 
 51 
 61 
 
 b 
 8 
 7 
 5 
 3 
 
 
 
 li 
 12 
 
 25 
 
 38 
 50 
 6'} 
 
 .4 
 
 .7 
 .3 
 .0 
 .7 
 3 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.21761 
 9.21836 
 9.21912 
 9.21987 
 9.22062 
 
 75 
 76 
 75 
 75 
 
 9.22361 
 9.22438 
 9.22516 
 9.22593 
 9.22670 
 
 77 
 78 
 77 
 77 
 
 0.77639 
 0.77562 
 0.77484 
 0.77407 
 0.77330 
 
 9.99400 
 9.99398 
 9.99396 
 9.99394 
 9.99392 
 
 30 
 
 29 
 28 
 27 
 26 
 
 
 6 
 
 7 
 8 
 
 7 
 
 7 
 8 
 10 
 
 ) 
 
 5 
 8 
 
 
 7 
 7 
 8 
 9 
 
 4 
 .4 
 .6 
 .9 
 
 35 
 36 
 37 
 38 
 39 
 
 9.22137 
 9.22211 
 9.22286 
 9.22361 
 9.22435 
 
 74 
 75 
 75 
 74 
 74 
 
 9.22747 
 9.22824 
 9.22901 
 9.22977 
 9.23054 
 
 77 
 77 
 76 
 77 
 
 0.77253 
 0.77176 
 0.77099 
 0.77023 
 0.76946 
 
 9.99390 
 9.99388 
 9.99385 
 9.99383 
 9.99381 
 
 25 
 24 
 23 
 22 
 21 
 
 1 
 1 
 1 
 4 
 
 9 
 
 
 
 
 o 
 
 11 
 
 12 
 25 
 37 
 50 
 
 fi 
 
 3 
 
 5 
 
 
 5 
 
 
 r. 
 
 11 
 12 
 24 
 
 37 
 49 
 fi1 
 
 .1 
 .3 
 .7 
 .0 
 .3 
 7 
 
 40 
 41 
 42 
 43 
 44 
 
 9.22509 
 9.22583 
 9.22657 
 9.22731 
 
 9.22805 
 
 74 
 74 
 74 
 74 
 70 
 
 9.23130 
 9.23206 
 9.23283 
 9.23359 
 9.23435 
 
 76 
 
 77 
 76 
 76 
 
 0.76870 
 0.76794 
 0.76717 
 0.76641 
 0.76565 
 
 9.99379 
 9.99377 
 9.99375 
 9.99372 
 9.99370 
 
 20 
 
 19 
 18 
 17 
 16 
 
 
 6 
 
 7 
 8 
 
 7. 
 
 7 
 8 
 9 
 
 J 
 
 3 
 5 
 
 7 
 
 7 
 7 
 8 
 9 
 
 2 
 
 .2 
 .4 
 .6 
 
 45 
 46 
 47 
 48 
 49 
 
 9.22878 
 9.22952 
 9.23025 
 9.23098 
 9.23171 
 
 74 
 73 
 73 
 73 
 
 9.23510 
 9.23586 
 9.23661 
 9.23737 
 9.23812 
 
 76 
 
 75 
 76 
 75 
 
 0.76490 
 0.76414 
 0.76339 
 0.76263 
 .0.76188 
 
 9.99368 
 9.99366 
 9.99364 
 
 15 
 14 
 13 
 12 
 11 
 
 1 
 2 
 3 
 4 
 
 9 
 
 
 
 
 
 11 
 12 
 24 
 36 
 
 48. 
 
 
 2 
 3 
 5 
 
 7 
 
 10 
 12 
 24 
 
 36 
 
 48 
 
 .8 
 
 
 
 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.23244 
 9.23317 
 9.23390 
 9.23462 
 9.23535 
 
 73 
 
 73 
 72 
 73 
 
 79 
 
 9.23887 
 9.23962 
 9.24037 
 9.24112 
 9.24186 
 
 75 
 75 
 75 
 74 
 
 0.76113 
 0.76038 
 0.75963 
 0.75888 
 0.75814 
 
 9.99357 
 9.99355 
 9.99353 
 9.99351 
 9.99348 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 5 
 
 6 
 7 
 
 8 
 
 
 
 60. 
 
 71 
 
 7.1 
 8.3 
 9.5 
 
 8 
 
 
 
 
 
 GO 
 
 3 
 
 .3 
 .4 
 .4 
 
 
 
 2 
 
 0.2 
 0.2 
 0.3 
 
 55 
 56 
 57 
 58 
 59 
 
 9.23607 
 9.23679 
 9.23752 
 9.23823 
 9.23895 
 
 72 
 73 
 
 71 
 72 
 
 79 
 
 9.24261 
 9.24335 
 9.24410 
 9.24484 
 9.24558 
 
 74 
 
 75 
 74 
 74 
 
 74. 
 
 0.75739 
 0.75665 
 0.75590 
 0.75516 
 0.75442 
 
 9.99346 
 9.99344 
 9.99342 
 9.99340 
 9.99337 
 
 5 
 4 
 3 
 
 2 
 
 1 
 
 9 
 10 
 
 20 
 30 
 40 
 
 1 
 1 
 
 2 
 3 
 4 
 
 0.7 
 1.8 
 3.7 
 5.5 
 7.3 
 
 
 
 
 1 
 1 
 
 2 
 
 .5 
 .5 
 .0 
 .5 
 .0 
 
 0.3 
 0.3 
 0.7 
 1.0 
 1.3 
 
 60 
 
 9.23967 
 
 
 9.24632 
 
 
 0.75368 
 
 9.99335 
 
 
 
 50 
 
 5 
 
 9.2 
 
 2 
 
 .5 
 
 1.7 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 ' 
 
 
 
 P. 
 
 P 
 
 
 
 80 
 
1038 
 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 10 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 
 
 P.P. 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.23967 
 9.24039 
 9.24110 
 9.24181 
 9.24253 
 
 72 
 71 
 71 
 
 72 
 
 9.24632 
 9.24706 
 9.24779 
 9.24853 
 9.24926 
 
 74 
 73 
 
 74 
 73 
 
 0.75368 
 0.75294 
 0.75221 
 0.75147 
 0.75074 
 
 9.99335 
 9.99333 
 9.99331 
 9.99328 
 9.99326 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 7 
 8 
 9 
 
 74 
 
 7.4 
 8.6 
 9.9 
 11 1 
 
 73 
 
 7.3 
 
 8.5 
 
 9.7 
 11 
 
 5 
 
 6 
 7 
 8 
 9 
 
 9.24324 
 9.24395 
 9.24466 
 9.24536 
 9.24607 
 
 71 
 71 
 70 
 71 
 
 9.25000 
 9.25073 
 9.25146 
 9.25219 
 9.25292 
 
 73 
 73 
 73 
 73 
 73 
 
 0.75000 
 0.74927 
 0.74854 
 0.74781 
 0.74708 
 
 9.99324 
 9.99322 
 9.99319 
 9.99317 
 9.99315 
 
 55 
 54 
 53 
 52 
 51 
 
 10 
 20 
 30 
 40 
 50 
 
 12.3 
 24.7 
 37.0 
 49.3 
 61.7 
 
 12.2 
 24.3 
 36.5 
 48.7 
 60.8 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.24677 
 9.24748 
 9.24818 
 9.24888 
 9.24958 
 
 71 
 70 
 70 
 70 
 70 
 
 9.25365 
 9.25437 
 9.25510 
 9.25582 
 9.25655 
 
 72 
 73 
 72 
 73 
 72 
 
 0.74635 
 0.74563 
 0.74490 
 0.74418 
 0.74346 
 
 9.99313 
 9.99310 
 9.99308 
 9.99306 
 9.99304 
 
 50 
 
 49 
 48 
 47 
 46 
 
 6 
 
 7 
 8 
 
 g 
 
 72 
 
 7.2 
 
 8.4 
 9.6 
 10 8 
 
 71 
 7.1 
 
 8.3 
 9.5 
 
 10 7 
 
 15 
 16 
 17 
 18 
 19 
 
 9.25028 
 9.25098 
 9.25168 
 9.25237 
 9.25307 
 
 70 
 70 
 69 
 70 
 
 9.25727 
 9.25799 
 9.25871 
 9.25943 
 9.26015 
 
 72 
 72 
 72 
 72 
 71 
 
 0.74273 
 0.74201 
 0.74129 
 0.74057 
 0.73985 
 
 9.99301 
 9.99299 
 9.99297 
 9.99294 
 9.99292 
 
 45 
 44 
 43 
 42 
 41 
 
 10 
 20 
 30 
 40 
 50 
 
 12.0 
 24.0 
 36.0 
 48.0 
 600 
 
 11.8 
 23.7 
 35.5 
 47.3 
 59.2 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.25376 
 9.25445 
 9.25514 
 9.25583 
 9.25652 
 
 69 
 69 
 69 
 69 
 
 fiQ 
 
 9.26086 
 9.26158 
 9.26229 
 9.26301 
 9.26372 
 
 72 
 71 
 72 
 71 
 
 0.73914 
 0.73842 
 0.73771 
 0.73699 
 0.73628 
 
 9.99290 
 9.99288 
 9.99285 
 9.99283 
 9.99281 
 
 40 
 
 39 
 38 
 37 
 36 
 
 6 
 
 7 
 8 
 
 70 
 
 7.0 
 8.2 
 9.3 
 
 69 
 
 6.9 
 8.1 
 9.2 
 
 25 
 26 
 
 27 
 28 
 29 
 
 9.25721 
 9.25790 
 9.25858 
 9.25927 
 9.25995 
 
 69 
 68 
 69 
 68 
 
 fiS 
 
 9.26443 
 9.26514 
 9.26585 
 9.26655 
 9.26726 
 
 71 
 71 
 70 
 71 
 71 
 
 0.73557 
 0.73486 
 0.73415 
 0.73345 
 0.73274 
 
 9.99278 
 9.99276 
 9.99274 
 9.99271 
 9.99269 
 
 35 
 34 
 33 
 32 
 31 
 
 10 
 20 
 30 
 40 
 50 
 
 11.7 
 23.3 
 35.0 
 46.7 
 583 
 
 10.4 
 11.5 
 23.0 
 34.5 
 46.0 
 575 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.26063 
 9.26131 
 9.26199 
 9.26267 
 9.26335 
 
 68 
 68 
 68 
 68 
 68 
 
 9.26797 
 9.26867 
 9.26937 
 9.27008 
 9.27078 
 
 70 
 70 
 71 
 70 
 70 
 
 0.73203 
 0.73133 
 0.73063 
 0.72992 
 0.72922 
 
 9.99267 
 9.99264 
 9.99262 
 9.99260 
 9.99257 
 
 30 
 
 29 
 28 
 27 
 26 
 
 6 
 
 7 
 . 8 
 
 68 
 
 6.8 
 7.9 
 9.1 
 
 67 
 
 6.7 
 7.8 
 8.9 
 
 35 
 36 
 37 
 38 
 39 
 
 9.26403 
 9.26470 
 9.26538 
 9.26605 
 9.26672 
 
 67 
 68 
 67 
 67 
 fi7 
 
 9.27148 
 9.27218 
 9.27288 
 9.27357 
 9.27427 
 
 70 
 70 
 69 
 
 70 
 
 0.72852 
 0.72782 
 0.72712 
 0.72643 
 0.72573 
 
 9.99255 
 9.99252 
 9.99250 
 9.99248 
 9.99245 
 
 25 
 24 
 23 
 22 
 21 
 
 9 
 10 
 20 
 30 
 40 
 
 CA 
 
 10.2 
 11.3 
 22.7 
 34.0 
 45.3 
 
 Kfi 7 
 
 10.1 
 11.2 
 22.3 
 33.5 
 44.7 
 
 CC Q 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.26739 
 9.26806 
 9.26873 
 9.26940 
 9.27007 
 
 67 
 67 
 67 
 67 
 fifi 
 
 9.27496 
 9.27566 
 9.27635 
 9.27704 
 9.27773 
 
 70 
 69 
 69 
 69 
 fiO 
 
 0.72504 
 0.72434 
 0.72365 
 0.72296 
 0.72227 
 
 9.99243 
 9.99241 
 9.99238 
 9.99236 
 9.99233 
 
 20 
 
 19 
 18 
 17 
 16 
 
 6 
 
 7 
 8 
 
 66 
 
 6.6 
 
 7.7 
 8.8 
 
 65 
 
 6.5 
 
 7.6 
 8.7 
 
 45 
 46 
 
 47 
 48 
 49 
 
 9.27073 
 9.27140 
 9.27206 
 9.27273 
 9.27339 
 
 67 
 66 
 67 
 66 
 66 
 
 9.27842 
 9.27911 
 9.27980 
 9.28049 
 9.28117 
 
 69 
 69 
 69 
 68 
 fiQ 
 
 0.72158 
 0.72089 
 0.72020 
 0.71951 
 0.71883. 
 
 9.99231 
 9.99229 
 9.99226 
 9.99224 
 9.99221 
 
 15 
 14 
 13 
 12 
 11 
 
 9 
 
 10 
 20 
 30 
 40 
 
 9.9 
 11.0 
 22.0 
 33.0 
 44.0 
 
 9.8 
 10.8 
 21.7 
 32.5 
 43.3 
 
 50 
 
 51 
 62 
 53 
 54 
 
 9.27405 
 9.27471 
 9.27537 
 9.27602 
 9.27668 
 
 66 
 66 
 65 
 66 
 66 
 
 9.28186 
 9.28254 
 9.28323 
 9.28391 
 9.28459 
 
 68 
 69 
 68 
 68 
 68 
 
 0.71814 
 0.71746 
 0.71677 
 0.71609 
 0.71541 
 
 9.99219 
 9.99217 
 9.99214 
 9.99212 
 9.99209 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 
 
 7 
 8 
 
 3 
 
 0.3 
 0.4 
 0.4 
 
 2 
 
 0.2 
 0.2 
 0.3 
 
 55 
 56 
 57 
 58 
 59 
 
 9.27734 
 9.27799 
 9.27864 
 9.27930 
 9.27995 
 
 65 
 65 
 66 
 65 
 
 9.28527 
 9.28595 
 9.28662 
 9.28730 
 9.28798 
 
 68 
 67 
 68 
 
 68 
 
 f\7 
 
 0.71473 
 0.71405 
 0.71338 
 0.71270 
 0.71202 
 
 9.99207 
 9.99204 
 9.99202 
 9.99200 
 9.99197 
 
 5 
 4 
 3 
 2 
 1 
 
 9 
 10 
 10 
 30 
 40 
 
 0.5 
 0.5 
 1.0 
 1.5 
 2.0 
 
 0.3 
 0.3 
 0.7 
 1.0 
 1.3 
 
 60 
 
 9.28060 
 
 
 9.28865 
 
 
 0.71135 
 
 9.99195 
 
 
 
 50 
 
 2.5 
 
 1.7 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 / 
 
 
 P. P 
 
 
 79 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 11 
 
 ' 
 
 L. Sin. 
 
 d. 
 
 L. Tang. 
 
 d. c. JL. Cotg. 
 
 L. Cos. 
 
 
 P.P. 
 
 
 
 1 
 
 3 
 4 
 
 9.28060 
 9.28125 
 9.28190 
 9.28254 
 9.28319 
 
 65 
 65 
 64 
 65 
 65 
 
 64 
 64 
 65 
 
 8 
 
 64 
 64 
 63 
 64 
 64 
 63 
 63 
 64 
 63 
 63 
 63 
 63 
 63 
 62 
 63 
 62 
 63 
 62 
 62 
 63 
 62 
 62 
 61 
 62 
 62 
 61 
 62 
 61 
 62 
 61 
 61 
 61 
 61 
 61 
 61 
 60 
 61 
 60 
 61 
 60 
 61 
 60 
 60 
 60 
 60 
 59 
 60 
 60 
 59 
 60 
 
 9.28865 
 9.28933 
 9.29000 
 9.29067 
 9.29134 
 
 68 
 67 
 67 
 67 
 67 
 
 67 
 67 
 67 
 
 if 
 
 66 
 67 
 66 
 66 
 66 
 66 
 66 
 66 
 66 
 65 
 66 
 65 
 65 
 66 
 65 
 65 
 66 
 65 
 65 
 64 
 65 
 64 
 65 
 64 
 64 
 65 
 64 
 64 
 64 
 64 
 63 
 64 
 63 
 64 
 63 
 64 
 63 
 63 
 63 
 63 
 63 
 63 
 63 
 62 
 63 
 62 
 63 
 62 
 62 
 62 
 
 0.71135 
 0.71007 
 0.71000 
 0.70933 
 0.70866 
 
 9.99195 
 9.99192 
 9.99190 
 9.99187 
 9.99185 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 68 
 
 6.8 
 7.9 
 9.1 
 10.2 
 11.3 
 22.7 
 34.0 
 45.3 
 56.7 
 
 66 
 
 6.6 
 7.7 
 8.8 
 9.9 
 11.0 
 22.0 
 33.0 
 44.0 
 55.0 
 
 64 
 
 6.4 
 7.5 
 8.5 
 9.6 
 10.7 
 21.3 
 32.0 
 42.7 
 53.3 
 
 62 
 
 6.2 
 7.2 
 8.3 
 9.3 
 10.3 
 20.7 
 31.0 
 41.3 
 51.7 
 
 60 
 
 6.0 
 7.0 
 8.0 
 9.0 
 10.0 
 20.0 
 30.0 
 40.0 
 50.0 
 
 3 
 
 0.3 
 0.4 
 0.4 
 0.5 
 0.5 
 1.0 
 1.5 
 2.0 
 2.5 
 
 67 
 
 6.7 
 7.8 
 8.9 
 10.1 
 11.2 
 22.3 
 33.5 
 44.7 
 55.8 
 
 65 
 
 6.5 
 7.6 
 8.7 
 9.8 
 10.8 
 21.7 
 3L.5 
 43.3 
 54.2 
 
 63 
 
 6.3 
 7.4 
 8.4 
 9.5 
 10.5 
 21.0 
 31.5 
 42.0 
 52.5 
 
 61 
 
 6.1 
 7.1 
 8.1 
 9.2 
 10.2 
 20.3 
 30.5 
 40.7 
 50.8 
 
 59 
 
 5.9 
 6.9 
 7.9 
 8.9 
 9.8 
 19.7 
 29.5 
 39.3 
 49.2 
 
 2 
 
 0.2 
 0.2 
 0.3 
 0.3 
 0.3 
 0.7 
 1.0 
 1.3 
 1.7 
 
 5 
 
 6 
 
 7 
 8 
 9 
 
 9.28384 
 9.28448 
 9.28512 
 9.28577 
 9.28641 
 
 9.29201 
 9.29268 
 9.29335 
 9.29402 
 9.29468 
 
 0.70799 
 0.70732 
 0.70665 
 0.70598 
 0.70532 
 
 9.99182 
 9.99180 
 9.99177 
 9.99175 
 9.99172 
 
 55 
 54 
 53 
 52 
 51 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.28705 
 9.28769 
 9.28833 
 9.28896 
 9.28960 
 
 9.29535 
 9.29601 
 9.29668 
 9.29734 
 9.29800 
 
 0.70465 
 0.70399 
 0.70332 
 0.70266 
 0.70200 
 
 9.99170 
 9.99167 
 9.99165 
 9.99162 
 9.99160 
 
 50 
 
 49 
 48 
 47 
 46 
 
 15 
 16 
 17 
 18 
 19 
 
 9.29024 
 9.29087 
 9.29150 
 9.29214 
 9.29277 
 
 9.29866 
 9.29932 
 9.29998 
 9.30064 
 9.30130 
 
 0.70134 
 0.70068 
 0.70002 
 0.69936 
 0.69870 
 
 9.99157 
 9.99155 
 9.99152 
 9.99150 
 9.99147 
 
 45 
 44 
 43 
 42 
 41 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.29340 
 9.29403 
 9.29466 
 9.29529 
 9.29591 
 
 9.30195 
 9.30261 
 9.30326 
 9.30391 
 9.30457 
 
 0.69805 
 0.69739 
 0.69674 
 0.69609 
 0.69543 
 
 9.99145 
 9.99142 
 9.99140 
 9.99137 
 9.99135 
 
 40 
 
 39 
 38 
 37 
 36 
 
 25 
 26 
 27 
 28 
 29 
 
 9.29654 
 9.29716 
 9.29779 
 9.29841 
 9.29903 
 
 9.30522 
 9.30587 
 9.30652 
 9.30717 
 9.30782 
 
 0.69478 
 0.69413 
 0.69348 
 0.69283 
 0.69218 
 
 9.99132 
 9.99130 
 9.99127 
 9.99124 
 9.99122 
 
 35 
 34 
 33 
 32 
 31 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.29966 
 9.30028 
 9.30090 
 9.30151 
 9.30213 
 
 9.30846 
 9.30911 
 9.30975 
 9.31040 
 9.31104 
 
 0.69154 
 0.69089 
 0.69025 
 0.68960 
 0.68896 
 
 9.99119 
 9.99117 
 9.99114 
 9.99112 
 9.99109 
 
 30 
 
 29 
 28 
 27 
 26 
 
 35 
 36 
 37 
 38 
 39 
 
 40 
 
 41 
 42 
 43 
 44 
 45 
 46 
 47 
 48 
 49 
 50 
 51 
 52 
 53 
 54 
 55 
 56 
 57 
 58 
 59 
 60 
 
 9.30275 
 9.30336 
 9.30398 
 9.30459 
 9.30521 
 
 9.31168 
 9.31233 
 9.31297 
 9.31361 
 9.31425 
 
 0.68832 
 0.68767 
 0.68703 
 0.68639 
 0.68575 
 
 9.99106 
 9.99104 
 9.99101 
 9.99099 
 9.99096 
 
 25 
 24 
 23 
 22 
 21 
 20 
 19 
 18 
 17 
 16 
 
 9.30582 
 9.30643 
 9.30704 
 9.30765 
 9.30826 
 
 9.31489 
 9.31552 
 9.3161C 
 9.31679 
 9.31743 
 
 0.68511 
 0.68448 
 0.68384 
 0.68321 
 0.68257 
 
 9.99093 
 9.99091 
 9.99088 
 9.99086 
 9.99083 
 
 9.30887 
 9.30947 
 9.31008 
 9.31068 
 9.31129 
 
 9.31806 
 9.31870 
 9.31933 
 9.31996 
 9.32059 
 
 0.68194 
 0.68130 
 0.68067 
 0.68004 
 0.67941 
 
 9.99080 
 9.99078 
 9.99075 
 9.99072 
 9.99070 
 
 15 
 14 
 13 
 12 
 11 
 
 9.31189 
 9.31250 
 9.31310 
 9.31370 
 9.31430 
 
 9.32122 
 9.32185 
 9.32248 
 9.32311 
 9.32373 
 
 0.67878 
 0.67815 
 0.67752 
 0.67689 
 0.67627 
 
 9.99067 
 9.99064 
 9.99062 
 9.99059 
 9.99056 
 
 10 
 
 9 
 8 
 7 
 6 
 
 9.31490 
 9.31549 
 9.31609 
 9.31669 
 9.31728 
 
 9.32436 
 9.32498 
 9.32561 
 9.32623 
 9.32685 
 9.32747 
 
 0.67564 
 0.67502 
 0.67439 
 0.67377 
 0.67315 
 
 9.99054 
 9.99051 
 9.99048 
 9.99046 
 9.99043 
 
 5 
 4 
 3 
 2 
 1 
 
 T 
 
 9.31788 
 
 0.67253 
 
 9.99040 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d. c. L.Tang. 
 
 L. Sin. 
 
 / 
 
 P.P. 
 
 76 C 
 
1040 
 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 12 
 
 1 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d. c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 
 P.P. 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.31788 
 9.31847 
 9.31907 
 9.31966 
 9.32025 
 
 59 
 60 
 59 
 59 
 59 
 59 
 59 
 59 
 58 
 59 
 59 
 58 
 58 
 59 
 58 
 58 
 58 
 58 
 58 
 58 
 58 
 57 
 58 
 57 
 58 
 57 
 57 
 58 
 57 
 57 
 57 
 56 
 57 
 57 
 57 
 56 
 57 
 56 
 56 
 57 
 56 
 56 
 56 
 56 
 56 
 56 
 55 
 56 
 55 
 56 
 55 
 56 
 55 
 55 
 55 
 55 
 55 
 55 
 55 
 55 
 
 9.32747 
 9.32810 
 9.32872 
 9.32933 
 9.32995 
 
 63 
 62 
 61 
 62 
 62 
 62 
 61 
 62 
 61 
 62 
 61 
 61 
 61 
 61 
 61 
 61 
 61 
 61 
 60 
 61 
 60 
 61 
 60 
 60 
 61 
 60 
 60 
 60 
 60 
 60 
 59 
 60 
 60 
 59 
 60 
 59 
 59 
 59 
 60 
 59 
 59 
 59 
 59 
 58 
 59 
 59 
 58 
 59 
 58 
 59 
 58 
 58 
 58 
 58 
 58 
 58 
 58 
 58 
 58 
 57 
 
 0.67253 
 0.67190 
 0.67128 
 0.67067 
 0.67005 
 
 9.99040 
 9.99038 
 9.99035 
 9.99032 
 9.99030 
 
 60 
 
 59 
 
 58 
 57 
 56 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 ' 50 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 63 
 
 6.3 
 7.4 
 8.4 
 9.5 
 10.5 
 21.0 
 31.5 
 42.0 
 52.5 
 
 61 
 
 6.1 
 7.1 
 8.1 
 9.2 
 10.2 
 20.3 
 30.5 
 40.7 
 50.8 
 
 5 
 6 f 
 7 ( 
 8 \ 
 9 I 
 10 < 
 20 IS 
 30 2< 
 40 ' 3< 
 50 4< 
 
 58 
 
 5.8 
 6.8 
 7.7 
 8.7 
 9.7 
 19.3 
 29.0 
 38.7 
 48.3 
 
 56 
 
 5.6 
 6.5 
 7.5 
 8.4 
 9.3 
 18.7 
 28.0 
 37.3 
 46.7 
 
 3 
 
 1 0.3 
 0.4 
 0.4 
 0.5 
 0.5 
 1.0 
 1.5 
 2.0 
 2.5 
 
 62 
 
 6.2 
 7.2 
 8.3 
 9.3 
 10.3 
 20.7 
 31.0 
 41.3 
 51.7 
 
 60 
 
 6.0 
 7.0 
 8.0 
 9.0 
 10.0 
 20.0 
 30.0 
 40.0 
 50.0 
 
 9 
 >.9 
 >.9 
 .9 
 !.9 
 1.8 
 ).7 
 >.5 
 1.3 
 >.2 
 
 57 
 5.7 
 
 6.7 
 7.6 
 8.6 
 9.5 
 19.0 
 28.5 
 38.0 
 47.5 
 
 55 
 
 5.5 
 
 6.4 
 7.3 
 
 8.3 
 9.2 
 
 18.3 
 27.5 
 36.7 
 45.8 
 
 2 
 
 0.2 
 0.2 
 0.3 
 0.3 
 0.3 
 0.7 
 1.0 
 1.3 
 1.7 
 
 5 
 6 
 7 
 8 
 9 
 10 
 11 
 12 
 13 
 14 
 
 9.32084 
 9.32143 
 9.32202 
 9.32261 
 9.32319 
 
 9.33057 
 9.33119 
 9.33180 
 9.33242 
 9.33303 
 
 0.66943 
 0.66881 
 0.66820 
 0.66758 
 0.66697 
 
 9.99027 
 9.99024 
 9.99022 
 9.99019 
 9.99016 
 
 55 
 54 
 53 
 52 
 51 
 
 9.32378 
 9.32437 
 9.32495 
 9.32553 
 9.32612 
 
 9.33365 
 9.33426 
 9.33487 
 9.33548 
 9.33609 
 
 0.66635 
 0.66574 
 0.66513 
 0.66452 
 0.66391 
 
 9.99013 
 9.99011 
 9.99008 
 9.99005 
 9.99002 
 
 50 
 
 49 
 48 
 47 
 46 
 
 15 
 16 
 17 
 18 
 19 
 
 9.32670 
 9.32728 
 9.32786 
 9.32844 
 9.32902 
 
 9.33670 
 9.33731 
 9.33792 
 9.33853 
 9.33913 
 
 0.66330 
 0.66269 
 0.66208 
 0.66147 
 0.66087 
 
 9.99000 
 9.98997 
 9.98994 
 9.98991 
 9.98989 
 
 45 
 44 
 43 
 42 
 41 
 
 20 
 
 21 
 22 
 23 
 24 
 ~25~ 
 26 
 27 
 28 
 29 
 
 9.32960 
 9.33018 
 9.33075 
 9.33133 
 9.33190 
 
 9.33974 
 9.34034 
 9.34095 
 9.34155 
 9.34215 
 
 0.66026 
 0.65966 
 0.65905 
 0.65845 
 0.65785 
 
 9.98986 
 9.98983 
 9.98980 
 9.98978 
 9.98975 
 
 40 
 
 39 
 38 
 37 
 36 
 35 
 34 
 33 
 32 
 31 
 
 9.33248 
 9.33305 
 9.33362 
 9.33420 
 9.33477 
 
 9.34276 
 9.34336 
 9.343% 
 9.34456 
 9.34516 
 
 0.65724 
 0.65664 
 0.65604 
 0.65544 
 0.65484 
 
 9.98972 
 9.98969 
 9.98967 
 9.98964 
 9.98961 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.33534 
 9.33591 
 9.33647 
 9.33704 
 9.33761 
 
 9.34576 
 9.34635 
 9.34695 
 9.34755 
 9.34814 
 
 0.65424 
 0.65365 
 0.65305 
 0.65245 
 0.65186 
 
 9.98958 
 9.98955 
 9.98953 
 9.98950 
 9.98947 
 
 30 
 
 29 
 28 
 27 
 26 
 
 35 
 36 
 37 
 38 
 39 
 40 
 41 
 42 
 43 
 44 
 45 
 46 
 47 
 48 
 49 
 
 9.33818 
 9.33874 
 9.33931 
 9.33987 
 9.34043 
 
 9.34874 
 9.34933 
 9.34992 
 9.35051 
 9.35111 
 
 0.65126 
 
 0.65067 
 0.65008 
 0.64949 
 0.64889 
 
 9.98944 
 9.98941 
 9.98938 
 9.98936 
 9.98933 
 
 25 
 24 
 23 
 22 
 21 
 
 9.34100 
 9.34156 
 9.34212 
 9.34268 
 9.34324 
 
 9.35170 
 9.35229 
 9.35288 
 9.35347 
 9.35405 
 
 0.64830 
 0.64771 
 0.64712 
 0.64653 
 0.64595 
 
 9.98930 
 9.98927 
 9.98924 
 9.98921 
 9.98919 
 
 20 
 
 19 
 18 
 17 
 16 
 
 9.34380 
 9.34436 
 9.34491 
 9.34547 
 9.34602 
 
 9.35464 
 9.35523 
 9.35581 
 9.35640 
 9.35698 
 
 0.64536 
 0.64477 
 C.64419 
 0.64360 
 0.64302 
 
 9.98916 
 9.98913 
 9.98910 
 9.98907 
 9.98904 
 
 15 
 14 
 13 
 12 
 11 
 
 50 
 51 
 
 52 
 53 
 54 
 
 9.34658 
 9.34713 
 9.34769 
 9.34824 
 9.34879 
 
 9.35757 
 9.35815 
 9.35873 
 9.35931 
 9.35989 
 
 0.64243 
 0.64185 
 0.64127 
 0.64069 
 0.64011 
 
 9.98901 
 9.98898 
 9.98896 
 9.98893 
 9.98890 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 55 
 56 
 57 
 58 
 59 
 
 9.34934 
 9.34989 
 9.35044 
 9.35099 
 9.35154 
 
 9.36047 
 9.36105 
 9.36163 
 9.36221 
 9.36279 
 
 0.63953 
 0.63895 
 0.63837 
 0.63779 
 0.63721 
 
 9.98887 
 9.98884 
 9.98881 
 9.98878 
 9.98875 
 
 5 
 4 
 3 
 2 
 1 
 
 60 
 
 9.35209 
 
 9.36336 
 
 0.63664 
 
 9.98872 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d. c. 
 
 L.Tang. 
 
 L. Sin. 
 
 ' 
 
 P.P. 
 
 77 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 
 13 
 
 1041 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 
 
 P.P. 
 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 9.35209 
 9.35263 
 9.35318 
 9.35373 
 9.35427 
 
 54 
 55 
 55 
 54 
 4 
 
 9.36336 
 9.36394 
 9.36452 
 9.36509 
 9.36566 
 
 58 
 58 
 57 
 57 
 
 CO 
 
 0.63664 
 0.63606 
 0.63548 
 0.63491 
 0.63434 
 
 9.98872 
 9.98869 
 9.98867 
 9.98864 
 9.98861 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 8 
 g 
 
 58 
 
 5.8 
 6.8 
 7.7 
 87 
 
 57 
 
 5.7 
 6.7 
 7.6 
 8 6 
 
 5 
 
 6 
 7 
 8 
 9 
 
 9.35481 
 9.35536 
 9.35590 
 9.35644 
 9.35698 
 
 55 
 54 
 54 
 54 
 54 
 
 9.36624 
 9.36681 
 9.36738 
 9.36795 
 9.36852 
 
 57 
 57 
 57 
 57 
 *S7 
 
 0.63376 
 0.63319 
 0.63262 
 0.63205 
 0.63148 
 
 9.98858 
 9.98855 
 9.98852 
 9.98849 
 9.98846 
 
 55 
 54 
 53 
 52 
 51 
 
 10 
 20 
 30 
 40 
 50, 
 
 9.7 
 19.3 
 29.0 
 
 38.7 
 48.3 
 
 9.5 
 19.0 
 28.5 
 38.0 
 47.5 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.35752 
 9.35806 
 9.35860 
 9.35914 
 9.35968 
 
 54 
 54 
 54 
 54 
 
 fiA ' 
 
 9.36909 
 9.36966 
 9.37023 
 9.37080 
 9.37137 
 
 57 
 
 57 
 57 
 57 
 
 CC 
 
 0.63091 
 0.63034 
 0.62977 
 0.62920 
 0.62863 
 
 9.98843 
 9.98840 
 9.98837 
 9.98834 
 9.98831 
 
 50 
 
 49 
 48 
 47 
 46 
 
 6 
 
 7 
 8 
 
 g 
 
 56 
 
 5.6 
 6.5 
 7.5 
 
 Q A, 
 
 55 
 
 5.5 
 6.4 
 7.3 
 
 
 
 15 
 16 
 17 
 
 18 
 19 
 
 9.36022 
 9.36075 
 9.36129 
 9.36182 
 9.36236 
 
 53 
 54 
 53 
 54 
 
 RQ 
 
 9.37193 
 9.37250 
 9.37306 
 9.37363 
 9.37419 
 
 57 
 56 
 57 
 56 
 
 PS] 
 
 0.62807 
 0.62750 
 0.62694 
 0.62637 
 0.62581 
 
 9.98828 
 9.98825 
 9.98822 
 9.98819 
 9.98816 
 
 45 
 44 
 43 
 42 
 41 
 
 10 
 
 20 
 30 
 40 
 50 
 
 9.3 
 18.7 
 28.0 
 37.3 
 46.7 
 
 9.2 
 18.3 
 
 27.5 
 36.7 
 45.8 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.36289 
 9.36342 
 9.36395 
 9.36449 
 9.36502 
 
 53 
 53 
 54 
 53 
 
 9.37476 
 9.37532 
 9.37588 
 9.37644 
 9.37700 
 
 56 
 56 
 56 
 56 
 
 0.62524 
 0.62468 
 0.62412 
 0.62356 
 0.62300 
 
 9.98813 
 9.98810 
 9.98807 
 9.98804 
 9.98801 
 
 40 
 
 39 
 38 
 37 
 36 
 
 
 5 
 
 6 G 
 7 C 
 8 7 
 
 4 
 .4 
 .3 
 .2 
 
 25 
 26 
 27 
 28 
 29 
 
 9.36555 
 9.36608 
 9.36660 
 9.36713 
 9.36766 
 
 53 
 52 
 53 
 53 
 
 9.37756 
 9.37812 
 9.37868 
 9.37924 
 9.37980 
 
 56 
 56 
 
 56 
 56 
 
 0.62244 
 0.62188 
 0.62132 
 0.62076 
 0.62020 
 
 9.98798 
 9.98795 
 9.98792 
 9.98789 
 9.98786 
 
 35 
 34 
 33 
 32 
 31 
 
 
 1C 
 20 1 
 30 2" 
 40 3( 
 50 4f 
 
 .0 
 
 .0 
 .0 
 .0 
 
 >.o 
 
 30 
 
 31 
 32 
 33 
 
 34 
 
 9.36819 
 9.36871 
 9.36924 
 9.36976 
 9.37028 
 
 52 
 53 
 52 
 52 
 
 9.38035 
 9.38091 
 9.38147 
 9.38202 
 9.38257 
 
 56 
 56 
 55 
 55 
 
 fSft 
 
 0.61965 
 0.61909 
 0.61853 
 0.61798 
 0.61743 
 
 9.98783 
 9.98780 
 9.98777 
 9.98774 
 9.98771 
 
 30 
 
 29 
 28 
 27 
 26 
 
 6 
 
 7 
 8 
 
 53 
 
 5.3 
 6.2 
 7.1 
 
 52 
 
 5.2 
 6.1 
 6.9 
 
 35 
 36 
 37 
 38 
 39 
 
 9.37081 
 9.37133 
 9.37185 
 9.37237 
 9.37289 
 
 52 
 52 
 52 
 52 
 
 eo 
 
 9.38313 
 9.38368 
 9.38423 
 9.38479 
 9.38534 
 
 55 
 55 
 56 
 55 
 FA 
 
 0.61687 
 0.61632 
 0.61577 
 0.61521 
 0.61466 
 
 9.98768 
 9.98765 
 9.98762 
 9.98759 
 9.98756 
 
 25 
 24 
 23 
 22 
 21 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 8.0 
 8.8 
 17.7 
 26.5 
 35.3 
 442 
 
 7.8 
 8.7 
 17.3 
 26.0 
 34.7 
 433 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.37341 
 9.37393 
 9.37445 
 9.37497 
 9.37549 
 
 52 
 
 52 
 52 
 52 
 
 9.38589 
 9.38644 
 9.38699 
 9.38754 
 9.38808 
 
 55 
 55 
 55 
 54 
 
 KK 
 
 0.61411 
 0.61356 
 0.61301 
 0.61246 
 0.61192 
 
 9.98753 
 9.98750 
 9.98746 
 9.98743 
 9.98740 
 
 20 
 
 19 
 18 
 17 
 16 
 
 6 
 
 7 
 8 
 
 51 
 
 5.1 
 6.0 
 
 6.8 
 
 4 
 0.4 
 0.5 
 0.5 
 
 45 
 46 
 47 
 48 
 49 
 
 9.37600 
 9.37652 
 9.37703 
 9.37755 
 9.37806 
 
 52 
 51 
 52 
 51 
 
 9.38863 
 9.38918 
 9.38972 
 9.39027 
 9.39082 
 
 55 
 54 
 55 
 55 
 
 0.61137 
 0.61082 
 0.61028 
 0.60973 
 0.60918 
 
 9.98737 
 9.98734 
 9.98731 
 
 9.98728 
 9.98725 
 
 15 
 14 
 13 
 12 
 11 
 
 9 
 10 
 20 
 30 
 40 
 F:A 
 
 V.V 
 8.5 
 17.0 
 25.5 
 34.0 
 
 49 S 
 
 0.6 
 0.7 
 1.3 
 2.0 
 2.7 
 
 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.37858 
 9.37909 
 9.37960 
 9.38011 
 9.38062 
 
 51 
 51 
 51 
 51 
 
 M 
 
 9.39136 
 9.39190 
 9.39245 
 9.39299 
 9.39353 
 
 54 
 55 
 
 54 
 54 
 54 
 
 0.60864 
 0.60810 
 0.60755 
 0.60701 
 0.60647 
 
 9.98722 
 9.98719 
 9.98715 
 9.98712 
 9.98709 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 
 7 
 8 
 
 3 
 
 0.3 
 0.4 
 0.4 
 
 2 
 
 0.2 
 0.2 
 0.3 
 
 55 
 
 56 
 57 
 58 
 59 
 
 9.38113 
 9.38164 
 9.38215 
 
 9.38266 
 9.38317 
 
 51 
 51 
 51 
 51 
 
 9.39407 
 9.39461 
 9.39515 
 9.39569 
 9.39623 
 
 54 
 54 
 54 
 54 
 fv4 
 
 0.60593 
 0.60539 
 0.60485 
 0.60431 
 0.60377 
 
 9.98706 
 9.98703 
 9.98700 
 9.98697 
 9.98694 
 
 5 
 4 
 3 
 2 
 1 
 
 S 
 1C 
 2C 
 3C 
 
 .4C 
 
 O.b 
 0.5 
 1.0 
 1.5 
 2.0 
 
 0.3 
 0.3 
 0.7 
 1.0 
 1.3 
 
 60 
 
 9.38368 
 
 
 9.39677 
 
 
 0.60323 
 
 9.98690 
 
 
 
 
 
 
 
 L.Cos 
 
 d 
 
 L. Cotg 
 
 do. 
 
 L.Tang 
 
 L. Sin. 
 
 / 
 
 
 P. I 
 
 i 
 
 
 66 
 
 
 
 
 76 
 
 
 
 
 
 
1042 
 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 14 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d. c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 
 P.P 
 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 9.38368 
 9.38418 
 9.38469 
 9.38519 
 9.38570 
 
 50 
 51 
 50 
 51 
 50 
 
 9.39677 
 9.39731 
 9.39785 
 9.39838 
 9.39892 
 
 54 
 54 
 53 
 54 
 53 
 
 0.60323 
 0.60269 
 0.60215 
 0.60162 
 0.60108 
 
 9.98690 
 9.98687 
 9.98684 
 9.98681 
 9.98678 
 
 3 
 
 3 
 3 
 3 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 7 
 
 54 
 
 5.4 
 6 3 
 
 53 
 
 5.3 
 
 6 2 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.38620 
 9.38670 
 9.38721 
 9.38771 
 9.38821 
 
 50 
 51 
 50 
 50 
 
 en 
 
 9.39945 
 9.39999 
 9.40052 
 9.40106 
 9.40159 
 
 54 
 
 53 
 54 
 53 
 
 KO 
 
 0.60055 
 0.60001 
 0.59948 
 0.59894 
 0.59841 
 
 9.98675 
 9.98671 
 9.98668 
 9.98665 
 9.98662 
 
 4 
 3 
 3 
 3 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 7.2 
 8.1 
 9.0 
 18.0 
 27.0 
 
 7!l 
 8.0 
 8.8 
 17.7 
 26.5 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.38871 
 9.38921 
 9.38971 
 9.39021 
 9.39071 
 
 50 
 50 
 50 
 50 
 *so 
 
 9.40212 
 9.40266 
 9.40319 
 9.40372 
 9.40425 
 
 54 
 53 
 53 
 53 
 
 to 
 
 0.59788 
 0.59734 
 0.59681 
 0.59628 
 0.59575 
 
 9.98659 
 9.98656 
 9.98652 
 9.98649 
 9.98646 
 
 3 
 4 
 3 
 3 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 36.0 
 45.0 
 
 ft? 
 
 35.3 
 44.2 
 
 51 
 
 15 
 16 
 17 
 18 
 19 
 
 9.39121 
 9.39170 
 9.39220 
 9.39270 
 9.39319 
 
 49 
 50 
 50 
 49 
 
 9.40478 
 9.40531 
 9.40584 
 9.40636 
 9.40689 
 
 53 
 
 53 
 52 
 53 
 
 0.59522 
 0.59469 
 0.59416 
 0.59364 
 0.59311 
 
 9.98643 
 9.98640 
 9.98636 
 9.98633 
 9.98630 
 
 3 
 4 
 3 
 3 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 7 
 8 
 9 
 10 
 
 5.2 
 6.1 
 6.9 
 
 7.8 
 8.7 
 
 5.1 
 6.0 
 6.8 
 7.7 
 8.5 
 
 ZO 
 
 21 
 22 
 23 
 24 
 
 9.39369 
 9.39418 
 9.39467 
 9.39517 
 9.39566 
 
 49 
 49 
 50 
 49 
 
 9.40742 
 9.40795 
 9.40847 
 9.40900 
 9.40952 
 
 53 
 52 
 53 
 52 
 
 KQ 
 
 0.59258 
 0.59205 
 0.59153 
 0.59100 
 0.59048 
 
 9.98627 
 9.98623 
 9.98620 
 9.98617 
 9.98614 
 
 4 
 3 
 3 
 3 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 IV. 3 
 26.0 
 34.7 
 43.3 
 
 17.0 
 25.5 
 34.0 
 42.5 
 
 25 
 26 
 27 
 28 
 29 
 
 9.39615 
 9.39664 
 9.39713 
 9.39762 
 9.39811 
 
 49 
 49 
 49 
 49 
 
 AQ 
 
 9.41005 
 9.41057 
 9.41109 
 9.41161 
 9.41214 
 
 52 
 
 52 
 52 
 53 
 
 KO 
 
 0.58995 
 0.58943 
 0.58891 
 0.58839 
 0.58786 
 
 9.98610 
 9.98607 
 9.98604 
 9.98601 
 9.98597 
 
 3 
 3 
 3 
 
 4 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 50 
 
 5.0 
 
 5.8 
 6.7 
 
 49 
 
 4.9 
 5.7 
 6.5 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.39860 
 9.39909 
 9.39958 
 9.40006 
 9.40055 
 
 49 
 49 
 48 
 49 
 
 48 
 
 9.41266 
 9.41318 
 9.41370 
 9.41422 
 9.41474 
 
 52 
 52 
 52 
 52 
 52 
 
 0.58734 
 0.58682 
 0.58630 
 0.58578 
 0.58526 
 
 9.98594 
 9.98591 
 9.98588 
 9.98584 
 9.98581 
 
 3 
 3 
 4 
 3 
 3 
 
 30 
 
 29 
 28 
 27 
 26 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 7.5 
 8.3 
 16.7 
 25.0 
 33.3 
 41 7 
 
 7.4 
 8.2 
 16.3 
 24.5 
 32.7 
 40 8 
 
 35 
 36 
 37 
 38 
 39 
 
 9.40103 
 9.40152 
 9.40200 
 9.40249 
 9.40297 
 
 49 
 48 
 49 
 48 
 
 9.41526 
 9.41578 
 9.41629 
 9.41681 
 9.41733 
 
 52 
 51 
 
 52 
 52 
 
 fVI 
 
 0.58474 
 0.58422 
 0.58371 
 0.58319 
 0.58267 
 
 9.98578 
 9.98574 
 9.98571 
 9.98568 
 9.98565 
 
 4 
 
 3 
 3 
 3 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 48 
 
 4.8 
 
 47 
 
 4.7 
 
 c k 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.40346 
 9.40394 
 9.40442 
 9.40490 
 9.40538 
 
 48 
 48 
 48 
 48 
 
 9.41784 
 9.41836 
 9.41887 
 9.41939 
 9.41990 
 
 52 
 51 
 52 
 51 
 
 ft1 
 
 0.58216 
 0.58164 
 0.58113 
 0.58061 
 0.58010 
 
 9.98561 
 9.98558 
 9.98555 
 9.98551 
 9.98548 
 
 3 
 3 
 
 4 
 3 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 6.4 
 7.2 
 8.0 
 16.0 
 MO 
 
 6.3 
 7.1 
 
 7.8 
 15.7 
 23.5 
 
 45 
 46 
 47 
 48 
 49 
 
 9.40586 
 9.40634 
 9.40682 
 9.40730 
 9.40778 
 
 48 
 48 
 48 
 48 
 47 
 
 9.42041 
 9.42093 
 9.42144 
 9.42195 
 9.42246 
 
 52 
 51 
 51 
 51 
 51 
 
 0.57959 
 0.57907 
 0.57856 
 0.57805 
 0.57754 
 
 9.98545 
 9.98541 
 9.98538 
 9.98535 
 9.98531 
 
 4 
 3 
 3 
 4 
 3 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 32.0 
 40.0 
 
 4 
 
 31.3 
 39.2 
 
 3 
 
 50 
 51 
 52 
 53 
 54 
 
 9.40825 
 9.40873 
 9.40921 
 9.40968 
 9.41016 
 
 48 
 48 
 47 
 48 
 47 
 
 9.42297 
 9.42348 
 9.42399 
 9.42450 
 9.42501 
 
 51 
 51 
 51 
 51 
 61 
 
 0.57703 
 0.57652 
 0.57601 
 0.57550 
 0.57499 
 
 9.98528 
 9.98525 
 9.98521 
 9.98518 
 9.98515 
 
 3 
 
 4 
 3 
 3 
 4 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 
 7 
 8 
 9 
 10 
 
 0.4 
 0.5 
 0.5 
 0.6 
 0.7 
 
 0.3 
 0.4 
 0.4 
 0.5 
 0.5 
 
 55 
 56 
 
 57 
 58 
 59 
 
 9.41063 
 9.41111 
 9.41158 
 9.41205 
 9.41252 
 
 48 
 47 
 47 
 47 
 
 40 
 
 9.42552 
 9.42603 
 9.42653 
 9.42704 
 9.42755 
 
 51 
 50 
 51 
 51 
 
 *)Q 
 
 0.57448 
 0.57397 
 0.57347 
 0.57296 
 0.57245 
 
 9.98511 
 9.98508 
 9.98505 
 9.98501 
 9.98498 
 
 3 
 
 4 
 3 
 
 4 
 
 5 
 
 4 
 3 
 2 
 
 1 
 
 20 
 30 
 40 
 50 
 
 1.3 
 2.0 
 2.7 
 3.3 
 
 1.0 
 1.5 
 2.0 
 2.5 
 
 60 
 
 9.41300 
 
 
 9.42805 
 
 
 0.57195 
 
 9.98494 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg 
 
 d. c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 / 
 
 
 P.P 
 
 
 75 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 15 
 
 1043 
 
 1 
 
 L. Sin. 
 
 d. 
 
 L.Tang 
 
 d.c. 
 
 L. Cotg 
 
 L. Cos. 
 
 d. 
 
 
 
 P. P 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.41300 
 9.41347 
 9.41394 
 9.41441 
 9.41488 
 
 47 
 47 
 47 
 47 
 47 
 
 9.42805 
 9.42856 
 9.42906 
 9.42957 
 9.43007 
 
 51 
 50 
 51 
 50 
 
 V) 
 
 0.57195 
 0.57144 
 0.57094 
 0.57043 
 0.56993 
 
 9.98494 
 9.98491 
 9.98488 
 9.98484 
 9.98481 
 
 3 
 3 
 4 
 3 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 51 
 5.1 
 
 fi 
 
 50 
 
 5.0 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.41535 
 9.41582 
 9.41628 
 9.41675 
 9.41722 
 
 47 
 46 
 47 
 47 
 46 
 
 9.43057 
 9.43108 
 9.43158 
 9.43208 
 9.43258 
 
 51 
 50 
 50 
 50 
 50 
 
 0.56943 
 0.56892 
 0.56842 
 0.56792 
 0.56742 
 
 9.98477 
 9.98474 
 9.98471 
 9.98467 
 9.98464 
 
 3 
 3 
 4 
 3 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 
 10 
 20 
 30 
 
 6.8 
 7.7 
 8.5 
 17.0 
 25.5 
 
 6.7 
 7.5 
 8.3 
 16.7 
 25.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.41768 
 9.41815 
 9.41861 
 9.41908 
 9.41954 
 
 47 
 46 
 47 
 46 
 47 
 
 9.43308 
 9.43358 
 9.43408 
 9.43458 
 9.43508 
 
 50 
 50 
 50 
 50 
 
 PLf) 
 
 0.56692 
 0.56642 
 0.56592 
 0.56542 
 0.56492 
 
 9.98460 
 9.98457 
 9.98453 
 9.98450 
 9.98447 
 
 3 
 4 
 3 
 3 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 34.0 
 42.5 
 
 49 
 
 33.3 
 41.7 
 
 48 
 
 15 
 16 
 17 
 18 
 19 
 
 9.42001 
 9.42047 
 9.42093 
 9.42140 
 9.42186 
 
 46 
 46 
 47 
 46 
 
 4fi 
 
 9.43558 
 9.43607 
 9.43657 
 9.43707 
 9.43756 
 
 49 
 50 
 50 
 49 
 
 0.56442 
 0.56393 
 0.56343 
 0.56293 
 0.56244 
 
 9.98443 
 9.98440 
 9.98436 
 9.98433 
 9.98429 
 
 3 
 4 
 3 
 
 4 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 7 
 8 
 9 
 10 
 
 4.9 
 5.7 
 6.5 
 7.4 
 8.2 
 
 4.8 
 5.6 
 6.4 
 7.2 
 8.0 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.42232 
 9.42278 
 9.42324 
 9.42370 
 9.42416 
 
 46 
 46 
 46 
 46 
 45 
 
 9.43806 
 9.43855 
 9.43905 
 9.43954 
 9.44004 
 
 49 
 50 
 49 
 50 
 4Q 
 
 0.56194 
 0.56145 
 0.56095 
 0.56046 
 0.55996 
 
 9.98426 
 9.98422 
 9.98419 
 9.98415 
 9.98412 
 
 4 
 3 
 4 
 3 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 16.3 
 24.5 
 32.7 
 40.8 
 
 16.0 
 24.0 
 32.0 
 40.0 
 
 25 
 26 
 27 
 28 
 29 
 
 9.42461 
 9.42507 
 9.42553 
 9.42599 
 9.42644 
 
 46 
 46 
 46 
 45 
 4fi 
 
 9.44053 
 9.44102 
 9.44151 
 9.44201 
 9.44250 
 
 49 
 49 
 50 
 49 
 
 0.55947 
 0.55898 
 0.55849 
 0.55799 
 0.55750 
 
 9.98409 
 9.98405 
 9.98402 
 9.98398 
 9.98395 
 
 4 
 3 
 4 
 3 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 47 
 
 4.7 
 5.5 
 6.3 
 
 46 
 
 4.6 
 5.4 
 6.1 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.42690 
 9.42735 
 9.42781 
 9.42826 
 9.42872 
 
 45 
 46 
 45 
 46 
 
 AK. 
 
 9.44299 
 9.44348 
 9.44397 
 9.44446 
 9.44495 
 
 49 
 49 
 49 
 49 
 4Q 
 
 0.55701 
 0.55652 
 0.55603 
 0.55554 
 0.55505 
 
 9.98391 
 9.98388 
 9.98384 
 9.98381 
 9.98377 
 
 3 
 4 
 3 
 
 4 
 
 4 
 
 30 
 
 29 
 28 
 27 
 26 
 
 9 
 
 10 
 20 
 30 
 40 
 50 
 
 7.1 
 7.8 
 15.7 
 23.5 
 31.3 
 392 
 
 6.9 
 7.7 
 15.3 
 23.0 
 30.7 
 38 3 
 
 35 
 36 
 37 
 38 
 39 
 
 9.42917 
 9.42962 
 9.43008 
 9.43053 
 9.43098 
 
 45 
 46 
 45 
 45 
 
 9.44544 
 9.44592 
 9.44641 
 9.44690 
 9.44738 
 
 48 
 49 
 49 
 48 
 
 0.55456 
 0.55408 
 0.55359 
 0.55310 
 0.55262 
 
 9.98373 
 9.98370 
 9.98366 
 9.98363 
 9.98359 
 
 3 
 4 
 3 
 
 4 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 45 
 
 4.5 
 
 44 
 4.4 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.43143 
 9.43188 
 9.43233 
 9.43278 
 9.43323 
 
 45 
 45 
 45 
 
 45 
 44 
 
 9.44787 
 9.44836 
 9.44884 
 9.44933 
 9.44981 
 
 49 
 48 
 49 
 
 48 
 40 
 
 0.55213 
 0.55164 
 0.55116 
 0.55067 
 0.55019 
 
 9.98356 
 9.98352 
 9.98349 
 9.98345 
 9.98342 
 
 4 
 3 
 4 
 3 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 
 9 
 10 
 20 
 30 
 
 6.0 
 6.8 
 7.5 
 15.0 
 TO.fi 
 
 5.9 
 6.6 
 7.3 
 14.7 
 22.0 
 
 45 
 
 46 
 
 47 
 48 
 49 
 
 9.43367 
 9.43412 
 9.43457 
 9.43502 
 9.43546 
 
 45 
 45 
 45 
 44 
 4c 
 
 9.45029 
 9.45078 
 9.45126 
 9.45174 
 9.45222 
 
 49 
 48 
 48 
 48 
 
 0.54971 
 0.54922 
 0.54874 
 0.54826 
 0.54778 
 
 9.98338 
 9.98334 
 9.98331 
 9.98327 
 9.98324 
 
 4 
 3 
 4 
 3 
 
 4 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 30.0 
 37.5 
 
 4 
 
 29.3 
 36.7 
 
 3 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.43591 
 9.43635 
 9.43680 
 9.43724 
 9.43769 
 
 44 
 
 45 
 44 
 45 
 44 
 
 9.45271 
 9.45319 
 9.45367 
 9.45415 
 9.45463 
 
 48 
 48 
 48 
 48 
 48 
 
 0.54729 
 0.54681 
 0.54633 
 0.54585 
 0.54537 
 
 9.98320 
 9.98317 
 9.98313 
 9.98309 
 9.98306 
 
 3 
 4 
 4 
 3 
 4 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 
 7 
 8 
 9 
 10 
 
 0.4 
 0.5 
 0.5 
 0.6 
 0.7 
 
 0.3 
 0.4 
 0.4 
 0.5 
 0.5 
 
 55 
 56 
 57 
 58 
 59 
 
 9.43813 
 9.43857 
 9.43901 
 9.43946 
 9.43990 
 
 44 
 
 44 
 45 
 44 
 44 
 
 9.45511 
 9.45559 
 9.45606 
 9.45654 
 9.45702 
 
 48 
 47 
 48 
 48 
 48 
 
 0.54489 
 0.54441 
 0.54394 
 0.54346 
 0.54298 
 
 9.98302 
 9.98299 
 9.98295 
 9.98291 
 9.98288 
 
 3 
 
 4 
 4 
 3 
 4 
 
 5 
 4 
 3 
 2 
 1 
 
 20 
 30 
 40 
 50 
 
 1.3 
 2.0 
 2.7 
 3.3 
 
 1.0 
 1.5 
 2.0 
 2.5 
 
 60 
 
 9.44034 
 
 
 9.45750 
 
 
 0.54250 
 
 9.98284 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 j. Cotg. 
 
 d.c. 
 
 ..Tang. 
 
 L. Sin. 
 
 d. 
 
 ' 
 
 
 P. P. 
 
 
 74 
 
1044 
 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 16 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang 
 
 d.c. 
 
 L. Cotg 
 
 L. Cos. 
 
 d. 
 
 
 
 P. P 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.44034 
 9.44078 
 9.44122 
 9.44166 
 9.44210 
 
 44 
 44 
 44 
 44 
 
 9.45750 
 9.45797 
 9.45845 
 9.45892 
 9.45940 
 
 47 
 
 48 
 47 
 
 48 
 
 0.54250 
 0.54203 
 0.54155 
 0.54108 
 0.54060 
 
 9.98284 
 9.98281 
 9.98277 
 9.98273 
 9.98270 
 
 3 
 4 
 4 
 3 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 7 
 
 48 
 
 4.8 
 5 6 
 
 47 
 
 4.7 
 5 5 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.44253 
 9.44297 
 9.44341 
 9.44385 
 9.44428 
 
 44 
 
 44 
 44 
 43 
 
 AA 
 
 9.45987 
 9.46035 
 9.46082 
 9.46130 
 9.46177 
 
 48 
 47 
 48 
 47 
 
 0.54013 
 0.53965 
 0.53918 
 0.53870 
 0.53823 
 
 9.98266 
 9.98262 
 9.98259 
 9.98255 
 9.98251 
 
 4 
 3 
 4 
 4 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 6.4 
 7.2 
 8.0 
 16.0 
 24.0 
 
 6.3 
 7.1 
 
 7.8 
 15.7 
 23.5 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.44472 
 9.44516 
 9.44559 
 9.44602 
 9.44646 
 
 44 
 43 
 43 
 44 
 43 
 
 9.46224 
 9.46271 
 9.46319 
 9.46366 
 9.46413 
 
 47 
 48 
 47 
 47 
 
 0.53776 
 0.53729 
 0.53681 
 0.53634 
 0.53587 
 
 9.98248 
 9.98244 
 9.98240 
 9.98237 
 9.98233 
 
 4 
 4 
 3 
 4 
 4 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 32.0 
 40.0 
 
 4R 
 
 31.3 
 39.2 
 
 45 
 
 15 
 16 
 
 17 
 18 
 19 
 
 9.44689 
 9.44733 
 9.44776 
 9.44819 
 9.44862 
 
 44 
 43 
 43 
 43 
 
 9.46460 
 9.46507 
 9.46554 
 9.46601 
 9.46648 
 
 47 
 47 
 47 
 47 
 
 0.53540 
 0.53493 
 0.53446 
 0.53399 
 0.53352 
 
 9.98229 
 9.98226 
 9.98222 
 9.98218 
 9.98215 
 
 3 
 4 
 4 
 3 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 7 
 
 8 
 9 
 10 
 
 4.6 
 5.4 
 6.1 
 6.9 
 7.7 
 
 4.5 
 5.3 
 6.0 
 6.8 
 7.5 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.44905 
 9.44948 
 9.44992 
 9.45035 
 9.45077 
 
 43 
 44 
 43 
 42 
 
 9.46694 
 9.46741 
 9.46788 
 9.46835 
 9.46881 
 
 47 
 47 
 47 
 46 
 
 0.53306 
 0.53259 
 0.53212 
 0.53165 
 0.53119 
 
 9.98211 
 9.98207 
 9.98204 
 9.98200 
 9.98196 
 
 4 
 3 
 4 
 4 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 15.3 
 23.0 
 30.7 
 38.3 
 
 15.0 
 22.5 
 30.0 
 37.5 
 
 26 
 27 
 28 
 29 
 
 9.45120 
 9.45163 
 9.45206 
 9.45249 
 9.45292 
 
 43 
 43 
 43 
 43 
 
 9.46928 
 9.46975 
 9.47021 
 9.47068 
 9.47114 
 
 47 
 46 
 47 
 46 N 
 
 0.53072 
 0.53025 
 0.52979 
 0.52932 
 0.52886 
 
 9.98192 
 9.98189 
 9.98185 
 9.98181 
 9.98177 
 
 3 
 
 4 
 4 
 4 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 7 
 8 
 
 44 
 
 4.4 
 5.1 
 5.9 
 
 43 
 
 4.3 
 
 5.0 
 5.7 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.45334 
 9.45377 
 9.45419 
 9.45462 
 9.45504 
 
 43 
 42 
 43 
 
 42 
 40 
 
 9.47160 
 9.47207 
 9.47253 
 9.47299 
 9.47346 
 
 47 
 46 
 46 
 47 
 
 0.52840 
 0.52793 
 0.52747 
 0.52701 
 0.52654 
 
 9.98174 
 9.98170 
 9.98166 
 9.98162 
 9.98159 
 
 4 
 4 
 4 
 3 
 
 30 
 
 29 
 28 
 27 
 26 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6.6 
 7.3 
 14.7 
 22.0 
 29.3 
 36 7 
 
 6.5 
 7.2 
 14.3 
 21.5 
 
 28.7 
 35 g 
 
 35 
 36 
 37 
 38 
 39 
 
 9.45547 
 9.45589 
 9.45632 
 9.45674 
 9.45716 
 
 42 
 43 
 42 
 42 
 40 
 
 9.47392 
 9.47438 
 9.47484 
 9.47530 
 9.47576 
 
 46 
 46 
 46 
 46 
 
 0.52608 
 0.52562 
 0.52516 
 0.52470 
 0.52424 
 
 9.98155 
 9.98151 
 9.98147 
 9.98144 
 9.98140 
 
 4 
 4 
 3 
 4 
 4 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 7 
 
 42 
 
 4.2 
 
 4 Q 
 
 41 
 
 4.1 
 
 4 Q 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.45758 
 9.45801 
 9.45843 
 9.45885 
 9.45927 
 
 43 
 
 42 
 42 
 42 
 
 9.47622 
 9.47668 
 9.47714 
 9.47760 
 9.47806 
 
 46 
 46 
 46 
 46 
 
 0.52378 
 0.52332 
 0.52286 
 0.52240 
 0.52194 
 
 9.98136 
 9.98132 
 9.98129 
 9.98125 
 9.98121 
 
 4 
 3 
 4 
 4 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 5.6 
 6.3 
 7.0 
 14.0 
 ?1 
 
 5.5 
 6.2 
 6.8 
 13.7' 
 20.5 
 
 45 
 46 
 47 
 48 
 49 
 
 9.45969 
 9.46011 
 9.46053 
 9.46095 
 9.46136 
 
 42 
 42 
 42 
 41 
 
 9.47852 
 9.47897 
 9.47943 
 9.47989 
 9.48035 
 
 45 
 46 
 46 
 
 46 
 
 0.52148 
 0.52103 
 0.52057 
 0.52011 
 0.51965 
 
 9.98117 
 9.98113 
 9.98110 
 9.98106 
 9.98102 
 
 4 
 3 
 4 
 4 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 2S.O 
 35.0 
 
 4 
 
 27.3 
 34.2 
 
 3 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.46178 
 9.46220 
 9.46262 
 9.46303 
 9.46345 
 
 42 
 42 
 41 
 42 
 41 
 
 9.48080 
 9.48126 
 9.48171 
 9.48217 
 9.48262 
 
 46 
 45 
 46 
 45 
 45 
 
 0.51920 
 0.51874 
 0.51829 
 0.51783 
 0.51738 
 
 9.98098 
 9.98094 
 9.98090 
 9.98087 
 9.98083 
 
 4 
 4 
 3 
 
 4 
 4 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 6 
 7 
 8 
 9 
 10 
 
 0.4 
 0.5 
 0.5 
 0.6 
 0.7 
 
 0.3 
 0.4 
 0.4 
 0.5 
 0.5 
 
 55 
 56 
 57 
 58 
 59 
 
 9.46386 
 9.46428 
 9.46469 
 9.46511 
 9.46552 
 
 42 
 41 
 42 
 41 
 40 
 
 9.48307 
 8.48353 
 9.48398 
 9.48443 
 9.48489 
 
 46 
 45 
 45 
 46 
 
 0.51693 
 0.51647 
 0.51602 
 0.51557 
 0.51511 
 
 9.98079 
 9.98075 
 9.98071 
 9.98067 
 9.98063 
 
 4 
 4 
 4 
 4 
 
 5 
 4 
 3 
 2 
 1 
 
 20 
 30 
 40 
 50 
 
 1.3 
 ,2.0 
 2.7 
 3.3 
 
 1.0 
 1.5 
 2.0 
 2.5 
 
 60 
 
 9.46594 
 
 
 9.48534 
 
 
 0.51466 
 
 9.98060 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 / 
 
 
 P.P. 
 
 
 73 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 17 
 
 1045 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg 
 
 L. Cos. 
 
 d. 
 
 1 
 
 P 
 
 .P 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.46594 
 9.46635 
 9.46676 
 9.46717 
 9.46758 
 
 41 
 41 
 41 
 41 
 
 42 
 
 9.48534 
 9.48579 
 9.48624 
 9.48669 
 9.48714 
 
 45 
 
 45 
 45 
 45 
 
 4c 
 
 0.51466 
 0.51421 
 0.51376 
 0.51331 
 0.51286 
 
 9.98060 
 9.98056 
 9.98052 
 9.98048 
 9.98044 
 
 4 
 4 
 
 4 
 4 
 
 60 
 
 59 
 
 58 
 57 K 
 
 5<> 5 
 
 A 
 
 < 
 
 5 
 
 .5 
 
 44 
 
 4.4 
 
 5 
 6 
 
 7 
 8 
 9 
 
 IF 
 
 11 
 
 12 
 13 
 14 
 
 9.46800 
 9.46841 
 9.46882 
 9.46923 
 9.46964 
 9.47005 
 9.47045 
 9.47086 
 9.47127 
 9.47168 
 
 41 
 41 
 41 
 41 
 41 
 40 
 41 
 41 
 41 
 41 
 
 9.48759 
 9.48804 
 9.48849 
 9.48894 
 9.48939 
 9.48984 
 9.49029 
 9.49073 
 9.49118 
 9.49163 
 
 45 
 45 
 45 
 45 
 45 
 45 
 44 
 45 
 45 
 44 
 
 0.51241 
 0.51196 
 0.51151 
 0.51106 
 0.51061 
 0.51016 
 0.50971 
 0.50927 
 0.50882 
 0.50837 
 
 9.98040 
 9.98036 
 9.98032 
 9.98029 
 9.98025 
 9.98021 
 9.98017 
 9.98013 
 9.98009 
 9.98005 
 
 4 
 4 
 3 
 4 
 4 
 4 
 4 
 4 
 4 
 
 55 8 
 54 9 
 53 10 
 52 20 
 51 30 
 50 40 
 49 50 
 48 
 47 
 46 
 
 e 
 e 
 
 if 
 
 21 
 
 3( 
 
 s: 
 
 .0 
 .8 
 .5 
 .0 
 .f> 
 .0 
 .5 
 
 4 
 
 5.9 
 6.6 
 7.3 
 14.7 
 22.0 
 29.3 
 36.7 
 
 3 
 
 15 
 16 
 
 17 
 18 
 19 
 
 9.47209 
 9.47249 
 9.47290 
 9.47330 
 9.47371 
 
 40 
 41 
 40 
 41 
 4f> 
 
 9.49207 
 9.49252 
 9.49296 
 9.49341 
 9.49385 
 
 45 
 44 
 45 
 44 
 4c 
 
 0.50793 
 0.50748 
 0.50704 
 0.50659 
 0.50615 
 
 9.98001 
 9.97997 
 9.97993 
 9.97989 
 9.97986 
 
 4 
 4 
 4 
 3 
 
 45 
 44 
 43 
 42 
 41 ] 
 
 6 
 
 7 
 
 8 
 9 
 
 
 4 
 
 6 
 5 
 6 
 7 
 
 3 
 
 
 7 
 5 
 2 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.47411 
 9.47452 
 9.47492 
 9.47533 
 9.47573 
 
 41 
 40 
 41 
 40 
 40 ' 
 
 9.49430 
 9.49474 
 9.49519 
 9.49563 
 9.49607 
 
 44 
 45 
 44 
 44 
 4c 
 
 0.50570 
 0.50526 
 0.50481 
 0.50437 
 0.50393 
 
 9.97982 
 9.97978 
 9.97974 
 9.97970 
 9.97966 
 
 4 
 4 
 4 
 4 
 
 40 ; 
 
 39 i 
 
 38 4 
 37 
 36 
 
 
 
 
 
 
 
 14 
 
 21 
 
 28 
 35 
 
 3 
 5 
 
 7 
 8 
 
 25 
 26 
 27 
 28 
 29 
 
 9.47613 
 9.47654 
 9.47694 
 9.47734 
 9.47774 
 
 41 
 40 
 40 
 40 
 40 
 
 9.49652 
 9.49696 
 9.49740 
 9.49784 
 9.49828 
 
 44 
 44 
 44 
 44 
 44 
 
 0.50348 
 0.50304 
 0.50260 
 0.50216 
 0.50172 
 
 9.97962 
 9.97958 
 9.97954 
 9.97950 
 9.97946 
 
 4 
 4 
 4 
 4 
 
 35 
 34 
 33 6 
 32 7 
 
 31 9 
 
 4 
 4 
 4 
 1 
 
 2 
 
 .2 
 .9 
 .6 
 
 41 
 4.1 
 4.8 
 5.5 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.47814 
 9.47854 
 9.47894 
 9.47934 
 9.47974 
 
 40 
 40 
 40 
 40 
 
 9.49872 
 949916 
 9.49960 
 9.50004 
 9.50048 
 
 44 
 44 
 44 
 44 
 
 0.50128 
 0.50084 
 0.50040 
 0.49996 
 0.49952 
 
 9.97942 
 9.97938 
 9.97934 
 9.97930 
 9.97926 
 
 4 
 
 4 
 4 
 
 4 
 
 30 . 
 1 20 
 
 28 on 
 97 1 
 
 V 40 
 oe 1 ^^ 
 
 25 m 
 
 1 
 
 14 
 21 
 2^ 
 K 
 
 .0 
 .0 
 .0 
 .0 
 
 
 6.8 
 13.7 
 20.5 
 27.3 
 342 
 
 35 
 36 
 37 
 38 
 39 
 
 9.48014 
 9.48054 
 9.48094 
 9.48133 
 9.48173 
 
 40 
 40 
 39 
 40 
 
 9.50092 
 9.50136 
 9.50180 
 9.50223 
 9.50267 
 
 44 
 44 
 43 
 44 
 
 0.49908 
 0.49864 
 0.49820 
 0.49777 
 0.49733 
 
 9.97922 
 9.97918 
 9.97914 
 9.97910 
 9.97906 
 
 4 
 4 
 4 
 4 
 
 25 1 
 24 
 23 
 22 , 
 21 | 
 
 4 
 
 4 
 ,] 
 
 
 
 .0 
 
 7 
 
 39 
 
 3.9 
 4 6 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.48213 
 9.48252 
 9.48292 
 9.48332 
 9.48371 
 
 39 
 40 
 . 40 
 39 
 
 9.50311 
 9.50355 
 9.50398 
 9.50442 
 9.50485 
 
 44 
 43 
 
 44 
 43 
 
 0.49689 
 0.49645 
 0.49602 
 0.49558 
 0.49515 
 
 9.97902 
 9.97898 
 9.97894 
 9.97890 
 9.97886 
 
 4 
 4 
 4 
 4 
 4 
 
 20 g 
 
 19 9 
 18 10 
 17 20 
 16 30 
 
 
 
 
 
 13 
 
 2C 
 
 .3 
 .0 
 .7 
 .3 
 .0 
 
 5.2 
 5.9 
 6.5 
 13.0 
 19.5 
 
 45 
 46 
 47 
 48 
 49 
 
 9.48411 
 9.48450 
 9.48490 
 9.48529 
 9.48568 
 
 39 
 40 
 39 
 39 
 
 9.50529 
 9.50572 
 9.50616 
 9.50659 
 9.50703 
 
 43 
 44 
 43 
 44 
 
 0.49471 
 0.49428 
 0.49384 
 0.49341 
 0.49297 
 
 9.97882 
 9.97878 
 9.97874 
 9.97870 
 9.97866 
 
 4 
 4 
 4 
 4 
 5 
 
 15 40 
 14 50 
 13 
 12 
 11 
 
 2< 
 33 
 
 5 
 
 .7 
 .3 
 
 4 
 
 26.0 
 32.5 
 
 3 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.48607 
 9.48647 
 9.48686 
 9.48725 
 9.48764 
 
 40 
 39 
 39 
 39 
 
 9.50746 
 9.50789 
 9.50833 
 9.50876 
 9.50919 
 
 43 
 44 
 43 
 43 
 
 0.49254 
 0.49211 
 0.49167 
 0.49124 
 0.49081 
 
 9.97861 
 9.97857 
 9.97853 
 9.97849 
 9.97845 
 
 4 
 4 
 4 
 4 
 4 
 
 10 6 ( 
 9 7 ( 
 8 8 ( 
 7 9 ( 
 6 |10 ( 
 
 ).5 
 ).6 
 ).7 
 
 ).8 
 ).8 
 
 
 0. 
 0. 
 0. 
 0. 
 
 4 0.3 
 5 0.4 
 5 0.4 
 6 0.5 
 7 0.5 
 
 55 
 56 
 57 
 58 
 59 
 
 9.48803 
 9.48842 
 9.48881 
 9.48920 
 9.48959 
 
 39 
 39 
 
 39 
 39 
 
 9.50962 
 9.51005 
 9.51048 
 9.51092 
 9.51135 
 
 43 
 43 
 44 
 43 
 43 
 
 0.49038 
 0.48995 
 0-.48952 
 0.48908 
 0.48865 
 
 9.97841 
 9.97837 
 9.97833 
 9.97829 
 9.97825 
 
 4 
 4 
 4 
 
 4 
 4 
 
 5 2u J 
 4 30 '< 
 
 40 
 
 2 50 4 
 1 
 
 ./ 
 5.5 
 ,.3 
 
 L2 
 
 1. 
 
 2. 
 2. 
 3. 
 
 3 1.0 
 1.5 
 7 2.0 
 3 2.5 
 
 60 
 
 9.48998 
 
 
 9.51178 
 
 
 0.48822 
 
 9.97821 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 ' 1 
 
 P 
 
 1 J . 
 
 
 
 
 
 
 
 72 
 
 
 
 
 
 
 
1046 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 18 
 
 t 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 
 P.P 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.48998 
 9.49037 
 9.49076 
 9.49115 
 9.49153 
 
 39 
 39 
 39 
 38 
 39 
 
 9.51178 
 9.51221 
 9.51264 
 9.51306 
 9.51349 
 
 43 
 43 
 42 
 43 
 43 
 
 0.48822 
 0.48779 
 0.48736 
 0.48694 
 0.48651 
 
 9.97821 
 9.97817 
 9.97812 
 9.97808 
 9.97804 
 
 4 
 5 
 4 
 4 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 43 
 
 4.3 
 5 
 
 42 
 
 4.2 
 4 9 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.49192 
 9.49231 
 9.49269 
 9.49308 
 9.49347 
 
 39 
 38 
 39 
 39 
 
 38 
 
 9.51392 
 9.51435 
 9.51478 
 9.51520 
 9.51563 
 
 43 
 43 
 42 
 43 
 40 
 
 0.48608 
 0.48565 
 0.48522 
 0.48480 
 0.48437 
 
 9.97800 
 9.97796 
 9.97792 
 9.97788 
 9.97784 
 
 4 
 4 
 4 
 4 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 5.7 
 6.5 
 7.2 
 14.3 
 21.5 
 
 5.6 
 6.3 
 7.0 
 14.0 
 21.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.49385 
 9.49424 
 9.49462 
 9.49500 
 9.49539 
 
 39 
 38 
 38 
 39 
 38 
 
 9.51606 
 9.51648 
 9.51691 
 9.51734 
 9.51776 
 
 42 
 43 
 43 
 42 
 
 XQ 
 
 0.48394 
 0.48352 
 0.48309 
 0.48266 
 0.48224 
 
 9.97779 
 9.97775 
 9.97771 
 9.97767 
 9.97763 
 
 4 
 
 4 
 4 
 4 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 28.7 
 35.8 
 
 4 
 
 28.0 
 35.0 
 
 | 
 
 15 
 16 
 17 
 18 
 19 
 
 9.49577 
 9.49615 
 9.49654 
 9.49692 
 9.49730 
 
 38 
 39 
 38 
 38 
 38 
 
 9.51819 
 9.51861 
 9.51903 
 9.51946 
 9.51988 
 
 42 
 42 
 43 
 42 
 
 0.48181 
 0.48139 
 0.48097 
 0.48054 
 0.48012 
 
 9.97759 
 9.97754 
 9.97750 
 9.97746 
 9.97742 
 
 5 
 
 4 
 
 4 
 4 
 
 45 
 44 
 43 
 
 42 
 41 
 
 ] 
 
 6 4 
 7 4 
 8 5 
 9 6 
 6 
 
 1 
 8 
 5 
 2 
 8 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.49768 
 9.49806 
 9.49844 
 9.49882 
 9.49920 
 
 38 
 
 38 
 38 
 38 
 38 
 
 9.52031 
 9.52073 
 9.52115 
 9.52157 
 9.52200 
 
 42 
 42 
 42 
 43 
 
 49 
 
 0.47969 
 0.47927 
 0.47885 
 0.47843 
 0.47800 
 
 9.97738 
 9.97734 
 9.97729 
 9.97725 
 9.97721 
 
 4 
 5 
 4 
 
 t 
 
 40 
 
 39 
 38 
 37 
 36 
 
 il 
 I 
 -I 
 1 
 
 13 
 20 
 27 
 34 
 
 7 
 5 
 3 
 2 
 
 25 
 26 
 27 
 28 
 29 
 
 9.49958 
 9.49996 
 9.50034 
 9.50072 
 9.50110 
 
 38 
 38 
 38 
 38 
 38 
 
 9.52242 
 9.52284 
 9.52326 
 9.52368 
 9.52410 
 
 42 
 42 
 42 
 42 
 42 
 
 0.47758 
 0.47716 
 0.47674 
 0.47632 
 0.47590 
 
 9.97717 
 9.97713 
 9.97708 
 9.97704 
 9.97700 
 
 4 
 5 
 4 
 4 
 4 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 39 
 
 3.9 
 4.6 
 5.2 
 
 38 
 
 3.8 
 4.4 
 5.1 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.50148 
 9.50185 
 9.50223 
 9.50261 
 9.50298 
 
 37 
 38 
 38 
 37 
 38 
 
 9.52452 
 9.52494 
 9.52536 
 9.52578 
 9.52620 
 
 42 
 42 
 42 
 42 
 41 
 
 0.47548 
 0.47506 
 0.47464 
 0.47422 
 0.47380 
 
 9.97696 
 9.97691 
 9.97687 
 9.97683 
 9.97679 
 
 5 
 
 4 
 4 
 4 
 
 30 
 
 29 
 28 
 27 
 26 
 
 10 
 20 
 30 
 40 
 50 
 
 6.5 
 13.0 
 19.5 
 26.0 
 32 5 
 
 6.3 
 12.7 
 19.0 
 25.3 
 31 7 
 
 35 
 36 
 37 
 38 
 39 
 
 9.50336 
 9.50374 
 9.50411 
 9.50449 
 9.50486 
 
 38 
 37 
 38 
 37 
 37 
 
 9.52661 
 9.52703 
 9.52745 
 9.52787 
 9.52829 
 
 42 
 42 
 42 
 42 
 
 0.47339 
 0.47297 
 0.47255 
 0.47213 
 0.47171 
 
 9.97674 
 9.97670 
 9.97666 
 9.97662 
 9.97657 
 
 4 
 4 
 4 
 5 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 37 
 
 3.7 
 
 36 
 
 3.6 
 
 40 
 41 
 
 42 
 43 
 44 
 
 9.50523 
 9.50561 
 9.50598 
 9.50635 
 9.50673 
 
 38 
 37 
 37 
 38 
 37 
 
 9.52870 
 9.52912 
 9.52953 
 9.52995 
 9.53037 
 
 42 
 41 
 42 
 42 
 
 0.47130 
 0.47088 
 0.47047 
 0.47005 
 0.46963 
 
 9.97653 
 9.97649 
 9.97645 
 9.97640 
 9.97636 
 
 4 
 4 
 5 
 4 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 4.9 
 5.6 
 6.2 
 12.3 
 18.5 
 
 4.8 
 5.4 
 6.0 
 12.0 
 18.0 
 
 45 
 46 
 47 
 48 
 49 
 
 9.50710 
 9.50747 
 9.50784 
 9.50821 
 9.50858 
 
 37 
 37 
 37 
 37 
 
 38 
 
 9.53078 
 9.53120 
 9.53161 
 9.53202 
 9.53244 
 
 42 
 41 
 41 
 42 
 
 0.46922 
 0.46880 
 0.46839 
 0.46798 
 0.46756 
 
 9.97632 
 9.97628 
 9.97623 
 9.97619 
 9.97615 
 
 4 
 5 
 4 
 4 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 24.7 
 30.8 
 
 5 
 
 24.0 
 30.0 
 
 4 
 
 50 
 51 
 52 
 53 
 54 
 
 55 
 56 
 57 
 58 
 59 
 60 
 
 9.50896 
 9.50933 
 9.50970 
 9.51007 
 9.51043 
 9.51080 
 9.51117 
 9.51154 
 9.51191 
 9.51227 
 9.51264 
 
 37 
 37 
 37 
 36 
 37 
 37 
 37 
 37 
 36 
 37 
 
 9.53285 
 9.53327 
 9.53368 
 9.53409 
 9.53450 
 9.53492~ 
 9.53533 
 9.53574 
 9.53615 
 9.53656 
 9.53697 
 
 42 
 41 
 41 
 41 
 42 
 41 
 41 
 41 
 41 
 41 
 
 0.46715 
 0.46673 
 0.46632 
 0.46591 
 0.46550 
 0.46508 
 0.46467 
 0.46426 
 0.46385 
 0.46344 
 0.46303 
 
 9.97610 
 9.97606 
 9.97602 
 9.97597 
 9.97593 
 9.97589 
 9.97584 
 9.97580 
 9.97576 
 9.97571 
 9.97567 
 
 4 
 4 
 5 
 4 
 4 
 5 
 4 
 4 
 5 
 4 
 
 10 
 
 9 
 8 
 7 
 6 
 5 
 4 
 3 
 2 
 1 
 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 0.5 
 0.6 
 0.7 
 0.8 
 0.8 
 1.7 
 2.5 
 3.3 
 4.2 
 
 0.4 
 0.5 
 0.5 
 0.6 
 0.7 
 1.3 
 2.0 
 2.7 
 3.3 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 / 
 
 
 P.P 
 
 
 71 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 19 
 
 1047- 
 
 1 
 
 L. Sin. 
 
 d. 
 
 .Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 
 P.P. 
 
 
 
 
 2 
 3 
 
 4 
 
 9.51264 
 9.51301 
 9.51338 
 9.51374 
 9.51411 
 
 37 
 37 
 36 
 37 
 
 Ofi 
 
 9.53697 
 9.53738 
 9.53779 
 9.53820 
 9.53861 
 
 41 
 41 
 41 
 41 
 41 
 
 0.46303 
 0.46262 
 0.46221 
 0.46180 
 0.46139 
 
 9.97567 
 9.97563 
 9.97558 
 9.97554 
 9.97550 
 
 4 
 5 
 
 4 
 4 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 41 
 
 4.1 
 
 4 8 
 
 40 
 
 4.0 
 
 4 7 
 
 5 
 
 6 
 
 1 7 
 8 
 9 
 
 9.51447 
 9.51484 
 9.51520 
 9.51557 
 9.51593 
 
 37 
 36 
 37 
 36 
 
 9.53902 
 9.53943 
 9.53984 
 9.54025 
 9.54065 
 
 41 
 41 
 41 
 40 
 4.1 
 
 0.46098 
 0.46057 
 0.46016 
 0.45975 
 0.45935 
 
 9.97545 
 9.97541 
 9.97536 
 9.97532 
 9.97528 
 
 4 
 5 
 4 
 4 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 5.5 
 6.2 
 6.8 
 13.7 
 20.5 
 
 5.3 
 6.0 
 6.7 
 13.3 
 20.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.51629 
 9.51666 
 9.51702 
 9.51738 
 9.51774 
 
 37 
 36 
 36 
 36 
 
 9.54106 
 9.54147 
 9.54187 
 9.54228 
 9.54269 
 
 41 
 40 
 41 
 41 
 
 0.45894 
 0.45853- 
 0.45813 
 0.45772 
 0.45731 
 
 9.97523 
 9.97519 
 9.97515 
 9 97510 
 9.97506 
 
 4 
 4 
 5 
 4 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 27.3 
 34.2 
 
 3< 
 
 26.7 
 33.3 
 
 i 
 
 15 
 16 
 17 
 18 
 19 
 
 9.51811 
 9.51847 
 9.51883 
 9.51919 
 9.51955 
 
 36 
 36 
 36 
 36 
 
 9.54309 
 9.54350 
 9.54390 
 9.54431 
 9.51471 
 
 41 
 
 40 
 41 
 40 
 
 0.45691 
 0.45650 
 0.45610 
 0.45569 
 0.45529 
 
 9.97501 
 9.97497 
 9.97492 
 9.97488 
 9.97484 
 
 4 
 5 
 4 
 4 
 
 45 
 44 
 43 
 42 
 
 41 
 
 1 
 
 6 3 
 7 4 
 8 5 
 9 5 
 6 
 
 9 
 6 
 2 
 9 
 5 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.51991 
 9.52027 
 9.52063 
 9.52099 
 9.52135 
 
 36 
 36 
 36 
 36 
 
 9.54512 
 9.54552 
 9.54593 
 9.54633 
 9.54673 
 
 40 
 41 
 
 40 
 40 
 
 0.45488 
 0.45448 
 0.45407 
 0.45367 
 0.45327 
 
 9.97479 
 9.97475 
 9.97470 
 9.97466 
 9.97461 
 
 4 
 5 
 
 4 
 5 
 4 
 
 40 
 
 39 
 38 
 37 
 36 
 
 2 
 2 
 4 
 i 
 
 13 
 19 
 26 
 .0 32 
 
 
 5 
 
 .5 
 
 25 
 26 
 
 27 
 28 
 29 
 
 9.52171 
 9.52207 
 9.52242 
 9.52278 
 9.52314 
 
 36 
 35 
 36 
 36 
 
 9.54714 
 9.54754 
 9.54794 
 9.54835 
 9.54875 
 
 40 
 40 
 41 
 40 
 
 0.45286 
 0.45246 
 0.45206 
 0.45165 
 0.45125 
 
 9.97457 
 9.97453 
 9.97448 
 9.97444 
 9.97439 
 
 4 
 5 
 4 
 5 
 4 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 7 
 8 
 
 Q 
 
 37 
 
 3.7 
 4.3 
 4.9 
 
 C fi 
 
 36 
 
 3.6 
 4.2 
 4.8 
 fi 4. 
 
 30 
 31 
 32 
 33 
 34 
 
 9.52350 
 9.52385 
 9.52421 
 9.52456 
 9.52492 
 
 35 
 
 36 
 35 
 36 
 
 9.54915 
 9.54955 
 9.54995 
 9.55035 
 9.55075 
 
 40 
 40 
 40 
 40 
 40 
 
 0.45085 
 0.45045 
 0.45005 
 0.44965 
 0.44925 
 
 9.97435 
 9.97430 
 9.97426 
 9.97421 
 9.97417 
 
 5 
 4 
 5 
 4 
 5 
 
 30 
 
 29 
 28 
 27 
 26 
 
 10 
 20 
 30 
 40 
 50 
 
 6.2 
 12.3 
 18.5 
 24.7 
 30.8 
 
 6.0 
 12.0 
 18.0 
 24.0 
 30.0 
 
 35 
 36 
 
 37 
 38 
 
 Li. 
 
 40 
 41 
 42 
 43 
 44 
 
 9.52527 
 9.52563 
 9.52598 
 9.52634 
 9.52669 
 9.52705 
 9,52740 
 9.52775 
 9.52811 
 9.52846 
 
 36 
 35 
 36 
 35 
 36 
 35 
 35 
 36 
 35 
 
 9.55115 
 9.55155 
 9.55195 
 955235 
 9.55275 
 9.55315 
 9.55355 
 9.55395 
 9.55434 
 9.55474 
 
 40 
 40 
 40 
 40 
 40 
 40 
 40 
 39 
 40 
 4ft 
 
 0.44885 
 0.44845 
 0.44805 
 0.44765 
 0.44725 
 1)744685 
 0.44645 
 0.44605 
 0.44566 
 0.44526 
 
 9.97412 
 9.97408 
 9.97403 
 9.97399 
 9.97394 
 9.97390 
 9.97385 
 9.97381 
 9.97376 
 9.97372 
 
 4 
 
 5 
 4 
 5 
 4 
 5 
 4 
 5 
 4 
 5 
 
 25 
 24 
 23 
 22 
 21 
 20 
 19 
 18 
 17 
 16 
 
 6 
 7 
 
 8 
 9 
 10 
 
 20 
 30 
 
 35 
 3.5 
 4.1 
 4.7 
 5.3 
 5.8 
 11.7 
 17.5 
 
 34 
 
 3.4 
 4.0 
 4.5 
 5.1 
 5.7 
 11.3 
 17.0 
 
 46 
 
 47 
 48 
 49 
 
 9.52881 
 9.52916 
 9.52951 
 9.52986 
 9.53021 
 
 35 
 35 
 35 
 35 
 
 9.55514 
 9.55554 
 9.55593 
 9.55633 
 9.55673 
 
 40 
 39 
 40 
 40 
 
 on 
 
 0.44486 
 0.44446 
 0.44407 
 0.44367 
 0.44327 
 
 9.97367 
 9.97363 
 9.97358 
 9.97353 
 9.97349 
 
 4 
 5 
 5 
 
 4 
 5 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 23.3 
 29.2 
 
 5 
 
 22.7 
 28.3 
 
 4 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.53056 
 9.53092 
 9.53126 
 9.53161 
 9.53196 
 
 36 
 34 
 35 
 35 
 
 9.55712 
 9.55752 
 9.55791 
 9.55831 
 9.55870 
 
 40 
 39 
 40 
 39 
 
 0.44288 
 0.44248 
 0.44209 
 0.44169 
 0.44130 
 
 9.97344 
 9.97340 
 9.97335 
 9.97331 
 9.97326 
 
 4 
 5 
 4 
 5 
 4 
 
 $0 
 
 9 
 
 8 
 7 
 6 
 
 6 
 7 
 8 
 9 
 10 
 
 0.5 
 0.6 
 0.7 
 0.8 
 0.8 
 
 0.4 
 0.5 
 0.5 
 0.6 
 0.7 
 
 55 
 1 56 
 
 I 57 
 1 58 
 1 59 
 
 9.53231 
 9.53266 
 9.53301 
 9.53336 
 9.53370 
 
 35 
 35 
 35 
 35 
 34 
 
 9.55910 
 9.S5&49 
 9.55989 
 9.56028 
 9.56067 
 
 39 
 40 
 39 
 39 
 4A 
 
 0.44090 
 0.44051 
 0.44011 
 0.43972 
 0.43933 
 
 9.97322 
 9.97317 
 9.97312 
 9.97308 
 9.97303 
 
 5 
 
 5 
 4 
 5 
 4 
 
 5 
 4 
 3 
 2 
 
 1 
 
 20 
 30 
 40 
 50 
 
 1.7 
 2.5 
 3.3 
 4.2 
 
 1.3 
 2.0 
 2.7 
 3.3 
 
 60 
 
 9.53405 
 
 
 9.56107 
 
 j ' ' 
 
 0.43893 
 
 9.97299 
 L Sin 
 
 d 
 
 
 
 / 
 
 
 P V 
 
 1 
 
 1 
 
 
 
 
 
 70 
 
 
 
 
 
 
 
1048 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 20 
 
 1 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg 
 
 L. Cos. 
 
 d. 
 
 
 
 P.P 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.53405 
 9.53440 
 9.53475 
 9.53509 
 9.53544 
 
 35 
 35 
 34 
 35 
 
 9.56107 
 9.56146 
 9.56185 
 9.56224 
 9.56264 
 
 39 
 39 
 39 
 40 
 
 0.43893 
 0.43854 
 0.43815 
 0.43776 
 0.43736 
 
 9.97299 
 9.97294 
 9.97289 
 9.97285 
 9.97280 
 
 5 
 5 
 4 
 5 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 40 
 
 4.0 
 
 39 
 
 3.9 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.53578 
 9.53613 
 9.53647 
 9.53682 
 9.53716 
 
 35 
 34 
 35 
 34 
 
 oe 
 
 9.56303 
 9.56342 
 9.56381 
 9.56420 
 9.56459 
 
 39 
 39 
 39 
 39 
 qq 
 
 0.43697 
 0.43658 
 0.43619 
 0.43580 
 0.43541 
 
 9.97276 
 9.97271 
 9.97266 
 9.97262 
 9.97257 
 
 5 
 5 
 4 
 5 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 
 m 
 
 5.3 
 .0 
 6.7 
 13.3 
 20,0 
 
 5.2 
 5.9 
 6.5 
 13.0 
 195 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.53751 
 9.53785 
 9.53819 
 9.53854 
 9.53888 
 
 34 
 34 
 35 
 34 
 
 04 
 
 9.56498 
 9.56537 
 9.56576 
 9.56615 
 9.56654 
 
 39 
 39 
 39 
 39 
 
 qq 
 
 0.43502 
 0.43463 
 0.43424 
 0.43385 
 0.43346 
 
 9.97252 
 9.97248 
 9.97243 
 9.97238 
 9.97234 
 
 4 
 5 
 5 
 4 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 26.7 
 33.3 
 
 38 
 
 26.0 
 32.5 
 
 37 
 
 15 
 16 
 17 
 18 
 19 
 
 9.53922 
 9.53957 
 9.53991 
 9.54025 
 9.54059 
 
 35 
 34 
 34 
 34 
 
 04. 
 
 9.56693 
 9.56732 
 9.56771 
 9.56810 
 9.56849 
 
 39 
 39 
 39 
 89 
 
 qo 
 
 0.43307 
 0.43268 
 0.43229 
 0.43190 
 0.43151 
 
 9.97229 
 9.97224 
 9.97220 
 9.97215 
 9.97210 
 
 5 
 
 4 
 5 
 5 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 7 
 8 
 9 
 10 
 
 3.8 
 4.4 
 5.1 
 5.7 
 6.3 
 
 3.7 
 4.3 
 4.9 
 5.6 
 6.2 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.54093 
 9,54127 
 9.54161 
 9.54195 
 9.54229 
 
 34 
 34 
 34 
 34 
 34 
 
 9.56887 
 9.56926 
 9.56965 
 9.57004 
 9.57042 
 
 89 
 
 39 
 39 
 38 
 
 qq 
 
 0.43113 
 0.43074 
 0.43035 
 0.42996 
 0.42958 
 
 9.97206 
 9.97201 
 9.97196 
 9.97192 
 9.97187 
 
 5 
 
 5 
 4 
 5 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 12.V 
 19.0 
 25.3 
 31.7 
 
 12.3 
 
 18.5 
 24.7 
 30.8 
 
 25 
 26 
 27 
 
 28 
 29 
 
 9.54263 
 9.54297 
 9.54331 
 9.54365 
 9.54399 
 
 34 
 
 34 
 34 
 34 
 
 9.57081 
 9.57120 
 9.57158 
 9.57197 
 9.57235 
 
 39 
 38 
 89 
 38 
 
 0.42919 
 0.42880 
 0.42842 
 0.42803 
 0.42765 
 
 9.97182 
 9.97178 
 9.97173 
 9.97168 
 9.97163 
 
 4 
 5 
 5 
 5 
 
 35 
 34 
 33 
 32 
 31 
 
 
 3 
 6 3 
 7 4 
 8 4 
 
 .5 
 .1 
 
 .7 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.54433 
 9.54466 
 9.54500 
 9.54534 
 9.54567 
 
 33 
 
 34 
 34 
 33 
 
 9.57274 
 9.57312 
 9.57351 
 9.57389 
 9.57428 
 
 38 
 39 
 38 
 39 
 
 0.42726 
 0.42688 
 0.42649 
 0.42611 
 0.42572 
 
 9.97159 
 9.97154 
 9.97149 
 9.97145 
 9.97140 
 
 5 
 5 
 4 
 5 
 
 30 
 
 29 
 28 
 27 
 26 
 
 
 
 I 
 
 i! 
 > i 
 { 
 
 9 5 
 LO 5 
 JO 11 
 JO 17 
 10 23 
 )0 29 
 
 .3 
 
 .8 
 .7 
 .5 
 .3 
 2 
 
 35 
 36 
 37 
 38 
 39 
 
 9.54601 
 9.54635 
 9.54668 
 9.54702 
 9.54735 
 
 34 
 
 33 
 34 
 33 
 
 9.57466 
 9.57504 
 9.57543 
 9.57581 
 9.57619 
 
 38 
 39 
 38 
 38 
 
 0.42534 
 0.42496 
 0.42457 
 0.42419 
 0.42381 
 
 9.97135 
 9.97130 
 9.97126 
 9.97121 
 9.97116 
 
 5 
 4 
 5 
 5 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 34 
 
 3.4 
 
 33 
 
 3.3 
 
 40 
 
 41 
 
 42 
 43 
 44 
 
 9.54769 
 9.54802 
 9.54836 
 9.54869 
 9.54903 
 
 33 
 34 
 33 
 34 
 
 OQ 
 
 9.57658 
 9.57696 
 9.57734 
 9.57772 
 9.57810 
 
 38 
 
 38 
 38 
 88 
 
 OQ 
 
 0.42342 
 0.42304 
 0.42266 
 0.42228 
 0.42190 
 
 9.97111 
 9.97107 
 9.97102 
 9.97097 
 9.97092 
 
 4 
 5 
 5 
 5 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 
 10 
 20 
 30 
 
 4.5 
 5.1 
 5.7 
 11.3 
 17,0 
 
 4.4 
 5.0 
 5.5 
 11.0 
 165 
 
 45 
 46 
 
 47 
 48 
 49 
 
 9.54936 
 9.54969 
 9.55003 
 9.55036 
 9.55069 
 
 33 
 34 
 33 
 33 
 
 OQ 
 
 9.57849 
 9.57887 
 9.57925 
 9.57963 
 9.58001 
 
 38 
 38 
 38 
 38 
 
 00 
 
 0.42151 
 0.42113 
 0.42075 
 0.42037 
 0.41999 
 
 9.97087 
 9.97083 
 9.97078 
 9.97073 
 9.97068 
 
 4 
 5 
 5 
 5 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 22.7 
 28.3 
 
 5 
 
 22.0 
 27.5 
 
 4 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.55102 
 9.55136 
 9.55169 
 9.55202 
 9.55235 
 
 34 
 33 
 33 
 33 
 
 9.58039 
 9.58077 
 9.58115 
 9.58153 
 9.58191 
 
 38 
 38 
 38 
 38 
 
 0.41961 
 0.41923 
 0.41885 
 0.41847 
 0.41809 
 
 9.97063 
 9.97059 
 9.97054 
 9.97049 
 9.97044 
 
 4 
 5 
 5 
 5 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 
 7 
 8 
 9 
 10 
 
 0.5 
 0.6 
 0.7 
 0.8 
 0.8 
 
 0.4 
 0.5 
 0.5 
 0.6 
 0.7 
 
 55 
 56 
 57 
 58 
 59 
 
 9.55268 
 9.55301 
 9.55334 
 9.55367 
 9.55400 
 
 33 
 33 
 33 
 33 
 
 OQ 
 
 9.58229 
 9.58267 
 9.58304 
 9.58342 
 9.58380 
 
 38 
 37 
 38 
 38 
 
 qa 
 
 0.41771 
 0.41733 
 0.41696 
 0.41658 
 0.41620 
 
 9.97039 
 9.97035 
 9.97030 
 9.97025 
 9.97020 
 
 4 
 5 
 5 
 5 
 
 5 
 4 
 3 
 2 
 
 1 
 
 20 
 30 
 40 
 50 
 
 1.7 
 2.5 
 3.3 
 4.2 
 
 1.3 
 2.0 
 2.7 
 3.3 
 
 60 
 
 9.55433 
 
 
 9.58418 
 
 
 0.41582 
 
 9.97015 
 
 
 
 
 
 
 
 
 L.Cos. 
 
 d. 
 
 j. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L.Sin^ 
 
 d. 
 
 / 
 
 
 P.P. 
 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 21 
 
 1049 
 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 
 P.P 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.55433 
 9.55466 
 9.55499 
 9.55532 
 9.55564 
 
 33 
 33 
 33 
 32 
 33 
 
 9.58418 
 9.58455 
 9.58493 
 9.58531 
 9.58569 
 
 37 
 38 
 38 
 38 
 37 
 
 0.41582 
 0.41545 
 0.41507 
 0.41469 
 0.41431 
 
 9.97015 
 9.97010 
 9.97005 
 9.97001 
 9.96996 
 
 5 
 5 
 4 
 5 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 38 
 
 3.8 
 
 37 
 
 3.7 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.55597 
 9.55630 
 9.55663 
 9.55695 
 9.55728 
 
 33 
 33 
 32 
 33 
 33 
 
 9.58606 
 9.58644 
 9.58681 
 9.58719 
 9.58757 
 
 38 
 37 
 38 
 38 
 
 07 
 
 0.41394 
 0.41356 
 0.41319 
 0.41281 
 0.41243 
 
 9.96991 
 9.96986 
 9.96981 
 9.96976 
 9.96971 
 
 5 
 5 
 5 
 5 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 5.1 
 5.7 
 6.3 
 12.7 
 190 
 
 4.9 
 5.6 
 6.2 
 12.3 
 18.5 
 
 10 
 11 
 
 12 
 13 
 14 
 
 9.55761 
 9.55793 
 9.55826 
 9.55858 
 9.55891 
 
 32 
 33 
 32 
 33 
 32 
 
 9.58794 
 9.58832 
 9.58869 
 9.58907 
 9.58944 
 
 38 
 37 
 38 
 37 
 37 
 
 0.41206 
 0.41168 
 0.41131 
 0.41093 
 0.41056 
 
 9.96966 
 9.96962 
 9.96957 
 9.96952 
 9.96947 
 
 4 
 5 
 5 
 5 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 25.3 
 31.7 
 
 36 
 
 24.7 
 30.8 
 
 33 
 
 15 
 16 
 17 
 18 
 19 
 
 9.55923 
 9.55956 
 9.55988 
 9.56021 
 9.56053 
 
 33 
 
 32 
 33 
 32 
 qo 
 
 9.58981 
 9.59019 
 9.59056 
 9.59094 
 9.59131 
 
 38 
 37 
 38 
 37 
 
 0.41019 
 0.40981 
 0.40944 
 0.40906 
 0.40869 
 
 9.96942 
 9.96937 
 9.96932 
 9.96927 
 9.96922 
 
 5 
 5 
 5 
 5 
 
 45 
 44 
 
 43 
 42 
 41 
 
 6 
 
 7 
 8 
 9 
 10 
 
 3.6 
 4.2 
 4.8 
 5.4 
 6.0 
 
 3.3 
 3.9 
 4.4 
 5.0 
 5.5 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.56085 
 9.56118 
 9.56150 
 9.56182 
 9.56215 
 
 33 
 32 
 32 
 33 
 
 qo 
 
 9.59168 
 9.59205 
 9.59243 
 9.59280 
 9.59317 
 
 37 
 38 
 37 
 37 
 07 
 
 0.40832 
 0.40795 
 0.40757 
 0.40720 
 0.40683 
 
 9.96917 
 9.96912 
 9.96907 
 9.96903 
 9.96898 
 
 5 
 5 
 4 
 5 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 12.0 
 18.0 
 24.0 
 30.0 
 
 11.0 
 16.5 
 22.0 
 27.5 
 
 25 
 26 
 27 
 28 
 29 
 
 9.56247 
 9.56279 
 9.56311 
 9.56343 
 9.56375 
 
 32 
 32 
 32 
 32 
 33 
 
 9.59354 
 9.59391 
 9.59429 
 9.59466 
 9.59503 
 
 37 
 38 
 37 
 37 
 37 
 
 0.40646 
 0.40609 
 0.40571 
 0.40534 
 0.40497 
 
 9.96893 
 9.96888 
 9.96883 
 9.96878 
 9.96873 
 
 5 
 5 
 5 
 5 
 5 
 
 35 
 34 
 33 
 32 
 31 
 
 
 3 
 
 6 3 
 
 7 3 
 8 4 
 
 2 
 
 .2 
 .7 
 .3 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.56408 
 9.56440 
 9.56472 
 9.56504 
 9.56536 
 
 32 
 
 32 
 32 
 32 
 
 00 
 
 9.59540 
 9.59577 
 9.59614 
 9.59651 
 9.59688 
 
 37 
 37 
 37 
 37 
 07 
 
 0.40460 
 0.40423 
 0.40386 
 0.40349 
 0.40312 
 
 9.96868 < 
 9.96863 
 9.96858 
 9.96853 
 9.96848 
 
 5 
 5 
 5 
 5 
 
 30 
 
 29 
 28 
 27 
 26 
 
 ] 
 
 f 
 
 A 
 
 F 
 
 9 4 
 5 
 !0 10 
 16 
 21 
 26 
 
 .8 
 .3 
 .7' 
 .0 
 .3 
 7 
 
 35 
 36 
 37 
 
 38 
 39 
 
 9.56568 
 9.56599 
 9.56631 
 9.56663 
 9.56695 
 
 31 
 32 
 32 
 32 
 32 
 
 9.59725 
 9.59762 
 9.59799 
 9.59835 
 9.59872 
 
 37 
 37 
 36 
 37 
 37 
 
 0.40275 
 0.40238 
 0.40201 
 0.40165 
 0.40128 
 
 9.96843 
 9.96838 
 9.96833 
 9.96828 
 9.96823 
 
 5 
 
 5 
 5 
 5 
 5 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 31 
 3.1 
 
 q c 
 
 6 
 
 0.6 
 
 7 
 
 40 
 41 
 42 
 43 
 44 
 
 9.56727 
 9.56759 
 9.56790 
 9.56822 
 9.56854 
 
 32 
 31 
 32 
 32 
 
 00 
 
 9.59909 
 9.59946 
 9.59983 
 9.60019 
 9.60056 
 
 37 
 37 
 36 
 37 
 07 
 
 0.40091 
 0.40054 
 0.40017 
 0.39981 
 0.39944 
 
 9.96818 
 9.96813 
 9.96808 
 9.96803 
 9.96798 
 
 5 
 
 5 
 5 
 5 
 
 K 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 4.1 
 
 4.7 
 5.2 
 10.3 
 15,5 
 
 0.8 
 0.9 
 1.0 
 2.0 
 3.0 
 
 45 
 
 46 
 47 
 48 
 49 
 
 9.56886 
 9.56917 
 9.56949 
 9.56980 
 9.57012 
 
 31 
 32 
 31 
 32 
 
 9.60093 
 9.60130 
 9.60166 
 9.60203 
 9.60240 
 
 37 
 36 
 37 
 37 
 
 0.39907 
 0.39870 
 0.39834 
 0.39797 
 0.39760 
 
 9.96793 
 9.96788 
 9.96783 
 9.96778 
 9.96772 
 
 5 
 5 
 5 
 6 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 20.7 
 25.8 
 
 5 
 
 4.0 
 5.0 
 
 4 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.57044 
 9.57075 
 9.57107 
 9.57138 
 9.57169 
 
 31 
 32 
 31 
 31 
 
 00 
 
 9.60276 
 9.60313 
 9.60349 
 9.60386 
 9.60422 
 
 37 
 36 
 37 
 36 
 37 
 
 0.39724 
 0.39687 
 0.89651 
 0.39614 
 0.39578 
 
 9.96767 
 9.96762 
 9.96757 
 9.96752 
 9.96747 
 
 5 
 5 
 5 
 5 
 5 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 
 7 
 8 
 9 
 10 
 
 0.5 
 0.6 
 0.7 
 0.8 
 0.8 
 
 0.4 
 0.5 
 0.5 
 0.6 
 0.7 
 
 55 
 56 
 57 
 58 
 59 
 
 9.57201 
 9.57232 
 9.57264 
 9.57295 
 9.57326 
 
 31 
 32 
 31 
 31 
 
 9.60459 
 9.60495 
 9.60532 
 9.60568 
 9.60605 
 
 36 
 
 37 
 36 
 37 
 36 
 
 0.39541 
 0.39505 
 0.39468 
 0.39432 
 0.39395 
 
 9.96742 
 9.96737 
 9.96732 
 9.96727 
 9.96722 
 
 5 
 5 
 5 
 5 
 5 
 
 5 
 4 
 3 
 2 
 1 
 
 20 
 30 
 40 
 50 
 
 l.V 
 2.5 
 3.3 
 4.2 
 
 1.3 
 2.0 
 2.7 
 3.3 
 
 60 
 
 9.57358 
 
 
 9.60641 
 
 
 0.39359 
 
 9.96717 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 / 
 
 
 P.P. 
 
 
 68 
 
1050 
 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 22 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 P.P. 
 
 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 10 
 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 
 9.57358 
 9.57389 
 9.57420 
 9.57451 
 9.57482 
 
 31 
 31 
 31 
 31 
 32 
 31 
 31 
 31 
 31 
 31 
 31 
 31 
 31 
 31 
 31 
 31 
 30 
 31 
 31 
 31 
 30 
 31 
 31 
 31 
 30 
 31 
 30 
 31 
 30 
 31 
 30 
 31 
 30 
 31 
 30 
 31 
 30 
 30 
 30 
 31 
 30 
 30 
 30 
 31 
 30 
 30 
 30 
 30 
 30 
 30 
 30 
 30 
 30 
 30 
 30 
 30 
 29 
 30 
 30 
 30 
 
 9.60641 
 9.60677 
 9.60714 
 9.60750 
 9.60786 
 
 36 
 37 
 36 
 36 
 37 
 36 
 36 
 36 
 36 
 37 
 36 
 36 
 36 
 36 
 36 
 36 
 36 
 36 
 36 
 36 
 36 
 36 
 36 
 36 
 36 
 35 
 36 
 36 
 36 
 35 
 36 
 36 
 36 
 35 
 36 
 35 
 36 
 36 
 35 
 36 
 35 
 36 
 35 
 36 
 35 
 36 
 35 
 35 
 36 
 35 
 35 
 36 
 35 
 35 
 35 
 36 
 
 y> 
 
 35 
 35 
 35 
 
 0.39359 
 0.39323 
 0.39286 
 0.39250 
 0.39214 
 
 9.96717 
 9.96711 
 9.96706 
 9.96701 
 9.96696 
 
 6 
 5 
 5 
 5 
 5 
 5 
 5 
 5 
 6 
 5 
 5 
 5 
 5 
 5 
 5 
 6 
 5 
 5 
 5 
 5 
 6 
 5 
 5 
 5 
 5 
 6 
 5 
 5 
 5 
 5 
 6 
 5 
 5 
 5 
 6 
 5 
 5 
 5 
 6 
 5 
 5 
 6 
 5 
 5 
 5 
 6 
 5 
 5 
 6 
 5 
 5 
 6 
 5 
 5 
 6 
 5 
 5 
 6 
 5 
 5 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 1 
 \ 
 
 .< 
 J 
 
 6 
 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 37 
 
 3.7 
 4.3 
 4.9 
 5.6 
 6.2 
 12.3 
 18.5 
 24.7 
 30.8 
 
 3 
 
 6 3 
 
 7 4 
 8 4 
 9 5 
 5 
 11 
 K> 17 
 10 23 
 >0 29 
 
 32 
 
 3.2 
 3.7 
 4.3 
 
 4.8 
 5.3 
 10.7 
 16.0 
 21.3 
 26.7 
 
 30 
 
 3.0 
 3.5 
 4.0 
 4.5 
 5.0 
 10.0 
 15.0 
 20.0 
 25.0 
 
 6 
 
 0.6 
 0.7 
 0.8 
 0.9 
 1.0 
 2.0 
 3.0 
 4.0 
 5.0 
 
 36 
 
 3.6 
 4.2 
 4.8 
 5.4 
 6.0 
 12.0 
 18.0 
 24.0 
 30.0 
 
 5 
 .5 
 .1 
 
 .7 
 .3 
 
 .8- 
 
 5 
 .3 
 .2 
 
 31 
 
 3.1 
 3.6 
 
 4.1 
 4.7 
 5.2 
 10.3 
 15.5 
 20.7 
 25.8 
 
 29 
 
 2.9 
 3.4 
 3.9 
 4.4 
 4.8 
 9.7 
 14.5 
 19.3 
 24.2 
 
 5 
 0.5 
 0.6 
 0.7 
 0.8 
 0.8 
 1.7 
 2.5 
 3.3 
 4.2 
 
 9.57514 
 9.57545 
 9.57576 
 9.57607 
 9.57638 
 9.57669 
 9.57700 
 9.57731 
 9.57762 
 9.57793 
 
 9.60823 
 9.60859 
 9.60895 
 9.60931 
 9.60967 
 9.61004" 
 9.61040 
 9.61076 
 9.61112 
 9.61148 
 
 0.39177 
 0.39141 
 0.39105 
 0.39069 
 0.39033 
 0.38996 
 0.38960 
 0.38924 
 0.38888 
 0.38852 
 
 9.96691 
 9.96686 
 9.96681 
 9.96676 
 9.96670 
 9.96665 
 9.96660 
 9.96655 
 9.96650 
 9.96645 
 
 55 
 54 
 53 
 52 
 51 
 ^0~ 
 49 
 48 
 47 
 46 
 
 9.57824 
 9.57855 
 9.57885 
 9.57916 
 9.57947 
 
 9.61184 
 9.61220 
 9.61256 
 9.61292 
 9.61328 
 
 0.38816 
 0.38780 
 0.38744 
 0.38708 
 0.38672 
 
 9.96640 
 9.96634 
 9.96629 
 9.96624 
 9.96619 
 
 45 
 44 
 43 
 42 
 
 41 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.57978 
 9.58008 
 9.58039 
 9.58070 
 9.58101 
 9.58131 
 9.58162 
 9.58192 
 9.58223 
 9.58253 
 9.58284 
 9.58314 
 9.58345 
 9.58375 
 9.58406 
 
 9.61364 
 9.61400 
 9.61436 
 9.61472 
 9.61508 
 
 0.38636 
 0.38600 
 0.38564 
 0.38528 
 0.38492 
 
 9.96614 
 9.96608 
 9.96603 
 9.96598 
 9.96593 
 
 40 
 
 39 
 38 
 37 
 36 
 lJ5~ 
 34 
 33 
 32 
 31 
 
 ~w 
 
 29 
 28 
 27 
 26 
 
 25 
 26 
 27 
 28 
 29 
 
 9.61544 
 9.61579 
 9.61615 
 9.61651 
 9.61687 
 
 0.38456 
 0.38421 
 0.38385 
 0.38349 
 0.38313 
 
 9.96588 
 9.96582 
 9.96577 
 9.96572 
 9.96567 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.6172t 
 9.61758 
 9.61794 
 9.61830 
 9.61865 
 
 0.38278 
 0.38242 
 0.38206 
 0.38170 
 0.38135 
 
 9.96562 
 9.96556 
 9.96551 
 9.96546 
 9.96541 
 
 35 
 36 
 37 
 38 
 39 
 40 
 41 
 42 
 43 
 44 
 45 
 46 
 47 
 48 
 49 
 
 9.58436 
 9.58467 
 9.58497 
 9.58527 
 9.58557 
 
 9.61901 
 9.61936 
 9.61972 
 9.62008 
 9.62043 
 
 0.38099 
 0.38064 
 0.38028 
 0.37992 
 0.37957 
 
 9.96535 
 9.96530 
 9.96525 
 9.96520 
 9.96514 
 
 25 
 24 
 23 
 22 
 21 
 
 9.58588 
 9.58618 
 9.58648 
 9.58678 
 9.58709 
 
 9.62079 
 9.62114 
 9.62150 
 9.62185 
 9.62221 
 
 0.37921 
 0.37886 
 0.37850 
 0.37815 
 0.37779 
 
 9.96509 
 9.96504 
 9.96498 
 9.96493 
 9.96488 
 
 20 
 
 19 
 18 
 17 
 16 
 15 
 14 
 13 
 12 
 11 
 
 9.58739 
 9.58769 
 9.58799 
 9.58829 
 9.58859 
 9.58889 
 9.58919 
 9.58949 
 9.58979 
 9.59009 
 
 9.62256 
 9.62292 
 9.62327 
 9.62362 
 9.62398 
 
 0.37744 
 0.37708 
 0.37673 
 0.37638 
 0.37602 
 
 9.96483 
 9.96477 
 9.96472 
 9.96467 
 9.96461 
 
 50 
 
 51 
 52 
 53 
 54 
 ~55~ 
 56 
 57 
 58 
 59 
 
 9.62433 
 9.62468 
 9.62504 
 9.62539 
 9.62574 
 
 0.37567 
 0.37532 
 0.37496 
 0.37461 
 0.37426 
 
 9.96456 
 9.96451 
 9.96445 
 9.96440 
 9.96435 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 9.59039 
 9.59069 
 9.59098 
 9.59128 
 9.59158 
 
 9.62609 
 9.62645 
 9.62680 
 9.62715 
 9.62750 
 
 0.37391 
 0.37355 
 0.37320 
 0.37285 
 0.37250 
 
 9.96429 
 9.96424 
 9.96419 
 9.96413 
 9.96408 
 
 5 
 4 
 3 
 2 
 1 
 
 60 
 
 9.59188 
 
 9.62785 
 
 0.37215 
 
 9.96403 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.tf. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 / 
 
 P.P. 
 
 67 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 23 
 
 1051 
 
 / 
 
 L. Sin.; 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 P.P. 
 
 
 
 1 
 
 2 
 3 
 4 
 
 6 
 
 7 
 8 
 9 
 
 9.59188 
 9.59218 
 9.59247 
 9.59277 
 9.59307 
 
 30 
 29 
 30 
 30 
 29 
 30 
 30 
 29 
 30 
 29 
 
 9.62785 
 9.62820 
 9.62855 
 9.62890 
 9.62926 
 
 35 
 35 
 35 
 36 
 35 
 35 
 35 
 35 
 35 
 34 
 35 
 35 
 35 
 35 
 35 
 35 
 34 
 35 
 35 
 35 
 35 
 34 
 35 
 35 
 34 
 35 
 34 
 35 
 35 
 34 
 35 
 34 
 35 
 34 
 35 
 34 
 35 
 34 
 34 
 35 
 34 
 34 
 35 
 34 
 34 
 35 
 34 
 34 
 34 
 34 
 35 
 34 
 34 
 34 
 34 
 34 
 34 
 34 
 34 
 34 
 
 0.37215 
 0.37180 
 0.37145 
 0.37110 
 0.37074 
 
 9.96403 
 9.96397 
 9.96392 
 9.96387 
 9.96381 
 
 6 
 5 
 5 
 6 
 5 
 6 
 5 
 5 
 6 
 5 
 6 
 5 
 5 
 6 
 5 
 6 
 5 
 6 
 5 
 6 
 5 
 5 
 6 
 5 
 6 
 5 . 
 6 
 5 
 6 
 5 
 6 
 5 
 6 
 5 
 6 
 5 
 6 
 5 
 6 
 5 
 6 
 5 
 6 
 6 
 5 
 6 
 5 
 6 
 5 
 6 
 6 
 5 
 6 
 5 
 6 
 6 
 5 
 6 
 5 
 6 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 1 
 
 2 
 3 
 4 
 
 5 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 ! 
 
 i 
 
 i 
 
 i 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 36 
 
 3.6 
 4.2 
 4.8 
 5.4 
 6.0 
 12.0 
 18.0 
 24.0 
 30.0 
 
 3 
 
 6 3 
 7 4 
 8 4 
 9 5 
 5 
 11 
 17 
 22 
 28 
 
 30 
 
 3.0 
 3.5 
 4.0 
 4.5 
 5.0 
 10.0 
 15.0 
 20.0 
 25.0 
 
 2 
 
 6 2 
 
 7 3 
 
 8 a 
 
 9 4 
 LO 4 
 JO 
 50 14 
 W IS 
 )0 2S 
 
 6 
 0.6 
 0.7 
 0.8 
 0.9 
 1.0 
 2.0 
 3.0 
 4.0 
 5.0 
 
 35 
 
 3.5 
 4.1 
 4.7 
 5.3 
 5.8 
 11.7 
 17.5 
 23.3 
 29.2 
 
 1 
 
 4 
 
 5 
 1 
 7 
 3 
 
 7 
 .3 
 
 29 
 
 2.9 
 3.4 
 3.9 
 4.4 
 4.8 
 9.7 
 14.5 
 19.3 
 24.2 
 
 8 
 
 .8 
 .3 
 .7 
 .2 
 .7 
 .3 
 .0 
 .7 
 .3 
 
 5 
 
 0.5 
 0.6 
 0.7 
 0.8 
 0.8 
 1.7 
 2.5 
 3.3 
 4.2 
 
 9.59336 
 9.59366 
 9.59396 
 9.59425 
 9.59455 
 
 9.62961 
 9.62996 
 9.63031 
 9.63066 
 9.63101 
 
 0.37039 
 0.37004 
 0.36969 
 0.36934 
 0.36899 
 
 9.96376 
 9.96370 
 9.96365 
 9.96360 
 9.96354 
 
 55 
 54 
 53 
 52 
 51 
 
 10 
 
 11 
 
 12 
 13 
 14 
 
 9.59484 
 9.59514 
 9.59543 
 9.59573 
 9.59602 
 
 30 
 29 
 30 
 29 
 30 
 29 
 29 
 30 
 29 
 29 
 30 
 29 
 29 
 29 
 29 
 30 
 29 
 29 
 29 
 29 
 29 
 29 
 29 
 29 
 29 
 29 
 29 
 29 
 29 
 28 
 29 
 29 
 29 
 28 
 29 
 29 
 29 
 28 
 29 
 28 
 29 
 29 
 28 
 29 
 28 
 29 
 28 
 29 
 28 
 28 
 
 9.63135 
 9.63170 
 9.63205 
 9.63240 
 9.63275 
 
 0.36865 
 0.36830 
 0.36795 
 0.36760 
 0.36725 
 
 9.96349 
 9.96343 
 9.96338 
 9.96333 
 9.96327 
 
 50 
 
 49 
 48 
 47 
 46 
 
 15 
 16 
 17 
 
 18 
 19 
 
 9.59632 
 9.59661 
 9.59690 
 9.59720 
 9.59749 
 
 9.63310 
 9.63345 
 9.63379 
 9.63414 
 9.63449 
 
 0.36690 
 0.36655 
 0.36621 
 0.36586 
 0.36551 
 
 9.96322 
 9.96316 
 9.96311 
 9.96305 
 9.96300 
 
 45 
 44 
 43 
 42 
 41 
 40 
 39 
 38 
 37 
 36 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.59778 
 9.59808 
 9.59837 
 9.59866 
 9.59895 
 
 9.63484 
 9.63519 
 9.63553 
 9.63588 
 9.63623 
 
 0.36516 
 0.36481 
 0.36447 
 0.36412 
 0.36377 
 
 9.96294 
 9.96289 
 9.96284 
 9.96278 
 9.96273 
 
 25 
 26 
 27 
 28 
 29 
 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 
 9.59924 
 9.59954 
 9.59983 
 9.60012 
 9.60041 
 
 9.63657 
 9.63692 
 9.63726 
 9.63761 
 9.63796 
 
 0.36343 
 0.36308 
 0.36274 
 0.36239 
 0.36204 
 
 9.96267 
 9.96262 
 9.96256 
 9.96251 
 9.96245 
 
 35 
 34 
 33 
 32 
 31 
 
 9.60070 
 9.60099 
 9.60128 
 9.60157 
 9.60186 
 
 9.63830 
 9.63865 
 9.63899 
 9.63934 
 9.63968 
 
 0.36170 
 0.36135 
 0.36101 
 0.36066 
 0.36032 
 
 9.96240 
 9.96234 
 9.96229 
 9.96223 
 9.96218 
 
 30 
 
 29 
 2S 
 27 
 26 
 25 
 24 
 23 
 22 
 21 
 
 9.60215 
 9.60244 
 9.60273 
 9.60302 
 9.60331 
 9.60359 
 9.60388 
 9.60417 
 9.60446 
 9.60474 
 
 9.64003 
 9.64037 
 9.64072 
 9.64106 
 9.64140 
 
 0.35997 
 0.35963 
 0.35928 
 0.35894 
 0.35860 
 
 9.96212 
 9.96207 
 9.96201 
 9.96196 
 9.96190 
 
 40 
 
 41 
 42 
 43 
 44 
 
 46 
 47 
 48 
 49 
 
 9.64175 
 9.64209 
 9.64243 
 9.64278 
 9.64312 
 
 0.35825 
 0.35791 
 0.35757 
 0.35722 
 0.35688 
 
 9.96185 
 9.96179 
 9.96174 
 9.96168 
 9.96162 
 
 20 
 
 19 
 18 
 17 
 16 
 
 9.60503 
 9.60532 
 9.60561 
 9.60589 
 9.60618 
 
 9.64346 
 9.64381 
 9.64415 
 9.64449 
 9.64483 
 9.64517 
 9.64552 
 9.64586 
 9.64620 
 9.64654 
 9.64688 
 9.64722 
 9.64756 
 9.64790 
 9.64824 
 
 0.35654 
 0.35619 
 0.35585 
 0.35551 
 0.35517 
 
 9.96157 
 9.96151 
 9.96146 
 9.96140 
 9.96135 
 
 15 
 14 
 13 
 12 
 11 
 
 50 
 
 51 
 52 
 53 
 
 54 
 
 9.60646 
 9.60675 
 9.60704 
 9.60732 
 9.60761 
 
 0.35483 
 0.35448 
 0.35414 
 0.35380 
 0.35346 
 0.35312 
 0.35278 
 0.35244 
 0.35210 
 0.35176 
 
 9.96129 
 9.96123 
 9.96118 
 9.96112 
 9.96107 
 
 10 
 
 9 
 8 
 7 
 6 
 
 55 
 56 
 57 
 58 
 59 
 
 9.60789 
 9.60818 
 9.60846 
 9.60875 
 9.60903 
 
 9.96101 
 9.96095 
 9.96090 
 9.96084 
 9.96079 
 
 5 
 4 
 3 
 2 
 1 
 
 60 
 
 9.60931 
 
 9.64858 
 
 0.35142 
 
 9.96073 
 
 
 
 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang 
 
 L. Sin. 
 
 d. 
 
 
 P. F. 
 
1052 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 24 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 P 
 
 P 
 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 9.60931 
 9.60960 
 9.60988 
 9.61016 
 9.61045 
 
 29 
 28 
 28 
 29 
 
 oo 
 
 9.64858 
 9.64892 
 9.64926 
 9.64960 
 9.64994 
 
 34 
 34 
 34 
 34 
 34 
 
 0.35142 
 0.35108 
 0.35074 
 0.35040 
 0.35006 
 
 9.96073 
 9.96067 
 9.96062 
 9.96056 
 9.96050 
 
 6 
 5 
 
 6 
 6 
 
 60 
 
 59 
 58 
 57 
 56 
 
 3 
 6 [ 
 
 7 4 
 
 4 
 
 .4 
 
 
 33 
 
 3.3 
 39 
 
 5 
 
 6 
 7 
 8 
 9 
 
 9.61073 
 9.61101 
 9.61129 
 9.61158 
 9.61186 
 
 28 
 28 
 29 
 28 
 
 9.65028 
 9.65062 
 9.65096 
 9.65130 
 9.65164 
 
 34 
 34 
 34 
 34 
 
 00 
 
 0.34972 
 0.34938 
 0.34904 
 0.34870 
 0.34836 
 
 9.96045 
 9.96039 
 9.96034 
 9.96028 
 9.96022 
 
 6 
 5 
 
 6 
 6 
 
 55 
 54 
 53 
 
 52 
 51 
 
 8 A 
 9 { 
 10 I 
 
 20 11 
 
 30 r 
 
 .5 
 >.l 
 >.7 
 .3 
 .0 
 
 4.4 
 5.0 
 5.5 
 11.0 
 16.5 
 
 10 
 11 
 12 
 13 
 14 
 
 9.61214 
 9.61242 
 9.61270 
 9.61298 
 9.61326 
 
 28 
 28 
 28 
 28 
 
 9.65197 
 9.65231 
 9.65265 
 9.65299 
 9.65333 
 
 34 
 34 
 34 
 34 
 
 00 
 
 0.34803 
 0.34769 
 0.34735 
 0.34701 
 0.34667 
 
 9.96017 
 9.96011 
 9.96005 
 9.96000 
 9.95994 
 
 6 
 6 
 5 
 6 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 X 
 50 2* 
 
 J.7 
 
 5.3 
 
 ? 
 
 22.0 
 27.5 
 
 9 
 
 15 
 16 
 17 
 
 18 
 19 
 
 9.61354 
 9.61382 
 9.61411 
 9.61438 
 9.61466 
 
 28 
 29 
 27 
 28 
 
 00 
 
 9.65366 
 9.65400 
 9.65434 
 9.65467 
 9.65501 
 
 34 
 34 
 33 
 34 
 
 <>A 
 
 0.34634 
 0.34600 
 0.34566 
 0.34533 
 0.34499 
 
 9.95988 
 9.95982 
 9.95977 
 9.95971 
 9.95965 
 
 6 
 5 
 6 
 6 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 7 
 8 
 9 
 10 
 
 2 
 8 
 
 3 
 4 
 4 
 
 .9 
 .4 
 .9 
 .4 
 .8 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.61494 
 9.61522 
 9.61550 
 9.61578 
 9.61606 
 
 28 
 28 
 28 
 28 
 
 00 
 
 9.65535 
 9.65568 
 9.65602 
 9.65636 
 9.65669 
 
 33 
 34 
 34 
 
 33 
 04 
 
 0.34465 
 0.34432 
 0.34398 
 0.34364 
 0.34331 
 
 9.95960 
 9.95954 
 9.95948 
 9.95942 
 9.95937 
 
 6 
 6 
 6 
 5 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 y 
 
 14 
 11 
 24 
 
 .7 
 .5 
 .3 
 .2 
 
 25 
 26 
 
 27 
 28 
 29 
 
 9.61634 
 9.61662 
 9.61689 
 9.61717 
 9.61745 
 
 28 
 
 27 
 28 
 28 
 
 OQ 
 
 9.65703 
 9.65736 
 9.65770 
 9.65803 
 9.65837 
 
 33 
 34 
 33 
 34 
 
 00 
 
 0.34297 
 0.34264 
 0.34230 
 0.34197 
 0.34163 
 
 9.95931 
 9.95925 
 9.95920 
 9.95914 
 9.95908 
 
 6 
 5 
 6 
 6 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 2 
 2 
 1 
 1 
 
 8 
 
 .8 
 .3 
 .7 
 
 30 
 31 
 32 
 33 
 34 
 
 9.61773 
 
 9.61800 
 9.61828 
 9.61856 
 9.61883 
 
 27 
 28 
 28 
 27 
 28 
 
 9.65870 
 9.65904 
 9.65937 
 9.65971 
 9.66004 
 
 34 
 33 
 34 
 33 
 
 34 
 
 0.34130 
 0.34096 
 0.34063 
 0.34029 
 0.33996 
 
 9.95902 
 9.95897 
 9.95891 
 9.95885 
 9.95879 
 
 5 
 
 6 
 6 
 6 
 g 
 
 30 
 
 29 
 28 
 27 
 26 
 
 10 
 20 
 30 
 40 
 50 
 
 4 
 ( 
 
 14 
 
 18 
 
 g 
 
 .7 
 .3 
 .0 
 .7 
 .3 
 
 35 
 36 
 37 
 
 38 
 39 
 
 9.61911 
 9.61939 
 9.61966 
 9.61994 
 9.62021 
 
 28 
 27 
 28 
 27 
 
 00 
 
 9.66038 
 9.66071 
 9.66104 
 9.66138 
 9.66171 
 
 33 
 33 
 34 
 33 
 
 0.33962 
 0.33929 
 0.33896 
 0.33862 
 0.33829 
 
 9.95873 
 9.95868 
 9.95862 
 9.95856 
 9.95850 
 
 5 
 6 
 6 
 6 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 2 
 
 2 
 
 7 
 .7 
 
 n 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.62049 
 9.62076 
 9.62104 
 9.62131 
 9.62159 
 
 27 
 28 
 27 
 28 
 27 
 
 9.66204 
 9.66238 
 9.66271 
 9.66304 
 9.66337 
 
 34 
 33 
 33 
 33 
 
 QA 
 
 0.33796 
 0.33762 
 0.33729 
 0.33696 
 0.33663 
 
 9.95844 
 9.95839 
 9.95833 
 9.95827 
 9.95821 
 
 6 
 
 6 
 6 
 6 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 3 
 4 
 4 
 9 
 13 
 
 .6 
 .1 
 .5 
 .0 
 .5 
 
 45 
 46 
 47 
 48 
 49 
 
 9.62186 
 9.62214 
 9.62241 
 9.62268 
 9.62296 
 
 28 
 27 
 27 
 28 
 27 
 
 9.66371 
 9.66404 
 9.66437 
 9.66470 
 9.66503 
 
 33 
 33 
 33 
 33 
 
 q-i 
 
 0.33629 
 0.33596 
 0.33563 
 0.33530 
 0.33497 
 
 9.95815 
 9.95810 
 9.95804 
 9.95798 
 9.95792 
 
 5 
 6 
 6 
 6 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 18 
 22 
 
 R 
 
 .0 
 .5 
 
 5 
 
 50 
 51 
 52 
 53 
 
 54 
 
 9.62323 
 9.62350 
 9.62377 
 9.62405 
 9.62432 
 
 27 
 27 
 28 
 27 
 27 
 
 9.66537 
 9.66570 
 9.66603 
 9.66636 
 9.66669 
 
 33 
 33 
 33 
 33 
 
 QO 
 
 0.33463 
 0.33430 
 0.33397 
 0.33364 
 
 0.33331 
 
 9.95786 
 9.95780 
 9.95775 
 9.95769 
 9.95763 
 
 6 
 5 
 
 6 
 
 6 
 g 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 ( 
 7 ( 
 8 C 
 9 ( 
 10 1 
 
 .6 
 .7 
 .8 
 .9 
 .0 
 
 0.5 
 0.6 
 0.7 
 0.8 
 0.8 
 
 55 
 56 
 57 
 58 
 59 
 
 9.62459 
 9.62486 
 9.62513 
 9.62541 
 9.62568 
 
 27 
 27 
 28 
 27 
 27 
 
 9.66702 
 9.66735 
 9.66768 
 9.66801 
 9.66834 
 
 33 
 33 
 33 
 33 
 33 
 
 0.332)8 
 0.33265 
 0.33232 
 0.33199 
 0.33166 
 
 9.95757 
 9.95751 
 9.95745 
 9.95739 
 9.95733 
 
 6 
 6 
 6 
 6 
 5 
 
 5 
 4 
 3 
 2 
 
 1 
 
 20 5 
 30 f 
 40 4 
 50 
 
 .0 
 .0 
 .0 
 .0 
 
 1.7 
 2.5 
 3.3 
 4.2 
 
 60 
 
 9.62595 
 
 
 9.66867 
 
 
 0.33133 
 
 9.95728 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 ' 
 
 P 
 
 p. 
 
 
 65 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 25 C 
 
 1053 
 
 J_ 
 
 L. Sin 
 
 d. 
 
 L.Tang 
 
 d.c. 
 
 L. Cotg 
 
 L. Cos. 
 
 d. 
 
 
 P 
 
 . I 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.62595 
 9.62622 
 9.62649 
 9.62676 
 9.62703 
 
 27 
 27 
 27 
 27 
 27 
 
 9.66867 
 9.66900 
 9.66933 
 9.66966 
 9.66999 
 
 33 
 33 
 33 
 33 
 33 
 
 0.33133 
 0.33100 
 0.33067 
 0.33034 
 0.33001 
 
 9.95728 
 9.95722 
 9.95716 
 9.95710 
 9.95704 
 
 6 
 6 
 6 
 6 
 
 60 
 
 59 
 58 
 57 
 56 
 
 : 
 6 ; 
 
 3 
 
 U 
 
 32 
 
 3.2 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.62730 
 9.62757 
 9.62784 
 9.62811 
 9.62838 
 
 27 
 27 
 27 
 27 
 27 
 
 9.67032 
 9.67065 
 9.67098 
 9.67131 
 9.67163 
 
 33 
 33 
 33 
 32 
 qq 
 
 0.32968 
 0.32935 
 0.32902 
 0.32869 
 0.32837 
 
 9.95698 
 9.95692 
 9.95686 
 9.95680 
 9.95674 
 
 6 
 6 
 6 
 6 
 6 
 
 55 
 54 
 53 
 52 
 51 
 
 8 < 
 9 I 
 10 I 
 20 11 
 30 1( 
 
 1.4 
 
 >.o 
 
 ).5 
 .0 
 > *> 
 
 3.7 
 4.3 
 4.8 
 5.3 
 10.7 
 160 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.62865 
 9.62892 
 9.62918 
 9.62945 
 9.62972 
 
 27 
 26 
 
 27 
 27 
 27 
 
 9.67196 
 9.67229 
 9.67262 
 9.67295 
 9.67327 
 
 33 
 33 
 33 
 32 
 
 0.32804 
 0.32771 
 0.32738 
 0.32705 
 0.32673 
 
 9.95668 
 9.95663 
 9.95657 
 9.95651 
 9.95645 
 
 6 
 5 
 
 6 
 6 
 6 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 % 
 50 2' 
 
 J.O 
 
 '.5 
 
 21.3 
 26.7 
 
 15 
 16 
 17 
 18 
 19 
 
 9.62999 
 9.63026 
 9.63052 
 9.63079 
 9.63106 
 
 27 
 26 
 27 
 27 
 27 
 
 9.67360 
 9.67393 
 9.67426 
 9.67458 
 9.67491 
 
 33 
 33 
 32 
 33 
 
 0.32640 
 0.32607 
 0.32574 
 0.32542 
 0.32509 
 
 9.95639 
 9.95633 
 9.95627 
 9.95621 
 9.95615 
 
 6 
 6 
 6 
 6 
 6 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 
 7 
 8 
 9 
 10 
 
 f 
 
 \ 
 
 i 
 
 4 
 A 
 
 .7 
 .2 
 .6 
 .1 
 .5 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.63133 
 9.63159 
 9.63186 
 9.63213 
 9.63239 
 
 26 
 27 
 27 
 26 
 27 
 
 9.67524 
 9.67556 
 9.67589 
 9.67622 
 9.67654 
 
 32 
 33 
 33 
 32 
 
 00 
 
 0.32476 
 0.32444 
 0.32411 
 0.32378 
 0.32346 
 
 9.95609 
 9.95603 
 9.95597 
 9.95591 
 9.95585 
 
 6 
 6 
 
 6 
 6 
 6 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 60 
 
 f 
 
 i;- 
 
 li 
 
 2^ 
 
 .0 
 .5 
 .0 
 .5 
 
 25 
 
 26 
 27 
 28 
 29 
 
 9.63266 
 9.63292 
 9.63319 
 9.63345 
 9.63372 
 
 26 
 
 27 
 26 
 27 
 26 
 
 9.67687 
 9.67719 
 9.67752 
 9.67785 
 9.67817 
 
 32 
 33 
 33 
 32 
 
 00 
 
 0.32313 
 0.32281 
 0.32248 
 0.32215 
 0.32183 
 
 9.95579 
 9.95573 
 9.95567 
 9.95561 
 9.95555 
 
 6 
 6 
 6 
 6 
 6 
 
 85 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 2 
 
 : 
 
 
 
 s 
 
 6 
 
 .6 
 .0 
 .5 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.63398 
 9.63425 
 9.63451 
 9.63478 
 9.63504 
 
 27 
 26 
 27 
 26 
 27 
 
 9.67850 
 9.67882 
 9.67915 
 9.67947 
 9.67980 
 
 32 
 83 
 32 
 33 
 32 
 
 0.32150 
 0.32118 
 0.32085 
 0.32053 
 0.32020 
 
 9.95549 
 9.95543 
 9.95537 
 9.95531 
 9.95525 
 
 6 
 6 
 6 
 6 
 6 
 
 30 
 
 29 
 28 
 27 
 26 
 
 9 
 10 
 20 
 30 
 40 
 fin 
 
 1 
 
 4 
 j 
 
 13 
 17 
 
 01 
 
 .9 
 .3 
 .7 
 .0 
 .3 
 7 
 
 35 
 36 
 37 
 
 38 
 39 
 
 9.63531 
 9.63557 
 9.63583 
 9.63610 
 9.63636 
 
 26 
 26 
 27 
 26 
 26 
 
 9.68012 
 9.68044 
 9.68077 
 9.68109 
 9.68142 
 
 32 
 33 
 32 
 33 
 32 
 
 0.31988 
 0.31956 
 0.31923 
 0.31891 
 0.31858 
 
 9.95519 
 9.95513 
 9.95507 
 9.95500 
 9.95494 
 
 6 
 6 
 7 
 6 
 
 25 
 
 24 
 23 
 22 
 21 
 
 6 
 
 1 
 
 
 7 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.63662 
 9.63689 
 9.63715 
 9.63741 
 9.63767 
 
 27 
 26 
 26 
 26 
 27 
 
 9.68174 
 9.68206 
 9.68239 
 9.68271 
 9.68303 
 
 32 
 33 
 32 
 32 
 
 00 
 
 0.31826 
 0.31794 
 0.31761 
 0.31729 
 0.31697 
 
 9.95488 
 9.95482 
 9.95476 
 9.95470 
 9.95464 
 
 6 
 6 
 6 
 6 
 
 20 
 
 19 
 
 18 
 17 
 16 
 
 8 
 9 
 10 
 
 20 
 30 
 
 
 
 1 
 1 
 
 2 
 
 s 
 
 9 
 
 1 
 2 
 3 
 5 
 
 45 
 46 
 47 
 
 48 
 49 
 
 9.63794 
 9.63820 
 9.63846 
 9.63872 
 9.63898 
 
 26 
 26 
 26 
 26 
 
 2fi 
 
 9.68336 
 9.68368 
 9.68400 
 9.68432 
 9.68465 
 
 32 
 32 
 32 
 33 
 
 00 
 
 0.31664 
 0.31632 
 0.31600 
 0.31568 
 0.31535 
 
 9.95458 
 9.95452 
 9.95446 
 9.95440 
 9.95434 
 
 6 
 6 
 6 
 6 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 60 
 
 1 
 
 4. 
 5. 
 
 ; 
 
 7 
 8 
 
 K 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.63924 
 9.63950 
 9.63976 
 9.64002 
 9.64028 
 
 26 
 26 
 26 
 26 
 9fi 
 
 9.68497 
 9.68529 
 9.68561 
 9.68593 
 9.68626 
 
 32 
 32 
 32 
 33 
 
 00 
 
 0.31503 
 0.31471 
 0.31439 
 0.31407 
 0.31374 
 
 9.95427 
 9.95421 
 9.95415 
 9.95409 
 9.95403 
 
 6 
 6 
 6 
 6 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 6 
 
 7 
 8 
 9 
 10 1 
 
 6 
 
 7 
 8 
 9 
 
 
 5 5 
 0.6 
 0.7 
 0.8 
 0.8 
 
 55 
 56 
 57 
 ! 58 
 59 
 
 9.64054 
 9.64080 
 9.64106 
 9.64132 
 9.64158 
 
 26 
 26 
 26 
 26 
 26 
 
 9.68658 
 9.68690 
 9.68722 
 9.68754 
 9.68786 
 
 32 
 32 
 32 
 32 
 32 
 
 0.31342 
 0.31310 
 0.31278 
 0.31246 
 0.31214 
 
 9.95397 
 9.95391 
 9.95384 
 9.95378 
 9.95372 
 
 6 
 7 
 6 
 6 
 g 
 
 5 
 4 
 3 
 2 
 1 
 
 20 2 
 30 3 
 40 4 
 50 5 
 
 
 
 
 
 
 1.7 
 
 2.5 
 3.3 
 4.2 
 
 SO 
 
 9.64184 
 
 
 9.68818 
 
 
 0.31182 
 
 9.95366 
 
 
 
 
 
 
 
 
 L. Cos, 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 / 
 
 P. 
 
 P. 
 
 
 64 
 
1054 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 26 
 
 _ 
 
 L. Sin. 
 
 d. 
 
 L.Tang 
 
 d.c. 
 
 L. Cotg 
 
 L. Cos. 
 
 d. 
 
 
 
 P 
 
 . P 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.64184 
 9.64210 
 9.64236 
 9.64262 
 9.64288 
 
 26 
 26 
 26 
 26 
 25 
 
 9.68818 
 9.68850 
 9.68882 
 9.68914 
 9.68946 
 
 32 
 32 
 32 
 32 
 
 00 
 
 0.31182 
 0.31150 
 0.31118 
 0.31086 
 0.31054 
 
 9.95366 
 9.95360 
 9.95354 
 9.95348 
 9.95341 
 
 6 
 6 
 6 
 
 7 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 : 
 
 2 
 
 5.2 
 
 f n 
 
 31 
 
 3.1 
 
 5 
 6 
 7 
 8 
 9 
 
 9.64313 
 9.64339 
 9.64365 
 9.64391 
 9.64417 
 
 26 
 26 
 26 
 26 
 
 OK 
 
 9.68978 
 9.69010 
 9.69042 
 9.69074 
 9.69106 
 
 32 
 32 
 32 
 32 
 
 00 
 
 0.31022 
 0.30990 
 0.30958 
 0.30926 
 0.30894 
 
 9.95335 
 9.95329 
 9.95323 
 9.95317 
 9.95310 
 
 6 
 6 
 6 
 7 
 
 55 
 54 
 53 
 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 t 
 ," , 
 
 i 
 K 
 it 
 
 1.3 
 
 U 
 
 U) 
 
 4.1 
 4.7 
 5.2 
 10.3 
 15.5 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.64442 
 9.64468 
 9.64494 
 9.64519 
 9.64545 
 
 26 
 26 
 25 
 26 
 
 9.69138 
 9.69170 
 9.69202 
 9.69234 
 9.69266 
 
 32 
 
 32 
 32 
 32 
 
 00 
 
 0.30862 
 0.30830 
 0.30798 
 0.30766 
 0.30734 
 
 9.95304 
 9.95298 
 9.95292 
 9.95286 
 9.95279 
 
 6 
 6 
 6 
 6 
 
 7 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 2 
 
 2( 
 
 .3 
 
 5.7 
 
 2 
 
 20.7 
 25.8 
 
 g 
 
 15 
 16 
 17 
 18 
 19 
 
 9.64571 
 9.64596 
 9.64622 
 9.64647 
 9.64673 
 
 25 
 26 
 26 
 26 
 25 
 
 9.69298 
 9.69329 
 9.69361 
 9.69393 
 9.69425 
 
 31 
 32 
 32 
 32 
 
 00 
 
 0.30702 
 0.30671 
 0.30639 
 0.30607 
 0.30575 
 
 9.95273 
 9.95267 
 9.95261 
 9.95254 
 9.95248 
 
 6 
 
 6 
 7 
 6 
 
 45 
 44 
 43 
 42 
 41 
 
 ; 
 
 6 
 
 7 
 8 
 9 
 
 
 2 
 I 
 
 3 
 8 
 4 
 
 .6 
 .0 
 .5 
 .9 
 .3 
 
 20 
 
 21 
 22 
 23 
 24 
 
 964698 
 9.64724 
 9.64749 
 9.64775 
 9.64800 
 
 26 
 26 
 26 
 26 
 2fi 
 
 9.69457 
 
 9.69488 
 9.69520 
 9.69552 
 9.69584 
 
 31 
 32 
 32 
 32 
 
 0.30543 
 0.30512 
 0.30480 
 0.30448 
 0.30416 
 
 9.95242 
 9.95236 
 9.95229 
 9.95223 
 9.95217 
 
 6 
 
 7 
 6 
 6 
 
 40 
 
 39 
 38 
 37 
 36 
 
 |i 
 
 H 
 ( 
 
 '0 
 
 
 
 
 8 
 It! 
 17 
 21 
 
 .7 
 .0 
 .3 
 .7 
 
 25 
 26 
 27 
 28 
 29 
 
 9.64826 
 9.64851 
 9.64877 
 9.64902 
 9.64927 
 
 25 
 26 
 25 
 25 
 2fi 
 
 9.69615 
 9.69647 
 9.69679 
 9.69710 
 9.69742 
 
 32 
 32 
 31 
 32 
 
 00 
 
 0.30385 
 0.30353 
 0.30321 
 0.30290 
 0.30258 
 
 9.95211 
 9.95204 
 9.95198 
 9.95192 
 9.95185 
 
 7 
 
 6 
 6 
 
 7 
 
 35 
 34 
 33 
 32 
 31 
 
 
 6 
 
 7 
 8 
 
 2 
 
 2 
 2 
 | 
 
 5 
 .5 
 .9 
 .3 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.64953 
 9.64978 
 9.65003 
 9.65029 
 9.65054 
 
 25 
 26 
 26 
 25 
 25 
 
 9.69774 
 9.69805 
 9.69837 
 9.69868 
 9.69900 
 
 31 
 32 
 31 
 32 
 
 00 
 
 0.30226 
 0.30195 
 0.30163 
 0.30132 
 0.30100 
 
 9.95179 
 9.95173 
 9.95167 
 9.95160 
 9.95154 
 
 6 
 6 
 
 7 
 6 
 
 30 
 
 29 
 28 
 27 
 26 
 
 1 
 
 ! 
 
 2 
 4 
 | 
 
 y 
 
 
 
 
 
 
 o 
 
 S 
 
 4 
 
 8 
 12 
 16 
 
 
 .8 
 .2 
 .3 
 .5 
 .7 
 g 
 
 35 
 36 
 37 
 38 
 39 
 
 9.65079 
 9.65104 
 9.65130 
 9.65155 
 9.65180 
 
 25 
 26 
 25 
 25 
 25 
 
 9.69932 
 9.69963 
 9.69995 
 9.70026 
 9.70058 
 
 31 
 32 
 31 
 82 
 
 01 
 
 0.30068 
 0.30037 
 0.30005 
 0.29974 
 0.29942 
 
 9.95148 
 9.95141 
 9.95135 
 9.95129 
 9.95122 
 
 7 
 6 
 6 
 7 
 
 25 
 24 
 23 
 22 
 21 
 
 
 6 
 
 2 
 
 2 
 
 4 
 .4 
 
 40 
 41 
 
 42 
 43 
 44 
 
 9.65205 
 9.65230 
 9.65255 
 9.65281 
 9.65306 
 
 25 
 25 
 26 
 25 
 25 
 
 9.70089 
 9.70121 
 9.70152 
 9.70184 
 9.70215 
 
 32 
 31 
 32 
 31 
 
 00 
 
 0.29911 
 0.29879 
 0.29848 
 0.29816 
 0.29785 
 
 9.95116 
 9.95110 
 9.95103 
 9.95097 
 9.95090 
 
 6 
 
 7 
 6 
 
 7 
 
 20 
 
 19 
 18 
 17 
 16 
 
 h 
 
 '2 
 I 
 
 8 
 9 
 
 
 
 
 3 
 3 
 
 4 
 8 
 1? 
 
 .2 
 6 
 .0 
 
 
 
 45 
 46 
 
 47 
 48 
 49 
 
 9.65331 
 9.65356 
 9.65381 
 9.65406 
 9.65431 
 
 25 
 25 
 25 
 25 
 25 
 
 9.70247 
 9.70278 
 9.70309 
 9.70341 
 9.70372 
 
 31 
 
 31 
 32. 
 31 
 32 
 
 0.29753 
 0.29722 
 0.29691 
 0.29659 
 0.29628 
 
 9.95084 
 &.95078 
 9.95071 
 9.95065 
 9.95059 
 
 6 
 7 
 6 
 6 
 
 15 
 14 
 13 
 12 
 11 
 
 4 
 5 
 
 
 
 
 16 
 20 
 
 7 
 
 
 
 
 6 
 
 50 
 51 
 52 
 53 
 64 
 
 9.65456 
 9.65481 
 9.65506 
 9.65531 
 9.65556 
 
 25 
 25 
 25 
 25 
 24 
 
 9.70404 
 9.70435 
 9.70466 
 9.70498 
 9.70529 
 
 31 
 31 . 
 32 
 31 
 
 o-i 
 
 0.29596 
 0.29565 
 0.29534 
 0.29502 
 0.29471 
 
 9.95052 
 9.95046 
 9.95039 
 9.95033 
 9.95027 
 
 6 
 7 
 6 
 6 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 
 
 7 
 8 
 9 
 10 
 
 
 
 
 1 
 
 1 
 
 .7 
 .8 
 .9 
 .1 
 .2 
 
 0.6 
 0.7 
 0.8 
 0.9 
 1.0 
 
 55 
 56 
 57 
 58 
 59 
 
 9.65580 
 9.65605 
 9.65630 
 9.65655 
 9.65680 
 
 25 
 25 
 25 
 25 
 25 
 
 9.70560 
 9.70592 
 9.70623 
 9.70654 
 9.70685 
 
 32 
 31 
 31 
 31 
 32 
 
 0.29440 
 0.29408 
 0.29377 
 0.29346 
 0.29315 
 
 9.95020 
 9.95014 
 9.95007 
 9.95001 
 9.94995 
 
 6 
 
 7 
 6 
 6 
 
 5 
 4 
 3 
 2 
 
 1 
 
 20 
 30 
 40 
 60 
 
 2 
 3 
 4 
 5 
 
 .3 
 .5 
 .7 
 .8 
 
 2.0 
 3.0 
 4.0 
 5.0 
 
 60 
 
 9.65705 
 
 
 9.70717 
 
 
 0.29283 
 
 9.94988 
 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 i 
 
 
 P. 
 
 P. 
 
 
 63? 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 27 
 
 1055 
 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d. c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 
 P.P. 
 
 
 1 
 
 9.65705 
 9.65729 
 9.65754 
 9.65779 
 9.65804 
 
 24 
 25 
 25 
 25 
 24 
 
 9.70717 
 9.70748 
 9.70779 
 9.70810 
 9.70841 
 
 31 
 31 
 31 
 31 
 32 
 
 0.29283 
 0.29252 
 0.29221 
 0.29190 
 0.29159 
 
 9.94988 
 9.94982 
 9.94975 
 9.94969 
 9.94962 
 
 6 
 
 7 
 6 
 7 
 g 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 32 
 
 3.2 
 
 3 7 
 
 31 
 
 3.1 
 3 6 
 
 ) 
 
 7 
 
 8 
 9 
 
 9.65828 
 9.65853 
 9.65878 
 9.65902 
 9.65927 
 
 25 
 25 
 24 
 25 
 25 
 
 9.70873 
 9.70904 
 9.70935 
 9.70966 
 9.70997 
 
 31 
 31 
 '31 
 31 
 
 O.1 
 
 0.29127 
 0.29096 
 0.29065 
 0.29034 
 0.29003 
 
 9.94956 
 9.94949 
 9.94943 
 9.94936 
 9.94930 
 
 7 
 6 
 7 
 6 
 
 7 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 
 20 
 30 
 
 4.3 
 
 4.8 
 5.3 
 10.7 
 16.0 
 
 4.1 
 4.7 
 5.2 
 10.3 
 15.5 
 
 
 
 3 
 14 
 
 9.65952 
 9.65976 
 9.66001 
 9.66025 
 9.66050 
 
 24 
 25 
 24 
 25 
 
 9.71028 
 9.71059 
 9.71090 
 9.71121 
 9.71153 
 
 31 
 31 
 31 
 32 
 
 0.28972 
 0.28941 
 0.28910 
 0.28879 
 0.28847 
 
 9.94923 
 9.94917 
 9.94911 
 9.94904 
 9.94898 
 
 6 
 6 
 7 
 6 
 
 7 
 
 50 
 
 49 
 
 48 
 47 
 46 
 
 40 
 50 
 
 21.3 
 26.7 
 
 3 
 
 20.7 
 25.8 
 
 j 
 
 6 
 17 
 18 
 19 
 
 9.66075 
 9.66099 
 9.66124 
 9.66148 
 9.66173 
 
 24 
 
 25 
 24 
 25 
 
 9.71184 
 9.71215 
 9.71246 
 9.71277 
 9.71308 
 
 31 
 31 
 31 
 31 
 
 01 
 
 0.28816 
 0.28785 
 0.28754 
 0.28723 
 0.28692 
 
 9.94891 
 9.94885 
 9.94878 
 9.94871 
 9.94865 
 
 6 
 
 7 
 7 
 6 
 7 
 
 45 
 44 
 43 
 42 
 41 
 
 1 
 
 6 3 
 7 3 
 8 4 
 9 4 
 5 
 
 
 5 
 
 5 
 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.66197 
 9.66221 
 9.66246 
 9.66270 
 9.66295 
 
 24 
 25 
 24 
 25 
 
 9.71339 
 9.71370 
 9.71401 
 9.71431 
 9.71462 
 
 31 
 31 
 30 
 31 
 31 
 
 0.28661 
 0.28630 
 0.28599 
 0.28569 
 0.28538 
 
 9.94858 
 9.94852 
 9.94845 
 9.94839 
 9.94832 
 
 6 
 
 7 
 6 
 7 
 g 
 
 40 
 
 39 
 38 
 37 
 36 
 
 2 
 
 S 
 4 
 E 
 
 10 
 15 
 20 
 >0 25 
 
 
 
 
 
 
 25 
 26 
 27 
 28 
 29 
 
 9.66319 
 9.66343 
 9.66368 
 9.66392 
 9.66416 
 
 24 
 25 
 24 
 24 
 25 
 
 9.71493 
 9.71524 
 9.71555 
 9.71586 
 9.71617 
 
 31 
 31 
 31 
 31 
 31 
 
 0.28507 
 0.28476 
 0.28445 
 0.28414 
 0.28383 
 
 9.94826 
 9.94819 
 9.94813 
 9.94806 
 9.94799 
 
 7 
 6 
 7 
 7 
 g 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 25 
 
 2.5 
 2.9 
 3.3 
 
 24 
 
 2.4 
 2.8 
 3.2 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.66441 
 9.66465 
 9.66489 
 9.66513 
 9.66537 
 
 24 
 24 
 24 
 24 
 
 9.71648 
 9.71679 
 9.71709 
 9.71740 
 9.71771 
 
 31 
 30 
 31 
 31 
 
 01 
 
 0.28352 
 0.28321 
 0.28291 
 0.28260 
 0.28229 
 
 9.94793 
 9.94786 
 9.94780 
 9.94773 
 9.94767 
 
 7 
 6 
 7 
 6 
 7 
 
 30 
 
 29 
 28 
 27 
 26 
 
 10 
 20 
 30 
 40 
 50 
 
 4.2 
 8.3 
 12.5 
 16.7 
 20.8 
 
 4.0 
 8.0 
 12.0 
 16.0 
 20.0 
 
 35 
 36 
 37 
 38 
 39 
 
 9.66562 
 9.66586 
 9.66610 
 9.66634 
 9.66658 
 
 24 
 24 
 24 
 24 
 04 
 
 9.71802 
 9.71833 
 9.71863 
 9.71894 
 9.71925 
 
 31 
 30 
 31 
 31 
 
 30 
 
 0.28198 
 0.28167 
 0.28137 
 0.28106 
 0.28075 
 
 9.94760 
 9.94753 
 9.94747 
 9.94740 
 9.94734 
 
 7 
 6 
 7 
 6 
 
 7 
 
 25 
 24 
 23 
 22 
 21 
 
 
 2 
 
 6 2 
 
 7 2 
 
 3 
 
 .3 
 
 7 
 
 40 
 41 
 
 42 
 3 
 
 9.66682 
 9.66706 
 9.66731 
 9.66755 
 9.66779 
 
 24 
 25 
 24 
 24 
 
 9.71955 
 9.71986 
 9.72017 
 9.72048 
 9.72078 
 
 31 
 31 
 31 
 30 
 
 01 
 
 0.28045 
 0.28014 
 0.27983 
 0.27952 
 0.27922 
 
 9.94727 
 9.94720 
 9.94714 
 9.94707 
 9.94700 
 
 7 
 6 
 7 
 7 
 g 
 
 20 
 
 19 
 18 
 17 
 16 
 
 
 8 3 
 9 3 
 LO 3 
 20 7 
 K) 11 
 
 .1 
 
 .5 
 
 .8 
 .7 
 .5 
 
 5 
 
 46 
 47 
 48 
 49 
 
 9.66803 
 9.66827 
 9.66851 
 9.66875 
 9.66899 
 
 24 
 24 
 24 
 24 
 
 9.72109 
 9.72140 
 9.72170 
 9.72201 
 9.72231 
 
 31 
 30 
 31 
 30 
 
 o-i 
 
 0.27891 
 0.27860 
 0.27830 
 0.27799 
 0.27769 
 
 9.94694 
 9.94687 
 9.94680 
 9.94674 
 9.94667 
 
 7 
 7 
 6 
 
 7 
 7 
 
 15 
 14 
 13 
 12 
 11 
 
 i 
 
 1 
 
 W 15 
 >0 19 
 
 7 
 
 .3 
 
 .2 
 
 6 
 
 
 
 53 
 54 
 
 9.66922 
 9.66943 
 9.66970 
 9.66994 
 9.67018 
 
 24 
 
 24 
 24 
 24 
 
 9.72262 
 9.72293 
 9.72323 
 9.72354 
 9.72384 
 
 31 
 30 
 31 
 30 
 
 0.27738 
 0.27707 
 0.27677 
 0.27646 
 0.27616 
 
 9.94660 
 9.94654 
 9.94647 
 9.94640 
 9.94634 
 
 6 
 
 7 
 7 
 6 
 
 7 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 6 
 7 
 8 
 9 
 10 
 
 LI 
 1.2 
 
 0.6 
 0.7 
 0.8 
 0.9 
 1.0 
 
 6 
 37 
 38 
 39 
 
 9.67042 
 9.67066 
 9.67090 
 9.67113 
 9.67137 
 
 24 
 
 24 
 23 
 24 
 
 9.72415 
 9.72445 
 9.72476 
 9.72506 
 9.72537 
 
 30 
 31 
 30 
 31 
 30 
 
 0.27585 
 0.27555 
 0.27524 
 0.27494 
 0.27463 
 
 9.94627 
 9.94620 
 9.94614 
 9.94607 
 9.94600 
 
 7 
 6 
 
 7 
 7 
 7 
 
 5 
 4 
 3 
 2 
 1 
 
 20 
 30 
 40 
 50 
 
 2.3 
 3.5 
 4.7 
 
 2.0 
 3.0 
 4.0 
 5.0 
 
 
 
 9.67161 
 
 
 9.72567 
 
 
 0.27433 
 
 9.94593 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg 
 
 d.c. 
 
 L.Tang 
 
 L. Sin. 
 
 d. 
 
 * 
 
 
 P.P 
 
 
 62 
 
1056 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 28 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d. c. 
 
 L. Cotg. 
 
 L. Cos. | 
 
 d. 
 
 
 
 F 
 
 .P 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.67161 
 9.67185 
 9.67208 
 9.67232 
 9.67256 
 
 24 
 23 
 
 24 
 24 
 
 9.72567 
 9.72598 
 9.72628 
 9.72659 
 9.72689 
 
 31 
 30 
 31 
 30 
 
 0.27433 
 0.27402 
 0.27372 
 0.27341 
 0.27311 
 
 9.94593 
 9.94587 
 9.94580 
 9.94573 
 9.94567 
 
 6 
 
 7 
 7 
 6 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 ! 
 J 
 j 
 
 II 
 
 .1 
 
 i; 
 
 30 
 
 3.0 
 3 5 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.67280 
 9.67303 
 9.67327 
 9.67350 
 9.67374 
 
 23 
 24 
 23 
 24 
 94 
 
 9.72720 
 9.72750 
 9.72780 
 9.72811 
 9.72841 
 
 30 
 30 
 31 
 30 
 
 01 
 
 0.27280 
 0.27250 
 0.27220 
 0.27189 
 0.27159 
 
 9.94560 
 9.94553 
 9.94546 
 9.94540 
 9.94533 
 
 7 
 7 
 6 
 7 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 4 
 4 
 " ; l 
 11 
 If 
 
 .1 
 .7 
 2 
 ;3 
 .5 
 
 4.0 
 4.5 
 5.0 
 10.0 
 15.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.67398 
 9.67421 
 9.67445 
 9.67468 
 9.67492 
 
 23 
 24 
 23 
 24 
 23 
 
 9.72872 
 9.72902 
 9.72932 
 9.72963 
 9.72993 
 
 30 
 30 
 31 
 30 
 
 on 
 
 0.27128 
 0.27098 
 0.27068 
 0.27037 
 0.27007 
 
 9.94526 
 9.94519 
 9.94513 
 9.94506 
 9.94499 
 
 7 
 6 
 7 
 
 7 
 
 7 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 2L 
 2 
 
 & 
 .8 
 
 ? 
 
 20.0 
 25.0 
 
 9 
 
 15 
 16 
 
 17 
 18 
 19 
 
 9.67515 
 9.67539 
 9.67562 
 9.67586 
 9.67609 
 
 24 
 23 
 24 
 23 
 
 9.73023 
 9.73054 
 9.73084 
 9.73114 
 9.73144 
 
 31 
 30 
 30 
 30 
 
 0.26977 
 0.26946 
 0.26916 
 0.26886 
 0.26856 
 
 9.94492 
 9.94485 
 9.94479 
 9.94472 
 9.94465 
 
 7 
 6 
 7 
 7 
 
 45 
 44 
 43 
 42 
 41 
 
 ] 
 
 6 
 
 7 
 
 cS 
 
 9 
 
 
 
 2 
 8 
 
 8 
 
 4 
 4 
 
 9 
 4 
 9 
 4 
 
 8 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.67633 
 9.67656 
 9.67680 
 9.67703 
 9.67726 
 
 23 
 24 
 23 
 23 
 04 
 
 9.73175 
 9.73205 
 9.73235 
 9.73265 
 9.73295 
 
 30 
 
 30 
 30 
 
 30 
 
 0.26825 
 0.26795 
 0.26765 
 0.26735 
 0.26705 
 
 9.94458 
 9.94451 
 9.94445 
 9.94438 
 9.94431 
 
 7 
 6 
 7 
 7 
 
 40 
 
 39 
 38 
 37 
 36 
 
 a 
 
 \ 
 
 : 4 
 
 I 
 
 1) 
 
 
 4) 
 
 i 
 
 14 
 19 
 21 
 
 .7 
 5 
 .3 
 2 
 
 25 
 
 26 
 27 
 28 
 29 
 
 9.67750 
 9.67773 
 9.67796 
 9.67820 
 9.67843 
 
 23 
 23 
 24 
 23 
 
 00 
 
 9.73326 
 9.73356 
 9.73386 
 9.73416 
 9.73446 
 
 30 
 30 
 30 
 30 
 
 OA 
 
 0.26674 
 0.26644 
 0.26614 
 0.26584 
 0.26554 
 
 9.94424 
 9.94417 
 9.94410 
 9.94404 
 9.94397 
 
 7 
 7 
 6 
 
 7 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 2 
 
 s 
 1 
 1 
 
 4 
 
 .4 
 
 .8 
 :l 
 
 23 
 
 2.3 
 2.7 
 3.1 
 
 30 
 31 
 
 32 
 33 
 34 
 
 9.67866 
 9.67890 
 9.67913 
 9.67936 
 9.67959 
 
 24 
 23 
 23 
 23 
 23 
 
 9.73476 
 9.73507 
 9.73537 
 9.73567 
 9.73597 
 
 31 
 30 
 30 
 30 
 
 on 
 
 0.26524 
 0.26493 
 0.26463 
 0.26433 
 0.26403 
 
 9.94390 
 9.94383 
 9.94376 
 9.94369 
 9.94362 
 
 7 
 7 
 7 
 7 
 7 
 
 30 
 
 29 
 28 
 27 
 26 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 4 
 * 
 ll 
 11 
 
 >f 
 
 .(> 
 .0 
 .0 
 .0 
 
 .0 
 
 D 
 
 3.5 
 3.8 
 7.7 
 11.5 
 15.3 
 19 2 
 
 35 
 36 
 37 
 38 
 39 
 
 9.67982 
 9.68006 
 9.68029 
 9.68052 
 9.68076 
 
 24 
 23 
 23 
 23 
 23 
 
 9.73627 
 9.73657 
 9.73687 
 9.73717 
 9.73747 
 
 30 
 30 
 30 
 30 
 
 on 
 
 0.26373 
 0.26343 
 0.26313 
 0.26283 
 0.26253 
 
 9.94355 
 9.94349 
 9.94342 
 9.94335 
 9.94328 
 
 6 
 
 7 
 7 
 7 
 
 7 
 
 25 
 24 
 
 23 
 22 
 21 
 
 
 6 
 
 2 
 
 2 
 
 2 
 
 .2 
 
 c 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.68098 
 9.68121 
 9.68144 
 9.68167 
 9.68190 
 
 23 
 23 
 23 
 23 
 23 
 
 9.73777 
 9.73807 
 9.73837 
 9.73867 
 9.73897 
 
 30 
 30 
 30 
 30 
 30 
 
 0.26223 
 0.26193 
 0.26163 
 0.26133 
 0.26103 
 
 9.94321 
 9.94314 
 9.94307 
 9.94300 
 9.94293 
 
 7 
 
 7 
 7 
 7 
 
 7 
 
 20 
 
 19 
 18 
 17 
 16 
 
 1l 
 
 1 
 
 8 
 
 9 
 
 !0 
 $0 
 
 2 
 3 
 3 
 
 7 
 11 
 
 .9 
 .3 
 .7 
 .3 
 .0 
 
 45 
 
 46 
 
 : 47 
 48 
 49 
 
 9.68213 
 9.68237 
 9.68260 
 9.68283 
 9.68305 
 
 24 
 23 
 23 
 22 
 23 
 
 9.73927 
 9.73957 
 9.73987 
 9.74017 
 9.74047 
 
 30 
 30 
 30 
 30 
 
 on 
 
 0.26073 
 0.26043 
 0.26013 
 0.25983 
 0.25953 
 
 9.94286 
 9.94279 
 9.94273 
 9.94266 
 9.94259 
 
 7 
 6 
 
 7 
 7 
 7 
 
 15 
 14 
 13 
 12 
 11 
 
 <: 
 { 
 
 K) 
 >0 
 
 14 
 
 18 
 
 7 
 
 .7 
 .3 
 
 g 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.68328 
 9.68351 
 9.68374 
 9.68397 
 9.68420 
 
 23 
 23 
 23 
 23 
 23 
 
 9.74077 
 9.74107 
 9.74137 
 9.74166 
 9.74196 
 
 30 
 30 
 29 
 30 
 
 OA 
 
 0.25923 
 0.25893 
 0.25863 
 0.25834 
 0.25804 
 
 9.94252 
 9.94245 
 9.94238 
 9.94231 
 9.94224 
 
 7 
 7 
 7 
 7 
 7 
 
 10 
 9 
 
 8 
 7 
 6 
 
 6 
 7 
 8 
 9 
 10 
 
 ( 
 
 ( 
 ( 
 
 1 
 ] 
 
 ).7 
 
 ).8 
 ).9 
 
 Li 
 
 .2 
 
 0.6 
 0.7 
 0.8 
 0.9 
 1.0 
 
 55 
 56 
 57 
 58 
 59 
 
 9.68443 
 9.68466 
 9.68489 
 9.68512 
 9.68534 
 
 23 
 23 
 
 23 
 22 
 23 
 
 9.74226 
 9.74256 
 9.74286 
 9.74316 
 9.74345 
 
 30 
 30 
 30 
 29 
 
 on 
 
 0.25774 
 0.25744 
 0.25714 
 0.25684 
 0.25655 
 
 9.94217 
 9.94210 
 9.94203 
 9.94196 
 9.94189 
 
 7 
 
 7 
 7 
 
 7 
 
 7 
 
 5 
 4 
 3 
 2 
 1 
 
 20 
 30 
 40 
 50 
 
 1 
 ^ 
 
 1 
 
 I:A 
 
 5.5 
 t.7 
 
 ).8 
 
 2.0 
 3.0 
 4.0 
 5.0 
 
 60 
 
 9.68557 
 
 
 9.74375 
 
 
 0.25625 
 
 9.94182 
 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 / 
 
 
 P 
 
 .P 
 
 
 61 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 29 
 
 1057 
 
 ' 
 
 L. Sin. 
 
 d. 
 
 L.Tang 
 
 d. c. |L. Cotg 
 
 L. Cos. 
 
 d. 
 
 
 P.P. 
 
 
 
 1 
 
 3 
 4 
 
 9.68557 
 9.68580 
 9.68603 
 9.68625 
 9.68648 
 
 23 
 
 23 
 22 
 23 
 23 
 23 
 22 
 23 
 23 
 22 
 23 
 22 
 23 
 23 
 22 
 23 
 22 
 23 
 22 
 23 
 22 
 23 
 22 
 23 
 22 
 22 
 23 
 22 
 23 
 22 
 22 
 23 
 22 
 22 
 22 
 23 
 22 
 22 
 22 
 22 
 23 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 22 
 
 9.74375 
 9.74405 
 9.74435 
 9.74465 
 9.74494 
 
 30 
 30 
 30 
 29 
 30 
 30 
 29 
 30 
 30 
 30 
 29 
 30 
 30 
 29 
 30 
 30 
 29 
 30 
 29 
 30 
 29 
 30 
 30 
 29 
 30 
 29 
 30 
 29 
 30 
 29 
 30 
 29 
 30 
 29 
 29 
 30 
 29 
 30 
 29 
 29 
 30 
 29 
 30 
 29 
 29 
 30 
 29 
 29 
 29 
 30 
 29 
 29 
 29 
 30 
 29 
 29 
 29 
 30 
 29 
 29 
 
 0.25625 
 0.25595 
 0.25565 
 0.25535 
 0.25506 
 
 9.94182 
 9.94175 
 9.94168 
 9.94161 
 9.94154 
 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 8 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 8 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 8 
 7 
 7 
 7 
 7 
 7 
 8 
 7 
 7 
 7 
 7 
 8 
 7 
 7 
 7 
 8 
 7 
 7 
 7 
 
 60 
 
 59 
 58 
 57 
 56 
 55 
 54 
 53 
 52 
 51 
 
 6 
 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 6 
 7 
 8 1 
 9 1 
 10 1 
 20 2 
 30 4 
 40 5 
 50 6 
 
 30 
 
 3.0 
 3.5 
 4.0 
 4.5 
 5.0 
 10.0 
 15.0 
 20.0 
 25.0 
 
 29 
 
 2.9 
 3.4 
 3.9 
 4.4 
 4.8 ' 
 9.7 
 14.5 
 19.3 
 24.2 
 
 23 
 
 2.3 
 
 2.7 
 3.1 
 3.5 
 3.8 
 7.7 
 11.5 
 15.3 
 19.2 
 
 22 
 
 2.2 
 2.6 
 2.9 
 3.3 
 3.7 
 7.3 
 11.0 
 14.7 
 18.3 
 
 5 7 
 
 .8 0.7 
 9 0.8 
 1 0.9 
 2 1.1 
 3 1.2 
 7 2.3 
 3.5 
 3 4.7 
 7 5.8 
 
 5 
 6 
 7 
 8 
 9 
 
 9.68671 
 9.68694 
 9.68716 
 9.68739 
 9.68762 
 
 9.74524 
 9.74554 
 9.74583 
 9.74613 
 9.74643 
 
 0.25476 
 0.25446 
 0.25417 
 0.25387 
 0.25357 
 
 9.94147 
 9.94140 
 9.94133 
 9.94126 
 9.94119 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.68784 
 9.68807 
 9.68829 
 9.68852 
 9.68875 
 
 9.74673 
 9.74702 
 9.74732 
 9.74762 
 9.74791 
 
 0.25327 
 0.25298 
 0.25268 
 0.25238 
 0.25209 
 
 9.94112 
 9.94105 
 9.94098 
 9.94090 
 9.94083 
 
 50 
 
 49 
 48 
 47 
 46 
 
 15 
 16 
 17 
 18 
 19 
 
 9.68897 
 9.68920 
 9.68942 
 9.68965 
 9.68987 
 
 9.74821 
 9.74851 
 9.74880 
 9.74910 
 9.74939 
 
 0.25179 
 0.25149 
 0.25120 
 0.25090 
 0.25061 
 
 9.94076 
 9.94069 
 9.94062 
 9.94055 
 9.94048 
 
 45 
 44 
 43 
 42 
 41 
 40 
 39 
 38 
 37 
 36 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.69010 
 9.69032 
 9.69055 
 9.69077 
 9.69100 
 
 9.74969 
 9.74998 
 9.75028 
 9.75058 
 9.75087 
 
 0.25031 
 0.25002 
 0.24972 
 0.24942 
 0.24913 
 
 9.94041 
 9.94034 
 9.94027 
 9.94020 
 9.94012 
 
 25 
 26 
 27 
 28 
 29 
 
 9.69122 
 9.69144 
 9.69167 
 9.69189 
 9.69212 
 
 9.75117 
 9.75146 
 9.75176 
 9.75205 
 9.75235 
 
 0.24883 
 0.24854 
 0.24824 
 0.24795 
 0.24765 
 
 9.94005 
 9.93998 
 9.93991 
 9.93984 
 9.93977 
 
 35 
 34 
 33 
 32 
 31 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.69234 
 9.69256 
 9.69279 
 9.69301 
 9.69323 
 
 9.75264 
 9.75294 
 9.75323 
 9.75353 
 9.75382 
 
 0.24736 
 0.24706 
 0.24677 
 0.24647 
 0.24618 
 
 9.93970 
 9.93963 
 9.93955 
 9.93948 
 9.93941 
 
 30 
 
 29 
 28 
 27 
 26 
 
 35 
 36 
 37 
 38 
 39 
 
 9.69345 
 9.69368 
 9.69390 
 9.69412 
 9.69434 
 
 9.75411 
 9.75441 
 9.75470 
 9.75500 
 9.75529 
 
 0.24589 
 0.24559 
 0.24530 
 0.24500 
 0.24471 
 
 9.93934 
 9.93927 
 9.93920 
 9.93912 
 9.93905 
 
 25 
 24 
 23 
 22 
 21 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.69456 
 9.69479 
 9.69501 
 9.69523 
 9.69545 
 
 9.75558 
 9.75588 
 9.75617 
 9.75647 
 9.75676 
 
 0.24442 
 0.24412 
 0.24383 
 0.24353 
 0.24324 
 
 9.93898 
 9.93891 
 9.93884 
 9.93876 
 9.93869 
 
 20 
 
 19 
 18 
 17 
 16 
 
 45 
 46 
 47 
 48 
 49 
 
 TF 
 
 51 
 52 
 53 
 54 
 
 9.69567 
 9.69-589 
 9.69611 
 9.69633 
 9.69655 
 
 9.75705 
 9.75735 
 9.75764 
 9.75793 
 9.75822 
 
 0.24295 
 0.24265 
 0.24236 
 0.24207 
 0.24178 
 
 9.93862 
 9.93855 
 9.93847 
 993840 
 9.93833 
 
 15 
 14 
 13 
 12 
 11 
 
 9.69677 
 9.69699 
 9.69721 
 9.69743 
 9.69765 
 
 9.75852 
 9.75881 
 9.75910 
 9.75939 
 9.75969 
 
 0.24148 
 0.24119 
 0.24090 
 0.24061 
 0.24031 
 
 9.93826 
 9.93819 
 9.93811 
 9.93804 
 9.93797 
 
 7 
 8 
 7 
 
 7 
 
 10 
 
 9 
 8 
 7 
 6 
 
 55 
 
 56 
 57 
 58 
 59 
 
 9.69787 
 9.69809 
 9.69831 
 9.69853 
 9.69875 
 
 9.75998 
 9.76027 
 9.76056 
 9.76086 
 9.76115 
 
 0.24002 
 0.23973 
 0.23944 
 0.23914 
 0.23885 
 
 9.93789 
 9.93782 
 9.93775 
 9.93768 
 9.93760 
 
 7 
 
 7 
 7 
 8 
 
 7 
 
 5 
 4 
 3 
 2 
 1 
 
 60 
 
 9.69897 
 
 9.76144 
 
 0.23856 
 
 9.93753 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 / 
 
 P.P. 
 
 67 
 
 60 
 
1058 LOGARITHMS &F TRIGONOMETRIC FUNCTIONS 
 
 30 
 
 ' 
 
 L. Bin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 P 
 
 r 
 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 9.69897 
 9.69919 
 9.69941 
 9.69963 
 9.69984 
 
 22 
 
 22 
 22 
 21 
 22 
 
 9.76144 
 9.76173 
 9.76202 
 9.76231 
 9.76261 
 
 29 
 29 
 29 
 30 
 
 9Q 
 
 0.23856 
 0.23827 
 0.23798 
 0.23769 
 0.23739 
 
 9.93753 
 9.93746 
 9.93738 
 9.93731 
 9.93724 
 
 7 
 8 
 7 
 7 
 
 60 
 
 59 
 58 
 57 
 56 
 
 3 
 
 6 3 
 7 3 
 
 
 
 .0 
 
 -, 
 
 29 
 
 2.9 
 3 4 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.70006 
 9.70028 
 9.70050 
 9.70072 
 9.70093 
 
 22 
 22 
 22 
 21 
 99 
 
 9.76290 
 9.76319 
 9.76348 
 9.76377 
 9.76406 
 
 29 
 29 
 29 
 29 
 
 0.23710 
 0.23681 
 0.23652 
 0.23623 
 0.23594 
 
 9.93717 
 9.93709 
 9.93702 
 9.93695 
 9.93687 
 
 8 
 
 7 
 7 
 8 
 
 55 
 54 
 53 
 52 
 51 
 
 8 4 
 9 4 
 10 5 
 20 10 
 30 15 
 
 .0 
 .5 
 .0 
 .0 
 
 .0 
 
 3.9 
 4.4 
 4.8 
 9.7 
 14.5 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.70115 
 9.70137 
 9.70159 
 9.70180 
 9.70202 
 
 22 
 22 
 21 
 
 22 
 22 
 
 9.76435 
 9.76464 
 9.76493 
 9.76522 
 9.76551 
 
 29 
 29 
 29 
 29 
 
 On 
 
 0.23565 
 0.23536 
 0.23507 
 0.23478 
 0.23449 
 
 9.93680 
 9.93673 
 9.93665 
 9.93658 
 9.93650 
 
 7 
 8 
 7 
 8 
 
 50 
 
 49 
 
 48 
 47 
 46 
 
 40 20 
 50 25 
 
 .0 
 .0 
 
 ? 
 
 19.3 
 24.2 
 
 8 
 
 15 
 16 
 17 
 18 
 19' 
 
 9.70224 
 9.70245 
 9.70267 
 9.70288 
 9.70310 
 
 21 
 22 
 21 
 
 22 
 22 
 
 9.76580 
 9.76609 
 9.76639 
 9.76668 
 9.76697 
 
 29 
 30 
 29 
 29 
 28 
 
 0.23420 
 0.23391 
 0.23361 
 0.23332 
 0.23303 
 
 9.93643 
 9.93636 
 9.93628 
 9.93621 
 9.93614 
 
 7 
 8 
 7 
 7 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 7 
 8 
 9 
 10 
 
 2 
 
 3 
 8 
 
 4 
 4 
 
 .8 
 .3 
 
 .7 
 .2 
 
 .7 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.70332 
 9.70353 
 9.70375 
 9.703% 
 9.70418 
 
 21 
 22 
 21 
 22 
 21 
 
 9.76725 
 9.76754 
 9.76783 
 9.76812 
 9.76841 
 
 29 
 29 
 29 
 29 
 
 on 
 
 0.23275 
 0.23246 
 0.23217 
 0.23188 
 0.23159 
 
 9.93606 
 9.93599 
 9.93591 
 9.93584 
 9.93577 
 
 7 
 8 
 
 7 
 7 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 y 
 
 14 
 18 
 23 
 
 .3 
 .0 
 .7 
 .3 
 
 25 
 26 
 
 27 
 28 
 29 
 
 9.70439 
 9.70461 
 9.70482 
 9.70504 
 9.70525 
 
 22 
 21 
 22 
 21 
 22 
 
 9.76870 
 9.76899 
 9.76928 
 9.76957 
 9.76986 
 
 29 
 29 
 29 
 29 
 
 OQ 
 
 0.23130 
 0.23101 
 0.23072 
 0.23043 
 0.23014 
 
 9.93569 
 9.93562 
 9.93554 
 9.93547 
 9.93539 
 
 7 
 8 
 7 
 8 
 
 7 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 2 
 
 2 
 2 
 2 
 
 2 
 
 .2 
 .6 
 .9 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.70547 
 9.70568 
 9.70590 
 9.70611 
 9.70633 
 
 21 
 22 
 21 
 22 
 21 
 
 9.77015 
 9.77044 
 9.77073 
 9.77101 
 9.77130 
 
 29 
 29 
 28 
 29 
 29 
 
 0.22985 
 0.22956 
 0.22927 
 0.22899 
 0.22870 
 
 9.93532 
 9.93525 
 9.93517 
 9.93510 
 9.93502 
 
 7 
 8 
 7 
 8 
 7 
 
 30 
 
 29 
 28 
 27 
 26 
 
 9 
 10 
 
 20 
 30 
 
 40 
 50 
 
 3 
 7 
 11 
 14 
 
 !* 
 
 .3 
 .7 
 .3 
 .0 
 .7 
 .3 
 
 35 
 36 
 37 
 38 
 39 
 
 9.70654 
 9.70675 
 9.70697 
 9.70718 
 9.70739 
 
 21 
 22 
 21 
 21 
 22 
 
 9.77159 
 
 9.77188 
 9.77217 
 9.77246 
 9.77274 
 
 29 
 29 
 29 
 28 
 
 on 
 
 0.22841 
 0.22812 
 0.22783 
 0.22754 
 0.22726 
 
 9.93495 
 9.93487 
 9.93480 
 9.93472 
 9.93465 
 
 8 
 
 7 
 8 
 
 7 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 2 
 
 2 
 
 1 
 
 .1 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.70761 
 9.70782 
 9.70803 
 9.70824 
 9.70846 
 
 21 
 21 
 21 
 22 
 21 
 
 9.77303 
 9.77332 
 9.77361 
 9.77390 
 9.77418 
 
 29 
 29 
 29 
 28 
 29 
 
 0.22697 
 0.22668 
 0.22639 
 0.22610 
 0.22582 
 
 9.93457 
 9.93450 
 9.93442 
 9.93435 
 9.93427 
 
 7 
 8 
 7 
 8 
 
 7 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 J 
 
 2 
 3 
 7 
 1( 
 
 .8 
 .2 
 .5 
 .0 
 .5 
 
 45 
 46 
 
 47 
 48 
 49 
 
 9.70867 
 9.70888 
 9.70909 
 9.70931 
 9.70952 
 
 21 
 21 
 22 
 21 
 21 
 
 9.77447 
 9.77476 
 9.77505 
 9.77533 
 9.77562 
 
 29 
 29 
 28 
 29 
 29 
 
 0.22553 
 0.22524 
 0.22495 
 0.22467 
 0.22438 
 
 9.93420 
 9.93412 
 9.93405 
 9.93397 
 9.93390 
 
 8 
 
 7 
 8 
 
 7 
 g 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 14 
 
 17 
 
 8 
 
 .0 
 .5 
 
 7 
 
 50 
 
 51 
 52 
 
 53 
 54 
 
 9.70973 
 9.70994 
 9.71015 
 9.71036 
 9.71058 
 
 21 
 
 21 
 21 
 22 
 21 
 
 9.77591 
 9.77619 
 9.77648 
 9.77677 
 9.77706 
 
 28 
 29 
 29 
 29 
 
 28 
 
 0.22409 
 0.22381 
 0.22352 
 0.22323 
 0.22294 
 
 9.93382 
 9.93375 
 9.93367 
 9.93360 
 9.93352 
 
 7 
 8 
 7 
 8 
 
 10 
 
 9 
 
 8 
 
 7 
 6 
 
 6 ( 
 
 7 ( 
 8 1 
 9 ] 
 10 ] 
 
 ).8 
 ).9 
 .1 
 .2 
 .3 
 
 0.7 
 0.8 
 0.9 
 1.1 
 1.2 
 
 55 
 56 
 57 
 58 
 59 
 
 9.71079 
 9.71100 
 9.71121 
 9.71142 
 9.71163 
 
 21 
 21 
 21 
 21 
 21 
 
 9.77734 
 9.77763 
 9.77791 
 9.77820 
 9.77849 
 
 29 
 28 
 29 
 29 
 
 OQ 
 
 0.22266 
 0.22237 
 0.22209 
 0.22180 
 0.22151 
 
 9.93344 
 9.93337 
 9.93329 
 9.93322 
 9.93314 
 
 7 
 8 
 7 
 8 
 
 5 
 4 
 3 
 2 
 1 
 
 20 '< 
 30 < 
 40 { 
 50 ( 
 
 >.7 
 1.0 
 >.3 
 5.7 
 
 2.3 
 3.5 
 4.7 
 5.8 
 
 60 
 
 9.71184 
 
 
 9.77877 
 
 
 0.22123 
 
 9.93307 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 / 
 
 P 
 
 .P 
 
 
 59 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 
 31 
 
 1059 
 
 t 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 P. 
 
 P. 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.71184 
 9.71205 
 9.71226 
 9.71247 
 9.71268 
 
 21 
 21 
 21 
 21 
 21 
 
 9.77877 
 9.77906 
 9.77935 
 9.77963 
 9.77992 
 
 29 
 29 
 28 
 29 
 
 OQ 
 
 0.22123 
 0.22094 
 0.22065 
 0.22037 
 0.22008 
 
 9.93307 
 9.93299 
 9.93291 
 9.93284 
 9.93276 
 
 8 
 8 
 7 
 8 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 29 
 
 2.9 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.71289 
 9.71310 
 9.71331 
 9.71352 
 9.71373 
 
 21 
 21 
 21 
 21 
 20 
 
 9.78020 
 9.78049 
 9.78077 
 9.78106 
 9.78135 
 
 29 
 
 28 
 29 
 29 
 28 
 
 0.21980 
 0.21951 
 0.21923 
 0.21894 
 0.21865 
 
 9.93269 
 9.93261 
 9.93253 
 9.93246 
 9.93238 
 
 8 
 8 
 
 7 
 8 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 3.9 
 4.4 
 4.8 
 9.7 
 14.5 
 
 10 
 11 
 
 12 
 13 
 14 
 
 9.71393 
 9.71414 
 9.71435 
 9.71456 
 9.71477 
 
 21 
 21 
 21 
 21 
 
 01 
 
 9.78163 
 9.78192 
 9.78220 
 9.78249 
 9.78277 
 
 29 
 28 
 29 
 28 
 
 OQ 
 
 0.21837 
 0.21808 
 0.21780 
 0.21751 
 0.21723 
 
 9.93230 
 9.93223 
 9.93215 
 9.93207 
 9.93200 
 
 7 
 8 
 8 
 
 7 
 
 SO 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 19.3 
 24.2 
 
 28 
 
 15 
 16 
 17 
 18 
 19 
 
 9.71498 
 9.71519 
 9.71539 
 9.71560 
 9.71581 
 
 21 
 20 
 21 
 21 
 21 
 
 9.78306 
 9.78334 
 9.78363 
 9.78391 
 9.78419 
 
 28 
 29 
 28 
 28 
 29 
 
 0.21694 
 0.21666 
 0.21637 
 0.21609 
 0.21581 
 
 9.93192 
 9.93184 
 9.93177 
 9.93169 
 9.93161 
 
 8 
 
 7 
 8 
 8 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 7 
 8 
 9 
 10 
 
 2.8 
 3.3 
 3.7 
 4.2 
 4.7 
 
 20 
 
 21 
 
 22 
 23 
 24 
 
 9.71602 
 9.71622 
 9.71643 
 9.71664 
 9.71685 
 
 20 
 21 
 21 
 21 
 
 9.78448 
 9.78476 
 9.78505 
 9.78533 
 9.78562 
 
 28 
 29 
 28 
 29 
 
 OQ 
 
 0.21552 
 0.21524 
 0.21495 
 0.21467 
 0.21438 
 
 9.93154 
 9.93146 
 9.93138 
 9.93131 
 9.93123 
 
 8 
 
 8 
 7 
 8 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 9.3 
 14.0 
 18.7 
 23.3 
 
 25 
 26 
 
 27 
 28 
 29 
 
 9.71705 
 9.71726 
 9.71747 
 9.71767 
 9.71788 
 
 21 
 21 
 
 20 
 21 
 
 9.78590 
 9.78618 
 9.78647 
 9.78675 
 9.78704 
 
 28 
 29 
 28 
 29 
 
 OQ 
 
 0.21410 
 0.21382 
 0.21353 
 0.21325 
 0.21296 
 
 9.93115 
 9.93108 
 9.93100 
 9.93092 
 9.93084 
 
 7 
 8 
 8 
 8 
 7 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 21 
 2.1 
 2.5 
 
 2.8 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.71809 
 9.71829 
 9.71850 
 9.71870 
 9.71891 
 
 20 
 21 
 20 
 21 
 
 9.78732 
 9.78760 
 9.78789 
 9.78817 
 9.78845 
 
 28 
 29 
 28 
 28 
 
 0.21268 
 0.21240 
 0.21211 
 0.21183 
 0.21155 
 
 9.93077 
 9.93069 
 9.93061 
 9.93053 
 9.93046 
 
 8 
 8 
 8 
 
 7 
 
 30 
 
 29 
 28 
 27 
 26 
 
 10 
 20 
 30 
 40 
 50 
 
 3.5 
 7.0 
 
 10.5 
 14.0 
 175 
 
 35 
 36 
 37 
 38 
 39 
 
 9.71911 
 9.71932 
 9.71952 
 9.71973 
 9.71994 
 
 21 
 20 
 21 
 21 
 
 9.78874 
 9.78902 
 9.78930 
 9.78959 
 9.78987 
 
 28 
 28 
 29 
 28 
 
 OQ 
 
 0.21126 
 0.21098 
 0.21070 
 0.21041 
 0.21013 
 
 9.93038 
 9.93030 
 9.93022 
 9.93014 
 9.93007 
 
 8 
 8 
 8 
 
 7 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 7 
 
 20 
 
 2.0 
 2 3 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.72014 
 9.72034 
 9.72055 
 9.72075 
 9.720% 
 
 20 
 21 
 20 
 21 
 20 
 
 9.79015 
 9.79043 
 9.79072 
 9.79100 
 9.79128 
 
 28 
 29 
 28 
 28 
 28 
 
 0.20985 
 0.20957 
 0.20928 
 0.20900 
 0.20872 
 
 9.92999 
 9.92991 
 9.92983 
 9.92976 
 9.92968 
 
 8 
 8 
 
 7 
 8 
 
 g 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 2.7 
 3.0 
 3.3 
 6.7 
 10.0 
 
 45 
 46 
 
 47 
 48 
 49 
 
 9.72116 
 9.72137 
 9.72157 
 9.72177 
 9.72198 
 
 21 
 20 
 20 
 21 
 
 9.79156 
 9.79185 
 9.79213 
 9.79241 
 9.79269 
 
 29 
 28 
 28 
 28 
 
 0.20844 
 0.20815 
 0.20787 
 0.20759 
 0.20731 
 
 9.92960 
 9.92952 
 9.92944 
 9.92936 
 9.92929 
 
 8 
 8 
 8 
 
 7 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 13.3 
 16.7 
 
 8 7 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.72218 
 9.72238 
 9.72259 
 9.72279 
 9.72299 
 
 20 
 21 
 20 
 20 
 
 9.79297 
 9.79326 
 9.79354 
 9.79382 
 9.79410 
 
 29 
 28 
 28 
 28 
 28 
 
 0.20703 
 0.20674 
 0.20646 
 0.20618 
 0.20590 
 
 9.92921 
 9.92913 
 9.92905 
 9.92897 
 9.92889 
 
 8 
 8 
 8 
 8 
 3 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 6 C 
 7 
 8 1 
 9 1 
 10 1 
 
 .8 0.7 
 .9 0.8 
 .1 0.9 
 .2 1.1 
 .3 1.2 
 
 55 
 56 
 57 
 58 
 59 
 
 9.72320 
 9.72340 
 9.72360 
 9.72381 
 9.72401 
 
 20 
 20 
 21 
 20 
 20 
 
 9.79438 
 9.79466 
 9.79495 
 9.79523 
 9.79551 
 
 28 
 29 
 28 
 28 
 28 
 
 0.20562 
 0.20534 
 0.20505 
 0.20477 
 0.20449 
 
 9.92881 
 9.92874 
 9.92866 
 9.92858 
 9.92850 
 
 7 
 8 
 8 
 8 
 8 
 
 5 
 4 
 3 
 2 
 1 
 
 20 2 
 30 4 
 40 
 50 ( 
 
 .7 2.3 
 .0 3.5 
 .3 4.7 
 .7 5.8 
 
 60 
 
 9.72421 
 
 
 9.79579 
 
 
 0.20421 
 
 9.92842 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 ' 
 
 P 
 
 .P. 
 
 
 
 
 
 
 58 
 
 
 
 
 
 
1060 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 32 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang 
 
 d.c. 
 
 L. Cotg 
 
 L. Cos. 
 
 d. 
 
 
 
 P. 
 
 P. 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.72421 
 9.72441 
 9.72461 
 9.72482 
 9.72502 
 
 20 
 20 
 21 
 20 
 20 
 
 9.79579 
 9.79607 
 9.79635 
 9.79663 
 9.79691 
 
 28 
 28 
 28 
 28 
 oc 
 
 0.20421 
 0.20393 
 0.20365 
 0.20337 
 0.20309 
 
 9.92842 
 9.92834 
 9.92826 
 9.92818 
 9.92810 
 
 8 
 8 
 8 
 8 
 7 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 2 
 
 1-1 
 
 9 
 
 .9 
 4 
 
 28 
 
 2.8 
 33 
 
 
 
 6 
 7 
 8 
 9 
 
 9.72522 
 9.72542 
 9.72562 
 9.72582 
 9.72602 
 
 20 
 20 
 20 
 20 
 20 
 
 9.79719 
 9.79747 
 9.79776 
 9.79804 
 9.79832 
 
 28 
 29 
 28 
 28 
 
 0.20281 
 0.20253 
 0.20224 
 0.20196 
 0.20168 
 
 9.92803 
 9.92795 
 9.92787 
 9.92779 
 9.92771 
 
 8 
 8 
 8 
 
 8 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 a 
 
 4 
 4 
 
 9 
 14 
 
 .9 
 .4 
 
 .8 
 .7 
 .8 
 
 3.7 
 4.2 
 4.7 
 9.3 
 14.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.72622 
 9.72643 
 9.72663 
 9.72683 
 9.72703 
 
 21 
 20 
 20 
 20 
 20 
 
 9.79860 
 9.79888 
 9.79916 
 9.79944 
 9.79972 
 
 28 
 28 
 28 
 28 
 oa 
 
 0.20140 
 0.20112 
 0.20084 
 0.20056 
 0.20028 
 
 9.92763 
 9.92755 
 9.92747 
 9.92739 
 9.92731 
 
 8 
 8 
 8 
 8 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 19 
 24 
 
 .8 
 
 .2 
 
 ? 
 
 18.7 
 23.3 
 
 7 
 
 15 
 16 
 17 
 18 
 19 
 
 9.72723 
 9.72743 
 9.72763 
 9.72783 
 9.72803 
 
 20 
 20 
 20 
 20 
 20 
 
 9.80000 
 9.80028 
 9.80056 
 9.80084 
 9.80112 
 
 28 
 28 
 28 
 28 
 28 
 
 0.20000 
 0.19972 
 0.19944 
 0.19916 
 0.19888 
 
 9.92723 
 9.92715 
 9.92707 
 9.92699 
 9.92691 
 
 8 
 8 
 8 
 8 
 
 45 
 44 
 43 
 42 
 41 
 
 
 6 
 
 7 
 
 9 
 10 
 
 2 
 8 
 
 8 
 4 
 4 
 
 .7 
 .2 
 .6 
 .1 
 .5 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.72823 
 9.72843 
 9.72863 
 9.72883 
 9.72902 
 
 20 
 20 
 20 
 19 
 90 
 
 9.80140 
 9.80168 
 9.80195 
 9.80223 
 9.80251 
 
 28 
 27 
 28 
 28 
 
 0.19860 
 0.19832 
 0.19805 
 0.19777 
 0.19749 
 
 9.92683 
 9.92675 
 9.92667 
 9.92659 
 9.92651 
 
 8 
 8 
 8 
 8 
 
 40 
 
 39 
 38 
 37 
 36 
 
 
 20 
 30 
 40 
 50 
 
 G 
 18 
 
 18 
 22 
 
 .0 
 .5 
 .0 
 .5 
 
 25 
 26 
 27 
 28 
 29 
 
 9.72922 
 9.72942 
 9.72962 
 9.72982 
 9.73002 
 
 20 
 20 
 20 
 20 
 20 
 
 9.80279 
 9.80307 
 9.80335 
 9.80363 
 9.80391 
 
 28 
 28 
 28 
 28 
 
 OQ 
 
 0.19721 
 0.19693 
 0.19665 
 0.19637 
 0.19609 
 
 9.92643 
 9.92635 
 9.92627 
 9.92619 
 9.92611 
 
 8 
 8 
 8 
 8 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 2 
 
 2 
 '2 
 2 
 
 a 
 
 6 
 
 8 
 
 20 
 
 2.0 
 
 2.3 
 
 2.7 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.73022 
 9.73041 
 9.73061 
 9.73081 
 9.73101 
 
 19 
 20 
 20 
 20 
 20 
 
 9.80419 
 9.80447 
 9.80474 
 9.80502 
 9.80530 
 
 28 
 27 
 28 
 28 
 28 
 
 0.19581 
 0.19553 
 0.19526 
 0.19498 
 0.19470 
 
 9.92603 
 9.92595 
 9.92587 
 9.92579 
 9.92571 
 
 8 
 8 
 8 
 8 
 
 30 
 
 29 
 28 
 27 
 26 
 
 10 
 20 
 30 
 40 
 
 ^ 
 
 3 
 
 7 
 
 10 
 14 
 17 
 
 5 
 
 5 
 
 5 
 
 3.3 
 6.7 
 10.0 
 13.3 
 167 
 
 35 
 36 
 37 
 38 
 39 
 
 9.73121 
 9.73140 
 9.73160 
 9.73180 
 9.73200 
 
 19 
 20 
 20 
 20 
 1Q 
 
 9.80558 
 9.80586 
 9.80614 
 9.80642 
 9.80669 
 
 28 
 28 
 28 
 27 
 
 0.19442 
 0.19414 
 0.19386 
 0.19358 
 0.19331 
 
 9.92563 
 9.92555 
 9.92546 
 9.92538 
 9.92530 
 
 8 
 9 
 8 
 8 
 
 25 
 21 
 23 
 22 
 21 
 
 
 6 
 
 19 
 
 1. 
 o 
 
 9 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.73219 
 9.73239 
 9.73259 
 9.73278 
 9.73298 
 
 20 
 20 
 19 
 20 
 90 
 
 9.80697 
 9.80725 
 9.80753 
 9.80781 
 9.80808 
 
 28 
 28 
 28 
 27 
 
 OQ 
 
 0.19303 
 0.19275 
 0.19247 
 0.19219 
 0.19192 
 
 9.92522 
 9.92514 
 9.92506 
 9.92498 
 9.92490 
 
 8 
 8 
 8 
 8 
 
 20 
 
 19 
 18 
 17 
 16 
 
 
 8 
 9 
 10 
 
 20 
 30 
 
 2. 
 2. 
 K 
 6 
 
 9 
 
 5 
 9 
 2 
 3 
 
 i 
 
 45 
 46 
 47 
 
 48 
 49 
 
 9.73318 
 9.73337 
 9.73357 
 9.73377 
 9.73396 
 
 19 
 
 20 
 20 
 19 
 20 
 
 9.80836 
 9.80864 
 9.80892 
 9.80919 
 9.80947 
 
 28 
 28 
 
 27 
 28 
 
 OQ 
 
 0.19164 
 0.19136 
 0.19108 
 0.19081 
 0.19053 
 
 9.92482 
 9.92473 
 9.92465 
 9.92457 
 9.92449 
 
 9 
 8 
 8 
 8 
 
 15 
 14 
 13 
 12 
 11 
 
 
 40 
 50 
 
 q 
 
 12. 
 15. 
 
 8 
 
 7 
 8 
 
 7 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.73416 
 9.73435 
 9.73455 
 9.73474 
 9.73494 
 
 19 
 
 20 - 
 19 
 20 
 
 -1Q 
 
 9.80975 
 9.81003 
 9.81030 
 9.81058 
 9.81086 
 
 28 
 27 
 28 
 
 28 
 
 0.19025 
 0.18997 
 0.18970 
 0.18942 
 0.18914 
 
 9.92441 
 9.92433 
 9.92425 
 9.92416 
 9.92408 
 
 8 
 8 
 9 
 8 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 
 7 
 8 
 9 
 10 
 
 0.9 
 1.1 
 1.2 
 1.4 
 
 1.5 
 
 O.J 
 
 OA 
 
 1.1 
 
 LS 
 1J 
 
 0.7 
 0.8 
 0.9 
 . 1.1 
 ! 1.2 
 
 55 
 56 
 57 
 58 
 59 
 
 9.73513 
 9.73533 
 9.73552 
 9.73572 
 9.73591 
 
 20 
 19 
 20 
 19 
 20 
 
 9.81113 
 9.81141 
 9.81169 
 9.81196 
 9.81224 
 
 28 
 28 
 27 
 28 
 28 
 
 0.18887 
 0.18859 
 0.18831 
 0.18804 
 0.18776 
 
 9.92400 
 9.92392 
 9.92384 
 9.92376 
 9.92367 
 
 8 
 8 
 8 
 9 
 
 5 
 4 
 3 
 2' 
 1 
 
 20 
 30 
 40 
 50 
 
 3.0 
 4.5 
 6.0 
 7.5 
 
 2.5 
 
 4.( 
 5.1 
 6.' 
 
 2.3 
 > 3.5 
 4.7 
 
 5.8 
 
 60 
 
 9.73611 
 
 
 9.81252 
 
 
 0.18748 
 
 9.92359 
 
 
 
 
 
 
 
 
 
 L.Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 ' 
 
 
 P. 
 
 P. 
 
 
 57 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 33 
 
 1061 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 P 
 
 .P 
 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 9.73611 
 9.73630 
 9.73650 
 9.73669 
 9.73689 
 
 19 
 20 
 19 
 20 
 
 9.81252 
 9.81279 
 9.81307 
 9.81335 
 9.81362 
 
 27 
 28 
 28 
 27 
 
 0.18748 
 0.18721 
 0.18693 
 0.18665 
 0.18638 
 
 9.92359 
 9.92351 
 9.92343 
 9.92335 
 9.92326 
 
 8 
 8 
 8 
 9 
 
 60 
 
 59 
 58 
 57 
 56 
 
 2 
 6 S 
 
 7 9 
 
 8 
 
 .8 
 
 ^ 
 
 27 
 
 2.7 
 3 2 
 
 5 
 
 6 
 
 7 
 8 
 9 
 
 9.73708 
 9.73727 
 9.73747 
 9.73766 
 9.73785 
 
 19 
 20 
 19 
 19 
 on 
 
 9.81390 
 9.81418 
 9.81445 
 9.81473 
 9.81500 
 
 28 
 27 
 28 
 27 
 
 OQ 
 
 0.18610 
 0.18582 
 0.18555 
 0.18527 
 0.18500 
 
 9.92318 
 9.92310 
 9.92302 
 9.92293 
 9.92285 
 
 8 
 8 
 9 
 8 
 
 55 
 54 
 53 
 52 
 51 
 
 8 S 
 9 4 
 10 4 
 20 
 30 14 
 
 .7 
 .2 
 .7 
 .8 
 .0 
 
 3.6 
 4.1 
 4.5 
 9.0 
 13.5 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.73805 
 9.73824 
 9.73843 
 9.73863 
 9.73882 
 
 19 
 19 
 20 
 19 
 
 HI 
 
 9.81528 
 9.81556 
 9.81583 
 9.81611 
 9.81638 
 
 28 
 27 
 28 
 27 
 28 
 
 0.18472 
 0.18444 
 0.18417 
 0.18389 
 0.18362 
 
 9.92277 
 9.92269 
 9.92260 
 9.92252 
 9.92244 
 
 8 
 9 
 8 
 8 
 9 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 18 
 50 23 
 
 .7 
 .3 
 
 ? 
 
 18.0 
 22.5 
 
 
 
 15 
 16 
 17 
 18 
 19 
 
 9.73901 
 9.73921 
 9.73940 
 9.73959 
 9.73978 
 
 20 
 19 
 
 19 
 19 
 
 9.81666 
 9.81693 
 9.81721 
 9.81748 
 9.81776 
 
 27 
 28 
 27 
 28 
 
 0.18334 
 0.18307 
 0.18279 
 0.18252 
 0.18224 
 
 9.92235 
 9.92227 
 9.92219 
 9.92211 
 9.92202 
 
 8 
 8 
 8 
 9 
 
 45 
 
 44 
 43 
 42 
 41 
 
 6 
 7 
 8 
 9 
 10 
 
 2 
 2 
 2 
 3 
 3 
 
 .0 
 .3 
 .7 
 .0 
 .3 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.73997 
 9.74017 
 9.74036 
 9.74055 
 9.74074 
 
 20 
 19 
 19 
 19 
 10 
 
 9.81803 
 9.81831 
 9.81858 
 9.81886 
 9.81913 
 
 28 
 27 
 28 
 
 27 
 
 OQ 
 
 0.18197 
 0.18169 
 0.18142 
 0.18114 
 0.18087 
 
 9.92194 
 9.92186 
 9.92177 
 9.92169 
 9.92161 
 
 8 
 9 
 8 
 8 
 9 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 6 
 
 10 
 13 
 1G 
 
 .7 
 .0 
 .3 
 .7 
 
 25 
 
 26 
 
 27 
 28 
 29 
 
 9.74093 
 9.74113 
 9.74132 
 9.74151 
 9.74170 
 
 20 
 19 
 19 
 19 
 
 9.81941 
 9.81968 
 9.81996 
 9.82023 
 9.82051 
 
 27 
 28 
 27 
 28 
 
 0.18059 
 0.18032 
 0.18004 
 0.17977 
 0.17949 
 
 9.92152 
 9.92144 
 9.92136 
 9.92127 
 9.92119 
 
 8 
 8 
 9 
 
 8 
 g 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 1 
 
 1 
 
 2 
 2 
 
 9 
 .9 
 
 .2 
 .5 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.74189 
 9.74208 
 9.74227 
 9.74246 
 9.74265 
 
 19 
 19 
 19 
 19 
 
 9.82078 
 9.82106 
 9.82133 
 9.82161 
 9.82188 
 
 28 
 27 
 28 
 27 
 97 
 
 0.17922 
 0.17894 
 0.17867 
 0.17839 
 0.17812 
 
 9.92111 
 9.92102 
 9.92094 
 9.92086 
 9.92077 
 
 9 
 8 
 8 
 9 
 g 
 
 30 
 
 29 
 28 
 27 
 26 
 
 10 
 20 
 30 
 40 
 50 
 
 3 
 
 e 
 9 
 
 12 
 15 
 
 .2 
 .3 
 .5 
 
 .7 
 .8 
 
 35 
 36 
 37 
 38 
 39 
 
 9.74284 
 9.74303 
 9.74322 
 9.74341 
 9.74360 
 
 19 
 19 
 19 
 19 
 
 1Q 
 
 9.82215 
 9.82243 
 9.82270 
 9.82298 
 9.82325 
 
 28 
 27 
 28 
 27 
 27 
 
 0.17785 
 0.17757 
 0.17730 
 0.17702 
 0.17675 
 
 9.92069 
 9.92060 
 9.92052 
 9.92044 
 9.92035 
 
 9 
 
 8 
 8 
 9 
 g 
 
 25 
 24 
 23 
 
 22 
 21 
 
 6 
 7 
 
 1 
 
 1 
 
 
 
 8 
 .8 
 1 
 
 40 
 41 
 
 42 
 43 
 44 
 
 9.74379 
 9.74398 
 9.74417 
 9.74436 
 9.74455 
 
 19 
 19 
 19 
 19 
 
 9.82352 
 9.82380 
 9.82407 
 9.82435 
 9.82462 
 
 28 
 27 
 28 
 27 
 97 
 
 0.17648 
 0.17620 
 0.17593 
 0.17565 
 0.17538 
 
 9.92027 
 9.92018 
 9.92010 
 9.92002 
 9.91993 
 
 9 
 8 
 8 
 9 
 
 g 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 2 
 2 
 3 
 6 
 9 
 
 .4 
 .7 
 .0 
 .0 
 .0 
 
 45 
 46 
 47 
 48 
 49 
 
 9.74474 
 9.74493 
 9.74512 
 9.74531 
 9.74549 
 
 19 
 19 
 19 
 18 
 
 9.82489 
 9.82517 
 9.82544 
 9.82571 
 9.82599 
 
 28 
 27 
 27 
 28 
 97 
 
 0.1751! 
 0.17483 
 0.17456 
 0.17429 
 0.17401 
 
 9.91985 
 9.91976 
 9.91968 
 9.91959 
 9.91951 
 
 9 
 8 
 9 
 8 
 9 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 12 
 15 
 
 9 
 
 .0 
 .0 
 
 8 
 
 To~ 
 
 51 
 52 
 53 
 54 
 
 9.74568 
 9.74587 
 9.74606 
 9.74625 
 9.74644 
 
 19 
 19 
 19 
 19 
 
 9.82626 
 9.82653 
 9.82681 
 9.82708 
 9.82735 
 
 27 
 28 
 27 
 27 
 
 0.17374 
 0.17347 
 0.17319 
 0.17292 
 0.17265 
 
 9.91942 
 9.91934 
 9.91925 
 9.91917 
 9.91908 
 
 8 
 9 
 8 
 9 
 
 g 
 
 10 
 
 9 
 8 
 7. 
 6 
 
 6 C 
 7 1 
 8 1 
 9 ] 
 10 1 
 
 .9 
 .1 
 .2 
 .4 
 .5 
 
 0.8 
 0.9 
 1.1 
 1.2 
 1.3 
 
 55 
 56 
 57 
 58 
 59 
 
 9.74662 
 9.74681 
 9.74700 
 9.74719 
 9.74737 
 
 19 
 Id 
 19 
 
 18 
 
 9.82762 
 9.82790 
 9.82817 
 9.82844 
 9.82871 
 
 28 
 27 
 27 
 27 
 28 
 
 0.17238 
 0.17210 
 0.17183 
 0.17156 
 0.17129 
 
 9.91900 
 9.91891 
 9.91883 
 9.91874 
 9.91866 
 
 9 
 8 
 9 
 8 
 9 
 
 5 
 4 
 3 
 2 
 1 
 
 20 
 30 4 
 40 6 
 50 "i 
 
 .0 
 .5 
 .0 
 .5 
 
 2.7 
 4.0 
 5.3 
 6.7 
 
 60 
 
 9.74756 
 
 
 9.82899 
 
 
 0.17101 
 
 9.91857 
 
 
 
 
 
 
 
 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 ' 
 
 P 
 
 .P 
 
 
 
 
 
 
 
 58 
 
 
 
 
 
 
 
1062 
 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 34 
 
 ' 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg 
 
 L. Cos. 
 
 d. 
 
 
 P.P. 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.74756 
 9.74775 
 9.74794 
 9.74812 
 9.74831 
 
 19 
 19 
 18 
 19 
 19 
 18 
 19 
 19 
 18 
 19 
 18 
 19 
 19 
 18 
 19 
 18 
 19 
 18 
 19 
 18 
 19 
 18 
 19 
 18 
 19 
 18 
 19 
 18 
 18 
 19 
 18 
 19 
 18 
 18 
 19 
 18 
 18 
 18 
 19 
 18 
 18 
 19 
 18 
 18 
 18 
 18 
 19 
 18 
 18 
 18 
 18 
 18 
 19 
 18 
 18 
 18 
 18 
 18 
 18 
 18 
 
 9.82899 
 9.82926 
 9.82953 
 9.82980 
 9.83008 
 
 27 
 27 
 
 27 
 28 
 27 
 27 
 27 
 28 
 27 
 27 
 27 
 27 
 27 
 28 
 27 
 27 
 27 
 27 
 27 
 27 
 28 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 28 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 26 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 27 
 
 0.17101 
 0.17074 
 0.17047 
 0.17020 
 0.16992 
 
 9.91857 
 9.91849 
 9.91840 
 9.91832 
 9.91823 
 
 8 
 9 
 8 
 9 
 
 8 
 9 
 8 
 9 
 8 
 9 
 9 
 8 
 9 
 8 
 9 
 9 
 8 
 9 
 8 
 9 
 9 
 8 
 9 
 9 
 8 
 9 
 9 
 8 
 9 
 9 
 8 
 9 
 9 
 8 
 9 
 9 
 9 
 8 
 9 
 9 
 8 
 9 
 9 
 9 
 8 
 9 
 9 
 9 
 9 
 8 
 9 
 9 
 9 
 9 
 8 
 9 
 9 
 9 
 9 
 9 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 : i 
 
 '5 
 ! 
 4 
 
 r 
 
 M 
 
 ' j 
 i 
 
 .'i 
 
 :l 
 
 ': \ 
 1 
 \ 
 
 4 
 5 
 
 6 
 7 
 8 
 9 
 10 
 20 
 30 
 40 
 50 
 
 J 
 
 *v 
 "ji 
 '[ , 
 i 
 I 
 If 
 
 2; 
 r> 
 
 7 
 X 
 9 
 
 \) 
 
 
 
 
 
 
 7 
 8 
 9 
 
 
 
 
 
 
 6 
 
 7 
 8 
 9 
 
 
 
 
 
 
 
 
 ] 
 1 
 1 
 1 
 
 3 
 
 4 
 6 
 
 7 
 
 !8 27 
 
 2.8 2.7 
 J.3 3.2 
 J.7 3.6 
 1.2 4.1 
 L7 4.5 
 ).3 9.0 
 1.0 13.5 
 5.7 18.0 
 5.3 22.5 
 
 26 
 
 2.6 
 3.0 
 3.5 
 3.9 
 4.3 
 8.7 
 13.0 
 17.3 
 21.7 
 
 19 
 
 1.9 
 2.2 
 2.5 
 2.9 
 3.2 
 6.3 
 9.5 
 12.7 
 15.8 
 
 18 
 
 1.8 
 2.1 
 2.4 
 2.7 
 3.0 
 6.0 
 9.0 
 12.0 
 15.0 
 
 9 8 
 
 .9 0.8 
 .1 0.9 
 .2 1.1 
 .4 1.2 
 .5 1.3 
 .0 2.7 
 .5 4.0 
 .0 5.3 
 .5 6.7 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.74850 
 9.74868 
 9.74887 
 9.74906 
 9.74924 
 
 9.83035 
 9.83062 
 9.83089 
 9.83117 
 9.83144 
 
 0.16965 
 0.16938 
 0.16911 
 
 o!l6856 
 
 9.91815 
 9.91806 
 9.91798 
 9.91789 
 9.91781 
 
 55 
 54 
 53 
 52 
 51 
 
 10 
 11 
 12 
 13 
 14 
 
 9.74943 
 9.74961 
 9.74980 
 9.74999 
 9.75017 
 
 9.83171 
 9.83198 
 9.83225 
 9.83252 
 9.83280 
 
 0.16829 
 ' 0.16802 
 0.16775 
 0.16748 
 0.16720 
 
 9.91772 
 9.91763 
 9.91755 
 9.91746 
 9.91738 
 
 50 
 
 49 
 48 
 47 
 46 
 
 15 
 16 
 17 
 18 
 19 
 
 9.75036 
 9.75054 
 9.75073 
 9.75091 
 9.75110 
 
 9.83307 
 9.83334 
 9.83361 
 9.83388 
 9.83415 
 
 0.16693 
 0.16666 
 0.16639 
 0.16612 
 0.16585 
 
 9.91729 
 9.91720 
 9.91712 
 9.91703 
 9.91695 
 
 45 
 44 
 43 
 42 
 41 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.75128 
 9.75147 
 9.75165 
 9.75184 
 9.75202 
 
 9.83442 
 9.83470 
 9.83497 
 9.83524 
 9.83551 
 
 0.16558 
 0.16530 
 0.16503 
 0.16476 
 0.16449 
 
 9.91686 
 9.91677 
 9.91669 
 9.91660 
 9.91651 
 
 40 
 
 39 
 38 
 37 
 36 
 
 25 
 26 
 27 
 28 
 29 
 "30" 
 31 
 32 
 33 
 34 
 
 9.75221 
 9.75239 
 9.75258 
 9.75276 
 9.75294 
 
 9.83578 
 9.83605 
 9.83632 
 9.83659 
 9.83686 
 
 0.16422 
 0.16395 
 0.16368 
 0.16341 
 0.16314 
 
 9.91643 
 9.91634 
 9.91625 
 9.91617 
 9.91608 
 
 35 
 34 
 33 
 32 
 31 
 
 9.75313 
 9.75331 
 9.75350 
 9.75368 
 9.75386 
 
 9.83713 
 9.83740 
 9.83768 
 9.83795 
 9.83822 
 
 0.16287 
 0.16260 
 0.16232 
 0.16205 
 0.16178 
 
 9.91599 
 9.91591 
 9.91582 
 9.91573 
 9.91565 
 
 30 
 
 29 
 28 
 27 
 26 
 
 35 
 36 
 37 
 38 
 39 
 
 9.75405 
 9.75423 
 9.75441 
 9.75459 
 9.75478 
 
 9.83849 
 9.83876 
 9.83903 
 9.83930 
 9.83957 
 
 0.16151 
 0.16124 
 0.16097 
 0.16070 
 0.16043 
 
 9.91556 
 9.91547 
 9.91538 
 9.91530 
 9.91521 
 
 25 
 24 
 23 
 22 
 21 
 
 20 
 
 19 
 18 
 17 
 16 
 
 14 
 13 
 12 
 11 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.75496 
 9.75514 
 9.75533 
 9.75551 
 9.75569 
 
 9.83984 
 9.84011 
 9.84038 
 9.84065 
 9.84092 
 
 0.16016 
 0.15989 
 0.15962 
 0.15935 
 0.15908 
 
 9.91512 
 9.91504 
 9.91495 
 9.91486 
 9.91477 
 
 45 
 46 
 47 
 48 
 49 
 
 9.75587 
 9.75605 
 9.75624 
 9.75642 
 9.75660 
 
 9.84119 
 9.84146 
 9.84173 
 9.84200 
 9.84227 
 
 0.15881 
 0.15854 
 0.15827 
 0.15800 
 0.15773 
 
 9.91469 
 9.91460 
 9.91451 
 9.91442 
 9.91433 
 
 50 
 
 51 
 
 52 
 53 
 54 
 55 
 56 
 57 
 58 
 59 
 
 9.75678 
 9.75696 
 9.75714 
 9.75733 
 9.75751 
 
 9.84254 
 9.84280 
 9.84307 
 9.84334 
 9.84361 
 
 0.15746 
 0.15720 
 0.15693 
 0.15666 
 0.15639 
 
 9.91425 
 9.91416 
 9.91407 
 9.91398 
 9.91389 
 
 10 
 
 9 
 8 
 7 
 6 
 
 9.75769 
 9.75787 
 9.75805 
 9.75823 
 9.75841 
 
 9.84388 
 9.84415 
 9.84442 
 9.84469 
 9.84496 
 
 0.15612 
 0.15585 
 0.15558 
 0.15531 
 0.15504 
 
 9.91381 
 9.91372 
 9.91363 
 9.91354 
 9.91345 
 
 5 
 4 
 3- 
 2 
 1 
 
 60 
 
 9.75859 
 
 9.84523 
 
 0.15477 
 
 9.91336 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotgr. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 P.P. 
 
 55 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 35 
 
 1063 
 
 1 
 
 L. Sin. 
 
 d. 
 
 L.Tang 
 
 d. c. 
 
 L. Cotg 
 
 L. Cos. 
 
 d. 
 
 
 I 
 
 '.P 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.75859 
 9.75877 
 9.75895 
 9.75913 
 9.75931 
 
 18 
 18 
 18 
 18 
 18 
 
 9.84523 
 9.84550 
 9.84576 
 9.84603 
 9.84630 
 
 27 
 26 
 27 
 27 
 27 
 
 0.15477 
 0.15450 
 0.15424 
 0.15397 
 0.15370 
 
 9.91336 
 9.91328 
 9.91319 
 9.91310 
 9.91301 
 
 8 
 9 
 9 
 9 
 
 60 
 
 59 
 
 58 
 57 
 56 
 
 2 
 
 6 5 
 
 7 
 
 7 
 
 >.7 
 ! 
 
 26 
 
 2.6 
 
 A 
 
 5 
 
 6 
 7 
 8 
 9 
 
 9.75949 
 9.75967 
 9.75985 
 9.76003 
 9.76021 
 
 18 
 18 
 18 
 18 
 18 
 
 9.84657 
 9.84684 
 9.84711 
 9.84738 
 9.84764 
 
 27 
 27 
 27 
 26 
 97 
 
 0.15343 
 0.15316 
 0.15289 
 0.15262 
 0.15236 
 
 9.91292 
 9.91283 
 9.91274 
 9.91266 
 9.91257 
 
 9 
 9 
 8 
 9 
 
 55 
 54 
 53 
 52 
 51 
 
 8 J 
 9 4 
 10 4 
 
 20 < 
 30 1J 
 
 .1 
 .5 
 .0 
 
 5 
 
 3.5 
 3.9 
 4.3 
 8.7 
 13.0 
 
 10 
 
 11 
 12 
 13 
 
 14 
 
 9.76039 
 9.76057 
 9.76075 
 9.76093 
 9.76111 
 
 18 
 18 
 18 
 18 
 18 
 
 9.84791 
 9.84818 
 9.84845 
 9.84872 
 9.84899 
 
 27 
 27 
 27 
 27 
 26 
 
 0.15209 
 0.15182 
 0.15155 
 0.15128 
 0.15101 
 
 9.91248 
 9.91239 
 9.91230 
 9.91221 
 9.91212 
 
 9 
 9 
 9 
 9 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 18 
 50 22 
 
 .0 
 .5 
 
 | 
 
 17.3 
 21.7 
 
 | 
 
 15 
 16 
 17 
 
 18 
 19 
 
 9.76129 
 9.76146 
 9.76164 
 9.76182 
 9.76200 
 
 17 
 
 18 
 18 
 18 
 18 
 
 9.84925 
 9.84952 
 9.84979 
 9.85006 
 9.85033 
 
 27 
 27 
 27 
 27 
 9fi 
 
 0.15075 
 0.15048 
 0.15021 
 0.14994 
 0.14967 
 
 9.91203 
 9.91194 
 9.91185 
 9.91176 
 9.91167 
 
 9 
 9 
 9 
 9 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 7 
 8 
 9 
 10 
 
 1 
 2 
 
 2 
 2 
 3 
 
 .8 
 .1 
 .4 
 .7 
 .0 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.76218 
 9.76236 
 9.76253 
 9.76271 
 9.76289 
 
 18 
 17 
 18 
 18 
 18 
 
 9.85059 
 9.85086 
 9.85113 
 9.85140 
 9.85166 
 
 27 
 27 
 27 
 26 
 27 
 
 0.14941 
 0.14914 
 0.14887 
 0.14860 
 0.14834 
 
 9.91158 
 9.91149 
 9.91141 
 9.91132 
 9.91123 
 
 9 
 8 
 9 
 9 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 6 
 9 
 12 
 15 
 
 .0 
 .0 
 .0 
 .0 
 
 25 
 26 
 
 27 
 28 
 29 
 
 9.76307 
 9.76324 
 9.76342 
 9.76360 
 9.76378 
 
 17 
 18 
 18 
 18 
 17 
 
 9.85193 
 9.85220 
 9.85247 
 9.85273 
 9.85300 
 
 27 
 27 
 26 
 27 
 
 0.14807 
 0.14780 
 0.14753 
 0.14727 
 0.14700 
 
 9.91114 
 9.91105 
 9.91096 
 9.91087 
 9.91078 
 
 9 
 9 
 9 
 9 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 1 
 
 1 
 
 2 
 
 2 
 
 7 
 
 .7 
 .0 
 .3 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.76395 
 9.76413 
 9.76431 
 9.76448 
 9.76466 
 
 18 
 18 
 17 
 18 
 
 -IQ 
 
 9.85327 
 9.85354 
 9.85380 
 9.85407 
 9.85434 
 
 27 
 26 
 27 
 27 
 oc 
 
 0.14673 
 0.14646 
 0.14620 
 0.14593 
 0.14566 
 
 9.91069 
 9.91060 
 9.91051 
 9.91042 
 9.91033' 
 
 9 
 9 
 9 
 9 
 10 
 
 30 
 
 29 
 
 28 
 27 
 26 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 2 
 2 
 5 
 8 
 11 
 }<\ 
 
 .6 
 .8 
 .7 
 .5 
 .3 
 2 
 
 35 
 36 
 37 
 38 
 39 
 
 9.76484 
 9.76501 
 9.76519 
 9.76537 
 9.76554 
 
 17 
 18 
 18 
 17 
 
 9.85460 
 9.85487 
 9.85514 
 9.85540 
 9.85567 
 
 27 
 27 
 26 
 27 
 
 0.14540 
 0.14513 
 0.14486 
 0.14460 
 0.14433 
 
 9.91023 
 9.91014 
 9.91005 
 9.90996 
 9.90987 
 
 9 
 9 
 9 
 9 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 7 
 
 1 
 
 1 
 
 3 
 
 
 n 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.76572 
 9.76590 
 9.76607 
 9.76625 
 9.76642 
 
 18 
 17 
 
 18 
 17 
 
 18 
 
 9.85594 
 9.85620 
 9.85647 
 9.85674 
 9.85700 
 
 26 
 27 
 27 
 26 
 97 
 
 0.14406 
 0.14380 
 0.14353 
 0.14326 
 0.14300 
 
 9.90978 
 9.90969 
 9.90960 
 9.90951 
 9.90942 
 
 9 
 9 
 9 
 9 
 9 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 1 
 1 
 1 
 3 
 5 
 
 3 
 5 
 7 
 3 
 
 
 45 
 46 
 47 
 48 
 49 
 
 9.76660 
 9.76677 
 9.76695 
 9.76712 
 9.76730 
 
 17 
 18 
 17 
 18 
 17 
 
 9.85727 
 9.85754 
 9.85780 
 9.85807 
 9.85834 
 
 27 
 26 
 27 
 27 
 9fi 
 
 0.14273 
 0.14246 
 0.14220 
 0.14193 
 0.14166 
 
 9.90933 
 9.90924 
 9.90915 
 9.90906 
 9.90896 
 
 9 
 9 
 9 
 10 
 9 
 
 15 
 14 
 
 13 
 12 
 11 
 
 40 
 50 
 
 6 
 
 8 
 
 B 
 
 7 
 3 
 
 8 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.76747 
 9.76765 
 976782 
 9.76800 
 9.76817 
 
 18 
 17 
 18 
 17 
 
 -IQ 
 
 9.85860 
 9.85887 
 9.85913 
 9.85940 
 9.85967 
 
 27 
 26 
 27 
 27 
 9fi 
 
 0.14140 
 0.14113 
 0.14087 
 0.14060 
 0.14033 
 
 9.90887 
 9.90878 
 9.90869 
 9.90860 
 9.90851 
 
 9 
 9 
 9 
 9 
 9 
 
 10 
 
 9 
 
 8. 
 
 6 
 
 6 
 7 1 
 8 1 
 9 1 
 10 1 
 
 .9 
 .1 
 .2 
 .4 
 .5 
 
 0.8 
 0.9 
 1.1 
 1.2 
 1.3 
 
 55 
 56 
 57 
 58 
 59 
 
 9.76835 
 9.76852 
 9.76870 
 9.76887 
 9.76904 
 
 17 
 18 
 17 
 17 
 
 9.85993 
 9.86020 
 9.86046 
 9.86073 
 9.86100 
 
 27 
 26 
 27 
 27 
 9fi 
 
 0.14007 
 0.13980 
 0.13954 
 0.13927 
 0.13900 
 
 9.90842 
 9.90832 
 9.90823 
 9.90814 
 9.90805 
 
 10 
 9 
 9 
 9 
 9 
 
 5 
 4 
 3 
 2 
 
 1 
 
 20 3 
 30 4 
 40 6 
 50 7 
 
 .U 
 
 .5 
 .0 
 .5 
 
 2.7 
 4.0 
 5.3 
 6.7 
 
 60 
 
 9.76922 
 
 
 9.86126 
 
 
 0.13874 
 
 9.90796 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.C. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 ' 
 
 P 
 
 P. 
 
 
 54 
 
1064 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 _ 36 
 
 1 
 
 L.Sin 
 
 d. 
 
 L.Tang 
 
 d. c 
 
 L. Cotg 
 
 L.Cos 
 
 d. 
 
 
 
 ! 
 
 M 
 
 t ' ' 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.76922 
 9.76939 
 9.76957 
 9.76974 
 9.76991 
 
 17 
 
 18 
 17 
 17 
 18 
 
 9.86126 
 9.86153 
 9.86179 
 9.86206 
 9.86232 
 
 27 
 26 
 27 
 26 
 27 
 
 0.13874 
 0.13847 
 0.13821 
 0.13794 
 0.13768 
 
 9.90796 
 9.90787 
 9.90777 
 9.90768 
 9.90759 
 
 1C 
 9 
 
 9 
 
 60 
 
 59 
 
 58 
 57 
 56 
 
 6 
 
 7 
 
 
 >7 
 
 2.7 
 3 
 
 26 
 
 2.6 
 3 
 
 5 
 6 
 7 
 8 
 9 
 
 9.77009 
 9.77026 
 9.77043 
 9.77061 
 9.77078 
 
 17 
 17 
 18 
 17 
 17 
 
 9.86259 
 9.86285 
 9.86312 
 9.86338 
 9.86365 
 
 26 
 
 27 
 26 
 27 
 97 
 
 0.13741 
 0.13715 
 0.13688 
 0.13662 
 0.13635 
 
 9.90750 
 9.90741 
 9.90731 
 9.90722 
 9.90713 
 
 9 
 10 
 9 
 9 
 
 55 
 54 
 53 
 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 1 
 
 3.6 
 1.1 
 1.5 
 
 ? ") 
 
 3.5 
 3.9 
 '4.3 
 
 8.7 
 13.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.77095 
 9.77112 
 9.77130 
 9.77147 
 9.77164 
 
 17 
 18 
 17 
 17 
 17 
 
 9.86392 
 9.86418 
 9.86445 
 9.86471 
 9.86498 
 
 26 
 27 
 26 
 27 
 
 0.13608 
 0.13582 
 0.13555 
 0.13529 
 0.13502 
 
 9.90704 
 9.90694 
 9.90685 
 9.90676 
 9.90667 
 
 10 
 9 
 9 
 9 
 10 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 1, 
 
 2 
 
 v'0 
 tf 
 
 J 
 
 17.3 
 21.7 
 
 8 
 
 15 
 16 
 17 
 18 
 19 
 
 9.77181 
 9.77199 
 9.77216 
 9.77233 
 9.77250 
 
 18 
 17 
 17 
 17 
 18 
 
 9.86524 
 9.86551 
 9.86577 
 9.86603 
 9.86630 
 
 27 
 26 
 26 
 
 27 
 
 0.13476 
 0.13449 
 0.13423 
 0.13397 
 0.13370 
 
 9.90657 
 9.90648 
 9.90639 
 9.90630 
 9.90620 
 
 9 
 9 
 9 
 10 
 
 45 
 44 
 43 
 42 
 41 
 
 
 6 
 
 7 
 8 
 9 
 
 
 1 
 
 4 
 ' -1 
 
 i 
 
 L.8 
 
 IA 
 1.7 
 5.0 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.77268 
 9.77285 
 9.77302 
 9.77319 
 9.77336 
 
 17 
 17 
 
 17 
 17 
 17 
 
 9.86656 
 9.86683 
 9.86709 
 9.86736 
 9.86762 
 
 27 
 26 
 27 
 26 
 27 
 
 0.13344 
 0.13317 
 0.13291 
 0.13264 
 0.13238 
 
 9.90611 
 9.90602 
 9.90592 
 9.90583 
 9.90574 
 
 9 
 10 
 9 
 9 
 9 
 
 40 
 
 39 
 38 
 37 
 36 
 
 ' 
 
 .JO 
 50 
 10 
 
 )0 
 
 ( 
 
 ( 
 
 ii 
 
 M 
 
 
 25 
 26 
 27 
 28 
 29 
 
 9.77353 
 9.77370 
 9.77387 
 9.77405 
 9.77422 
 
 17 
 17 
 18 
 17 
 17 
 
 9.86789 
 9.86815 
 9.86842 
 9.86868 
 9.86894 
 
 26 
 27 
 26 
 26 
 
 0.13211 
 0.13185 
 0.13158 
 0.13132 
 0.13106 
 
 9.90565 
 9.90555 
 9.90546 
 9.90537 
 9.90527 
 
 10 
 9 
 9 
 10 
 
 35 
 34 
 33 
 32 
 31 
 
 
 f> 
 7 
 8 
 
 I 
 
 i 
 
 ! 
 
 J'j 
 .7 
 .0 
 .3 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.77439 
 9.77456 
 9.77473 
 9.77490 
 9.77507 
 
 17 
 17 
 17 
 
 17 
 17 
 
 9.86921 
 9,86947 
 9.86974 
 9.87000- 
 9.87027 
 
 26 
 27 
 26 
 27 
 2fi 
 
 0.13079 
 0.13053 
 0.13026 
 0.13000 
 0.12973 
 
 9.90518 
 9.90509 
 9.90499 
 9.90490 
 9.90480 
 
 9 
 10 
 9 
 10 
 
 30 
 
 29 
 28 
 27 
 26 
 
 ': 
 
 f * 
 \ "\ 
 
 9 
 
 
 JO 
 
 
 
 
 o 
 
 S 
 5 
 8 
 11 
 1 1 
 
 .6 
 .8- 
 .7 
 .5 
 .3 
 2 
 
 35 
 36 
 37 
 38 
 39 
 
 9.77524 
 9.77541 
 9.77558 
 9.77575 
 9.77592 
 
 17 
 17 
 17 
 17 
 17 
 
 9.87053 
 9.87079 
 9.87106 
 9.87132 
 9.87158 
 
 26 
 27 
 26 
 
 26 
 27 
 
 0.12947 
 0.12921 
 0.12894 
 0.12868 
 0.12842 
 
 9.90471 
 9.90462 
 9.90452 
 9.90443 
 9.90434 
 
 9 
 10 
 9 
 9 
 
 1ft 
 
 25 
 24 
 23 
 22 
 21 
 
 
 6 
 
 r 
 i 
 
 6 
 .6 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.77609 
 9.77626 
 9.77643 
 9.77660 
 9.77677 
 
 17 
 17 
 17 
 17 
 17 
 
 9.87185 
 9.87211 
 9.87238 
 9.87264 
 9.87290 
 
 26 
 
 27 
 26 
 26 
 
 0.12815 
 0.12789 
 0.12762 
 0.12736 
 0.12710 
 
 9.90424 
 9.90415 
 9.90405 
 9.90396 
 9.90386 
 
 9 
 10 
 9 
 10 
 
 20 
 
 19 
 18 
 17 
 16 
 
 j 
 * < 
 
 r' j] 
 
 8 
 9 
 
 
 
 
 2 
 2 
 5 
 
 8 
 
 .1 
 .4 
 .7 
 .3 
 
 .0 
 
 45 
 46 
 47 
 48 
 49 
 
 9.77694 
 9.77711 
 9.77728 
 9.77744 
 9.77761 
 
 17 
 17 
 16 
 17 
 17 
 
 9.87317 
 9.87343 
 9.87369 
 9.87396 
 
 9.87422 
 
 26 
 
 26 
 27 
 26 
 
 0.12683 
 0.12657 
 0.12631 
 0.12604 
 0.12578 
 
 9.90377 
 9.90368 
 9.90358 
 9.90349 
 9.90339 
 
 9 
 10 
 9 
 10 
 
 15 
 14 
 13 
 12 
 11 
 
 4 
 
 5 
 
 
 
 
 1 
 
 10 
 13 
 
 Q 
 
 .7 
 .3 
 
 g 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.77778 
 9.77795 
 9.77812 
 9.77829 
 9.77846 
 
 17 
 17 
 17 
 17 
 16 
 
 9.87448 
 9.87475 
 9.87501 
 9.87527 
 9.87554 
 
 27 
 26 
 26 
 27 
 26 
 
 0.12552 
 0.12525 
 0.12499 
 0.12473 
 0.12446 
 
 9.90330 
 9.90320 
 9.90311 
 9.90301 
 9.90292 
 
 10 
 9 
 10 
 9 
 10 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 
 
 7 
 8 
 9 
 10 
 
 1 
 
 I 
 
 1 
 1 
 1 
 
 
 
 
 
 8 
 
 5 
 
 7 
 
 0.9 
 1.1 
 1.2 
 1.4 
 1.5 
 
 55 
 56 
 57 
 58 
 59 
 
 9.77862 
 9.77879 
 9.77896 
 9.77913 
 9.77930 
 
 17 
 17 
 17 
 17 
 16 
 
 9.87580 
 9.87606 
 9.87633 
 9.87659 
 9.87685 
 
 26 
 27 
 26 
 26 
 26 
 
 0.12420 
 0.12394 
 0.12367 
 0.12341 
 0.12315 
 
 9.90282 
 9.90273 
 9.90263 
 9.90254 
 9.90244 
 
 9 
 10 
 9 
 10 
 9 
 
 5 
 4 
 3 
 2 
 1 
 
 20 
 30 
 40 
 50 
 
 3 
 
 5 
 6 
 
 8 
 
 3 
 
 
 7 
 3 
 
 3.0 
 4.5 
 6.0 
 7.5 
 
 60 
 
 9.77946 
 
 
 9.87711 
 
 
 0.12289 
 
 9.90235 
 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin 
 
 d. 
 
 /" 
 
 
 P. 
 
 P. 
 
 
 53 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 37 
 
 1065 
 
 > 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 P 
 
 .P. 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.77946 
 9.77963 
 9.77980 
 9.77997 
 9.78013 
 
 17 
 17 
 17 
 16 
 17 
 
 9.87711 
 9.87738 
 9.87764 
 9.87790 
 9.87817 
 
 27 
 26 
 26 
 27 
 26 
 
 0.12289 
 0.12262 
 0.12236 
 0.12210 
 0.12183 
 
 9.90235 
 9.90225 
 9.90216 
 9.90206 
 9.90197 
 
 10 
 9 
 10 
 9 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 27 
 
 2.7 
 q o 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.78030 
 9.78047 
 9.78063 
 9.78080 
 9.78097 
 
 17 
 
 16 
 17 
 17 
 
 9.87843 
 9.87869 
 9.87895 
 9.87922 
 9.87948 
 
 26 
 26 
 27 
 26 
 2fi 
 
 0.12157 
 0.12131 
 0.12105 
 0.12078 
 0.12052 
 
 9.90187 
 9.90178 
 9.90168 
 9.90159 
 9.90149 
 
 9 
 10 
 9 
 10 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 3.6 
 4.1 
 4.5 
 9.0 
 13.5 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.78113 
 9.78130 
 9.78147 
 9.78163 
 9.78180 
 
 17 
 17 
 16 
 17 
 
 9.87974 
 9.88000 
 9.88027 
 9.88053 
 9.88079 
 
 26 
 27 
 26 
 26 
 26 
 
 0.12026 
 0.12000 
 0.11973 
 0.11947 
 0.11921 
 
 9.90139 
 9.90130 
 9.90120 
 9.90111 
 9.90101 
 
 9 
 10 
 9 
 10 
 
 SO 
 
 49 
 
 48 
 47 
 46 
 
 40 
 50 
 
 18.0 
 22.5 
 
 26 
 
 15 
 16 
 17 
 
 18 
 19 
 
 9.78197 
 9.78213 
 9.78230 
 9.78246 
 9.78263 
 
 16 
 17 
 16 
 17 
 17 
 
 9.88105 
 9.88131 
 9.88158 
 9.88184 
 9.88210 
 
 26 
 27 
 26 
 26 
 26 
 
 0.11895 
 0.11869 
 0.11842 
 0.11816 
 0.11790 
 
 9.90091 
 9.90082 
 9.90072 
 9.90063 
 9.90053 
 
 9 
 10 
 9 
 10 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 7 
 8 
 9 
 10 
 
 2.6 
 3.0 
 3.5 
 3.9 
 4.3 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.78280 
 9.78296 
 9.78313 
 9.78329 
 9.78346 
 
 16 
 17 
 16 
 17 
 
 9.88236 
 
 9.88262 
 9.88289 
 9.88315 
 9.88341 
 
 26 
 27 
 26 
 26 
 26 
 
 0.11764 
 0.11738 
 0.11711 
 0.11685 
 0.11659 
 
 9.90043 
 9.90034 
 9.90024 
 9.90014 
 9.90005 
 
 9 
 10 
 10 
 9 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 8.7 
 13.0 
 17.3 
 21.7 
 
 25 
 26 
 27 
 28 
 29 
 
 9.78362 
 9.78379 
 9.78395 
 9.78412 
 9.78428 
 
 17 
 16 
 17 
 16 
 
 9.88367 
 9.88393 
 9.88420 
 9.88446 
 9.88472 
 
 26 
 27 
 26 
 26 
 26 
 
 0.11633 
 0.11607 
 0.11580 
 0.11554 
 0.11528 
 
 9.89995 
 9.89985 
 9.89976 
 9.89966 
 9.89956 
 
 10 
 9 
 10 
 10 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 17 
 
 1.7 
 2.0 
 2.3 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.78445 
 9.78461 
 9.78478 
 9.78494 
 9.78510 
 
 16 
 17 
 16 
 16 
 
 9.88498 
 9.88524 
 9.88550 
 9.88577 
 9.88603 
 
 26 
 26 
 27 
 26 
 26 
 
 0.11502 
 0.11476 
 0.11450 
 0.11423 
 0.11397 
 
 9.89947 
 9.89937 
 9.89927 
 9.89918 
 9.89908 
 
 10 
 10 
 9 
 10 
 
 30 
 
 29 
 
 28 
 27 
 26 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 2.6 
 2.8 
 5.7 
 8.5 
 11.3 
 142 
 
 35 
 36 
 37 
 38 
 39 
 
 9.78527 
 9.78543 
 9.78560 
 9.78576 
 9.78592 
 
 16 
 
 17 
 16 
 16 
 17 
 
 9.88629 
 9.88655 
 9.88681 
 9.88707 
 9.88733 
 
 26 
 26 
 26 
 26 
 26 
 
 0.11371 
 0.11345 
 0.11319 
 0.11293 
 0.11267 
 
 9.89898 
 9.89888 
 9.89879 
 9.89869 
 9.89859 
 
 10 
 9 
 10 
 10 
 10 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 7 
 
 16 
 
 1.6 
 1 9 
 
 40 
 
 41 
 
 42 
 43 
 44 
 
 9.78609 
 9.78625 
 9.78642 
 9.78658 
 9.78674 
 
 16 
 17 
 16 
 16 
 
 9.88759 
 9.88786 
 9.88812 
 9.88838 
 9.88864 
 
 27 
 26 
 26 
 26 
 26 
 
 0.11241 
 0.11214 
 0.11188 
 0.11162 
 0.11136 
 
 9.89849 
 9.89840 
 9.89830 
 9.89820 
 9.89810 
 
 9 
 10 
 10 
 10 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 2.1 
 2.4 
 2.7 
 5.3 
 8.0 
 
 45 
 
 46 
 47 
 
 48 
 49 
 
 9.78691 
 9.78707 
 9.78723 
 9.78739 
 9.78756 
 
 16 
 16 
 16 
 17 
 
 9.88890 
 9.88916 
 9.88942 
 9.88968 
 9.88994 
 
 26 
 26 
 26 
 26 
 26 
 
 0.11110 
 0.11084 
 0.11058 
 0.11032 
 0.11006 
 
 9.89801 
 9.89791 
 9.89781 
 9.89771 
 9.89761 
 
 10 
 10 
 10 
 10 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 
 50 
 
 | 
 
 10.7 
 13.3 
 
 9 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.78772 
 9.78788 
 9.78805 
 9.78821 
 9.78837 
 
 16 
 17 
 16 
 16 
 16 
 
 9.89020 
 9.89046 
 9.89073 
 9.89099 
 9.89125 
 
 26 
 27 
 26 
 26 
 
 9g 
 
 0.10980 
 0.10954 
 0.10927 
 0.10901 
 0.10875 
 
 9.89752 
 9.89742 
 9.89732 
 9.89722 
 9.89712 
 
 10 
 10 
 10 
 10 
 10 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 6 1 
 
 7 1 
 8 1 
 9 1 
 10 1 
 
 .0 0.9 
 .2 1.1 
 .3 1.2 
 .5 1.4 
 .7 1.5 
 
 55 
 56 
 57 
 58 
 59 
 
 9.78853 
 9.78869 
 9.78886 
 9.78902 
 9.78918 
 
 16 
 17 
 16 
 16 
 16 
 
 9.89151 
 9.89177 
 9.89203 
 9.89229 
 9.89255 
 
 26 
 26 
 26 
 26 
 26 
 
 0.10849 
 0.10823 
 0.10797 
 0.10771 
 0.10745 
 
 9.89702 
 9.89693 
 9.89683 
 9.89673 
 9.89663 
 
 9 
 
 10 
 10 
 10 
 10 
 
 5 
 4 
 3 
 2 
 
 1 
 
 20 3 
 30 5 
 40 6 
 50 8 
 
 .3 3.0 
 .0 4.5 
 .7 6.0 
 .3 7.5 
 
 60 
 
 9.78934 
 
 
 9.89281 
 
 
 0.10719 
 
 9.89653 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 / 
 
 P 
 
 .P. 
 
 52 
 
1066 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 38 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 
 P 
 
 P 
 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.78934 
 9.78950 
 9.78967 
 9.78983 
 9.78999 
 
 16 
 17 
 16 
 16 
 Ifi 
 
 9.89281 
 9.89307 
 9.89333 
 9.89359 
 9.89385 
 
 26 
 26 
 26 
 26 
 2fi 
 
 0.10719 
 0.10693 
 0.10667 
 0.10641 
 0.10615 
 
 9.89653 
 9.89643 
 9.89633 
 9.89624 
 9.89614 
 
 10 
 10 
 9 
 10 
 10 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 *j 
 
 2 
 
 2 
 
 3 
 
 6 
 .6 
 
 Q 
 
 25 
 
 2.5 
 2 9 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.79015 
 9.79031 
 9.79047 
 9.79063 
 9.79079- 
 
 16 
 16 
 16 
 16 
 
 16 
 
 9.89411 
 9.89437 
 9.89463 
 9.89489 
 9.89515 
 
 26 
 26 
 26 
 26 
 26 
 
 0.10589 
 0.10563 
 0.10537 
 0.10511 
 0.10485 
 
 9.89604 
 9.89594 
 9.89584 
 9.89574 
 9.89564 
 
 10 
 10 
 10 
 10 
 10 
 
 55 
 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 3 
 3 
 4 
 
 8 
 1?, 
 
 5 
 9 
 8 
 7 
 
 
 3.3 
 3.8 
 4.2 
 8.3 
 12.6 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.79095 
 9.79111 
 9.79128 
 9.79144 
 9.79160 
 
 16 
 17 
 16 
 16 
 Ifi 
 
 9.89541 
 9.89567 
 9.89593 
 9.89619 
 9.89645 
 
 26 
 26 
 26 
 26 
 9fi 
 
 0.10459 
 0.10433 
 0.10407 
 0.10381 
 0.10355 
 
 9.89554 
 9.89544 
 9.89534 
 9.89524 
 9.89514 
 
 10 
 10 
 10 
 10 
 
 10 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 17 
 21 
 
 3 
 
 7 
 
 1 
 
 16.7 
 20.8 
 
 7 
 
 15 
 16 
 17 
 18 
 19 
 
 9.79176 
 9.79192 
 9.79208 
 9.79224 
 9.79240 
 
 16 
 16 
 16 
 16 
 Ifi 
 
 9.89671 
 9.89697 
 9.89723 
 9.89749 
 9.89775 
 
 26 
 26 
 26 
 26 
 9fi 
 
 0.10329 
 0.10303 
 0.10277 
 0.10251 
 0.10225 
 
 9.89504 
 9.89495 
 9.89485 
 9.89475 
 9.89465 
 
 9 
 
 10 
 10 
 10 
 10 
 
 45 
 44 
 43 
 42 
 41 
 
 [: 
 
 6 
 
 7 
 8 
 9 
 
 
 1 
 '3 
 -3 
 5 
 5 
 
 .7 
 .0 
 .3 
 .6 
 
 .8 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.79256 
 9.79272 
 9.79288 
 9.79304 
 9.79319 
 
 16 
 16 
 16 
 15 
 Ifi 
 
 9.89801 
 9.89827 
 9.89853 
 9.89879 
 9.89905 
 
 26 
 26 
 26 
 26 
 9fi 
 
 0.10199 
 0.10173 
 0.10147 
 0.10121 
 0.10095 
 
 9.89455 
 9.89445 
 9.89435 
 9.89425 
 9.89415 
 
 10 
 10 
 10 
 10 
 10 
 
 40 
 
 39 
 38 
 37 
 36 
 
 j ! 
 < 
 
 '. i 
 
 ^U 
 
 io 
 
 10 
 >U 
 
 '.i 
 
 11 
 
 U 
 
 .7 
 .5 
 .3 
 .2 
 
 25 
 26 
 
 27 
 28 
 29 
 
 9.79335 
 9.79351 
 9.79367 
 9.79383 
 9.79399 
 
 16 
 16 
 16 
 16 
 
 9.89931 
 9.89957 
 9.89983 
 9.90009 
 9.90035 
 
 26 
 26 
 26 
 26 
 
 0.10069 
 0.10043 
 0.10017 
 0.09991 
 0.09965 
 
 9.89405 
 9.89395 
 9.89385 
 9.89375 
 9.89364 
 
 10 
 10 
 10 
 
 11 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 1 
 
 1 
 1 
 
 2 
 
 3 
 
 6 
 9 
 
 1 
 
 15 
 1.5 
 1.8 
 2.0 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.79415 
 9.79431 
 9.79447 
 9.79463 
 9.79478 
 
 16 
 16 
 16 
 15 
 Ifi 
 
 9.90061 
 9.90086 
 9.90112 
 9.90138 
 9.90164 
 
 25 
 26 
 26 
 26 
 2fi 
 
 0.09939 
 0.09914 
 0.09888 
 0.09862 
 0.09836 
 
 9.89354 
 9.89344 
 9.89334 
 9.89324 
 9.89314 
 
 10 
 10 
 10 
 10 
 10 
 
 30 
 
 29 
 
 28 
 27 
 26 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 2 
 2 
 5 
 8 
 10 
 IS 
 
 4 
 7 
 3 
 
 .0 
 7 
 8 
 
 2.3 
 2.5 
 5.0 
 7.5 
 10.0 
 125 
 
 35 
 36 
 37 
 38 
 39 
 
 9.79494 
 9.79510 
 9.79526 
 9.79542 
 9.79558 
 
 16 
 16 
 16 
 16 
 TS 
 
 9.90190 
 9.90216 
 9.90242 
 9.90268 
 9.90294 
 
 26 
 26 
 26 
 26 
 2fi 
 
 0.09810 
 0.09784 
 0.09758 
 0.09732 
 0.09706 
 
 9.89304 
 9.89294 
 9.89284 
 9.89274 
 9.89264 
 
 10 
 10 
 10 
 10 
 10 
 
 25 
 24 
 23 
 22 
 21 
 
 
 6 
 
 7 
 
 1 
 
 1 
 ] 
 
 1' ' 
 
 1 
 3 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.79573 
 9.79589 
 9.79605 
 9.79621 
 9.79636 
 
 16 
 16 
 16 
 15 
 
 9.90320 
 9.90346 
 9.90371 
 9.90397 
 9.90423 
 
 26 
 25 . 
 26 
 26 
 
 0.09680 
 0.09654 
 0.09629 
 0.09603 
 0.09577 
 
 9.89254 
 9.89244 
 9.89233 
 9.89223 
 9.89213 
 
 10 
 
 11 
 
 10 
 10 
 10 
 
 20 
 
 19 
 18 
 17 
 16 
 
 
 8 
 9 
 10 
 20 
 -to 
 
 1 
 1 
 1 
 
 3 
 6 
 
 5 
 7 
 8 
 7 
 5 
 
 45 
 46 
 47 
 48 
 49 
 
 9.79652 
 9.79668 
 9.79684 
 9.79699 
 9.79715 
 
 16 
 16 
 15 
 16 
 Ifi 
 
 9.90449 
 9.90475 
 9.90501 
 9.90527 
 9.90553 
 
 26 
 26 
 26 
 26 
 
 nr. 
 
 0.09551 
 0.09525 
 0.09499 
 0.09473 
 0.09447 
 
 9.89203 
 9.89193 
 9.89183 
 9.89173 
 9.89162 
 
 10 
 10 
 10 
 
 11 
 
 10 
 
 15 
 14 
 13 
 12 
 11 
 
 
 40 
 50 
 
 | 
 
 7 
 9 
 
 n 
 
 3 
 2 
 
 9 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.79731 
 9.79746 
 9.79762 
 9.79778 
 9.79793 
 
 15 
 16 
 16 
 15 
 
 9.90578 
 9.90604 
 9.90630 
 9.90656 
 9.90682 
 
 26 
 26 
 26 
 26 
 
 0.09422 
 0.09396 
 0.09370 
 0.09344 
 0.09318 
 
 9.89152 
 9.89142 
 9.89132 
 9.89122 
 9.89112 
 
 10 
 10 
 10 
 10 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 6 
 
 7 
 8 
 9 
 10 
 
 1 
 1 
 
 1 
 1 
 
 1 
 
 .0 
 .2 
 
 .3 
 .5 
 
 .7 
 
 0.9 
 1.1 
 1.2 
 1.4 
 1.5 
 
 55 
 56 
 57 
 58 
 59 
 
 9.79809 
 9.79825 
 9.79840 
 9.79856 
 9.79872 
 
 16 
 15 
 16 
 16 
 
 IK 
 
 9.90708 
 9.90734 
 9.90759 
 9.90785 
 9.90811 
 
 26 
 25 
 26 
 26 
 Qfi 
 
 0.09292 
 0.09266 
 0.09241 
 0.09215 
 0.09189 
 
 9.89101 
 9.89091 
 9.89081 
 9.89071 
 9.89060 
 
 10 
 10 
 10 
 
 11 
 
 10 
 
 5 
 4 
 3 
 2 
 1 
 
 20 
 30 
 40 
 50 
 
 3 
 5 
 6 
 
 8 
 
 .3 
 .0 
 .7 
 .3 
 
 3.0 
 4.5 
 6.0 
 
 7.5 
 
 60 
 
 9.79887 
 
 
 9.90837 
 
 
 0.09163 
 
 9.89050 
 
 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 r 
 
 
 P 
 
 P 
 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 39 
 
 1067 
 
 ' 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg.l L. Cos. 
 
 d. 
 
 
 P 
 
 .P. 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.79887 
 9.79903 
 9.79918 
 9.79934 
 9.79950 
 
 16 
 15 
 16 
 16 
 
 1C 
 
 9.90837 
 9.90863 
 9.90889 
 9.90914 
 9.90940 
 
 26 
 26 
 25 
 26 
 
 0.09163 9.89050 
 0.09137 9.89040 
 0.09111 9.89030 
 0.09086 9.89020 
 0.09060 9.89009 
 
 10 
 10 
 10 
 11 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 26 
 
 2.6 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.79965 
 9.79981 
 9.79996 
 9.80012 
 9.80027 
 
 16 
 15 
 16 
 15 
 16 
 
 9.90966 
 9.90992 
 9.91018 
 9.91043 
 9.91069 
 
 26 
 26 
 25 
 26 
 
 0.09034 9.88999 
 0.09008 9.88989 
 0.08982 9.88978 
 0.08957 9.88968 
 0.08931 9.88958 
 
 10 
 11 
 10 
 10 
 
 55 
 54 
 53 
 52 
 51 
 
 "8 
 9 
 10 
 20 
 30 
 
 3.5 
 3.9 
 4.3 
 8.7 
 13.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.80043 
 9.80058 
 9.80074 
 9.80089 
 9.80105 
 
 15 
 16 
 15 
 16 
 
 1C 
 
 9.91095 
 9.91121 
 9.91147 
 9.91172 
 9.91198 
 
 26 
 26 
 25 
 26 
 
 0.08905 9.88948 
 0.08879 9.88937 
 0.08853 9.88927 
 0.08828 9.88917 
 0.08802 9.88906 
 
 11 
 10 
 10 
 
 11 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 17.3 
 21.7 
 
 25 
 
 15 
 16 
 17 
 18 
 19 
 
 9.80120 
 9.80136 
 9.80151 
 9,80166 
 9.80182 
 
 16 
 15 
 15 
 16 
 
 lit 
 
 9.91224 
 9.91250 
 9.91276 
 9.91301 
 9.91327 
 
 26 
 26 
 25 
 26 
 
 0.08776 9.88896 
 0.08750 9.88886 
 0.08724 9.88875 
 0.08699 9.88865 
 0.08673 9.88855 
 
 10 
 
 11 
 
 10 
 10 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 
 7 
 8 
 9 
 10 
 
 2.5 
 2.9 
 3.3 
 3.8 
 4.2 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.80197 
 9.80213 
 9.80228 
 9.80244 
 9.80259 
 
 16 
 15 
 16 
 15 
 15 
 
 9.91353 
 9.91379 
 9.91404 
 9.91430 
 9.91456 
 
 26 
 25 
 26 
 26 
 2fi 
 
 0.08647 9.88844 
 0.08621 9.88834 
 0.08596 9.88824 
 0.08570 9.88813 
 0.08544 9.88803 
 
 10 
 10 
 
 11 
 
 10 
 10 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 8.3 
 12.5 
 16.7 
 20.8 
 
 25 
 26 
 27 
 28 
 29 
 
 9.80274 
 9.80290 
 9.8C305 
 9.80320 
 9.80336 
 
 16 
 15 
 15 
 16 
 
 9.91482 
 9.91507 
 9.91533 
 9.91559 
 9.91585 
 
 25 
 26 
 26 
 26 
 
 0.08518 9.88793 
 0.08493 9.88782 
 0.08467 9.88772 
 0.08441 9.88761 
 0.08415 9.88751 
 
 11 
 
 10 
 
 11 
 
 10 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 16 
 1.6 
 1.9 
 2.1 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.80351 
 9.80366 
 9.80382 
 9.80397 
 9.80412 
 
 15 
 16 
 15 
 15 
 16 
 
 9.91610 
 9.91636 
 9.91662 
 9.916S8 
 9.91713 
 
 26 
 26 
 26 
 25 
 9fi 
 
 0.08390 9.88741 
 0.08364 9.88730 
 0.08338 9.88720 
 0.08312 9.88709 
 0.08287 9.88699 
 
 11 
 
 10 
 
 11 
 
 10 
 11 
 
 30 
 
 29 
 28 
 27 
 26 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 2.4 
 
 2.7 
 5.3 
 8.0 
 10.7 
 133 
 
 35 
 36 
 37 
 38 
 39 
 
 9.80428 
 9.80443 
 9.80458 
 9.80473 
 9.80489 
 
 15 
 15 
 15 
 16 
 
 1C 
 
 9.91739 
 9.91765 
 9.91791 
 9.91816 
 9.91842 
 
 26 
 26 
 25 
 26 
 
 0.08261 9.88688 
 0.08235 9.88678 
 0.08209 9.88668 
 0.08184 9.88657 
 0.08158 9.88647 
 
 10 
 10 
 
 11 
 
 10 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 15 
 
 1.5 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.80504 
 9.80519 
 9.80534 
 9.80550 
 9.80565 
 
 15 
 15 
 16 
 15 
 
 9.91868 
 9.91893 
 9.91919 
 9.91945 
 9.91971 
 
 25 
 26 
 26 
 26 
 
 0.08132 9.88636 
 0.08107 9.88626 
 0.08081 9.88615 
 0.08055 9.88605 
 0.08029 9.88594 
 
 10 
 
 11 
 
 10 
 
 11 
 
 20 
 
 19 
 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 2.0 
 2.3 
 2.5 
 5.0 
 
 7.5 
 
 45 
 46 
 47 
 48 
 49 
 
 9.80580 
 9.80595* 
 9.80610 
 9.80625 
 9.80641 
 
 15 
 15 
 15 
 16 
 15 
 
 9.91996 
 9.92022 
 9.92048 
 9.92073 
 9.92099 
 
 26 
 26 
 25 
 26 
 9fi 
 
 0.08004 9.88584 
 0.07978 9.88573 
 0.07952 9.88563 
 0.07927 9.88552 
 0.07901 9.88542 
 
 11 
 
 10 
 
 11 
 
 10 
 11 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 | 
 
 10.0 
 12.5 
 
 1 10 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.80656 
 9.80671 
 9.80686 
 9.80701 
 9.80716 
 
 15 
 15 
 15 
 15 
 15 
 
 9.92125 
 9.92150 
 9.92176 
 9.92202 
 9.92227 
 
 25 
 26 
 26 
 25 
 2fi 
 
 0.07875 9.88531 
 0.07850 9.88521 
 0.07824 9.88510 
 0.07798 9.88499 
 0.07773 9.88489 
 
 10 
 
 11 
 11 
 
 10 
 11 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 6 1 
 
 7 1 
 8 1 
 9 1 
 10 1 
 
 1 1.0 
 3 1.2 
 5 1.3 
 7 1.5 
 8 1.7 
 
 55 
 56 
 57 
 58 
 59 
 
 9.80731 
 9.80746 
 9.80762 
 9.80777 
 9.80792 
 
 15 
 16 
 15 
 15 
 
 -1C 
 
 9.92253 
 9.92279 
 9.92304 
 9.92330 
 9.92356 
 
 26 
 25 
 26 
 26 
 
 OK 
 
 0.07747 9.88478 
 0.07721 9.88468 
 0.07696 9.88457 
 0.07670 9.88447 
 0.07644 9.88436 
 
 10 
 
 11 
 
 10 
 
 11 
 
 11 
 
 5 
 4 
 3 
 2 
 1 
 
 20 3 
 30 5 
 40 7 
 50 9 
 
 7 3.3 
 5 5.0 
 3 6.7 
 2 8.3 
 
 60 
 
 9.80807 
 
 
 9.92381 
 
 
 0.07619 9.88425 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 rt.c. 
 
 L.Tang. | L. Sin. 
 
 d. 
 
 / 
 
 P 
 
 P. 
 
 50 
 
1068 
 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 40 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 P 
 
 .P. 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.80807 
 9.80822 
 9.80837 
 9.80852 
 9.80867 
 
 15 
 15 
 15 
 15 
 -ic 
 
 9.92381 
 9.92407 
 9.92433 
 9.92458 
 9.92484 
 
 26 
 26 
 25 
 26 
 26 
 
 0.07619 
 0.07593 
 0.07567 
 0.07542 
 0.07516 
 
 9.88425 
 9.88415 
 9.88404 
 9.88394 
 9.88383 
 
 10 
 11 
 10 
 
 11 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 26 
 
 2.6 
 3 
 
 5 
 
 6 
 7 
 8 
 9 
 
 9.80882 
 9.80897 
 9.80912 
 9.80927 
 9.80942 
 
 15 
 15 
 15 
 15 
 
 9.92510 
 9.92535 
 9.92561 
 9.92587 
 9.92612 
 
 25 
 26 
 26 
 25 
 9fi 
 
 0.07490 
 0.07465 
 0.07439 
 0.07413 
 0.07388 
 
 9.88372 
 9.88362 
 9.88351 
 9.88340 
 9.88330 
 
 10 
 
 11 
 11 
 
 10 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 3.5 
 3.9 
 4.3 
 
 8.7 
 13.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.80957 
 9.80972 
 9.80987 
 9.81002 
 9.81017 
 
 15 
 15 
 15 
 15 
 
 9.92638 
 9.92663 
 9.92689 
 9.92715 
 9.92740 
 
 25 
 26 
 26 
 25 
 2fi 
 
 0.07362 
 0.07337 
 0.07311 
 0.07285 
 0.07260 
 
 9.88319 
 9.88308 
 9.88298 
 9.88287 
 9.88276 
 
 11 
 
 10 
 
 11 
 11 
 in 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 17.3 
 
 21.7 
 
 25 
 
 15 
 16 
 17 
 18 
 19 
 
 9.81032 
 9.81047 
 9.81061 
 9.81076 
 9.81091 
 
 15 
 14 
 15 
 15 
 IS 
 
 9.92766 
 9.92792 
 9.92817 
 9.92843 
 9.92868 
 
 26 
 25 
 26 
 25 
 26 
 
 0.07234 
 0.07208 
 0.07183 
 0.07157 
 0.07132 
 
 9.88266 
 9.88255 
 9.88244 
 9.88234 
 9.88223 
 
 11 
 11 
 
 10 
 
 11 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 7 
 8 
 9 
 10 
 
 2.5 
 2.9 
 3.3 
 3.8 
 4.2 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.81106 
 9.81121 
 9.81136 
 9.81151 
 9.81166 
 
 15 
 15 
 15 
 15 
 14 
 
 9.92894 
 9.92920 
 9.92945 
 9.92971 
 9.92996 
 
 26 
 25 
 26 
 25 
 26 
 
 0.07106 
 0.07080 
 0.07055 
 0.07029 
 0.07004 
 
 9.88212 
 9.88201 
 9.88191 
 9.88180 
 9.88169 
 
 11 
 
 10 
 
 11 
 11 
 
 n 
 
 40 
 
 39 
 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 8.3 
 12.5 
 16.7 
 20.8 
 
 25 
 26 
 27 
 
 28 
 29 
 
 9.81180 
 9.81195 
 9.81210 
 9.81225 
 9.81240 
 
 15 
 15 
 15 
 15 
 
 9.93022 
 9.93048 
 9.93073 
 9.93099 
 9.93124 
 
 26 
 25 
 26 
 25 
 
 0.06978 
 0.06952 
 0.06927 
 0.06901 
 0.06876 
 
 9.88158 
 9.88148 
 9.88137 
 9.88126 
 9.88115 
 
 10 
 
 11 
 11 
 11 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 15 
 1.5 
 1.8 
 2.0 
 
 SO 
 
 81 
 32 
 33 
 34 
 
 9.81254 
 9.81269 
 9.81284 
 9.81299 
 9.81314 
 
 15 
 15 
 15 
 15 
 
 9.93150 
 9.93175 
 9.93201 
 9.93227 
 9.93252 
 
 25 
 26 
 26 
 25 
 
 9fi 
 
 0.06850 
 0.06825 
 0.06799 
 0.06773 
 0.06748 
 
 9.88105 
 9.88094 
 9.88083 
 9.88072 
 9.88061 
 
 11 
 11 
 11 
 11 
 
 1ft 
 
 30 
 
 29 
 28 
 27 
 26 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 2.3 
 2.5 
 
 5.0 
 7.5 
 10.0 
 12 5 
 
 35 
 36 
 37 
 38 
 39 
 
 9.81328 
 9.81343 
 9.81358 
 9.81372 
 9.81387 
 
 15 
 15 
 14 
 
 15 
 
 1C 
 
 9.93278 
 9.93303 
 9.93329 
 9.93354 
 9.93380 
 
 25 
 26 
 25 
 26 
 
 9fi 
 
 0.06722 
 0.06697 
 0.06671 
 0.06646 
 0.06620 
 
 9.88051 
 9.88040 
 9.88029 
 9.88018 
 9.88007 
 
 11 
 11 
 11 
 11 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 14 
 
 1.4 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.81402 
 9.81417 
 9.81431 
 9.81446 
 9.81461 
 
 15 
 14 
 15 
 15 
 14 
 
 9.93406 
 9.93431 
 9.93457 
 9.93482 
 9.93508 
 
 25 
 26 
 25 
 26 
 25 
 
 0.06594 
 0.06569 
 0.06543 
 0.06518 
 0.06492 
 
 9.87996 
 9.87985 
 9.87975 
 9.87964 
 9.87953 
 
 11 
 
 10 
 
 11 
 11 
 
 J]_ 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 1.9 
 2.1 
 2.3 
 
 4.7 
 7.0 
 
 45 
 46 
 47 
 48 
 49 
 
 9.81475 
 9.81490 
 9.81505 
 9.81519 
 9.81534 
 
 15 
 15 
 14 
 15 
 
 1C 
 
 9.93533 
 9.93559 
 9.93584 
 9.93610 
 9.93636 
 
 26 
 25 
 26 
 26 
 
 0.06467 
 0.06441 
 0.06416 
 0.06390 
 0.06364 
 
 9.87942 
 9.87931 
 9.87920 
 9.87909 
 9.87898 
 
 11 
 11 
 11 
 11 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 9.3 
 11.7 
 
 1 10 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.81549 
 9.81563 
 9.81578 
 9.81592 
 9.81607 
 
 14 
 15 
 14 
 15 
 15 
 
 9.93661 
 9.93687 
 9.93712 
 9.93738 
 9.93763 
 
 26 
 25 
 26 
 25 
 Ofi 
 
 0.06339 
 0.06313 
 0.06288 
 0.06262 
 0.06237 
 
 9.87887 
 9.87877 
 9.87866 
 9.87855 
 9.87844 
 
 10 
 
 11 
 11 
 11 
 
 10 
 
 9 
 8 
 7 
 6 
 
 6 1 
 7 1 
 8 1 
 9 1 
 10 1 
 
 .1 1.0 
 .3 1.2 
 .5 1.3 
 .7 1.5 
 
 .8 1.7 
 
 55 
 56 
 57 
 58 
 59 
 
 9.81622 
 9.81636 
 9.81651 
 9.81665 
 9.81680 
 
 14 
 15 
 14 
 15 
 
 9.93789 
 9.93814 
 9.93840 
 9.93865 
 9.93891 
 
 25 
 26 
 25 
 26 
 
 0.06211 
 0.06186 
 0.06160 
 0.06135 
 0.06109 
 
 9.87833 
 9.87822 
 9.87811 
 9.87800 
 9.87789 
 
 11 
 11 
 11 
 11 
 
 5 
 4 
 3 
 2 
 1 
 
 20 3 
 30 5 
 40 7 
 50 9 
 
 .7 3.3 
 .5 5.0 
 3 6.7 
 .2 8.3 
 
 60 
 
 9.81694 
 
 
 9.93916 
 
 
 0.06084 
 
 9.87778 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.G. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 i 
 
 P 
 
 P. 
 
 49 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 41 
 
 1069 
 
 '_ 
 
 L. Sin. 
 
 d. 
 
 L.Tang 
 
 d.c. 
 
 L. Cotg 
 
 L. Cos 
 
 d. 
 
 
 P 
 
 .P. 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.81694 
 9.81709 
 9.81723 
 9.81738 
 9.81752 
 
 15 
 14 
 15 
 14 
 15 
 
 9.93916 
 9.93942 
 9.93967 
 9.93993 
 9.94018 
 
 26 
 25 
 26 
 25 
 9fi 
 
 0.06084 
 0.06058 
 0.06033 
 0.06007 
 0.05982 
 
 9.87778 
 9.87767 
 9.87756 
 9.87745 
 9.87734 
 
 11 
 11 
 11 
 11 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 26 
 
 2.6 
 
 5 
 
 6 
 
 7 
 8 
 9 
 
 9.81767 
 9.81781 
 9.81796 
 9.81810 
 9.81825 
 
 14 
 15 
 14 
 15 
 14 
 
 9.94044 
 9.94069 
 9.94095 
 9.94120 
 9.94146 
 
 25 
 26 
 25 
 26 
 25 
 
 0.05956 
 0.05931 
 0.05905 
 0.05880 
 0.05854 
 
 9.87723 
 9.87712 
 9.87701 
 9.87690 
 9.87679 
 
 11 
 11 
 11 
 11 
 11 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 3.5 
 3.9 
 4.3 
 8.7 
 13.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.81839 
 9.81854 
 9.81868 
 9.81882 
 9.81897 
 
 15 
 
 14 
 14 
 15 
 14 
 
 9.94171 
 9.94197 
 9.94222 
 9.94248 
 9.94273 
 
 26 
 25 
 26 
 25 
 
 26 
 
 0.05829 
 0.05803 
 0.05778 
 0.05752 
 0.05727 
 
 9.87668 
 9.87657 
 9.87646 
 9.87635 
 9.87624 
 
 11 
 11 
 11 
 11 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 17.3 
 21.7 
 
 25 
 
 15 
 
 16 
 17 
 18 
 19 
 
 9.81911 
 9.81926 
 9.81940 
 9.81955 
 9.81969 
 
 15 
 14 
 15 
 14 
 14 
 
 9.94299 
 9.94324 
 9.94350 
 9.94375 
 9.94401 
 
 25 
 26 
 25 
 26 
 25 
 
 0.05701 
 0.05676 
 0.05650 
 0.05625 
 0.65599 
 
 9.87613 
 9.87601 
 9.87590 
 9.87579 
 9.87568 
 
 12 
 11 
 11 
 11 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 
 7 
 8 
 9 
 
 10 
 
 2.5 
 2.9 
 3.3 
 3.8 
 4.2 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.81983 
 9.81998 
 9.82012 
 9.82026 
 9.82041 
 
 15 
 14 
 14 
 15 
 
 9.94426 
 9.94452 
 9.94477 
 9.94503 
 9.94528 
 
 26 
 25 
 26 
 25 
 
 0.05574 
 0.05548 
 0.05523 
 0.05497 
 0.05472 
 
 9.87557 
 9.87546 
 9.87535 
 9.87524 
 9.87513 
 
 11 
 11 
 11 
 11 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 8.3 
 12.5 
 16.7 
 20.8 
 
 25 
 26 
 
 27 
 28 
 29 
 
 9.82055 
 9.82069 
 9.82084 
 9.82098 
 9.82112 
 
 14 
 15 
 14 
 14 
 14 
 
 9.94554 
 9.94579 
 9.94604 
 9.94630 
 9.94655 
 
 25 
 25 
 26 
 25 
 9fi 
 
 0.05446 
 0.05421 
 0.05396 
 0.05370 
 0.05345 
 
 9.87501 
 9.87490 
 9.87479 
 9.87468 
 9.87457 
 
 11 
 
 11 
 11 
 11 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 15 
 1.5 
 18 
 2.0 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.82126 
 9.82141 
 9.82155 
 9.82169 
 9.82184 
 
 15 
 14 
 14 
 15 
 14 
 
 9.94681 
 9.94706 
 9.94732 
 5.94757 
 9.94783 
 
 25 
 26 
 25 
 26 
 25 
 
 0.05319 
 0.05294 
 0.05268 
 0.05243 
 0.05217 
 
 9.87446 
 9.87434 
 9.87423 
 9.87412 
 9.87401 
 
 12 
 11 
 11 
 11 
 
 30 
 
 29 
 
 28 
 27 
 26 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 2.3 
 
 2.5 
 5.0 
 7.5 
 10.0 
 12 5 
 
 35 
 36 
 37 
 38 
 39 
 
 9.82198 
 9.82212 
 9.82226 
 9.82240 
 9.82255 
 
 14 
 14 
 14 
 15 
 14. 
 
 9.94808 
 9.94834 
 9.94859 
 9.94884 
 9.94910 
 
 26 
 25 
 25 
 26 
 
 oc 
 
 0.05192 
 0.05166 
 0.05141 
 0.05116 
 0.05090 
 
 9.87390 
 9.87378 
 9.87367 
 9.87356 
 9.87345 
 
 12 
 11 
 11 
 11 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 14 
 
 1.4 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.82269 
 9.82283 
 9.82297 
 9.82311 
 9.82326 
 
 14 
 14 
 14 
 15 
 14 
 
 9.94935 
 9.94961 
 9.94986 
 9.95012 
 9.95037 
 
 26 
 25 
 26 
 25 
 25 
 
 0.05065 
 0.05039 
 0.05014 
 0.04988 
 0.04963 
 
 9.87334 
 9.87322 
 9.87311 
 9.87300 
 9.87288 
 
 12 
 11 
 11 
 12 
 11 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 1.9 
 2.1 
 2.3 
 
 4.7 
 7.0 
 
 45 
 46 
 47 
 48 
 49 
 
 9.82340 
 9.82354 
 9.82368 
 9.82382 
 9.82396 
 
 14 
 14 
 14 
 14 
 14 
 
 9.95062 
 9.95088 
 9.95113 
 9.95139 
 9.95164 
 
 26 
 25 
 26 
 25 
 26 
 
 0.04938 
 0.04912 
 0.04887 
 0.04861 
 0.04836 
 
 9.87277 
 9.87266 
 9.87255 
 9.87243 
 9.87232 
 
 11 
 11 
 12 
 11 
 11 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 | 
 
 9.3 
 11.7 
 
 2 II 
 
 SO 
 
 51 
 52 
 53 
 54 
 
 9.82410 
 9.82424 
 9.82439 
 9.82453 
 9.82467 
 
 14 
 
 15 
 14 
 14 
 14 
 
 9.95190 
 9.95215 
 9.95240 
 9.95266 
 9.95291 
 
 25 
 25 
 26 
 25 
 26 
 
 0.04810 
 0.04785 
 0.04760 
 0.04734 
 0.04709 
 
 9.87221 
 9.87209 
 9.87198 
 9.87187 
 9.87175 
 
 12 
 11 
 11 
 12 
 11 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 6 1 
 7 1 
 8 1 
 9 1 
 10 2 
 
 .2 1.1 
 .4 1.3 
 .6 1.5 
 .8 1.7 
 
 1.8 
 
 55 
 56 
 57 
 58 
 59 
 
 9.82481 
 9.82495 
 9.82509 
 9.82523 
 9.82537 
 
 14 
 14 
 14 
 14 
 14 
 
 9.95317 
 9.95342 
 9.95368 
 9.95393 
 9.95418 
 
 25 
 26 
 25 
 25 
 26 
 
 0.04683 
 0.04658 
 0.04632 
 0.04607 
 0.04582 
 
 9.87164 
 9.87153 
 9.87141 
 9.87130 
 9.87119 
 
 11 
 
 12 
 11 
 11 
 12 
 
 5 
 4 
 3 
 2 
 1 
 
 20 4 
 30 6 
 40 8 
 50 10 
 
 .0 3.7 
 .0 5.5 
 .0 7.3 
 .0 9.2 
 
 60 
 
 9.82551 
 
 
 9.95444 
 
 
 0.04556 
 
 9.87107 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L.CotgJ 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 ' 
 
 P. 
 
 P. 
 
 48 
 
1070 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 42 
 
 t 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 P 
 
 .P. 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 9.82551 
 9.82565 
 9.82579 
 9.82593 
 9.82607 
 
 14 
 14 
 14 
 14 
 
 9.95444 
 9.95469 
 9.95495 
 9.95520 
 9.95545 
 
 25 
 26 
 25 
 25 
 
 9fi 
 
 0.04556 
 0.04531 
 0.04505 
 0.04480 
 0.04455 
 
 9.87107 
 9.87096 
 9.87085 
 9.87073 
 9.87062 
 
 11 
 
 11 
 12 
 11 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 26 
 
 2.6 
 3 
 
 5 
 
 6 
 7 
 8 
 9 
 
 9.82621 
 9.82635 
 9.82649 
 9.82663 
 9.82677 
 
 14 
 14 
 14 
 14 
 14 
 
 9.95571 
 9.95596 
 9.95622 
 9.95647 
 9.95672 
 
 25 
 26 
 25 
 25 
 26 
 
 0.04429 
 0.04404 
 0.04378 
 0.04353 
 0.04328 
 
 9.87050 
 9.87039 
 9.87028 
 9.87016 
 9.87005 
 
 11 
 11 
 12 
 11 
 
 19 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 3.5 
 3.9 
 4.3 
 
 8.7 
 13.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.82691 
 9.82705 
 9.82719 
 9.82733 
 9.82747 
 
 14 
 14 
 
 14 
 14 
 14 
 
 9.95698 
 9.95723 
 9.95748 
 9.95774 
 9.95799 
 
 25 
 25 
 26 
 25 
 
 26 
 
 0.04302 
 0.04277 
 0.04252 
 0.04226 
 0.04201 
 
 9.86993 
 9.86982 
 9.86970 
 9.86959 
 9.86947 
 
 11 
 
 12 
 11 
 12 
 jl 
 
 50 
 
 49 
 48 
 47 
 46 
 
 40 
 
 50 
 
 17.3 
 21.7 
 
 25 
 
 15 
 16 
 17 
 18 
 19 
 
 9.82761 
 9.82775 
 9.82788 
 9.82802 
 9.82816 
 
 14 
 13 
 14 
 J4 
 
 14 
 
 9.95825 
 9.95850 
 9.95875 
 9.95901 
 9.95926 
 
 25 
 25 
 26 
 25 
 2fi 
 
 0.04175 
 0.04150 
 0.04125 
 0.04099 
 0.04074 
 
 9.86936 
 9.86924 
 9.86913 
 9.86902 
 9.86890 
 
 12 
 11 
 11 
 12 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 7 
 8 
 9 
 10 
 
 2.5 
 2.9 
 3.3 
 3.8 
 4.2 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.82830 
 9.82844 
 9.82858 
 9.82872 
 9.82885 
 
 14 
 14 
 14 
 13 
 14 
 
 9.95952 
 9.95977 
 9.96002 
 9.96028 
 9.96053 
 
 25 
 25 
 26 
 25 
 25 
 
 0.04048 
 0.04023 
 0.03998 
 0.03972 
 0.03947 
 
 9.86879 
 9.86867 
 9.86855 
 9.86844 
 9.86832 
 
 12 
 12 
 11 
 12 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 
 40 
 50 
 
 8.3 
 12.5 
 16.7 
 20.8 
 
 25 
 26 
 
 27 
 28 
 29 
 
 9.82899 
 9.82913 
 9.82927 
 9.82941 
 9.82955 
 
 14 
 14 
 14 
 14 
 13 
 
 9.96078 
 9.96104 
 9.96129 
 9.96155 
 9.96180 
 
 26 
 25 
 26 
 25 
 
 OX 
 
 0.03922 
 0.03896 
 0.03871 
 0.03845 
 0.03820 
 
 9.86821 
 9.86809 
 9.86798 
 9.86786 
 9.86775 
 
 12 
 11 
 12 
 11 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 14 
 
 1.4 
 1.6 
 1.9 
 
 30 
 
 31 
 32 
 33 
 34 
 
 9.82968 
 9.82982 
 9.82996 
 9.83010 
 9.83023 
 
 14 
 14 
 14 
 13 
 14 
 
 9.96205 
 9.96231 
 9.96256 
 9.96281 
 9.96307 
 
 26 
 25 
 25 
 26 
 25 
 
 0.03795 
 0.03769 
 0.03744 
 0.03719 
 0.03693 
 
 9.86763 
 9.86752 
 9.86740 
 9.86728 
 9.86717 
 
 11 
 12 
 12 
 11 
 
 30 
 
 29 
 28 
 27 
 26 
 
 9 
 10 
 20 
 30 
 40 
 50 
 
 2.1 
 2.3 
 4.7 
 7.0 
 9.3 
 11 7 
 
 35 
 36 
 37 
 38 
 39 
 
 9.83037 
 9.83051 
 9.83065 
 9.83078 
 9.83092 
 
 14 
 14 
 13 
 14 
 14 
 
 9.96332 
 9.96357 
 9.96383 
 9.96408 
 9.96433 
 
 25 
 
 26 
 25 
 25 
 26 
 
 0.03668 
 0.03643 
 0.03617 
 0.03592 
 0.03567 
 
 9.86705 
 9.86694 
 9.86682 
 9.86670 
 9.86659 
 
 11 
 
 12 
 12 
 11 
 19 
 
 25 
 
 24 
 23 
 22 
 21 
 
 6 
 
 7 
 
 13 
 
 1.3 
 1 ^ 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.83106 
 9.83120 
 9.83133 
 9.83147 
 9.83161 
 
 14 
 
 13 
 14 
 14 
 13 
 
 9.96459 
 9.96484 
 9.96510 
 9.96535 
 9.96560 
 
 25 
 
 26 
 25 
 25 
 26 
 
 0.03541 
 0.03516 
 0.03490 
 0.03465 
 0.03440 
 
 9.86647 
 9.86635 
 9.86624 
 9.86612 
 9.86600 
 
 12 
 11 
 12 
 12 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 1.7 
 2.0 
 2.2 
 4.3 
 6.5 
 
 45 
 46 
 47 
 48 
 49 
 
 9.83174 
 9.83188 
 9.83202 
 9.83215 
 9.83229 
 
 14 
 14 
 13 
 14 
 13 
 
 9.96586 
 9.96611 
 9.96636 
 9.96662 
 9.96687 
 
 25 
 25 
 26 
 25 
 25 
 
 0.03414 
 0.03389 
 0.03364 
 0.03338 
 0.03313 
 
 9.86589 
 9.86577 
 9.86565 
 9.86554 
 9.86542 
 
 12 
 12 
 11 
 12 
 19 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 60 
 
 8.7 
 10.8 
 
 2 II 
 
 50 
 
 51 
 52 
 53 
 
 54 
 
 9.83242 
 9.83256 
 9.83270 
 9.83283 
 9.83297 
 
 14 
 14 
 13 
 14 
 13 
 
 9.96712 
 9.96738 
 9.96763 
 9.96788 
 9.96814 
 
 26 
 25 
 25 
 26 
 25 
 
 0.03288 
 0.03262 
 0.03237 
 0.03212 
 0.03186 
 
 9.86530 
 9.86518 
 9.86507 
 9.86495 
 9.86483 
 
 12 
 11 
 12 
 12 
 
 10 
 9 
 8 
 
 7 
 6 
 
 6 1 
 7 ] 
 8 ] 
 9 ] 
 
 10 ; 
 
 L.2 1.1 
 .4 1.3 
 ..6 1.5 
 ..8 1.7 
 5.0 1.8 
 
 55 
 
 56 
 57 
 58 
 59 
 
 9.83310 
 9.83324 
 9.83338 
 9.83351 
 9.83365 
 
 14 
 14 
 13 
 14 
 13 
 
 9.96839 
 9.96864 
 9.96890 
 9.96915 
 9.96940 
 
 26 
 25 
 25 
 26 
 
 0.03161 
 0.03136 
 0.03110 
 0.03085 
 0.03060 
 
 9.86472 
 9.86460 
 9.86448 
 9.86436 
 9.86425 
 
 12 
 12 
 12 
 11 
 12 
 
 5 
 4 
 3 
 2 
 1 
 
 20 4 
 30 ( 
 40 * 
 50 1( 
 
 1.0 3.7 
 >.0 5.5 
 5.0 7.3 
 >.0 9.2 
 
 60 
 
 9.83378 
 
 
 9.96966 
 
 
 0.03034 
 
 9.86413 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 / 
 
 P 
 
 P. 
 
 47 
 
LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 43 
 
 1071 
 
 / 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 P 
 
 P. 
 
 
 
 1 
 
 2 
 3 
 
 4 
 
 9.83378 
 9.83392 
 9.83405 
 9.83419 
 9.83432 
 
 14 
 13 
 14 
 13 
 14 
 
 9.96966 
 9.96991 
 9.97016 
 9.97042 
 9.97067 
 
 25 
 25 
 26 
 25 
 25 
 
 0.03034 
 0.03009 
 0.02984 
 0.02958 
 0.02933 
 
 9.86413 
 9.86401 
 9.86389 
 9.86377 
 9.86366 
 
 12 
 12 
 12 
 11 
 
 60 
 
 59 
 58 
 57 
 56 
 
 6 
 
 7 
 
 26 
 
 2.6 
 3 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.83446 
 9.83459 
 9.83473 
 9.83486 
 9.83500 
 
 13 
 14 
 13 
 14 
 
 -iq 
 
 9.97092 
 9.97118 
 9.97143 
 9.97168 
 9.97193 
 
 26 
 25 
 
 25 
 25 
 
 0.02908 
 0.02882 
 0.02857 
 0.02832 
 0.02807 
 
 9.86354 
 9.86342 
 9.86330 
 9.86318 
 9.86306 
 
 12 
 12 
 12 
 12 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 3.5 
 3.9 
 
 4.3 
 8.7 
 18.0 
 
 10 
 11 
 
 12 
 13 
 14 
 
 9.83513 
 9.83527 
 9.83540 
 9.83554 
 9.83567 
 
 14 
 13 
 14 
 13 
 14 
 
 9.97219 
 9.97244 
 9.97269 
 9.97295 
 9.97320 
 
 25 
 
 25 
 26 
 25 
 25 
 
 0.02781 
 0.02756 
 0.02731 
 0.02705 
 0.02680 
 
 9.86295 
 9.86283 
 9.86271 
 9.86259 
 9.86247 
 
 12 
 12 
 12 
 12 
 12 
 
 50 
 
 49 
 
 48 
 47 
 46 
 
 40 
 50 
 
 17.3 
 21.7 
 
 25 
 
 15 
 16 
 17 
 18 
 19 
 
 9.83581 
 9.83594 
 9.83608 
 9.83621 
 9.83634 
 
 13 
 14 
 13 
 13 
 
 9.97345 
 9.97371 
 9.97396 
 9.97421 
 9.97447 
 
 26 
 25 
 25 
 26 
 
 0.02655 
 0.02629 
 0.02604 
 0.02579 
 0.02553 
 
 9.86235 
 9.86223 
 9.86211 
 9.86200 
 9.86188 
 
 12 
 12 
 11 
 12 
 12 
 
 45 
 44 
 43 
 
 42 
 41 
 
 6 
 
 7 
 8 
 9 
 10 
 
 2.5 
 2.9 
 3.3 
 3.8 
 4.2 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.83648 
 9.83661 
 9.83674 
 9.83688 
 9.83701 
 
 13 
 13 
 14 
 13 
 
 9.97472 
 9.97497 
 9.97523 
 9.97548 
 9.97573 
 
 25 
 26 
 25 
 25 
 
 0.02528 
 0.02503 
 0.02477 
 0.02452 
 0.02427 
 
 9.86176 
 9.86164 
 9.86152 
 9.86140 
 9.86128 
 
 12 
 12 
 12 
 12 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 8.3 
 12.5 
 16.7 
 20.8 
 
 25 
 26 
 27 
 28 
 29 
 
 9.83715 
 9.83728 
 9.83741 
 9.83755 
 9.83768 
 
 13 
 13 
 14 
 13 
 
 9.97598 
 9.97624 
 9.97649 
 9.97674 
 9.97700 
 
 26 
 25 
 25 
 26 
 
 oc 
 
 0.02402 
 0.02376 
 0.02351 
 0.02326 
 0.02300 
 
 9.86116 
 9.86104 
 9.86092 
 9.86080 
 9.86068 
 
 12 
 12 
 12 
 12 
 12 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 14 
 
 1.4 
 1.6 
 1.9 
 
 30 
 31 
 32 
 33 
 34 
 
 9.83781 
 9.83795 
 9.83808 
 9.83821 
 9.83834 
 
 14 
 13 
 13 
 13 
 14 
 
 9.97725 
 9.97750 
 9.97776 
 9.97801 
 9.97826 
 
 25 
 26 
 25 
 25 
 25 
 
 0.02275 
 0.02250 
 0.02224 
 0.02199 
 0.02174 
 
 9.86056 
 9.86044 
 9.86032 
 9.86020 
 9.86008 
 
 12 
 12 
 12 
 12 
 12 
 
 30 
 
 29 
 
 28 
 27 
 26 
 
 10 
 20 
 30 
 40 
 50 
 
 2.3 
 
 4.7 
 7.0 
 9.3 
 11.7 
 
 35 
 36 
 37 
 38 
 39 
 
 9.83848 
 9.83861 
 9.83874 
 9.83887 
 9.83901 
 
 13 
 13 
 13 
 14 
 
 9.97851 
 9.97877 
 9.97902 
 9.97927 
 9.97953 
 
 26 
 25 
 25 
 26 
 
 OE 
 
 0.02149 
 0.02123 
 0.02098 
 0.02073 
 0.02047 
 
 9.85996 
 9.85984 
 9.85972 
 9.85960 
 9.85948 
 
 12 
 12 
 12 
 12 
 12 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 7 
 
 13 
 1.3 
 
 1 5 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.83914 
 9.83927 
 9.83940 
 9.83954 
 9.83967 
 
 13 
 13 
 14 
 13 
 
 10 
 
 9.97978 
 9.98003 
 9.98029 
 9.98054 
 9.98079 
 
 25 
 26 
 25 
 25 
 25 
 
 0.02022 
 0.01997 
 0.01971 
 0.01946 
 0.01921 
 
 9.85936 
 9.85924 
 9.85912 
 9.85900 
 9.85888 
 
 12 
 12 
 12 
 12 
 12 
 
 20 
 
 19 
 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 1.7 
 2.0 
 2.2 
 4.3 
 6.5 
 
 45 
 
 46 
 
 47 
 48 
 49 
 
 9.83980 
 9.83993 
 9.84006 
 9.84020 
 9.84033 
 
 13 
 13 
 14 
 13 
 
 9.98104 
 9.98130 
 9.98155 
 9.98180 
 9.98206 
 
 26 
 25 
 25 
 26 
 
 0.01896 
 0.01870 
 0.01845 
 0.01820 
 0.01794 
 
 9.85876 
 9.85864 
 9.85851 
 9.85839 
 9.85827 
 
 12 
 13 
 12 
 12 
 12 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 8.7 
 10.8 
 
 2 II 
 
 50 
 
 51 
 52 
 53 
 54 
 
 9.84046 
 9.84059 
 9.84072 
 9.84085 
 9.84098 
 
 13 
 13 
 13 
 13 
 
 9.98231 
 9.98256 
 9.98281 
 9.98307 
 9.98332 
 
 25 
 25 
 26 
 25 
 9^ 
 
 0.01769 
 0.01744 
 0.01719 
 0.01693 
 0.01668 
 
 9.85815 
 9.85803 
 9.85791 
 9.85779 
 9.85766 
 
 12 
 12 
 12 
 13 
 12 
 
 10 
 9 
 8 
 7 
 6 
 
 6 
 
 7 
 8 
 9 
 10 
 
 1.2 1.1 
 1.4 1.3 
 1.6 1.5 
 
 1.8 1.7 
 2.0 1.8 
 
 55 
 56 
 57 
 58 
 59 
 
 9.84112 
 9.84125 
 9.84138 
 9.84151 
 9.84164 
 
 13 
 13 
 13 
 13 
 
 9.98357 
 9.98383 
 9.98408 
 9.98433 
 9.98458 
 
 26 
 25 
 25 
 25 
 2fi 
 
 0.01643 
 0.01617 
 0.01592 
 0.01567 
 0.01542 
 
 9.85754 
 9.85742 
 9.85730 
 9.85718 
 9.85706 
 
 12 
 12 
 12 
 12 
 13 
 
 5 
 4 
 3 
 2 
 1 
 
 20 
 30 
 40 
 50 1 
 
 4.0 3.7 
 6.0 5.5 
 8.0 7.3 
 0.0 9.2 
 
 60 
 
 9.84177 
 
 
 9.98484 
 
 
 0.01516 
 
 9.85693 
 
 
 
 
 
 
 
 L. Cos. 
 
 d 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 
 P 
 
 .P. 
 
 46 
 
1072 
 
 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 
 
 A.AO 
 
 1 
 
 L. Sin. 
 
 d. 
 
 L.Tang. 
 
 d.c. 
 
 L. Cotg. 
 
 L. Cos. 
 
 d. 
 
 
 P 
 
 .P. 
 
 
 
 1 
 
 2 
 3 
 4 
 
 9.84177 
 9.84190 
 9.84203 
 9.84216 
 9.84229 
 
 13 
 13 
 13 
 13 
 
 10 
 
 9.98484 
 9.98509 
 9.98534 
 9.98560 
 9.98585 
 
 25 
 25 
 26 
 25 
 
 OK 
 
 0.01516 
 0.01491 
 0.01466 
 0.01440 
 0.01415 
 
 9.85693 
 9.85681 
 9.85669 
 9.85657 
 9.85645 
 
 12 
 12 
 12 
 12 
 
 iq 
 
 60 
 
 59 
 
 58 
 57 
 56 
 
 6 
 
 7 
 
 26 
 2.6 
 30 
 
 5 
 6 
 
 7 
 8 
 9 
 
 9.84242 
 9.84255 
 9.84269 
 9.84282 
 9.84295 
 
 13 
 14 
 13 
 13 
 
 9.98610 
 9.98635 
 9.98661 
 9.98686 
 9.98711 
 
 25 
 26 
 25 
 25 
 
 0.01390 
 0.01365 
 0.01339 
 0.01314 
 0.01289 
 
 9.85632 
 9.85620 
 9.85608 
 9.85596 
 9.85583 
 
 12 
 12 
 12 
 13 
 
 55 
 54 
 53 
 52 
 51 
 
 8 
 9 
 10 
 20 
 30 
 
 3.5 
 3.9 
 4.3 
 
 8.7 
 13.0 
 
 10 
 
 11 
 12 
 13 
 14 
 
 9.84308 
 9.84321 
 9.84334 
 9.84347 
 9.84360 
 
 13 
 13 
 13 
 13 
 
 to 
 
 9.98737 
 9.98762 
 9.98787 
 9.98812 
 9.98838 
 
 25 
 25 
 25 
 26 
 
 oc 
 
 0.01263 
 0.01238 
 0.01213 
 0.01188 
 0.01162 
 
 9.85571 
 9.85559 
 9.85547 
 9.85534 
 9.85522 
 
 12 
 12 
 13 
 12 
 19 
 
 SO 
 
 49 
 48 
 47 
 46 
 
 40 
 50 
 
 17.3 
 21.7 
 
 25 
 
 15 
 16 
 17 
 18 
 19 
 
 9.84373 
 9.84385 
 9.84398 
 9.84411 
 9.84424 
 
 12 
 13 
 13 
 
 13 
 
 TO 
 
 9.98863 
 9.98888 
 9.98913 
 9.98939 
 9.98964 
 
 25 
 25 
 26 
 25 
 
 oc 
 
 0.01137 
 0.01112 
 0.01087 
 0.01061 
 0.01036 
 
 9.85510 
 9.85497 
 9.85485 
 9.85473 
 9.85460 
 
 13 
 12 
 12 
 13 
 12 
 
 45 
 44 
 43 
 42 
 41 
 
 6 
 
 7 
 8 
 9 
 10 
 
 2.5 ' 
 2.9 
 3.3 
 8.8 
 4.2 
 
 20 
 
 21 
 22 
 23 
 24 
 
 9.84437 
 9.84450 
 9.84463 
 9.84476 
 9.84489 
 
 13 
 13 
 13 
 13 
 
 9.98989 
 9.99015 
 9.99040 
 9.99065 
 9.99090 
 
 26 
 25 
 25 
 25 
 
 0.01011 
 0.00985 
 0.00960 
 0.00935 
 0.00910 
 
 9.85448 
 9.85436 
 9.85423 
 9.85411 
 9.85399 
 
 12 
 13 
 12 
 12 
 
 iq 
 
 40 
 
 39 
 38 
 37 
 36 
 
 20 
 30 
 40 
 50 
 
 8.3 
 12.5 
 16.7 
 20.8 
 
 25 
 26 
 
 27 
 28 
 29 
 
 9.84502 
 9.84515 
 9.84528 
 9.84540 
 9.84553 
 
 13 
 13 
 12 
 13 
 
 9.99116 
 9.99141 
 9.99166 
 9.99191 
 9.99217 
 
 25 
 25 
 25 
 26 
 
 nr. 
 
 0.00884 
 0.00859 
 0.00834 
 0.00809 
 0.00783 
 
 9.85386 
 9.85374 
 9.85361 
 9.85349 
 9.85337 
 
 12 
 13 
 12 
 12 
 13 
 
 35 
 34 
 33 
 32 
 31 
 
 6 
 
 7 
 8 
 
 14 
 
 1.4 
 1.6 
 1.9 
 
 SO 
 
 31 
 32 
 33 
 34 
 
 9.84566 
 9.84579 
 9.84592 
 9.84605 
 9.84618 
 
 13 
 13 
 13 
 
 13 
 19 
 
 9.99242 
 9.99267 
 9.99293 
 9.99318 
 9.99343 
 
 25 
 26 
 25 
 25 
 
 OK 
 
 0.00758 
 0.00733 
 0.00707 
 0.00682 
 0.00657 
 
 9.85324 
 9.85312 
 9.85299 
 9.85287 
 9.85274 
 
 12 
 13 
 12 
 13 
 12 
 
 30 
 
 29 
 28 
 27 
 26 
 
 10 
 20 
 30 
 40 
 50 
 
 2.3 
 
 4.7 
 7.0 
 9.3 
 11.7 
 
 35 
 36 
 37 
 38 
 
 9.84630 
 9.84643 
 9.84656 
 9.84669 
 9.84682 
 
 13 
 13 
 13 
 13 
 
 9.99368 
 9.99394 
 9.99419 
 9.99444 
 9.99469 
 
 26 
 25 
 25 
 25 
 
 0.00632 
 0.00606 
 0.00581 
 0.00556 
 0.00531 
 
 9.85262 
 9.85250 
 9.85237 
 9.85225 
 9.85212 
 
 12 
 13 
 12 
 13 
 12 
 
 25 
 24 
 23 
 22 
 21 
 
 6 
 
 <j 
 
 13 
 1.3 
 
 1 c 
 
 40 
 
 41 
 42 
 43 
 44 
 
 9.84694 
 9.84707 
 9.84720 
 9.84733 
 9.84745 
 
 13 
 13 
 13 
 12 
 
 9.99495 
 9.99520 
 9.99545 
 9.99570 
 9.99596 
 
 25 
 25 
 25 
 26 
 
 Oft 
 
 0.00505 
 0.00480 
 0.00455 
 0.00430 
 0.00404 
 
 9.85200 
 9.85187 
 9.85175 
 9.85162 
 9.85150 
 
 13 
 12 
 13 
 12 
 13 
 
 20 
 
 19 
 18 
 17 
 16 
 
 8 
 9 
 10 
 20 
 30 
 
 1.7 
 2.0 
 2.2 
 4.3 
 6.5 
 
 45 
 46 
 47 
 48 
 49 
 
 9.84758 
 9.84771 
 9.84784 
 9.84796 
 9.84809 
 
 13 
 13 
 12 
 13 
 
 9.99621 
 9.99646 
 9.99672 
 9.99697 
 9.99722 
 
 25 
 26 
 25 
 25 
 
 0.00379 
 0.00354 
 0.00328 
 0.00303 
 0.00278 
 
 9.85137 
 9.85125 
 9.85112 
 9.85100 
 9.85087 
 
 12 
 13 
 12 
 13 
 
 iq 
 
 15 
 14 
 13 
 12 
 11 
 
 40 
 50 
 
 8.7 
 10.8 
 
 12 
 
 50 
 
 51 
 52 
 53 
 
 54 
 
 9.84822 
 9.84835 
 9.84847 
 9.84860 
 9.84873 
 
 13 
 12 
 13 
 13 
 
 to 
 
 9.99747 
 9.99773 
 9.99798 
 9.99823 
 9.99848 
 
 26 
 25 
 25 
 25 
 9,fi 
 
 0.00253 
 0.00227 
 0.00202 
 0.00177 
 0.00152 
 
 9.85074 
 9.85062 
 9.85049 
 9.85037 
 9.85024 
 
 12 
 13 
 12 
 13 
 12 
 
 10 
 
 9 
 8 
 
 7 
 6 
 
 6 
 
 7 
 8 
 9 
 10 
 
 1.2 
 1.4 
 1.6 
 1.8 
 2.0 
 
 55 
 56 
 57 
 58 
 59 
 
 9.84885 
 9.84898 
 9.84911 
 9.84923 
 9.84936 
 
 13 
 13 
 12 
 13 
 
 9.99874 
 9.99899 
 9.99924 
 9.99949 
 9.99975 
 
 25 
 25 
 25 
 26 
 
 oc 
 
 0.00126 
 0.00101 
 0.00076 
 0.00051 
 0.00025 
 
 9.85012 
 9.84999 
 9.84986 
 9.84974 
 9.84961 
 
 13 
 13 
 12 
 13 
 12 
 
 5 
 4 
 3 
 2 
 1 
 
 20 
 30 
 40 
 50 
 
 4.0 
 6.0 
 8.0 
 10.0 
 
 60 
 
 9.84949 
 
 
 0.00000 
 
 
 0.00000 
 
 9.84949 
 
 
 
 
 
 
 
 L. Cos. 
 
 d. 
 
 L. Cotg. 
 
 d.c. 
 
 L.Tang. 
 
 L. Sin. 
 
 d. 
 
 ' 
 
 P 
 
 P. 
 
 45 C 
 
TRAVERSE TABLES 1073 
 
 TRAVERSE TABLES 
 
 To use the tables, find the number of degrees in the left-hand column if 
 the angle is less than 45, and in the right-hand column if greater than 45. 
 The numbers on the same line running across the page are the latitudes and 
 departures for that angle and for the respective distances, 1, 2, 3, 4, 5, 6, 7, 8, 9, 
 which appear at the top and bottom of the pages. Thus, if the bearing of a 
 line is 10 and the distance 4, the latitude will be 3.939 and the departure 
 .695; with the same bearing, and the distance 8, the latitude will be 7.878 and 
 the departure 1.389. The latitude and departure for 80 is 10 times the lati- 
 tude and departure for 8, and is found by moving the decimal point one place 
 to the right; that for 500 is 100 times the latitude and departure for '5, and is 
 found by moving the decimal point two places to the right and so on._ By 
 moving the decimal point one, two, or more places to the right, the latitude 
 and departure may be found for any multiple of any number given in the 
 table. In finding the latitude and departure for any number such as 453, the 
 number is resolved into three numbers viz.: 400, 50, 3, and the latitude and 
 departure for each taken from the table and then added together. 
 
 Rule. Write down the latitude and departure, neglecting the decimal points, 
 for the first figure of the given distance; write under them the latitude and depar- 
 ture for the second figure, setting them one place farther to the right; under these, 
 place the, latitude and departure for the third figure, setting them one place still 
 farther to the right, and so continue until all the figures of the given distance have 
 been used; add these latitudes and departures, and point off on the right of their 
 sums a number of decimal places equal to the number of decimal places to which 
 the tables being used are carried; the resulting numbers will be the latitude and 
 departure of the given distance in feet, links, chains, or whatever unit of measure- 
 ment is adopted. 
 
 EXAMPLE. A bearing is 16 and the distance 725 ft.; what is the latitude 
 and departure? 
 
 SOLUTION. Applying the rule just given: 
 
 Distances Latitudes Departures 
 
 700 6729 1929 
 
 20 1923 0551 
 
 5 4806 1378 
 
 725 696.936 199.788 
 
 Taking the nearest whole numbers and rejecting the decimals the latitude 
 and departure are found to be 697 and 200 respectively. 
 
 When a occurs in the given number, the next figure must be set two 
 places tc the right as in the following example: 
 
 EXAMPLES. The bearing is 22 and the distance 907 ft.; required, the lati- 
 tude and departure. 
 
 SOLUTION. Applying the rule just given. 
 
 Distances Latitudes Departures 
 
 900 8345 3371 
 
 ~7 6490 2622 
 
 907 840.990 339.722 
 
 Here the place of both in the distance column and in the latitude and 
 departure columns is occupied by a dash . Rejecting the decimals, the 
 latitude is 841 ft. and the departure 340 ft. 
 
 When the bearing is more than 45, the names of the- columns must be 
 read from the bottom of the page. The latitude of any bearing as 
 the departure of its complement, 30; and the departure of any bearing, as 
 30, is the latitude of its complement, 60 Where the bearings are given 
 in smaller fractions of degrees than is. found in the table, the latitudes and 
 departures can be found by interpolation. 
 
 68 
 
1074 
 
 LATITUDES AND DEPARTURES 
 
 1 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 .E 
 
 1 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 1 
 
 
 
 1.000 
 
 0.000 
 
 2.000 
 
 0.000 
 
 3.000 
 
 0.000 
 
 4.000 
 
 0.000 
 
 5.000 
 
 90 
 
 0* 
 
 1.000 
 
 0.004 
 
 2.000 
 
 0.009 
 
 3.000 
 
 0.013 
 
 4.000. 
 
 0.017 
 
 5.000 
 
 89* 
 
 0* 
 
 1.000 
 
 0.009 
 
 2.000 
 
 0.017 
 
 3.000 
 
 0.026 
 
 4.000 
 
 0.035 
 
 5.000 
 
 
 0* 
 
 1.000 
 
 0.013 
 
 2.000 
 
 0.026 
 
 3.000 
 
 0.039 
 
 4.000 
 
 0.052 
 
 5.000 
 
 89* 
 
 1 
 
 1.000 
 
 0.017 
 
 2.000 
 
 0.035 
 
 3.000 
 
 0.052 
 
 3.999 
 
 0.070 
 
 4.999 
 
 89 
 
 1* 
 
 1.000 
 
 0.022 
 
 2.000 
 
 0.044 
 
 2.999 
 
 0.065 
 
 3.999 
 
 0.087 
 
 4.999 
 
 88* 
 
 It 
 
 1.000 
 
 0.026 
 
 1.999 
 
 0.052 
 
 2.999 
 
 0.079 
 
 3.999 
 
 0.105 
 
 4.998 
 
 
 1* 
 
 1.000 
 
 0.031 
 
 1.999 
 
 0.061 
 
 2.999 
 
 0.092 
 
 3.998 
 
 0.122 
 
 4.998 
 
 88* 
 
 2 
 
 0.999 
 
 0.035 
 
 1.999 
 
 0.070 
 
 2.998 
 
 0.105 
 
 3.998 
 
 0.140 
 
 4.997 
 
 88 
 
 2* 
 
 0.999 
 
 0.039 
 
 1.998 
 
 0.079 
 
 2.998 
 
 0.118 
 
 3.997 
 
 0.157 
 
 4.996 
 
 87* 
 
 2* 
 
 0.999 
 
 0.044 
 
 1.998 
 
 0.087 
 
 2.997 
 
 0.131 
 
 3.996 
 
 0.174 
 
 4.995 
 
 
 2* 
 
 0.999 
 
 0.048 
 
 1.998 
 
 0.096 
 
 2.997 
 
 0.144 
 
 3.995 
 
 0.192 
 
 4.994 
 
 87* 
 
 3 
 
 0.999 
 
 0.052 
 
 1.997 
 
 0.105 
 
 2.996 
 
 0.157 
 
 3.995 
 
 0.209 
 
 4.993 
 
 87 
 
 3* 
 
 0.998 
 
 0.057 
 
 1.997 
 
 0.113 
 
 2.995 
 
 0.170 
 
 3.994 
 
 0.227 
 
 4.992 
 
 86* 
 
 3* 
 
 0.998 
 
 0.061 
 
 1.996 
 
 0.122 
 
 2.994 
 
 0.183 
 
 3.993 
 
 0.244 
 
 4.991 
 
 
 3* 
 
 0.998 
 
 0.065 
 
 1.996 
 
 0.131 
 
 2.994 
 
 0.196 
 
 3.991 
 
 0.262 
 
 4.989 
 
 86- 
 
 4 
 
 0.998 
 
 0.070 
 
 1.995 
 
 0.140 
 
 2.993 
 
 0.209 
 
 3.990 
 
 0.279 
 
 4.988 
 
 86 
 
 4* 
 
 0.997 
 
 0.074 
 
 1.995 
 
 0.148 
 
 2.992 
 
 0.222 
 
 3.989 
 
 0.296 
 
 4.986 
 
 85* 
 
 4* 
 
 0.997 
 
 0.078 
 
 1.994 
 
 0.157 
 
 2.991 
 
 0.235 
 
 3.988 
 
 0.314 
 
 4.985 
 
 
 4* 
 
 0.997 
 
 0.083 
 
 1.993 
 
 0.166 
 
 2.990 
 
 0.248 
 
 3.986 
 
 0.331 
 
 4.983 
 
 85* 
 
 5 
 
 0.996 
 
 0.087 
 
 1.992 
 
 0.174 
 
 2.989 
 
 0.261 
 
 3.985 
 
 0.349 
 
 4.981 
 
 85 
 
 5* 
 
 0.996 
 
 0.092 
 
 1.992 
 
 0.183 
 
 2.987 
 
 0.275 
 
 3.983 
 
 0.366 
 
 4.979 
 
 84* 
 
 6* 
 
 0.995 
 
 0.096 
 
 1.991 
 
 0.192 
 
 2.986 
 
 0.288 
 
 3.982 
 
 0.383 
 
 4.977 
 
 84i 
 
 5* 
 
 0.995 
 
 0.100 
 
 .1.990 
 
 0.200 
 
 2.985 
 
 0.301 
 
 3.980 
 
 0.401 
 
 4.975 
 
 84* 
 
 6 
 
 0.995 
 
 0.105 
 
 1.989 
 
 0.209 
 
 2.984 
 
 0.314 
 
 3.978 
 
 0.418 
 
 4.973 
 
 84 
 
 6* 
 
 0.994 
 
 0.109 
 
 1.988 
 
 0.218 
 
 2.982 
 
 0.327 
 
 3.976 
 
 0.435 
 
 4.970 
 
 83* 
 
 65 
 
 0.994 
 
 0.113 
 
 1.987 
 
 0.226 
 
 2.981 
 
 0.340 
 
 3.974 
 
 0.453 
 
 4.968 
 
 83* 
 
 6* 
 
 0.993 
 
 0.118 
 
 1.986 
 
 0.235 
 
 2.979 
 
 0.353 
 
 3.972 
 
 0.470 
 
 4.965 
 
 83* 
 
 7 
 
 0.993 
 
 0.122 
 
 1.985 
 
 0.244 
 
 2.978 
 
 0.366 
 
 3.970 
 
 0.487 
 
 4.963 
 
 83 
 
 7* 
 
 0.992 
 
 0.126 
 
 1.984 
 
 0.252 
 
 2.976 
 
 0.379 
 
 3.968 
 
 0.505 
 
 4.960 
 
 82* 
 
 7i 
 
 0.991 
 
 0.131 
 
 1.983 
 
 0.261 
 
 2.974 
 
 0.392 
 
 3.966 
 
 0.522 
 
 4.957 
 
 
 7* 
 
 0.991 
 
 0.135 
 
 1.982 
 
 0.270 
 
 2.973 
 
 0.405 
 
 3.963 
 
 0.539 
 
 4.954 
 
 82* 
 
 8 
 
 0.990 
 
 0.139 
 
 1.981 
 
 0.278 
 
 2.971 
 
 0.418 
 
 3.961 
 
 0.557 
 
 4.951 
 
 82 
 
 8* 
 
 0.990 
 
 0.143 
 
 1.979 
 
 0.287 
 
 2.969 
 
 0.430 
 
 3.959 
 
 0.574 
 
 4.948 
 
 81* 
 
 8* 
 
 0.989 
 
 0.148 
 
 1.978 
 
 0.296 
 
 2.967 
 
 0.443 
 
 a 956 
 
 0.591 
 
 4.945 
 
 81* 
 
 8* 
 
 0.988 
 
 0.152 
 
 1.977 
 
 0.304 
 
 2.965 
 
 0.456 
 
 3.953 
 
 0.608 
 
 4.942 
 
 81* 
 
 9 
 
 0.988 
 
 0.156 
 
 1.975 
 
 0.313 
 
 2.963 
 
 0.469 
 
 3.951 
 
 0.626 
 
 4.938 
 
 81 
 
 9* 
 
 0.987 
 
 0.161 
 
 1.974 
 
 0.321 
 
 2.961 
 
 0.482 
 
 3.948 
 
 0.643 
 
 4.935 
 
 80* 
 
 9* 
 
 0.986 
 
 0.165 
 
 1.973 
 
 0.330 
 
 2.959 
 
 0.495 
 
 3.945 
 
 0.660 
 
 4.931 
 
 
 9* 
 
 0.986 
 
 0.169 
 
 1.971 
 
 0.339 
 
 2.957 
 
 0.508 
 
 3.942 
 
 0.677 
 
 4.928 
 
 80* 
 
 10 
 
 0.985 
 
 0.174 
 
 1.970 
 
 0.347 
 
 2.954 
 
 0.521 
 
 3.939 
 
 0.695 
 
 4.924 
 
 80 
 
 10* 
 
 0.984 
 
 0.178 
 
 1.968 
 
 0.356 
 
 2.952 
 
 0.534 
 
 3.936 
 
 0.712 
 
 4.920 
 
 79* 
 
 
 0.983 
 
 0.182 
 
 1.967 
 
 0.364 
 
 2.950 
 
 0.547 
 
 3.933 
 
 0.729 
 
 4.916 
 
 79* 
 
 10* 
 
 0.982 
 
 0.187 
 
 1.965 
 
 0.373 
 
 2.947 
 
 0.560 
 
 3.930 
 
 0.746 
 
 4.912 
 
 79* 
 
 1 1 
 
 0.982 
 
 0.191 
 
 1.963 
 
 0.382 
 
 2.945 
 
 0.572 
 
 3.927 
 
 0.763 
 
 4.908 
 
 79 
 
 11* 
 
 0.981 
 
 0.195 
 
 1.962 
 
 0.390 
 
 2.942 
 
 0.585 
 
 3.923 
 
 0.780 
 
 4.904 
 
 78* 
 
 11* 
 
 0.980 
 
 0.199 
 
 1.960 
 
 0.399 
 
 2.940 
 
 0.598 
 
 3.920 
 
 0.797 
 
 4.900 
 
 
 
 0.979 
 
 0.204 
 
 1.958 
 
 0.407 
 
 2.937 
 
 0.611 
 
 3.916 
 
 0.815 
 
 4.895 
 
 78-*- 
 
 *2 
 
 0.978 
 
 0.208 
 
 1.956 
 
 0.416 
 
 2.934 
 
 0.624 
 
 3.913 
 
 0.832 
 
 4.891 
 
 78 
 
 12* 
 
 0.977 
 
 0.212 
 
 1.954 
 
 0.424 
 
 2.932 
 
 0.637 
 
 3.909 
 
 0.849 
 
 4.886 
 
 77* 
 
 m 
 
 0.976 
 
 0.216 
 
 1.953 
 
 0.433 
 
 2.929 
 
 0.649 
 
 3.905 
 
 0.866 
 
 4.881 
 
 77* 
 
 
 0.975 
 
 0.221 
 
 1.951 
 
 0.441 
 
 2.926 
 
 0.662 
 
 3.901 
 
 0.883 
 
 4.877 
 
 77* 
 
 *3 
 
 0.974 
 
 0.225 
 
 1.949 
 
 0.450 
 
 2.923 
 
 0.675 
 
 3.897 
 
 0.900 
 
 4.872 
 
 77 
 
 1 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 bo 
 
 1 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 1 
 
LATITUDES AND DEPARTURES 
 
 1075 
 
 - 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 oo 
 
 c 
 
 1 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 1 
 
 
 
 0.000 
 
 6.000 
 
 0.000 
 
 7.000 
 
 0.000 
 
 8.000 
 
 0.000 
 
 9.000 
 
 0.000 
 
 90 
 
 0* 
 
 0.022 
 
 6.000 
 
 0.026 
 
 7.000 
 
 0.031 
 
 8.000 
 
 0.035 
 
 9.000 
 
 0.039 
 
 89* 
 
 0* 
 
 0.044 
 
 6.000 
 
 0.052 
 
 7.000 
 
 0.061 
 
 8.000 
 
 0.070 
 
 9.000 
 
 0.079 
 
 89* 
 
 0* 
 
 0.065 
 
 5.999 
 
 0.079 
 
 6.999 
 
 0.092 
 
 7.999 
 
 0.105 
 
 8.999 
 
 0.118 
 
 89* 
 
 1 
 
 0.087 
 
 5.999 
 
 0.105 
 
 6.999 
 
 0.122 
 
 7.999 
 
 0.140 
 
 8.999 
 
 0.157 
 
 89 
 
 1* 
 
 0.109 
 
 5.999 
 
 0.131 
 
 6.998 
 
 0.153 
 
 7.998 
 
 0.175 
 
 8.998 
 
 0.196 
 
 88* 
 
 1* 
 
 0.131 
 
 5.998 
 
 0.157 
 
 6.998 
 
 0.183 
 
 7.997 
 
 0.209 
 
 8.997 
 
 0.236 
 
 88* 
 
 1* 
 
 0.153 
 
 5.997 
 
 0.183 
 
 6.997 
 
 0.214 
 
 7.996 
 
 0.244 
 
 8.996 
 
 0.275 
 
 88* 
 
 2 
 
 0.174 
 
 5.996 
 
 0.209 
 
 6.996 
 
 0.244 
 
 7.995 
 
 0.279 
 
 8.995 
 
 0.314 
 
 88 
 
 2* 
 
 0.196 
 
 5.995 
 
 0.236 
 
 6.995 
 
 0.275 
 
 7.994 
 
 0.314 
 
 8.993 
 
 0.353 
 
 87* 
 
 2* 
 
 0.218 
 
 5.994 
 
 0.262 
 
 6.993 
 
 0.305 
 
 7.992 
 
 0.349 
 
 8.991 
 
 0.393 
 
 87* 
 
 2* 
 
 0.240 
 
 5.993 
 
 0.288 
 
 6.992 
 
 0.336 
 
 7.991 
 
 0.384 
 
 8.990 
 
 0.432 
 
 87* 
 
 3 
 
 0.262 
 
 5.992 
 
 0.314 
 
 6.990 
 
 0.366 
 
 7.989 
 
 0.419 
 
 8.988 
 
 0.471 
 
 87 
 
 
 0.283 
 
 5.990 
 
 0.340 
 
 6.989 
 
 0.397 
 
 7.987 
 
 0.454 
 
 8.986 
 
 0.510 
 
 86* 
 
 3* 
 
 0.305 
 
 5.989 
 
 0.366 
 
 6.987 
 
 0.427 
 
 7.985 
 
 0.488 
 
 8.983 
 
 0.549 
 
 86* 
 
 3* 
 
 0.327 
 
 5.987 
 
 0.392 
 
 6.985 
 
 0.458 
 
 7.983 
 
 0.523 
 
 8.981 
 
 0.589 
 
 86* 
 
 4 
 
 0.349 
 
 5.985 
 
 0.419 
 
 6.983 
 
 0.488 
 
 7.981 
 
 0.558 
 
 8.978 
 
 0.628 
 
 
 
 0.371 
 
 5.984 
 
 0.445 
 
 6.981 
 
 0.519 
 
 7.978 
 
 0.593 
 
 8.975 
 
 0.667 
 
 85* 
 
 4* 
 
 0.392 
 
 5.982 
 
 0.471 
 
 6.978 
 
 0.549 
 
 7.975 
 
 0.628 
 
 8.972 
 
 0.706 
 
 85* 
 
 4* 
 
 0.414 
 
 5.979 
 
 0.497 
 
 6.976 
 
 0.580 
 
 7.973 
 
 0.662 
 
 8.969 
 
 0.745 
 
 85* 
 
 5 
 
 0.436 
 
 5.977 
 
 0.523 
 
 6.973 
 
 0.610 
 
 7.970 
 
 0.697 
 
 8.966 
 
 0.784 
 
 85 
 
 
 0.458 
 
 5.975 
 
 0.549 
 
 6.971 
 
 0.641 
 
 7.966 
 
 0.732 
 
 8.962 
 
 0.824 
 
 84* 
 
 5* 
 
 0.479 
 
 5.972 
 
 0.575 
 
 6.968 
 
 0.671 
 
 7.963 
 
 0.767 
 
 8.959 
 
 0.863 
 
 84* 
 
 5* 
 
 0.501 
 
 5.970 
 
 0.601 
 
 6.965 
 
 0.701 
 
 7.960 
 
 0.802 
 
 8.955 
 
 0.902 
 
 84* 
 
 6 
 
 0.523 
 
 5.967 
 
 0.627 
 
 6.962 
 
 0.732 
 
 7.956 
 
 0.836 
 
 8.951 
 
 0.941 
 
 84 
 
 
 0.544 
 
 5.964 
 
 0.653 
 
 6.958 
 
 0.762 
 
 7.952 
 
 0.871 
 
 8.947 
 
 0.980 
 
 83* 
 
 6* 
 
 0.566 
 
 5.961 
 
 0.679 
 
 6.955 
 
 0.792 
 
 7.949 
 
 0.906 
 
 8.942 
 
 1.019 
 
 
 6* 
 
 0.588 
 
 5.958 
 
 0.705 
 
 6.951 
 
 0.823 
 
 7.945 
 
 0.940 
 
 8.938 
 
 1.058 
 
 
 7 
 
 0.609 
 
 5.955 
 
 0.731 
 
 6.948 
 
 0.853 
 
 7.940 
 
 0.975 
 
 8.933 
 
 1.097 
 
 
 
 7* 
 
 0.631 
 
 5.952 
 
 0.757 
 
 6.944 
 
 0.883 
 
 7.936 
 
 1.010 
 
 8.928 
 
 1.136 
 
 82* 
 
 7* 
 
 0.653 
 
 5.949 
 
 0.783 
 
 6.940 
 
 0.914 
 
 7.932 
 
 1.044 
 
 8.923 
 
 1.175 
 
 82* 
 
 7* 
 
 0.674 
 
 5.945 
 
 0.809 
 
 6.936 
 
 0.944 
 
 7.927 
 
 1.079 
 
 8.918 
 
 1.214 
 
 82* 
 
 8 
 
 0.696 
 
 5.942 
 
 0.835 
 
 6.932 
 
 0.974 
 
 7.922 
 
 1.113 
 
 8.912 
 
 1.253 
 
 82 
 
 
 0.717 
 
 5.938 
 
 0.861 
 
 6.928 
 
 1.004 
 
 7.917 
 
 1.148 
 
 8.907 
 
 1.291 
 
 81* 
 
 8* 
 
 0.739 
 
 5.934 
 
 0.887 
 
 6.923 
 
 1.035 
 
 7.912 
 
 1.182 
 
 8.901 
 
 1.330 
 
 81* 
 
 8* 
 
 0.761 
 
 5.930 
 
 0.913 
 
 6.919 
 
 1.065 
 
 7.907 
 
 1.217 
 
 8.895 
 
 1.369 
 
 81* 
 
 9 
 
 0.782 
 
 5.926 
 
 0.939 
 
 6.914 
 
 1.095 
 
 7.902 
 
 1.251 
 
 8.889 
 
 1.408 
 
 81 
 
 
 0.804 
 
 5.922 
 
 0.964 
 
 6.909 
 
 1.125 
 
 7.896 
 
 1.286 
 
 8.883 
 
 1.447 
 
 80* 
 
 9* 
 
 0.825 
 
 5.918 
 
 0.990 
 
 6.904 
 
 1.155 
 
 7.890 
 
 1.320 
 
 8.877 
 
 1.485 
 
 80* 
 
 9* 
 
 0.847 
 
 5.913 
 
 1.016 
 
 6.899 
 
 1.185 
 
 7.884 
 
 1.355 
 
 8.870 
 
 1.524 
 
 80* 
 
 10 
 
 0.868 
 
 5.909 
 
 1.042 
 
 6.894 
 
 1.216 
 
 7.878 
 
 1.389 
 
 8.863 
 
 1.563 
 
 80 
 
 III 
 
 10* 
 
 0.890 
 0.911 
 0.933 
 
 5.904 
 5.900 
 5.895 
 
 1.068 
 1.093 
 1.119 
 
 6.888 
 6.883 
 6.877 
 
 1.246 
 1.276 
 1.306 
 
 7.872 
 7.866 
 7.860 
 
 1.424 
 1.458 
 1.492 
 
 8.856 
 8.849 
 8.842 
 
 1.601 
 1.640 
 1.679 
 
 79* 
 
 III 
 
 11 
 
 0.954 
 
 5.890 
 
 1.145 
 
 6.871 
 
 1.336 
 
 7.853 
 
 1.526 
 
 8.835 
 
 1.717 
 
 79 
 
 11* 
 
 0.975 
 
 5.885 
 
 1.171 
 
 6.866 
 
 1.366 
 
 7.846 
 
 1.561 
 
 8.827 
 
 1.756 
 
 78* 
 
 11* 
 
 0.997 
 
 5.880 
 
 1.196 
 
 6.859 
 
 1.396 
 
 7.839 
 
 1.595 
 
 8.819 
 
 1.794 
 
 78* 
 
 11* 
 
 1.018 
 
 5.874 
 
 1.222 
 
 6.853 
 
 1.425 
 
 7.832 
 
 1.629 
 
 8.811 
 
 1.833 
 
 78* 
 
 12 
 
 1.040 
 
 5.869 
 
 1.247 
 
 6.847 
 
 1.455 
 
 7.825 
 
 1.663 
 
 8.803 
 
 1.871 
 
 78 
 
 
 1.061 
 
 5.863 
 
 1.273 
 
 6.841 
 
 1.485 
 
 7.818 
 
 1.697 
 
 8.795 
 
 1.910 
 
 77* 
 
 12* 
 1 
 
 1.082 
 1.103 
 1.125 
 
 5.858 
 5.852 
 5.846 
 
 1.299 
 1.324 
 1.350 
 
 6.834 
 6.827 
 6.821 
 
 1.515 
 1.545 
 1.575 
 
 7.810 
 7.803 
 7.795 
 
 1.732 
 1.766 
 1.800 
 
 8.787 
 8.778 
 8.769 
 
 1.948 
 1.986 
 2.025 
 
 77* 
 77* 
 77 
 
 f 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 bo 
 c 
 
 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 : 
 
 CD 
 
1076 
 
 LATITUDES AND DEPARTURES 
 
 00 
 
 i 
 
 2 
 
 3 
 
 4 
 
 5 
 
 bo 
 e 
 
 1 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 a 
 
 13 
 
 0.974 
 
 0.225 
 
 1.949 
 
 0.450 
 
 2.923 
 
 0.675 
 
 3.897 
 
 0.900 
 
 4.872 
 
 77 
 
 13* 
 
 0.973 
 
 0.229 
 
 1.947 
 
 0.458 
 
 2.920 
 
 0.688 
 
 3.894 
 
 0.917 
 
 4.867 
 
 76* 
 
 ill 
 
 0.972 
 0.971 
 
 0.233 
 0.238 
 
 1.945 
 1.943 
 
 0.467 
 0.475 
 
 2.917 
 2.914 
 
 0.700 
 0.713 
 
 3.889 
 3.885 
 
 0.934 
 0.951 
 
 4.862 
 4.857 
 
 ?8 
 
 14 
 
 0.970 
 
 0.242 
 
 1.941 
 
 0.484 
 
 2.911 
 
 0.726 
 
 3.881 
 
 C.968 
 
 4.851 
 
 76 
 
 14* 
 
 0.969 
 
 0.246 
 
 1.938 
 
 0.492 
 
 2.908 
 
 0.738 
 
 3.877 
 
 0.985 
 
 4.846 
 
 75* 
 
 14* 
 
 0.968 
 
 0.250 
 
 1.936 
 
 0.501 
 
 2.904 
 
 0.751 
 
 3.873 
 
 1.002 
 
 4.841 
 
 75* 
 
 14* 
 
 0.967 
 
 0.255 
 
 1.934 
 
 0.509 
 
 2.901 
 
 0.764 
 
 3.868 
 
 1.018 
 
 4.835 
 
 75* 
 
 15 
 
 0.966 
 
 0.259 
 
 1.932 
 
 0.518 
 
 2.898 
 
 0.776 
 
 3.864 
 
 1.035 
 
 4.830 
 
 75 
 
 15- 
 
 0.965 
 
 0.263 
 
 1.930 
 
 0.526 
 
 2.894 
 
 0.789 
 
 3.859 
 
 1.052 
 
 4.824 
 
 74* 
 
 15* 
 
 0.964 
 
 0.267 
 
 1.927 
 
 0.534 
 
 2.891 
 
 0.802 
 
 3.855 
 
 1.069 
 
 4.818 
 
 74* 
 
 15* 
 
 0.962 
 
 0.271 
 
 1.925 
 
 0.543 
 
 2.887 
 
 0.814 
 
 3.850 
 
 1.086 
 
 4.812 
 
 74* 
 
 16 
 
 0.961 
 
 0.276 
 
 1.923 
 
 0.551 
 
 2.884 
 
 0.827 
 
 3.845 
 
 1.103 
 
 4.806 
 
 74 
 
 16* 
 
 0.960 
 
 0.280 
 
 1.920 
 
 0.560 
 
 2.880 
 
 0.839 
 
 3.840 
 
 1.119 
 
 4.800 
 
 73* 
 
 
 0.959 
 
 0.284 
 
 1.918 
 
 0.568 
 
 2.876 
 
 0.852 
 
 3.835 
 
 1.136 
 
 4.794 
 
 73* 
 
 
 0.958 
 
 0.288 
 
 1.915 
 
 0.576 
 
 2.873 
 
 0.865 
 
 3.830 
 
 1.153 
 
 4.788 
 
 73* 
 
 
 0.956 
 
 0.292 
 
 1.913 
 
 0.585 
 
 2.869 
 
 0.877 
 
 3.825 
 
 1.169 
 
 4.782 
 
 73 
 
 17*- 
 
 0.955 
 
 0.297 
 
 1.910 
 
 0.593 
 
 2.865 
 
 0.890 
 
 3.820 
 
 1.186 
 
 4.775 
 
 72* 
 
 17* 
 
 0.954 
 
 0.301 
 
 1.907 
 
 0.601 
 
 2.861 
 
 0.902 
 
 3.815 
 
 1.203 
 
 4.769 
 
 72* 
 
 17* 
 
 0.952 
 
 0.305 
 
 1.905 
 
 0.610 
 
 2.857 
 
 0.915 
 
 3.810 
 
 1.220 
 
 4.762 
 
 72* 
 
 18 
 
 0.951 
 
 0.309 
 
 1.902 
 
 0.618 
 
 2.853 
 
 0.927 
 
 3.804 
 
 1.236 
 
 4.755 
 
 72 
 
 18* 
 
 0.950 
 
 0.313 
 
 1.899 
 
 0.626 
 
 2.849 
 
 0.939 
 
 3.799 
 
 1.253 
 
 4.748 
 
 71* 
 
 18* 
 
 0.948 
 
 0.317 
 
 1.897 
 
 0.635 
 
 2.845 
 
 0.952 
 
 3.793 
 
 1.269 
 
 4.742 
 
 71* 
 
 18* 
 
 0.947 
 
 0.321 
 
 1.894 
 
 0.643 
 
 2.841 
 
 0.964 
 
 3.788 
 
 1.286 
 
 4.735 
 
 71* 
 
 19 
 
 0.946 
 
 0.326 
 
 1.891 
 
 0.651 
 
 2.837 
 
 0.977 
 
 3.782 
 
 1.302 
 
 4.728 
 
 71 
 
 19* 
 
 0.944 
 
 0.330 
 
 1.888 
 
 0.659 
 
 2.832 
 
 0.989 
 
 3.776 
 
 1.319 
 
 4.720 
 
 70* 
 
 19* 
 
 0.943 
 
 0.334 
 
 1.885 
 
 0.668 
 
 2.828 
 
 1.001 
 
 3.771 
 
 1.335 
 
 4.713 
 
 70* 
 
 19* 
 
 0.941 
 
 0.338 
 
 1.882 
 
 0.676 
 
 2.824 
 
 1.014 
 
 3.765 
 
 1.352 
 
 4.706 
 
 70* 
 
 20 
 
 0.940 
 
 0.342 
 
 1.879 
 
 0.684 
 
 2.819 
 
 1.026 
 
 3.759 
 
 1.368 
 
 4.698 
 
 70 
 
 20i 
 
 0.938 
 
 0.346 
 
 1.876 
 
 0.692 
 
 2.815 
 
 1.038 
 
 3.753 
 
 1.384 
 
 4.691 
 
 69* 
 
 20* 
 
 0.937 
 
 0.350 
 
 1.873 
 
 0.700 
 
 2.810 
 
 1.051 
 
 3.747 
 
 1.401 
 
 4.683 
 
 69* 
 
 20* 
 
 0.935 
 
 0.354 
 
 1.870 
 
 0.709 
 
 2.805 
 
 1.063 
 
 3.741 
 
 1.417 
 
 4.676 
 
 69* 
 
 21 
 
 0.934 
 
 0.358 
 
 1.867 
 
 0.717 
 
 2.801 
 
 1.075 
 
 3.734 
 
 1.433 
 
 4.668 
 
 69 
 
 2H 
 
 0.932 
 
 0.362 
 
 1.864 
 
 0.725 
 
 2.796 
 
 1.087 
 
 3.728 
 
 1.450 
 
 4.660 
 
 68* 
 
 21* 
 
 0.930 
 
 0.367 
 
 1.861 
 
 0.733 
 
 2.791 
 
 1.100 
 
 3.722 
 
 1.466 
 
 4.652 
 
 68* 
 
 
 0.929 
 
 0.371 
 
 1.858 
 
 0.741 
 
 2.786 
 
 1.112 
 
 3.715 
 
 1.482 
 
 4.644 
 
 68* 
 
 22 
 
 0.927 
 
 0.375 
 
 1.854 
 
 0.749 
 
 2.782 
 
 1.124 
 
 3.709 
 
 1.498 
 
 4.636 
 
 68 
 
 22* 
 
 0.926 
 
 0.379 
 
 1.851 
 
 0.757 
 
 2.777 
 
 1.136 
 
 3.702 
 
 1.515 
 
 4.628 
 
 67* 
 
 22* 
 
 0.924 
 
 0.383 
 
 1.848 
 
 0.765 
 
 2.772 
 
 1.148 
 
 3.696 
 
 1.531 
 
 4.619 
 
 67* 
 
 22* 
 
 0.922 
 
 0.387 
 
 1.844 
 
 0.773 
 
 2.767 
 
 1.160 
 
 3.689 
 
 1.547 
 
 4.611 
 
 67* 
 
 23 
 
 0.921 
 
 0.391 
 
 1.841 
 
 0.781 
 
 2.762 
 
 1.172 
 
 3.682 
 
 1.563 
 
 4.603 
 
 67 
 
 23* 
 
 0.919 
 
 0.395 
 
 1.838 
 
 0.789 
 
 2.756 
 
 1.184 
 
 3.675 
 
 1.579 
 
 4.594 
 
 66* 
 
 23* 
 
 0.917 
 
 0.399 
 
 1.834 
 
 0.797 
 
 2.751 
 
 1.196 
 
 3.668 
 
 1.595 
 
 4.585 
 
 66* 
 
 23* 
 
 0.915 
 
 0.403 
 
 1.831 
 
 0.805 
 
 2.746 
 
 1.208 
 
 3.661 
 
 1.611 
 
 4.577 
 
 66* 
 
 24 
 
 0.914 
 
 0.407 
 
 1.827 
 
 0.813 
 
 2.741 
 
 1.220 
 
 3.654 
 
 1.627 
 
 4.568 
 
 68 
 
 24* 
 
 0.912 
 
 0.411 
 
 1.824 
 
 0.821 
 
 2.735 
 
 1.232 
 
 3.647 
 
 1.643 
 
 4.559 
 
 65* 
 
 24* 
 
 0.910 
 
 0.415 
 
 1.820 
 
 0.829 
 
 2.730 
 
 1.244 
 
 3.640 
 
 1.659 
 
 4.550 
 
 65* 
 
 24* 
 
 0.908 
 
 0.419 
 
 1.816 
 
 0.837 
 
 2.724 
 
 1.256 
 
 3.633 
 
 1.675 
 
 4.541 
 
 65* 
 
 25 
 
 0.906 
 
 0.423 
 
 1.813 
 
 0.845 
 
 2.719 
 
 1.268 
 
 3.625 
 
 1.690 
 
 4.532 
 
 65 
 
 25* 
 
 0.904 
 
 0.427 
 
 1.809 
 
 0.853 
 
 2.713 
 
 1.280 
 
 3.618 
 
 1.706 
 
 4.522 
 
 64* 
 
 25* 
 
 0.903 
 
 0.431 
 
 1.805 
 
 0.861 
 
 2.708 
 
 1.292 
 
 3.610 
 
 1.722 
 
 4.513 
 
 64* 
 
 25* 
 
 0.901 
 
 0.434 
 
 1.801 
 
 0.869 
 
 2.702 
 
 1.303 
 
 3.603 
 
 1.738 
 
 4.503 
 
 64* 
 
 26 
 
 0.899 
 
 0.438 
 
 1.798 
 
 0.877 
 
 2.696 
 
 1.315 
 
 3.595 
 
 1.753 
 
 4.494 
 
 64 
 
 ? 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 ? 
 
 ~ 
 
 
 
 
 
 
 
 
 
 
 c 
 
 i 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 a 
 
LATITUDES AND DEPARTURES 
 
 1077 
 
 ? 
 
 5 
 
 ( 
 
 1 
 
 
 r 
 
 ( 
 
 1 
 
 ! 
 
 | 
 
 be 
 
 JE 
 
 1 
 oa 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 i 
 
 13 
 
 1.125 
 
 5.846 
 
 1.350 
 
 6.821 
 
 1.575 
 
 7.795 
 
 1.800 
 
 8.769 
 
 2.025 
 
 77 
 
 13i 
 
 1.146 
 
 5.840 
 
 1.375 
 
 6.814 
 
 1.604 
 
 7.787 
 
 1.834 
 
 8.760 
 
 2.063 
 
 76? 
 
 13i 
 
 1.167 
 
 5.834 
 
 1.401 
 
 6.807 
 
 1.634 
 
 7.779 
 
 1.868 
 
 8.751 
 
 2.101 
 
 76i 
 
 13? 
 
 1.188 
 
 5.828 
 
 1.426 
 
 6.799 
 
 1.664 
 
 7.771 
 
 1.902 
 
 8.742 
 
 2.139 
 
 76i 
 
 14 
 
 1.210 
 
 5.822 
 
 1.452 
 
 6.792 
 
 1.693 
 
 7.762 
 
 1.935 
 
 8.733 
 
 2.177 
 
 76 
 
 14i 
 
 1.231 
 
 5.815 
 
 1.477 
 
 6.785 
 
 1.723 
 
 7.754 
 
 1.969 
 
 8.723 
 
 2.215 
 
 75? 
 
 1 
 
 1.252 
 
 5.809 
 
 1.502 
 
 6.777 
 
 1.753 
 
 7.745 
 
 2.003 
 
 8.713 
 
 2.253 
 
 75i 
 
 14* 
 
 1.273 
 
 5.802 
 
 1.528 
 
 6.769 
 
 1.782 
 
 7.736 
 
 2.037 
 
 8.703 
 
 2.291 
 
 75^ 
 
 15 
 
 1.294 
 
 5.796 
 
 1.553 
 
 6.761 
 
 1.812 
 
 7.727 
 
 2.071 
 
 8.693 
 
 2.329 
 
 76 
 
 1*1 
 
 1.315 
 
 5.789 
 
 1.578 
 
 6.754 
 
 1.841 
 
 7.718 
 
 2.104 
 
 8.683 
 
 2.367 
 
 74? 
 
 15i 
 
 1.336 
 
 5.782 
 
 1.603 
 
 6.745 
 
 1.871 
 
 7.709 
 
 2.138 
 
 8.673 
 
 2.405 
 
 74* 
 
 15? 
 
 1.357 
 
 5.775 
 
 1.629 
 
 6.737 
 
 1.900 
 
 7.700 
 
 2.172 
 
 8.662 
 
 2.443 
 
 74f 
 
 16 
 
 1.378 
 
 5.768 
 
 1.654 
 
 6.729 
 
 1.929 
 
 7.690 
 
 2.205 
 
 8.651 
 
 2.481 
 
 74 
 
 wi 
 
 1.399 
 
 5.760 
 
 1.679 
 
 6.720 
 
 1.959 
 
 7.680 
 
 2.239 
 
 8.640 
 
 2.518 
 
 73? 
 
 161 
 
 1.420 
 
 5.753 
 
 1.704 
 
 6.712 
 
 1.988 
 
 7.671 
 
 2.272 
 
 8.629 
 
 2.556 
 
 73i 
 
 16? 
 
 1.441 
 
 5.745 
 
 1.729 
 
 6-703 
 
 2.017 
 
 7.661 
 
 2.306 
 
 8.618 
 
 2.594 
 
 73i 
 
 17 
 
 1.462 
 
 5.738 
 
 1.754 
 
 6.694 
 
 2.047 
 
 7.650 
 
 2.339 
 
 8.607 
 
 2.631 
 
 73 
 
 17i 
 
 1.483 
 
 5.730 
 
 1.779 
 
 6.685 
 
 2.076 
 
 7.640 
 
 2.372 
 
 8.595 
 
 2.669 
 
 72? 
 
 17$ 
 
 1.504 
 
 5.722 
 
 1.804 
 
 6.676 
 
 2.105 
 
 7.630 
 
 2.406 
 
 8.583 
 
 2.706 
 
 72i 
 
 17? 
 
 1.524 
 
 5.714 
 
 1.829 
 
 6.667 
 
 2.134 
 
 7.619 
 
 2.439 
 
 8.572 
 
 2.744 
 
 72i 
 
 18 
 
 1.545 
 
 5.706 
 
 1.854 
 
 6.657 
 
 2.163 
 
 7.608 
 
 2.472 
 
 8.560 
 
 2.781 
 
 72 
 
 I8i 
 
 1.566 
 
 5.698 
 
 1.879 
 
 6.648 
 
 2.192 
 
 7.598 
 
 2.505 
 
 8.547 
 
 2.818 
 
 71? 
 
 18| 
 
 1.587 
 
 5.690 
 
 1.904 
 
 6.638 
 
 2.221 
 
 7.587 
 
 2.538 
 
 8.535 
 
 2.856 
 
 TO 
 
 18| 
 
 1.607 
 
 5.682 
 
 1.929 
 
 6.629 
 
 2.250 
 
 7.575 
 
 2.572 
 
 8.522 
 
 2.893 
 
 7H 
 
 19 
 
 1.628 
 
 5.673 
 
 1.953 
 
 6.619 
 
 2.279 
 
 7.564 
 
 2.605 
 
 8.510 
 
 2.930 
 
 71 
 
 19i 
 
 1.648 
 
 5.665 
 
 1.978 
 
 6.609 
 
 2.308 
 
 7.553 
 
 2.638 
 
 8.497 
 
 2.967 
 
 70? 
 
 19* 
 
 1.669 
 
 5.656 
 
 2.003 
 
 6.598 
 
 2.337 
 
 7.541 
 
 2.670 
 
 8.484 
 
 3.004 
 
 70 
 
 19? 
 
 1.690 
 
 5.647 
 
 2.028 
 
 6.588 
 
 2.365 
 
 7.529 
 
 2.703 
 
 8.471 
 
 3.041 
 
 70i 
 
 20 
 
 1.710 
 
 5.638 
 
 2.052 
 
 6.578 
 
 2.394 
 
 7.518 
 
 2.736 
 
 8.457 
 
 3.078 
 
 70 
 
 20i 
 
 1.731 
 
 5.629 
 
 2.077 
 
 6.567 
 
 2.423 
 
 7.506 
 
 2.769 
 
 8.444 
 
 3.115 
 
 69? 
 
 20 
 
 1.751 
 
 5.620 
 
 2.101 
 
 6.557 
 
 2.451 
 
 7.493 
 
 2.802 
 
 8.430 
 
 3.152 
 
 69* 
 
 20? 
 
 1.771 
 
 5.611 
 
 2.126 
 
 6.546 
 
 2.480 
 
 7.481 
 
 2.834 
 
 8.'416 
 
 3.189 
 
 69i 
 
 21 
 
 1.792 
 
 5.601 
 
 2.150 
 
 6.535 
 
 2.509 
 
 7.469 
 
 2.867 
 
 8.402 
 
 3.225 
 
 69 
 
 211 
 
 1.812 
 
 5.592 
 
 2.175 
 
 6.524 
 
 2.537 
 
 7.456 
 
 2.900 
 
 8.388 
 
 3.262 
 
 68? 
 
 2H 
 
 1.833 
 
 5.582 
 
 2.199 
 
 6.513 
 
 2.566 
 
 7.443 
 
 2.932 
 
 8.374 
 
 3.299 
 
 68i 
 
 2l| 
 
 1.853 
 
 5.573 
 
 2.223 
 
 6.502 
 
 2.594 
 
 7.430 
 
 2.964 
 
 8.359 
 
 3.335 
 
 68i 
 
 22 
 
 1.873 
 
 5.563 
 
 2.248 
 
 6.490 
 
 2.622 
 
 7.417 
 
 2.997 
 
 8.345 
 
 3.371 
 
 68 
 
 22i 
 
 1.893 
 
 5.553 
 
 2.272 
 
 6.479 
 
 2.651 
 
 7.404 
 
 3.029 
 
 8.330 
 
 3.408 
 
 67? 
 
 22| 
 
 1.913 
 
 5.543 
 
 2.296 
 
 6.467 
 
 2.679 
 
 7.391 
 
 3.061 
 
 8.315 
 
 3.444 
 
 67i 
 
 22? 
 
 1.934 
 
 5.533 
 
 2.320 
 
 6.4,55 
 
 2.707 
 
 7.378 
 
 3.094 
 
 8.300 
 
 3.480 
 
 67i 
 
 23 
 
 1.954 
 
 5.523 
 
 2.344 
 
 6.444 
 
 2.735 
 
 7.364 
 
 3.126 
 
 8.285 
 
 3.517 
 
 67 
 
 23i 
 
 1.974 
 
 5.513 
 
 2.368 
 
 6.432 
 
 2.763 
 
 7.350 
 
 3.158 
 
 8.269 
 
 3.553 
 
 66? 
 
 23i 
 
 1.994 
 
 5.502 
 
 2.392 
 
 6.419 
 
 2.791 
 
 7.336 
 
 3.190 
 
 8.254 
 
 3.589 
 
 66^ 
 
 23? 
 
 2.014 
 
 5.492 
 
 2.416 
 
 6.407 
 
 2.819 
 
 7.322 
 
 3.222 
 
 8.238 
 
 3.625 
 
 66| 
 
 24 
 
 2.034 
 
 5.481 
 
 2.440 
 
 6.395 
 
 2.847 
 
 7.308 
 
 3.254 
 
 8.222 
 
 3.661 
 
 66 
 
 24| 
 
 2.054 
 
 5.471 
 
 2.464 
 
 6.382 
 
 2.875 
 
 7.294 
 
 3.286 
 
 8.206 
 
 3.696 
 
 65? 
 
 24 
 
 2.073 
 
 5.460 
 
 2.488 
 
 6.370 
 
 2.903 
 
 7.280 
 
 3.318 
 
 8.190 
 
 3.732 
 
 65* 
 
 24? 
 
 2.093 
 
 5.449 
 
 2.512 
 
 6.357 
 
 2.931 
 
 7.265 
 
 3.349 
 
 8.173 
 
 3.768 
 
 65i 
 
 25 
 
 2.113 
 
 5.438 
 
 2.536 
 
 6.344 
 
 2.958 
 
 7.250 
 
 3.381 
 
 8.157 
 
 3.804 
 
 65 
 
 25i 
 
 2.133 
 
 5.427 
 
 2.559 
 
 6.331 
 
 2.986 
 
 7.236 
 
 3.413 
 
 8.140 
 
 3.839 
 
 64? 
 
 25 
 
 2.153 
 
 5.416 
 
 2.583 
 
 6.318 
 
 3.014 
 
 7.221 
 
 3.444 
 
 8.123 
 
 3.875 
 
 64i 
 
 25? 
 
 2.172 
 
 5.404 
 
 2.607 
 
 6.305 
 
 3.041 
 
 7.206 
 
 3.476 
 
 8.106 
 
 3.910 
 
 64| 
 
 26 
 
 2.192 
 
 5.393 
 
 2.630 
 
 6.292 
 
 3.069 
 
 7.190 
 
 3.507 
 
 8.089 
 
 3.945 
 
 64 
 
 c 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat.. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 / 
 
 I 
 
 a 
 00 
 
 5 
 
 
 i 
 
 
 1 
 
 I 
 
 I 
 
 1 
 
 1 
 
 
 
1078 
 
 LATITUDES AND DEPARTURES 
 
 * 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 M 
 C 
 
 1 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 a 
 00 
 
 28 
 
 0.899 
 
 0.438 
 
 1.798 
 
 0.877 
 
 2.696 
 
 1.315 
 
 3.595 
 
 1.753 
 
 4.494 
 
 64 
 
 26* 
 
 0.897 
 
 0.442 
 
 1.794 
 
 0.885 
 
 2.691 
 
 1.327 
 
 3.587 
 
 1.769 
 
 4.484 
 
 63* 
 
 26i 
 
 0.895 
 
 0.446 
 
 1.790 
 
 0.892 
 
 2.685 
 
 1.339 
 
 3.580 
 
 1.785 
 
 4.475 
 
 63i 
 
 26* 
 
 0.893 
 
 0.450 
 
 1.786 
 
 0.900 
 
 2.679 
 
 1.350 
 
 3.572 
 
 1.800 
 
 4.465 
 
 63* 
 
 27 
 
 0.891 
 
 0.454 
 
 1.782 
 
 0.908 
 
 2.673 
 
 1.362 
 
 3.564 
 
 1.816 
 
 4.455 
 
 63 
 
 27* 
 
 0.889 
 
 0.458 
 
 1.778 
 
 0.916 
 
 2.667 
 
 1.374 
 
 3.556 
 
 1.831 
 
 4.445 
 
 62* 
 
 
 0.887 
 
 0.462 
 
 1.774 
 
 0.923 
 
 2.661 
 
 1.385 
 
 3.548 
 
 1.847 
 
 4.435 
 
 
 27* 
 
 0.885 
 
 0.466 
 
 1.770 
 
 0.931 
 
 2.655 
 
 1.397 
 
 3.540 
 
 1.862 
 
 4.425 
 
 62* 
 
 28 
 
 0.883 
 
 0.469 
 
 1.766 
 
 0.939 
 
 2.649 
 
 1.408 
 
 3.532 
 
 1.878 
 
 4.415 
 
 62 
 
 28* 
 
 0.881 
 
 0.473 
 
 1.762 
 
 0.947 
 
 2.643 
 
 1.420 
 
 3.524 
 
 1.893 
 
 4.404 
 
 61* 
 
 
 0.879 
 
 0.477 
 
 1.758 
 
 0.954 
 
 2.636 
 
 1.431 
 
 3.515 
 
 1.909 
 
 4.394 
 
 
 28! 
 
 0.877 
 
 0.481 
 
 1.753 
 
 0.962 
 
 2.630 
 
 1.443 
 
 3.507 
 
 1.924 
 
 4.384 
 
 61* 
 
 29 
 
 0.875 
 
 0.485 
 
 1.749 
 
 0.970 
 
 2.624 
 
 1.454 
 
 3.498 
 
 1.939 
 
 4.373 
 
 81 
 
 29* 
 
 0.872 
 
 0.'489 
 
 1.745 
 
 0.977 
 
 2.617 
 
 1.466 
 
 3.490 
 
 1.954 
 
 4.362 
 
 60* 
 
 291 
 
 0.870 
 
 0.492 
 
 1.741 
 
 0.985 
 
 2.611 
 
 1.477 
 
 3.481 
 
 1.970 
 
 4.352 
 
 60s 
 
 29* 
 
 0.868 
 
 0.496 
 
 1.736 
 
 0.992 
 
 2.605 
 
 1.489 
 
 3.473 
 
 1.985 
 
 4.341 
 
 60* 
 
 30 
 
 0.866 
 
 0.500 
 
 1.732 
 
 1.000 
 
 2.598 
 
 1.500 
 
 3.464 
 
 2.000 
 
 4.330 
 
 60 
 
 30* 
 
 0.864 
 
 0.504 
 
 1.728 
 
 1.008 
 
 2.592 
 
 1.511 
 
 3.455 
 
 2.015 
 
 4.319 
 
 59* 
 
 30i 
 
 0.862 
 
 0.508 
 
 1.723 
 
 1.015 
 
 2.585 
 
 1.523 
 
 3.447 
 
 2.030 
 
 4.308 
 
 59* 
 
 30* 
 
 0.859 
 
 0.511 
 
 1.719 
 
 1.023 
 
 2.578 
 
 1.534 
 
 3.438 
 
 2.045 
 
 4.297 
 
 59* 
 
 31 
 
 0.857 
 
 0.515 
 
 1.714 
 
 1.030 
 
 2.572 
 
 1.545 
 
 3.429 
 
 2.060 
 
 4.286 
 
 59 
 
 31* 
 
 0.855 
 
 0.519 
 
 1.710 
 
 1.038 
 
 2.565 
 
 1.556 
 
 3.420 
 
 2.075 
 
 4.275 
 
 58* 
 
 3H 
 
 0.853 
 
 0.522 
 
 1.705 
 
 1.045 
 
 2.558 
 
 1.567 
 
 3.411 
 
 2.090 
 
 4.263 
 
 
 31* 
 
 0.850 
 
 0.526 
 
 1.701 
 
 1.052 
 
 2.551 
 
 1.579 
 
 3.401 
 
 2.105 
 
 4.252 
 
 58- 
 
 32 
 
 0.848 
 
 0.530 
 
 1.696 
 
 1.060 
 
 2.544 
 
 1.590 
 
 3.392 
 
 2.120 
 
 4.240 
 
 58 
 
 32* 
 
 0.846 
 
 0.534 
 
 1.691 
 
 1.067 
 
 2.537 
 
 1.601 
 
 3.383 
 
 2.134 
 
 4.229 
 
 57* 
 
 
 0.843 
 
 0.537 
 
 1.687 
 
 1.075 
 
 2.530 
 
 1.612 
 
 3.374 
 
 2.149 
 
 4.217 
 
 
 32* 
 
 0.841 
 
 0.541 
 
 1.682 
 
 1.082 
 
 2.523 
 
 1.623 
 
 3.364 
 
 2.164 
 
 4.205 
 
 57* 
 
 33 
 
 0.839 
 
 0.545 
 
 1.677 
 
 1.089 
 
 2.516 
 
 1.634 
 
 3.355 
 
 2.179 
 
 4.193 
 
 57 
 
 33* 
 
 0.836 
 
 0.548 
 
 1.673 
 
 1.097 
 
 2.509 
 
 1.645 
 
 3.345 
 
 2.193 
 
 4.181 
 
 56* 
 
 33* 
 
 0.834 
 
 0.552 
 
 1.668 
 
 1.104 
 
 2.502 
 
 1.656 
 
 3.336 
 
 2.208 
 
 4.169 
 
 56i 
 
 33* 
 
 0.831 
 
 0.556 
 
 1.663 
 
 1.111 
 
 2.494 
 
 1.667 
 
 3.326 
 
 2.222 
 
 4.157 
 
 56* 
 
 34 
 
 0.829 
 
 0.559 
 
 1.658 
 
 1.118 
 
 2.487 
 
 1.678 
 
 3.316 
 
 2.237 
 
 4.145 
 
 56 
 
 34* 
 
 0.827 
 
 0.563 
 
 1.653 
 
 1.126 
 
 2.480 
 
 1.688 
 
 3.306 
 
 2.251 
 
 4.133 
 
 55* 
 
 
 0.824 
 
 0.566 
 
 1.648 
 
 1.133 
 
 2.472 
 
 1.699 
 
 3.297 
 
 2.266 
 
 4.121 
 
 55i 
 
 34* 
 
 0.822 
 
 0.570 
 
 1.643 
 
 1.140 
 
 2.465 
 
 1.710 
 
 3.287 
 
 2.280 
 
 4.108 
 
 55* 
 
 35 
 
 0.819 
 
 0.574 
 
 1.638 
 
 1.147 
 
 2.457 
 
 1.721 
 
 3.277 
 
 2.294 
 
 4.096 
 
 55 
 
 35* 
 
 0.817 
 
 0.577 
 
 1.633 
 
 1.154 
 
 2.450 
 
 1.731 
 
 3.267 
 
 2.309 
 
 4.083 
 
 54* 
 
 35i 
 
 0.814 
 
 0.581 
 
 1.628 
 
 1.161 
 
 2.442 
 
 1.742 
 
 3.257 
 
 2.323 
 
 4.071 
 
 54* 
 
 35* 
 
 0.812 
 
 0.584 
 
 1.623 
 
 1.168 
 
 2.435 
 
 1.753 
 
 3.246 
 
 2.337 
 
 4.058 
 
 54* 
 
 36 
 
 0.809 
 
 0.588 
 
 1.618 
 
 1.176 
 
 2.427 
 
 1.763 
 
 3.236 
 
 2.351 
 
 4.045 
 
 54 
 
 36* 
 
 0.806 
 
 0.591 
 
 1.613 
 
 1.183 
 
 2.419 
 
 1.774 
 
 3.226 
 
 2.365 
 
 4.032 
 
 53* 
 
 36 * 
 
 0.804 
 
 0.595 
 
 1.608 
 
 1.190 
 
 2.412 
 
 1.784 
 
 3.215 
 
 2.379 
 
 4.019 
 
 
 36* 
 
 0.801 
 
 0.598 
 
 1.603 
 
 1.197 
 
 2.404 
 
 1.795 
 
 3.205 
 
 2.393 
 
 4.006 
 
 53* 
 
 37 
 
 0.799 
 
 0.602 
 
 1.597 
 
 1.204 
 
 2.396 
 
 1.805 
 
 3.195 
 
 2.407 
 
 3.993 
 
 53 
 
 37* 
 
 0.796 
 
 0.605 
 
 1.592 
 
 1.211 
 
 2.388 
 
 1.816 
 
 3.184 
 
 2.421 
 
 3.980 
 
 52* 
 
 
 0.793 
 
 0.609 
 
 1.587 
 
 1.218 
 
 2.380 
 
 1.826 
 
 3.173 
 
 2.435 
 
 3.967 
 
 
 37* 
 
 0.791 
 
 0.612 
 
 1.581 
 
 1.224 
 
 2.372 
 
 1.837 
 
 3.163 
 
 2.449 
 
 3.953 
 
 52* 
 
 38 
 
 0.788 
 
 0.616 
 
 1.576 
 
 1.231 
 
 2.364 
 
 1.847 
 
 3.152 
 
 2.463 
 
 3.940 
 
 52 
 
 
 0.785 
 
 0.619 
 
 1.571 
 
 1.238 
 
 2.356 
 
 1.857 
 
 3.141 
 
 2.476 
 
 3.927 
 
 51* 
 
 38| 
 
 0.783 
 
 0.623 
 
 1.565 
 
 1.245 
 
 2.348 
 
 1.868 
 
 3.130 
 
 2.490 
 
 3.913 
 
 51* 
 
 38* 
 
 0.780 
 
 0.626 
 
 1.560 
 
 1.252 
 
 2.340 
 
 1.878 
 
 3.120 
 
 2.504 
 
 3.899 
 
 51* 
 
 39 
 
 0.777 
 
 0.629 
 
 1.554 
 
 1.259 
 
 2.331 
 
 1.888 
 
 3.109 
 
 2.517 
 
 3.886 
 
 51 
 
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 Dep. 
 
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 3 
 
 4 
 
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LATITUDES AND DEPARTURES 
 
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 5 
 
 6 
 
 7 
 
 8 
 
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 2.192 
 
 5.393 
 
 2.630 
 
 6.292 
 
 3.069 
 
 7.190 
 
 3.507 
 
 8.089 
 
 3.945 
 
 64 
 
 26} 
 
 2.211 
 
 5.381 
 
 2.654 
 
 6.278 
 
 3.096 
 
 7.175 
 
 3.538 
 
 8.072 
 
 3.981 
 
 63* 
 
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 2.231 
 2.250 
 
 5.370 
 5.358 
 
 2.677 
 2.701 
 
 6.265 
 6.251 
 
 3.123 
 3.151 
 
 7.160 
 7.144 
 
 3.570 
 3.601 
 
 8.054 
 8.037 
 
 4.016 
 4.051 
 
 1! 
 
 27 
 
 2.270 
 
 5.346 
 
 2.724 
 
 6.237 
 
 3.178 
 
 7.128 
 
 3.632 
 
 8.019 
 
 4.086 
 
 63 
 
 27} 
 
 2.289 
 
 5.334 
 
 2.747 
 
 6.223 
 
 3.205 
 
 7.112 
 
 3.663 
 
 8.001 
 
 4.121 
 
 62* 
 
 274 
 
 2.309 
 
 5.322 
 
 2.770 
 
 6.209 
 
 3.232 
 
 7.096 
 
 3.694 
 
 7.983 
 
 4.156 
 
 62* 
 
 27* 
 
 2.328 
 
 5.310 
 
 2.794 
 
 6.195 
 
 3.259 
 
 7.080 
 
 3.725 
 
 7.965 
 
 4.190 
 
 62} 
 
 28 
 
 2.347 
 
 5.298 
 
 2.817 
 
 6.181 
 
 3.286 
 
 7.064 
 
 3.756 
 
 7.947 
 
 4.225 
 
 62 
 
 28} 
 
 2.367 
 
 5.285 
 
 2.840 
 
 6.166 
 
 3.313 
 
 7.047 
 
 3.787 
 
 7.928 
 
 4.260 
 
 61* 
 
 28* 
 
 2.386 
 
 5.273 
 
 2.863 
 
 6.152 
 
 3.340 
 
 7.031 
 
 3.817 
 
 7.909 
 
 4.294 
 
 61* 
 
 28* 
 
 2.405 
 
 5.260 
 
 2.886 
 
 6.137 
 
 3.367 
 
 7.014 
 
 3.848 
 
 7.891 
 
 4.329 
 
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 2.424 
 
 5.248 
 
 2.909 
 
 6.122 
 
 3.394 
 
 6.997 
 
 3.878 
 
 7.872 
 
 4.363 
 
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 29} 
 
 2.443 
 
 5.235 
 
 2.932 
 
 6.107 
 
 3.420 
 
 6.980 
 
 3.909 
 
 7.852 
 
 4.398 
 
 60* 
 
 29* 
 
 2.462 
 
 5.222 
 
 2.955 
 
 6.093 
 
 3.447 
 
 6.963 
 
 3.939 
 
 7.833 
 
 4.432 
 
 60* 
 
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 2.481 
 
 5.209 
 
 2.977 
 
 6.077 
 
 3.474 
 
 6.946 
 
 3.970 
 
 7.814 
 
 4.466 
 
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 2.500 
 
 5.196 
 
 3.000 
 
 6.062 
 
 3.500 
 
 6.928 
 
 4.000 
 
 7.794 
 
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 2.519 
 
 5.183 
 
 3.023 
 
 6.047 
 
 3.526 
 
 6.911 
 
 4.030 
 
 7.775 
 
 4.534 
 
 59* 
 
 30* 
 
 2.538 
 
 5.170 
 
 3.045 
 
 6.031 
 
 3.553 
 
 6.893 
 
 4.060 
 
 7.755 
 
 4.568 
 
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 2.556 
 
 5.156 
 
 3.068 
 
 6.016 
 
 3.579 
 
 6.875 
 
 4.090 
 
 7.735 
 
 4.602 
 
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 2.575 
 
 5.143 
 
 3.090 
 
 6.000 
 
 3.605 
 
 6.857 
 
 4.120 
 
 7.715 
 
 4.635 
 
 59 
 
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 2.594 
 
 5.129 
 
 3.113 
 
 5.984 
 
 3.631 
 
 6.839 
 
 4.150 
 
 7.694 
 
 4.669 
 
 58* 
 
 3H 
 
 2.612 
 
 5.116 
 
 3.135 
 
 5.968 
 
 3.657 
 
 6.821 
 
 4.180 
 
 7.674 
 
 4.702 
 
 58* 
 
 31* 
 
 2.631 
 
 5.102 
 
 3.157 
 
 5.952 
 
 3.683 
 
 6.803 
 
 4.210 
 
 7.653 
 
 4.736 
 
 58} 
 
 32 
 
 2.650 
 
 5.088 
 
 3.180 
 
 5.936 
 
 3.709 
 
 6.784 
 
 4.239 
 
 7.632 
 
 4.769 
 
 58 
 
 32} 
 
 2.668 
 
 5.074 
 
 3.202 
 
 5.920 
 
 3.735 
 
 6.766 
 
 4.269 
 
 7.612 
 
 4.802 
 
 57* 
 
 32* 
 
 2.686 
 
 5.060 
 
 3.224 
 
 5.904 
 
 3.761 
 
 6.747 
 
 4.298 
 
 7.591 
 
 4.836 
 
 57* 
 
 32* 
 
 2.705 
 
 5.046 
 
 3.246 
 
 5.887 
 
 3.787 
 
 6.728 
 
 4.328 
 
 7.569 
 
 4.869 
 
 57} 
 
 33 
 
 2.723 
 
 5.032 
 
 3.268 
 
 5.871 
 
 3.812 
 
 6.709 
 
 4.357 
 
 7.548 
 
 4.902 
 
 57 
 
 33} 
 
 2.741 
 
 5.018 
 
 3.290 
 
 5.854 
 
 3.838 
 
 6.690 
 
 4.386 
 
 7.527 
 
 4.935 
 
 56* 
 
 33* 
 
 2.760 
 
 5.003 
 
 3.312 
 
 5.837 
 
 3.864 
 
 6.671 
 
 4.416 
 
 7.505 
 
 4.967 
 
 56* 
 
 33* 
 
 2.778 
 
 4.989 
 
 3.333 
 
 5.820 
 
 3.889 
 
 6.652 
 
 4.445 
 
 7.483 
 
 5.000 
 
 56} 
 
 34 
 
 2.796 
 
 4.974 
 
 3.355 
 
 5.803 
 
 3.914 
 
 6.632 
 
 4.474 
 
 7.461 
 
 5.033 
 
 56 
 
 34} 
 
 2.814 
 
 4.960 
 
 3.377 
 
 5.786 
 
 3.940 
 
 6.613 
 
 4.502 
 
 7.439 
 
 5.065 
 
 55* 
 
 m 
 
 2.832 
 
 4.945 
 
 3.398 
 
 5.769 
 
 3.965 
 
 6.593 
 
 4.531 
 
 7.417 
 
 5.098 
 
 55* 
 
 34* 
 
 2.850 
 
 4.930 
 
 3.420 
 
 5.752 
 
 3.990 
 
 6.573 
 
 4.560 
 
 7.395 
 
 5.130 
 
 55} 
 
 35 
 
 2.868 
 
 4.915 
 
 3.441 
 
 5.734 
 
 4.015 
 
 6.553 
 
 4.589 
 
 7.372 
 
 5.162 
 
 55 
 
 35} 
 
 2.886 
 
 4.900 
 
 3.463 
 
 5.716 
 
 4.040 
 
 6.533 
 
 4.617 
 
 7.350 
 
 5.194 
 
 54* 
 
 35* 
 
 2.904 
 
 4.885 
 
 3.484 
 
 5.699 
 
 4.065 
 
 6.513 
 
 4.646 
 
 7.327 
 
 5.226 
 
 54* 
 
 35* 
 
 2.921 
 
 4.869 
 
 3.505 
 
 5.681 
 
 4.090 
 
 6.493 
 
 4.674 
 
 7.304 
 
 5.258 
 
 54} 
 
 36 
 
 2.939 
 
 4.854 
 
 3.527 
 
 5.663 
 
 4.115 
 
 6.472 
 
 4.702 
 
 7.281 
 
 5.290 
 
 54 
 
 36} 
 
 2.957 
 
 4.839 
 
 3.548 
 
 5.645 
 
 4.139 
 
 6.452 
 
 4.730 
 
 7.258 
 
 5.322 
 
 53* 
 
 36* 
 
 2.974 
 
 4.823 
 
 3.569 
 
 5.627 
 
 4.164 
 
 6.431 
 
 4.759 
 
 7.235 
 
 5.353 
 
 53* 
 
 36* 
 
 2.992 
 
 4.808 
 
 3.590 
 
 5.609 
 
 4.188 
 
 6.410 
 
 4.787 
 
 7.211 
 
 5.385 
 
 53} 
 
 37 
 
 3.009 
 
 4.792 
 
 3.611 
 
 5.590 
 
 4.213 
 
 6.389 
 
 4.815 
 
 7.188 
 
 5.416 
 
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 3.026 
 
 4.776 
 
 3.632 
 
 5.572 
 
 4.237 
 
 6.368 
 
 4.842 
 
 7.164 
 
 5.448 
 
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 3.044 
 
 4.760 
 
 3.653 
 
 5.554 
 
 4.261 
 
 6.347 
 
 4.870 
 
 7.140 
 
 5.479 
 
 52* 
 
 37* 
 
 3.061 
 
 4.744 
 
 3.673 
 
 5.535 
 
 4.286 
 
 6.326 
 
 4.898 
 
 7.116 
 
 5.510 
 
 52} 
 
 38 
 
 3.078 
 
 4.728 
 
 3.694 
 
 5.516 
 
 4.310 
 
 6.304 
 
 4.925 
 
 7.092 
 
 5.541 
 
 52 
 
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 3.095 
 
 4.712 
 
 3.715 
 
 5.497 
 
 4.334 
 
 6.283 
 
 4.953 
 
 7.068 
 
 5.572 
 
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 3.113 
 
 4.696 
 
 3.735 
 
 5.478 
 
 4.358 
 
 6.261 
 
 4.980 
 
 7.043 
 
 5.603 
 
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 3.130 
 
 4.679 
 
 3.756 
 
 5.459 
 
 4.381 
 
 6.239 
 
 5.007 
 
 7.019 
 
 5.633 
 
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 3.147 
 
 4.663 
 
 3.776 
 
 5.440 
 
 4.405 
 
 6.217 
 
 5.035 
 
 6.994 
 
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 LATITUDES AND DEPARTURES 
 
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 0.777 
 
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 3.109 
 
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 0.774 
 
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 3.872 
 
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 0.772 
 
 0.636 
 
 1.543 
 
 1.272 
 
 2.315 
 
 1.908 
 
 3.086 
 
 2.544 
 
 3.858 
 
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 0.769 
 
 0.639 
 
 1.538 
 
 1.279 
 
 2.307 
 
 1.918 
 
 3.075 
 
 2.558 
 
 3.844 
 
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 0.766 
 
 0.643 
 
 1.532 
 
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 0.760 
 
 0.649 
 
 1.521 
 
 1.299 
 
 2.281 
 
 1.948 
 
 3.042 
 
 2.598 
 
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 0.758 
 
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 0.755 
 
 0.656 
 
 1.509 
 
 1.312 
 
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 0.752 
 
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 1.504 
 
 1.319 
 
 2.256 
 
 1.978 
 
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 2.637 
 
 3.759 
 
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 0.749 
 
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 2.984 
 
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 0.743 
 
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 2.961 
 
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 0.737 
 
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 1.475 
 
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 2.212 
 
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 0.734 
 
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 0.725 
 
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 3.612 
 
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 0.719 
 
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 1.439 
 
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 2.877 
 
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 3.597 
 
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 0.716 
 
 0.698 
 
 1.433 
 
 1.396 
 
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 2.093 
 
 2.865 
 
 2.791 
 
 3.582 
 
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 44* 
 
 0.713 
 
 0.701 
 
 1.427 
 
 1.402 
 
 2.140 
 
 2.103 
 
 2.853 
 
 2.804 
 
 3.566 
 
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 44*. 
 
 0.710 
 
 0.704 
 
 1.420 
 
 1.408 
 
 2.131 
 
 2.112 
 
 2.841 
 
 2.816 
 
 3.551 
 
 45} 
 
 45 
 
 0.707 
 
 0.707 
 
 1.414 
 
 1.414 
 
 2.121 
 
 2.121 
 
 2.828 
 
 2.828 
 
 3.536 
 
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 6 
 
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 8 
 
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 39 
 
 3.147 
 
 4.663 
 
 3.776 
 
 5.440 
 
 4.405 
 
 6.217 
 
 5.035 
 
 6.994 
 
 5.664 
 
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 39} 
 
 3.164 
 
 4.646 
 
 3.796 
 
 5.421 
 
 4.429 
 
 6.195 
 
 5.062 
 
 6.970 
 
 5.694 
 
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 39* 
 
 3.180 
 
 4.630 
 
 3.816 
 
 5.401 
 
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 6.173 
 
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 6.945 
 
 5.725 
 
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 3.197 
 
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 3.837 
 
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 4.476 
 
 6.151 
 
 5.116 
 
 6.920 
 
 5.755 
 
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 3.214 
 
 4.596 
 
 3.857 
 
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 4.500 
 
 6.128 
 
 5.142 
 
 6.894 
 
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 3.231 
 
 4.579 
 
 3.877 
 
 5.343 
 
 4.523 
 
 6.106 
 
 5.169 
 
 6.869 
 
 5.815 
 
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 40* 
 
 3.247 
 
 4.562 
 
 3.897 
 
 5.323 
 
 4.546 
 
 6.083 
 
 5.196 
 
 6.844 
 
 5.845 
 
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 3.264 
 
 4.545 
 
 3.917 
 
 5.303 
 
 4.569 
 
 6.061 
 
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 6.818 
 
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 49} 
 
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 3.280 
 
 4.528 
 
 3.936 
 
 5.283 
 
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 6.038 
 
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 6.792 
 
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 3.297 
 
 4.511 
 
 3.956 
 
 5.263 
 
 4.615 
 
 6.015 
 
 5.275 
 
 6.767 
 
 5.934 
 
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 3.313 
 
 4.494 
 
 3.976 
 
 5.243 
 
 4.638 
 
 5.992 
 
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 6.741 
 
 5.964 
 
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 3.329 
 
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 5.968 
 
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 6.715 
 
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 3.346 
 
 4.459 
 
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 5.202 
 
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 3.362 
 
 4.441 
 
 4.034 
 
 5.182 
 
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 42* 
 
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 4.424 
 
 4.054 
 
 5.161 
 
 4.729 
 
 5.898 
 
 5.405 
 
 6.635 
 
 6.080 
 
 47* 
 
 42* 
 
 3.394 
 
 4.406 
 
 4.073 
 
 5.140 
 
 4.752 
 
 5.875 
 
 5.430 
 
 6.609 
 
 6.109 
 
 47} 
 
 43 
 
 3.410 
 
 4.388 
 
 4.092 
 
 5.119 
 
 4.774 
 
 5.851 
 
 5.456 
 
 6.582 
 
 6.138 
 
 47 
 
 43} 
 
 3.426 
 
 4.370 
 
 4.111 
 
 5.099 
 
 4.796 
 
 5.827 
 
 5.481 
 
 6.555 
 
 6.167 
 
 46* 
 
 43* 
 
 3.442 
 
 4.352 
 
 4.130 
 
 5.078 
 
 4.818 
 
 5.803 
 
 5.507 
 
 6.528 
 
 6.195 
 
 46* 
 
 43* 
 
 3.458 
 
 4.334 
 
 4.149 
 
 5.057 
 
 4.841 
 
 5.779 
 
 5.532 
 
 6.501 
 
 6.224 
 
 46} 
 
 44 
 
 3.473 
 
 4.316 
 
 4.168 
 
 5.035 
 
 4.863 
 
 5.755 
 
 5.557 
 
 6.474 
 
 6.252 
 
 46 
 
 44} 
 
 3.489 
 
 4.298 
 
 4.187 
 
 5.014 
 
 4.885 
 
 5.730 
 
 5.582 
 
 6.447 
 
 6.280 
 
 45* 
 
 44* 
 
 3.505 
 
 4.280 
 
 4.206 
 
 4.993 
 
 4.906 
 
 5.706 
 
 5.607 
 
 6.419 
 
 6.308 
 
 45* 
 
 44* 
 
 3.520 
 
 4.261 
 
 4.224 
 
 4.971 
 
 4.928 
 
 5.681 
 
 5.632 
 
 6.392 
 
 6.336 
 
 45} 
 
 45 
 
 3.536 
 
 4.243 
 
 4.243 
 
 4.950 
 
 4.950 
 
 5.657 
 
 5.657 
 
 6.364 
 
 6.364 
 
 45 
 
 Bear- 
 ing 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Dep. 
 
 Lat. 
 
 Bear- 
 
 ing 
 
CIRCUMFERENCES AND AREAS 
 
 1081 
 
 SQUARES, CUBES, SQUARE AND CUBE ROOTS, 
 CIRCUMFERENCES, AND AREAS 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Boot 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 1 
 
 1 
 
 1 
 
 1.0000 
 
 l.'OOOO 
 
 1.000000000 
 
 3.1416 
 
 0.7854 
 
 2 
 
 4 
 
 8 
 
 1.4142 
 
 1.2599 
 
 .500000000 
 
 6.2832 
 
 3.1416 
 
 3 
 
 9 
 
 27 
 
 1.7321 
 
 1.4422 
 
 .333333333 
 
 9.4248 
 
 7.0686 
 
 4 
 
 16 
 
 64 
 
 2.0000 
 
 1.5874 
 
 .250000000 
 
 12.5664 
 
 12.5664 
 
 5 
 
 25 
 
 125 
 
 2.2361 
 
 1.7100 
 
 .200000000 
 
 15.7080 
 
 19.635 
 
 6 
 
 36 
 
 216 
 
 2.4495 
 
 1.8171 
 
 .166666667 
 
 18.850 
 
 28.274 
 
 7 
 
 49 
 
 343 
 
 2.6458 
 
 1.9129 
 
 .142857143 
 
 21.991 
 
 38.485 
 
 8 
 
 64 
 
 512 
 
 2.8284 
 
 2.0000 
 
 .125000000 
 
 25.133 
 
 50.266 
 
 9 
 
 81 
 
 729 
 
 3.0000 
 
 2.0801 
 
 .111111111 
 
 28.274 
 
 63.617 
 
 10 
 
 100 
 
 1,000 
 
 3.1623 
 
 2.1544 
 
 .100000000 
 
 31.416 
 
 78.540 
 
 11 
 
 121 
 
 1,331 
 
 3.3166 
 
 2.2240 
 
 .090909091 
 
 34.558 
 
 95.033 
 
 12 
 
 144 
 
 1,728 
 
 3.4641 
 
 2.2894 
 
 .083333333 
 
 37.699 
 
 113.10 
 
 13 
 
 169 
 
 2,197 
 
 3.6056 
 
 2.3513 
 
 .076923077 
 
 40.841 
 
 132.73 
 
 14 
 
 196 
 
 2,744 
 
 3.7417 
 
 2.4101 
 
 .071428571 
 
 43.982 
 
 153.94 
 
 15 
 
 225 
 
 3,375 
 
 3.8730 
 
 2.4662 
 
 .066666667 
 
 47.124 
 
 176.71 
 
 16 
 
 256 
 
 4,096 
 
 4.0000 
 
 2.5198 
 
 .062500000 
 
 50.265 
 
 201.06 
 
 17 
 
 289 
 
 4,913 
 
 4.1231 
 
 2.5713 
 
 .058823529 
 
 53.407 
 
 226.98 
 
 18 
 
 324 
 
 5,832 
 
 4.2426 
 
 2.6207 
 
 .055555556 
 
 56.549 
 
 254.47 
 
 19 
 
 361 
 
 6,859 
 
 4.3589 
 
 2.6684 
 
 .052631579 
 
 59.690 
 
 283.53 
 
 20 
 
 400 
 
 8,000 
 
 4.4721 
 
 2.7144 
 
 .050000000 
 
 62.832 
 
 314.16 
 
 21 
 
 441 
 
 9,261 
 
 4.5826 
 
 2.7589 
 
 .047619048 
 
 65.973 
 
 346.36 
 
 22 
 
 484 
 
 10,648 
 
 4.6904 
 
 2.8020 
 
 .045454545 
 
 69.115 
 
 380.13 
 
 23 
 
 529 
 
 12,167 
 
 4.7958 
 
 2.8439 
 
 .043478261 
 
 72.257 
 
 415.48 
 
 24 
 
 576 
 
 13,824 
 
 4.8990 
 
 2.8845 
 
 .041666667 
 
 75.398 
 
 452.39 
 
 25 
 
 625 
 
 15,625 
 
 5.0000 
 
 2.9240 
 
 .040000000 
 
 78.540 
 
 490.87 
 
 26 
 
 676 
 
 17,576 
 
 5.0990 
 
 2.9625 
 
 .038461538 
 
 81.681 
 
 530.93 
 
 27 
 
 729 
 
 19,683 
 
 5.1962 
 
 3.0000 
 
 .037037037 
 
 84.823 
 
 572.56 
 
 28 
 
 784 
 
 21,952 
 
 5.2915 
 
 3.0366 
 
 .035714286 
 
 87.965 
 
 615.75 
 
 29 
 
 841 
 
 24,389 
 
 5.3852 
 
 3.0723 
 
 .034482759 
 
 91.106 
 
 660.52 
 
 30 
 
 900 
 
 27,000 
 
 5.4772 
 
 3.1072 
 
 .033333333 
 
 94.248 
 
 706.86 
 
 31 
 
 961 
 
 29,791 
 
 5.5678 
 
 3.1414 
 
 .0322580G5 
 
 97.389 
 
 754.77 
 
 32 
 
 1,024 
 
 32,768 - 
 
 5.6569 
 
 3.1748 
 
 .031250000 
 
 100.53 
 
 804.25 
 
 33 
 
 1,089 
 
 35,937 
 
 5.7446 
 
 3.2075 
 
 .030303030 
 
 103.67 
 
 855.30 
 
 34 
 
 1,156 
 
 39,304 
 
 5.8310 
 
 3.2396 
 
 .029411765 
 
 106.81 
 
 907.92 
 
 35 
 
 1,225 
 
 42,875 
 
 5.9161 
 
 3.2717 
 
 .028571429 
 
 109.96 
 
 962.11 
 
 36 
 
 1,296 
 
 46,656 
 
 6.0000 
 
 3.3019 
 
 .027777778 
 
 113.10 
 
 1,017.88 
 
 37 
 
 1,369 
 
 50,653 
 
 6.0828 
 
 3.3322 
 
 .027027027 
 
 116.24 
 
 1,075.21 
 
 38 
 
 1,444 
 
 54,872 
 
 6.1644 
 
 3.3620 
 
 .026315789 
 
 119.38 
 
 1,134.11 
 
 39 
 
 1,521 
 
 59,319 
 
 6.2450 
 
 3.3912 
 
 .025641026 
 
 122.52 
 
 1,194.59 
 
 40 
 
 1,600 
 
 64,000 
 
 6.3246 
 
 3.4200 
 
 .025000000 
 
 125.66 
 
 1,256.64 
 
 41 
 
 1,681 
 
 68,921 
 
 6.4031 
 
 3.4482 
 
 .024390244 
 
 128.81 
 
 1,320.25 
 
 42 
 
 1,764 
 
 74,088 
 
 6.4807 
 
 3.4760 
 
 .023809524 
 
 131.95 
 
 1,385.44 
 
 43 
 
 1,849 
 
 79,507 
 
 6.5574 
 
 3 5034 
 
 .023255814 
 
 135.09 
 
 1,452.20 
 
 44 
 
 1,936 
 
 85,184 
 
 6.6332 
 
 3 5303 
 
 .022727273 
 
 138.23 
 
 1,520.53 
 
 45 
 
 2,025 
 
 91,125 
 
 6.7082 
 
 3.5569 
 
 .022222222 
 
 141.37 
 
 1,590.43 
 
 46 
 
 2,116 
 
 97,336 
 
 67823 
 
 35830 
 
 .021739130 
 
 144.51 
 
 1.661.90 
 
 47 
 
 2,209 
 
 103,823 
 
 68557 
 
 36088 
 
 .021276600 
 
 147.65 
 
 1,734.94 
 
 48 
 
 2,304 
 
 110,592 
 
 6.9282 
 
 3.6342 
 
 .020833333 
 
 150.80 
 
 1,809.56 
 
 49 
 
 2,401 
 
 117,649 
 
 7.0000 
 
 36593 
 
 .020408163 
 
 153.94 
 
 1,885.74 
 
 50 
 
 2,500 
 
 125,000 
 
 7.0711 
 
 3.6840 
 
 .020000000 
 
 157.08 
 
 1,963.50 
 
 51 
 
 2,601 
 
 132,651 
 
 7.1414 
 
 3.7084 
 
 .019607843 
 
 160.22 
 
 2,042.82 
 
 52 
 
 2,704 
 
 140,608 
 
 7.2111 
 
 3.7325 
 
 .019230769 
 
 163.36 
 
 2,123.72 
 
 53 
 
 2,809 
 
 148,877 
 
 7.2801 
 
 3.7563 
 
 .018867925 
 
 66.50 
 
 2,206.18 
 
 54 
 
 2,916 
 
 157,464 
 
 7.3485 
 
 3.7798 
 
 .018518519 
 
 69.65 
 
 2,290.22 
 
 55 
 
 3,025 
 
 166,375 
 
 7.4162 
 
 3.8030 
 
 .018181818 
 
 72.79 
 
 2,375.83 
 
1082 
 
 SQUARES, CUBES, SQUARE AND CUBE ROOTS 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum 
 
 Area 
 
 56 
 
 3,136 
 
 175,616 
 
 7.4833 
 
 3.8259 
 
 .017857143 
 
 175.93 
 
 2,463.01 
 
 57 
 
 3,249 
 
 185,193 
 
 7.5498 
 
 3.8485 
 
 .017543860 
 
 179.07 
 
 2,551.76 
 
 58 
 
 3,364 
 
 195,112 
 
 7.6158 
 
 3.8709 
 
 .017241379 
 
 182.21 
 
 2,642.08 
 
 59 
 
 3,481 
 
 205,379 
 
 7.6811 
 
 3.8930 
 
 .016949153 
 
 185.35 
 
 2,733.97 
 
 60 
 
 3,600 
 
 216,000 
 
 7.7460 
 
 3.9149 
 
 .016666667 
 
 188.50 
 
 2,827.43 
 
 61 
 
 3,721 
 
 226,981 
 
 7.8102 
 
 3.9365 
 
 .016393443 
 
 191.64 
 
 2,922.47 
 
 62 
 
 3,844 
 
 238,328 
 
 7.8740 
 
 3.9579 
 
 .016129032 
 
 194.78 
 
 3,019.07 
 
 63 
 
 3,969 
 
 250,047 
 
 7.9373 
 
 3.9791 
 
 .015873016 
 
 197.92 
 
 3,117.25 
 
 64 
 
 4,096 
 
 262,144 
 
 8.0000 
 
 4.0000 
 
 .015625000 
 
 201.06 
 
 3,216.99 
 
 65 
 
 4,225 
 
 274,625 
 
 8.0623 
 
 4.0207 
 
 .015384615 
 
 204.20 
 
 3,318.31 
 
 66 
 
 4,356 
 
 287,496 
 
 8.1240 
 
 4.0412 
 
 .015151515 
 
 207.34 
 
 3,421.19 
 
 67 
 
 4,489 
 
 300,763 
 
 8.1854 
 
 4.0615 
 
 .014925373 
 
 210.49 
 
 3,525.65 
 
 68 
 
 4,624 
 
 314,432 
 
 8.2462 
 
 4.0817 
 
 .014705882 
 
 213.63 
 
 3,631.68 
 
 69 
 
 4,761 
 
 328,509 
 
 8.3066 
 
 4.1016 
 
 .014492754 
 
 216.77 
 
 3,739.28 
 
 70 
 
 4,900 
 
 343,000 
 
 8.3666 
 
 4.1213 
 
 .014285714 
 
 219.91 
 
 3,848.45 
 
 71 
 
 5,041 
 
 357,911 
 
 8.4261 
 
 4.1408 
 
 .014084517 
 
 223.05 
 
 3,959.19 
 
 72 
 
 5,184 
 
 373,248 
 
 8.4853 
 
 4.1602 
 
 .013888889 
 
 226.19 
 
 4,071.50 
 
 73 
 
 5,329 
 
 389,017 
 
 8.5440 
 
 4.1793 
 
 .013698630 
 
 229.34 
 
 4,185.39 
 
 74 
 
 5,476 
 
 405,224 
 
 8.6023 
 
 4.1983 
 
 .013513514 
 
 232.48 
 
 4,300.84 
 
 75 
 
 5,625 
 
 421,875 
 
 8.6603 
 
 4.2172 
 
 .013333333 
 
 235.62 
 
 4,417.86 
 
 76 
 
 5,776 
 
 438,976 
 
 8.7178 
 
 4.2358 
 
 .013157895 
 
 238.76 
 
 4,536.46 
 
 77 
 
 5,929 
 
 456,533 
 
 8.7750 
 
 4.2543 
 
 .012987013 
 
 241.90 
 
 4,656.63 
 
 78 
 
 6,084 
 
 474,552 
 
 8.8318 
 
 4.2727 
 
 .012820513 
 
 245.04 
 
 4,778.36 
 
 79 
 
 6,241 
 
 493,039 
 
 8.8882 
 
 4.2908 
 
 .012658228 
 
 248.19 
 
 4,901.67 
 
 80 
 
 6,400 
 
 512,000 
 
 8.9443 
 
 4.3089 
 
 .012500000 
 
 251.33 
 
 5,026.55 
 
 81 
 
 6,561 
 
 531,441 
 
 9.0000 
 
 4.3267 
 
 .012345679 
 
 254.47 
 
 5,153.00 
 
 82 
 
 6,724 
 
 551,368 
 
 9.0554 
 
 4.3445 
 
 .012195122 
 
 257.61 
 
 5,281.02 
 
 83 
 
 6,889 
 
 571,787 
 
 9.1104 
 
 4.3621 
 
 .012048193 
 
 260.75 
 
 5,410.61 
 
 84 
 
 7,056 
 
 592,704 
 
 9.1652 
 
 4.3795 
 
 .011904762 
 
 263.89 
 
 5,541.77 
 
 85 
 
 7,225 
 
 614,125 
 
 9.2195 
 
 4.3968 
 
 .011764706 
 
 267.04 
 
 5,674.50 
 
 86 
 
 7,396 
 
 636,056 
 
 9.2736 
 
 4.4140 
 
 .011627907 
 
 270.18 
 
 5,808.80 
 
 87 
 
 7,569 
 
 658,503 
 
 9.3274 
 
 4.4310 
 
 .011494253 
 
 273.32 
 
 5,944.68 
 
 88 
 
 7,744 
 
 681,472 
 
 9.3808 
 
 4.4480 
 
 .011363636 
 
 276.46 
 
 6,082.12 
 
 89 
 
 7,921 
 
 704,969 
 
 9.4340 
 
 4.4647 
 
 .011235955 
 
 279.60 
 
 6,221.14 
 
 90 
 
 8,100 
 
 729,000 
 
 9.4868 
 
 4.4814 
 
 .011111111 
 
 282.74 
 
 6,361.73 
 
 91 
 
 8,281 
 
 753,571 
 
 9.5394 
 
 4.4979 
 
 .010989011 
 
 285.88 
 
 6,503.88 
 
 92 
 
 8,464 
 
 778,688 
 
 9.5917 
 
 4.5144 
 
 .010869565 
 
 289.03 
 
 6,647.61 
 
 93 
 
 8,649 
 
 804,357 
 
 9.6437 
 
 4.5307 
 
 .010752688 
 
 292.17 
 
 6,792.91 
 
 94 
 
 8,836 
 
 830,584 
 
 9.6954 
 
 4.5468 
 
 .010638298 
 
 295.31 
 
 6,939.78 
 
 95 
 
 9,025 
 
 857,375 
 
 9.7468 
 
 4.5629 
 
 .030526316 
 
 298.45 
 
 7,088.22 
 
 96 
 
 9,216 
 
 884,736 
 
 9.7980 
 
 4.5789 
 
 .010416667 
 
 301.59 
 
 7,238.23 
 
 97 
 
 9,409 
 
 912,673 
 
 9.8489 
 
 4.5947 
 
 .010309278 
 
 304.73 
 
 7,389.81 
 
 98 
 
 9,604 
 
 941,192 
 
 9.8995 
 
 4.6104 
 
 .010204082 
 
 307.88 
 
 7,542.96 
 
 99 
 
 9,801 
 
 970,299 
 
 9.9499 
 
 4.6261 
 
 .010101010 
 
 311.02 
 
 7,697.69 
 
 100 
 
 10,000 
 
 1,000,000 
 
 10.0000 
 
 4.6416 
 
 .010000000 
 
 314.16 
 
 7,853.98 
 
 101 
 
 10,201 
 
 1,030,301 
 
 10.0499 
 
 4.6570 
 
 .009900990 
 
 317.30 
 
 8,011.85 
 
 102 
 
 10,404 
 
 1,061,208 
 
 10.0995 
 
 4.6723 
 
 .009803922 
 
 320.44 
 
 8,171.28 
 
 103 
 
 10,609 
 
 1,092,727 
 
 10.1489 
 
 4.6875 
 
 .009708738 
 
 323.58 
 
 8,332.29 
 
 104 
 
 10,816 
 
 1,124,864 
 
 10.1980 
 
 4.7027 
 
 .009615385 
 
 326.73 
 
 8,494.87 
 
 105 
 
 11,025 
 
 1,157,625 
 
 10.2470 
 
 4.7177 
 
 .009523810 
 
 329.87 
 
 8,659.01 
 
 106 
 
 11,236 
 
 1,191,016 
 
 10.2956 
 
 4.7326 
 
 .009433962 
 
 333.01 
 
 8,824.73 
 
 107 
 
 11,449 
 
 1,225,043 
 
 10.3441 
 
 4.7475 
 
 .009345794 
 
 336.15 
 
 8,992.02 
 
 108 
 
 11,664 
 
 1,259,712 
 
 10.3923 
 
 4.7622 
 
 .009259259 
 
 339.29 
 
 9,160.88 
 
 109 
 
 11,881 
 
 1,295,029 
 
 10.4403 
 
 4.7769 
 
 .009174312 
 
 342.43 
 
 9,331.32 
 
 110 
 
 12,100 
 
 1,331,000 
 
 10.4881 
 
 4.7914 
 
 .009090909 
 
 345.58 
 
 9,503.32 
 
 111 
 
 12,321 
 
 1,367,631 
 
 10.5357 
 
 4.8059 
 
 .009009009 
 
 348.72 
 
 9,676.89 
 
 112 
 
 12,544 
 
 1,404,928 
 
 10.5830 
 
 4.8203 
 
 .008928571 
 
 351.86 
 
 9,852.03 
 
 113 
 
 12,769 
 
 1,442,897 
 
 10.6301 
 
 4.8346 
 
 .008849558 
 
 355.00 
 
 10,028.75 
 
 114 
 
 12,996 
 
 1,481,544 
 
 10.6771 
 
 4.8488 
 
 .008771930 
 
 358.14 
 
 10,207.03 
 
 115 
 
 13,225 
 
 1,520,875 
 
 10.7238 
 
 4.8629 
 
 .008695652 
 
 361.28 
 
 10,386.89 
 
 116 
 
 13,456 
 
 1,560,896 
 
 10.7703 
 
 4.8770 
 
 .008020690 
 
 364.42 
 
 10,568.32 
 
 117 
 
 13,689 
 
 1,601,613 
 
 10.8167 
 
 4.8910 
 
 .008547009 
 
 367.57 
 
 10,751.32 
 
 118 
 
 13,924 
 
 1,643,032 
 
 10.8628 
 
 4.9049 
 
 .008474576 
 
 370.71 
 
 10,935.88 
 
CIRCUMFERENCES, AND AREAS 
 
 1083 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 119 
 
 14,161 
 
 1,685,159 
 
 10.9087 
 
 4.9187 
 
 .008403361 
 
 373.85 
 
 11,122.02 
 
 120 
 
 14,400 
 
 1,728,000 
 
 10.9545 
 
 4.9324 
 
 .008333333 
 
 376.99 
 
 11,309.73 
 
 121 
 
 14,641 
 
 1,771,561 
 
 11.0000 
 
 4.9461 
 
 .008264463 
 
 380.13 
 
 11,499.01 
 
 122 
 
 14,834 
 
 1,815,848 
 
 11.0454 
 
 4.9597 
 
 .008196721 
 
 383.27 
 
 11,689.87 
 
 123 
 
 15,129 
 
 1,860,867 
 
 11.0905 
 
 4.9732 
 
 .008130081 
 
 386.42 
 
 11,882.29 
 
 124 
 
 15,376 
 
 1,906,624 
 
 11.1355 
 
 4.9866 
 
 .008064516 
 
 389.56 
 
 12,076.28 
 
 125 
 
 15,625 
 
 1,953,125 
 
 11.1803 
 
 5.0000 
 
 .008000000 
 
 392.70 
 
 12,271.85 
 
 126 
 
 15,876 
 
 2,000,376 
 
 11.2250 
 
 5.0133 
 
 .007936508 
 
 395.84 
 
 12,468.98 
 
 127 
 
 16,129 
 
 2,048,383 
 
 11.2694 
 
 5.0265 
 
 .007874016 
 
 398.98 
 
 12,667.69 
 
 128 
 
 16,384 
 
 2,097,152 
 
 11.3137 
 
 5.0397 
 
 .007812500 
 
 402.12 
 
 12,867.96 
 
 129 
 
 16,641 
 
 2,146,689 
 
 11.3578 
 
 5.0528 
 
 .007751938 
 
 405.27 
 
 13,069.81 
 
 130 
 
 16,900 
 
 2,197,000 
 
 11.4018 
 
 5.0658 
 
 .007692308 
 
 408.41 
 
 13,273.23 
 
 131 
 
 17,161 
 
 2,248,091 
 
 11.4455 
 
 5.0788 
 
 .007633588 
 
 411.55 
 
 13,478.22 
 
 132 
 
 17,424 
 
 2,299,968 
 
 11.4891 
 
 5.0916 
 
 .007575758 
 
 414.69 
 
 13,684.78 
 
 133 
 
 17,689 
 
 2,352,637 
 
 11.5326 
 
 5.1045 
 
 .007518797 
 
 417.83 
 
 13,892.91 
 
 134 
 
 17,956 
 
 2,406,104 
 
 11.5758 
 
 5.1172 
 
 .007462687 
 
 420.97 
 
 14,102.61 
 
 135 
 
 18,225 
 
 2,460,375 
 
 11.6190 
 
 5.1299 
 
 .007407407 
 
 424.12 
 
 14,313.88 
 
 136 
 
 18,496 
 
 2,515,456 
 
 11.6619 
 
 5.1426 
 
 .007352941 
 
 427.26 
 
 14,526.72 
 
 137 
 
 18,769 
 
 2,571,353 
 
 11.7047 
 
 5.1551 
 
 .007299270 
 
 430.40 
 
 14,741.14 
 
 138 
 
 19,044 
 
 2,628,072 
 
 11.7473 
 
 5.1676 
 
 .007246377 
 
 433.54 
 
 14,957.12 
 
 139 
 
 19,321 
 
 2,685,619 
 
 11.7898 
 
 5.1801 
 
 .007194245 
 
 436.68 
 
 15,174.68 
 
 140 
 
 19,600 
 
 2,744,000 
 
 11.8322 
 
 5.1925 
 
 .007142857 
 
 439.82 
 
 15,393.80 
 
 141 
 
 19,881 
 
 2,803,221 
 
 11.8743 
 
 5.2048 
 
 .007092199 
 
 442.96 
 
 15,614.50 
 
 142 
 
 20,164 
 
 2,863,288 
 
 11.9164 
 
 5.2171 
 
 .007042254 
 
 446.11 
 
 15,836.77 
 
 143 
 
 20,449 
 
 2,924,207 
 
 11.9583 
 
 5.2293 
 
 .006993007 
 
 449.25 
 
 16,060.61 
 
 144 
 
 20,736 
 
 2,985,984 
 
 12.0000 
 
 5.2415 
 
 .006944444 
 
 452.39 
 
 16,286.02 
 
 145 
 
 21,025 
 
 3,048,625 
 
 12.0416 
 
 5.2536 
 
 .006896552 
 
 455.53 
 
 16,513.00 
 
 146 
 
 21,316 
 
 3,112,136 
 
 12.0830 
 
 5.2656 
 
 .006849315 
 
 458.67 
 
 16,741.55 
 
 147 
 
 21,609 
 
 3,176,523 
 
 12.1244 
 
 5.2776 
 
 .006802721 
 
 461.81 
 
 16,971.67 
 
 148 
 
 21,904 
 
 3,241,792 
 
 12.1655 
 
 5.2896 
 
 .006756757 
 
 464.96 
 
 17,203.36 
 
 149 
 
 22,201 
 
 3,307,949 
 
 12.2066 
 
 5.3015 
 
 .006711409 
 
 468.10 
 
 17,436.62 
 
 150 
 
 22,500 
 
 3,375,000 
 
 12.2474 
 
 5.3133 
 
 .006666667 
 
 471.24 
 
 17,671.46 
 
 151 
 
 22,801 
 
 3,442,951 
 
 12.2882 
 
 5.3251 
 
 .006622517 
 
 474.38 
 
 17,907.86 
 
 152 
 
 23,104 
 
 3,511,008 
 
 12.3288 
 
 5.3368 
 
 .006578947 
 
 477.52 
 
 18,145.84 
 
 153 
 
 23,409 
 
 3,581,577 
 
 12.3693 
 
 5.3485 
 
 .006535948 
 
 480.66 
 
 18,385.39 
 
 154 
 
 23,716 
 
 3,652,264 
 
 12.4097 
 
 5.3601 
 
 .006493506 
 
 483.81 
 
 18,626.50 
 
 155 
 
 24,025 
 
 3,723,875 
 
 12.4499 
 
 5.3717 
 
 .006451613 
 
 486.95 
 
 18,869.19 
 
 156 
 
 24,336 
 
 3,796,416 
 
 12.4900 
 
 5.3832 
 
 .006410256 
 
 490.09 
 
 19,113.45 
 
 157 
 
 24,649 
 
 3,869,893 
 
 12.5300 
 
 5.3947 
 
 .006369427 
 
 493.23 
 
 19,359.28 
 
 158 
 
 24,964 
 
 3,944,312 
 
 12.5698 
 
 5.4061 
 
 .006329114 
 
 496.37 
 
 19,606.68 
 
 159 
 
 25,281 
 
 4,019,679 
 
 12.6095 
 
 5.4175 
 
 .006289308 
 
 499.51 
 
 19,855.65 
 
 160 
 
 25,600 
 
 4,096,000 
 
 12.6491 
 
 5.4288 
 
 .006250000 
 
 502.65 
 
 20,106.19 
 
 161 
 
 25,921 
 
 4,173,281 
 
 12.6886 
 
 5.4401 
 
 .006211180 
 
 505.80 
 
 20,358.31 
 
 162 
 
 26,244 
 
 4,251,528 
 
 12.7279 
 
 5.4514 
 
 .006172840 
 
 508.94 
 
 20,611.99 
 
 163 
 
 26,569 
 
 4,330,747 
 
 12.7671 
 
 5.4626 
 
 .006134969 
 
 512.08 
 
 20,867.24 
 
 164 
 
 26,896 
 
 4,410,944 
 
 12.8062 
 
 5.4737 
 
 .006097561 
 
 515.22 
 
 21,124.07 
 
 165 
 
 27,225 
 
 4,492,125 
 
 12.8452 
 
 5.4848 
 
 .006060606 
 
 518.36 
 
 21,382.46 
 
 166 
 
 27,556 
 
 4,574,296 
 
 12.8841 
 
 5.4959 
 
 .006024096 
 
 521.50 
 
 21,642.43 
 
 167 
 
 27,889 
 
 4,657,463 
 
 12.9228 
 
 5.5069 
 
 .005988024 
 
 524.65 
 
 21,903.97 
 
 168 
 
 28,224 
 
 4,741,632 
 
 12.9615 
 
 5.5178 
 
 .005952381 
 
 527.79 
 
 22,167.08 
 
 169 
 
 28,561 
 
 4,826,809 
 
 13.0000 
 
 5.5288 
 
 .005917160 
 
 530.93 
 
 22,431.76 
 
 170 
 
 28,900 
 
 4,913,000 
 
 13.9384 
 
 5.5397 
 
 .005882353 
 
 534.07 
 
 22,698.01 
 
 171 
 
 29,241 
 
 5,000,211 
 
 13.0767 
 
 5.5505 
 
 .005847953 
 
 537.21 
 
 22,965.83 
 
 172 
 
 29,584 
 
 5,088,448 
 
 13.1149 
 
 5.5613 
 
 .005813953 
 
 540.35 
 
 23,235.22 
 
 173 
 
 29,929 
 
 5,177,717 
 
 13.1529 
 
 5.5721 
 
 .005780347 
 
 543.50 
 
 23,506.18 
 
 174 
 
 30,276 
 
 5,268,024 
 
 13.1909 
 
 5.5828 
 
 .005747126 
 
 546.64 
 
 23,778.71 
 
 175 
 
 30,625 
 
 5,359,375 
 
 13.2288 
 
 5.5934 
 
 .005714286 
 
 549.78 
 
 24,052.82 
 
 176 
 
 30,976 
 
 5,451,776 
 
 13.2665 
 
 5.6041 
 
 .005681818 
 
 552.92 
 
 24,328.49 
 
 177 
 
 31,329 
 
 5,545,233 
 
 13.3041 
 
 5.6147 
 
 .005649718 
 
 556.06 
 
 24,605.74 
 
 178 
 
 31,684 
 
 5,639,752 
 
 13.3417 
 
 5.6252 
 
 .005617978 
 
 559.20 
 
 24,884.56 
 
 179 
 
 32,041 
 
 5,735,339 
 
 13.3791 
 
 5.6357 
 
 .005586592 
 
 562.35 
 
 25,164.94 
 
 180 
 
 32,400 
 
 5,832,000 
 
 13.4164 
 
 5.6462 
 
 .005555556 
 
 565.49 
 
 25,446.90 
 
 181 
 
 32,761 
 
 5,929,741 
 
 13.4536 
 
 5.6567 
 
 .005524862 
 
 568.63 
 
 25,730.48 
 
1084 
 
 SQUARES, CUBES, SQUARE AND CUBE ROOTS 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 182 
 
 33,124 
 
 6,028,568 
 
 13.4907 
 
 5.6671 
 
 .005494505 
 
 571.77 
 
 26,015.53 
 
 183 
 
 33,489 
 
 6,128,487 
 
 13.5277 
 
 5.6774 
 
 .005464481 
 
 574.91 
 
 26,302.20 
 
 184 
 
 83,856 
 
 6,229,504 
 
 13.5647 
 
 5.6877 
 
 .005434783 
 
 578.05 
 
 26,590.44 
 
 185 
 
 34,225 
 
 6,331,625 
 
 13.6015 
 
 5.6980 
 
 .005405405 
 
 581.19 
 
 26,880.25 
 
 186 
 
 34,596 
 
 6,434,856 
 
 13.6382 
 
 5.7083 
 
 .005376344 
 
 584.34 
 
 27,171.63 
 
 187 
 
 34,969 
 
 6,539,203 
 
 13.6748 
 
 5.7185 
 
 .005347594 
 
 587.48 
 
 27,464.59 
 
 188 
 
 35,344 
 
 6,644,672 
 
 13.7113 
 
 5.7287 
 
 .005319149 
 
 590.62 
 
 27,759.11 
 
 189 
 
 35,721 
 
 6,751,269 
 
 13.7477 
 
 5.7388 
 
 .005291005 
 
 593.76 
 
 28,055.21 
 
 190 
 
 36,100 
 
 6,859,000 
 
 13.7840 
 
 5.7489 
 
 .005263158 
 
 596.90 
 
 28,352.87 
 
 191 
 
 36,481 
 
 6,967,871 
 
 13.8203 
 
 5.7590 
 
 .005235602 
 
 600.04 
 
 28,652.11 
 
 192 
 
 36,864 
 
 7,077,888 
 
 13.8564 
 
 5.7690 
 
 .005208333 
 
 603.19 
 
 28,952.92 
 
 193 
 
 37,249 
 
 7,189,017 
 
 13.8924 
 
 5.7790 
 
 .005181347 
 
 606.33 
 
 29,255.30 
 
 194 
 
 37,636 
 
 7,301,384 
 
 13.9284 
 
 5.7890 
 
 .005154639 
 
 609.47 
 
 29,559.25 
 
 195 
 
 38,025 
 
 7,414,875 
 
 13.9642 
 
 5.7989 
 
 .005128205 
 
 612.61 
 
 29,864.77 
 
 196 
 
 38,416 
 
 7,529,536 
 
 14.0000 
 
 5.8088 
 
 .005102041 
 
 615.75 
 
 30,171.86 
 
 197 
 
 38,809 
 
 7,645,373 
 
 14.0357 
 
 5.8186 
 
 .005076142 
 
 618.89 
 
 30,480.52 
 
 198 
 
 39,204 
 
 7,762,392 
 
 14.0712 
 
 5.8285 
 
 .005050505 
 
 622.04 
 
 30,790.75 
 
 199 
 
 39,601 
 
 7,880,599 
 
 14.1067 
 
 5.8383 
 
 .005025126 
 
 625.18 
 
 31,102.55 
 
 200 
 
 40,000 
 
 8,000,000 
 
 14.1421 
 
 5.8480 
 
 .005000000 
 
 628.32 
 
 31,415.93 
 
 201 
 
 40,401 
 
 8,120,601 
 
 14.1774 
 
 5.8578 
 
 .004975124 
 
 631.46 
 
 31,730.87 
 
 202 
 
 40,804 
 
 8,242,408 
 
 14.2127 
 
 5.8675 
 
 .004950495 
 
 634.60 
 
 32,047.39 
 
 203 
 
 41,209 
 
 8,365,427 
 
 14.2478 
 
 5.8771 
 
 .004926108 
 
 637.74 
 
 32,365.47 
 
 204 
 
 41,616 
 
 8,489,664 
 
 14.2829 
 
 5.8868 
 
 .004901961 
 
 640.88 
 
 32,685.13 
 
 205 
 
 42,025 
 
 8,615,125 
 
 14.3178 
 
 5.8964 
 
 .004878049 
 
 644.03 
 
 33,006.36 
 
 206 
 
 42,436 
 
 8,741,816 
 
 14.3527 
 
 5.9059 
 
 .004854369 
 
 647.17 
 
 33,329.16 
 
 207 
 
 42,849 
 
 8,869,743 
 
 14.3875 
 
 5.9155 
 
 .004830918 
 
 650.31 
 
 33,653.53 
 
 208 
 
 43,264 
 
 8,998,912 
 
 14.4222 
 
 5.9250 
 
 .004807692 
 
 653.45 
 
 33,979.47 
 
 209 
 
 43,681 
 
 9,129,329 
 
 14.4568 
 
 5.9345 
 
 .004784689 
 
 656.59 
 
 34.306.98 
 
 210 
 
 44,100 
 
 9,261,000 
 
 14.4914 
 
 5.9439 
 
 .004761905 
 
 659.73 
 
 34,636.06 
 
 211 
 
 44,521 
 
 9,393,931 
 
 14.5258 
 
 5.9533 
 
 .004739336 
 
 662.88 
 
 34,966.71 
 
 212 
 
 44,944 
 
 9,528.128 
 
 14.5608 
 
 5.9627 
 
 .004716981 
 
 666.02 
 
 35,298.94 
 
 213 
 
 45,369 
 
 9,663,597 
 
 14.5945 
 
 5.9721 
 
 .004694836 
 
 669.16 
 
 35,632.73 
 
 214 
 
 45,796 
 
 9,800,344 
 
 14.6287 
 
 5.9814 
 
 .004672897 
 
 672.30 
 
 35,968.09 
 
 215 
 
 46,225 
 
 9,938,375 
 
 14.6629 
 
 5.9907 
 
 .004651163 
 
 675.44 
 
 36,305.03 
 
 216 
 
 46,656 
 
 10,077,696 
 
 14.6969 
 
 6.0000 
 
 .004629630 
 
 678.58 
 
 36,643.54 
 
 217 
 
 47,089 
 
 10,218,313 
 
 14.7309 
 
 6.0092 
 
 .004608295 
 
 681.73 
 
 36,983.61 
 
 218 
 
 47,524 
 
 10,360,232 
 
 14.7648 
 
 6.0185 
 
 .004587156 
 
 684.87 
 
 37,325.26 
 
 219 
 
 47,961 
 
 10,503,459 
 
 14.7986 
 
 6.0277 
 
 .004566210 
 
 688.01 
 
 37,668.48 
 
 220 
 
 48,400 
 
 10,648,000 
 
 14.8324 
 
 6.0368 
 
 .004545455 
 
 691.15 
 
 38,013.27 
 
 221 
 
 48,841 
 
 10,793,861 
 
 14.8661 
 
 6.0459 
 
 .004524887 
 
 694.29 
 
 38,359.63 
 
 222 
 
 49,284 
 
 10,941,048 
 
 14.8997 
 
 6.0550 
 
 .004504505 
 
 697.43 
 
 38,707.56 
 
 223 
 
 49,729 
 
 11,089,567 
 
 14.9332 
 
 6.0641 
 
 .004484305 
 
 700.58 
 
 39,057.07 
 
 224 
 
 50,176 
 
 11,239,424 
 
 14.9666 
 
 6.0732 
 
 .004464286 
 
 703.72 
 
 39,408.14 
 
 225 
 
 50,625 
 
 11,390,625 
 
 15.0000 
 
 6.0822 
 
 .004444444 
 
 706.86 
 
 39,760.78 
 
 226 
 
 51,076 
 
 11,543,176 
 
 15.0333 
 
 6.0912 
 
 .004424779 
 
 710.00 
 
 40,115.00 
 
 227 
 
 51,529 
 
 11,697,083 
 
 15.0665 
 
 6.1002 
 
 .004405286 
 
 713.14 
 
 40,470.78 
 
 228 
 
 51,984 
 
 11,852,352 
 
 15.0997 
 
 6.1091 
 
 .004385965 
 
 716.28 
 
 40,828.14 
 
 229 
 
 52,441 
 
 12,008,989 
 
 15.1327 
 
 6.1180 
 
 .004366812 
 
 719.42 
 
 41,187.07 
 
 230 
 
 52,900 
 
 12,167,000 
 
 15.1658 
 
 6.1269 
 
 .004347826 
 
 722.57 
 
 41,547.56 
 
 231 
 
 53,361 
 
 12,326,391 
 
 15.1987 
 
 6.1358 
 
 .004329004 
 
 725.71 
 
 41,909.63 
 
 232 
 
 53,824 
 
 12,487,168 
 
 15.2315 
 
 6.1446 
 
 .004310345 
 
 728.85 
 
 42,273.27 
 
 233 
 
 54,289 
 
 12,649,337 
 
 15.2643 
 
 6.1534 
 
 .004291845 
 
 731.99 
 
 42,638.48 
 
 234 
 
 54,756 
 
 12,812,904 
 
 15.2971 
 
 6.1622 
 
 .004273504 
 
 735.13 
 
 43,005.26 
 
 235 
 
 55,225 
 
 12,977,875 
 
 15.3297 
 
 6.1710 
 
 .004255319 
 
 738.27 
 
 43,373.61 
 
 236 
 
 55,696 
 
 13,144,256 
 
 15.3623 
 
 6.1797 
 
 .004237288 
 
 741.42 
 
 43,743.54 
 
 237 
 
 56,169 
 
 13,312,053 
 
 15.3948 
 
 6.1885 
 
 .004219409 
 
 744.56 
 
 44,115.03 
 
 238 
 
 56,644 
 
 13,481,272 
 
 15.4272 
 
 6.1672 
 
 .004201681 
 
 747.70 
 
 44,488.09 
 
 239 
 
 57,121 
 
 13,651,919 
 
 15.4596 
 
 6.2058 
 
 .004184100 
 
 750.84 
 
 44,862.73 
 
 240 
 
 57,600 
 
 13,824,000 
 
 15.4919 
 
 6.2145 
 
 .004166667 
 
 753.98 
 
 45,238.93 
 
 241 
 
 58,081 
 
 13,997,521 
 
 15.5242 
 
 6.2231 
 
 .004149378 
 
 757.12 
 
 45,616.71 
 
 242 
 
 58,564 
 
 14,172,488 
 
 15.5563 
 
 6.2317 
 
 .004132231 
 
 760.27 
 
 45,996.06 
 
 243 
 
 59,049 
 
 14,348,907 
 
 15.5885 
 
 6.2403 
 
 .004115226 
 
 763.41 
 
 46,376.98 
 
 244 
 
 59,536 
 
 14,526,784 
 
 15.6205 
 
 6.2488 
 
 .004098361 
 
 766.55 
 
 46,759.47 
 
CIRCUMFERENCES, AND AREAS 
 
 1085 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 245 
 
 60,025 
 
 14,706,125 
 
 15.6525 
 
 6.2573 
 
 .004081633 
 
 769.69 
 
 47,143.52 
 
 246 
 
 60,516 
 
 14,886,936 
 
 15.6844 
 
 6.2658 
 
 .004065041 
 
 772.83 
 
 47,529.16 
 
 247 
 
 61,009 
 
 15,069,223 
 
 15.7162 
 
 6.2743 
 
 .004048583 
 
 775.97 
 
 47,916.36 
 
 248 
 
 61,504 
 
 15,252,992 
 
 15.7480 
 
 6.2828 
 
 .004032258 
 
 779.11 
 
 48,305.13 
 
 249 
 
 62,001 
 
 15,438,249 
 
 15.7797 
 
 6.2912 
 
 .004016064 
 
 782.26 
 
 48,695.47 
 
 250 
 
 62,500 
 
 15,625,000 
 
 15.8114 
 
 6.2996 
 
 .004000000 
 
 785.40 
 
 49,087.39 
 
 251 
 
 63,001 
 
 15,813,251 
 
 15.8430 
 
 6.3080 
 
 .003984064 
 
 788.54 
 
 49,480.87 
 
 252 
 
 63,504 
 
 16,003,008 
 
 15.8745 
 
 6.3164 
 
 .003968254 
 
 791.68 
 
 49,875.92 
 
 253 
 
 64,009 
 
 16,194,277 
 
 15.9060 
 
 6.3247 
 
 .003952569 
 
 794.82 
 
 50,272.55 
 
 254 
 
 64,516 
 
 16,387,064 
 
 15.9374 
 
 6.3330 
 
 .003937008 
 
 797.96 
 
 50,670.75 
 
 255 
 
 65,025 
 
 16,581,375 
 
 15.9687 
 
 6.3413 
 
 .003921569 
 
 801.11 
 
 51,070.52 
 
 256 
 
 65,536 
 
 16,777,216 
 
 16.0000 
 
 6.3496 
 
 .003906250 
 
 804.25 
 
 51,471.85 
 
 257 
 
 66,049 
 
 16,974,593 
 
 16.0312 
 
 6.3579 
 
 .003891051 
 
 807.39 
 
 51,874.76 
 
 258 
 
 66,564 
 
 17,173,512 
 
 16.0624 
 
 6.3661 
 
 .003875969 
 
 810.53 
 
 52,279.24 
 
 259 
 
 67,081 
 
 17,373,979 
 
 16.0935 
 
 6.3743 
 
 .003861004 
 
 813.67 
 
 52,685.29 
 
 260 
 
 67,600 
 
 17,576,000 
 
 16.1245 
 
 6.3825 
 
 .003846154 
 
 816.81 
 
 53,092.92 
 
 261 
 
 68,121 
 
 17,779,581 
 
 16.1555 
 
 6.3907 
 
 .003831418 
 
 819.96 
 
 53,502.11 
 
 262 
 
 68,644 
 
 17,984,728 
 
 16.1864 
 
 6.3988 
 
 .003816794 
 
 823.10 
 
 53,912.87 
 
 263 
 
 69,169 
 
 18,191,447 
 
 16.2173 
 
 6.4070 
 
 .003802281 
 
 826.24 
 
 54,325.21 
 
 264 
 
 69,696 
 
 18,399,744 
 
 16.2481 
 
 6.4151 
 
 .003787879 
 
 829.38 
 
 54,739.11 
 
 265 
 
 70,225 
 
 18,609,625 
 
 16.2788 
 
 6.4232 
 
 .003773585 
 
 832.52 
 
 55,154.59 
 
 266 
 
 70,756 
 
 18,821,096 
 
 16.3095 
 
 6.4312 
 
 .003759398 
 
 835.66 
 
 55,571.63 
 
 267 
 
 71,289 
 
 19,034,163 
 
 16.3401 
 
 6.4393 
 
 .003745318 
 
 838.81 
 
 55,990.25 
 
 268 
 
 71,824 
 
 19,248,832 
 
 16.3707 
 
 6.4473 
 
 .003731343 
 
 841.95 
 
 56,410.44 
 
 269 
 
 72,361 
 
 19,465,109 
 
 16.4012 
 
 6.4553 
 
 .003717472 
 
 845.09 
 
 56,832.20 
 
 .270 
 
 72,900 
 
 19,683,000 
 
 16.4317 
 
 6.4633 
 
 .003703704 
 
 848.23 
 
 57,255.53 
 
 271 
 
 73,441 
 
 19,902,511 
 
 16.4621 
 
 6.4713 
 
 .003690037 
 
 851.37 
 
 57,680.43 
 
 272 
 
 73,984 
 
 20,123,643 
 
 16.4924 
 
 6.4792 
 
 .003676471 
 
 854.51 
 
 58,106.90 
 
 273 
 
 74,529 
 
 20,346,417 
 
 16.5227 
 
 6.4872 
 
 .003663004 
 
 857.65 
 
 58,534.94 
 
 274 
 
 75,076 
 
 20,570,824 
 
 16.5529 
 
 6.4951 
 
 .003649635 
 
 860.80 
 
 58,964.55 
 
 275 
 
 75,625 
 
 20,796,875 
 
 16.5831 
 
 6.5030 
 
 .003636364 
 
 863.94 
 
 59,395.74 
 
 276 
 
 76,176 
 
 21,024,576 
 
 16.6132 
 
 6.5108 
 
 .003623188 
 
 867.08 
 
 59,828.49 
 
 277 
 
 76,729 
 
 21,253,933 
 
 16.6433 
 
 6.5187 
 
 .003610108 
 
 870.22 
 
 60,262.82 
 
 278 
 
 77,284 
 
 21,484,952 
 
 16.6783 
 
 6.5265 
 
 .003597122 
 
 873.36 
 
 60,698.71 
 
 279 
 
 77,841 
 
 21,717,639 
 
 16.7033 
 
 6.5343 
 
 .003584229 
 
 876.50 
 
 61,136.18 
 
 280 
 
 78,400 
 
 21,952,000 
 
 16.7332 
 
 6.5421 
 
 .003571429 
 
 879.65 
 
 61,575.22 
 
 281 
 
 78,961 
 
 22,188,041 
 
 16.7631 
 
 6.5499 
 
 .003558719 
 
 882.79 
 
 62,015.82 
 
 282 
 
 79,524 
 
 22,425,768 
 
 16.7929 
 
 6.5577 
 
 .003546099 
 
 885.93 
 
 62,458.00 
 
 283 
 
 80,089 
 
 22,665,187 
 
 16.8226 
 
 6.5654 
 
 .003533569 
 
 889.07 
 
 62,901.75 
 
 284 
 
 80,656 
 
 22,906,304 
 
 16.8523 
 
 6.5731 
 
 .003522127 
 
 892.21 
 
 63,347.07 
 
 285 
 
 81,225 
 
 23,149,125 
 
 16.8819 
 
 6.5808 
 
 .003508772 
 
 895.35 
 
 63,793.97 
 
 286 
 
 81,796 
 
 23,393,656 
 
 16.9115 
 
 6.5885 
 
 .003496503 
 
 898.50 
 
 64,242.43 
 
 287 
 
 82,369 
 
 23,639,903 
 
 16.9411 
 
 6.5962 
 
 .003484321 
 
 901.64 
 
 64,692.46 
 
 288 
 
 82,944 
 
 23,887,872 
 
 16.9706 
 
 6.6039 
 
 .003472222 
 
 904.78 
 
 65,144.07 
 
 289 
 
 83,521 
 
 24,137,569 
 
 17.0000 
 
 6.6115 
 
 .003460208 
 
 907.92 
 
 65,597.24 
 
 290 
 
 84,100 
 
 24,389,000 
 
 17.0294 
 
 6.6191 
 
 .003448276 
 
 911.06 
 
 66,051.99 
 
 291 
 
 84,681 
 
 24,642,171 
 
 17.0587 
 
 6.6267 
 
 .003436426 
 
 914.20 
 
 66,508.30 
 
 292 
 
 85,264 
 
 24,897,088 
 
 17.0880 
 
 6.6343 
 
 .003424658 
 
 917.35 
 
 66,966.19 
 
 293 
 
 85,849 
 
 25,153,757 
 
 17.1172 
 
 6.6119 
 
 .003412969 
 
 920.49 
 
 67,425.65 
 
 294 
 
 86,436 
 
 25,412,184 
 
 17.1464 
 
 6.6494 
 
 .003401361 
 
 923.63 
 
 67,886.68 
 
 295 
 
 87,025 
 
 25,672,375 
 
 17.1756 
 
 6.6569 
 
 .003389831 
 
 926.77 
 
 68,349.28 
 
 296 
 
 87,616 
 
 25,934,836 
 
 17.2047 
 
 6.6644 
 
 .003378378 
 
 929:91 
 
 68,813.45 
 
 297 
 
 88,209 
 
 26,198,073 
 
 17.2337 
 
 6.6719 
 
 .003367003 
 
 933.05 
 
 69,279.19 
 
 298 
 
 88,804 
 
 26,463,592 
 
 17.2627 
 
 6.6794 
 
 .003355705 
 
 936.19 
 
 69,746.50 
 
 299 
 
 89,401 
 
 26,730,899 
 
 17.2916 
 
 6.6869 
 
 .003344482 
 
 939.34 
 
 70,215.38 
 
 300 
 
 90,000 
 
 27,000,000 
 
 17.3205 
 
 6.6943 
 
 .003333333 
 
 942.48 
 
 70,685.83 
 
 301 
 
 90,601 
 
 27,270,901 
 
 17.3494 
 
 6.7018 
 
 .003322259 
 
 945.62 
 
 71,157.86 
 
 302 
 
 91,204 
 
 27,543,608 
 
 17.3781 
 
 6.7092 
 
 .003311258 
 
 948.76 
 
 71,631.45 
 
 303 
 
 91,809 
 
 27,818,127 
 
 17.4069 
 
 6.7166 
 
 .003301330 
 
 951.90 
 
 72,106.62 
 
 304 
 
 92,416 
 
 28,094,464 
 
 17.4356 
 
 6.7240 
 
 .003289474 
 
 955.04 
 
 72,583.36 
 
 305 
 
 93.025 
 
 28,372,625 
 
 17.4642 
 
 6.7313 
 
 .003278689 
 
 958.19 
 
 73,061.66 
 
 306 
 
 93,636 
 
 28,652,616 
 
 17.4929 
 
 6.7387 
 
 .003267974 
 
 961.33 
 
 73,541.54 
 
 307 
 
 94,249 
 
 28,934,443 
 
 17.5214 
 
 6.7460 
 
 .003257329 
 
 964.47 
 
 74,022.99 
 
1086 
 
 SQUARES, CUBES, SQUARE AND CUBE ROOTS 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 308 
 
 94,864 
 
 29,218,112 
 
 17.5499 
 
 6.7533 
 
 .003246753 
 
 967.61 
 
 74,506.01 
 
 309 
 
 95,481 
 
 29,503,629 
 
 17.5784 
 
 6.7606 
 
 .003236246 
 
 970.75 
 
 74,990.60 
 
 310 
 
 96,100 
 
 29,791,000 
 
 17.6068 
 
 6.7679 
 
 .003225806 
 
 973.89 
 
 75,476.76 
 
 311 
 
 96,721 
 
 30,080,231 
 
 17.6352 
 
 6.7752 
 
 .003215434 
 
 977.04 
 
 75,964.50 
 
 312 
 
 97,344 
 
 30,371,328 
 
 17.6635 
 
 6.7824 
 
 .003205128 
 
 980.18 
 
 76,453.80 
 
 313 
 
 97,969 
 
 30,664,297 
 
 17.6918 
 
 6.7897 
 
 .003194888 
 
 983.32 
 
 76,944.67 
 
 314 
 
 98,596 
 
 30,959,144 
 
 17.7200 
 
 6.7969 
 
 .003184713 
 
 986.46 
 
 77,437.12 
 
 315 
 
 99,225 
 
 31,255,875 
 
 17.7482 
 
 6.8041 
 
 .003174603 
 
 989.60 
 
 77,931.13 
 
 316 
 
 99,856 
 
 31,554,496 
 
 17.7764 
 
 6.8113 
 
 .003164557 
 
 992.74 
 
 78,426.72 
 
 317 
 
 100,489 
 
 31,855,013 
 
 17.8045 
 
 6.8185 
 
 .003154574 
 
 995.88 
 
 78,923.88 
 
 318 
 
 101,124 
 
 32,157,432 
 
 17.8326 
 
 6.8256 
 
 .003144654 
 
 999.03 
 
 79,422.60 
 
 319 
 
 101,761 
 
 32,461,759 
 
 17.8606 
 
 6.8328 
 
 .003134796 
 
 1,002.17 
 
 79,922.90 
 
 320 
 
 102,400 
 
 32,768,000 
 
 17.8885 
 
 6.8399 
 
 .003125000 
 
 1,005.31 
 
 80,424.77 
 
 321 
 
 103,041 
 
 33,076,161 
 
 17.9165 
 
 6.8470 
 
 .003115265 
 
 1,008.45 
 
 80,928.21 
 
 322 
 
 103,684 
 
 33,386,248 
 
 17.9444 
 
 6.8541 
 
 .003105690 
 
 1,011.59 
 
 81,433.22 
 
 323 
 
 104,329 
 
 33,698,267 
 
 17.9722 
 
 6.8612 
 
 .003095975 
 
 1,014.73 81,939.80 
 
 324 
 
 104,976 
 
 34,012,224 
 
 18.0000 
 
 6.8683 
 
 .003086420 
 
 1,017.88 82,447.96 
 
 325 
 
 105,625 
 
 34,328,125 
 
 18.0278 
 
 6.8753 
 
 .003076923 
 
 1,021.02 
 
 82,957.68 
 
 326 
 
 106,276 
 
 34,645,976 
 
 18.0555 
 
 6.8824 
 
 .003067485 
 
 1,024.16 
 
 83,468.98 
 
 327 
 
 106,929 
 
 34,965,783 
 
 18.0831 
 
 6.8894 
 
 .003058104 
 
 1,027.30 
 
 83,981.84 
 
 328 
 
 107,584 
 
 35,287,552 
 
 18.1108 
 
 6.8964 
 
 .003048780 
 
 1,030.44 
 
 84,496.28 
 
 329 
 
 108,241 
 
 35,611,289 
 
 18.1384 
 
 6.9034 
 
 .003039514 
 
 1,033.58 
 
 85,012.28 
 
 330 
 
 108,900 
 
 35,937,000 
 
 18.1659 
 
 6.9104 
 
 .003030303 
 
 1,036.73 
 
 85,529.86 
 
 331 
 
 109,561 
 
 36,264,691 
 
 18.1934 
 
 6.9174 
 
 .003021148 
 
 1,039.87 
 
 86,049.01 
 
 332 
 
 110,224 
 
 36,594,368 
 
 18.2209 
 
 6.9244 
 
 .003012048 
 
 1,043.01 
 
 86,569.73 
 
 333 
 
 110,889 
 
 36,926,037 
 
 18.2483 
 
 6.9313 
 
 .003003003 
 
 1,046.15 
 
 87,092.02 
 
 334 
 
 111,556 
 
 37,259,704 
 
 18.2757 
 
 6.9382 
 
 .002994012 
 
 1,049.29 
 
 87,615.88 
 
 335 
 
 112,225 
 
 37,595,375 
 
 18.3030 
 
 6.9451 
 
 .002985075 
 
 1,052.43 
 
 88,141.31 
 
 336 
 
 112,896 
 
 37,933,056 
 
 18.3303 
 
 6.9521 
 
 .002976190 
 
 1,055.58 
 
 88,668.31 
 
 337 
 
 113,569 
 
 38,272,753 
 
 18.3576 
 
 6.9589 
 
 .002967359 
 
 1,058.72 
 
 89,196.88 
 
 338 
 
 114,244 
 
 38,614,472 
 
 18.3848 
 
 6.9658 
 
 .002958580 
 
 1,061.86 
 
 89,727.03 
 
 339 
 
 114,921 
 
 38,958,219 
 
 18.4120 
 
 6.9727 
 
 .002949853 
 
 1,065.00 
 
 90,258.74 
 
 340 
 
 115,600 
 
 39,304,000 
 
 18.4391 
 
 6.9795 
 
 .002941176 
 
 1,068.14 
 
 90,792.03 
 
 341 
 
 116,281 
 
 39,651,821 
 
 18.4662 
 
 6.9864 
 
 .002932551 
 
 1,071.28 
 
 91,326.88 
 
 342 
 
 116,964 
 
 40,001,688 
 
 18.4932 
 
 6.9932 
 
 .002923977 
 
 1,074.42 
 
 91 ,863.31 
 
 343 
 
 117,649 
 
 40,353,607 
 
 18.5203 
 
 7.0000 
 
 .002915452 
 
 1,077.57 
 
 92,401.31 
 
 344 
 
 118,336 
 
 40,707,584 
 
 18.5472 
 
 7.0068 
 
 .002906977 
 
 1,080.71 
 
 92,940.88 
 
 345 
 
 119,025 
 
 41,063,625 
 
 18.5742 
 
 7.0136 
 
 .002898551 
 
 1,083.85 
 
 93,482.02 
 
 346 
 
 119,716 
 
 41,421,736 
 
 18.6011 
 
 7.0203 
 
 .002890173 
 
 1,086.99 
 
 94,024.73 
 
 347 
 
 120,409 
 
 41,781,923 
 
 18.6279 
 
 7.0271 
 
 .002881844 
 
 1,090.13 
 
 94,569.01 
 
 348 
 
 121,104 
 
 42,144,192 
 
 18.6548 
 
 7.0338 
 
 .002873563 
 
 1,093.27 
 
 95,114.86 
 
 349 
 
 121,801 
 
 42,508,549 
 
 18.6815 
 
 7.0406 
 
 .002865330 
 
 1,096.42 
 
 95,662.28 
 
 350 
 
 122,500 
 
 42,875,000 
 
 18.7083 
 
 7.0473 
 
 .002857143 
 
 1,099.56 
 
 96,211.28 
 
 351 
 
 123,201 
 
 43,243,551 
 
 18.7350 
 
 7.0540 
 
 .002849003 
 
 1,102.70 
 
 96,761.84 
 
 352 
 
 123,904 
 
 43,614,208 
 
 18.7617 
 
 7.0607 
 
 .002840909 
 
 1,105.84 
 
 97,313.97 
 
 353 
 
 124,609 
 
 43,986,977 
 
 18.7883 
 
 7.0674 
 
 .002832861 
 
 1,108.98 
 
 97,867.68 
 
 354 
 
 125,316 
 
 44,361,864 
 
 18.8149 
 
 7.0740 
 
 .002824859 
 
 1,112.12 
 
 98,422.96 
 
 355 
 
 126,025 
 
 44,738,875 
 
 18.8414 
 
 7.0807 
 
 .002816901 
 
 1,115.27 
 
 98,979.80 
 
 356 
 
 126,736 
 
 45,118,016 
 
 18.8680 
 
 7.0873 
 
 .002808989 
 
 1,118.41 
 
 99,538.22 
 
 357 
 
 127,449 
 
 45,499,293 
 
 18.8944 
 
 7.0940 
 
 .002801120 
 
 1,121.55 
 
 100,098.21 
 
 358 
 
 128,164 
 
 45,882,712 
 
 18.9209 
 
 7.1006 
 
 .002793296 
 
 1,124.69 
 
 100,659.77 
 
 359 
 
 128,881 
 
 46,268,279 
 
 18.9473 
 
 7.1072 
 
 .002785515 
 
 1,127.83 
 
 101,222.90 
 
 360 
 
 129,600 
 
 46,656,000 
 
 18.9737 
 
 7.1138 
 
 .002777778 
 
 1,130.97 
 
 101,787.60 
 
 361 
 
 130,321 
 
 47,045,881 
 
 19.0000 
 
 7.1204 
 
 .002770083 
 
 1,134.11 
 
 102,353.87 
 
 362 
 
 131,044 
 
 47,437,928 
 
 19.0263 
 
 7.1269 
 
 .002762431 
 
 1,137.26 
 
 102,921.72 
 
 363 
 
 131,769 
 
 47,832,147 
 
 19.0526 
 
 7.1335 
 
 .002754821 
 
 1,140.40 
 
 103,491.13 
 
 364 
 
 132,496 
 
 48,228,544 
 
 19.0788 
 
 7.1400 
 
 .002747253 
 
 1,143.54 
 
 104,062.12 
 
 365 
 
 133,225 
 
 48,627,125 
 
 19.1050 
 
 7.1466 
 
 .002739726 
 
 1,146.68 
 
 104,634.67 
 
 366 
 
 133,956 
 
 49,027,896 
 
 19.1311 
 
 7.1531 
 
 .002732240 
 
 1,149.82 
 
 105,208.80 
 
 367 
 
 134,689 
 
 49,430,863 
 
 19.1572 
 
 7.1596 
 
 .002724796 
 
 1,152.96 
 
 105,784.49 
 
 368 
 
 135,424 
 
 49,836,032 
 
 19.1833 
 
 7.1661 
 
 .002717391 
 
 1,156.11 
 
 106,361.76 
 
 369 
 
 136,161 
 
 50,243,409 
 
 19.2094 
 
 7.1726 
 
 .002710027 
 
 1,159.25 
 
 106,940.60 
 
 370 
 
 136,900 
 
 50,653,000 
 
 19.2354 
 
 7.1791 
 
 .002702703 
 
 1,162.39 
 
 107,521.01 
 
CIRCUMFERENCES, AND AREAS 
 
 1087 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 371 
 
 137,641 
 
 51,064,811 
 
 19.2614 
 
 7.1855 
 
 .002695418 
 
 1,165.53 
 
 108,102.99 
 
 372 
 
 138,384 
 
 51,478,848 
 
 19.2873 
 
 7.1920 
 
 .002688172 
 
 1,168.67 
 
 108,686.54 
 
 373 
 
 139,129 
 
 51,895,117 
 
 19.3132 
 
 7.1984 
 
 .002680965 
 
 1,171.81 
 
 109,271.66 
 
 374 
 
 139,876 
 
 52,313,624 
 
 19.3391 
 
 7.2048 
 
 .002673797 
 
 1,174.96 
 
 109,858.35 
 
 375 
 
 140,625 
 
 52,734,375 
 
 19.3649 
 
 7.2112 
 
 .002666667 
 
 1,178.10 
 
 110,446.62 
 
 376 
 
 141,376 
 
 53,157,376 
 
 19.3907 
 
 7.2177 
 
 .002659574 
 
 1,181.24 
 
 111,036.45 
 
 377 
 
 142,129 
 
 53,582,633 
 
 19.4165 
 
 7.2240 
 
 .002652520 
 
 1,184.38 
 
 111,627.86 
 
 378 
 
 142,884 
 
 54,010,152 
 
 19.4422 
 
 7.2304 
 
 .002645503 
 
 1,187.52 
 
 112,220.83 
 
 379 
 
 143; 641 
 
 54,439,939 
 
 19.4679 
 
 7.2368 
 
 .002638521 
 
 1,190.66 
 
 112,815.38 
 
 380 
 
 144,400 
 
 54,872,000 
 
 19.4936 
 
 7.2432 
 
 .002631579 
 
 1,193.81 
 
 113,411.49 
 
 381 
 
 145,161 
 
 55,306,341 
 
 19.5192 
 
 7.2495 
 
 .002624672 
 
 1,196.95 
 
 114,009.18 
 
 382 
 
 145,924 
 
 55,742,968 
 
 19.5448 
 
 7.2558 
 
 .002617801 
 
 1,200.09 
 
 114,608.44 
 
 383 
 
 146,689 
 
 56,181,887 
 
 19.5704 
 
 7.2622 
 
 .002610966 
 
 1,203.23 
 
 115,209.27 
 
 384 
 
 147,456 
 
 56,623,104 
 
 19.5959 
 
 7.2685 
 
 .002604167 
 
 1,206.37 
 
 115,811.67 
 
 385 
 
 148,225 
 
 57,066,625 
 
 19.6214 
 
 7.2748 
 
 .002597403 
 
 1,209.51 
 
 116,415.64 
 
 386 
 
 148,996 
 
 57,512,456 
 
 19.6469 
 
 7.2811 
 
 .002590674 
 
 1,212.65 
 
 117,021.18 
 
 387 
 
 149,769 
 
 57,960,603 
 
 19.6723 
 
 7.2874 
 
 .002583979 
 
 1,215.80 
 
 117,628.30 
 
 388 
 
 150,544 
 
 58,411,072 
 
 19.6977 
 
 7.2936 
 
 .002577320 
 
 1,218.94 
 
 118,236.98 
 
 389 
 
 151,321 
 
 68,863,869 
 
 19.7231 
 
 7.2999 
 
 .002570694 
 
 1,222.08 
 
 118,847.24 
 
 390 
 
 152,100 
 
 59,319,000 
 
 19.7484 
 
 7.3061 
 
 .002564103 
 
 1,225.22 
 
 119,459.06 
 
 391 
 
 152,881 
 
 59,776,471 
 
 19.7737 
 
 7.3124 
 
 .002557545 
 
 1,228.36 
 
 120,072.46 
 
 392 
 
 153,664 
 
 60,236,288 
 
 19.7990 
 
 7.3186 
 
 .002551020 
 
 1,231.50 
 
 120,687.42 
 
 393 
 
 154,449 
 
 60,698,457 
 
 19.8242 
 
 7.3248 
 
 .002544529 
 
 1,234.65 
 
 121,303.96 
 
 394 
 
 155,236 
 
 61,162,984 
 
 19.8494 
 
 7.3310 
 
 .002538071 
 
 1,237.79 
 
 121,922.07 
 
 395 
 
 156,025 
 
 61,629,875 
 
 19.8746 
 
 7.3372 
 
 .002531646 
 
 1,240.93 
 
 122,541.75 
 
 396 
 
 156,816 
 
 62,099,136 
 
 19.8997 
 
 7.3434 
 
 .002525253 
 
 1,244.07 
 
 123,163.00 
 
 397 
 
 157,609 
 
 62,570,773 
 
 19.9249 
 
 7.3496 
 
 .002518892 
 
 1,247.21 
 
 123,785.82 
 
 398 
 
 158,404 
 
 63,044,792 
 
 19.9499 
 
 7.3558 
 
 .002512563 
 
 1,250.35 
 
 124,410.21 
 
 399 
 
 159,201 
 
 63,521,199 
 
 19.9750 
 
 7.3619 
 
 .002506266 
 
 1,253.50 
 
 125,036.17 
 
 400 
 
 160,000 
 
 64,000,000 
 
 20.0000 
 
 7.3681 
 
 .002500000 
 
 1,256.64 
 
 125,663.71 
 
 401 
 
 160,801 
 
 64,481,201 
 
 20.0250 
 
 7.3742 
 
 .002493766 
 
 1,259.78 
 
 126,292.81 
 
 402 
 
 161,604 
 
 64,964,808 
 
 20.0499 
 
 7.3803 
 
 .002487562 
 
 1,262.92 
 
 126,923.48 
 
 403 
 
 162,409 
 
 65,450,827 
 
 20.0749 
 
 7.3864 
 
 .002481390 
 
 1,266.06 
 
 127,555.73 
 
 404 
 
 163,216 
 
 65,939,264 
 
 20.0998 
 
 7.3925 
 
 .002475248 
 
 1,269.20 
 
 128.189.55 
 
 405 
 
 164,025 
 
 66,430,125 
 
 20.1246 
 
 7.3986 
 
 .002469136 
 
 1.272.35 
 
 128,824.93 
 
 406 
 
 164,836 
 
 66,923,416 
 
 20.1494 
 
 7.4047 
 
 .002463054 
 
 1,275.49 
 
 129,461.89 
 
 407 
 
 165,649 
 
 67,419,143 
 
 20.1742 
 
 7.4108 
 
 .002457002 
 
 1,278.63 
 
 130,100.42 
 
 408 
 
 166,464 
 
 67,917,312 
 
 20.1990 
 
 7.4169 
 
 .002450980 
 
 1,281.77 
 
 130,740.52 
 
 409 
 
 167,281 
 
 68,417,929 
 
 20.2237 
 
 7.4229 
 
 .002444988 
 
 1,284.91 
 
 131,382.19 
 
 410 
 
 168,100 
 
 68,921,000 
 
 20.2485 
 
 7.4290 
 
 .002439024 
 
 1,288.05 
 
 132,025.43 
 
 411 
 
 168,921 
 
 69,426,531 
 
 20.2731 
 
 7.4350 
 
 .002433090 
 
 1,291.19 
 
 132,670.24 
 
 412 
 
 169,744 
 
 69,934,528 
 
 20.2978 
 
 7.4410 
 
 .002427184 
 
 1,294.34 
 
 133,316.63 
 
 413 
 
 170,569 
 
 70,444,997 
 
 20.3224 
 
 7.4470 
 
 .002421308 
 
 1,297.48 
 
 133,964.58 
 
 414 
 
 171,396 
 
 70,957,944 
 
 20.3470 
 
 7.4530 
 
 .002415459 
 
 1,300.62 
 
 134,614.10 
 
 415 
 
 172,225 
 
 71,473,375 
 
 20.3715 
 
 7.4590 
 
 .002409639 
 
 1,303.76 
 
 135,265.20 
 
 416 
 
 173,056 
 
 71,991,296 
 
 20.3961 
 
 7.4650 
 
 .002406846 
 
 1,306.90 
 
 135,917.86 
 
 417 
 
 173,889 
 
 72,511,713 
 
 20.4206 
 
 7.4710 
 
 .002398082 
 
 1,310.04 
 
 136,572.10 
 
 418 
 
 174,724 
 
 73,034,632 
 
 20.4450 
 
 7.4770 
 
 .002392344 
 
 1,313.19 
 
 137,227.91 
 
 419 
 
 175,561 
 
 73,560,059 
 
 20.4695 
 
 7.4829 
 
 .002386635 
 
 1,316.33 
 
 137,885.29 
 
 420 
 
 176,400 
 
 74,088,000 
 
 20.4939 
 
 7.4889 
 
 .002380952 
 
 1,319.47 
 
 138,544.24 
 
 421 
 
 177,241 
 
 74,618,461 
 
 20.5183 
 
 7.4948 
 
 .002375297 
 
 1,322.61 
 
 139,204.76 
 
 422 
 
 178,084 
 
 75,151,448 
 
 20.5426 
 
 7.5007 
 
 .002369668 
 
 1,325.75 
 
 139,866.85 
 
 423 
 
 178,929 
 
 75,686,967 
 
 20.5670 
 
 7.5067 
 
 .002364066 
 
 1,328.89 
 
 140,530.51 
 
 424 
 
 179,776 
 
 76,225,024 
 
 20.5913 
 
 7.5126 
 
 .002358491 
 
 1,332.04 
 
 141,195.74 
 
 425 
 
 180,625 
 
 76,765,625 
 
 20.6155 
 
 7.5185 
 
 .002352941 
 
 1,335.18 
 
 141,862.54 
 
 426 
 
 181,476 
 
 77,308,776 
 
 20.6398 
 
 7.5244 
 
 .002347418 
 
 1,338.32 
 
 142,530.92 
 
 427 
 
 182J329 
 
 77,854,483 
 
 20.6640 
 
 7.5302 
 
 .002341920 
 
 1,341.46 
 
 143,200.86 
 
 428 
 
 183,184 
 
 78,402,752 
 
 20.6882 
 
 7.5361 
 
 .002336449 
 
 1,344.60 
 
 143,872.38 
 
 429 
 
 184,041 
 
 78,953,589 
 
 20.7123 
 
 7.5420 
 
 .002331002 
 
 1,347.74 
 
 144,545.46 
 
 430 
 
 184[900 
 
 79,507,000 
 
 20.7364 
 
 7.5478 
 
 .002325581 
 
 1,350.88 
 
 145,220.12 
 
 431 
 
 185,761 
 
 80,062,991 
 
 20.7605 
 
 7.5537 
 
 .002320186 
 
 1,354.03 
 
 145.896.35 
 
 432 
 
 186' 624 
 
 80,621,568 
 
 20.7846 
 
 7.5595 
 
 .002314815 
 
 1,357.17 
 
 146,574.15 
 
 433 
 
 187,489 
 
 81,182,737 
 
 20.8087 
 
 7.5654 
 
 .002309469 
 
 1,360.31 
 
 147,253.52 
 
1088 
 
 SQUARES, CUBES, SQUARE AND CUBE ROOTS 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 434 
 
 188,356 
 
 81,746,504 
 
 20.8327 
 
 7.5712 
 
 .002304147 
 
 1,363.45 
 
 147,934.46 
 
 435 
 
 189,225 
 
 82,312,875 
 
 20.8567 
 
 7.5770 
 
 .002298851 
 
 1,366.59 
 
 148,616.97 
 
 436 
 
 190,096 
 
 82,881,856 
 
 20.8806 
 
 7.5828 
 
 .002293578 
 
 1,369.73 
 
 149,301.05 
 
 437 
 
 190,969 
 
 83,453,453 
 
 20.9045 
 
 7.5886 
 
 .002288330 
 
 1,372.88 
 
 149,986.70 
 
 438 
 
 191,844 
 
 84,027,672 
 
 20.9284 
 
 7.5944 
 
 .002283105 
 
 1,376.02 
 
 150,673.93 
 
 439 
 
 192,721 
 
 84,604,519 
 
 20.9523 
 
 7.6001 
 
 .002277904 
 
 1,379.16 
 
 151,362.72 
 
 440 
 
 193,600 
 
 85,184,000 
 
 20.9762 
 
 7.6059 
 
 .002272727 
 
 1,382.30 
 
 152,053.08 
 
 441 
 
 194,481 
 
 85,766,121 
 
 21.0000 
 
 7.6117 
 
 .002267574 
 
 1,385.44 
 
 152,745.02 
 
 442 
 
 195,364 
 
 86,350,888 
 
 21.0238 
 
 7.6174 
 
 .002262443 
 
 1,388.58 
 
 153,438.53 
 
 443 
 
 196,249 
 
 86,938,307 
 
 21.0476 
 
 7.6232 
 
 .002257336 
 
 1,391.73 
 
 154,133.60 
 
 444 
 
 197,136 
 
 87,528,384 
 
 21.0713 
 
 7.6289 
 
 .002252252 
 
 1,394.87 
 
 154,830.25 
 
 445 
 
 198,025 
 
 88,121,125 
 
 21.0950 
 
 7.6346 
 
 .002247191 
 
 1,398.01 
 
 155,528.47 
 
 446 
 
 198,916 
 
 88,716,536 
 
 21.1187 
 
 7.6403 
 
 .002242152 
 
 1,401.15 
 
 156,228.26 
 
 447 
 
 199,809 
 
 89,314,623 
 
 21.1424 
 
 7.6460 
 
 .002237136 
 
 1,404.29 
 
 156,929.62 
 
 448 
 
 200,704 
 
 89,915,392 
 
 21.1660 
 
 7.6517 
 
 .002232143 
 
 1,407.43 
 
 157,632.55 
 
 449 
 
 201,601 
 
 90,518,849 
 
 21.1896 
 
 7.6574 
 
 .002227171 
 
 1,410.58 
 
 158,337.06 
 
 450 
 
 202,500 
 
 91,125,000 
 
 21.2132 
 
 7.6631 
 
 .002222222 
 
 1,413.72 
 
 159,043.13 
 
 451 
 
 203,401 
 
 91,733,851 
 
 21.2368 
 
 7.6688 
 
 .002217295 
 
 1,416.86 
 
 159,750.77 
 
 452 
 
 204,304 
 
 92,345,408 
 
 21.2603 
 
 7.6744 
 
 .002212389 
 
 1,420.00 
 
 160,459.99 
 
 453 
 
 205,209 
 
 92,959,677 
 
 21.2838 
 
 7.6801 
 
 .002207506 
 
 1,423.14 
 
 161,170.77 
 
 454 
 
 206,116 
 
 93,576,664 
 
 21.3073 
 
 7.6857 
 
 .002202643 
 
 1,426.28 
 
 161,883.13 
 
 455 
 
 207,025 
 
 94,196,375 
 
 21.3307 
 
 7.6914 
 
 .002197802 
 
 1,429.42 
 
 162,597.05 
 
 456 
 
 207,936 
 
 94,818,816 
 
 21.3542 
 
 7.6970 
 
 .002192982 
 
 1,432.57 
 
 163,312.55 
 
 457 
 
 208,849 
 
 95,443,993 
 
 21.3776 
 
 7.7026 
 
 .002188184 
 
 1,435.71 
 
 164,029.62 
 
 458 
 
 209,764 
 
 96,071,912 
 
 21.4009 
 
 7.7082 
 
 .002183406 
 
 1,438.85 
 
 164,748.26 
 
 459 
 
 210,681 
 
 96,702,579 
 
 21.4243 
 
 7.7188 
 
 .002178649 
 
 1,441.99 
 
 165,468.47 
 
 460 ' 
 
 211,600 
 
 97,336,000 
 
 21.4476 
 
 7.7194 
 
 .002173913 
 
 1,445.13 
 
 166,190.25 
 
 461 
 
 212,521 
 
 97,972,181 
 
 21.4709 
 
 7.7250 
 
 .002169197 
 
 1,448.27 
 
 166,913.60 
 
 462 
 
 213,444 
 
 98,611,128 
 
 21.4942 
 
 7.7306 
 
 .002164502 
 
 1,451.42 
 
 167,638.53 
 
 463 
 
 214,369 
 
 99,252,847 
 
 21.5174 
 
 7.7362 
 
 .002159827 
 
 1,454.56 
 
 168,365.02 
 
 464 
 
 215,296 
 
 99,897,344 
 
 21.5407 
 
 7.7418 
 
 .002155172 
 
 1,457.70 
 
 169,093.08 
 
 465 
 
 216,225 
 
 100,544,625 
 
 21.5639 
 
 7.7473 
 
 .002150538 
 
 1,460.84 
 
 169,822.72 
 
 466 
 
 217,156 
 
 101,194,696 
 
 21.5870 
 
 7.7529 
 
 .002145923 
 
 1,463.98 
 
 170,553.92 
 
 467 
 
 218,089 
 
 101,847,563 
 
 21.6102 
 
 7.7584 
 
 .002141328 
 
 1,467.12 
 
 171,286.70 
 
 468 
 
 219,024 
 
 102,503,232 
 
 21.6333 
 
 7.7639 
 
 .002136752 
 
 1,470.27 
 
 172,021.05 
 
 469 
 
 219,961 
 
 103,161,709 
 
 21.6564 
 
 7.7695 
 
 .002132196 
 
 1,473.41 
 
 172,756.97 
 
 470 
 
 220,900 
 
 103,823,000 
 
 21.6795 
 
 7.7750 
 
 .002127660 
 
 1,476.55 
 
 173,494.45 
 
 471 
 
 221,841 
 
 104,487,111 
 
 21.7025 
 
 7.7805 
 
 .002123142 
 
 1,479.69 
 
 174,233.51 
 
 472 
 
 222,784 
 
 105,154,048 
 
 21.7256 
 
 7.7860 
 
 .002118644 
 
 1,482.83 
 
 174,974.14 
 
 473 
 
 223,729 
 
 105,823,817 
 
 21.7486 
 
 7.7915 
 
 .002114165 
 
 1,485.97 
 
 175,716.35 
 
 474 
 
 224,676 
 
 106,496,424 
 
 21.7715 
 
 7.7970 
 
 .002109705 
 
 1,489.11 
 
 176,460.12 
 
 475 
 
 225,625 
 
 107,171,875 
 
 21.7945 
 
 7.8025 
 
 .002105263 
 
 1,492.26 
 
 177,205.46 
 
 476 
 
 226,576 
 
 107,850,176 
 
 21.8174 
 
 7.8079 
 
 .002100840 
 
 1,495.40 
 
 177,952.37 
 
 477 
 
 227,529 
 
 108,531,333 
 
 21.8403 
 
 7.8134 
 
 .002096486 
 
 1,498.54 
 
 178,700.86 
 
 478 
 
 228,484 
 
 109,215,352 
 
 21.8632 
 
 7.8188 
 
 .002092050 
 
 1,501.68 
 
 179,450.91 
 
 479 
 
 229,441 
 
 109,902,239 
 
 21.8861 
 
 7.8243 
 
 .002087683 
 
 1,504.82 
 
 180,202.54 
 
 480 
 
 230,400 
 
 110,592,000 
 
 21.9089 
 
 7.8297 
 
 .002083333 
 
 1,507.96 
 
 180,955.74 
 
 481 
 
 231,361 
 
 111,284,641 
 
 21.9317 
 
 7.8352 
 
 .002079002 
 
 1,511.11 
 
 181,710.50 
 
 482 
 
 232,324 
 
 111,980,168 
 
 21.9545 
 
 7.8406 
 
 .002074689 
 
 1,514.25 
 
 182,466.84 
 
 483 
 
 233,289 
 
 112,678,587 
 
 21.9775 
 
 7.8460 
 
 .002070393 
 
 1.517.39 
 
 183,224.75 
 
 484 
 
 234,256 
 
 113,379,904 
 
 22.0000 
 
 7.8514 
 
 .002066116 
 
 1,520.53 
 
 183,984.23 
 
 485 
 
 235,225 
 
 114,084,125 
 
 22.0227 
 
 7.8568 
 
 .002061856 
 
 1,523.67 
 
 184,745.28 
 
 486 
 
 236,196 
 
 114,791,256 
 
 22.0454 
 
 7.8622 
 
 .002057613 
 
 1,526.81 
 
 185,507.90 
 
 487 
 
 237,169 
 
 115,501,303 
 
 22.0681 
 
 7.8676 
 
 .002053388 
 
 1,529.96 
 
 186,272.10 
 
 488 
 
 238,144 
 
 116,214,272 
 
 22.0907 
 
 7.8730 
 
 .002049180 
 
 1,533.10 
 
 187,037.86 
 
 489 
 
 239,121 
 
 116,930,169 
 
 22.1133 
 
 7.8784 
 
 .002044990 
 
 1,536.24 
 
 87,805.19 
 
 490 
 
 240,100 
 
 117,649,000 
 
 22.1359 
 
 7.8837 
 
 .002040816 
 
 1,539.38 
 
 188,574.10 
 
 491 
 
 241,081 
 
 118,370,771 
 
 22.1585 
 
 7.8891 
 
 .002036660 
 
 1,542.52 
 
 89,344.57 
 
 492 
 
 242,064 
 
 119,095,488 
 
 22.1811 
 
 7.8944 
 
 .002032520 
 
 1,545.66 
 
 190,116.62 
 
 493 
 
 243,049 
 
 119,823,157 
 
 22.2036 
 
 7.8998 
 
 .002028398 
 
 1,548.81 
 
 190,890.24 
 
 494 
 
 244,036 
 
 120,553,784 
 
 22.2261 
 
 7.9051 
 
 .002024291 
 
 1,551.95 
 
 91,665.43 
 
 495 
 
 245,025 
 
 121,287,375 
 
 22.2486 
 
 7.9105 
 
 .002020292 
 
 1,555.09 
 
 92,442.18 
 
 496 
 
 246,016 
 
 122,023,936 
 
 22.2711 
 
 7.9158 
 
 .002016129 
 
 1,558.23 
 
 193,220.51 
 
CIRCUMFERENCES, AND AREAS 1089 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 497 
 
 247,009 
 
 122,763,473 
 
 22.2935 
 
 7.9211 
 
 .002012072 
 
 1,561.37 
 
 194,000.41 
 
 498 
 
 248,004 
 
 123,505,992 
 
 22.3159 
 
 7.9264 
 
 .002008032 
 
 1,564.51 
 
 194,781.89 
 
 499 
 
 249,001 
 
 124,251,499 
 
 22.3383 
 
 7.9317 
 
 .002004008 
 
 1,567.65 
 
 195,564.93 
 
 500 
 
 250,000 
 
 125,000,000 
 
 22.3607 
 
 7.9370 
 
 .002000000 
 
 1,570.80 
 
 196,349.54 
 
 501 
 
 251,001 
 
 125,751,501 
 
 22.3830 
 
 7.9423 
 
 .001996008 
 
 1,573.94 
 
 197,135.72 
 
 502 
 
 252,004 
 
 126,506,008 
 
 22.4054 
 
 7.9476 
 
 .001992032 
 
 1,577.08 
 
 197,923.48 
 
 503 
 
 253,009 
 
 127,263,527 
 
 22.4277 
 
 7.9528 
 
 .001988072 
 
 1,580.22 
 
 198,712.80 
 
 504 
 
 254,016 
 
 128,024,064 
 
 22.4499 
 
 7.9581 
 
 .001984127 
 
 1,583.36 
 
 199,503.70 
 
 505 
 
 255,025 
 
 128,787,625 
 
 22.4722 
 
 7.9634 
 
 .001980198 
 
 1,586.50 
 
 200,296.17 
 
 506 
 
 256,036 
 
 129,554,216 
 
 22.4944 
 
 7.9686 
 
 .001976285 
 
 1,589.65 
 
 201,090.20 
 
 507 
 
 257,049 
 
 130,323,843 
 
 22.5167 
 
 7.9739 
 
 .001972387 
 
 1,592.79 
 
 201,885.81 
 
 508 
 
 258,064 
 
 131,096,512 
 
 22.5389 
 
 7.9791 
 
 .001968504 
 
 1,595.93 
 
 202,682.99 
 
 509 
 
 259,081 
 
 131,872,229 
 
 22.5610 
 
 7.9843 
 
 .001964637 
 
 1,599.07 
 
 203,481.74 
 
 510 
 
 260,100 
 
 132,651,000 . 
 
 22.5832 
 
 7.9895 
 
 .001960785 
 
 1,602.21 
 
 204,282.06 
 
 511 
 
 261,121 
 
 133,432,831 
 
 22.6053 
 
 7.9948 
 
 .001956947 
 
 1,605.35 
 
 205,083.95 
 
 512 
 
 262,144 
 
 134,217,728 
 
 22.6274 
 
 8.0000 
 
 .001953125 
 
 1,608.50 
 
 205; 887.42 
 
 513 
 
 263,169 
 
 135,005,697 
 
 22.6495 
 
 8.0052 
 
 .001949318 
 
 1,611.64 
 
 206,692.45 
 
 514 
 
 264,196 
 
 135,796,744 
 
 22.6716 
 
 8.0104 
 
 .001945525 
 
 1,614.78 
 
 207,499.05 
 
 515 
 
 265,225 
 
 136,590,875 
 
 22.6936 
 
 8.0156 
 
 .001941748 
 
 1,617.92 
 
 208,307.23 
 
 516 
 
 266,256 
 
 137,388,096 
 
 22.7156 
 
 8.0208 
 
 .001937984 
 
 1,621.06 
 
 209,116.97 
 
 517 
 
 267,289 
 
 138,188,413 
 
 22.7376 
 
 8.0260 
 
 .001934236 
 
 1,624.20 
 
 209,928.29 
 
 518 
 
 268,324 
 
 138,991,832 
 
 22.7596 
 
 8.0311 
 
 .001930502 
 
 1,627.34 
 
 210,741.18 
 
 519 
 
 269,361 
 
 139,798,359 
 
 22.7816 
 
 8.0363 
 
 .001926782 
 
 1,630.49 
 
 211,555.63 
 
 520 
 
 270,400 
 
 140,608,000 
 
 22.8035 
 
 8.0415 
 
 .001923077 
 
 1,633.63 
 
 212,371.66 
 
 521 
 
 271,411 
 
 141,420,761 
 
 22.8254 
 
 8.0466 
 
 .001919386 
 
 1,636.77 
 
 213,189.26 
 
 522 
 
 272,484 
 
 142,236,648 
 
 22.8473 
 
 8.0517 
 
 .001915709 
 
 1,639.91 
 
 214,008.43 
 
 523 
 
 273,529 
 
 143,055,667 
 
 22.8692 
 
 8.0569 
 
 .001912046 
 
 1,643.05 
 
 214,829.17 
 
 524 
 
 274,576 
 
 143,877,824 
 
 22.8910 
 
 8.0620 
 
 .001908397 
 
 1,646.19 
 
 215,651.49 
 
 525 
 
 275,625 
 
 144,703,125 
 
 22.9129 
 
 8.0671 
 
 .001904762 
 
 1,649.34 
 
 216,475.37 
 
 526 
 
 276,676 
 
 145,531,576 
 
 22.9347 
 
 8.0723 
 
 .001901141 
 
 1,652.48 
 
 217,300.82 
 
 527 
 
 277,729 
 
 146,363,183 
 
 22.9565 
 
 8.0774 
 
 .001897533 
 
 1,655.62 
 
 218,127.85 
 
 528 
 
 278,784 
 
 147,197,952 
 
 22.9783 
 
 8.0825 
 
 .001893939 
 
 1,658.76 
 
 218,956.44 
 
 529 
 
 279,841 
 
 148,035,889 
 
 23.0000 
 
 8.0876 
 
 .001890359 
 
 1,661.90 
 
 219,786.61 
 
 530 
 
 280,900 
 
 148,877,001 
 
 23.0217 
 
 8.0927 
 
 .001886792 
 
 1,665.04 
 
 220,618.34 
 
 531 
 
 281,961 
 
 149,721,291 
 
 23.0434 
 
 8.0978 
 
 .001883239 
 
 1,668.19 
 
 221,451.65 
 
 532 
 
 283,024 
 
 150,568,768 
 
 23.0651 
 
 8.1028 
 
 .001879699 
 
 1,671.33 
 
 222,286.53 
 
 533 
 
 284,089 
 
 151,419,437 
 
 23.0868 
 
 8.1079 
 
 .001876173 
 
 1,674.47 
 
 223,122.98 
 
 534 
 
 285,156 
 
 152,273,304 
 
 23.1084 
 
 8.1130 
 
 .001872659 
 
 1,677.61 
 
 223,961.00 
 
 535 
 
 286,225 
 
 153,130,375 
 
 23.1301 
 
 8.1180 
 
 .001869159 
 
 1,686.75 
 
 224,800.59 
 
 536 
 
 287,296 
 
 153,990,656 
 
 23.1517 
 
 8.1231 
 
 .001865672 
 
 1,683.89 
 
 225,641.75 
 
 537 
 
 288,369 
 
 154,854,153 
 
 23.1733 
 
 8.1281 
 
 .001862197 
 
 1,687.04 
 
 226,484.48 
 
 538 
 
 289,444 
 
 155,720,872 
 
 23.1948 
 
 8.1332 
 
 .001858736 
 
 1,690.18 
 
 227,328.79 
 
 539 
 
 290,521 
 
 156,590,819 
 
 23.2164 
 
 8.1382 
 
 .001855288 
 
 1,693.32 
 
 228,174.66 
 
 540 
 
 291,600 
 
 157,464,000 
 
 23.2379 
 
 8.1433 
 
 .001851852 
 
 1,696.46 
 
 229,022.10 
 
 541 
 
 292,681 
 
 158,340,421 
 
 23.2594 
 
 8.1483 
 
 .001848429 
 
 1,699.60 
 
 229,871.12 
 
 512 
 
 293,764 
 
 159,220,088 
 
 23.2809 
 
 8.1533 
 
 .001845018 
 
 1,702.74 
 
 230,721.71 
 
 543 
 
 294,849 
 
 160,103,007 
 
 23.3024 
 
 8.1583 
 
 .001841621 
 
 1,705.88 
 
 231,573.86 
 
 544 
 
 295,936 
 
 160,989,184 
 
 23.3238 
 
 8.1633 
 
 .001838235 
 
 1,709.03 
 
 232,427.59 
 
 545 
 
 297,025 
 
 161,878,625 
 
 23.3452 
 
 8.1683 
 
 .001834862 
 
 1,712.17 
 
 233,282.89 
 
 546 
 
 298,116 
 
 162,771,336 
 
 23.3666 
 
 8.1733 
 
 .001831502 
 
 1,715.31 
 
 234,139.76 
 
 547 
 
 299,209 
 
 163,667,323 
 
 23.3880 
 
 8.17&3 
 
 .001828154 
 
 1,718.45 
 
 234,998.20 
 
 548 
 
 300,304 
 
 164,566,592 
 
 23.4094 
 
 8.1833 
 
 .001824818 
 
 1,721.59 
 
 235,858.21 
 
 549 
 
 301,401 
 
 165,469,149 
 
 23.4307 
 
 8.1882 
 
 .001821494 
 
 1,724.73 
 
 236,719.79 
 
 550 
 
 302500 
 
 166,375,000 
 
 23.4521 
 
 8.1932 
 
 .001818182 
 
 1,727.88 
 
 237,582.94 
 
 551 
 
 303,601 
 
 167,284,151 
 
 23.4734 
 
 8.1982 
 
 .001814882 
 
 1,731.02 
 
 238,447.67 
 
 552 
 
 304,704 
 
 168,196,608 
 
 23.4947 
 
 8.2031 
 
 .001811594 
 
 1,734.16 
 
 239,313.96 
 
 553 
 
 305,809 
 
 169,112,377 
 
 23.5160 
 
 8.2081 
 
 .001808318 
 
 1,737.30 
 
 240,181.83 
 
 554 
 
 306,916 
 
 170,031,464 
 
 23.5372 
 
 8.2130 
 
 .001805054 
 
 1,740.44 
 
 241,051.26 
 
 555 
 
 308,025 
 
 170,953,875 
 
 23.5584 
 
 8.2180 
 
 .001801802 
 
 1,743.58 
 
 241,922.27 
 
 556 
 
 309,136 
 
 171,879,616 
 
 23.5797 
 
 8.2229 
 
 .001798561 
 
 1,746.73 
 
 242,794.85 
 
 557 
 
 310,249 
 
 172,808,693 
 
 23.6008 
 
 8.2278 
 
 .001795332 
 
 1,749.87 
 
 243,668.99 
 
 558 
 569 
 
 311,364 
 312,481 
 
 173,741,112 
 174,676,879 
 
 23.6220 
 23.6432 
 
 8.2327 
 8.2377 
 
 .001792115 
 .001788909 
 
 1,753.01 
 1,756.15 
 
 244,544.71 
 245,422.00 
 
 69 
 
1090 
 
 SQUARES, CUBES, SQUARE AND CUBE ROOTS 
 
 No 
 
 Square 
 
 Cube 
 
 Sq.Roo 
 
 Cu.Roo 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 660 
 
 313,600 
 
 175,616,000 
 
 23.664 
 
 8.2426 
 
 .001785714 
 
 1,759.29 
 
 246,300.86 
 
 561 
 
 314,721 
 
 176,558,481 
 
 23.6854 
 
 8.2475 
 
 .001782531 
 
 1,762.43 
 
 247,181.30 
 
 562 
 
 315,844 
 
 177,504,328 
 
 23.7065 
 
 8.2524 
 
 .001779359 
 
 1,765.58 
 
 248,063.30 
 
 563 
 
 316,969 
 
 178,453,547 
 
 23.7276 
 
 8.2573 
 
 .001776199 
 
 1,768.72 
 
 248,946.87 
 
 564 
 
 318,096 
 
 179,406,144 
 
 23.7487 
 
 8.2621 
 
 .001773050 
 
 1,771.86 
 
 249,832.01 
 
 565 
 
 319,225 
 
 180,362,125 
 
 23.7697 
 
 8.2670 
 
 .001769912 
 
 1,775.00 
 
 250,718.73 
 
 566 
 
 320,356 
 
 181,321,496 
 
 23.7908 
 
 8.2719 
 
 .001766784 
 
 1,778.14 
 
 251,607.01 
 
 567 
 
 321,489 
 
 182,284,263 
 
 23.8118 
 
 8.2768 
 
 .001763668 
 
 1,781.28 
 
 252,496.87 
 
 568 
 
 322,624 
 
 183,250,432 
 
 23.8328 
 
 8.2816 
 
 .001760563 
 
 1,784.42 
 
 253,388.30 
 
 569 
 
 323,761 
 
 184,220,009 
 
 23.8537 
 
 8.2865 
 
 .001757469 
 
 1,787.57 
 
 254,281.29 
 
 570 
 
 324,900 
 
 185,193,000 
 
 23.8747 
 
 8.2913 
 
 .001754386 
 
 1,790.71 
 
 255,175.86 
 
 571 
 
 326,041 
 
 186,169,411 
 
 23.8956 
 
 8.2962 
 
 .001751313 
 
 1,793.85 
 
 256,072.00 
 
 572 
 
 327,184 
 
 187,149,248 
 
 23.9165 
 
 8.3010 
 
 .001748252 
 
 1,796.99 
 
 256,969.71 
 
 573 
 
 328,329 
 
 188,132,517 
 
 23.9374 
 
 8.3059 
 
 .001745201 
 
 1,800.13 
 
 257,868.99 
 
 674 
 
 329,476 
 
 189,119,224 
 
 23.9583 
 
 8.3107 
 
 .001742164 
 
 1,803.27 
 
 258,769.85 
 
 575 
 
 330,625 
 
 190,109,375 
 
 23.9792 
 
 8.3155 
 
 .001739130 
 
 1,806.42 
 
 259,672.27 
 
 576 
 
 331,776 
 
 191,102,976 
 
 24.0000 
 
 8.3203 
 
 .001736111 
 
 1,809.56 
 
 260,576.26 
 
 577 
 
 332,929 
 
 192,100,033 
 
 24.0208 
 
 8.3251 
 
 .001733102 
 
 1,812.70 
 
 261,481.83 
 
 578 
 
 334,084 
 
 193,100,552 
 
 24.0416 
 
 8.3300 
 
 .001730104 
 
 1,815.84 
 
 262,388.96 
 
 579 
 
 335,241 
 
 194,104,539 
 
 24.0624 
 
 8.3348 
 
 .001727116 
 
 1,818.98 
 
 263,297.67 
 
 580 
 
 336,400 
 
 195,112,000 
 
 24.0832 
 
 8.3396 
 
 .001724138 
 
 ,822.12 
 
 264,207.94 
 
 581 
 
 337,561 
 
 196,122,941 
 
 24.1039 
 
 8.3443 
 
 .001721170 
 
 ,825.27 
 
 65,119.79 
 
 582 
 
 338,724 
 
 197,137,368 
 
 24.1247 
 
 8.3491 
 
 .001718213 
 
 ,828.41 
 
 66,033.21 
 
 583 
 
 339,889 
 
 198,155,287 
 
 24.1454 
 
 8.3539 
 
 .001715266 
 
 ,831.55 
 
 66,948.20 
 
 584 
 
 341,056 
 
 199,176,704 
 
 24.1661 
 
 8.3587 
 
 .001712329 
 
 ,834.69 
 
 67,864.76 
 
 585 
 
 342,225 
 
 200,201,625 
 
 24.1868 
 
 8.3634 
 
 .001709402 
 
 ,837.83 
 
 68,782.89 
 
 586 
 
 343,396 
 
 201,230,056 
 
 24.2074 
 
 8.3682 
 
 .001706485 
 
 ,840.97 
 
 69,702.59 
 
 587 
 
 344,569 
 
 202,262,003 
 
 24.2281 
 
 8.3730 
 
 .001703578 
 
 ,844.11 
 
 270,623.86 
 
 588 
 
 345,744 
 
 203,297,472 
 
 24.2487 
 
 8.3777 
 
 .001700680, 
 
 ,847.26 
 
 271,546.70 
 
 589 
 
 346,921 
 
 204,336,469 
 
 24.2693 
 
 8.3825 
 
 .001697793 
 
 ,850.40 
 
 272,471.12 
 
 590 
 
 348,100 
 
 205,379,000 
 
 24.2899 
 
 8.3872 
 
 .001694915 
 
 ,853.54 
 
 273,397.10 
 
 591 
 
 349,281 
 
 206,425,071 
 
 24.3105 
 
 8.3919 
 
 .001692047 
 
 856.68 
 
 274,324.66 
 
 592 
 
 350,464 
 
 207,474,688 
 
 24.3311 
 
 8.3967 
 
 .001689189 
 
 859.82 
 
 275,253.78 
 
 593 
 
 351,649 
 
 208,527,857 
 
 24.3516 
 
 8.4014 
 
 .001686341 
 
 862.96 
 
 276,184.48 
 
 594 
 
 352,836 
 
 209,584,584 
 
 24.3721 
 
 8.4061 
 
 .001683502 
 
 866.11 
 
 277,116.75 
 
 595 
 
 354,025 
 
 210,644,875 
 
 24.3926 
 
 8.4108 
 
 .001680672 
 
 869.25 
 
 278,050.58 
 
 596 
 
 355,216 
 
 211,708,736 
 
 24.4131 
 
 8.4155 
 
 .001677852 
 
 872.39 
 
 278,985.99 
 
 597 
 
 356,409 
 
 212,776,173 
 
 24.4336 
 
 8.4202 
 
 .001675042 
 
 875.53 
 
 279.922.97 
 
 598 
 
 357,604 
 
 213,847,192 
 
 24.4540 
 
 8.4249 
 
 .001672241 
 
 878.67 
 
 280,861.52 
 
 599 
 
 358,801 
 
 214,921,799 
 
 24.4745 
 
 8.4296 
 
 001669449 
 
 881.81 
 
 281,801.65 
 
 600 
 
 360,000 
 
 216,000,000 
 
 24.4949 
 
 8.4343 
 
 001666667 
 
 884.96 
 
 282,743.34 
 
 601 
 
 361,201 
 
 217,081,801 
 
 24.5153 
 
 8.4390 
 
 001663894 
 
 888.10 
 
 283,686.60 
 
 602 
 
 362,404 
 
 218,167,208 
 
 24.5357 
 
 8.4437 
 
 001661130 
 
 891.24 
 
 284,631.44 
 
 603 
 
 363,609 
 
 219,256,227 
 
 24.5561 
 
 8.4484 
 
 001658375 
 
 894.38 
 
 285,577.84 
 
 604 
 
 364,816 
 
 220,348,864 
 
 24.5764 
 
 8.4530 
 
 001655629 
 
 897.52 
 
 286,525.82 
 
 605 
 
 366,025 
 
 221,445,125 
 
 24.5968 
 
 8.4577 
 
 001652893 
 
 900.66 
 
 287,475.36 
 
 606 
 
 367,236 
 
 222,545,016 
 
 24.6171 
 
 8.4623 
 
 001650165 
 
 903.81 
 
 288,426.48 
 
 607 
 
 368,449 
 
 223,648,543 
 
 24.6374 
 
 8.4670 
 
 001647446 
 
 906.95 
 
 289,379.17 
 
 608 
 
 369,664 
 
 224,755,712 
 
 24.6577 
 
 8.4716 
 
 001644737 
 
 910.09 
 
 290,333.43 
 
 609 
 
 370,881 
 
 225,866,529 
 
 4.6779 
 
 8.4763 
 
 001642036 
 
 913.23 
 
 291,289.26 
 
 610 
 
 372,100 
 
 226,981,000 
 
 24.6982 
 
 8.4809 
 
 001639344 
 
 916.37 . 
 
 292,246.66 
 
 611 
 
 373,321 
 
 228,099,131 
 
 24.7184 
 
 8.4856 
 
 001636661 
 
 919.51 
 
 293,205.63 
 
 612 
 
 374,544 
 
 229,220,928 
 
 4.7386 
 
 8.4902 
 
 001633987 
 
 922.65 
 
 294,166.17 
 
 613 
 
 375,769 
 
 230,346,397 
 
 4.7588 
 
 8.4948 
 
 001631321 
 
 925.80 
 
 295.128.28 
 
 614 
 
 376,996 
 
 231,475,544 
 
 4.7790 
 
 8.4994 
 
 001628664 
 
 928.94 1296,091.97 
 
 615 
 
 378,225 
 
 232,608,375 
 
 4.7992 
 
 8.5040 
 
 001626016 
 
 932.08 J 
 
 J97.057.22 
 
 616 
 
 379,456 
 
 233,744,896 
 
 24.8193 
 
 8.5086 
 
 001623377 
 
 935.22 I 
 
 298,024.05 
 
 617 
 
 380,689 
 
 234,885,113 
 
 24.8395 
 
 8.5132 
 
 001620746 
 
 938.36 I 
 
 598,992.44 
 
 618 
 
 381,924 
 
 236,029,032 
 
 24.8596 
 
 8.5178 
 
 001618123 
 
 941.50 J 
 
 !99,962.41 
 
 619 
 
 383,161 
 
 237,176,659 
 
 24.8797 
 
 8.5224 
 
 001615509 
 
 944.65 c 
 
 00,933.95 
 
 620 
 
 384,400 
 
 238,328,000 
 
 4.8998 
 
 8.5270 
 
 001612903 
 
 947.79 r c 
 
 01,907.05 
 
 621 
 
 385,641 
 
 239,483,061 
 
 24.9199 
 
 8.5316 
 
 001610306 
 
 950.93 ? 
 
 02,881.73 
 
 622 
 
 386,884 
 
 240,641,848 
 
 4.9399 
 
 8.5362 
 
 001607717 
 
 954.07 2 
 
 .03,857.98 
 
CIRCUMFERENCES, AND AREAS 
 
 1091 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Boot 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 623 
 
 388,129 
 
 241,804,367 
 
 24.9600 
 
 8.5408 
 
 .001605136 
 
 1,957.21 
 
 304,835.80 
 
 624 
 
 389,376 
 
 242,970,624 
 
 24.9800 
 
 8.5453 
 
 .001602564 
 
 1,960.35 
 
 305,815.20 
 
 625 
 
 390,625 
 
 244,140,625 
 
 25.0000 
 
 8.5499 
 
 .001600000 
 
 1,963.50 
 
 306,796.16 
 
 626 
 
 391,876 
 
 245,314,376 
 
 25.0200 
 
 8.5544 
 
 .001597444 
 
 1,966.64 
 
 307,778.69 
 
 627 
 
 393,129 
 
 246,491,883 
 
 25.0400 
 
 8.5589 
 
 .001594896 
 
 1,969.78 
 
 308,762.79 
 
 628 
 
 394,384 
 
 247,673,152 
 
 25.0599 
 
 8.5635 
 
 .001592357 
 
 1,972.92 
 
 309,748.47 
 
 629 
 
 395,641 
 
 248,858,189 
 
 25.0799 
 
 8.5681 
 
 .001589825 
 
 1,976.06 
 
 310,735.71 
 
 630 
 
 396,900 
 
 250,047,000 
 
 25.0998 
 
 8.5726 
 
 .001587302 
 
 1,979.20 
 
 311,724.53 
 
 631 
 
 398,161 
 
 251,239,591 
 
 25.1197 
 
 8.5772 
 
 .001584786 
 
 1,982.35 
 
 312,714.92 
 
 632 
 
 399,424 
 
 252,435,968 
 
 25.1396 
 
 8.5817 
 
 .001582278 
 
 1,985.49 
 
 313,706.88 
 
 633 
 
 400,689 
 
 253,636,137 
 
 25.1595 
 
 8.5862 
 
 .001579779 
 
 1,988.63 
 
 314,700.40 
 
 634 
 
 401,956 
 
 254,840,104 
 
 25.1794 
 
 8.5907 
 
 .001577287 
 
 1,991.77 
 
 315,695.50 
 
 635 
 
 403,225 
 
 256,047,875 
 
 25.1992 
 
 8.5952 
 
 .001574803 
 
 1,994.91 
 
 316,692.17 
 
 636 
 
 404,496 
 
 257,259,456 
 
 25.2190 
 
 8.5997 
 
 .D01572327 
 
 1,998.05 
 
 317,690.42 
 
 637 
 
 405,769 
 
 258,474,853 
 
 25.2389 
 
 8.6043 
 
 .001569859 
 
 2,001.19 
 
 318,690.23 
 
 638 
 
 407,044 
 
 259,694,072 
 
 25.2587 
 
 8.6088 
 
 .001567398 
 
 2,004.34 
 
 319,691.61 
 
 639 
 
 408,321 
 
 260,917,119 
 
 25.2784 
 
 8.6132 
 
 .001564945 
 
 2,007.48 
 
 320,694.56 
 
 ; 640 
 
 409,600 
 
 262,144,000 
 
 25.2982 
 
 8.6177 
 
 .001562500 
 
 2,010.62 
 
 321,699.09 
 
 641 
 
 410,881 
 
 263,374,721 
 
 25.3180 
 
 8.6222 
 
 .001560062 
 
 2,013.76 
 
 322.705.18 
 
 642 
 
 412,164 
 
 264,609,288 
 
 25.3377 
 
 8.6267 
 
 .001557632 
 
 2,016.90 
 
 323,712.85 
 
 643 
 
 413,449 
 
 265,847,707 
 
 25.3574 
 
 8.6312 
 
 .001555210 
 
 2,020.04 
 
 324,722.09 
 
 644 
 
 414,736 
 
 267,089,984 
 
 25.3772 
 
 8.6357 
 
 .001552795 
 
 2,023.19 
 
 325,732.89 
 
 645 
 
 416,125 
 
 268,336,125 
 
 25.3969 
 
 8.6401 
 
 .001550388 
 
 2,026.33 
 
 326,745.27 
 
 646 
 
 417,316 
 
 269,585,136 
 
 25.4165 
 
 8.6446 
 
 .001547988 
 
 2,029.47 
 
 327,759.22 
 
 647 
 
 418,609 
 
 270,840,023 
 
 25.4362 
 
 8.6490 
 
 .001545595 
 
 2,032.61 
 
 328,774.74 
 
 648 
 
 419,904 
 
 272,097,792 
 
 25.4558 
 
 8.6535 
 
 .001543210 
 
 2,035.75 
 
 329,791.83 
 
 649 
 
 421,201 
 
 273,359,449 
 
 25.4755 
 
 8.6579 
 
 .001540832 
 
 2,038.89 
 
 330,810.49 
 
 650 
 
 422,500 
 
 274,625,000 
 
 25.4951 
 
 8.6624 
 
 .001538462 
 
 2,042.04 
 
 331,830.72 
 
 651 
 
 423,801 
 
 275,894,451 
 
 25.5147 
 
 8.6668 
 
 .001536098 
 
 2,045.18 
 
 332,852.53 
 
 652 
 
 425,104 
 
 277,167,808 
 
 25.5343 
 
 8.6713 
 
 .001533742 
 
 2,048.32 
 
 333,875.90 
 
 653 
 
 426,409 
 
 278,445,077 
 
 25.5539 
 
 8.6757 
 
 .001531394 
 
 2,051.46 
 
 334,900.85 
 
 654 
 
 427,716 
 
 279,726,264 
 
 25.5734 
 
 8.6801 
 
 .001529052 
 
 2,054.60 
 
 335,927.36 
 
 655 
 
 429,025 
 
 281,011,375 
 
 25.5930 
 
 8.6845 
 
 .001526718 
 
 2,057.74 
 
 336,955.45 
 
 656 
 
 430,336 
 
 282,300,416 
 
 25.6125 
 
 8.6890 
 
 .001524390 
 
 2,060.88 
 
 337,985.10 
 
 657 
 
 431,639 
 
 283,593,393 
 
 25.6320 
 
 8.6934 
 
 .001522070 
 
 2,064.03 
 
 339,016.33 
 
 658 
 
 432,964 
 
 284,890,312 
 
 25.6515 
 
 8.6978 
 
 .001519751 
 
 2,067.17 
 
 340,049.13 
 
 659 
 
 434,281 
 
 286,191,179 
 
 25.6710 
 
 8.7022 
 
 .001517451 
 
 2,070.31 
 
 341,083.50 
 
 660 
 
 435,600 
 
 287,496,000 
 
 25.6905 
 
 8.7066 
 
 .001515152 
 
 2,073.45 
 
 342,119.44 
 
 661 
 
 436,921 
 
 288,804,781 
 
 25.7099 
 
 8.7110 
 
 .001512859 
 
 2,076.59 
 
 343,156.95 
 
 1 662 
 
 438,244 
 
 290,117,528 
 
 25.7294 
 
 8.7154 
 
 .001510574 
 
 2,079.73 
 
 344,196.03 
 
 1 663 
 
 439,569 
 
 291,434,247 
 
 25.7488 
 
 8.7198 
 
 .001508296 
 
 2,082.88 
 
 345,236.69 
 
 1 664 
 
 440,896 
 
 292,754,944 
 
 25.7682 
 
 8.7241 
 
 .001506024 
 
 ,086.02 
 
 346,278.91 
 
 I 665 
 
 442,225 
 
 294,079,625 
 
 25.7876 
 
 8.7285 
 
 .001503759 
 
 ,089.16 
 
 347,322.70 
 
 1 666 
 
 443,556 
 
 295,408,296 
 
 25.8070 
 
 8.7329 
 
 .001501502 
 
 ,092.30 
 
 348,368.07 
 
 II 667 
 
 444,899 
 
 296,740,963 
 
 25.8263 
 
 8.7373 
 
 .001499250 
 
 ,095.44 
 
 349,415.00 
 
 II 668 
 
 446,224 
 
 298,077,632 
 
 25.8457 
 
 8.7416 
 
 .001497006 
 
 ,098.58 
 
 350,463.51 
 
 1 669 
 
 447,561 
 
 299,418,309 
 
 25.8650 
 
 8.7460 
 
 .001494768 
 
 ,101.73 
 
 351,513.59 
 
 1 670 
 
 448,900 
 
 300,763,000 
 
 25.8844 
 
 8.7593 
 
 .001492537 
 
 ,104.87 
 
 352,565.24 
 
 I 671 
 
 450,241 
 
 302,111,711 
 
 25.9037 
 
 8.7547 
 
 .001490313 
 
 ,108.01 
 
 353,618.45 
 
 II 672 
 
 451,584 
 
 303,464,448 
 
 25.9230 
 
 8.7590 
 
 .001488095 
 
 ,111.15 
 
 354,673.24 
 
 1 673 
 
 452,929 
 
 304,821,217 
 
 25.9422 
 
 8.7634 
 
 .001485884 
 
 ,114.29 
 
 355,729.60 
 
 1 C74 
 
 454,276 
 
 306,182,024 
 
 25.9615 
 
 8.7677 
 
 .001483680 
 
 ,117.43 
 
 356,787.54 
 
 1 675 
 
 455,625 
 
 307,546,875 
 
 25.9808 
 
 8.7721 
 
 .001481481 
 
 ,120.58 
 
 357,847.04 
 
 1 676 
 
 456,976 
 
 308,915,776 
 
 26.0000 
 
 8.7764 
 
 .001479290 
 
 ,123.72 
 
 358,908.11 
 
 1 677 
 
 458,329 
 
 310,288,733 
 
 26.0192 
 
 8.7807 
 
 .001477105 
 
 ,126.86 
 
 359,970.75 
 
 I 1 678 
 
 459,684 
 
 311,665,752 
 
 26.0384 
 
 8.7850 
 
 .001474926 
 
 ,130.00 
 
 361,034.97 
 
 I 679 
 
 461,041 
 
 313,046,839 
 
 26.0576 
 
 8.7893 
 
 .001472754 
 
 ,133.14 
 
 362,100.75 
 
 1 680 
 
 462,400 
 
 314,432,000 
 
 26.0768 
 
 8.7937 
 
 .001470588 
 
 ,136.28 
 
 363,168.11 
 
 1 681 
 
 463,761 
 
 315,821,241 
 
 26.0960 
 
 8.7980 
 
 .001468429 
 
 ,139.42 
 
 364,237.04 
 
 1 682 
 
 465,124 
 
 317,214,568 
 
 26.1151 
 
 8.8023 
 
 .001466276 
 
 ,142.57 
 
 365,307.54 
 
 1 683 
 
 466,489 
 
 318,611,987 
 
 26.1343 
 
 8.8066 
 
 .001464129 
 
 ,145.71 
 
 366,379.60 
 
 1 684 
 
 467,856 
 
 320,013,504 
 
 26.1534 
 
 8.8109 
 
 .001461988 
 
 ,148.85 
 
 367,453.24 
 
 1 685 
 
 469,225 
 
 321,419,125 
 
 26.1725 
 
 8.8152 
 
 .001459854 
 
 ,151.99 
 
 368,528.45 
 
1092 
 
 SQUARES, CUBES, SQUARE AND CUBE ROOTS 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 686 
 
 470,596 
 
 322,828,856 
 
 26.1916 
 
 8.8194 
 
 .001457726 
 
 2,155.13 
 
 369,605.23 
 
 687 
 
 471,969 
 
 324,242,703 
 
 26.2107 
 
 8.8237 
 
 .001455604 
 
 2,158.27 
 
 370,683.59 
 
 688 
 
 473,344 
 
 325,660,672 
 
 26.2298 
 
 8.8280 
 
 .001453488 
 
 2,161.42 
 
 371,763.51 
 
 689 
 
 474,721 
 
 327,082,769 
 
 26.2488 
 
 8.8323 
 
 .001451379 
 
 2,164.56 
 
 372,845.00 
 
 690 
 
 476,100 
 
 328,509,000 
 
 26.2679 
 
 8.8366 
 
 .001449275 
 
 2,167.70 
 
 373,928.07 
 
 691 
 
 477,481 
 
 329,939,371 
 
 26.2869 
 
 8.8408 
 
 .001447178 
 
 2,170.84 
 
 375,012.70 
 
 692 
 
 478,864 
 
 331,373,888 
 
 26.3059 
 
 8.8451 
 
 .001445087 
 
 2,173.98 
 
 376,098.91 
 
 693 
 
 480,249 
 
 332,812,557 
 
 26.3249 
 
 8.8493 
 
 .001443001 
 
 2,177.12 
 
 377,186.68 
 
 694 
 
 481,636 
 
 334,255,384 
 
 26.3439 
 
 8.8536 
 
 .001440922 
 
 2,180.27 
 
 378,276.03 
 
 695 
 
 483,025 
 
 335,702,375 
 
 26.3629 
 
 8.8578 
 
 .001438849 
 
 2,183.41 
 
 379,366.95 
 
 696 
 
 484,416 
 
 337,153,536 
 
 26.3818 
 
 8.8621 
 
 .001436782 
 
 2,186.55 
 
 380,459.44 
 
 697 
 
 485,809 
 
 338,608,873 
 
 26.4008 
 
 8.8663 
 
 .001434720 
 
 2,189.69 
 
 381,553.50 
 
 698 
 
 487,204 
 
 340,068,392 
 
 26.4197 
 
 8.8706 
 
 .001432665 
 
 2,192.83 
 
 382,649.13 
 
 699 
 
 488,601 
 
 341,532,099 
 
 26.4386 
 
 8.8748 
 
 .001430615 
 
 2,195.97 
 
 383,746.33 
 
 700 
 
 490,000 
 
 343,000,000 
 
 26.4575 
 
 8.8790 
 
 .001428571 
 
 2,199.11 
 
 384,845.10 
 
 701 
 
 491,401 
 
 344,472,101 
 
 26.4764 
 
 8.8833 
 
 .001426534 
 
 2,202.26 
 
 385,945.44 
 
 702 
 
 492,804 
 
 345,948,408 
 
 26.4953 
 
 8.8875 
 
 .001424501 
 
 2,205.40 
 
 387,047.36 
 
 703 
 
 494,209 
 
 347,428,927 
 
 26.5141 
 
 8.8917 
 
 .001422475 
 
 2,208.54 
 
 388,150.84 
 
 704 
 
 495,616 
 
 348,913,664 
 
 26.5330 
 
 8.8959 
 
 .001420455 
 
 2,211.68 
 
 389,255.90 
 
 705 
 
 497,025 
 
 350,402,625 
 
 26.5518 
 
 8.9001 
 
 .001418440 
 
 2,214.82 
 
 390,362.52 
 
 706 
 
 498,436 
 
 351,895,816 
 
 26.5707 
 
 8.9043 
 
 .001416431 
 
 2,217.96 
 
 391,470.72 
 
 707 
 
 499,849 
 
 353,393,243 
 
 26.5895 
 
 8.9085 
 
 .001414427 
 
 2,221.11 
 
 392,580.49 
 
 708 
 
 501,264 
 
 354,894,912 
 
 26.6083 
 
 8.9127 
 
 .001412429 
 
 2,224.25 
 
 393,691.82 
 
 709 
 
 502,681 
 
 356,400,829 
 
 26.6271 
 
 8.9169 
 
 .001410437 
 
 2,227.39 
 
 394,804.73 
 
 710 
 
 504,100 
 
 357,911,000 
 
 26.6458 
 
 8.9211 
 
 .001408451 
 
 2,230.53 
 
 395,919.21 
 
 711 
 
 505,521 
 
 359,425,431 
 
 26.6646 
 
 8.9253 
 
 .001406470 
 
 2,233.67 
 
 397,035.26 
 
 712 
 
 506,944 
 
 360,944,128 
 
 26.6833 
 
 8.9295 
 
 .001404494 
 
 2,236.81 
 
 398,152.89 
 
 713 
 
 508,369 
 
 362,467,097 
 
 26.7021 
 
 8.9337 
 
 .001402525 
 
 2,239.96 
 
 399,272.08 
 
 714 
 
 509,796 
 
 363,994,344 
 
 26.7208 
 
 8.9378 
 
 .001400560 
 
 2,243.10 
 
 400,392.84 
 
 715 
 
 511,225 
 
 365,525,875 
 
 26.7395 
 
 8.9420 
 
 .001398601 
 
 2,246.24 
 
 401,515.18 
 
 716 
 
 512,656 
 
 367,061,696 
 
 26.7582 
 
 8.9462 
 
 .001396648 
 
 2,249.38 
 
 402,639.08 
 
 717 
 
 514,089 
 
 368,601,813 
 
 26.7769 
 
 8.9503 
 
 .001394700 
 
 2,252.52 
 
 403,764.56 
 
 718 
 
 515,524 
 
 370,146,232 
 
 26.7955 
 
 8.9545 
 
 .001392758 
 
 2,255.66 
 
 404,891.60 
 
 719 
 
 516,961 
 
 371,694,959 
 
 26.8142 
 
 8.9587 
 
 .001390821 
 
 2,258.81 
 
 406,020.22 
 
 720 
 
 518,400 
 
 373,248,000 
 
 26.8328 
 
 8.9628 
 
 .001388889 
 
 2,261.95 
 
 407,150.41 
 
 721 
 
 519,841 
 
 374,805,361 
 
 26.8514 
 
 8.9670 
 
 .001386963 
 
 2,265.09 
 
 408,282.17 
 
 722 
 
 521,284 
 
 376,367,048 
 
 26.8701 
 
 8.9711 
 
 .001385042 
 
 2,268.23 
 
 409,415.50 
 
 723 
 
 522,729 
 
 377,933,067 
 
 26.8887 
 
 8.9752 
 
 .001383126 
 
 2,271.37 
 
 410,550.40 
 
 724 
 
 524,176 
 
 379,503,424 
 
 26.9072 
 
 8.9794 
 
 .001381215 
 
 2,274.51 
 
 411,686.87 
 
 725 
 
 525,625 
 
 381,078,125 
 
 26.9258 
 
 8.9835 
 
 .001379310 
 
 2,277.65 
 
 412,824.91 
 
 726 
 
 527,076 
 
 382,657,176 
 
 26.9444 
 
 8.9876 
 
 .001377410 
 
 2,280.80 
 
 413,964.52 
 
 727 
 
 528,529 
 
 384,240,583 
 
 26.9629 
 
 8.9918 
 
 .001375516 
 
 2,283.94 
 
 415,105.71 
 
 728 
 
 529,984 
 
 385,828,352 
 
 26.9815 
 
 8.9959 
 
 .001373626 
 
 2,287.08 
 
 416,248.46 
 
 729 
 
 531,441 
 
 387,420,489 
 
 27.0000 
 
 9.0000 
 
 .001371742 
 
 2,290.22 
 
 417,392.79 
 
 730 
 
 532,900 
 
 389,017,000 
 
 27.0185 
 
 9.0041 
 
 .001369863 
 
 2,293.36 
 
 418,538.68 
 
 731 
 
 534,361 
 
 390,617,891 
 
 27.0370 
 
 9.0082 
 
 .001367989 
 
 2,296.50 
 
 419,686.15 
 
 732 
 
 535,824 
 
 392,223,168 
 
 27.0555 
 
 9.0123 
 
 .001366120 
 
 2,299.65 
 
 420,835.19 
 
 733 
 
 537,289 
 
 393,832,837 
 
 27.0740 
 
 9.0164 
 
 .001364256 
 
 2,302.79 
 
 421,985.79 
 
 734 
 
 538,756 
 
 395,446,904 
 
 27.0924 
 
 9.0205 
 
 .001362398 
 
 2,305.93 
 
 423,137.97 
 
 735 
 
 540,225 
 
 397,065,375 
 
 27.1109 
 
 9.0246 
 
 .001360544 
 
 2,309.07 
 
 424,291.72 
 
 736 
 
 54 J, 696 
 
 398,688,256 
 
 27.1293 
 
 9.0287 
 
 .001358696 
 
 2,312.21 
 
 425,447.04 
 
 737 
 
 543,169 
 
 400,315,553 
 
 27.1477 
 
 9.0328 
 
 .001356852 
 
 2,315.35 
 
 426,603.94 
 
 738 
 
 544,644 
 
 401,947,272 
 
 27.1662 
 
 9.0369 
 
 .001355014 
 
 2,318.50 
 
 427,762.40 
 
 739 
 
 546,121 
 
 403,583,419 
 
 27.1846 
 
 9.0410 
 
 .001353180 
 
 2,321.64 
 
 428,922.43 
 
 740 
 
 547,600 
 
 405,224,000 
 
 27.2029 
 
 9.0450 
 
 .001351351 
 
 2,324.78 
 
 430,084.03 
 
 741 
 
 549,801 
 
 406,869,021 
 
 27.2213 
 
 9.0491 
 
 .001349528 
 
 2,327.92 
 
 431,247.21 
 
 742 
 
 550,564 
 
 408,518,488 
 
 27.2397 
 
 9.0532 
 
 .001347709 
 
 2,331.06 
 
 432,411.95 
 
 743 
 
 552,049 
 
 410,172,407 
 
 27.2580 
 
 9.0572 
 
 .001345895 
 
 2,334.20 
 
 433,578.27 
 
 744 
 
 553,536 
 
 411,830,784 
 
 27.2764 
 
 9.0613 
 
 .001344086 
 
 2,337.34 
 
 434,746.16 
 
 745 
 
 555,025 
 
 413,493,625 
 
 27.2947 
 
 9.0654 
 
 .001342282 
 
 2,340.49 
 
 435,915.62 
 
 746 
 
 556,516 
 
 415,160,936 
 
 27.3130 
 
 9.0694 
 
 .001340483 
 
 2,343.63 
 
 437,086.64 
 
 747 
 
 558,009 
 
 416,832,723 
 
 27.3313 
 
 9.0735 
 
 .001338688 
 
 2,346.77 
 
 438,259.24 
 
 748 
 
 559,504 
 
 418,508,992 
 
 27.3496 
 
 9.0775 
 
 .001336898 
 
 2,349.91 
 
 439,433.41 
 
CIRCUMFERENCES, AND AREAS 
 
 1093 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 749 
 
 561,001 
 
 420,189,749 
 
 27.3679 
 
 9.0816 
 
 .001335113 
 
 2,353.05 
 
 440,609.16 
 
 750 
 
 562,500 
 
 421,875,000 
 
 27.3861 
 
 9.0856 
 
 .001333333 
 
 2,356.19 
 
 441,786.47 
 
 751 
 
 564,001 
 
 423,564,751 
 
 27.4044 
 
 9.0896 
 
 .001331558 
 
 2,359.34 
 
 442,965.35 
 
 752 
 
 565,504 
 
 425,259,008 
 
 27.4226 
 
 9.0937 
 
 .001329787 
 
 2,362.48 
 
 444,145.80 
 
 753 
 
 567.009 
 
 426,957,777 
 
 27.4408 
 
 9.0977 
 
 .001328021 
 
 2,365.62 
 
 445,327.83 
 
 754 
 
 568i516 
 
 428,661,064 
 
 27.4591 
 
 9.1017 
 
 .001326260 
 
 2,368.76 
 
 446,511.42 
 
 755 
 
 570,025 
 
 430,368,875 
 
 27.4773 
 
 9.1057 
 
 .001324503 
 
 2,371.90 
 
 447,696.59 
 
 756 
 
 571,536 
 
 432,081,216 
 
 27.4955 
 
 9.1098 
 
 .001322751 
 
 2,375.04 
 
 448,883.32 
 
 757 
 
 573,049 
 
 433,798,093 
 
 27.5136 
 
 9.1138 
 
 .001321004 
 
 2,378.19 
 
 450,071.63 
 
 758 
 
 574,564 
 
 435,519,512 
 
 27.5318 
 
 9.1178 
 
 .001319261 
 
 2,381.33 
 
 451,261.51 
 
 759 
 
 576,081 
 
 437,245,479 
 
 27.5500 
 
 9.1218 
 
 .001317523 
 
 2,384.47 
 
 452,452.96 
 
 760 
 
 577,600 
 
 438,976,000 
 
 27.5681 
 
 9.1258 
 
 .001315789 
 
 2,387.61 
 
 453,645.98 
 
 761 
 
 579,121 
 
 440,711,081 
 
 27.5862 
 
 9.1298 
 
 .001314060 
 
 2,390.75 
 
 454,840.57 
 
 762 
 
 580,644 
 
 442,450,728 
 
 27.6043 
 
 9.1338 
 
 .001312336 
 
 2,393.89 
 
 456,036.73 
 
 763 
 
 582,169 
 
 444,194,947 
 
 27.6225 
 
 9.1378 
 
 .001310616 
 
 2,397.04 
 
 457,234.46 
 
 764 
 
 583,696 
 
 445,943,744 
 
 27.6405 
 
 9.1418 
 
 .001308901 
 
 2,400.18 
 
 458,433.77 
 
 765 
 
 585,225 
 
 447,697,125 
 
 27.6586 
 
 9.1458 
 
 .001307190 
 
 2,403.32 
 
 459,634.64 
 
 766 
 
 586,756 
 
 449,455,096 
 
 27.6767 
 
 9.1498 
 
 .001305483 
 
 2,406.46 
 
 460,837.08 
 
 767 
 
 588,289 
 
 451,217,663 
 
 27.6948 
 
 9.1537 
 
 .001303781 
 
 2,409.60 
 
 462,041.10 
 
 768 
 
 589,824 
 
 452,984,832 
 
 27.7128 
 
 9.1577 
 
 .001302083 
 
 2,412.74 
 
 463,246.69 
 
 769 
 
 591,361 
 
 454,756,609 
 
 27.7308 
 
 9.1617 
 
 .001300390 
 
 2,415.88 
 
 464,453.84 
 
 770 
 
 592,900 
 
 456,533,000 
 
 27.7489 
 
 9.1657 
 
 .001298701 
 
 2,419.03 
 
 465,662.57 
 
 771 
 
 594,441 
 
 458,314,011 
 
 27.7669 
 
 9.1696 
 
 .001297017 
 
 2,422.17 
 
 466,872.87 
 
 772 
 
 595,984 
 
 460,099,648 
 
 27.7849 
 
 9.1736 
 
 .001295337 
 
 2,425.31 
 
 468,084.74 
 
 773 
 
 597,529 
 
 461,889,917 
 
 27.8029 
 
 9.1775 
 
 .001293661 
 
 2,428.45 
 
 469,298.18 
 
 774 
 
 599,076 
 
 463,684.824 
 
 27.8209 
 
 9.1815 
 
 .001291990 
 
 2,431.59 
 
 470,513.19 
 
 775 
 
 600,625 
 
 465,484,375 
 
 27.8388 
 
 9.1855 
 
 .001290323 
 
 2,434.73 
 
 471,729.77 
 
 776 
 
 602,176 
 
 467,288,576 
 
 27.8568 
 
 9.1894 
 
 .001288660 
 
 2,437.88 
 
 472,947.92 
 
 777 
 
 603,729 
 
 469,097,433 
 
 27.8747 
 
 9.1933 
 
 .001287001 
 
 2,441.02 
 
 474,167.65 
 
 778 
 
 605,284 
 
 470,910,952 
 
 27.8927 
 
 9.1973 
 
 .001285347 
 
 2,444.16 
 
 475,388.94 
 
 779 
 
 606,841 
 
 472,729,139 
 
 27.9106 
 
 9.2012 
 
 .001283697 
 
 2,447.30 
 
 476,611.81 
 
 780 
 
 608,400 
 
 474,552,000 
 
 27.9285 
 
 9.2052 
 
 .001282051 
 
 2,450.44 
 
 477,836.24 
 
 781 
 
 609,961 
 
 476,379,541 
 
 27.9464 
 
 9.2091 
 
 .001280410 
 
 2,453.58 
 
 479,062.25 
 
 782 
 
 611,524 
 
 478,211,768 
 
 27.9643 
 
 9.2130 
 
 .001278772 
 
 2,456.73 
 
 480,289.83 
 
 783 
 
 613,089 
 
 480,048,687 
 
 27 9821 
 
 9.2170 
 
 .001277139 
 
 2,459.87 
 
 481,518.97 
 
 784 
 
 614,656 
 
 481,890,304 
 
 28.0000 
 
 9.2209 
 
 .001275510 
 
 2,463.01 
 
 482,749.69 
 
 785 
 
 616,225 
 
 483,736,625 
 
 28.0179 
 
 9.2248 
 
 .001273885 
 
 2,466.15 
 
 483,981.98 
 
 786 
 
 617,796 
 
 485,587,656 
 
 28.0357 
 
 9.2287 
 
 .001272265 
 
 2,469.29 
 
 485,215.84 
 
 787 
 
 619,369 
 
 487,443,403 
 
 28.0535 
 
 9.2326 
 
 .001270648 
 
 2,472.43 
 
 486,451.28 
 
 788 
 
 620,944 
 
 489,303,872 
 
 28.0713 
 
 9.2365 
 
 .001269036 
 
 2,475.58 
 
 487,688.28 
 
 789 
 
 622,521 
 
 491,169,069 
 
 28.0891 
 
 9.2404 
 
 .001267427 
 
 2,478.72 
 
 488,926.85 
 
 790 
 
 624,100 
 
 493,039,000 
 
 28.1069 
 
 9.2443 
 
 .001265823 
 
 2,481.86 
 
 490,166.99 
 
 791 
 
 625,681 
 
 494,913,671 
 
 28.1247 
 
 9.2482 
 
 .001264223 
 
 2,485.00 
 
 491,408.71 
 
 792 
 
 627,264 
 
 496,793,088 
 
 28.1425 
 
 9.2521 
 
 .001262626 
 
 2,488.14 
 
 492,651.99 
 
 793 
 
 628,849 
 
 498,677,257 
 
 28.1603 
 
 9.2560 
 
 .001261034 
 
 2,491.28 
 
 493,896.85 
 
 794 
 
 630,436 
 
 500,566,184 
 
 28.1780 
 
 9.2599 
 
 .001259446 
 
 2,494.42 
 
 495,143.28 
 
 795 
 
 632,025 
 
 502,459,875 
 
 28.1957 
 
 9.2638 
 
 .001257862 
 
 2,497.57 
 
 496,391.27 
 
 796 
 
 633,616 
 
 504,358,336 
 
 28.2135 
 
 9.2677 
 
 .001256281 
 
 2,500.71 
 
 497,640.84 
 
 797 
 
 635,209 
 
 506,261,573 
 
 28.2312 
 
 9.2716 
 
 .001254705 
 
 2,503.85 
 
 498,891.98 
 
 798 
 
 636,804 
 
 508,169,592 
 
 28.2489 
 
 9.2754 
 
 .001253133 
 
 2,506.99 
 
 500,144.69 
 
 799 
 
 638,401 
 
 510,082,399 
 
 28.2666 
 
 9.2793 
 
 .001251364 
 
 2,510.13 
 
 501,398.97 
 
 800 
 
 640,000 
 
 512,000,000 
 
 28.2843 
 
 9.2832 
 
 ..001250000 
 
 2,513.27 
 
 502,654.82 
 
 801 
 
 641,601 
 
 513,922,401 
 
 28.3019 
 
 9.2870 
 
 .001248439 
 
 2,516.42 
 
 503,912.25 
 
 802 
 
 643,204 
 
 515,849,608 
 
 28.3196 
 
 9.2909 
 
 .001246883 
 
 2,519.56 
 
 505,171.24 
 
 803 
 
 644,809 
 
 517,781,627 
 
 28.3373 
 
 9.2948 
 
 .001245330 
 
 2,522.70 
 
 506,431.80 
 
 804 
 
 646,416 
 
 519,718,464 
 
 28.3549 
 
 9.2986 
 
 .001243781 
 
 2,525.84 
 
 507,693.94 
 
 805 
 
 648,025 
 
 521,660,125 
 
 28.3725 
 
 9.3025 
 
 .001242236 
 
 2,'528.98' 
 
 508,957.64 
 
 806 
 
 649,636 
 
 523,606,616 
 
 28.3901 
 
 9.3063 
 
 .001240695 
 
 2,532.12 
 
 510,222.92 
 
 807 
 
 651,249 
 
 525,557,943 
 
 28.4077 
 
 9.3102 
 
 .001239157 
 
 2,535.27 
 
 511,489.77 
 
 808 
 
 652,864 
 
 527,514,112 
 
 28.4253 
 
 9.3140 
 
 .001237624 
 
 2,538.41 
 
 512,758.19 
 
 809 
 
 654,481 
 
 529,475,129 
 
 28.4429 
 
 9.3179 
 
 .001236094 
 
 2,541.55 
 
 514,028.18 
 
 810 
 
 656100 
 
 531,441,000 
 
 28.4605 
 
 9.3217 
 
 .001234568 
 
 2,544.69 
 
 515,299.74 
 
 811 
 
 657,721 
 
 533,411,731 
 
 28.4781 
 
 9.3255 
 
 .001233046 
 
 2,547.83 
 
 516,572.87 
 
1094 
 
 SQUARES, CUBES, SQUARE AND CUBE ROOTS 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cn. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 812 
 
 659,344 
 
 535,387,328 
 
 28.4956 
 
 9.3294 
 
 .001231527 
 
 2,550.97 
 
 517,847.57 
 
 813 
 
 660,969 
 
 537,367,797 
 
 28.5132 
 
 9.3332 
 
 .001230012 
 
 2,554.11 
 
 519,123.84 
 
 814 
 
 662,596 
 
 539,353,144 
 
 28.5307 
 
 9.3370 
 
 .001228501 
 
 2,557.26 
 
 520,401.68 
 
 815 
 
 664,225 
 
 541,343,375 
 
 28.5482 
 
 9.3408 
 
 .001226994 
 
 2,560.40 
 
 521,681.10 
 
 816 
 
 665,856 
 
 543,338,496 
 
 28.5657 
 
 9.3447 
 
 .001225490 
 
 2,563.54 
 
 522,962.08 
 
 817 
 
 667,489 
 
 545,338,513 
 
 28.5832 
 
 9.3485 
 
 .001223990 
 
 2,566.68 
 
 524,244.63 
 
 818 
 
 669,124 
 
 547,343,432 
 
 28.6007 
 
 9.3523 
 
 .001222494 
 
 2,569.82 
 
 525,528.76 
 
 819 
 
 670,761 
 
 549,353,259 
 
 28.6182 
 
 9.3561 
 
 .001221001 
 
 2,572.96 
 
 526,814.46 
 
 820 
 
 672,400 
 
 551,368,000 
 
 28.6356 
 
 9.3599 
 
 .001219512 
 
 2,576.11 
 
 528,101.73 
 
 821 
 
 674,041 
 
 553,387,661 
 
 28.6531 
 
 9.3637 
 
 .001218027 
 
 2,579.25 
 
 529,390.56 
 
 822 
 
 675,584 
 
 555,412,248 
 
 28.6705 
 
 9.3675 
 
 .001216545 
 
 2,582.39 
 
 530,680.97 
 
 823 
 
 677,329 
 
 557,441,767 
 
 28.6880 
 
 9.3713 
 
 .001215067 
 
 2,585.53 
 
 531,972.95 
 
 824 
 
 678,976 
 
 559,476,224 
 
 28.7054 
 
 9.3751 
 
 .001213592 
 
 2,588.67 
 
 533,266.50 
 
 825 
 
 680,625 
 
 561,515,625 
 
 28.7228 
 
 9.3789 
 
 .001212121 
 
 2,591.81 
 
 534,561.62 
 
 826 
 
 682,276 
 
 563,559,976 
 
 28.7402 
 
 9.3827 
 
 .001210654 
 
 2,594.96 
 
 535,858.32 
 
 827 
 
 683,929 
 
 565,609,283 
 
 28.7576 
 
 9.3865 
 
 .001209190 
 
 2,598.10 
 
 537,156.58 
 
 828 
 
 685,584 
 
 567,663,552 
 
 28.7750 
 
 93902 
 
 .001207729 
 
 2,601.24 
 
 538,456.41 
 
 829 
 
 687,241 
 
 569,722,789 
 
 28.7924 
 
 9.3940 
 
 .001206273 
 
 2,604.38 
 
 539,757.82 
 
 830 
 
 688,900 
 
 571,787,000 
 
 28.8097 
 
 9.3978 
 
 .001204819 
 
 2,607.52 
 
 541,060.79 
 
 831 
 
 690,561 
 
 573,856,191 
 
 28.8271 
 
 9.4016 
 
 .001203369 
 
 2,610.66 
 
 542,365.34 
 
 832 
 
 692,224 
 
 575,930,368 
 
 28.8444 
 
 9.4053 
 
 .001201923 
 
 2,613.81 
 
 543,671.46 
 
 833 
 
 693,889 
 
 578,009,537 
 
 28.8617 
 
 9.4091 
 
 .001200480 
 
 2,616.95 
 
 544,979.15 
 
 834 
 
 695,556 
 
 580,093,704 
 
 28.8791 
 
 9.4129 
 
 .001199041 
 
 2,620.09 
 
 546,288.40 
 
 835 
 
 697,225 
 
 582,182,875 
 
 28.8964 
 
 9.4166 
 
 .001197605 
 
 2,623.23 
 
 547,599.23 
 
 836 
 
 698,896 
 
 584,277,056 
 
 28.9137 
 
 9.4204 
 
 .001196172 
 
 2,626.37 
 
 548,911.63 
 
 837 
 
 700,569 
 
 586,376,253 
 
 28.9310 
 
 9.4241 
 
 .001194743 
 
 2,629.51 
 
 550,225.61 
 
 838 
 
 702,244 
 
 588,480,472 
 
 28.9482 
 
 9.4279 
 
 .001193317 
 
 2,632.65 
 
 551,541.15 
 
 839 
 
 703,921 
 
 590,589,719 
 
 2H.%f>5 
 
 9.4316 
 
 .001191895 
 
 2,635.80 
 
 552,858.26 
 
 840 
 
 705,600 
 
 592,704,000 
 
 28.9828 
 
 9.4354 
 
 .001190476 
 
 2,638.94 
 
 554,176.94 
 
 841 
 
 707,281 
 
 594,823,321 
 
 29.0000 
 
 9.4391 
 
 .001189061 
 
 2,642.08 
 
 555,497.20 
 
 842 
 
 708,964 
 
 596,947,688 
 
 29.0172 
 
 9.4429 
 
 .001187648 
 
 2,645.22 
 
 556,819.02 
 
 843 
 
 710,649 
 
 599,077,107 
 
 29.0345 
 
 9.4466 
 
 .001186240 
 
 2,648.36 
 
 558,142.42 
 
 344 
 
 712,336 
 
 601,211,584 
 
 29.0517 
 
 9.4503 
 
 .001184834 
 
 2,651.50 
 
 559,467.39 
 
 845 
 
 714,025 
 
 603,351,125 
 
 29.0689 
 
 9.4541 
 
 .001183432 
 
 2,654.65 
 
 560,793.92 
 
 846 
 
 715,716 
 
 605,495,736 
 
 29.0861 
 
 9.4578 
 
 .001182033 
 
 2,657.79 
 
 562,122.03 
 
 847 
 
 717,409 
 
 607,645,423 
 
 29.1033 
 
 9.4615 
 
 .001180638 
 
 2,660.93 
 
 563,451.71 
 
 848 
 
 719,104 
 
 609,800,192 
 
 29.1204 
 
 9.4652 
 
 .001179245 
 
 2,664.07 
 
 564,782.96 
 
 849 
 
 720,801 
 
 611,960,049 
 
 29.1376 
 
 9.4690 
 
 .001177856 
 
 2,667.21 
 
 566,115.78 
 
 850 
 
 722,500 
 
 614,125,000 
 
 29.1548 
 
 9.4727 
 
 .001176471 
 
 2,670.35 
 
 567,450.17 
 
 851 
 
 724,201 
 
 616,295,051 
 
 29.1719 
 
 9.4764 
 
 .001175088 
 
 2,673.50 
 
 568,786.14 
 
 852 
 
 725,904 
 
 618,470,208 
 
 29.1890 
 
 9.4801 
 
 .001173709 
 
 2,676.64 
 
 570,123.67 
 
 853 
 
 727,609 
 
 620,650,477 
 
 29.2062 
 
 9.4838 
 
 .001172333 
 
 2,679.78 
 
 571,462.77 
 
 854 
 
 729,316 
 
 622,835,864 
 
 29.2233 
 
 9.4875 
 
 .001170960 
 
 2,682.92 
 
 572,803.45 
 
 855 
 
 731,025 
 
 625,026,375 
 
 29.2404 
 
 9.4912 
 
 .001169591 
 
 2,686.06 
 
 574,145.69 
 
 856 
 
 732,736 
 
 627,222,016 
 
 29.2575 
 
 9.4949 
 
 .001168224 
 
 2,689.20 
 
 575,489.51 
 
 857 
 
 734,449 
 
 629,422,793 
 
 29.2746 
 
 9.4986 
 
 .001166861 
 
 2,692.34 
 
 576,834.90 
 
 858 
 
 736,164 
 
 631,628,712 
 
 29.2916 
 
 9.5023 
 
 .001165501 
 
 2,695.49 
 
 578,181.85 
 
 859 
 
 737,881 
 
 633,839,779 
 
 29.3087 
 
 9.5060 
 
 .001164144 
 
 2,698.63 
 
 579,530.38 
 
 860 
 
 739,600 
 
 636,056,000 
 
 29.3258 
 
 9.5097 
 
 .001162791 
 
 2,701.77 
 
 580,880.48 
 
 861 
 
 741,321 
 
 638,277,381 
 
 29.3428 
 
 9.5135 
 
 .001161440 
 
 2,704.91 
 
 582,232.15 
 
 862 
 
 743,044 
 
 640,503,928 
 
 29.3598 
 
 9.5171 
 
 .001160093 
 
 2,708.05 
 
 583,585.39 
 
 863 
 
 744,769 
 
 642,735,647 
 
 29.3769 
 
 9.5207 
 
 .001158749 
 
 2,711.19 
 
 584,940.20 
 
 864 
 
 746,496 
 
 644,972,544 
 
 29.3939 
 
 9.5244 
 
 .001157407 
 
 2,714.34 
 
 586,296.59 
 
 865 
 
 748,225 
 
 647,214,625 
 
 29.4109 
 
 9.5281 
 
 .001156069 
 
 2,717.48 
 
 587,654.54 
 
 866 
 
 749,956 
 
 649,461,896 
 
 29.4279 
 
 9.5317 
 
 .001154734 
 
 2,720.62 
 
 589,014.07 
 
 867 
 
 751,689 
 
 651,714,363 
 
 29.4449 
 
 9.5354 
 
 .001153403 
 
 2,723.76 
 
 590,375.16 
 
 868 
 
 753,424 
 
 653,972,032 
 
 29.4618 
 
 9.5391 
 
 .001152074 
 
 2,726.90 
 
 591,737.83 
 
 869 
 
 755,161 
 
 656,234,909 
 
 29.4788 
 
 9.5427 
 
 .001150748 
 
 2,730.04 
 
 593,102.06 
 
 870 
 
 756,900 
 
 658,503,000 
 
 29.4958 
 
 9.5464 
 
 .001149425 
 
 2,733.19 
 
 594,467.87 
 
 871 
 
 758,641 
 
 660,776,311 
 
 29.5127 
 
 9.5501 
 
 .001148106 
 
 2,736.33 
 
 595,835.25 
 
 872 
 
 760,384 
 
 663,054,848 
 
 29.5296 
 
 9.5537 
 
 .001146789 
 
 2,739.47 
 
 597,204.20 
 
 873 
 
 762,129 
 
 665,338,617 
 
 29.5466 
 
 9.5574 
 
 .001145475 
 
 2,742.61 
 
 598,574.72 
 
 874 
 
 763,876 
 
 667,627,624 
 
 29.5635 
 
 9.5610 
 
 .001144165 
 
 2,745.75 
 
 599,946.81 
 
CIRCUMFERENCES, AND AREAS 
 
 1095 
 
 NO. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Ciroum. 
 
 Area 
 
 875 
 
 765,625 
 
 669,921,875 
 
 29.5804 
 
 9.5647 
 
 .001142857 
 
 2,748.89 
 
 601,320.47 
 
 876 
 
 767,376 
 
 672,221,376 
 
 29.5973 
 
 9.5683 
 
 .001141553 
 
 2,752.04 
 
 602,695.70 
 
 877 
 
 769,129 
 
 674,526,133 
 
 29.6142 
 
 9.5719 
 
 .001140251 
 
 2,755.18 
 
 604,072.50 
 
 878 
 
 770,884 
 
 676,836,152 
 
 29.6311 
 
 9.5756 
 
 .001138952 
 
 2,758.32 
 
 605,450.88 
 
 879 
 
 772,641 
 
 679,151,439 
 
 29.6479 
 
 9.5792 
 
 .001137656 
 
 2,761.46 
 
 606,830.82 
 
 880 
 
 774,400 
 
 681,472,000 
 
 29.6648 
 
 9.5828 
 
 .001136364 
 
 2,764.60 
 
 608,212.34 
 
 881 
 
 776,161 
 
 683,797,841 
 
 29.6816 
 
 9.5865 
 
 .001135074 
 
 2,767.74 
 
 609,595.42 
 
 882 
 
 777,924 
 
 686,128,968 
 
 29.6985 
 
 9.5901 
 
 .001133787 
 
 2,770.88 
 
 610,980.08 
 
 883 
 
 779,689 
 
 688,465,387 
 
 29.7153 
 
 9.5937 
 
 .001132503 
 
 2,774.03 
 
 612,366.31 
 
 884 
 
 781,456 
 
 690,807,104 
 
 29.7321 
 
 9.5973 
 
 .001131222 
 
 2,777.17 
 
 613,754.11 
 
 885 
 
 783,225 
 
 693,154,125 
 
 29.7489 
 
 9.6010 
 
 .001129944 
 
 2,780.31 
 
 615,143.48 
 
 886 
 
 784,996 
 
 695,506,456 
 
 29.7658 
 
 9.6046 
 
 .001128668 
 
 2,783.45 
 
 616,534.42 
 
 887 
 
 786,769 
 
 697,864,103 
 
 29.7825 
 
 9.6082 
 
 .001127396 
 
 2,786.59 
 
 617,926.93 
 
 1 888 
 
 788,544 
 
 700,227,072 
 
 29.7993 
 
 9.6118 
 
 .001126126 
 
 2,789.73 
 
 619,321.01 
 
 I 889 
 
 790,321 
 
 702,595,369 
 
 29.8161 
 
 9.6154 
 
 .001124859 
 
 2,792.88 
 
 620,716.66 
 
 890 
 
 792,100 
 
 704,969,000 
 
 29.8329 
 
 9.6190 
 
 .001123596 
 
 2,796.02 
 
 622,113.89 
 
 891 
 
 793,881 
 
 707,347,971 
 
 29.8496 
 
 9.6226 
 
 .001122334 
 
 2,799.16 
 
 623,512.68 
 
 892 
 
 795,664 
 
 707,932,288 
 
 29.8664 
 
 9.6262 
 
 .001121076 
 
 2,802.30 
 
 624,913.04 
 
 893 
 
 797,449 
 
 712,121,957 
 
 29.8831 
 
 9.6298 
 
 .001119821 
 
 2,805.44 
 
 626,314.98 
 
 894 
 
 799,236 
 
 714,516,984 
 
 29.8998 
 
 9.6334 
 
 .001118568 
 
 2,808.58 
 
 627,718.49 
 
 895 
 
 801,025 
 
 716,917,375 
 
 29.9166 
 
 9.6370 
 
 .001117818 
 
 2,811.73 
 
 629,123.56 
 
 896 
 
 802,816 
 
 719,323,136 
 
 29.9333 
 
 9.6406 
 
 .001116071 
 
 2,814.87 
 
 630,530.21 
 
 1 897 
 
 804,609 
 
 721,734,273 
 
 29.9500 
 
 9.6442 
 
 .001114827 
 
 2,818.01 
 
 631,938.43 
 
 898 
 
 806,404 
 
 724,150,792 
 
 29.9666 
 
 9.6477 
 
 .001113586 
 
 2,821.15 
 
 633,348.22 
 
 899 
 
 808,201 
 
 726,572,699 
 
 29.9833 
 
 9.6513 
 
 .001112347 
 
 2,824.29 
 
 634,759.58 
 
 900 
 
 810,000 
 
 729,000,000 
 
 30.0000 
 
 9.6549 
 
 .001111111 
 
 2,827.43 
 
 636,172.51 
 
 901 
 
 811,801 
 
 731,432,701 
 
 30.0167 
 
 9.6585 
 
 .001109878 
 
 2,830.58 
 
 637,587.01 
 
 902 
 
 813,604 
 
 733,870,808 
 
 30.0333 
 
 9.6620 
 
 .001108647 
 
 2,833.72 
 
 639,003.09 
 
 903 
 
 815,409 
 
 736,314,327 
 
 30.0500 
 
 9.6656 
 
 .001107420 
 
 2,836.86 
 
 640,420.73 
 
 904 
 
 817,216 
 
 738,763,264 
 
 30.0666 
 
 9.6692 
 
 .001106195 
 
 2,840.00 
 
 641,839.95 
 
 905 
 
 819,025 
 
 741,217,625 
 
 30.0832 
 
 9.6727 
 
 .001104972 
 
 2,843.14 
 
 643,260.73 
 
 906 
 
 820,836 
 
 743,677,416 
 
 30.0998 
 
 9.6763 
 
 .001103753 
 
 2,846.28 
 
 644,683.09 
 
 907 
 
 822,649 
 
 746,142,643 
 
 30.1164 
 
 9.6799 
 
 .001102536 
 
 2,849.42 
 
 646,107.01 
 
 908 
 
 824,464 
 
 748,613,312 
 
 30.1330 
 
 9.6834 
 
 .001101322 
 
 2,852.57 
 
 647,532.51 
 
 909 
 
 826,281 
 
 751,089,429 
 
 30.1496 
 
 9.6870 
 
 .001100110 
 
 2,855.71 
 
 648,959.58 
 
 910 
 
 828,100 
 
 753,571,000 
 
 30.1662 
 
 9.6905 
 
 .001098901 
 
 2,858.85 
 
 650,388.22 
 
 911 
 
 829,921 
 
 756,058,031 
 
 30.1828 
 
 9.6941 
 
 .001091695 
 
 2,861.99 
 
 651,818.43 
 
 912 
 
 831,744 
 
 758,550,825 
 
 30.1993 
 
 9.6976 
 
 .001096491 
 
 2,865.13 
 
 653,250.21 
 
 913 
 
 833,569 
 
 761,048,497 
 
 30.2159 
 
 9.7012 
 
 .001095290 
 
 2,868.27 
 
 654,683.56 
 
 914 
 
 835,396 
 
 763,551,944 
 
 30.2324 
 
 9.7047 
 
 .001094092 
 
 2,871.42 
 
 656,118.48 
 
 915 
 
 837,225 
 
 766,060,875 
 
 30.2490 
 
 9.7082 
 
 .001092896 
 
 2,874.56 
 
 657,554.98 
 
 916 
 
 839,056 
 
 768,575,296 
 
 30.2655 
 
 9.7118 
 
 .001091703 
 
 2,877.70 
 
 658,993.04 
 
 917 
 
 840,889 
 
 771,095,213 
 
 30.2820 
 
 9.7153 
 
 .001090513 
 
 2,880.84 
 
 660,432.68 
 
 918 
 
 842,724 
 
 773,620,632 
 
 30.2985 
 
 9.7188 
 
 .001089325 
 
 2,883.98 
 
 661,873.88 
 
 1 919 
 
 844,561 
 
 776,151,559 
 
 30.3150 
 
 9.7224 
 
 .001088139 
 
 2.887.12 
 
 663,316.66 
 
 920 
 
 846,400 
 
 778.688,000 
 
 30.3315 
 
 9.7259 
 
 .001086957 
 
 2,890.27 
 
 664,761.01 
 
 921 
 
 848,241 
 
 78i;229,961 
 
 30.3480 
 
 9.7294 
 
 .001085776 
 
 2,893.41 
 
 666,206.92 
 
 922 
 
 850,084 
 
 783,777,448 
 
 30.3645 
 
 9.7329 
 
 .001084599 
 
 2,896.55 
 
 667,654.41 
 
 923 
 
 851,929 
 
 786,330,467 
 
 30.3809 
 
 9.7364 
 
 .001083423 
 
 2,899.69 
 
 669,103.47 
 
 924 
 
 853,776 
 
 788,889,024 
 
 30.3974 
 
 9.7400 
 
 .001082251 
 
 2,902.83 
 
 670,554.10 
 
 925 
 
 855,625 
 
 791,453,125" 
 
 30.4138 
 
 9.7435 
 
 .001081081 
 
 2,905.97 
 
 672,006.30 
 
 926 
 
 857,476 
 
 794,022,776 
 
 30.4302 
 
 9.7470 
 
 .001079914 
 
 2,909.11 
 
 673,460.08 
 
 927 
 
 859,329 
 
 796,597,983 
 
 30.4467 
 
 9.7505 
 
 .001078749 
 
 2,912.26 
 
 674,915.42 
 
 928 
 
 861,184 
 
 799,178,752 
 
 30.4631 
 
 9.7540 
 
 .001077586 
 
 2,915.40 
 
 676,372.33 
 
 929 
 
 863,041 
 
 801,765.089 
 
 30.4795 
 
 9.7575 
 
 .001076426 
 
 2,918.54 
 
 677,830.82 
 
 930 
 
 864,900 
 
 804,357,000 
 
 30.4959 
 
 9.7610 
 
 .001075269 
 
 2,921.68 
 
 679,290.87 
 
 931 
 
 866,761 
 
 806,954,491 
 
 30.5123 
 
 9.7645 
 
 .001074114 
 
 2,924.82 
 
 680,752.50 
 
 932 
 
 868,624 
 
 809,557,568 
 
 30.5287 
 
 9.7680 
 
 .001072961 
 
 2,927.96 
 
 682,215.69 
 
 933 
 
 870,489 
 
 812,166,237 
 
 30.5450 
 
 9.7715 
 
 .001071811 
 
 2,931.11 
 
 683,680.46 
 
 934 
 
 872,356 
 
 814,780,504 
 
 30.5614 
 
 9.7750 
 
 .001070664 
 
 2,934.25 
 
 685,146.80 
 
 1 935 
 
 874,225 
 
 817,400,375 
 
 30.5778 
 
 9.7785 
 
 .001069519 
 
 2,937.39 
 
 686,614.71 
 
 936 
 
 876.096 
 
 820,025,856 
 
 30.5941 
 
 9.7829 
 
 .001068376 
 
 2,940.53 
 
 688,084.19 
 
 937 
 
 877,969 
 
 822,656,953 
 
 30.6105 
 
 9.7854 
 
 .001067236 
 
 2,943.67 
 
 689,555.24 
 
1096 
 
 SQUARES, CUBES, SQUARE AND CUBE ROOTS 
 
 No. 
 
 Square 
 
 Cube 
 
 Sq. Root 
 
 Cu. Root 
 
 Reciprocal 
 
 Circum. 
 
 Area 
 
 938 
 
 879,844 
 
 825,293,672 
 
 30.6268 
 
 9.7889 
 
 .001066098 
 
 2,946.81 
 
 691,027.86 
 
 939 
 
 881,721 
 
 827,936,019 
 
 30.6431 
 
 9.7924 
 
 .001064963 
 
 2,949.96 
 
 692,502.05 
 
 940 
 
 883,600 
 
 830,584,000 
 
 30.6594 
 
 9.7959 
 
 .001063830 
 
 2,953.10 
 
 693,977.82 
 
 941 
 
 885,481 
 
 833,237,621 
 
 30.6757 
 
 9.7993 
 
 .001062699 
 
 2,956.24 
 
 695,455.15 
 
 942 
 
 887,364 
 
 835,896,888 
 
 30.6920 
 
 9.8028 
 
 .001061571 
 
 2,959.38 
 
 696,934.06 
 
 943 
 
 889,249 
 
 838,561,807 
 
 30.7083 
 
 9.8063 
 
 .001060445 
 
 2,962.52 
 
 698,414.53 
 
 944 
 
 891,136 
 
 841,232,384 
 
 30.7246 
 
 9.8097 
 
 .001059322 
 
 2,965.66 
 
 699,896.58 
 
 945 
 
 893,025 
 
 843,908,625 
 
 30.7409 
 
 9.8132 
 
 .001058201 
 
 2,968.81 
 
 701,380.19 
 
 946 
 
 894,916 
 
 846,590,536 
 
 30.7571 
 
 9.8167 
 
 .001057082 
 
 2,971.95 
 
 702,865.38 
 
 947 
 
 896,808 
 
 849,278,123 
 
 30.7734 
 
 9.8201 
 
 .001055966 
 
 2,975.09 
 
 704,352.14 
 
 948 
 
 898,704 
 
 851,971,392 
 
 30.7896 
 
 9.8236 
 
 .001054852 
 
 2,978.23 
 
 705,840.47 
 
 949 
 
 900,601 
 
 854,670,349 
 
 30.8058 
 
 9.8270 
 
 .001053741 
 
 2,981.37 
 
 707,330.37 
 
 950 
 
 902,500 
 
 857,375,000 
 
 30.8221 
 
 9.8305 
 
 .001052632 
 
 2,984.51 
 
 708,821.84 
 
 951 
 
 904,401 
 
 860,085,351 
 
 30.8383 
 
 9.8339 
 
 .001051525 
 
 2,987.65 
 
 710,314.88 
 
 952 
 
 906,304 
 
 862,801,408 
 
 30.8545 
 
 9.8374 
 
 .001050420 
 
 2,990.80 
 
 711,809.50 
 
 953 
 
 908,209 
 
 865,523,177 
 
 30.8707 
 
 9.8408 
 
 .001049318 
 
 2,993.94 
 
 713,305.68 
 
 954 
 
 910,116 
 
 868,250,664 
 
 30.8869 
 
 9.8443 
 
 .001048218 
 
 2,997.08 
 
 714,803.43 
 
 955 
 
 912,025 
 
 870,983,875 
 
 30.9031 
 
 9.8477 
 
 .001047120 
 
 3,000.22 
 
 716,302.76 
 
 956 
 
 913,936 
 
 873,722,816 
 
 30.9192 
 
 9.8511 
 
 .001046025 
 
 3,003.36 
 
 717,803.66 
 
 957 
 
 915,849 
 
 876,467,493 
 
 30.9354 
 
 9.8546 
 
 .001044932 
 
 3,006.50 
 
 719,306.12 
 
 958 
 
 917,764 
 
 879,217,912 
 
 30.9516 
 
 9.8580 
 
 .001043841 
 
 3,009.65 
 
 720,810.16 
 
 959 
 
 919,681 
 
 881,974,079 
 
 30.9677 
 
 9.8614 
 
 .001042753 
 
 3,012.79 
 
 722,315.77 
 
 960 
 
 921,600 
 
 884,736,000 
 
 30.9839 
 
 9.8648 
 
 .001041667 
 
 3,015.93 
 
 723,822.95 
 
 961 
 
 923,521 
 
 887,503,681 
 
 31.0000 
 
 9.8683 
 
 .001040583 
 
 3,019.07 
 
 725,331.70 
 
 962 
 
 925,444 
 
 890,277,128 
 
 31.0161 
 
 9.8717 
 
 .001039501 
 
 3,022.21 
 
 726,842.02 
 
 963 
 
 927,369 
 
 893,056,347 
 
 31.0322 
 
 9.8751 
 
 .001038422 
 
 3,025.35 
 
 728,353.91 
 
 964 
 
 929,296 
 
 895,841,344 
 
 31.0483 
 
 9.8785 
 
 .001037344 
 
 3,028.50 
 
 729,867.37 
 
 965 
 
 931,225 
 
 898,632,125 
 
 31.0644 
 
 9.8819 
 
 .001036269 
 
 3,031.64 
 
 731,382.40 
 
 966 
 
 933,156 
 
 901,428,696 
 
 31.0805 
 
 9.8854 
 
 .001035197 
 
 3,034.78 
 
 732,899.01 
 
 967 
 
 935,089 
 
 904,231,063 
 
 31.0966 
 
 9.8888 
 
 .001034126 
 
 3,037.92 
 
 734,417.18 
 
 968 
 
 937,024 
 
 907,039,232 
 
 31.1127 
 
 9.8922 
 
 .001033058 
 
 3,041.06 
 
 735,936.93 
 
 969 
 
 938,961 
 
 909,853,209 
 
 31.1288 
 
 9.8956 
 
 .001031992 
 
 3,044.20 
 
 737,458.24 
 
 970 
 
 940,900 
 
 912,673,000 
 
 31.1448 
 
 9.8990 
 
 .001030928 
 
 3,047.34 
 
 738,981.13 
 
 971 
 
 942,841 
 
 915,498,611 
 
 31.1609 
 
 9.9024 
 
 .001029866 
 
 3,050.49 
 
 740,505.59 
 
 972 
 
 944,784 
 
 918,330,048 
 
 31.1769 
 
 9.9058 
 
 .001028807 
 
 3,053.63 
 
 742,031.62 
 
 973 
 
 946,729 
 
 921,167,317 
 
 31.1929 
 
 9.9092 
 
 .001027749 
 
 3,056.77 
 
 743,559.22 
 
 974 
 
 948,676 
 
 924,010,424 
 
 31.2090 
 
 9.9126 
 
 .001026694 
 
 3,059.91 
 
 745,088.39 
 
 975 
 
 950,625 
 
 926,859,375 
 
 31.2250 
 
 9.9160 
 
 .001025641 
 
 3,063.05 
 
 746,619.13 
 
 976 
 
 952,576 
 
 929,714,176 
 
 31.2410 
 
 9.9194 
 
 .001024590 
 
 3,066.19 
 
 748,151.44 
 
 977 
 
 954,529 
 
 932,574,833 
 
 31.2570 
 
 9.9228 
 
 .001023541 
 
 3,069.34 
 
 749,685.32 
 
 978 
 
 956,484 
 
 935,441,352 
 
 31.2730 
 
 9.9261 
 
 .001022495 
 
 3,072.48 
 
 751,220.78 
 
 979 
 
 958,441 
 
 938,313,739 
 
 31.2890 
 
 9.9295 
 
 .001021450 
 
 3,075.62 
 
 752,757.80 
 
 980 
 
 960,400 
 
 941,192,000 
 
 31.3050 
 
 9.9329 
 
 .001020408 
 
 3.078.76 
 
 754,296.40 
 
 981 
 
 962,361 
 
 944,076,141 
 
 31.3209 
 
 9.9363 
 
 .001019168 
 
 3,081.90 
 
 755,836.56 
 
 982 
 
 964,324 
 
 946,966,168 
 
 31.3369 
 
 9.9396 
 
 .001018330 
 
 3,085.04 
 
 757,378.30 
 
 983 
 
 966,289 
 
 949,862,087 
 
 31.3528 
 
 9.9430 
 
 .001017294 
 
 3,088.19 
 
 758,921.61 
 
 984 
 
 968,256 
 
 952,763,904 
 
 31.3688 
 
 9.9464 
 
 .001016260 
 
 3,091.33 
 
 760,466.48 
 
 985 
 
 970,225 
 
 955,671,625 
 
 31.3847 
 
 9.9497 
 
 .001015228 
 
 3,094.47 
 
 762,012.93 
 
 986 
 
 972,196 
 
 958,585,256 
 
 31.4006 
 
 9.9531 
 
 .001014199 
 
 3,097.61 
 
 763,560.95 
 
 987 
 
 974,169 
 
 961,504,803 
 
 31.4166 
 
 9.9565 
 
 .001013171 
 
 3,100.75 
 
 765,110.54 
 
 988 
 
 976,144 
 
 964,430,272 
 
 31.4325 
 
 9.9598 
 
 .001012146 
 
 3,103.89 
 
 766,661.70 
 
 989 
 
 978,121 
 
 967,361,669 
 
 31.4484 
 
 9.9632 
 
 .001011122 
 
 3,107.04 
 
 768,214.44 
 
 990 
 
 980,100 
 
 970,299,000 
 
 31.4643 
 
 9.9666 
 
 .001010101 
 
 3,110.18 
 
 769,768.74 
 
 991 
 
 982,081 
 
 973,242,271 
 
 31.4802 
 
 9.9699 
 
 .001009082 
 
 3,113.32 
 
 771,324.61 
 
 992 
 
 984,064 
 
 976,191,488 
 
 31.4960 
 
 9.9733 
 
 .001008065 
 
 3,116.46 
 
 772,882.06 
 
 993 
 
 986,049 
 
 979,146,657 
 
 31.5119 
 
 9.9766 
 
 .001007049 
 
 3,119.60 
 
 774,441.07 
 
 994 
 
 988,036 
 
 982,107,784 
 
 31.5278 
 
 9.9800 
 
 .001006036 
 
 3,122.74 
 
 776,001.66 
 
 995 
 
 990,025 
 
 985,074,875 
 
 31.5436 
 
 9.9833 
 
 .001005025 
 
 3,125.88 
 
 777,563.82 
 
 996 
 
 992,016 
 
 988,047,936 
 
 31.5595 
 
 9.9866 
 
 .001004016 
 
 3,129.03 
 
 779,127.54 
 
 997 
 
 994,009 
 
 991,026,973 
 
 31.5753 
 
 9.9900 
 
 .001003009 
 
 3,132.17 
 
 780,692.84 
 
 998 
 
 996,004 
 
 994,011,992 
 
 31.5911 
 
 9.9933 
 
 .001002004 
 
 3,135.31 
 
 782,259.71 
 
 999 
 
 998,001 
 
 997,002,999 
 
 31.6070 
 
 9.9967 
 
 .001001001 
 
 3,138.45 
 
 783,828.15 
 
 1000 
 
 1,000,000 
 
 1,000,000,000 
 
 31.6228 
 
 10.0000 
 
 .001000000 
 
 3,141.59 
 
 -85,398.16 
 
CIRCUMFERENCES AND AREAS OF CIRCLES 1097 
 
 CIRCUMFERENCES AND AREAS OF CIRCLES FROM 1-64 to 100 
 
 Diam. 
 
 Circum. Area 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 i 
 
 .0491 
 
 .0002 
 
 6 
 
 
 18.8496 
 
 28.2744 
 
 13 
 
 41.2335 
 
 135.297 
 
 $s 
 
 .0982 
 
 .0008 
 
 6- 
 
 
 19.2423 
 
 29.4648 
 
 13 
 
 
 41.6262 
 
 137.887 
 
 JL 
 
 .1963 
 
 .0031 
 
 6 
 
 
 19.6350 
 
 30.6797 
 
 
 42.0189 
 
 140.501 
 
 I 
 
 .3927 
 
 .0123 
 
 6 
 
 
 20.0277 
 
 31.9191 
 
 13* 
 
 42.4116 
 
 143.139 
 
 T S 6 
 
 .5890 
 
 .0276 
 
 6 
 
 
 20.4204 
 
 33.1831 
 
 13* 
 
 42.8043 
 
 145.802 
 
 i 
 
 .7854 
 
 .0491 
 
 6 
 
 
 20.8131 
 
 34.4717 
 
 13? 
 
 43.1970 
 
 148.490 
 
 A 
 
 .9817 
 
 .0767 
 
 6* 
 
 21.2058 
 
 35.7848 
 
 13* 
 
 43.5897 
 
 151.202 
 
 i 
 
 1.1781 
 
 .1104 
 
 61 
 
 
 21.5985 
 
 37.1224 
 
 14 , 
 
 43.9824 
 
 153.938 
 
 7 
 
 1.3744 
 
 .1503 
 
 7 
 
 
 21.9912 
 
 38.4846 
 
 
 44.3751 
 
 156.700 
 
 J 
 
 1.5708 
 
 .1963 
 
 7* 
 
 22.3839 
 
 39.8713 
 
 14* 
 
 44.7678 
 
 159.485 
 
 A 
 
 1.7671 
 
 .2485 
 
 7; 
 
 - 
 
 22.7766 
 
 41.2826 
 
 14 4 
 
 45.1605 
 
 162.296 
 
 1 
 
 1.9635 
 
 .3068 
 
 7 
 
 
 23.1693 
 
 42.7184 
 
 14* 
 
 45.5532 
 
 165.130 
 
 
 2.1598 
 
 .3712 
 
 7 
 
 
 23.5620 
 
 44.1787 
 
 14 
 
 
 45.9459 
 
 167.990 
 
 a 
 
 2.3562 
 
 .4418 
 
 7 
 
 
 
 23.9547 
 
 45.6636 
 
 14 
 
 
 46.3386 
 
 170.874 
 
 ri 
 
 2.5525 
 
 .5185 
 
 7i 
 
 
 24.3474 
 
 47.1731 
 
 
 46.7313 
 
 173.782 
 
 j 
 
 2.7489 
 
 .6013 
 
 7- 
 
 
 24.7401 
 
 48.7071 
 
 15* 
 
 47.1240 
 
 176.715 
 
 ti 
 
 2.9452 
 
 .6903 
 
 8 
 
 
 25.1328 
 
 50.265C 
 
 15 - 
 
 47.5167 
 
 179.673 
 
 1 
 
 3.1416 
 
 .7854 
 
 8- 
 
 . 
 
 25.5255 
 
 51.8487 
 
 15i 
 
 47.9094 
 
 182.655 
 
 H 
 
 3.5343 
 
 .9940 
 
 8; 
 
 . 
 
 25.9182 
 
 53.4563 
 
 15* 
 
 48.3021 
 
 185.661 
 
 l{ 
 
 3.9270 
 
 1.2272 
 
 8 
 
 
 
 26.3109 
 
 55.0884 
 
 15* 
 
 48.C948 
 
 188.692 
 
 If 
 
 4.3197 
 
 1.4849 
 
 8* 
 
 26.7036 
 
 56.7451 
 
 15* 
 
 49.0875 
 
 191.748 
 
 l* 
 
 4.7124 
 
 1.7671 
 
 8 
 
 
 
 27.0963 
 
 58.4264 
 
 15J 
 
 49.4802 
 
 194.828 
 
 if 
 
 5.1051 
 
 2.0739 
 
 
 
 27.4890 
 
 60.1322 
 
 15* 
 
 49.8729 
 
 197.933 
 
 If 
 
 5.4978 
 
 2.4053 
 
 8 
 
 
 27.8817 
 
 61.8625 
 
 16 
 
 50.2656 
 
 201.062 
 
 1* 
 
 5.8905 
 
 2.7612 
 
 9 
 
 
 28.2744 
 
 63.6174 
 
 16 
 
 
 50.6583 
 
 204.216 
 
 2 
 
 6.2832 
 
 3.1416 
 
 9- 
 
 . 
 
 28.6671 
 
 65.3968 
 
 16 
 
 
 51.0510 
 
 207.395 
 
 2* 
 
 6.6759 
 
 3.5466 
 
 9; 
 
 
 29.0598 
 
 67.2008 
 
 16 
 
 
 51.4437 
 
 210.598 
 
 3 
 
 7.0686 
 
 3.9761 
 
 9 
 
 
 29.4525 
 
 69.0293 
 
 16 
 
 
 51.8364 
 
 213.825 
 
 2* 
 
 7.4613 
 
 4.4301 
 
 9 
 
 
 29.8452 
 
 70.8823 
 
 16 
 
 52.2291 
 
 217.077 
 
 2* 
 
 7.8540 
 
 4.9087 
 
 9 
 
 
 
 30.2379 
 
 72.7599 
 
 16J 
 
 52.6218 
 
 220.354 
 
 
 8.2467 
 
 5.4119 
 
 9 
 
 
 
 30.6306 
 
 74.6621 
 
 16* 
 
 53.0145 
 
 223.655 
 
 2* 
 
 8.6394 
 
 5.9396 
 
 9i 
 
 
 31.0233 
 
 76.589 
 
 17 
 
 53.4072 
 
 226.981 
 
 2* . 
 
 9.0321 
 
 6.4918 
 
 10 
 
 
 31.4160 
 
 78.540 
 
 17 
 
 
 53.7999 
 
 230.331 
 
 3 
 
 9.4248 
 
 7.0686 
 
 10- 
 
 . 
 
 31.8087 
 
 80.516 
 
 17 
 
 
 54.1926 
 
 233.706 
 
 3* 
 
 9.8175 
 
 7.6699 
 
 10 
 
 
 32.2014 
 
 82.516 
 
 17 
 
 
 54.5853 
 
 237.105 
 
 3 
 
 10.2102 
 
 8.2958 
 
 10* 
 
 32.5941 
 
 84.541 
 
 17 
 
 
 54.9780 
 
 240.529 
 
 3* 
 
 10.6029 
 
 8.9462 
 
 10 
 
 
 
 32.9868 
 
 86.590 
 
 17 
 
 
 55.3707 
 
 243.977 
 
 3* 
 
 10.9956 
 
 9.6211 
 
 10 
 
 
 
 33.3795 
 
 88.664 
 
 17 
 
 
 55.7634 
 
 247.450 
 
 
 11.3883 
 
 10.3206 
 
 10J 
 
 33.7722 
 
 90.763 
 
 
 56.1561 
 
 250.948 
 
 3} 
 
 11.7810 
 
 11.0447 
 
 10 
 
 
 34.1649 
 
 92.886 
 
 18* 
 
 56.5488 
 
 254.470 
 
 3* 
 
 12.1737 
 
 11.7933 
 
 11 
 
 
 34.5576 
 
 95.033 
 
 18* 
 
 56.9415 
 
 258.016 
 
 4 
 
 12.5664 
 
 12.5664 
 
 11- 
 
 . 
 
 34.9503 
 
 97.205 
 
 18- 
 
 57.3342 
 
 261.587 
 
 4* 
 
 12.9591 
 
 13.3641 
 
 11 
 
 
 35.3430 
 
 99.402 
 
 18* 
 
 57.7269 
 
 265.183 
 
 3 
 
 13.3518 
 
 14.1863 
 
 11* 
 
 35.7357 
 
 101.623 
 
 18* 
 
 58.1106 
 
 268.803 
 
 4* 
 
 13.7445 
 
 15.0330 
 
 11 
 
 i 
 
 36.1284 
 
 103.869 
 
 18 
 
 
 58.5123 
 
 272.448 
 
 4* 
 
 14.1372 
 
 15.9043 
 
 11 
 
 
 
 36.5211 
 
 106.139 
 
 18 
 
 
 58.9050 
 
 276.117 
 
 
 14.5299 
 
 16.8002 
 
 11 
 
 
 
 36.9138 
 
 108.434 
 
 18* 
 
 59.2977 
 
 279.811 
 
 4 
 
 14.9226 
 
 17.7206 
 
 111 
 
 
 
 37.3065 
 
 110.754 
 
 19 
 
 59.6904 
 
 283.529 
 
 4* 
 
 15.3153 
 
 18.6555 
 
 12 
 
 
 37.6992 
 
 113.098 
 
 19 
 
 
 60.0831 
 
 287.272 
 
 5 
 
 15.7080 
 
 19.6350 
 
 12- 
 
 
 38.0919 
 
 115.466 
 
 19, 
 
 
 60.4758 
 
 291.040 
 
 
 16.1007 
 
 20.6290 
 
 12 
 
 
 38.4846 
 
 117.859 
 
 19- 
 
 
 60.8685 
 
 294.832 
 
 rjl 
 
 16.4934 
 
 21.6476 
 
 12 
 
 
 38.8773 
 
 120.277 
 
 19 
 
 
 61.2612 
 
 29S.&48 
 
 5i 
 
 16.8861 
 
 22.6907 
 
 12 
 
 
 39.2700 
 
 122.719 
 
 19 
 
 
 61.6539 
 
 302.489 
 
 c? 
 
 17 2788 
 
 23.7583 
 
 12 
 
 
 39.6627 
 
 125.185 
 
 19 
 
 
 62.0466 
 
 306.355 
 
 5* 
 
 17.6715 
 
 24.8505 
 
 12 
 
 
 40.0554 
 
 127.677 
 
 19 
 
 
 62.4393 
 
 310.245 
 
 5f 
 
 18.0642 
 
 25.9673 
 
 
 
 
 40.4481 
 
 130.192 
 
 20 
 
 62.8320 
 
 314.160 
 
 5* 
 
 18.4569 
 
 27.1086 
 
 13 
 
 
 40.8408 
 
 132.733 
 
 20* 
 
 63.2247 
 
 318.099 
 
1098 
 
 CIRCUMFERENCES AND AREAS OF CIRCLES 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 20} 
 
 63.6174 
 
 322.063 
 
 28 
 
 \ ' 
 
 88.3575 
 
 621.264 
 
 36 
 
 113.098 
 
 1,017.878 
 
 20f 
 
 64.0101 
 
 326.051 
 
 28 
 
 I 
 
 88.7502 
 
 626.798 
 
 36 1 
 
 113.490 
 
 1,024.960 
 
 201 
 
 64.4028 
 
 330.064 
 
 28 
 
 ( 
 
 89.1429 
 
 632.357 
 
 36* 
 
 113.883 
 
 1,032.065 
 
 
 64.7955 
 
 334.102 
 
 28 
 
 1 
 
 89.5356 
 
 637.941 
 
 36| 
 
 114.276 
 
 1,039.195 
 
 20* 
 
 65.1882 
 
 338.164 
 
 28 
 
 t ; -' 
 
 89.9283 
 
 643.549 
 
 36| 
 
 114.668 
 
 1,046.349 
 
 201 
 
 65.5809 
 
 342.250 
 
 28* 
 
 90.3210 
 
 649.182 
 
 
 115.061 
 
 1,053.528 
 
 21 
 
 65.9736 
 
 346.361 
 
 28 
 
 f, 
 
 90.7137 
 
 654.840 
 
 36* 
 
 115.454 
 
 1,060.732 
 
 21; 
 
 66.3663 
 
 350.497 
 
 29 
 
 
 91.1064 
 
 660.521 
 
 361 
 
 115.846 
 
 1,067.960 
 
 21; 
 
 66.7590 
 
 354.657 
 
 29 
 
 
 91.4991 
 
 666.228 
 
 37 
 
 116.239 
 
 1,075.213 
 
 21- 
 
 67.1517 
 
 358.842 
 
 29 
 
 
 91.8918 
 
 671.959 
 
 371 
 
 116.632 
 
 1,082.490 
 
 2li 
 
 67.5444 
 
 363.051 
 
 29 
 
 
 92.2845 
 
 677.714 
 
 8?| 
 
 117.025 
 
 1,089.792 
 
 21i 
 
 67.9371 
 
 367.285 
 
 29 
 
 
 92.6772 
 
 683.494 
 
 37* 
 
 117.417 
 
 1,097.118 
 
 21; 
 
 68.3298 
 
 371.543 
 
 29 
 
 
 93.0699 
 
 689.299 
 
 371 
 
 117.810 
 
 1,104.469 
 
 211 
 
 68.7225 
 
 375.826 
 
 29 
 
 
 93.4626 
 
 695.128 
 
 37* 
 
 118.203 
 
 1,111.844 
 
 22 
 
 69.1152 
 
 380.134 
 
 291 
 
 93.8553 
 
 700.982 
 
 37* 
 
 118.595 
 
 1,119.244 
 
 22} 
 
 69.5079 
 
 384.466 
 
 30 
 
 
 94.2480 
 
 706.860 
 
 371 
 
 118.988 
 
 1,126.669 
 
 22- 
 
 69.9006 
 
 388.822 
 
 30 
 
 I 
 
 94.6407 
 
 712.763 
 
 38 
 
 119.381 
 
 1,134.118 
 
 22f 
 
 70.2933 
 
 393.203 
 
 30* 
 
 95.0334 
 
 718.690 
 
 38} 
 
 119.773 
 
 1,141.591 
 
 22y 
 
 70.6860 
 
 397.609 
 
 30 
 
 \\~ 
 
 95.4261 
 
 724.642 
 
 38} 
 
 120.166 
 
 1,149.089 
 
 224 
 
 71.0787 
 
 402.038 
 
 30 
 
 
 95.8188 
 
 730.618 
 
 38| 
 
 120.559 
 
 1,156.612 
 
 22* 
 
 71.4714' 
 
 406.494 
 
 30 
 
 
 96.2115 
 
 736.619 
 
 38} 
 
 120.952 
 
 1,164.159 
 
 221 
 
 71.8641 
 
 410.973 
 
 30 
 
 } 
 
 96.6042 
 
 742.645 
 
 
 121.344 
 
 1,171.731 
 
 23 
 
 72.2568 
 
 415.477 
 
 30- 
 
 > _ 
 
 96.9969 
 
 748.695 
 
 38* 
 
 121.737 
 
 1,179.327 
 
 23 - 
 
 72.6495 
 
 420.004 
 
 31 
 
 
 97.3896 
 
 754.769 
 
 381 
 
 122.130 
 
 1,186.948 
 
 23! 
 
 73.0422 
 
 424.558 
 
 31- 
 
 
 97.7823 
 
 760.869 
 
 39 
 
 122.522 
 
 1,194.593 
 
 23f 
 
 73.4349 
 
 429.135 
 
 31 
 
 
 98.1750 
 
 766.992 
 
 391 
 
 122.915 
 
 1,202.263 
 
 231 
 
 73.8276 
 
 433.737 
 
 31 
 
 
 98.5677 
 
 773.140 
 
 39| 
 
 123.308 
 
 1,209.958 
 
 23| 
 
 74.2203 
 
 438.364 
 
 31 
 
 
 98.9604 
 
 779.313 
 
 
 123.700 
 
 1,217.677 
 
 23* 
 
 74.6130 
 
 443.015 
 
 31; 
 
 
 99.3531 
 
 785.510 
 
 39! 
 
 124.093 
 
 1,225.420 
 
 231 
 
 75.0057 
 
 447.690 
 
 31 
 
 
 99.7458 
 
 791.732 
 
 39* 
 
 124.486 
 
 1,233.188 
 
 24 j 
 
 75.3984 
 
 452.390 
 
 31j 
 
 
 
 100.1385 
 
 797.979 
 
 39* 
 
 124.879 
 
 1,240.981 
 
 
 75.7911 
 
 457.115 
 
 32 
 
 
 100.5312 
 
 804.250 
 
 391 
 
 125.271 
 
 1,248.798 
 
 24- 
 
 76.1838 
 
 461.864 
 
 32; 
 
 
 100.9239 
 
 810.545 
 
 40 
 
 125.664 
 
 1,256.640 
 
 24| 
 
 76.5765 
 
 466.638 
 
 32 
 
 
 101.3166 
 
 816.865 
 
 40} 
 
 126.057 
 
 1,264.510 
 
 
 76.9692 
 
 471.436 
 
 32; 
 
 
 101.7093 
 
 823.210 
 
 40| 
 
 126.449 
 
 1,272.400 
 
 24| 
 
 77.3619 
 
 476.259 
 
 32, 
 
 
 102.1020 
 
 829.579 
 
 40* 
 
 126.842 
 
 1,280.310 
 
 24* 
 
 77.7546 
 
 481.107 
 
 32i 
 
 
 102.4947 
 
 835.972 
 
 401 
 
 127.235 
 
 1,288.250 
 
 241 
 
 78.1473 
 
 485.979 
 
 323 
 
 
 102.8874 
 
 842.391 
 
 40| 
 
 127.627 
 
 1,296.220 
 
 25 
 
 78.5400 
 
 490.875 
 
 321 
 
 103.280 
 
 848.833 
 
 40* 
 
 128.020 
 
 1,304.210 
 
 25 1 
 
 78.9327 
 
 495.796 
 
 33 
 
 
 103.673 
 
 855.301 
 
 401 
 
 128.413 
 
 1,312.220 
 
 25} 
 
 79.3254 
 
 500.742 
 
 33i 
 
 
 104.065 
 
 861.792 
 
 41 
 
 128.806 
 
 1,320.260 
 
 25f 
 
 79.7181 
 
 505.712 
 
 33: 
 
 
 104.458 
 
 868.309 
 
 41} 
 
 129.198 
 
 1,328.320 
 
 25} 
 
 80.1108 
 
 510.706 
 
 33; 
 
 
 104.851 
 
 874.850 
 
 
 129.591 
 
 1,336.410 
 
 25| 
 
 80.5035 
 
 515.726 
 
 33i 
 
 
 105.244 
 
 881.415 
 
 41f 
 
 129.984 
 
 1,344.520 
 
 25* 
 
 80.8962 
 
 520.769 
 
 33i 
 
 
 105.636 
 
 888.005 
 
 
 130.376 
 
 1,352.660 
 
 251 
 
 81.2889 
 
 525.838 
 
 33; 
 
 
 106.029 
 
 894.620 
 
 4l| 
 
 130.769 
 
 1,360.820 
 
 26 
 
 81.6816 
 
 530.930 
 
 
 
 106.422 
 
 901.259 
 
 41* 
 
 131.162 
 
 1,369.000 
 
 26} 
 
 82.0743 
 
 536.048 
 
 34 1 
 
 
 106.814 
 
 907.922 
 
 411 
 
 131.554 
 
 1,377.210 
 
 26|- 
 
 82.4670 
 
 541.190 
 
 34! 
 
 
 107.207 
 
 914.611 
 
 42 
 
 131.947 
 
 1,385.450 
 
 26| 
 
 82.8597 
 
 546.356 
 
 34* 
 
 107.600 
 
 921.323 
 
 42} 
 
 132.340 
 
 1,393.700 
 
 26} 
 
 83.2524 
 
 551.547 
 
 34| 
 
 
 107.992 
 
 928.061 
 
 42} 
 
 132.733 
 
 1,401.990 
 
 26| 
 
 83.6451 
 
 556.763 
 
 
 
 108.385 
 
 934.822 
 
 42* 
 
 133.125 
 
 1,410.300 
 
 26* 
 
 84.0378 
 
 562.003 
 
 34i 
 
 
 108.778 
 
 941.609 
 
 421 
 
 133.518 
 
 1,418.630 
 
 261 
 
 84.4305 
 
 567.267 
 
 34; 
 
 
 109.171 
 
 948.420 
 
 42| 
 
 133.911 
 
 1,426.990 
 
 27 
 
 84.8232 
 
 572.557 
 
 
 
 109.563 
 
 955.255 
 
 42* 
 
 134.303 
 
 1,435.370 
 
 27} 
 
 85.2159 
 
 577.870 
 
 35* 
 
 
 109.956 
 
 962.115 
 
 421 
 
 134.696 
 
 1,443.770 
 
 27} 
 
 85.6086 
 
 583.209 
 
 351 
 
 
 110.349 
 
 969.000 
 
 43 
 
 135.089 
 
 1,452.200 
 
 27* 
 
 86.0013 
 
 588.571 
 
 35^ 
 
 110.741 
 
 975.909 
 
 43} 
 
 135.481 
 
 1,460.660 
 
 271 
 
 86.3940 
 
 593.959 
 
 358 
 
 
 111.134 
 
 982.842 
 
 43} 
 
 135.874 
 
 1,469.140 
 
 27* 
 
 86.7867 
 
 599.371 
 
 35* 
 
 
 111.527 
 
 989.800 
 
 43J 
 
 136.267 
 
 1,477.640 
 
 27* 
 
 87.1794 
 
 604.807 
 
 35| 
 
 111.919 
 
 996.783 
 
 431 
 
 136.660 
 
 1,486.170 
 
 271 
 
 87.5721 
 
 610.268 
 
 351 
 
 
 112.312 
 
 1,003.790 
 
 43| 
 
 137.052 
 
 1,494.730 
 
 28 
 
 87.9648 
 
 615.754 
 
 351 
 
 112.705 
 
 1,010.822 
 
 43* 
 
 137.445 
 
 1,503.300 
 
CIRCUMFERENCES AND AREAS OF CIRCLES 
 
 1099 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 43} 
 
 137.838 
 
 1,511.910 
 
 51$ 
 
 162.578 
 
 2,103.35 
 
 59| 
 
 187.318 
 
 2,792.21 
 
 44 
 
 138.230 
 
 1,520.530 
 
 51} 
 
 162.970 
 
 2,113.52 
 
 59$ 
 
 187.711 
 
 2,803.93 
 
 44} 
 
 138.623 
 
 1,529.190 
 
 52 
 
 163.363 
 
 2,123.72 
 
 59} 
 
 188.103 
 
 2,815.67 
 
 44} 
 
 139.016 
 
 1,537.860 
 
 52} 
 
 163.756 
 
 2,133.94 
 
 60 
 
 188.496 
 
 2,827.44 
 
 44f 
 
 139.408 
 
 1,546.56 
 
 52} 
 
 164.149 
 
 2,144.19 
 
 60} 
 
 188.889 
 
 2,839.23 
 
 44} 
 
 139.801 
 
 1,555.29 
 
 52f 
 
 164.541 
 
 2,154.46 
 
 60} 
 
 189.281 
 
 2,851.05 
 
 44| 
 
 140.194 
 
 1,564.04 
 
 52} 
 
 164.934 
 
 2,164.76 
 
 60f 
 
 189.674 
 
 2,862.89 
 
 44$ 
 
 140.587 
 
 1,572.81 
 
 52| 
 
 165.327 
 
 2,175.08 
 
 60} 
 
 190.067 
 
 2,874.76 
 
 44} 
 
 140.979 
 
 1,581.61 
 
 52$ 
 
 165.719 
 
 2,185.42 
 
 60| 
 
 190.459 
 
 2,886.65 
 
 45 I 
 
 141.372 
 
 1,590.43 
 
 52} 
 
 166.112 
 
 2,195.79 
 
 60$ 
 
 190.852 
 
 2,898.57 
 
 
 141.765 
 
 1,599.28 
 
 53 
 
 166.505 
 
 2,206.19 
 
 60} 
 
 191.245 
 
 2,910.51 
 
 45{ 
 
 142.157 
 
 1,608.16 
 
 53} 
 
 166.897 
 
 2,216.61 
 
 61 
 
 191.638 
 
 2,922.47 
 
 45| 
 
 142.550 
 
 1,617.05 
 
 53} 
 
 167.290 
 
 2,227.05 
 
 61} 
 
 192.030 
 
 2,934.46 
 
 
 142.943 
 
 1,625.97 
 
 53f 
 
 167.683 
 
 2,237.52 
 
 61} 
 
 192.423 
 
 2,946.48 
 
 45| 
 
 143.335 
 
 1,634.92 
 
 53} 
 
 168.076 
 
 2,248.01 
 
 61 a 
 
 192.816 
 
 2,958.52 
 
 45$ 
 
 143.728 
 
 1,643.89 
 
 53| 
 
 168.468 
 
 2,258.53 
 
 61} 
 
 193.208 
 
 2,970.58 
 
 45} 
 
 144.121 
 
 1,652.89 
 
 53$ 
 
 168.861 
 
 2,269.07 
 
 
 193.601 
 
 2,982.67 
 
 46 
 
 144.514 
 
 1,661.91 
 
 53} 
 
 169.254 
 
 2,279.64 
 
 61$ 
 
 193.994 
 
 2,994.78 
 
 46} 
 
 144.906 
 
 1,670.95 
 
 54 
 
 169.646 
 
 2,290.23 
 
 61} 
 
 194.386 
 
 3,006.92 
 
 46} 
 
 145.299 
 
 1,680.02 
 
 54} 
 
 170.039 
 
 2,300.84 
 
 62 
 
 194.779 
 
 3,019.08 
 
 46| 
 
 145.692 
 
 1,689.11 
 
 54} 
 
 170.432 
 
 2,311.48 
 
 62} 
 
 195.172 
 
 3,031.26 
 
 46} 
 
 146.084 
 
 1,698.23 
 
 54f 
 
 170.824 
 
 2,322.15 
 
 62} 
 
 195.565 
 
 3,043.47 
 
 46| 
 
 146.477 
 
 1,707.37 
 
 54} 
 
 171.217 
 
 2,332.83 
 
 62| 
 
 195.957 
 
 3,055.71 
 
 46$ 
 
 146.870 
 
 1,716.54 
 
 54f 
 
 171.610 
 
 2,343.55 
 
 62} 
 
 196.350 
 
 3,067.97 
 
 46} 
 
 147.262 
 
 1,725.73 
 
 
 172.003 
 
 2,354.29 
 
 62| 
 
 196.743 
 
 3,080.25 
 
 47 
 
 147.655 
 
 1,734.95 
 
 54} 
 
 172.395 
 
 2,365.05 
 
 62$ 
 
 197.135 
 
 3,092.56 
 
 47} 
 
 148.048 
 
 1,744.19 
 
 55 
 
 172.788 
 
 2,375.83 
 
 62} 
 
 197.528 
 
 3,104.89 
 
 47| 
 47| 
 
 148.441 
 148.833 
 
 1,753.45 
 1,762.74 
 
 1! 
 
 173.181 
 173.573 
 
 2,386.65 
 2,397.48 
 
 63 
 63} 
 
 197.921 
 198.313 
 
 3,117.25 
 3,129.64 
 
 47} 
 
 149.226 
 
 1,772.06 
 
 55| 
 
 173.966 
 
 2,408.34 
 
 63} 
 
 198.706 
 
 3,142.04 
 
 47| 
 
 149.619 
 
 1,781.40 
 
 55} 
 
 174.359 
 
 2,419.23 
 
 63f 
 
 199.099 
 
 3,154.47 
 
 47$ 
 
 150.011 
 
 1,790.76 
 
 55| 
 
 174.751 
 
 2,430.14 
 
 63} 
 
 199.492 
 
 3,166.93 
 
 47} 
 
 150.404 
 
 1,800.15 
 
 55$ 
 
 175.144 
 
 2,441.07 
 
 63| 
 
 199.884 
 
 3,179.41 
 
 48 
 
 150.797 
 
 1,809.56 
 
 55} 
 
 175.537 
 
 2,452.03 
 
 63$ 
 
 200.277 
 
 3,191.91 
 
 48} 
 
 151.189 
 
 1,819.00 
 
 56 
 
 175.930 
 
 2,463.01 
 
 63} 
 
 200.670 
 
 3,204.44 
 
 48} 
 
 a 
 
 151.582 
 151.975 
 152.368 
 
 1,828.46 
 1,837.95 
 1,847.46 
 
 1 
 
 176.322 
 176.715 
 177.108 
 
 2,474.02 
 2,485.05 
 2,496.11 
 
 64 
 
 64} 
 64} 
 
 201.062 
 201.455 
 201.848 
 
 3,217.00 
 3,229.58 
 3,242.18 
 
 48| 
 
 152.760 
 
 1,856.99 
 
 56 1 
 
 177.500 
 
 2,507.19 
 
 64| 
 
 202.240 
 
 3,254.81 
 
 48$ 
 
 153.153 
 
 1,866.55 
 
 56| 
 
 177.893 
 
 2,518.30 
 
 64} 
 
 202.633 
 
 3,267.46 
 
 48} 
 
 153.546 
 
 1,876.14 
 
 
 178.286 
 
 2,529.43 
 
 64| 
 
 203.026 
 
 3,280.14 
 
 49 
 
 153.938 
 
 1,885.75 
 
 56} 
 
 178.678 
 
 2,540.58 
 
 64$ 
 
 203.419 
 
 3,292.84 
 
 1 
 
 154.331 
 154.724 
 
 1,895.38 
 1,905.04 
 
 57 
 57} 
 
 179.071 
 179.464 
 
 2,551.76 
 2,562.97 
 
 64} 
 65 
 
 203.811 
 204.204 
 
 3,305.56 
 3,318.31 
 
 
 155.116 
 155.509 
 
 1,914.72 
 1,924.43 
 
 57; 
 
 179.857 
 180.249 
 
 2,574.20 
 2,585.45 
 
 i? 
 
 204.597 
 204.989 
 
 3,331.09 
 3,343.89 
 
 49| 
 
 155.902 
 
 1,934.16 
 
 57i- 
 
 180.642 
 
 2,596.73 
 
 65f 
 
 205.382 
 
 3,356.71 
 
 49$ 
 
 156.295 
 
 1,943.91 
 
 674 
 
 181.035 
 
 2,608.03 
 
 65} 
 
 205.775 
 
 3,369.56 
 
 491 
 
 156.687 
 
 1,953.69 
 
 57; 
 
 181.427 
 
 2,619.36 
 
 65* 
 
 206.167 
 
 3,382.44 
 
 50 
 1 
 
 157.080 
 157.473 
 157.865 
 
 1,963.50 
 1,973.33 
 1,983.18 
 
 57} 
 58 
 58} 
 
 181.820 
 182.213 
 182.605 
 
 2,630.71 
 2,642.09 
 2,653.49 
 
 65$ 
 65} 
 66 
 
 206.560 
 206.953 
 207.346 
 
 3,395.33 
 3,408.26 
 3,421.20 
 
 
 158.258 
 
 1,993.06 
 
 58} 
 
 182.998 
 
 2,664.91 
 
 m 
 
 207.738 
 
 3,434.17 
 
 1 
 
 158.651 
 159.043 
 159 436 
 
 2,002.97 
 2,012.89 
 2,022.85 
 
 58| 
 58}. 
 
 183.391 
 183.784 
 184.176 
 
 2,676.36 
 2,687.84 
 2,699.33 
 
 eel 
 
 66| 
 66} 
 
 208.131 
 208.524 
 208.916 
 
 8,447.17 
 3,460.19 
 3,473.24 
 
 51 
 
 51} 
 
 51f 
 
 159.829 
 160.222 
 160.614 
 161.007 
 161.400 
 161.792 
 
 2,032.82 
 2,042.83 
 2,052.85 
 2,062.90 
 2,072.98 
 2 083.08 
 
 58} 
 59 i 
 
 59| 
 
 184.569 
 184.962 
 185.354 
 185.747 
 186.140 
 186.532 
 
 2,710.86 
 2,722.41 
 2,733.98 
 2,745.57 
 2,757.20 
 2,768.84 
 
 66| 
 66$ 
 66} 
 67 
 67} 
 67} 
 
 209.309 
 209.702 
 210.094 
 210.487 
 210.880 
 211.273 
 
 3,486.30 
 3,499.40 
 3,512.52 
 3,525.66 
 3,538.83 
 3,552.02 
 
 51| 
 
 162.185 
 
 2,093.20 
 
 59} 
 
 186.925 
 
 2,780.51 
 
 67| 
 
 211.665 
 
 3,565.24 
 
1100 
 
 CIRCUMFERENCES AND AREAS OF CIRCLES 
 
 Diarn. 
 
 Circum. 
 
 Area 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 67} 
 
 212.058 
 
 3,578.48 
 
 75| 
 
 236.798 
 
 4,462.16 
 
 83} 
 
 261.538 
 
 5,443.26 
 
 67| 
 
 212.451 
 
 3,591.74 
 
 75} 
 
 237.191 
 
 4,476.98 
 
 83* 
 
 261.931 
 
 5,459.62 
 
 67* 
 
 212.843 
 
 3,605.04 
 
 75| 
 
 237.583 
 
 4,491.81 
 
 83} 
 
 262.324 
 
 5,476.01 
 
 67* 
 
 213.236 
 
 3,618.35 
 
 75* 
 
 237.976 
 
 4,506.67 
 
 83! 
 
 262.716 
 
 5,492.41 
 
 68 
 
 213.629 
 
 3,631.69 
 
 75* 
 
 238.369 
 
 4,521.56 
 
 83* 
 
 263.109 
 
 5,508.84 
 
 68} 
 
 214.021 
 
 3,645.05 
 
 76 
 
 238.762 
 
 4,536.47 
 
 83} 
 
 263.502 
 
 5,525.30 
 
 68} 
 
 214.414 
 
 3,658.44 
 
 76} 
 
 239.154 
 
 4,551.41 
 
 84 
 
 263,894 
 
 5,541.78 
 
 68f 
 
 214.807 
 
 3,671.86 
 
 76} 
 
 239.547 
 
 4,566.36 
 
 84} 
 
 264.287 
 
 5,558.29 
 
 68} 
 
 215.200 
 
 3,685.29 
 
 76| 
 
 239.940 
 
 4,581.35 
 
 84} 
 
 264.680 
 
 5,574.82 
 
 68| 
 
 215.592 
 
 3,698.76 
 
 76} 
 
 240.332 
 
 4,596.36 
 
 84| 
 
 265.072 
 
 5,591.37 
 
 68* 
 
 215.985 
 
 3,712.24 
 
 76| 
 
 240.725 
 
 4,611.39 
 
 84} 
 
 265.465 
 
 5,607.95 
 
 68} 
 
 216.378 
 
 3,725.75 
 
 76* 
 
 241.118 
 
 4,626.45 
 
 84! 
 
 265.858 
 
 5,624.56 
 
 69 
 
 216.770 
 
 3,739.29 
 
 76} 
 
 241.510 
 
 4,641.53 
 
 84* 
 
 266.251 
 
 5,641.18 
 
 69} 
 
 217.163 
 
 3,752.85 
 
 77 
 
 241.903 
 
 4,656.64 
 
 84} 
 
 266.643 
 
 5,657.84 
 
 69} 
 
 217.556 
 
 3,766.43 
 
 77} 
 
 242.296 
 
 4,671.77 
 
 85 
 
 267.036 
 
 5,674.51 
 
 69J 
 
 217.948 
 
 3,780.04 
 
 77| 
 
 242.689 
 
 4,686.92 
 
 85} 
 
 267.429 
 
 5,691.22 
 
 69} 
 
 218.341 
 
 3,793.68 
 
 77J 
 
 243.081 
 
 4,702.10 
 
 85- 
 
 267.821 
 
 5,707.94 
 
 69! 
 
 218.734 
 
 3,807.34 
 
 77} 
 
 243.474 
 
 4,717.31 
 
 851 
 
 268.214 
 
 5,724.69 
 
 69* 
 
 219.127 
 
 3,821.02 
 
 77! 
 
 243.867 
 
 4,732.54 
 
 85} 
 
 268.607 
 
 5,741.47 
 
 69* 
 
 219.519 
 
 3,834.73 
 
 77$ 
 
 244.259 
 
 4,747.79 
 
 85| 
 
 268.999 
 
 5,758.27 
 
 70 
 
 219.912 
 
 3,848.46 
 
 77* 
 
 244.652 
 
 4,763.07 
 
 85* 
 
 269.392 
 
 5,775.10 
 
 70} 
 
 220.305 
 
 3,862.22 
 
 78 
 
 245.045 
 
 4,778.37 
 
 85} 
 
 269.785 
 
 5,791.94 
 
 7(4 
 
 220.697 
 
 3,876.00 
 
 78} 
 
 245.437 
 
 4,793.70 
 
 86 
 
 270.178 
 
 5,808.82 
 
 70| 
 
 221.090 
 
 3,889.80 
 
 78} 
 
 245.830 
 
 4,809.05 
 
 86J 
 
 270.570 
 
 5,825.72 
 
 70} 
 
 221.483 
 
 3,903.63 
 
 78| 
 
 246.223 
 
 4,824.43 
 
 86} 
 
 270.963 
 
 5,842.64 
 
 70| 
 
 221.875 
 
 3,917.49 
 
 78} 
 
 246.616 
 
 4,839.83 
 
 86| 
 
 271.356 
 
 5.859.59 
 
 70* 
 
 222.268 
 
 3,931.37 
 
 78| 
 
 247.008 
 
 4,855.26 
 
 86} 
 
 271.748 
 
 5,876.56 
 
 70} 
 
 222.661 
 
 3,945.27 
 
 78* 
 
 247.401 
 
 4,870.71 
 
 86| 
 
 272.141 
 
 5,893.55 
 
 71 
 
 223.054 
 
 3,959.20 
 
 78} 
 
 247.794 
 
 4,886.18 
 
 86* 
 
 272.534 
 
 5,910.58 
 
 71} 
 
 223.446 
 
 3,973.15 
 
 79 
 
 248.186 
 
 4,901.68 
 
 86} 
 
 272.926 
 
 5,927.62 
 
 71} 
 
 223.839 
 
 3,987.13 
 
 79} 
 
 248.579 
 
 4,917.21 
 
 87 
 
 273.319 
 
 5,944.69 
 
 71! 
 7U 
 
 224.232 
 224.624 
 
 4,001.13 
 4,015.16 
 
 79} 
 79| 
 
 248.972 
 249.364 
 
 4,932.75 
 4,948.33 
 
 87} 
 
 87} 
 
 273.712 
 274.105 
 
 5,961.79 
 5,978.91 
 
 71| 
 
 225.017 
 
 4,029.21 
 
 79} 
 
 249.757 
 
 4,963.92 
 
 87| 
 
 274.497 
 
 5,996.05 
 
 71* 
 
 225.410 
 
 4,043.29 
 
 79| 
 
 250.150 
 
 4,979.55 
 
 87} 
 
 274.890 
 
 6,013.22 
 
 71} 
 
 225.802 
 
 4,057.39 
 
 79* 
 
 250.543 
 
 4,995.19 
 
 87! 
 
 275.283 
 
 6,030.41 
 
 72 
 
 226.195 
 
 4,071.51 
 
 79} 
 
 250.935 
 
 5,010.86 
 
 87* 
 
 275.675 
 
 6,047.63 
 
 72} 
 
 226.588 
 
 4,085.66 
 
 80 
 
 251.328 
 
 5,026.56 
 
 87} 
 
 276.068 
 
 6,064.87 
 
 72| 
 
 226.981 
 
 4,099.84 
 
 80} 
 
 251.721 
 
 5,042.28 
 
 88 
 
 276.461 
 
 6,082.14 
 
 72| 
 
 227.373 
 
 4,114.04 
 
 80} 
 
 252.113 
 
 5,058.03 
 
 88} 
 
 276.853 
 
 6,099.43 
 
 72* 
 
 227.766 
 
 4,128.26 
 
 
 252.506 
 
 5,073.79 
 
 88} 
 
 277.246 
 
 6,116.74 
 
 72| 
 
 228.159 
 
 4,142.51 
 
 80} 
 
 252.899 
 
 5,089.59 
 
 88} 
 
 277.629 
 
 6,134.08 
 
 72* 
 
 228.551 
 
 4,156.78 
 
 80| 
 
 253.291 
 
 5,105.41 
 
 88} 
 
 278.032 
 
 6,151.45 
 
 72* 
 
 228.944 
 
 4,171.08 
 
 80* 
 
 253.684 
 
 5,121.25 
 
 88! 
 
 278.424 
 
 6,168.84 
 
 73 
 
 229.337 
 
 4,185.40 
 
 80} 
 
 254.077 
 
 5,137.12 
 
 88* 
 
 278.817 
 
 6,186.25 
 
 73} 
 
 229.729 
 
 4,199.74 
 
 81 
 
 254.470 
 
 5,153.01 
 
 88} 
 
 279.210 
 
 6,203.69 
 
 73} 
 
 230.122 
 
 4,214.11 
 
 81} 
 
 254.862 
 
 5,168.93 
 
 8 
 
 279.602 
 
 6,221.15 
 
 78t 
 
 230.515 
 
 4,228.51 
 
 81} 
 
 255.255 
 
 5,184.87 
 
 
 279.995 
 
 6,238.64 
 
 73} 
 
 230.908 
 
 4,242.93 
 
 81J 
 
 255.648 
 
 5,200.83 
 
 ggi 
 
 280.388 
 
 6,256.15 
 
 73| 
 
 231.300 
 
 4,257.37 
 
 81} 
 
 256.040 
 
 5,216.82 
 
 89| 
 
 280.780 
 
 6,273.69 
 
 73* 
 
 231.693 
 
 4,271.84 
 
 81| 
 
 256.433 
 
 5,232.84 
 
 89} 
 
 281.173 
 
 6,291.25 
 
 73} 
 
 232.086 
 
 4,286.33 
 
 81* 
 
 256.826 
 
 5,248.88 
 
 89! 
 
 281.566 
 
 6,308.84 
 
 74 
 
 232.478 
 
 4,300.85 
 
 81} 
 
 257.218 
 
 5,264.94 
 
 89* 
 
 281.959 
 
 6,326.45 
 
 74} 
 
 232.871 
 
 4,315.39 
 
 82 
 
 257.611 
 
 5,281.03 
 
 89} 
 
 282.351 
 
 6,344.08 
 
 74 
 74| 
 
 233.264 
 233.656 
 
 4,329.96 
 4,344.55 
 
 82} 
 82} 
 
 258.004 
 258.397 
 
 5,297.14 
 5,313.28 
 
 90 
 90} 
 
 282.744 
 283.137 
 
 6,361.74 
 6,379.42 
 
 74} 
 
 234.049 
 
 4,359.17 
 
 82f 
 
 258.789 
 
 5,329.44 
 
 90} 
 
 283.529 
 
 6,397.13 
 
 74| 
 
 234.442 
 
 4,373.81 
 
 82} 
 
 259.182 
 
 5,345.63 
 
 90f 
 
 283.922 
 
 6,414.86 
 
 74* 
 
 234.835 
 
 4,388.47 
 
 82! 
 
 259.575 
 
 5,361.84 
 
 90} 
 
 284.315 
 
 6,432.62 
 
 74} 
 
 235.227 
 
 4,403.16 
 
 82* 
 
 259.967 
 
 5,378.08 
 
 90! 
 
 284.707 
 
 6,450.40 
 
 75 
 
 235.620 
 
 4,417.87 
 
 82} 
 
 260.360 
 
 5,394.34 
 
 90* 
 
 285.100 
 
 6,468.21 
 
 75} 
 
 236.013 
 
 4,432.61 
 
 83 
 
 250.753 
 
 5,410.62 
 
 90} 
 
 285.493 
 
 6,486.04 
 
 75* 
 
 236.405 
 
 4,447.38 
 
 83} 
 
 261.145 
 
 5,426.93 
 
 91 
 
 285.886 
 
 6,503.90 
 
A GLOSSARY OF MINING TERMS 
 
 1101 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 Diam. 
 
 Circum. 
 
 Area 
 
 9U 
 
 286.278 
 
 6,521.78 
 
 CM * 
 *^*T 
 
 295.703 
 
 6,958.26 
 
 97j 
 
 
 305.128 
 
 7,408.89 
 
 9l| 
 
 286.671 
 
 6,539.68 
 
 94^ 
 
 296.096 
 
 6,976.76 
 
 97- 
 
 
 305.521 
 
 7,427.97 
 
 91$ 
 
 287.064 
 
 6,557.61 
 
 94| 
 
 296.488 
 
 6,995.28 
 
 97, 
 
 
 305.913 
 
 7,447.08 
 
 9H 
 
 287.456 
 
 6,575.56 
 
 
 296.881 
 
 7,013.82 
 
 97, 
 
 
 306.306 
 
 7,466.21 
 
 91| 
 
 287.849 
 
 6,593.54 
 
 94f 
 
 297.274 
 
 7,032.39 
 
 97j 
 
 
 306.699 
 
 7,485.37 
 
 91 f 
 
 288.242 
 
 6,611.55 
 
 94* 
 
 297.667 
 
 7,050.98 
 
 97; 
 
 
 307.091 
 
 7,504.55 
 
 
 288.634 
 
 6,629.57 
 
 94J 
 
 298.059 
 
 7,069.59 
 
 97* 
 
 307.484 
 
 7,523.75 
 
 92 ! 
 
 289.027 
 
 6,647.63 
 
 95 
 
 298.452 
 
 7,088.24 
 
 98 
 
 307.877 
 
 7,542.98 
 
 
 289.420 
 
 6,665.70 
 
 95i 
 
 298.845 
 
 7,106.90 
 
 98; 
 
 
 308.270 
 
 7,562.24 
 
 92^- 
 
 289.813 
 
 6,683.80 
 
 9-4 
 
 299.237 
 
 7,125.59 
 
 98- 
 
 
 308.662 
 
 7,581.52 
 
 92| 
 
 290.205 
 
 6,701.93 
 
 96| 
 
 299.630 
 
 7,144.31 
 
 9s; 
 
 
 309.055 
 
 7,600.82 
 
 92* 
 
 290.598 
 
 6,720.08 
 
 
 300.023 
 
 7,163.04 
 
 98- 
 
 
 309.448 
 
 7,620.15 
 
 92| 
 
 290.991 
 
 6,738.25 
 
 95f 
 
 300.415 
 
 7,181.81 
 
 98 
 
 
 309.840 
 
 7,639.50 
 
 92* 
 
 291.383 
 
 6,756.45 
 
 95* 
 
 300.808 
 
 7,200.60 
 
 98 : 
 
 
 310.233 
 
 7,658.88 
 
 
 291.776 
 
 6,774.68 
 
 95* 
 
 301.201 
 
 7,219.41 
 
 98* 
 
 310.626 
 
 7,678.28 
 
 93 
 
 292.169 
 
 6,792.92 
 
 96 
 
 301.594 
 
 7,238.25 
 
 99 
 
 311.018 
 
 7,697.71 
 
 
 292.562 
 
 6,811.20 
 
 96 
 
 301.986 
 
 7,257.11 
 
 99J 
 
 311.411 
 
 7,717.16 
 
 93- 
 
 292.954 
 
 6,829.49 
 
 96i 
 
 302.379 
 
 7,275.99 
 
 99i 
 
 311.804 
 
 7,736.63 
 
 93| 
 
 293.347 
 
 6,847.82 
 
 96f 
 
 302.772 
 
 7,294.91 
 
 99| 
 
 312.196 
 
 7,756.13 
 
 93i 
 
 293.740 
 
 6,866.16 
 
 96} 
 
 303.164 
 
 7,313.84 
 
 99* 
 
 312.589 
 
 7,775.66 
 
 93| 
 
 294.132 
 
 6,884.53 
 
 96| 
 
 303.557 
 
 7,332.80 
 
 99| 
 
 312.982 
 
 7,795.21 
 
 93* 
 
 294.525 
 
 6,902.93 
 
 96* 
 
 303.950 
 
 7,351.79 
 
 99* 
 
 313.375 
 
 7,814.78 
 
 93J 
 
 294.918 
 
 6,921.35 
 
 96* 
 
 304.342 
 
 7,370.79 
 
 99* 
 
 313.767 
 
 7,834.38 
 
 94 
 
 295.310 
 
 6,939.79 
 
 97 
 
 304.735 
 
 7,389.83 
 
 100 
 
 314.160 
 
 7,854.00 
 
 The preceding table may be used to determine the diameter when 
 the circumference or area is known. Thus, the diameter of a circle having 
 an area of 7,200 sq. in. is approximately 95* in. 
 
 A GLOSSARY OF MINING TERMS 
 
 The glossary of mining terms here presented is taken largely from that 
 given in the 10th Edition of the Coal and Metal Miners' Pocketbook. This 
 was a combination of glossaries including: Raymond's Glossary of Mining 
 and Metallurgical Terms, Powers' Pocketbook for Miners and Metallurgists, 
 Locke's Miners' Pocketbook, Vol. AC, Second Pennsylvania Geological 
 Survey, Ilhseng's Manual of Mining, Chism's Encyclopedia of Mexican 
 Mining Law, a Glossary of Terms as Used in Coal Mining, by W. S. Gresley, 
 llth Annual Report of the State Mine Inspector of Missouri, Bullman's 
 Colliery Working and Management, Reynolds' Handbook of Mining Laws, 
 Report of the Mine Inspector of Tennessee for 1897, Smithsonian Report 
 for 1886, and words from other stray sources. In the present glossary 
 words which may be applied only to metal mining have been omitted. 
 Many words also not found in the original list have been added. Other 
 terms also have been included which are by no means peculiar to the coal- 
 mining industry. It has been the aim, however, to include such terms as are 
 in common use by those engaged in coal production regardless of whether 
 they apply only to that industry or to others as well. Various foreign 
 words have been selected as being those which an American is most likely to 
 encounter. This list is, however, by no means exhaustive. For a large num- 
 ber of purely local terms used in the various coal fields of Great Britain the 
 reader is referred to Mr. Gresley's glossary. 
 
1102 A GLOSSARY OF MINING TERMS 
 
 GLOSSARY 
 
 Abattis (Leicester). Cross-packing of branches or rough wood, used to keep 
 roads open for ventilation. 
 
 Absolute Pressure. The pressure reckoned from a vacuum. 
 
 Absolute Temperature. The temperature reckoned from the absolute zero, 
 - 459.2 F. or -273 C. 
 
 Accompt (Cornish). Settling day or place. 
 
 Achicar (Mexican). To diminish the quantity of water^in any gallery or 
 working, generally by carrying it out in buckets or in leather bags. 
 Achicadores. Laborers employed for said purpose. Achichinques. 
 Same as Achicadores. Also applied to hangers^n about police courts, 
 etc. Such people as are generally called strikers in the United States. 
 
 Acreage Rent (English). Royalty or rent for working minerals. 
 
 Addlings (North of England). Earnings. 
 
 Ademador (Spanish). Mine carpenter, or timberman. 
 
 Ademar (Spanish). To timber. 
 
 Adit. A nearly horizontal passage from the surface, by which a mine is 
 entered and unwatered with just sufficient slope to insure drainage. 
 In the United States, an adit driven across the measures is usually called 
 a tunnel, though the latter, strictly speaking, passes entirely through a 
 hill, and is open at both ends. 
 
 Aodobe. Sun-dried brick. 
 
 A dventurers. Original prospectors. 
 
 Adverse. To oppose the granting of a patent to a mining claim. 
 
 Adze. A curved cutting instrument for dressing timber. * 
 
 Aerage (French). Ventilation. 
 
 Aerometers. The air pistons of a Struve ventilator. 
 
 Aerophore. The name given to an apparatus that wilt enable a man to enter 
 places in mines filled with explosive or other deadly gases, with safety. 
 
 Afterdamp. The gaseous mixture resulting from an explosion of firedamp. 
 
 Agent. The manager of a mining property. 
 
 Ahondar (Spanish). To sink. 
 
 Air. The current of atmospheric air circulating through and ventilating the 
 workings of a mine. 
 
 Air Box. Wooden tubes used to convey air for ventilating headings or 
 sinkings or other local ventilation. 
 
 Air Compartment. An air-tight portion of any shaft, winze, rise, or level, 
 used for improving ventilation. 
 
 Air-Course. See Airway. 
 
 Air Crossing. A bridge that carries one air-course over another, an overcast 
 
 Air Cushion. A cushion or spring caused by confined air. 
 
 Air Door. A door for the regulation of currents of air through the workings 
 of a mine. 
 
 Air-End Way (Locke). Ventilation levels run parallel with main level. 
 
 Air Furnace. A ventilation furnace. 
 
 Air Gates (Locke). (1) Underground roadways, used principally for ventilat- 
 ing purposes. (2) An air regulator. 
 
 Air Head (Staff). Ventilation ways. 
 
 Air Heading. -An airway, or air course. 
 
 Air Hole (Powers). A hole drilled in advance to improve ventilation by 
 communication with other workings or the surface. 
 
 Airless End. The extremity of a stall in longwall workings in which there'is 
 no current of air, or circulation of ventilation, but which is kept pure by 
 diffusion and by the ingress and egress of cars, men, etc. 
 
 Air Level. A level or airway of former workings made use of in subsequent 
 deeper mining operations for ventilating purposes. 
 
 Air Oven. A heated chamber for drying samples of ore, coal, etc. 
 
 Air Pipe. A pipe made of canvas or metal, or a wooden box used in con- 
 veying air to the workmen, or for rock drills or air locomotives. 
 
 Air-Shaft. A shaft or pit used expressly for ventilation. 
 
 Air Slit (Yorks). A short head between other air heads. 
 
 Air Sollar. A brattice carried beneath the tram rails or road bed in a head- 
 ing or gangway. 
 
 Air Stack. A stack or chimney built over a shaft for ventilation. 
 
 Airway. Any passage through which air is carried. 
 
 Ailch Piece. Parts of a pump in which the valves are fixed. 
 
 Albanil (Spanish). Mason. 
 
A GLOSSARY OF MINING TERMS 1103 
 
 Alive (Cornish). Productive. 
 
 Alluvium. Gravel, sand, and mud deposited by streams. 
 
 Almagre (Spanish). Red ocher. 
 
 Alternating Motion. Up and down, or backward and forward motion. 
 
 Alto (Mexican). The hanging wall of a vein. See Respaldos. 
 
 Amygdaloidal. Almond-shaped. 
 
 Analysis. The determination of the original elements and the proportions 
 
 of each in a substance. 
 Anemometer. An instrument used for measuring the velocity of a ventilating 
 
 current by means of a revolving vane wheel. 
 
 Angle Beam. A two-limbed beam used for turning angles in shafts, etc. 
 Anhydrous. Without water in its composition. 
 Anneal. To toughen or soften metals, glass, etc., by first heating and then 
 
 cooling very slowly or quickly depending on the metal. 
 Anthracite. Coal containing a small percentage of volatile matter. 
 Anticline. A flexure or fold in which the rocks on the opposite sides of the 
 
 fold dip away from each other, like the two legs of the letter A. The 
 
 inclination on one side may be much greater than on the opposite side. 
 
 An anticlinal is said to be overturned when the rocks on both sides dip 
 
 in the same direction. 
 Anticlinal Axis. The ridge of a saddle in a mineral vein, or the line along 
 
 the summit of a vein, from which the vein dips in opposite directions. 
 Anticlinal Flexure; Anticlinal Fold. An anticline. 
 Antiguos, Los (Mexican). The Spanish or Indian miners of colonial 
 
 times. 
 Aparejo (Mexican). A rigid pair of large stuffed pads connected over the 
 
 back of a pack mule by an unpadded portion to protect body of mule 
 
 when heavy or irregularly shaped loads are carried. 
 Aperos (Mexican). All kinds of mining supplies in general. Aperador. A 
 
 storekeeper. 
 Apex. The landing point at the top of a slope or inclined plane, the knuckle; 
 
 also, the top of an anticlinal. In the U. S. Revised Statutes, the end or 
 
 edge of a vein nearest the surface. 
 A pique (Mexican). Perpendicular. 
 
 Apron (English). (1) A covering of timber, stone, or metal, to protect a sur- 
 face against the action of water flowing over it. (2) A hinged extension 
 
 to a loading chute. 
 Aqua Fortis. Nitric acid. 
 
 Aquo Regia. A mixture of hydrochloric acid and nitric acid. 
 Aqueduct. An artificial channel for carrying water. 
 Arajo (Mexican). See Hatajo. 
 Arch (Cornish). Portion of lode left standing to support hanging wall, or 
 
 because too poor. 
 
 Archean. An early period of geological time. 
 Arching. Brickwork or stonework forming the roof of any underground 
 
 roadway. 
 Arenaceous. Sandy; rocks are arenaceous when they contain a considerable 
 
 percentage of sand. 
 Arenillas (Spanish). Refuse earth. 
 
 Argillaceous. Clayey; rocks are argillaceous when they contain a consider- 
 able percentage of clay, or have some of the characteristics of clay. 
 Argol. Crude tartar deposited from wine. 
 Arm. The inclined leg of a set of timber. 
 Arrastrar (Mexican). To drag along the ground. Arrastrar el Agua.To 
 
 almost completely exhaust the water in a sump or working. 
 Arroba (Mexican). 25 Ib. 
 Artesian Well. An artificial channel of escape, made by a bore hole, for a 
 
 subterranean stream, subject to hydrostatic pressure. 
 Ascensional Ventilation. The arrangement of the ventilating currents in 
 
 such a manner that the air shall continuously rise until reaching the 
 
 bottom of the upcast shaft. Particularly applicable to steep seams. 
 Ashlar. A facing of cut stone applied to a backing of rubble or rough 
 
 masonry or brickwork. 
 
 Aspirail (French). Opening for ventilation. 
 Assay. The determination of the quality and quantity of any particular 
 
 substance in a mineral. Assayer. One who performs assays. 
 Assessment Work. The annual work necessary to hold a mining claim. 
 Astel. Overhead boarding in a gallery. 
 
1104 A GLOSSARY OF MINING TERMS 
 
 Astyllen (Cornish). Small dam in an adit; partition between ore and deads 
 on grass. 
 
 Atacador (Mexican). A tamping bar or tamping stick. 
 
 Atecas (Mexican). Same as Achicadores, etc. 
 
 Atierres (Spanish). Refuse rock or dirt inside a mine, gob. 
 
 Attle (Cornish). Refuse rock. 
 
 Attle (Addle). The waste of a mine. 
 
 Attrition. The act of wearing away by friction. 
 
 Auger Stem. The iron rod or bar to which the bit is attached. 
 
 Auget. Priming tube. 
 
 Ausscharen (German). Junction of lodes. 
 
 Auszimmern (German). Timbering. 
 
 Aviador (Spanish). One who provides the capital to work a mine. Avio. 
 Money furnished to the proprietors of a mine to work the mine by 
 another peison, the Aviador. Avio Contract. A contract between two 
 parties for working a mine by which one of the parties, the aviador, 
 furnishes the money to the proprietors for working the mine. 
 
 Axis. An imaginary line passing through a body that may be supposed to 
 revolve around it. 
 
 Azimuth. The azimuth of a body is that arc of the horizon that is included 
 between the meridian circle at the given place and a vertical plane 
 passing through the body. It is always measured from due north 
 around to the right. 
 
 Atoic. The age of rocks that were formed before animal life existed. 
 
 Back. (1) A plane or cleavage in coal, etc., having frequently a smooth 
 parting and some sooty coal included in it. (2) The inner end of a head- 
 ing or gangway. (3) To throw back into the gob or waste the small 
 slack, dirt, etc. (4) To roll large coals out of a waste for loading into cars. 
 
 Back Balance. (I) A self-acting incline in the mine, where a balance car and 
 a carriage in which the mine car is placed are used. The loaded car upon 
 the carriage will hoist the balance car, and the balance car will hoist the 
 carriage and empty car. (2) A weight moving vertically or on an in- 
 cline which places tension upon a tension carriage. 
 
 Backbye Work. Work done between the shaft and the working face, in 
 contradistinction to face work, or work done at the face. 
 
 Back Casing. A wall or lining of dry bricks used in sinking through drift 
 deposits, the permanent walling being built up within it. The use of 
 timber cribs and planking serves the same purpose. 
 
 Back End (England). The last portion of a jud. 
 
 Backing. (1) The rough masonry of a wall faced with finer work. (2) 
 Earth deposited behind a retaining wall, etc. (3) Timbers let into 
 notches in the rock across the top of a level. 
 
 Backing Deals. Deal boards or planking placed at the back of curbs for 
 supporting the sides of a shaft that is liable to run. 
 
 Back Joint. Joint plane more or less parallel to the strike of the cleavage, 
 and frequently vertical. 
 
 Backlash. (1) Backward suction of air-currents produced after an explosion 
 of firedamp. (2) Reentry of air into a fan. (3) Lost motion or play 
 between the teeth of gears. 
 
 Back Pressure. The loss, expressed in pounds per square inch, due to getting 
 the steam out of the cylinder of an engine after it has done its work. 
 
 Back Shift. Afternoon shift. 
 
 Back Skin (North of England). A leather jacket for wet workings. 
 
 Backstay. A wrought-iron forked bar attached to the back of cars when 
 ascending an inclined plane, which throws them off the rails if the rope or 
 coupling breaks. 
 
 Baff Ends. Long wooden edges for adjusting linings in sinking shafts dur- 
 ing the operation of fixing the lining. 
 
 Baffle. (1) To brush out firedamp. (2) A firebrick partition to guide the 
 flue gases through a boiler. 
 
 Bait. Provisions. 
 
 Bajo (Mexican) The footwall of a vein. See Respaldo. 
 
 Bal (Cornish). A mine. 
 
 Balance. (1) The counterpoise or weights attached to the drum of a winding 
 engine, to assist the engine in lifting the load out of a shaft bottom and 
 in helping it to slacken speed when the cage reaches the surface. It 
 consists often of a bunch of heavy chains suspended in a shallow shaft, 
 
A GLOSSARY OF MINING TERMS 1105 
 
 the chains resting on the shaft bottom as unwound off the balance drum 
 attached to the main shaft of the engine. (2) Scales used in chemical 
 analysis and assaying. 
 
 Balance Bob. A large beam or lever attached to the main rods of a Cornish 
 pumping engine, carrying on its outer end a counterpoise. 
 
 Balance Box. A large box placed on one end of a balance bob and filled 
 with old iron, rock, etc., to counterbalance the weight of the pump rods. 
 
 Balance Brow. An inclined plane in steep seams on which a platform on 
 wheels travels and carries the cars of coal. 
 
 Balance Car. A small weighted truck mounted upon a short inclined track, 
 and carrying a sheave around which the rope of an endless haulage 
 system passes as it winds off the drum. 
 
 Balance Pit. A pit or shaft in which a balance rises or falls. 
 
 Balanzon (Mexican). The balance bob of a Cornish pump. 
 
 Balk. (1) A more or less sudden thinning put of a seam of coal. (2) Irregu- 
 lar-shaped masses of stone intruding into a coal seam, or bulgings out 
 of the stone roof into the seam. (3) A bar of timber supporting the roof 
 of a mine, or for carrying any heavy load. 
 
 Ballast. Broken stone, gravel, sand, etc., used for keeping railroad ties 
 steady. 
 
 Bancos (Spanish). Horses in a vein or cross-courses. 
 
 Band. A seam or thin stratum of stone or other refuse in a seam of coal, 
 a parting. 
 
 Bank. (1) The top of the shaft, or out of the shaft. (2) The surface around 
 the mouth of a shaft. (3) To manipulate coals, etc., on the bank. 
 (4) The whole or sometimes only one side or one end of a working place 
 underground. (5) A large heap of mineral on the surface. 
 
 Bank Chain. A chain that includes the bank of a river or creek. 
 
 Bank Claim (Australian). Mining right on bank of stream. 
 
 Bank Head. The upper end of an inclined plane, next to the engine or drum, 
 made nearly level. 
 
 Bank Right (Australian). Right to divert water to bank claim. 
 
 Banksman. The man in attendance at the top of the shaft, superintending 
 the work of banking. 
 
 Bankwork. A system of working coal in South Yorkshire. 
 
 Bank to Bank. A shift. 
 
 Bannocking. See Kirving. 
 
 Bar. A length of timber placed horizontally for supporting the root. In 
 some cases, bars of wrought iron, about 3 in. X 1 in. X 5 ft. are used. 
 
 Bargain. Portion of mine worked by a gang on contract. 
 
 Baring. See Stripping. 
 
 Barmaster (Derbyshire). Mine manager, agent, and engineer. 
 
 Barney. A small car, used on inclined planes and slopes to push the mine 
 car up the slope. Barney Pit. A pit at the bottom of a slope or plane 
 into which the barney runs to allow the mine car to pass over it. 
 
 Barra (Mexican). (1) A bar, as of gold, silver, iron, steel, etc. (2) A cer- 
 tain share in a mine. The ancient Spanish laws, from time immemorial, 
 considered a mine as divided into 24 parts, and each part was called a 
 
 Barra Viuda, or Aviada (Mexican). These are "barras" or shares that par- 
 ticipate in the profits, but not in the expenses, of mining concerns. 
 Their share of the expenses is paid by the other shares. Non-assessable 
 
 Barranca (Mexican). A ravine, a gulch. What is improperly called in the 
 
 United States a canyon or canon. 
 Barrena (Mexican). A hand drill for opening holes in rocks for blasting 
 
 Barrenarse (Mexican). When two mines or two workings (as a shaft or 
 
 winze, or a gallery), communicate with each other. 
 Barren Ground. Strata unproductive of seams of coal, etc., of a workable 
 
 thickness. 
 Barreno (Mexican). (1) A drill hole for blasting purposes. In mechanics, any 
 
 bored hole (2) A communication between two mines or two workings. 
 Barretero (Mexican). A miner of the first class; one that knows how to 
 
 point his holes, drill, and blast, or work with a gad. 
 Barrier Pillar. A solid block or rib of coal, etc., left un worked between two 
 
 collieries or mines for security against accidents arising from influx ot 
 
 water. 
 
 70 
 
1106 A GLOSSARY OF MINING TERMS 
 
 Barrier System. The method of working a colliery by pillar and stall, where 
 
 solid ribs or barriers of coal are left in between a set or series of working 
 
 places. 
 Barrow. (1) A box with two handles at one end and a wheel at the other. 
 
 (2) Heap of waste stuff raised from a mine: a dump. 
 Bar Timbering. A system of supporting a tunnel roof by long top bars, while 
 
 the whole lower tunnel core is taken out, leaving an open space for the 
 
 masons to run up the arching. Under certain conditions, the bars are 
 
 withdrawn after the masonry is completed, otherwise they are bricked in 
 
 and not drawn. 
 Basin. (1) A coal field having some resemblance in form to a basin. (2) 
 
 The synclinal axis of a seam of coal or stratum of rock. 
 Basket. A measure of weight = 2 cwt. 
 Basque. Crucible or furnace lining. 
 Bass (Derbyshire). Indurated clay. 
 Basset. Outcrop of a lode or stratum. 
 Bastard. A particularly hard massive rock or boulder. 
 Batch. An amount of concrete material. 
 Ball (English). (1) A highly bituminous shale found in the coal measures. 
 
 (2) Hardened clay, but not fireclay. Same as Bend and Bind. 
 Batten. A piece of.thin board less than 12 in. in width. 
 Batter. The inclination of a face of masonry or of any inclined portion of 
 
 a frame or metal structure. 
 Battery. (1) A structure built to keep coal from sliding down a chute or 
 
 breast. (2) An embankment or platform on which miners work. (3) 
 
 A set of stamps. (4) Two or more boilers with a common setting. 
 Bay. An open space for waste between two packs in a longwall working. 
 
 See Board. 
 
 Bay of Biscay Country. (Geological). See Crab Holes. 
 
 Beans (North of England). All coal that will pass through about J-S-in. screen. 
 Bear. A deposit of iron at the bottom of a furnace. 
 Bear; to Bear In. Underholing or undermining; driving in at the top or at 
 
 the side of a working. 
 Bearers. Pieces of timber 3 or 4 ft. longer than the breadth of a shaft, which 
 
 are fixed into the solid rock at the sides at certain intervals apart; used 
 
 as foundations for sets of timber. 
 Bearing. (1) The course by a compass. (2) The span or length in the clear 
 
 between the points of support of a beam, etc. (3) The points of support 
 
 of a beam, shaft, axle, etc. 
 Bearing Door. A door placed for the purpose of directing and regulating the 
 
 amount of ventilation passing through an entire district of a mine. 
 Bearing In. The depth or distance under of the undercut or holing. 
 Bearing-up Pulley. A pulley wheel fixed in a frame and arranged to tighten 
 
 up or take up the slack rope in endless-rope haulage. 
 Bearing-up Stop. A partition of brattice or plank that serves to conduct air 
 
 to a face. 
 
 Beat (Cornish). To cut away a lode. 
 
 Beataway. Working hard ground by means of wedges and sledge hammers. 
 Bed. (1) The level surface of a rock upon which a curb or crib is laid. (2) 
 
 A stratum of coal, ironstone, clay, etc. 
 
 Bed Claim (Australian). A claim that includes the bed of a river or creek. 
 Bede. Miners' pickax. 
 Bedplate, A large plate of iron used as a foundation for an engine or other 
 
 machine. 
 
 Bed Rock. The solid rock underlying the soil, drift, or alluvial deposits. 
 Beehive Oven. -The ordinary circular or rectangular arched oven in which 
 
 coke is made without the recovery of any byproducts other than in some 
 
 instances the heat. 
 
 Bef ore-Breast. Rock or vein, which still lies ahead. 
 Bell. Overhanging rock or slate, of a bell-like form, disconnected from the 
 
 main roof. 
 
 Belly. A swelling mass of mineral in a lode. 
 Bench. (1) A natural terrace marking the outcrop of any stratum. (2) A 
 
 stratum of coal forming a portion of the vein. 
 Benching. To break up with wedges the bottom coals when the holing is 
 
 done in the middle of the seam. 
 
 Benching Up (North of England). Working on top of coal. 
 Bench Mark. A mark cut in a tree, rock or on some solid structure whose 
 
A GLOSSARY OF MINING TERMS 1107 
 
 elevation is known. Used by surveyors for reference in determining 
 elevations. 
 
 Bench Working. The system of working one or more seams or beds of min- 
 eral by open working or stripping, in stages or steps. 
 
 Bend (Derbyshire). Indurated clay. 
 
 Bessemer Steel. Steel made by the Bessemer process. 
 
 Beton (English). Concrete of hydraulic cement with broken stone, bricks, 
 gravel, etc. 
 
 Bevel. The slope formed by trimming away on edge. 
 
 Bevel Gear. A gear-wheel whose teeth are inclined to the axis of the wheel. 
 
 Biche. A hollow-ended tool for recovering boring rods. 
 
 Billy Boy. A boy who attends a Billy Playfair. 
 
 Billy Playfair. A mechanical contrivance for weighing coal, consisting of an 
 iron trough with a sort of hopper bottom, into which all the small coal 
 passing through the screen is conducted and weighed off and emptied 
 from time to time. 
 
 Bin. A box or receptacle used for tools, stones, ore, coal, etc. 
 
 Bind, or Binder. Indurated argillaceous shales or clay, very commonly 
 forming the roof of a coal seam and frequently containing clay iron- 
 stone. See Bait. 
 
 Binding. Hiring men. 
 
 Bit. (1) A piece of steel placed in the cutting edge of a drill or point of a 
 pick. (2) The cutting tool of a mining machine. 
 
 Blackband. Carbonaceous ironstone in beds, mingled with coaly matter 
 sufficient for its own calcination. 
 
 Black Bait, or Black Stone. Black carbonaceous shale. 
 
 Black Butts. See Black Ends. 
 
 Blackdamp. Carbonic-acid gas. 
 
 Black Dimaonds. Coal. 
 
 Black Ends. Beehive coke of inferior quality due to mismanipulation or dis- 
 coloration. 
 
 Black Jack. (1) Properly speaking, dark varieties of zinc blend, but many 
 miners apply it to any black mineral. (2) Crude black oil used to oil 
 mine cars. Often called Black Strap. 
 
 Black Lead. Graphite. 
 
 Black Stone. A carbonaceous shale. 
 
 Blast. (1) The sudden rush of fire, gas, and dust of an explosion through the 
 workings and roadways of a mine. (2) To cut or bring down coal, rocks, 
 etc., by the explosion 9f gunpowder, dynamite, etc. 
 
 Blasting Barrel. A small pipe used for blasting in wet or gaseous places. 
 
 Blast Pipe. A pipe for supplying air to furnaces^ 
 
 Blind Coal. Coal altered by the heat of a trap dike. 
 
 Blind Creek. (1) A creek in which water flows only in very wet weather. 
 (2) (Australasian) Dry watercourse. 
 
 Blind Drift. (1) A horizontal passage in the mine not yet connected with the 
 other workings. (2) A drift not opening to daylight. 
 
 Blind Joint. Obscure bedding plane. 
 
 Blind Lead, or Blind Lode. A vein having no visible outcrop. 
 
 Blind Level. (1) An incomplete level. (2) A drainage level. 
 
 Blind Shaft, or Blind Pit. A shaft not coming to the surface. 
 
 Bloat. A hammer swelled at the eye. 
 
 Block Claim (Australian). A square mining claim. 
 
 Block Coal. Coal that breaks in large rectangular lumps. 
 
 Block Reefs. Reefs showing frequent contractions longitudinally. 
 
 Block Tin. Cast tin. 
 
 Bloomary. A forge for making wrought iron. 
 
 Blossom. The decomposed outcrop, float, surface stain, or any indicating 
 traces of a coal bed or mineral deposit. Blossom Rock. (1) Colored 
 veinstone detached from an outcrop. (2) The rock detached from a 
 vein, but which has not been transported. 
 
 Blow. (1) To blast with gunpowder, etc. (2) A dam or stopping is said to 
 blow when gas escapes through it. 
 
 Blower. (1) A sudden emission or outburst of gas in a mine. (2) Any 
 emission of gas from a coal seam similar to that from an ordinary gas 
 burner. (3) A type of centrifugal fan used largely to force air into 
 furnaces. (4) A blowdown ventilating fan. 
 
 Blow Fan. A small centrifugal fan used to force air through canvas pipes or 
 wooden boxes to the workmen. 
 
1108 A GLOSSARY OF MINING TERMS 
 
 Slowdown Fan. A force fan. 
 
 Blown-out Shot. A shot that has blown out the tamping, but not broken 
 the coal or rock. 
 
 Blow Off. To let off excess of steam from a boiler. 
 
 Blow Out. (1) To finish a smelting campaign. (2) A blown-out shot. 
 (3) The decomposed mineral exposure of a vein. 
 
 Blowpipe. An instrument for creating a blast whereby the heat of a flame or 
 lamp can be better utilized. 
 
 Blue Cap. The blue halo of ignited gas (firedamp and air) on the top of the 
 flame in a safety lamp. 
 
 Blue Elvan (Cornish). Greenstone. 
 
 Blue John. Fluorspar. 
 
 Blue Metal. A local term for shale possessing a bluish color. 
 
 Blue Peach (Cornish). A slate-blue fine-grained schorl. 
 
 Bluestone. (1) Sulphate of copper. (2) Lapis lazuli. (3) Basalt. (4) 
 Maryland, a gray gneiss^ in Ohio, a gray sandstone; in the District of 
 Columbia, a mica schist; in New York, a blue-gray sandstone; in Penu- 
 sylvania, a blue-gray sandstone. (5) A popular term among stone men 
 not sufficiently definite to be of value. 
 
 Bluff. Blunt. 
 
 Board. A wide heading usually from 3 to 5 yd. wide. 
 
 Boar d-and- Pillar. A system of working coal where the first stage of exca- 
 vation is accomplished with the roof sustained by pillars of coal left 
 between the breasts; often called Breast-and-Pillar. 
 
 Bob. An oscillating bell-crank, or lever, through which the motion of an 
 engine is transmitted to the pump rods in an engine or pumping pit. 
 There are J. bobs, L bobs, and V bobs. 
 
 Boca or Boca Mina (Mexican). Mouth or mine mouth. This is the name 
 applied to the principal or first opening of a mine, or to the one where 
 the miners are accustomed to descend. 
 
 Bochorno (Mexican). Excessive heat, with want of ventilation, so that the 
 lights go out. See Vapores. 
 
 Body.~(l) An ore body, or pocket of mineral deposit. (2) The thickness of 
 a lubricating oil or other liquid; also the measure of that thickness 
 expressed in the number of seconds in which a given quantity of the 
 oil at a given temperature flows through a given aperture. 
 
 Boleo (Mexican). A dump pile for waste rock. 
 
 Bond. (1) The arrangement of blocks of stone or brickwork to form a firm 
 structure by a judicious overlapping of each other so as to break J9int. 
 (2) An agreement for hiring men. (3) Apparatus for electrically join- 
 ing the ends of adjacent rails. A cross bond joins both rails of a track. 
 
 Bone. Slaty coal or carbonaceous shale found in coal seams. 
 
 Bone Ash. Burnt bones pulverized and sifted. 
 
 Bonnet. (1) The overhead cover of a cage. (2) A cover for the gauze of a 
 safety lamp. (3) A cap piece for an upright timber. (4) The upper 
 part of a valve containing the stuffing box. 
 
 Booming. Ground sluicing on a large scale by emptying the contents of a 
 reservoir at once on material collected below, thus removing boulders. 
 
 Bord (English). A narrow breast. 
 
 Bord-and-Pillar (English). See Pillar-and-Breast. 
 
 Bord Room. The space excavated in driving a bord. The term is used in 
 connection with the "ridding" of the fallen stone in old bords when 
 driving roads across them in pillar working; thus, "ridding across the 
 old bord room." 
 
 Bord Ways Course. The direction at right angles to the main cleavage 
 planes. In some mining districts it is termed "on face." 
 
 Bore. To drill. 
 
 Bore Hole. A hole made with a drill, auger, or other tools, in coal, rock, or 
 other material. 
 
 Bort. Amorphous dark diamond. 
 
 Bosh. The plane in a blast furnace where the greatest diameter is reached. 
 
 Boss (English). (1) An increase of the diameter at any part of the shaft. 
 (2) A person in charge of a piece of work. 
 
 Botas (Mexican). Buckets made of an entire ox skin, to take out water. 
 
 Botryoidal. Grape-like in appearance. 
 
 Bottle Chock. A pulley with a wide grooved face for guiding a cable around 
 a turn in the track, an angle sheave. 
 
 Bottle Jack (English), An appliance for lifting heavy weights. 
 
A GLOSSARY OF MINING TERMS 1109 
 
 Bottom. (1) The landing at the bottom of the shaft or slope. (2) The lowest 
 point of mining operations. (3) The floor, bottom rock, or stratum 
 underlying a coal bed. (4) In alluvial, the bed rock or reef. 
 Bottomer, Bottomman. The person that loads the cages at the pit bottom 
 
 and gives the signal to bank. The onsetter or bottom eager. 
 Bottom Joint. Joint or bedding plane, horizontal or nearly so. 
 Bottom Lift. (1) The deepest column of a pump. (2) The lowest or deepest 
 
 lift or level of a mine. 
 
 Bottom Pillars. Large pillars left around the bottom of a shaft. 
 Boulders. Loose rounded masses of stone detached from the parent rock. 
 Bounce. A sudden spalling off of the sides of ribs and pillars due to excessive 
 
 pressure; a bump. 
 Bow. The handle of a kibble. 
 Bowk. An iron barrel or tub used for hoisting rock and other d6bris when 
 
 sinking a shaft. 
 
 Bowke (Staffordshire). A small wooden box for hauling ironstone under- 
 ground. 
 
 Box. (1) A 12' to 14' section of a sluice. (2) A mine car. 
 Box Bill. Tool for recovering boring rods. 
 
 Boxing. A method of securing shafts solely by slabs and wooden pegs. 
 Brace. ^1) An inclined beam, bar, or strut for sustaining compression or 
 
 tension. See Tie-Brace, Sway-Brace. (2) A platform at the top of a 
 
 shaft on which miners stand to work the tackle. (3) (Cornish) Building 
 
 at pit mouth. 
 Brace Heads. Wooden handles or bars for raising and rotating the rods 
 
 when boring a deep hole. 
 
 Braize. (1) Charcoal dust. (2) Pine coke refuse or breeze. 
 Brake Sieve. Hand jigger. 
 Brances. Iron pyrites in coal. 
 Branch. Small vein shooting off from main lode. 
 Brashy. Short and tender. 
 
 Brasque. A mixture of clay and coke or charcoal used for furnace bottoms. 
 Brass. (1) Iron pyrites in coal. (2) An alloy of copper and zinc. 
 Brasses (English). Pitting of brass in plummer blocks, etc., for diminishing 
 
 the friction of revolving journals that rest upon them. 
 Brat. A thin bed of coal mixed with pyrites or limestone. 
 Brattice. A lining or partition. 
 
 Brattice Cloth. Ducking or canvas used for making a brattice. 
 Brazzil (North of England). Iron pyrites in coal. 
 Breaker. In anthracite mining, the structure in which the coal is broken, 
 
 sized, and cleaned for market. Known also as Coal Breaker. 
 Breaker Boy. A boy who works in a coal breaker. 
 Breakstaff. The lever for blowing a blacksmiths' bellows, or for working bore 
 
 rods up and down. 
 
 Breakthrough. A narrow passage cut through a pillar connecting rooms. 
 Breast. (1) A stall, board, or room in which coal is mined. (2) The face or 
 
 wall of a quarry is sometimes called by this name. 
 Breast-and-PiUar. A system of working coal by boards or rooms with pillars 
 
 of coal between them. 
 Breast Wall (English). A wall built to prevent the falling of a vertical face 
 
 cut into the natural soil. 
 
 Breccia. A rock composed of angular fragments cemented together. 
 Breeding Fire. See Gob Fire. 
 Breese. Fine slack. 
 
 Breeze. Small coke, probably same as braize or braise. 
 Brettis (Derbyshire). A timber crib filled with slack. 
 Bridge. (1) A platform on wheels running on rails for covering the mouth 
 
 of a shaft or slope. (2) A track or platform passing over an inclined 
 
 haulageway and which can be raised out of the way of ascending and 
 
 descending cars. (3) An air crossing. 
 
 Bridle Bar. The transverse bar connecting the points of a switch. 
 Bridle Chains. Short chains by which a cage, car, or gunboat is attached to 
 
 a winding rope; of use in case the rope pulls out of its socket. 
 Briquets. Fuel made of slack or culm and pressed into brick form. 
 Broaching Bit. A tool for reopening a bore hole that has been partially 
 
 closed by swelling of the walls. 
 Brob. A spike to prevent timber slipping. 
 Broil (Cornish). Traces of a vein in loose matter. 
 
1110 A GLOSSARY OF MINING TERMS 
 
 Broken. A. district of coal pillars in process of removal, so called in contra- 
 distinction to the first working of a seam by bord-and-wall, or working in 
 
 the "whole." See Whole Working. 
 Broken Coal. Anthracite coal that will pass through a mesh or bars about 
 
 3i to 4J in., and over a mesh 2f in. square. 
 Bronce (Mexican). In mining, copper or iron pyrites. 
 Brooching. Smoothing. 
 Brow. An underground roadway leading to a working place driven either to 
 
 the rise or to the dip. 
 
 Brown Coal. Lignite. A fuel classed between peat and bituminous coal. 
 Brown Spar. Dolomite containing carbonate of iron. 
 Brownstone. (1) Decomposed iron pyrites. (2) Brown sandstone. 
 Brujula (Mexican). A surveyors' (or marine) magnetic compass. 
 Brush. (1) To mix air with the gas in a mine working by swinging a jacket, 
 
 etc., which creates a current. (2) To "brush" the roof is to take down 
 
 some of the roof slate to increase the height or headroom. 
 Bryle (Cornish). Traces of a vein in loose matter. 
 Bucket. (1) An iron or wooden receptacle for hoisting ore, or for raising rock 
 
 in shaft sinking. (2) The top valve or clack of a pump. 
 Bucket Pump. A lifting pump, consisting of buckets fastened to an endless 
 
 belt or chain. 
 
 Bucket Sword. A wrought-iron rod to which the pump bucket is attached. 
 Bucket Tree. The pipe between the working barrel and the wind bore. 
 Bucking Hammer. An iron disk, provided with a handle, used for breaking 
 
 up minerals by hand. 
 Buckstay. An iron or steel brace resting upon or built into a boiler setting or 
 
 furnace wall to support the brickwork. 
 Buckwheat. Anthracite coal that will pass through a mesh of about $ in. 
 
 and over a mesh \ in. 
 Buddling. Washing. 
 
 Bug Dust. Fine coal; the cutting produced by a chain machine or puncher. 
 Buggy. A small mine car. 
 
 Bug Hole. A small cavity usually lined with crystals. 
 Building. A built-up block or pillar of stone or coal to support the roof. 
 Bulkhead. (1) A tight partition or stopping. (2) The end of a flume carry- 
 ing water for hydraulicking. 
 
 Bull. An iron rod used in ramming clay to line a shot hole. 
 Bulldog. A barney. 
 Bull Engine. A single, direct-acting pumping engine, the pump rods forming 
 
 a continuation of the piston rod. 
 Butter Shot. A second shot put in close to, and to do the work not done by, 
 
 a blown-out shot, loose powder being used. 
 Bulling. Lining a shot hole with clay. 
 Bull Pump. A single-acting pumping engine in which the steam cylinder is 
 
 placed over the shaft or slope and the pump rods are attached directly to 
 
 the piston rod. The steam enters below the piston and raises the pump 
 
 rods; the water is pumped on the down stroke by the weight of the 
 
 rods. 
 
 Bull Pup. A worthless claim. 
 Bull Wheel. (1) A wheel on which the rope carrying the boring rod is coiled 
 
 when boring by steam machinery. (2) The principal wheel of any 
 
 machine, usually a driving wheel. 
 Bully. A miners' hammer. 
 Bump. See Bounce. 
 
 Bunding. A staging in a level for carrying debris. 
 Bunkers. (1) Steam coal consumed on board ship. (2) Receptacles placed 
 
 near a boiler for holding a supply of fuel. 
 Bunions. Timbers placed horizontally across a shaft or slope to carry the 
 
 cage guides, pump rods, column pipe, etc.; also, to strengthen the shaft 
 
 timbering. 
 Burden. (1) Earth overlying a bed of useful mineral. (2) The proportion of 
 
 ore and flux to fuel in the charge of a blast furnace. 
 Burr. Solid rock. 
 Burrow. Refuse heap. 
 
 Buscones (Spanish). Prospectors, fossickers, tribute workers. 
 Bush. To line a circular hole with a ring of metal, to prevent the hole from 
 
 wearing out. 
 Butt. (1) Coal surface exposed at right angles to the face; the "ends" of 
 
A GLOSSARY OF MINING TERMS 1111 
 
 the coal. (2) The butt of a slate quarry is where the overlying rock 
 comes in contact with an inclined stratum of slate rock. 
 
 Butt Entry. A gallery driven at right angles with the butt joint. 
 
 Butterfly Valve. A circular valve that revolves on an axis passing through its 
 center. 
 
 Butt Heading. See Butt Entry. 
 
 Butty. A partner in a contract for driving or mining; a comrade, crony. 
 Sometimes called "Buddy." 
 
 By Level. A side level driven for some unusual but necessary purpose. 
 
 Byproduct Oven. A coke oven arranged to conserve and recover the various 
 byproducts of the coking process. 
 
 Byproducts. Products of coking other than coke. The more common by- 
 products are gas, tar, benzol and ammonium sulphate. 
 
 Caballo (Mexican). A "horse" or mass of barren rock in a vein. 
 
 Cabin. (1) A miner's house. (2) A small room in the mine for the use of the 
 
 officials. 
 
 Cable Drilling. Rope drilling. 
 
 Cage. A platform on which mine cars are raised to the surface. 
 Cage Guides. Vertical rods of pine, iron, or steel, or wire rope, fixed in a 
 
 shaft, between which cages run, and whereby they are prevented from 
 
 striking one another or against any portion of the shaft. 
 Cager. The person that puts the cars on the cage at the bottpm or top of the 
 
 shaft. 
 Cage Seat. Scaffolding, sometimes fitted with strorrg springs, to receive the 
 
 shock, and on which the cage drops when reaching the pit bottom. 
 Cage Sheets. Short props or catches on which cages stand during caging or 
 
 changing cars. 
 
 Caking Coal. Coal that agglomerates on the grate. 
 Cola (Spanish). Prospecting pit. 
 Calcareous. Containing lime. 
 Calcine. To heat a substance, not sufficiently to melt it, but enough to drive 
 
 off the volatile contents. 
 California Pump. A rude pump made of a wooden box through which an 
 
 endless belt with floats circulates; used for pumping water from shallow 
 
 ground. 
 
 Catty s (Cornish). Stratified rocks traversed by lodes. 
 Cam. (1) A curved arm attached to a revolving shaft for raising stamps. 
 
 (2) Carbonate of lime and fluorspar, found on the joints of lodes. 
 Camino (Mexican). Any gallery, winze, or shaft inside of a mine used for 
 
 general transit. 
 
 Campaign. The length of time a furnace remains in blast. 
 Cafiada (Mexican). See Barranca. 
 Canch, or Caunche. (1) A thickness of stone required to be removed to make 
 
 height or to improve the gradient of a road at a fault. If above a seam, 
 
 it is termed a "top canch;" if below, a "bottom canch." (2) A trench 
 
 with sloping sides and very narrow bottom. 
 Cand (Cornish). Fluorspar. 
 Cank (Derbyshire). Whinstone. 
 Canker. The ocherous sediment in coal-pit waters. 
 Cannel Coal. See Classification of Coals (page 378). 
 
 Canon (Mexican). (1) A level, drift, or gallery within a mine. (2) A steep- 
 sided ravine. Canon de Guia.A. drift along the vein. 
 Cants (English). The pieces forming the ends of buckets of a waterwheel 
 Cap. (1) A piece of plank placed on top of a prop. See, also, Collar. ( 
 
 The pale bluish elongation of the flame of a lamp caused by the pre: 
 
 of RclS. 
 
 Cap Rock. The upper rock that covers the bed rock. 
 
 Capstan. A. vertical axle used for heavy hoisting, and worked by horizontal 
 arms or bars. 
 
 Captain. Cornish name for manager or boss of a mine. 
 
 Cor __Any car used for the conveyance of coal along the gangways or haul- 
 age roads of a mine. 
 
 Carat. A weight nearly equal to 4 grams. , 
 
 Carbon. A combustible elementary substance forming the largest compo- 
 nent part of coal. 
 
 Carbonaceous. Coaly, C9ntainmg carbon or coal. 
 
 Carbonate, Carbonic acid combined with a base. 
 
1112 A GLOSSARY OF MINING TERMS 
 
 Carboniferous. Containing or carrying coal. 
 
 Cargo, (Mexican). A charge. A mule load, generally of 300 lb., but variable 
 in different parts of Mexico. 
 
 Carriage. See Cage and Slope Cage. 
 
 Cartridge. Paper or waterproof cylindrical case filled with explosive forming 
 the charge for blasting. 
 
 Cascajo (Mexican). Gravel. 
 
 Case. A fissure admitting water into a mine. 
 
 Case-harden. To convert the outer surface of wrought iron into hard steel 
 by heating it while in contact with charcoal, cyanide, etc., and quenching. 
 
 Casing. Tubing inserted in a bore hole to keep out water or to protect the 
 sides from collapsing. 
 
 Cast Iron. Pig iron that contains carbon (up to 5%), silicon, sulphur, phos- 
 phorus, etc. 
 
 Cata (Spanish). A mine denounced but not worked. 
 
 Catches. (1) Iron levers or props at the top and bottom of a shaft. (2) 
 Stops fitted on a cage to prevent cars from running off. 
 
 Cauf (North of England). A coal bucket or basket. 
 
 Cauldron Bottoms. The fossil remains or the "casts" of the trunks of sigil- 
 laria that have remained vertical above or below the seam. 
 
 Caulk. To fill seams or joints with something to prevent leaking. 
 
 Counter, or Counter Lode (Cornish). A vein running obliquely across the 
 regular veins of the district. 
 
 Cave, or Cave In. A caving-in of the roof strata of a mine, sometimes ex- 
 tending to the surface. 
 
 Cavils. Lots drawn by the hewers each quarter year to determine their 
 working places. 
 
 Cement. A binding material. 
 
 Center. A temporary support, serving at the same time as a guide to the 
 masons, placed under an arch during the progress of its construction. 
 
 Centrifugal Force. A force drawing away from the center. 
 
 Centripetal Force. A force drawing toward the center. 
 
 CH 4. Marsh gas (see page 859) . 
 
 Chain. A measure 66 or 100 ft. long, divided into 100 links. 
 
 Chain-Brow Way. An underground inclined plane worked on the endless- 
 chain system of haulage. 
 
 Chain Pillar. A pillar left to protect the gangway and air-course, and run- 
 ning parallel to these passages. 
 
 Chain Road. An underground wagonway worked on the endless-chain sys- 
 tem of haulage. 
 
 Chair. Sometimes applied to keeps. 
 
 Chamber. See Breast. 
 
 Char co (Mexican). A pool of water. 
 
 Charge. (1) The amount of powder or other explosive used in one blast or 
 shot. (2) The material fed into a furnace at one time. 
 
 Charquear( Mexican). To dip out water from pools within the mine, throw- 
 it into gutters or pipes that will conduct it to the shaft. 
 
 Check. A metal token used to identify the cars loaded by each particular 
 miner. 
 
 Check-Battery. A battery to close the lower part of a chute, acting as a 
 check to the flow of coal and as an air stopping. 
 
 Checker Coal. Anthracite coal that seems to be made up of rectangular 
 grains. 
 
 Check-Weighman. A man appointed and paid by the miners to check the 
 weighing of the coal at the surface. 
 
 Cheek. Wall. 
 
 Chestnut Coal. Anthracite coal that will pass through a mesh If in. square 
 and over a mesh f in. square (see page 952). 
 
 Chiflon (Mexican). A narrow drift directed obliquely downwards, any 
 pipe from which issues water or air under pressure, or at high velocity. 
 
 Chilian Mill. A roller mill for crushing ore or other material. 
 
 Chill Hardening. Giving a greater hardness to the outside of cast iron by 
 pouring it into iron molds, which causes the skin of the casting to cool 
 rapidly. 
 
 Chimney. A furnace or air stack. 
 
 Chinese Pump. Like a California pump, but made entirely of wood. 
 
 Chock. (1) A square pillar for supporting the roof, constructed of prop 
 timber laid up in alternate cross-layers, in log-cabin style, the center 
 
A GLOSSARY OF MINING TERMS 1113 
 
 being filled with waste. (2) A wooden or other block used to prevent 
 the movement of a car or other body. (3) To secure with chocks. 
 
 Chokedamp. See Blackdamp. 
 
 Churn Drill. A long iron bar -with a cutting end of steel, worked by raising 
 and letting it fall. When worked by blows of a hammer or sledge, it 
 is called a "jumper." 
 
 Chute (also spelled Shute). (1) A narrow inclined passage in a mine, down 
 which coal or ore is either pushed or slides by gravity. (2) The load- 
 ing chute of a tipple. 
 
 Cielo. (Mexican). A ceiling. Trabajar de Cielo. Overhead stoping. 
 
 Clack. A valve that is opened and closed by the force of the water; a check 
 valve. 
 
 Clack Door. The opening into the valve chamber to facilitate repairs and 
 renewals without unseating the pump or breaking the connections. 
 
 Clack Piece. The casting forming the valve chamber. 
 
 Clack Seal. The receptacle for the valve to rest on. 
 
 Cloggy (North of England). When coal is tightly joined to the roof. 
 
 Claim. A portion of ground staked out and held by virtue of a miner's right. 
 
 Clanny. A type of.safety lamp invented by Dr. Clanny. 
 
 Claslic. Constituted of rocks or minerals that are fragments derived from 
 other rocks. 
 
 Clay Band. Argillaceous iron ore; common in many coal measures. 
 
 Clay Course. A clay seam or gouge found at the sides of some veins. 
 
 Claying Bar. A bar for molding clay in a wet bore hole. 
 
 Clearance. (1) The distance between the piston at the end of its stroke and 
 the end of the cylinder^ (2) The volume or entire space filled with 
 steam at end of a stroke, including the space between piston and cylinder 
 head, and the steam ducts to the valve seat. 
 
 Cleat. (1) Vertical cleavage of coal seams, irrespective of dip or strike. (2) 
 A small piece of wood nailed to two planks to keep them together, or 
 nailed to any structure to make a support for something else. 
 
 Cleavage. The property of splitting more readily in some directions than in 
 others. 
 
 Clinometer. An instrument used to measure the angle of dip. 
 
 Clod. Soft and tough shale or slate forming the roof or floor of a coal seam. 
 
 Clunch (English). Under clay, fireclay. 
 
 Clutch. A device for transmitting motion at will from one shaft to another 
 or to some other machine part such as a pulley, or vice versa. 
 
 Coal Breaker. See Breaker. 
 
 Coal Cutter. A machine for holing or undercutting coal. 
 
 Coal Dust. Very finely powdered coal suspended in the airways or deposited 
 along the passages of a mine. 
 
 Coal Measures. Strata of coal with the attendant rocks. 
 
 Coal Pipes (North of England). Very thin irregular coal beds. 
 
 Coal Road. An underground roadway or heading in coal. 
 
 Coal Smut. See Blossom. 
 
 Coaly Rashings. Soft dark shale, in small pieces, containing much carbona- 
 ceous matter. 
 
 Cobbing Hammer. A short two-faced hammer for breaking minerals to sizes. 
 
 Cockermeg, or Cockers. Timber used to hold coal face while it is being 
 undercut. 
 
 Cod (North of England). The bearing of an axle. 
 
 Cojer (Derbyshire). To calk a shaft by ramming clay behind the lining. 
 
 Coffer. Mortar box of a battery. 
 
 Coffer Dam. An enclosure built in the water, and then pumped dry so as to 
 permit masonry or other work to be carried on inside of it. 
 
 Coffin (Cornish). An old pit. 
 
 Cog. (1) A chock. (2) A wooden gear tooth. (3) Loosely, any gear tooth 
 or even gear wheel 
 
 Cohete (Mexican). A rocket; applied to a blast within a mine or outside. 
 
 Coil Drag. A tool for picking pebbles, etc., from drill holes. 
 
 Coke. The fixed carbon and ash of coal sintered together. 
 
 Collar. (1) A flat ring surrounding anything closely. (2) Collar of a mine 
 shaft is the first wood frame of the shaft. (3) The bar or crosspiece of a 
 framing in entry timbering. (4) The mouth or portal of a slope or the 
 first set of timber therein. 
 
 Colliery. The whole coal mine plant, including the mine and all adjuncts. 
 
 Colliery Warnings (English). Telegraphic messages sent from signal-service 
 
1114 A GLOSSARY OF MINING TERMS 
 
 stations to the principal colliery centers to warn managers of mines 
 
 when sudden falls of the barometer occur. 
 Column, or Column Pipe. The pipe conveying the drainage water from the 
 
 mine to the surface. 
 Comer (Mexican). To eat. Comer 'se los Pilares. To take out the last 
 
 vestiges of mineral from the sides and rock pillars of a mine. 
 Conchoidal. Shell-like, such as the curved fracture of flint. 
 Concrete. Artificial stone, formed by mixing broken stone, gravel, etc., with 
 
 lime, cement, tar, or other binder. When hydraulic cement is used 
 
 instead of lime, the mixture is called belon (English). 
 Concretion. A cemented aggregation of one or more kinds of minerals 
 
 around a nucleus. 
 Conduit. (1) A covered waterway. (2) An airway. (3) A pipe or box for 
 
 enclosing and protecting an electrical conductor. 
 Conduit Hole. A flat hole drilled for blasting up a thin piece in the bottom 
 
 of a level. 
 
 Conductors (English). See Guides. 
 Conformable. Strata are conformable when they lie one over the other with 
 
 the same dip. 
 Conglomerate. The rock formation underlying the Coal Measures; a rock 
 
 containing or consisting of pebbles, or of fragments of other rocks 
 
 cemented together; English Pudding Rock or millstone grit. 
 Conical Drum. The rope roll or drum of a winding engine, constructed in 
 
 the form of two truncated cones placed back to back, the outer ends 
 
 being usually the smaller in diameter. 
 Contact. Union of different f9rmations. 
 Contact Lode or Vein. A vein lying between two differently constituted 
 
 rocks. 
 
 Contour. (I) The line that bounds the figure of an object. (2) In survey- 
 ing, a contour line is a line every point of which is at an equal elevation. 
 Contramina (Mexican). Countermine. Any communication between two 
 
 or more mines. Also, a tunnel communicating with a shaft. 
 Cope, or Coup. An exchange of working places between hewers. 
 Corbond. An irregular mass from a lode. 
 
 Cord. (1) A cord weighs about 8 tons. (2) '128 cu. ft. of firewood. 
 Core Drill. A diamond or other hollow drill for securing cores. 
 Cores. Cylinder-shaped pieces of rock produced by the diamond-drill sys- 
 tem of boring. 
 
 Corf. A mine wagon or tub. 
 Cornish Pumps. A single-acting pump, in which the motion is transmitted 
 
 through a walking beam; in other respects similar to a Bull Pump. 
 Cor tar Pillar (Mexican). To form a rock support or pillar within a mine, 
 
 at the opening of a cross-cut or elsewhere. 
 Cortar Sogas (Mexican). Literally, to cut the ropes. To abandon the mine, 
 
 taking away everything useful or movable. 
 Corve. A mining wagon or tub. 
 
 Costean (Cornish). To prospect a lode by sinking pits on its supposed course. 
 Costeaning. Trenching for a lode. 
 Cost Book (Cornish). Mining accounts. 
 
 Cotton Rock. (1) Decomposed chert. (2) A variety of earthy limestone. 
 Coulee. (1) A solidified stream or sheet of lava extending down a volcano, 
 
 often forming a ridge or spur. (2) A deep gulch or water channel, 
 
 usually dry. 
 Counter. (1) A cross-vein. (2) (English) An apparatus for recording the 
 
 number of strokes made by a Cornish pumping engine or other machine, 
 
 or the revolutions of a shaft or pully. (3) A secondary haulageway in 
 
 a coal mine. 
 Counter chute. A chute down which coal is dumped to a lower level or 
 
 gangway. 
 Counter gangway. A level or gangway driven at a higher level than the 
 
 main one. 
 
 Country. The formation traversed by a lode. 
 Country Rock. The main rock of the region through which the veins cut, or 
 
 that surrounding the veins. 
 
 Course. The direction of a line in regard to the points of compass. 
 Coursing or Coursing the Air. Conducting it through the different portions 
 
 of a mine by means of doors, stoppings, and brattices. 
 Cow. A self-acting brake. 
 
A GLOSSARY OF MINING TERMS 1115 
 
 Coyoting. Irregular mining by small pits. 
 
 Crab. A variety of windlass or capstan consisting of a short shaft or axle, 
 either horizontal or vertical, which serves as a rope drum for raising' 
 weights; it may be worked by a winch or handspikes. 
 
 Crab Holes. Holes often met with in the bed rock of alluvial. Also depres- 
 sions on the surface owing to unequal disintegration of the underlying 
 rock; a sink hole or pot hole. 
 
 Cradle Dump. A rocking tipple for dumping cars. See Dump. 
 
 Cramp (English). (1) A short bar of metal having its two ends bent down- 
 wards at right angles for insertion into two adjoining pieces of stone, 
 wood, etc,, to hold them together. (2) A pillar left for support in a 
 mine. 
 
 Cranch. Part of a vein left by previous workers. 
 
 Crane (English). A hoisting machine consisting of a revolving vertical 
 post or stalk, a projecting jib, and a stay for sustaining the outer end of 
 the jib; these do not change their relative positions as they do in a der- 
 rick. There is also a rope drum with winding rope, etc. (2) 
 
 movable or traveling lifting d 
 heaval of 
 
 (2) Any 
 
 Creep. The gradual upheaval of the floor or sagging of the roof of mine 
 
 workings due to the weighting action of the roof and a tender floor. 
 Creston (Mexican). The outcrop or apex of a vein or mineral deposit. 
 Crevice. A fissure. 
 Criadero (Mexican). (1) A mineral deposit of irregular form, not vein-like. 
 
 (2) Any mineral deposit. This latter is the more modern sense, and 
 
 the word is so used in the mining laws at present in force in Mexico. 
 Crib. (1) A structure composed of horizontal timbers laid on one another, 
 
 or a framework built like a log cabin. See Chock. (2) A miner's lunch- 
 
 eon. (3) See Curb. 
 Crib Kettle. A dinner pail. 
 Cribbing. Close timbering, as the lining of a shaft, or the construction of 
 
 cribs of timber, or timber and earth or rock to support a roof. 
 Cribble. A sieve. 
 
 Crisol (Mexican). A crucible of any kind. 
 Crop. See Outcrop. 
 
 Crop Fall. A caving in of the surface at or near the outcrop of a bed of coal. 
 Cropping Coal. The leaving of a small thickness of coal at the bottom of the 
 
 seam in a working place, usually in order to keep back water. The coal 
 
 so left is termed "Cropper Coal." 
 
 Cropping Out. Appearing at the surface; outcropping. 
 Croppings. Portions of a vein as seen exposed at the surface. 
 Cross-Course. A vein lying more or less at right angles to the regular vein of 
 
 the district. 
 Crosscut. (1) A tunnel driven through or across the measures from one 
 
 seam to another. (2) A small passageway driven at right angles to the 
 
 main gangway to connect it with a parallel gangway or air-course. 
 Crosses and Holes (Derbyshire). Made in the ground by the discoverer of a 
 
 lode to temporarily secure possession. 
 Cross-Heading. A passage driven for ventilation from the airway to the 
 
 gangway, or from one breast through the pillar to the adjoining 
 
 working. 
 Cross-Heading, or Cross-Gateway. A road kept through goaf and cutting off 
 
 the gateways at right angles or diagonally. 
 Cross-Hole. See Crosscut (2). 
 Cross-Latches. See Latches. 
 Cross-Vein. An intersecting vein. 
 Crouan (Cornish). Granite. 
 
 Crowbar. A strong iron bar with a slightly curved or flattened end. 
 Crowfoot. A tool for drawing broken boring rods. 
 Crown Tree. A piece of timber set on props to support the roof. 
 Crucero (Mexican). A crosscut for ventilation to get around a horse, or to 
 
 prospect for the vein. 
 Crucible. (1) The bottom of a cupola furnace in which the molten materials 
 
 collect. (2) Pots for smelting assays in or used in making coal analyses. 
 Crush. See Squeeze, Thrust. 
 
 Crusher. A machine used for crushing ores, rock or coal. 
 Crushing. Reduction of mineral in size by machinery. 
 Crystal. A solid of definite geometrical form which mineral (or sometimes 
 
 organic) matter has assumed. 
 
1116 A GLOSSARY OF MINING TERMS 
 
 Culm. Anthracite-coal dirt. 
 
 Culm Bank, or Culm Dump. Heaps of culm now generally kept separate 
 
 from the rock and slate dumps. 
 Cuna (Mexican). Literally, a wedge. A short drill or picker generally 
 
 known in the United States as a "gad." 
 Cundy. -The open space in the gob of long-wall work. 
 Cupel. A cup made of bone ash for absorbing litharge. 
 Curb. (1) A timber frame intended as a support or foundation for the lining 
 
 of a shaft. (2) The heavy frame or sill at the top of a shaft. 
 Curbing. The wooden lining of a shaft. 
 Curtain. A sheet of canvas or other material used to control or deflect an 
 
 air current. 
 
 Cut. (1) To strike or reach a vein. (2) To excavate in the side of a hill. 
 Cutter. A term employed in speaking of any coal-cutting or rock-cutting 
 
 machines; the men operating them, or the men engaged in underholing 
 
 by pick or drill. 
 Cutting Down. To cut down a shaft is to increase its sectional area. 
 
 Dam. A timber bulkhead, or a masonry or brick stopping built to prevent 
 the water in old workings from flooding other workings, or to confine 
 the water in a mine flooded to drown out a mine fire. 
 
 Damp. Mine gases and gaseous mixtures are called damps. See also After- 
 damp, Blackdamp, Firedamp, Stinkdamp. 
 
 Dan (North of England). A truck without wheels. 
 
 Danger Board. See Fireboard. 
 
 Dant (North of England). Soft inferior coal. 
 
 Dap. A notch cut in a timber to receive another timber. 
 
 Datum Water Level. The level at which water is first struck in a shaft sunk 
 on a reef or gutter.. 
 
 Davy. A safety lamp invented by Sir Humphrey Davy. 
 
 Day. Light seen at the top of a shaft. 
 
 Day Fall. See Crop Fall. 
 
 Day Shift. The relay of men working in the daytime. 
 
 Dead. The air of a mine is said to be dead or heavy when it contains car- 
 bonic-acid gas, or when the ventilation is sluggish. 
 
 Dead. (1) Unproductive. (2) Unventilated. 
 
 Dead Roast. To completely drive off all volatile substances. 
 
 Deads. Waste or rubbish from a mine. 
 
 Dead Work. 'Exploratory or prospecting work that is not directly productive; 
 brushing roof, lifting bottom, cleaning up falls, blowing rock, etc. 
 
 Dean (Cornish). The end of a level. 
 
 Debris. Fragments from any kind of disintegration. 
 
 Deep (English). (1) "To the deep," toward the lower portion of a mine; 
 hence, the lower workings. (2) A pasasge driven downward in the 
 measure being worked. The main deep is the principal or hoisting slope. 
 
 Delta. A triangularly shaped piece of alluvial land at the mouth of a river. 
 
 Demasia (Mexican). A piece of unoccupied ground between two mining 
 concessions. 
 
 Denudation. The laying bare by water or other agency. 
 
 Denuncio (Mexican). Denouncement. The act of applying for a mining 
 concession under the old mining laws. 
 
 Deposit. (1) Irregular mineral bodies not veins. (2) A bed or any sedi- 
 mentary formation. 
 
 Deputy (English). (1) A man who fixes and withdraws the timber supporting 
 the roof of a mine, and attends to the safety of the roof and sides, builds 
 stoppings, puts up bratticing, and looks after the safety of the hewers, 
 etc. (2) An underground official -who sees to the general safety of a 
 certain number of stalls or of a district, but does not set the timber him- 
 self, although he has to see that it is properly and sufficiently done. (3) 
 (American) A deputy sheriff. 
 
 Derrick. (!) A crane in which the rope or chain forming the stay can be let 
 out or hauled in at pleasure, thus altering the inclination of a jib. 
 (2) The structure erected to sink a drill hole and the framework above 
 shafts are sometimes called by this name. 
 
 Derrumbe, or Derrumbamineto (Mexican). The caving in of the whole or a 
 portion of a mine. 
 
 Desaguador (Spanish). A water pipe or drain. 
 
 Desague (Mexican). Drainage of a mine by any means. 
 
A GLOSSARY OF MINING TERMS 1117 
 
 Descargar (Mexican). Literally, "to unload." Descargar un Homo. To 
 tear down a furnace. 
 
 Descubridora (Mexican). The first mine opened in a new district or on a 
 new mineral deposit. 
 
 Desmontar (Mexican). Literally, to clear away underbrush. In mining, to 
 take away useless and barren rocks; to remove rubbish. 
 
 Despensa (Mexican). (1) A pantry or storeroom. (2) A secure room to lock 
 up rich ore. 
 
 Dfspoblar (Mexican). To suspend work in a mine. 
 
 Dessue (Cornish). To cut away the ground beside a thin vein so as to 
 remove the latter entire. 
 
 Destajo (Mexican). (1) A contract to do any kind of work in 9r about a mine 
 or elsewhere for a fixed price. (2) Piece work, as distinguished from 
 time work. Destajero. A contractor for piece work. 
 
 Detaching Hook. A self-acting mechanical contrivance for setting free a 
 winding rope from a cage when the latter is raised beyond a certain point 
 in the head-gear; the rope being released, the cage remains suspended in 
 the frame. 
 
 Diagonal Joints. Joints diagonal to the strike of the cleavage. 
 
 Dial (English). An instrument similar to a surveyor's compass, with vernier 
 attached. 
 
 Dialing. Surveying. 
 
 Die. The bottom iron block of a battery, or grinding pan on which the shoe 
 acts. 
 
 Digger or Dredge. A machine for removing coal from the bed of streams, the 
 coal having -washed down from collieries or culm banks above. 
 
 Digging. Mining operations in coal or other minerals. 
 
 Dike. See also Dyke. 
 
 Ditties, or Ginneys. Short self-acting inclines where one or two tubs at a time 
 are run. 
 
 Dip. (1) To slope downwards. (2) The inclination of strata with a horizon- 
 tal plane. (3) The lower workings of a mine. 
 
 Dip Joint. Vertical joints about parallel to the direction of the cleavage dip. 
 
 Dippa (Cornish). A small catch- water pit. 
 
 Dirt Fault. A confusion in a seam of coal, the top and bottom of the seam 
 being well defined, but the body of the vein being soft and dirty. 
 
 Disintegration. Separation by mechanical means, not by decomposition. 
 
 Ditch. (1) The drainage gutter in a mine. (2) A drainage gutter on the sur- 
 face. (3) An open conveyor of water for hydraulic or irrigation purposes. 
 
 Divide. The top of a ridge, hill, or mountain. 
 
 Dividing Slate. A stratum of slate separating two benches of coal. See 
 Parting. 
 
 Divining, or Dowsing Rod. A small forked hazel twig that, when held loosely 
 in the hands, is supposed to dip downwards when passing over water or 
 metallic minerals. 
 
 Dizzue (Cornish). See Dessue. 
 
 Dog. (1) An iron bar, spiked at the ends, with which timbers are held 
 together or steadied. (2) A short heavy iron bar, used as a drag behind 
 a car or trip of cars when ascending a slope to prevent their running back 
 back down the slope in case of accident. See Drag. (3) A pawl. 
 
 Dog Hole. A little opening from one place in a mine to another, smaller than 
 a breakthrough. 
 
 Dog Iron. A short bar of iron with both ends pointed and bent down so as to 
 hold together two pieces of wood into which the points are driven. Or 
 one end may be bent down and pointed, while the other is formed into 
 an eye, so that if the point be driven into a log, the other end may be 
 used to haul on. 
 
 Dolly. (1) A machine for breaking up minerals, being a rough pestle and 
 mortar, the former being attached to a spring pole by a rope. (2) A 
 tool used to sharpen drills. (3) A bar against which rivets are driven. 
 
 Donk (North of England). Soft mineral found in cross- veins. 
 
 Donkey Engine (English). (1) A small steam engine attached to a large one, 
 and fed from the same boiler; used for pumping water into the boiler. 
 (2) A small steam engine. 
 
 Door Piece (English). The portion of a lift of pumps in which the clack or 
 valve is situated. 
 
 Doors. Wooden doors in underground roads or airways to deflect the air 
 current. 
 
1118 A GLOSSARY OF MINING TERMS 
 
 Door Tender. A boy whose duty it is to open and close a mine door before 
 and after the passage of a train of mine cars; a trapper. 
 
 Dope. (1) An absorbent for holding a thick liquid. The material that 
 absorbs the nitroglycerine in explosives. (2) Powder cartridges. 
 
 Double Shift. When there are two sets of men at work, one set relieving the 
 other. 
 
 Double Tape Fuse. Fuse of superior quality, or having a heavier and stronger 
 covering. 
 
 Double Timber. Two props with a bar placed across the tops of them to sup- 
 port the roof and sides. 
 
 Downcast. The opening through which the fresh air is drawn or forced into 
 the mine; the intake. 
 
 Draftage. A deduction made from the gross weight of mineral when trans- 
 ported, to allow for loss. 
 
 Drag. (1) The frictional resistance offered to a current of air in a mine. 
 (2) See Dog. 
 
 Draw. (1) To "draw" the pillars; robbing the pillars after the breasts are 
 exhausted. (2) An effect of creep upon the pillars of a mine. 
 
 Draw a Charge. (1) To take a charge from a furnace. (2) Remove explo- 
 sives (3) Removing the coke from an oven. 
 
 Drawlift. A pump that receives its water by suction and will not force 
 it above its head. 
 
 Draw-Hole. An aperture in a battery through which the coal is drawn. 
 
 Draw Slate. Fragile slate above a coal measure, which must be removed to 
 prevent caving. 
 
 Drawing an Entry. Removing the last of the coal from an entry. 
 
 Drawn. The condition in which an entry or room is left after all the coal 
 has been removed. See Robbed. 
 
 Dresser (Staffordshire). A large coal pick. 
 
 Drift. (1) A horizontal passage underground. A drift follows the vein, as 
 distinguished from a crosscut, which intersects it, or a level or gallery, 
 which may do either. (2) In coal mining, a gangway above water, 
 level, driven from the surface in the seam. (3) Unstratificd diluvium. 
 
 Drifting. (1) Driving a drift. (2) Cars, locomotives, etc., "drift " when they 
 will run by gravity but not attain a dangerous speed. 
 
 Drill. An instrument used in boring holes. 
 
 Drive (Drift). A horizontal passage in a lode. 
 
 Drive. To cut an opening through strata. 
 
 Driving. Excavating horizontal passages, in contradistinction to sinking or 
 raising. 
 
 Driving on Line. Keeping a heading or breast accurately on a given course 
 by means of a compass or transit. 
 
 Dropper. (1) A spur dropping into the lode. (2) A feeder. (3) A branch 
 leaving the vein on the footwall side. (4) Water dropping from the roof. 
 
 Drop Shaft. A monkey shaft down which earth and other matter are lowered 
 by means of a drop (i.e., a kind of pulley with break attached); the 
 empty bucket is brought up as the full one is lowered. 
 
 Druggon (Staffordshire). A vessel for carrying fresh water into a mine. 
 
 Drum. The cylinder or pulley on which the winding ropes are coiled or 
 wound. 
 
 Drum Rings. Cast-iron rings with projections to which are bolted the 
 lagging forming the surface for the ropes to lap upon. 
 
 Drummy. Sounding loose, open, shaky, or dangerous when tested. 
 
 Druse. A cavity lined with small crystals. 
 
 Duck Machine. An arrangement of two boxes, one working within the 
 other, for forcing air into mines. 
 
 Duelas (Mexican). Staves of a barrel or cask, etc. 
 
 Dumb'd. Choked, said of a sieve or grating. 
 
 Dumb Drift. A short tunnel or passage connecting the main return airways 
 of a mine with the upcast shaft some distance above the furnace, in 
 order to prevent the return air laden with mine gases from passing 
 through or over the ventilating furnace. 
 
 Dump. (1) A pile or heap of ore, coal, culm, slate, or rock. (2) The tipple 
 by which the cars are dumped. (3) To unload a car by tipping it up. 
 (4) The pile of mullock as discharged from a mine. 
 
 Dumper. A car so constructed that the body may be revolved to dump the 
 material in front or on either side of the track. 
 
 Durn (Cornish). A timber frame. 
 
A GLOSSARY OF MINING TERMS 1119 
 
 Durr (German). Barren ground. 
 
 Dust. See Coal Dust. 
 
 Duty. The unit of measure of the work of a pumping engine expressed in 
 
 foot-pounds of work obtained from a bushel, or 100 lb., or other unit of 
 
 fuel. 
 Dyke, or Dike. (1) A wall of ignepus rock passing through strata.gtvith or 
 
 without accompanying dislocation of the strata. (2) A fissure filled with 
 
 igneous matter. (3) Barren rock. 
 Dzhu (Cornish). See dessue. 
 
 Ear. The inlet or intake of a fan. 
 
 Echado (Mexican). The dip of the vein. 
 
 Edge Coals (English). Highly inclined seams of coal, or those having a dip 
 
 greater than 30. 
 Efflorescence. An incrustation by a secondary mineral, due to loss of water of 
 
 crystallization. 
 Egg Coal. Anthracite coal that will pass through a 2J-in. square mesh and 
 
 over a 2-in. square mesh (see page 952). 
 
 Elbow. A sharp bend, as in a lode or pipe, a pipe-bend fitting. 
 Electric Blast. Instantaneous blasting of material by means of electricity. 
 Elevator Pump. An endless band with buckets attached, running over two 
 
 drums for draining shallow ground. 
 
 Elvan. A Cornish name applied to most dike rocks of that county, irre- 
 spective of the mineral constitution, but in the present day restricted 
 
 to quartz porphyries. 
 Emborrascarse (Mexican). To go barren by the vein terminating or pinching 
 
 out, etc. 
 
 Empties. Empty mine or railroad cars. 
 Encino (Mexican). Live oak. 
 End Joint (End Cleat). A joint or cleat in a seam about at right angles to 
 
 the principal or face cleats. 
 Endless Chain. A system of haulage or pumping by the moving of an endless 
 
 chain. 
 Endless Rope. A system of haulage same as endless chain, except that a 
 
 wire rope is used instead of chain. 
 End, or End-On. Working a seam of coal at right angles to the principal 
 
 or face cleats. 
 Engine Plane. An incline up which loaded cars are drawn by a rope 
 
 operated by an engine located at the top or bottom of the incline. The 
 
 empty cars descend by gravity, pulling the rope after them. 
 Engineer. (1) One who has charge of the surveying or machinery about a 
 
 mine. (2) One who runs an engine. 
 
 Entibar (Mexican). To timber a mine or any part thereof. 
 Entry. A main haulage road, gangway, or airway. An underground passage 
 
 used for haulage or ventilation, or as a manway. 
 Entry Stumps. Pillars of coal left in the mouths of abandoned rooms to 
 
 support the road, entry, or gangway till the entry pillars are drawn. 
 Erosion. The wearing away of rocks bv the elements. 
 Escaleras (Mexican). Ladders, generally made of notched sticks. 
 Escarpment. A nearly vertical natural face of rock or soil. 
 Escoria (Mexican). Slag of cinders. 
 Escorial. Slag pile. 
 
 Exploder. A chemical employed for the instantaneous explosion of powder. 
 Exploitation. The working of a mine, and similar undertakings; the exami- 
 nation instituted for that purpose. 
 Exploration. Development. 
 
 Explosion. Sudden ignition of a body of firedamp, dust, etc. 
 Eye (English). (1) A circular hole in a bar for receiving a pin and for 
 
 other purposes. (2) The eye of a shaft is the very beginning of a pit. 
 
 (3) The eye of a fan is the central or intake opening. 
 
 F ace> (i) The place at which the material is actually being worked, either 
 in a breast or heading or in longwall. (2) The end of a drift or 
 
 Face-On. When the face of the breast or entry is parallel to the face cleats 
 
 of the seam (see page 614). 
 Face Wall A. wall built to sustain a face cut into the natural earth, m 
 
 distinction to a retaining wall, which supports earth deposited behind it. 
 
1120 A GLOSSARY OF MINING TERMS 
 
 Faenas (Mexican). Dead work, in the way of development. 
 
 Fahlband (German). A course impregnated with metallic sulphides. 
 
 Fall. (1) A"masss of roof or side which has fallen in any part of a mine. 
 (2) To blast or wedge down coal. 
 
 False Bedding. Irregular lamination, wherein the laminae, though for 
 shoflfc distances parallel to each other, are oblique to the general strati- 
 fication, of the mass at varying angles and directions. 
 
 False Bottom. A movable bottom in some apparatus. 
 
 False Cleavage. A secondary slip cleavage superinduced on slaty cleavage. 
 
 False Set. A temporary set of timber used until work is far enough advanced 
 to put in a permanent set. 
 
 Famp (North of England). Thin beds of soft tough shale. 
 
 Fan. A machine for creating a circulation of air in a mine. 
 
 Fan Drift. A short tunnel or conduit leading from the top of the air-shaft to 
 the fan. 
 
 Fanega (Mexican). A Spanish measure of about 2\ bushels. 
 
 Fang (Derbyshire). An air-course. 
 
 Fascines (English). Bunches of twigs and small branches for forming 
 foundations or retaining walls in soft ground. 
 
 Fast. (1) A road driven in a seam with the solid coal at each side. "Fast 
 at an end," or "fast at one side," implies that one side is solid coal and 
 the other open to the goaf or some previous excavation. (2) Bed rock. 
 
 Fast End. An end of a breast of coal that requires cutting. 
 
 Fat Coals. Those containing volatile oily matters. 
 
 Fathom (English). 6 ft. 
 
 Fault. A fracture or disturbance of the strata breaking the continuity of 
 the formation. 
 
 Feather. A slightly projecting narrow rib lengthwise on a shaft, arranged 
 to catch into a corresponding groove in anything that surrounds and 
 slides along the shaft. 
 
 Feather Edge. (1) A passage from false to true bottom. (2) The thin end 
 of a wedge-shaped piece of rock or coal. 
 
 Feed. Forward motion imparted to the cutters or drills of -rock-drilling or 
 coal-cutting machinery, either hand or automatic. 
 
 Feeder. (1) A runner of water. (2) A small blower of gas. (3) A device 
 for feeding at a uniform rate to any machine process. 
 
 Fend-Off (English). A sort of bell-crank for turning a pump rod past the 
 angle of a crooked shaft. 
 
 Fiery. Containing explosive gas. 
 
 Fines. Very small material produced in breaking up large lumps. 
 
 Fire. (1) A miners' term for firedamp. (2) To blast with gunpowder or 
 other explosive. (3) A word shouted by miners to warn one another 
 when a shot is to be fired. 
 
 Fire-Bars (English). The iron bars of a grate on which the fuel rests. 
 
 Fireboard. A piece of board with the word fire painted upon it and sus- 
 pended to a prop, etc., in the workings, to caution men not to take a 
 naked light beyond it, or to pass it without the consent of the foreman 
 or his assistants. 
 
 Fire Boss. An underground official who examines the mine for gas and 
 inspects safety lamps taken into the mine. 
 
 Fireclay. Any clay that will withstand a great heat without vitrifying. 
 
 Firedamp. (1) A mixture of light carburetted hydrogen (CHi) and air in 
 explosive proportions; often applied to CHt alone or to any explosive 
 mixture of mine gases. 
 
 Fireman. See Fire Boss. 
 
 Fire-Setting. The process of exposing very hard rock to intense heat, ren- 
 dering it thereby easier for breaking down. 
 
 First Aid. The assistance or treatment which should be given an injured 
 person immediately upon injury or as soon thereafter as possible. 
 
 First Working. See Whole Working. 
 
 Firsts. The best mineral picked from a mine. 
 
 Fish. To join two beams, rails, etc., together by long pieces at their 
 sides. 
 
 Fish Plates. The bars used to join the ends of adjacent rails in a track 
 
 Fissure. An extensive crack. 
 
 Fissure Vein. Any mineralized crevice in the rock of very great depth. 
 
 Flag. A track signal or target. 
 
 Flags. Broad flat stones for paving. 
 
A GLOSSARY OF MINING TERMS 1121 
 
 Flagstone. Any kind of a stone that separates naturally into thin tabular 
 plates suitable for pavements and curbing. Especially applicable to 
 sandstone and schists. 
 
 Flang (Cornish). A double-pointed pick. 
 
 Flange (English). A projecting ledge or rim. 
 
 Flat. (1) A district or set of workings separated by faults, old workings, or 
 barriers of solid coal. (2) The siding or station laid with two or more 
 lines of railway, to which the putters bring the full cars from the work- 
 ing face, and where they get the empty cars to take back. (3) The area 
 of working places, from which coal is brought to the same station, is also 
 called "flat." 
 
 Flat Rod. A horizontal rod for conveying power to a distance. 
 
 Flats. (1) Narrow decomposed parts of limestones that are mineralized. 
 
 (2) Flatcars. 
 
 Flat Sheet. Sheet-iron flooring at landings and in the plats, chambers, and 
 
 junctions of drives, to facilitate the turning and management of trucks. 
 Flat Wall (Cornish). Foot-wall. 
 
 Float. Broken and transported particles or boulders of vein matter. 
 Float Stones. Loose boulders from lodes lying on or near the surface. 
 Flood Gate (English). A gate to let off excess of water in flood or other 
 
 times. 
 Floor. (1) The stratum of rock upon which a seam of coal immediately 
 
 lies. (2) That part of a mine upon which you walk or upon which 
 
 the road bed is laid. 
 
 Flucan. A soft, greasy, clayey substance found in the joints of veins. 
 Fluke. A rod for cleaning out drill holes. 
 Flume. An artificial watercourse. 
 Flush. (1) To clean out a line of pipes, gutters, etc., by letting in a sudden 
 
 rush of water. (2) The splitting of the edges of stone under pressure. 
 
 (3) Forming an even continuous line or surface. (4) To fill a mine 
 with fine material. Sometimes called slush. 
 
 Following Stone. Roof stone that falls on the removal of the seam. 
 Foot-Hole. Holes cut in the sides of shafts or winzes to enable miners to 
 
 ascend and descend. 
 Foot-Piece. (1) A wedge of wood or part- of a slab placed on the foot- wall 
 
 against which a stull piece is jammed. (2) A piece of wood placed on 
 
 the floor of a drive to support a leg or prop of timber. 
 Foot-Wall. The lower boundary of a lode. 
 Footway. Ladders in mines. 
 Force Fan. See Blowdown Fan. 
 
 Force Piece. Diagonal timbering to secure the ground. 
 Force Pump. A pump that forces water above its valves. 
 Forebay. Penstock. The reservoir from which water passes directly to a 
 
 waterwheel. 
 
 Forepoling. Driving the poles over the timbers so that their ends project 
 beyond the last set of timber, so as to protect the miner from roof falls; 
 
 used also in quicksand or other loose material. 
 
 Forewinning. The first working of a seam in distinction from pillar drawing. 
 Fork. (1) A deep receptacle in the rock, to enable a pump to extract the 
 
 bottom water. A pump is said to be "going in fork" when the water is 
 
 so low that air is sucked through the windbore. (2) (Cornish) Bottom 
 
 of sump. (3) (Derbyshire) Prop for soft ground. 
 Formation. A series of strata that belong to a single geological age. 
 Fossil. Organic remains or impressions of them found in mineral matter. 
 Pother (North of England). i chaldron. 
 Frame Set The legs and cap or collar arranged so as to support a passage 
 
 mined out of the rock or lode; also called Framing. 
 F ree , Coal is said to be "free" when it is loose and easily mined, or whe: 
 
 will "run" without mining. 
 Free Miner. Licensed miner. 
 Fresno (Mexican). An ash tree. 
 Fronton (Mexican). Any working face. 
 
 Furnace. A^large coal fire at 'or near the bottom 9f an upcast shaft, for pro- 
 ducing a current of air for ventilating the mine. 
 
 Furnace Shaft. The upcast shaft in furnace ventilation. 
 
 Fuse, (i) A hollow tube filled with an explosive mixture for igniting car- 
 tridges. (2) To melt. 
 71 
 
1122 A GLOSSARY OF MINING TERMS 
 
 Gad. (1) A small steel wedge used for loosening jointy ground, (2) A 
 
 pointed chisel. 
 
 Gale. A grant of mining ground. 
 
 Galera (Mexican). A shed; any long or large room; a storehouse. 
 Callage. Royalty. 
 Gallery. A horizontal passage. 
 Gallows Frame. The frame supporting a pulley over which the hoisting rope 
 
 passes to the engine. 
 Gang. A set of miners, a "shift." 
 Gangway. The main haulage road or level. 
 Canister. A hard, compact, extremely silicious fireclay. 
 Gas. See Firedamp. Any firedamp mixture in a mine is called gas. 
 Gas Coal. Bituminous coal containing a large percentage of volatile 
 
 matter. 
 
 Gash Vein. A wedge-shaped vein. 
 Gasket. A band or ring of any material put between the flanges of pipes, 
 
 etc., before bolting, to make them water-tight or steam-tight. 
 Gale. An underground road connecting a stall or breast with a main road. 
 Gateway. (1) A road kept through goaf in longwall working. (2) A gang- 
 way having ventilating doors. 
 Gauge Door. A wooden door fixed in an airway for regulating the supply 
 
 of ventilation necessary for a certain district or number of men. 
 Gauge Pressure. The pressure shown by an ordinary steam gauge. It is 
 
 the pressure above that of the atmosphere. 
 
 Gears, or Pair of Gears. (1) Two props and a plank, the plank being sup- 
 ported by the props at either end. (2) Toothed wheels for transmitting 
 
 motion. 
 
 Geodes. Large nodules of stone with a hollow in the center. 
 Geordie. A safety lamp invented by George Stephenson. 
 Geyser. Natural fountain of hot water and steam. 
 Gib. (1) A short prop of timber by which coal is supported while being 
 
 holed or undercut. (2) A piece of metal often used in the same hole 
 
 with a wedge-shaped key for holding pieces together. 
 Ginneys. See Dillies. 
 Gin, or Horse Gin. A vertical drum and framework by which the minerals 
 
 and dirt are raised from a shallow pit. 
 Giraffe. A mechanical appliance for receiving and tipping a car full of mineral 
 
 or waste rock when it arrives at the surface. 
 Girdle. A thin bed or band of stone. A roof is described as a post roof 
 
 with metal girdles, or a metal roof with post girdles, according as the 
 
 post or the metal predominates. 
 Goaf, or Goave. That part of a mine from which the coal has been worked 
 
 away, and the space more or less filled up with waste. 
 Gob. (1) Another word for Goaf. (2) To leave coal and other minerals- 
 
 that are not marketable in the mine. (3) To stow or pack any useless 
 
 underground roadway with rubbish. 
 Gob Fire. Spontaneous combustion underground of fine coal and slack in 
 
 the gob. 
 
 Gobbing Up. Filling with waste. 
 
 Gob Road. A roadway in a mine carried through the goaf. 
 Going Headways, or Going Bord. A headway or bord laid with rails, and 
 
 used for conveying the coal tubs to and from the face. 
 Golpeador (Mexican). A striker, in hand drilling. 
 Goths (Staffordshire). Sudden burstings of coal from the face, owing to 
 
 tension caused by unequal pressure. 
 Gouge. The layer of clay, or decomposed rock, that lies along the wall or 
 
 walls of a vein. It is not always valueless. 
 
 Grade. The amount of fall or inclination in ditches, flumes, roads, etc. 
 Grain. An obscure vertical cleavage usually more or less parallel to the end 
 
 or dip joints. 
 Granza (Mexican). Metallic minerals from the size of rice to that of hens' 
 
 eggs. 
 
 Grass. The surface of the ground. 
 Grate Coal. See Broken Coal. 
 Grating. A. perforated iron sheet or wire gauze placed in front of reducing 
 
 machinery. 
 
 Gravel. Water-worn stones about the size of marbles. 
 Gray Metal, Shale of a grayish color. 
 
A GLOSSARY OF MINING TERMS 1123 
 
 Graywacke. A compact gray sandstone frequently found in Paleozoic 
 
 formations. 
 Greenstone. A general term employed to designate green-colored igneous 
 
 rocks, as dionte, dolerite, diabase, gabbro, etc. 
 Grid. (1) A grated opening. (2) A section of electrical resistance, usually 
 
 made of cast iron. 
 
 Griddle. A coarse sieve used for sifting ores, clay, etc. 
 Grizzly. A bar screen. 
 
 Ground Rent. Rent paid for surface occupied by the plant, etc., of a colliery 
 Groundsill. A log laid on the floor of a drive on which the legs of a set of 
 
 timber rest. 
 Grout (English). Thin mortar poured into the interstices between stones 
 
 and bricks. 
 
 Grove (Derbyshire). A mine. 
 
 Grub Stake. The mining outfit or supplies furnished to a prospector on con- 
 dition of sharing in his finds. 
 Guag (Cornish). Worked-out ground. 
 Gualdria (Mexican). A long and stout beam, generally sustaining other 
 
 beams or some heavy weight. 
 
 Guarda Raya (Mexican). A landmark; a monument. ' 
 Guides. See Cage Guides. 
 Guijo (Mexican). A pointed pivot, upon which turns the upright center 
 
 piece of an arrastre, of a door, etc. 
 Gunboat. A self-dumping car, holding from 5 to 8 tons of coal, used upon 
 
 inclined planes or slopes. They are filled by emptying the mine cars 
 
 into them at the foot of the slope. 
 Gunnies (Cornish). 3 ft. 
 Gutter. (1) A small water-draining channel. 
 
 Hade. The inclination of a vein or fault, taking the vertical as zero. 
 Half Course. (1) At an angle of 45 from general or previous course. (2) 
 
 Half on the level and half on the dip. 
 Half Set. One leg piece and a cap. 
 Hammer-and-Plate. A signaling apparatus. 
 
 Hand Barrow. A long box or platform with handles at each end. 
 Hand Dog. A kind of spanner or wrench for screwing up and disconnecting 
 
 the joints of boring rods at the surface. 
 
 Handspike. A wooden lever for working a capstan or windlass. 
 Hanger-On. The man that runs the loaded cars on to the cages and gives 
 
 the signal to hoist. See Cager. 
 Hanging Spear Rod. Wooden pump rods adjustable by screws, etc., by which 
 
 a sinking set of pumps is suspended in a shaft. 
 Hanging Wall. In metalliferous mining, the stratum lying geologically 
 
 directly above a bed or vein. 
 Hatajo (Mexican). A drove of pack mules. 
 Hat Rollers. Cast-iron or steel rollers shaped like a hat, revolving on a 
 
 vertical pin, for guiding inclined haulage ropes around curves. 
 Hatter. A miner working by himself on his own account. 
 Haulage Clip. Levers, jaws, wedges, etc., by which cars, singly or in trains, 
 
 are connected to the hauling ropes. 
 Hauling. The drawing of conveying of the product of the mine from the 
 
 working places to the bottom of the hoisting shaft, or slope. 
 Haunches. The parts of an arch from the keystone to the skew back. 
 Hazle (North of England). Sandstone mixed with shale. 
 Head. (1) Pressure of water in pounds per square inch. (2) Any subter- 
 ranean passage driven in solid coal. (3) That part of a face nearest 
 
 Head, or Sluice Head (Australia and New Zealand). A supply of 1 cu. ft. of 
 water per second, regardless of the head, pressure, or size of orifice. 
 
 Head-Block. (1) A stop at the head of a slope or shaft to stop cars from 
 going down the shaft or slope. (2) A cap piece. 
 
 Headboard. A wedge of wood placed against the hanging wall, and against 
 which one end of the stull piece is jammed. 
 
 Header. (I) A rock that heads off or delays progress. (2) A blast hole at or 
 above the head. (3) A stone or brick laid lengthwise at right angles to 
 the face of the masonry. (4) The Stanley Header is an entry boring 
 machine that bores the entire section of the entry in one operation. 
 
 Head-Gear, The pulley frame erected over a shaft. 
 
1124 A GLOSSARY OF MINING TERMS 
 
 Head-House. When the head-frame is housed in, the structure is known by 
 
 this name. 
 
 Heading. (1) A continuous passage for air or for use as a manway; a gang- 
 way or entry. (2) A connecting passage between two rooms, breasts, 
 
 or other working places. 
 Head-Piece. A cap; a collar. 
 
 Headrace. An aqueduct for bringing a supply of water on to the ground. 
 Headstocks. Gallows frame; head-frame. 
 Headways. (1) A road; usually 9 ft. wide, in a direction parallel to the 
 
 main-cleavage planes of the coal seams, which direction is called 
 
 "headways course," and is generally 'about north and south in the 
 
 Newcastle coal field. It is termed "on end" in other districts. (2) 
 
 Cross- headings. 
 Heave. The shifting of rocks, seams, or lodes on the face of a cross-course, 
 
 etc. 
 Heaving. The rising of the thill (or floor) of a seam where the coal has been 
 
 removed. 
 
 Hechado (Spanish). Dip. 
 
 Heel of Coal. A small body of coal left under a larger body as a support. 
 Heel of a Shot. In blasting, the front of a shot, or the face of the shot 
 
 farthest from the charge. 
 
 Heep Stead (English). The entire surface plant of a colliery. 
 Helper. A miner's assistant, who works under the direction of the miner. 
 Helve A. handle. 
 
 Hewer. A collier that cuts coal; a digger. 
 High Reef. The bed rock or reef is frequently found to rise more abruptly 
 
 on one side of a gutter than on the other, and this abrupt reef is termed 
 
 a high reef. 
 Hitch. (1) A fault or dislocation of less throw than the thickness of the 
 
 seam in which it occurs. (2) Step cut in the rock or lode for holding 
 
 stay-beams, or timber, etc., for various purposes. 
 Hoarding. A temporary close fence of boards placed around a work in 
 
 progress. 
 Hogback. A roll occurring in the floor and not in the roof, the coal being 
 
 cut out or nearly so, for a distance. 
 Hoister. A machine used in hoisting the product. It may be operated by 
 
 steampower or horsepower. 
 Hole. (1) To undercut a seam of coal by hand or machine. (2) A bore 
 
 hole. (3) To make a communication from one part of a mine to 
 
 another. 
 Holing. (1) The portion of the seam or underclay removed from beneath 
 
 the coal before it is broken down. (2) A short passage connecting two 
 
 roads. (3) See Kirving. 
 Holing Through. Driving a passage through to make connection with 
 
 another part of the same workings, or with those in an adjacent mine. 
 Hood. See Bonnet. 
 
 Hopper. A coal pocket; a funnel-shaped feeding trough. 
 Horn Coal. Coal worked partly end-on and partly face-on. 
 Horse Gin. A gearing for winding by horsepower. 
 
 Horsepower. The power that will raise 33,000 Ib. 1 ft. high per minute. 
 Horse, or Horsebacks. (1) Natural channels cut or washed away by water in 
 
 a coal seam and filled up with shale and sandstone. Sometimes a bank 
 
 or ridge of foreign matter in a coal seam. (2) A mass of country rock 
 
 lying within a vein or bed. (3) Any irregularity cutting out a portion 
 
 of the vein. See Dirt Fault and Rock Fault. 
 Horse Whim. A vertical drum worked by a horse, for hauling or hoisting. 
 
 Called also Horse Gin. 
 Hose. A strong flexible pipe made of leather, canvas, rubber, etc., and used 
 
 for the conveyance of water, steam, or air under pressure to any particu- 
 lar point. 
 H Piece. The portion of a column pipe containing the valves of the 
 
 pump. 
 
 Hueco (Mexican). See Demasia.. 
 
 Hulk (Cornish). To pick out the soft portions of a lode. 
 Hundido (Mexican). See Derrumbe. 
 Hungry. Worthless looking. 
 
 Hurdy Gurdy. A waterwheel that receives motion from the force of travel- 
 ing water. 
 
A GLOSSARY OF MINING TERMS 1126 
 
 Hung Shot. A shot which does not explode immediately upon detonation 
 
 or ignition. 
 
 Hutch. (English) A mine car. 
 Hydraulic Cement. A mixture of lime, magnesia, alumina, and silica that 
 
 solidifies beneath water. 
 Hydraulicking. Working or removing auriferous or other gravel b'eds by 
 
 hydraulic power. 
 Hydrocarbons. Compounds of hydrogen and carbon. 
 
 Igneous Rocks. Those that have been in a more or less fused state. 
 
 Inbye. In a direction inward toward the face of the workings, or away from 
 the entrance. 
 
 Incline. Short for inclined plane. Any inclined heading or slope road or 
 track having a general inclination or grade in one direction. 
 
 Indicator. (1) A mechanical contrivance attached to winding, hauling, or 
 other machinery, which shows the position of the cages in the shaft or 
 the cars on an incline during their journey or run. (2) An apparatus for 
 showing the presence of firedamp in mines, the temperature of goaves, 
 the speed of a ventilator, pressure of steam, air, or water, etc. 
 
 Indicator Card, or Diagram. A diagram showing the variation of steam 
 pressure in the cylinder of an engine during an entire stroke or revo- 
 lution. 
 
 Indoor Catches. Strong beams in Cornish pumping-engine houses to catch 
 the beam in case of a smash, thus preventing damage to the engine 
 itself. 
 
 In-Fork. When a pump continues working after water has receded below 
 the holes of the wind bore. 
 
 Ingot. A lump of cast metal. 
 
 In Place. A vein or deposit in its original position. 
 
 Inset. The entrance to a mine at the bottom, or part way down a shaft 
 where the cages are loaded. 
 
 Inside Slope. A slope on which coal is raised from a lower to a higher 
 gangway. 
 
 Inspector. A government official whose duties are to enforce the laws regu- 
 lating the working of mines. 
 
 Instroke. The right to take coal from a royalty to the surface by a shaft in 
 an adjoining royalty. A rent is usually charged for this privilege. 
 
 Intake. (1) The passage through which the fresh air is drawn or forced in 
 a mine, commencing at the bottom of a downcast shaft, or the mouth 
 of a slope. (2) The fresh air passing int9 a colliery. 
 
 Inversion. Such a change in the dip of a vein or seam as makes the foot- 
 wall or floor the upper and the hanging wall or roof the lower of the two. 
 
 Irestone (Cornish). Any hard tough stone. 
 
 Iron Man. A coal-cutting machine. 
 
 Jacal (Mexican). See Xacal. 
 
 Jack. (1) A lantern-shaped case made of tin, in which safety lamps are 
 carried in strong currents of air.. (?,) A device for lifting heavy weights. 
 
 Jacket. (1) An extra surface covering, as a steam jacket. (2) A water- 
 jacket is a furnace having double iron walls, between which water 
 circulates. 
 
 Jack-Lamp. A Davy lamp, with the addition of a glass cylinder outside 
 the gauze. 
 
 Jars. In rope drilling, two long links which take up the shock of impact 
 when the falling tools strike the bottom of the hole. 
 
 Jenkin. A road cut in a pillar of coal in a bordways direction, that is, at 
 right angles to the main cleavage planes. 
 
 Jig. (1) A self-acting incline. (2) A machine for separating ores or minerals 
 from worthless rock by means of their difference in specific gravity ; 
 also called Jigger or Washer. 
 
 Jigger. (1) A kind of coupling hook for connecting cars on an incline. 
 (2) An allowance of liquor sometimes issued to workmen (almost 
 obsolete). (3) See Jig. 
 
 Jigging. Separating heavy from light particles by agitation in water. 
 
 Jockey. A self-acting apparatus carried on the front truck of a set for re- 
 leasing it from the hauling rope. 
 
 Joggle. A joint of trusses or sets of timber for receiving pressure at right 
 angles, or nearly so. 
 
1126 A GLOSSARY OF MINING TERMS 
 
 Joints. (1). Divisional planes that divide the rock in a quarry into natural 
 blocks. There are usually two or three nearly parallel series, called by 
 quarrymen end joints, back joints, and bottom joints, according to their 
 position. (2) In coal seams, the less pronounced cleats or vertical 
 cleavages in the coal. The shorter cleats, about at right angles to the 
 face cleats and the bedding plane of the coal. 
 
 Jud. (1) A portion of the working face loosened by "kirying" underneath, 
 and "nicking" up one side. The operation of kirying and nicking is 
 spoken of as "making a jud." (2) The term jud is also applied to a 
 working place, usually 6 to 8 yd. wide, driven in a pillar of coal. When 
 a jud has been driven the distance required, the timber and rails are 
 removed, and this is termed "drawing a jud." 
 
 Judge (Derbyshire and North of England). A measuring staff. 
 
 Jugglers, or Jugulars. Timbers set obliquely against the rib in a breast, to 
 form a triangular passage to be used as a manway, airway, or chute. 
 
 Jump. An upthrow or a downthrow fault. 
 
 Jumper. A hand drill used in boring holes in rock for blasting. 
 
 Kann (Cornish). Fluorspar. 
 
 Kazen (Cornish). A sieve. 
 
 Keeker. An official that superintends the screening and cleaning of the coal. 
 
 Keel Wedge. A long iron wedge for driving over the top of a pick hilt. 
 
 Keeps, or Keps. Wings, catches, or rests to hold the cage at rest when it 
 
 reaches any landing. 
 Kenner. Time for quitting work. 
 
 Kerf. The undercut made to assist the breaking of the coal. 
 Kerve (North of England). In coal mining, to cut under. 
 Kettle or Kettle Bottom. The petrified stump of a tree or other fossil in the 
 
 roof of a mine. 
 Key. (1) An iron bar of suitable size and taper for filling the keyways of 
 
 shaft and pulley so as to keep both together. (2) A kind of spanner 
 
 used in deep boring by hand. 
 Kibble. See Bowk. Often made with a bow or handle, and carrying over a 
 
 ton of d6bris. 
 Kick Back. A track arrangement for reversing the direction of travel of 
 
 cars moving by gravity. 
 
 Kickup. An apparatus for emptying trucks. 
 Kieve. Tossing tub. 
 Killas (Cornish). Clay slate. 
 Kiln. A chamber built of stone or brick, or sunk in the ground, for burning 
 
 minerals in. 
 
 Kind. (1) Tender, soft, easy. (2) Likely looking stone. 
 Kind-Chaudron. A system of sinking shafts through water-bearing strata. 
 Kirving (North of England). The cutting made beneath the coal seam. 
 Kist. The wooden box or chest in which the deputy keeps his tools. The 
 
 chest is always placed at the flat or lamp station, and this spot is often 
 
 referred to by the expression "at the kist." 
 Kit. Any workman's necessary outfit, as tools, etc. 
 Kitty. A squib made of a straw tube filled with powder. 
 Knee Piece. A bent piece of piping. 
 Knocker. A lever that strikes on a plate of iron at the mouth of a shaft, by 
 
 means of which miners below can signal to those on the top. 
 Knocker Line. The signal line extending down the shaft from the knocker. 
 Koepe System. A system of hoisting without using drums, the rope being 
 
 endless and passing over pulleys instead of around a drum. 
 
 Labor (Mexican). Mine workings in general. Specifically, a stope or any 
 other place where mineral is being taken out. 
 
 Ladder-way, Ladder Road. The particular shaft, or compartment of a shaft, 
 used for ladders. 
 
 Lagging. (1) Small round timbers, slabs, or plank, driven in behind the 
 1 egs and over the collar, to prevent pieces of the sides or roof from falling 
 through. ("2) Long pieces of timber closely fitted together and fastened 
 to the drum rings to form a surface for the rope to wind onto. 
 
 Lamina. Sheets not naturally separated, but which may be forced apart. 
 
 Lamp Men. Cleaners, repairers, and those having charge of the safety 
 lamps at a colliery. 
 
 Lamp Stations, Certain fixed stations in a mine at which safety lamps 
 
A GLOSSARY OF MINING TERMS 1127 
 
 are allowed to be opened and relighted by men appointed for that 
 purpose, or beyond which, on no pretense, is a naked light allowed 
 to be taken. 
 
 Lander. The man that receives a load of mineral at the mouth of a shaft. 
 
 Lander's Crook. A hook or tongs for upsetting the bucket of hoisted rock. 
 
 Landing. (1) A level stage for loading or unloading a cage or skip. (2) 
 The top or bottom of a slope, shaft, or inclined plane. 
 
 Land Sale. The sale of coal loaded into carts or wagons for local consump- 
 tion. 
 
 Land-Sale Collieries. Those selling the entire product for local consump- 
 tion, and shipping none by rail or water. 
 
 Lap. One coil of rope on a drum or pulley. 
 
 Large. The largest lumps of coal sent to the surface, or all coal that is hand 
 picked or does not pass over screens; also, the large coal that passes 
 over screens. 
 
 Larry. (1) A car to which an endless rope is attached, fixed at the inside 
 end of the road, forming part of the appliance for taking up slack rope. 
 See Balance Car. (2) See Barney. (3) A car with a hopper bottom and 
 adjustable chutes for feeding coke ovens. 
 
 Latches. (1) A synonym of switch. Applied to the split rail and hinged 
 switches. (2) Hinged switch points, or short pieces of rail that form 
 rail crossings. 
 
 Lateral. From the side. 
 
 Lath. A plank laid over a framed center or used in poling. 
 
 Launder. Water trough. 
 
 Laundry Box. The box at the surface receiving the water pumped up 
 from below. 
 
 Lava. A common term for all rock matter that has flowed from a volcano or 
 fissure. 
 
 Lazadores (Mexican). Men formerly employed in recruiting Indians for 
 work in the mines by the gentle persuasion of a lasso. 
 
 Lazy Back (Staffordshire). A coal stack, or pile of coal. 
 
 Leader. A seam of coal too small to be worked profitably, but often being a 
 guide to larger seams lying in known proximity to it. 
 
 Leat. A small water ditch. 
 
 Leg. A wooden prop supporting one end of a collar. 
 
 Leg Piece. An upright log placed against the side of a drive to support the 
 cap piece. 
 
 Lefiador (Mexican). One that cuts, carries, or furnishes wood for com- 
 bustible. 
 
 Level. A road or gangway running parallel or nearly so with the strike 
 of the seam. 
 
 Lid. A cap piece used in timbering. 
 
 Lift. (1) The vertical height traveled by a cage in a shaft. (2) The lift of a 
 pump is the theoretical height from the level of the water in the sump 
 to the point of discharge. (3) The distance between the first level and 
 the surface, or between two levels. (4) The levels of a shaft or slope. 
 
 Lifting Guards. Fencing placed around the mouth of a shaft, which is 
 lifted out of the way by the ascending cage. 
 
 Lignite. A coal of a woody character containing about 66% carbon and 
 having a brown streak. 
 
 Lime Cartridge. A charge or measured quantity of compressed dry caustic 
 lime made up into a cartridge and used instead of gunpowder for 
 breaking down coal. Water is applied to the cartridge, and the expan- 
 sion breaks down the coal without producing a flame. 
 
 Lime Coal. Small coal suitable for lime burning. 
 
 Lines. Plumb-lines, not less than two in number, hung from hooks or 
 spads driven in wooden plugs. A line drawn through the centers of 
 the two strings or wires, as the case may be, represents the bearing or 
 course to be driven on. 
 
 Lining. The planks arranged against frame sets. 
 
 Linternilla (Mexican). The drum of a Horse Whim. 
 
 Lip Screen. (I) A small screen or screen bars, placed at the draw hole of a 
 coal pocket to take out the fine coal. (2) A stepped coal screen. 
 
 Little Giant. The name given to a special sort of hydraulic nozzle used & 
 sluicing purposes. 
 
 Llaves (Mexican). Horizontal cross-beams in a shaft, or the upright pieces 
 that sustain the roof beams in a drift or tunnel. 
 
1128 A GLOSSARY OF MINING TERMS 
 
 Loaded Track. Track used for loaded cars. 
 
 Loader. One that fills the mine cars at the working places. 
 
 Loam. Any natural mixture of sand and clay that is neither distinctly sandy 
 nor clayey. 
 
 Location. The first approximate staking out or survey of a mining claim, in 
 distinction from a Patent Survey, or a Patented Claim. 
 
 Location Survey. See Location. 
 
 Lode (Cornish). Strictly a fissure in the country rock filled with mineral; 
 usually applied to metalliferous lodes. In general miners' usage, a lode, 
 vein, or ledge is a tabular deposit of valuable minerals between definite 
 boundaries. Whether it be a fissure formation or not is not always 
 known, and does not affect the legal title under the United States federal 
 and local statutes and customs relative to lodes. But it must not be a 
 placer, i.e., it must consist of quartz or other rock in place, and bearing 
 valuable mineral. 
 
 Logs. Portions of trunks of trees cut to length and built up so as to raise 
 the mouth or collar of a shaft from the surface, in order to give the 
 requisite space for the dumping of mullock and mineral. 
 
 Long-Pillar Work. A system of working coal seams in three separate opera- 
 tions: (a) Large pillars are left; (b) a number of parallel headings are 
 driven through the block; and (c) the ribs or narrow pillars are worked 
 away in both directions. 
 
 Long Ton. 2,240 Ib. 
 
 Longwall. A system of working a seam of coal in which the whole seam is 
 taken out and no pillars left, excepting the shaft pillars, and sometimes 
 the main-road pillars. 
 
 Loose End. (1) A portion of a seam worked on two sides. (2) A portion 
 that projects in the shape of a wedge between previous workings. 
 
 Low Grade. Not rich in mineral. 
 
 Lumber. Timber cut to the various sizes and shapes for carpenters' purposes. 
 
 Lumbreras (Mexican). Ventilating shafts in a mine or other underground 
 work. 
 
 Lump Coal. (1) All coal (anthracite only) larger than broken coal, or, when 
 steamboat coal is made, lumps larger than this size. (2) In soft coal, all 
 coal passing over the screen. 
 
 Lute. An adhesive clay used either to protect any iron vessel from too 
 strong a heat or for securing air- and gas-tight joints. 
 
 Lye (English). A siding or turnout. 
 
 Machote (Mexican). A stake or permanent bench mark fixed in an under- 
 ground working, from which the length and progress thereof is measured. 
 Magnetic Needle. Needle used in surveying. 
 Magnetic North. The direction indicated by the north end of the magnetic 
 
 needle. 
 Magnetic Meridian. The line or great circle in which the magnetic needle 
 
 sets at any given place. 
 Main Road. The principal haulage road of a mine from which the several 
 
 crossroads lead to the working face. 
 Main Rod (English). See Pump Rod. 
 Main Rope. In tail-rope haulage, the rope that draws the loaded cars 
 
 out. 
 
 Makings (North of England). Small coal produced in kirving; fines. 
 Malacate (Mexican). A Horse Whim; now extended to any hoisting machine 
 
 used in mines. 
 
 Mamposteria (Mexican). Mason work. 
 Manager. An official who has the control and supervision of a mine, both 
 
 under and above ground. 
 Man Engine. An apparatus consisting of one or two reciprocating rods, to 
 
 which suitable stages are attached, used for lowering and raising men 
 
 in shafts. 
 Manhole. (1) A refuge hole constructed in the side of a gangway, tunnel, 
 
 or slope. (2) A hole in boilers through which a man can get into the 
 
 boiler to examine and repair it. 
 Manway. A small passage used as a traveling way for the miner, and also 
 
 often used as an airway or chute, or both. 
 Marco (Mexican). A weight of 8 oz. 
 Marcus. A patented shaker screen with a non-harmonic or quick-return 
 
 motion. 
 
A GLOSSARY OF MINING TERMS 1129 
 
 MarL Clay containing calcareous matter. 
 
 Marlinespike. A sharp-pointed and gradually tapered round iron, used in 
 splicing ropes. 
 
 Marrow. A partner. 
 
 Marsaut Lamp. A type of safety lamp whose chief characteristic is the 
 multiple-gauze chimneys. 
 
 Marsh Gas. CH4, often used synonymously with Firedamp (see page 859). 
 
 Match. (1) A charge of gunpowder put into a paper several inches long, and 
 used for igniting explosives. (2) The touch end of a squib. 
 
 Mattock. A kind of pick with broad ends for digging. 
 
 Maul. A driver's hammer. 
 
 Maundril. A pick with two shanks and points, used for getting coal, etc. 
 
 Mear (Derbyshire). 32 yd. along the vein. 
 
 Measures. Strata. 
 
 Mecha (Mexican). A wick for a lamp or candle; a torch. 
 
 Merced (Mexican). A gift, grant, or concession. 
 
 Meridian. A north and south line, either true or approximate. 
 
 Metal. (1) In coal mining, indurated clay or slate. (2) An element that 
 forms a base by combining with oxygen and which is solid at ordinary 
 temperature (with exception of quicksilver), opaque (except in the thin- 
 nest possible films), has a metallic luster, and is a good conductor of 
 heat and electricity, and, as a rule, of a higher specific gravity than the 
 non-metals. (3) (Mexican) All kinds of metalliferous minerals are called 
 "metal" in Mexico. 
 
 Mill Cinder. The slag from the puddling furnace of a rolling mill. 
 
 Mill Hole. An auxiliary shaft connecting a stope or other excavation with 
 the level below. 
 
 Mine. Any excavation made for the extraction of minerals. 
 
 Miner. One who mines. 
 
 Mineral. Any constituent of the earth's crust that has a definite com- 
 position. 
 
 Mineral Oil. Petroleum obtained from the earth, and its distillates. 
 
 Miner o (Mexican). A mine owner; a mining captain; an underground boss. 
 
 Mine Road. Any mine track used for general haulage. 
 
 Mine Run. The entire unscreened output of a mine. 
 
 Miner o Mayor (Mexican). The head mining captain. A mining workman 
 is called Operario. 
 
 Miners' Dial. An instrument used in surveying underground workings. 
 
 Miners' Inch. A measure of water varying in different districts, being the 
 quantity of water that passes through a slit 1 in. high, of a certain width 
 under a given head (see page 309). 
 
 Miner's Right. An annual permit from the Government to occupy and work 
 mineral land. 
 
 Mining. In its broad sense, it embraces all that is concerned with the 
 extraction of minerals and their complete utilization. 
 
 Mining Engineer. A man having knowledge and experience in the many 
 departments of mining. 
 
 Mining Retreating. A process of min-ng by which the vein is untouched 
 until after all the gangways, etc., are driven, when the mineral extraction 
 begins at the boundary and progresses toward the shaft. 
 
 Mistress (North of England). A miner's lamp. 
 
 Moil. (1) A short length of steel rod tapered to a point, used for cutting 
 hitches, etc. (2) To cut with a moil. 
 
 Monitor. See Gunboat. 
 
 Monkey. The hammer or ram of a pile driver. 
 
 Monkey Drift. A small drift driven in for prospecting purposes, or a crosscut 
 driven to an airway above the gangway. 
 
 Monkey Gangway. A small gangway parallel with the mam gangway. 
 
 Monkey Rolls. The smaller rolls in an anthracite breaker. 
 
 Monkey Shaft. A shaft rising from a lower to a higher level. 
 
 Monoclinal. Applied to an area in which the rocks all dip in the same 
 direction. 
 
 Mop. Some material surrounding a drill in the form of a disk, to prevent 
 water from splashing up. 
 
 Morgan. (Cape of Good Hope). A surface measure = 2.11 acres. 
 
 Mortise. A hole cut in one piece of timber, etc., to receive the tenon that 
 projects from another piece. 
 
 Mote (Moat). A straw filled with gunpowder, for igniting a snot. 
 
1130 A GLOSSARY OF MINING TERMS 
 
 Mother Gate. The main road of a district in longwall working. 
 
 Mother Lode (Main Lode). The principal vein of any district. 
 
 Motive Column. The length of a column of air whose weight is equal to the 
 difference in weight of like columns of air in downcast and upcast shafts. 
 The ventilating pressure in furnace ventilation is measured by the differ- 
 ence of the weights of the air columns in the two shafts. 
 
 Mouth. The top of a shaft or slope, or the entrance to a drift or tunnel. 
 
 Moyle. An iron with a sharp steel point, for driving into clefts when 
 levering off rock. 
 
 Muck. (1) Any material, particularly refuse, removed from a mine, shaft 
 or slope. (2) To remove refuse. 
 
 Mucker. One who mucks or removes refuse; a shoveler. 
 
 Muckle. Soft clay overlying or underlying coal. 
 
 Mucks (Staffordshire). Bad earthy coal. 
 
 Muescas (Mexican). Notches in a stick; mortises; notches cut in a round 
 or square beam, for the purpose of using it as a ladder. 
 
 Mueseler Lamp. A type of safety lamp invented and used in the collieries 
 of Belgium. Its chief characteristic is the inner sheet-iron chimney for 
 increasing the draft of the lamp. 
 
 Muffle. A thin clay oven heated from the outside. 
 
 Mullock. Country rock and worthless minerals taken from a mine. 
 
 Mundic. Iron pyrites. 
 
 Naked Light. A candle or any form of lamp that is not a safety lamp. 
 Narrow Work. (1) All work for which a price per yard of length driven is 
 
 paid, and which, therefore, must be measured. (2) Headings, chutes, 
 
 crosscuts, gangways, etc. 
 
 Natas (Mexican). Same as Escoria or Grasa. 
 Natural Ventilation. Ventilation of a mine without either furnace or other 
 
 artificial means; the heat imparted to the air by the strata, men, animals, 
 
 and lights in the mine, causing it to flow in one direction, or to ascend. 
 Neck. A cylindrical body of rock differing from the country around it. 
 Needle'. (1) A sharp-pointed metal rod with which a small hole is made 
 
 through the stemming to the cartridge in blasting operations. (2) A 
 
 hitch cut in the side rock to receive the end of a timber. 
 Nick. To cut or shear coal after holing. 
 Nicking. (1) A vertical cutting or shearing up one side of a face of coal. 
 
 (2) The chipping of the coal along the rib of an entry or room which is 
 
 usually the first indications of a squeeze. 
 Night Shift. The set of men that work during the night. 
 Nip. When the roof and floor of a coal seam come close together, pinching 
 
 the coal between them. 
 Nipper. An errand boy, particularly one who carries steel, bits, etc., to be 
 
 sharpened. 
 
 Nip Out. The disappearance of a coal seam by the thickening of the adjoin- 
 ing strata, which takes its place. 
 
 Nitro. A corrupted abbreviation for nitroglycerine or dynamite. 
 Nodules. Concretions that are frequently found to enclose organic re- 
 
 mains. 
 
 Nogs. Logs of wood piled one on another to support the roof. See Chock. 
 Nook. The corner of a working place made by the face with one sfde. 
 Noria (Spanish). An endless chain of buckets. 
 Nozzle. The front nose piece of bellows or blast pipe for a furnace, or of a 
 
 water pipe. 
 
 Nut Coal. A contraction of the term chestnut coal. 
 Nuts. Small lumps of coal that will pass through a screen or bars, the spaces 
 
 between which vary in width from to 2^ in. 
 
 Ocote (Mexican). Pitch pine. 
 
 Odd Work. Work other than that done by contract, such as repairing 
 roads, constructing stoppings, dams, etc. 
 
 Offtake. The raised portion of an upcast shaft above the surface, for carrying 
 off smoke and steam, etc., produced by the furnaces and engines under- 
 ground. 
 
 Oil Shale. Shale containing such a proportion of hydrocarbons as to be 
 capable of yielding mineral oil on slow distillation. 
 
 Oil Smellers. Men that profess to be able to indicate where petroleum oil is 
 to be found. 
 
A GLOSSARY OF MINING TERMS 1131 
 
 Old Man. (1) Old workings in a mine. (2) An appliance for holding a drill 
 
 ratchet. 
 
 Oolitic. A structure peculiar to certain rocks, resembling the roe of a fish. 
 Open Cast. Workings having no roof. 
 Open Cutting. (1) An excavation made on the surface for the purpose 
 
 of getting a face wherein a tunnel can be driven. (2) Any surface 
 
 excavation. 
 Openings, an Opening. Any excavation on a coal or ore bed, or to reach the 
 
 same; a mine. 
 Openwork. An open cut. 
 Operario (Mexican). A working miner. 
 
 Operator. The individual or company actually working a colliery. 
 Ores. Minerals or mineral masses from which metals or metallic combina- 
 tions can be extracted on a large scale in an economic manner. 
 Outburst. A blower. A sudden emission of large quantities of occluded gas. 
 Outbye. In the direction of the shaft or slope bottom, or toward the outside. 
 Outcrop. The portion of a vein or bed, or any stratum appearing at the 
 
 surface, or occurring immediately below the soil or diluvial drift. 
 Outcropping. See Cropping Out. 
 Outlet. A passage furnishing an outlet for air, for the miners, for water, or 
 
 for the mineral mined. 
 Output. The product of a mine sent to market, or the total product of a 
 
 mine. 
 
 Outset. The walling of shafts built up above the original level of the ground. 
 Outstroke Rent. The rent that the owner of a royalty receives on coal brought 
 
 into his royalty from adjacent properties. 
 Outtake. The passage by which the ventilating current is taken out of the 
 
 mine; the upcast. 
 Overburden. The covering of rock, earth, etc., overlying a mineral deposit 
 
 that must be removed before effective work can be performed. 
 Overcast. A passage through which the ventilating current is conveyed over 
 
 a gangway or airway. 
 
 Overhand Sloping. The ordinary method of stoping upwards. 
 Overlap 'Fault. A fault in which the shifted strata double back over them- 
 selves. 
 Overman. One who has charge of the workings while the men are in the 
 
 mine. He takes his orders from the Underviewer. 
 Overwind. To hoist the cage into or over the top of the head-frame. 
 Oyamel (Mexican). White pine. 
 
 Pack. A rough wall or block of coal or stone built up to support the roof. 
 Packing. The material placed in stuffingboxes, etc., to prevent leaks. 
 Pack Wall. A wall of stone or rubbish built on either side of a mine road, to 
 
 carry the roof and keep the sides up. 
 
 Paleozoic. The oldest series of rocks in which fossils of animals occur. 
 Paler o (Mexican). A mine carpenter. 
 Palm. A piece of stout leather fitting the palm of the hand, and secured by 
 
 a loop to the thumb; this has a flat indented plate for forcing the needle. 
 Palm Needle. A straight triangular-sectioned needle, used for sewing canvas. 
 Palo (Mexican). A stick; a piece of timber. 
 Panel. (1) A large rectangular block or pillar of coal measuring, say, 
 
 130 by 100 yd. (2) A group of breasts or rooms separated from the 
 
 other workings by large pillars. 
 Panel Working. A system of working coal seams in which the colliery is 
 
 divided up into large squares or panels, isolated or surrounded by solid 
 
 ribs of coal, in each of which a separate set of breasts and pillars is 
 
 worked, and the ventilation is kept distinct, that is, every panel has its 
 
 own circulation, the air of one not passing into the adjoining one, but 
 
 being carried direct to the main return airway. 
 Parcionero (Mexican). A partner in a mining contract. 
 Parrot Coal. A kind of coal that splits or cracks with a chattering noise 
 
 when on the fire. 
 Parting. (I) Any thin interstratified bed of earthy material. (2) A side 
 
 track or turnout in a haulage road. 
 Pass. (1) A convenient hole for throwing down ore to a lower level. (2) A 
 
 passage left in old workings for men to travel in from one level to 
 
 another. 
 Pass-By. A siding in which cars pass one another underground; a turnout. 
 
1132 A GLOSSARY OF MINING TERMS 
 
 Pass-Into. When one mineral gradually passes into another without any 
 
 sudden change. 
 
 Patch or Patcher. A driver's assistant or helper; a brakeman or triprider. 
 Patented Claim. A claim to which a patent right has been secured from the 
 
 government, by compliance with the laws relating to such claims. 
 Patent Fuel. Small coal mixed with small amounts of pitch, tar or other 
 
 binder and compressed by machinery into bricks. 
 Patent Survey. An accurate survey of a claim by a deputized surveyor as 
 
 required by law in order to secure a patent right to the claim. 
 Pavement. The floor. 
 Pay Out. To slacken or let out rope. 
 Pay Rock. Mineralized rock. 
 Pay Streak. Mineralized part of rock. 
 Peach Stone (Cornish). Chlorite schist. 
 Pea Coal. A small size of anthracite coal (see page 952). 
 Peas. Small coal about J to } in. cube. 
 Peat. The decomposed partly carbonized organic matter of bogs, swamps, 
 
 etc. 
 
 Penstock. See Forebay. 
 Pent House. A wooden covering for the protection of sinkers working in a 
 
 pit bottom. 
 P entice. A few pieces of timber laid as a roof over men's heads, to screen 
 
 them when working in dangerous places, e.g., at the bottom of shafts. 
 Pestle. A hard rod for pounding minerals, etc. 
 
 Peter Out. To "peter.out" is to thin out, or gradually decrease in thickness. 
 Petrifaction. Organic remains converted into stone. 
 Petrol. Variant for petroleum or its derivatives, particularly gasoline or 
 
 motor spirit. 
 Pick. (1) A tool for cutting and holing coal. (2) To dress the sides or 
 
 face of an excavation with a pick. 
 Picker. (1) A small tool used to pull up the wick of a miner's lamp. (2) 
 
 A person who picks the slate from the coal in a coal breaker or tipple. 
 Picking Chute. A chute in an anthracite breaker along which boys are 
 
 stationed to pick the slate from coal. 
 Picking Table. (1) A flat or slightly inclined platform on which anthracite 
 
 coal is run to be picked free from slate. (2) A sorting table. (3) A 
 
 moving belt or steel apron on which coal is picked. 
 Pico (Mexican). A striking or sledge hammer. 
 Picture. A screen to keep off falling water from men at work. 
 Pig. A piece of lead or iron cast into a long rough mold. 
 Pigsty Timbering. Hollow pillars built up of logs of wood laid crosswise 
 
 for supporting heavy weights. 
 Pike. A pick. 
 Pileta (Mexican). A sump. 
 Piling. Long pieces of timber driven into soft ground for the purpose of 
 
 securing a solid base on which to build any superstructure Sheet 
 
 piling consists of planks or steel shapes driven into the ground to pre- 
 vent an influx of water, quicksand and the like. 
 Pillar. (1) A solid block of coal, etc., varying in area from a few square 
 
 yards to several acres. (2) Sometimes applied to a timber support. 
 Pillar-and-Room. A system of working coal by which solid blocks of coal 
 
 are left on either side of the rooms, entries, etc., to support the roof until 
 
 the rooms are driven up, after which they are drawn out. 
 Pillar-and-Stall. See Breast-and-Pillar. 
 
 Pillar Roads. Working roads or inclines in pillars having a range of long- 
 wall faces on either side. 
 Pinch. A contraction in the vein. 
 
 Pinch Out. When a lode or stratum runs out to nothing. 
 Pipe. An elongated body of mineral. Also the name given to the fossil 
 
 trunks of trees found in coal veins. 
 Pipe Clay. A. soft white clay. 
 
 Piped Air. Air carried into the working place by pipes or brattices. 
 Pit. (1) A shaft. (2) The underground portion of a colliery, including all 
 
 workings. (3) A gravel pit. 
 Pit Bank. The raised ground or platform where the coal is sorted and 
 
 screened at the surface. 
 Pit Bottom. The portion of a mine immediately around the bottom of a shaft 
 
 or slope. See Shaft Bottom. 
 
A GLOSSARY OF MINING TERMS 1133 
 
 Pitch, (1) Rise of a seam. (2) Grade of an incline. (3) Inclination. (4) 
 (Cornish) A part of a lode let out to be worked on shares or by the 
 
 piece. 
 
 Pit Coal. Generally signifies the bituminous varieties of coal. 
 Pit Frame. See Head-Frame. 
 
 Pit Headman. The man who has charge at the top of the shaft or slope. 
 Pitman. A miner; also, one who looks after the pumps, etc. 
 Pit Prop. A piece 9f timber used as a temporary support for the roof. 
 Pit Rails. Mine rails for underground roads. 
 
 Pit^Room. The extent of underground workings in use or available for use. 
 Pit's Eye. Pit bottom or entrance into a shaft. 
 Pit Top. The mouth of a shaft or slope. 
 Place. The portion of coal face allotted to a hewer is spoken of as his 
 
 "working place," or simply "place." 
 Plan. (1) The system on which a colliery is worked as Long-wall, Pillar- 
 
 and-Breast, etc. (2) A map or plan of the colliery showing outside 
 
 improvements and underground workings. (3) (Mexican) The very 
 
 lowest working in a mine. Trabajar de Plan. To work to gain 
 
 depth. 
 Plane. A main road, either level or inclined, along which coal is conveyed 
 
 by engine power or gravity. 
 Plane Table. A simple surveying instrument by means of which one can 
 
 plot in the field. 
 Plank Dam. A water-tight stopping fixed in a heading constructed of 
 
 timber placed across the passage, one upon another, sidewise, and tightly 
 
 wedged. 
 Plank Tubbing. Shaft lining of planks driven down vertically behind 
 
 wooden cribs all around the shaft, all joints being tightly wedged, to 
 
 keep back the water. 
 Plant. The shafts or slope, tunnels, engine houses, railways, machinery, 
 
 workshops, etc., of a colliery or other mine. 
 Plat, or Map. A map of the surface and underground workings, or of either; 
 
 to draw such a map from survey. 
 
 Plate (North of England). Scaly shale in limestone beds. 
 Plates. Metal rails 4 ft. long. 
 Plenum. A mode of ventilating a mine or a heading by forcing fresh air 
 
 into it. 
 
 Plomada (Mexican). A plumb-line or plumb-bob. 
 Plugging. When drift water forces its way through the puddle clay into 
 
 the shaft, holes are bored through the slabs near the leakage point, and 
 
 plugs of c'ay forced into them until the leakage is stopped. 
 Plumb. Vertical. 
 Plummet. (1) A heavy weight attached to a string or fine copper wire used 
 
 for determining the verticality of shaft timbering. (2) A plumb-bob 
 
 setting a surveying instrument over a point. 
 
 Plunger. The solid ram of a force pump working in the plunger case. 
 Plunger Case. The pump cylinder or barrel in which the plunger works. 
 Poblar (Mexican). To set men at work in a mine. 
 Pocket. (1) A thickening out of a seam of coal or other mineral over a small 
 
 area. (2) A hopper-shaped receptacle from which coal or ore is loaded 
 
 into cars or boats. 
 Pole Tools. Drilling tools used in drilling in the old fashion, with rods, now 
 
 superseded by the rope-drilling method. 
 
 Poll Pick. A pick having the longer end pointed and the shorter end ham- 
 mer-shaped. 
 
 Polrot (Cornish). Waterwheel pit. 
 
 Poppet Heads. The pulley frame or hoisting gear over a shaft. 
 Poppet (Puppet). (1) A pulley frame or the head-gear over a shaft. (2) A 
 
 valve that lifts bodily from its seat instead of being hinged. 
 p os l. (i) Any upright timber; applied particularly to the timbers used for 
 
 propping. See Prop. (2) Local term for sandstone. Post stone may 
 
 be "strong," "framey," "short," or "broken." 
 
 Post-and-Stall. A system of working coal much the same as Pillar-and-Stall. 
 Post-Tertiary. Strata younger than the Tertiary formation. 
 Pot Bottom. A large boulder in the roof slate, having the appearance of the 
 
 rounded bottom of a pot, and which easily becomes detached. 
 Pot Growan (Cornish). Decomposed granite. 
 Pot Hole. A circular hole in the rock caused by the action of stones whirled 
 
1134 A GLOSSARY OF MINING TERMS 
 
 around by the water when the strata was covered by water. They are 
 generally filled with sand and drift. 
 
 Power Drill. A rock drill employing steam, air, or electricity as a motor. 
 
 Prian (Cornish). Soft white clay. 
 
 Pricker. (1) A thin brass rod for making a hole in the stemming when 
 blasting, for the insertion of a fuse. (2) A piece of bent wire by which 
 the size of the flame in a safety lamp is regulated without removing the 
 top of the lamp. 
 
 Prong (English). The forked end of the bucket-pump rods for attachment 
 to the traveling valve and seat. 
 
 Prop. A wooden or metal temporary support for the roof. 
 
 Propping. The timbering of a mine. 
 
 Prospect. The name given to underground workings whose value has not 
 yet been made manifest. A prospect is to a mine what mineral is to ore. 
 
 Prospect Hole. Any shaft or drift hole put down for the purpose of prospect- 
 ing the ground. 
 
 Prospecting. Examining a tract of country in search of minerals. 
 
 Prospector. One engaged in searching for minerals. 
 
 Prospect Tunnel or Entry. A tunnel or entry driven through barren measures 
 or a fault to ascertain the character of strata beyond. 
 
 Protector Lamp. A safety lamp whose flame cannot be exposed to the out- 
 side atmosphere, as the action of opening the lamp extinguishes the 
 light. 
 
 Prove. (1) To ascertain, by boring, driving, etc., the position and character 
 of a coal seam, a fault, etc. (2) To examine a mine in search of fire- 
 damp, etc., known as "proving the pit." 
 
 Proving Hole. (1) A bore hole driven for prospecting purposes'. (2) A 
 small heading driven in to find a bed or vein lost by a dislocation of 
 the strata, or to prove the quality of the mineral in advance of the other 
 workings. 
 
 Pudding Rock. Conglomerate. 
 
 Puddle. (1) Earth well rammed into a trench, etc., to prevent leaking. (2) 
 A process for converting cast iron into wrought iron. 
 
 Pueble (Mexican). The actual working of a mine; the aggregation of persons 
 employed therein. 
 
 Puertas (Mexican). Massive barren rocks, or "horses," occurring in a vein. 
 
 Pug Mill. A mill for preparing clay for making bricks, pottery, etc. 
 
 Pulley. (1) The wheel over which a winding rope passes at the top of the 
 head-gear. (2) Small wooden cylinders over which a winding rope is 
 carried on the floor or sides of a plane. 
 
 Pulleying. Overwinding or drawing up a cage into the pulley frame. 
 
 Pump. Any mechanism for raising water. 
 
 Pump Bob. See Bob. 
 
 Pump Ring. A flat iron ring that, when lapped with tarred baize or engine 
 shag, secures the jpints of water columns. 
 
 Pump Rods. Heavy timbers by which the motion of the engine is trans- 
 mitted to the pump. In Cornish and bull pumps, the weight of the 
 rods makes the effective (pumping) stroke, the engine merely lifting 
 the rods on the up stroke. 
 
 Pump Slope. A slope used for pumping machinery. 
 
 Pump Station. An enlargement made in the shaft, slope, or gangway, to 
 receive the pump. 
 
 Pump Tree. Cast-iron pipes, generally 9 ft. long, of which the column or set 
 is formed. 
 
 Punch-and-Thirl. A kind of pillar-and-stall system of working. 
 
 Punch Prop. A short timber prop set on the top of a crown tree, or used in 
 holding, as a sprag. 
 
 Pyran (Cornish). See Prian. 
 
 Pyrites. Sulphide of iron, copper, etc. 
 
 Pyrometer. An instrument for measuring high degrees of heat. 
 
 Quarry. (1) An open surface excavation for working valuable rocks or 
 minerals. (2) An underground excavation for obtaining stone for 
 stowage or pack walls. 
 
 Quaternary. Post-tertiary period. 
 
 Quemados (Mexican). Burnt stuff. Any dark cinder-like mineral encoun- 
 tered in a vein or mineral deposit, generally manganiferous. 
 
 Quick (Adjective). Soft, running ground. Quick (Noun). Productive. 
 
A GLOSSARY OF MINING TERMS 1135 
 
 Quicksand. Soft watery strata easily moved, or readily yielding to pressure. 
 Quicksilver. Mercury. 
 
 Quitdpepena (Mexican). A watchman that searches the miners as they 
 come out at the mouth of a mine. 
 
 Race. A channel for conducting water to or from the place where it per- 
 forms work. The former is termed the headrace, and the latter the 
 
 tailrace. 
 Rack (Cornish). A toothed gear of infinite radius, i.e. a straight gear or one 
 
 whose pitch line has no curvature. 
 
 Rafter Timbering. That in which the timbers appear like roof rafters. 
 Rag Wheel. Sprocket wheel. A wheel with teeth or pins that catch into the 
 
 links of chains. 
 Rails. The iron or steel portion of the tramway or railroad or their wooden 
 
 counterparts. 
 
 Rake (Cornish). (1) A vein. (2) (Derbyshire) Fissure vein crossing strata. 
 Ram. (1) The plunger of a pump. (2) A device for raising water. (3) A 
 
 machine for drawing a coke charge from an oven. 
 Ramal (Mexican). A branch vein. 
 
 Ramalear (Mexican). To branch off into various divisions. 
 Ramble. Stone of little coherence above a seam that falls readily on the 
 
 removal of the coal. See Following Stone. 
 Ranee. A pillar of coal. 
 Rapper. A lever with a hammer attached at one end, which signals by 
 
 striking a plate of metal, when the signaling wire to which it is attached 
 
 is pulled. 
 Rash. A term used to designate the bottom of a mine when soft and slaty; 
 
 also the top* 
 
 Reacher. A slim prop reaching from one wall to the other. 
 Reamer. An enlarging tool. 
 
 Reaming. Enlarging the diameter of a bore hole. 
 Receiving Pit. A shallow pit for containing material run into it. 
 Red- Ash Coal. Coal that produces a reddish ash when burnt. 
 Red Rab (Cornish). Red slaty rock. 
 Refuge Chamber. A chamber shut off from the rest of the mine, stored with 
 
 food, etc., and to be used by the survivors in case of a mine disaster. 
 Refuge Hole. A place formed in the side of an underground passage in which 
 
 a man can take refuge during the passing of a train, or when shots are 
 
 fired. 
 Regulator. A door in a mine, the opening or shutting of which regulates the 
 
 supply of ventilation to a district of the mine. 
 Reliz (Spanish). Wall of lode. 
 Rendrock. A variety of dynamite. 
 Repairman. A workman whose duty it is to repair tracks, doors, brattices, 
 
 or to reset timbers, etc., under the direction of the foreman. 
 Rescue and Recovery. The work of removing live men or dead bodies after 
 
 a mine disaster; also putting the mine in shape for operation again. 
 Reserve. Mineral already opened up by shafts, winzes, levels, etc., which 
 
 may be secured at short notice for any emergency.' 
 Reservoir. An artificially built, dammed, or excavated place for holding a 
 
 reserve of water. 
 Respaldos (Mexican). The walls enclosing a vein. Respaldo Alto. The 
 
 hanging wall. Respaldo Bajo. 'The foot-wall. 
 Rests, Keeps, Wings. Supports on which a cage rests when the loaded car 
 
 is being taken off and the empty one put on. 
 Resue. See Stripping. 
 
 Retort Oven. A coke oven which conserves the gas evolved. 
 Return. The air-course along which the vitiated air of a mine is returned 
 
 or conducted back to the upcast shaft. 
 
 Return Air. The air that has been passed through the workings. 
 Reverberator y. A class of furnaces in which the flame from the fire-grate is 
 
 made to beat down on the charge in the body of the furnace. 
 Reversed Fault. See Overlap Fault. 
 Rib. The side of a pillar. 
 
 Rib-and-Pillar.A. system of working, similar to Pillar-and-Stall. 
 Ribbon A. line of bedding or a thin bed appearing on the cleavage surface 
 
 and sometimes of a different color. 
 Rick. Open heap in which coal is coked. 
 
1136 A GLOSSARY OF MINING TERMS 
 
 Ridding. Clearing away fallen stone and debris. 
 
 Riddle. (1) An oblong frame holding iron bars parallel to each other, used 
 
 for sifting material that is thrown against it. (2) A hand operated sieve. 
 Ride, Riding. To be conveyed on a cage or mine car. 
 Rider. (1) A guide frame for steadying a sinking bucket. (2) Boys that 
 
 ride on trips on mechanical haulage roads. (3) A thin seam of coal 
 
 overlying a thicker one. 
 
 Right Shore. The right shore of a river is on the right hand when descend- 
 ing the river. 
 
 Rim Rock. Bed rock forming a boundary to gravel deposit. 
 Ring. (1) A complete circle of tubbing plates placed round a circular shaft. 
 
 (2) Troughs placed in shafts to catch the falling water, and so arranged 
 
 as to convey it to a certain point. 
 
 Ripping. Removing stone from its natural position above the seam. 
 Rise. The inclination of the strata, when looking up the pitch. 
 Rise Workings. Underground workings carried on to the rise or high side 
 
 of the shaft. 
 Road. (1) Any underground passageway or gallery. (2) The iron rails, 
 
 etc., of underground roads. 
 
 Rob. To cut away or reduce the size of pillars of coal. 
 Robbing. The taking of mineral from pillars. 
 Robbing an Entry. See Drawing an Entry. 
 
 Rock. A mixture of different minerals in varying proportions. 
 Rock Chute. See Slate Chute. 
 Rock Drill. A rock-boring machine worked by hand, compressed air, steam, 
 
 or electrical power. 
 Rock Fault. A replacement of a coal seam over greater or less area, by some 
 
 other rock, usually sandstone. * 
 
 Rodding. The operation of fixing or repairing wooden eye guides in shafts. 
 Roll. An inequality in the roof or floor of a mine. 
 Roller. A small steel, iron, or wooden wheel or cylinder upon which the 
 
 hauling rope is carried just above the floor. 
 Rolleyway. A main haulage road. 
 Rolling Ground. When the surface is much varied by many small hills and 
 
 valleys. 
 Rolls. Cast-iron cylinders, either plain or fitted with steel teeth, used to 
 
 break coal and other materials into various sizes. 
 Roof. The top of any subterranean passage. 
 Room. Synonymous with Breast. 
 
 Room-and-Rance. A system of working coal similar to Pillar-and-Stall. 
 Rope Roll. The drum of a winding engine. 
 Round Coal. Coal in large lumps, either hand-picked, or, after passing over 
 
 screens, to take out the small. 
 
 Royalty. The price paid per ton to the owner of mineral land by the lessee. 
 Rubbing Surface. The total area of a given length of airway; that is, the 
 
 area of top, bottom, and sides added together, or the perimeter multi- 
 plied by the length. 
 Rubble. Coarse pieces of rock. 
 
 Rumbo (Mexican). -'The course or direction of a vein. 
 Run. (1) The sliding and crushing of pillars of coal. (2) The length of a 
 
 lease or tract on the strike of the seam. 
 Run Coal. Soft bituminous coal. 
 
 Rung, Rundle, or Round. A step or cross-bar of a ladder. 
 Runner. A man or boy whose duty it is to run mine cars by gravity from 
 
 working places to the gangway. 
 Running Lift. A sinking set q pumps constructed to lengthen or shorten 
 
 at will, by means of a sliding or telescoping wind bore. 
 Rush. An old-fashioned way of exploding blasts by filling a hollow stalk 
 
 with slow powder and then igniting it. 
 Rush Together. See Caved In. 
 Rusty. Stained by iron oxide. 
 
 Saddle. An anticlinal, a hogback. 
 
 Saddleback. A depression in the strata. See Roll. 
 
 Safety Cage. A cage fitted with an apparatus for arresting its motion in the 
 
 shaft in case the rope breaks. 
 Safely Car. See Barney. 
 Safety Catches. Appliances fitted to cages, to make them safety cages. 
 
A GLOSSARY OF MINING TERMS 1137 
 
 Safety Door. A strongly constructed door, hinged to the roof, and always 
 kept open and hung near to the main door, for immediate use when 
 main door is damaged by an explosion or otherwise. 
 
 Safety First. A term often applied to accident prevention and first aid 
 and to rescue and recovery training in general. 
 
 Safety Fuse. A cord with slow-burning powder in the center for exploding 
 charged blast holes. 
 
 Safely Lamp. (1) A miner's lamp in which the flame is protected in such a 
 manner that an explosive mixture of air and firedamp can be detected 
 by the mixture burning inside the gauze. (2) An electric cap or hand 
 lamp which will not ignite gas even when broken. 
 
 Sag. A depression, e.g., m ropes, ranges of mountains, etc., also in mine 
 floors. 
 
 Sagre, or Seggar. A local term for fireclay, often forming the floor (or thill) 
 of coal seams. 
 
 Salting. (1) Changing the value of the ore in a mine or of ore samples 
 before they have been assayed, so that the assay will show much higher 
 values than it should. (2) Sprinkling salt on the floors of underground 
 passages in very dry mines, in order to lay. the dust. 
 
 Sample. A representative specimen of coal from a much larger amount as 
 a carload, shipload, or from the face of a room. 
 
 Sampler. (1) An instrument or apparatus for taking samples. (2) One 
 whose duty it is to select the samples for an assay or analysis, or to 
 prepare the mineral to be tested, by grinding and sampling. 
 
 Samson Post. An upright supporting the working beam that communicates 
 oscillatory motion to pump or drill rod. 
 
 Sand Bag. A bag filled with sand for preventing a washout by obstructing 
 the flow. 
 
 Sand Pump. A sludger; a cylinder provided with a stem (or other) valve, 
 lowered into a drill hole to remove the pulverized rock. 
 
 Scaffolding. (1) Incrustations on the inside of a blast furnace. (2) False- 
 work employed in building. 
 
 Scale. (1) A small portion of the ventilating current m a mine passing 
 through a certain size of aperture. (2) The rate of wages to be paid, 
 which varies under certain contingencies. (3) A weighing apparatus 
 (4) Incrustation on the inside of a boiler. 
 
 Scnle Door. See Regulator. 
 
 Scallop. To hew coal without kirying or nicking or shot firing. 
 
 Schist. Crystalline or metamorphic rocks having a slaty structure. 
 
 Schute. See Chute. 
 
 Scissors Fault. A fault of dislocation, in which two beds are thrown so as to 
 cross each other. 
 
 Scoop. A large-sized shovel with a scoop-shaped blade. 
 
 Scoria. Ashes. _ 
 
 Scrap. (1) Worthless or obsolete iron, copper, machinery, etc. (2) To 
 
 Scraper. (1) A tool for cleaning the dust out of the bore hole. (2) A 
 mechanical contrivance used at colleries to scrape the culm or slack 
 along a trough to the place of deposit. 
 
 Screen. (1) A mechanical apparatus for sizing, materials. (2) A cloth brat- 
 tice or curtain hung across a road in a mine, to direct the ventilation. 
 
 Serin (Derbyshire). A small vein. 
 
 Sculping. Fracturing the state along the gram, i.e., across the cleavage. 
 
 Scupper Nails. Nails with broad heads, for nailing down canvas, etc. 
 
 Sea Coal. That which is transported by sea. 
 
 Sealing. Shutting off all air from a mine or a part of a mine by stoppings. 
 
 Seam. Synonymous with Bed, Vein, etc. 
 
 Seam-Out A term applied to a shot or blast that has simply blown out ; 
 softer stratum of the deposit in which it was placed, without dislodging 
 the other strata or layers of the seam. . . 
 
 Second Outlet (Second Opening). A passageway out of a mine, for use in case 
 of accident to the main outlet. 
 
 Seconds. Second-class coal, not best. , 
 
 Second Working. The operation of getting or working out the pillars formed 
 by the first working. . . , 
 
 Section. (I) A vertical or horizontal exposure of strata. (2) A drawing or 
 sketch representing the rock strata as cut by a vertical or a horizontal 
 plane. 
 72 
 
1138 A GLOSSARY OF MINING TERMS 
 
 Sedimentary Rocks. Rocks formed from deposits of sediment by wind or 
 water. 
 
 Seedbag. A water-tight packing of flaxseed around the tube in a drill hole, 
 to prevent the influx into the hole of water from above. 
 
 Segregations. Detached portions of veins in place. 
 
 Self- Acting Plane. An inclined plane upon which the weight or force of 
 gravity acting on the full cars is sufficient to overcome the resistance of 
 the empties; in other words, the full car, running down, pulls the other 
 car up. 
 
 Self-Detaching Hook. A self-acting hook for setting free a hoisting rope in 
 case of overwinding. 
 
 Selvage. The clay seam on the walls of veins; gouge. 
 
 Separation Doors. The main doors at or near the shaft or slope bottom, 
 which separate the intake from the return airways. 
 
 Separation Valve. A massive cast-iron plate suspended from the roof of a 
 return airway through which all the return air of a separate district 
 flows, allowing the air to always flow past or underneath it; but in 
 the event of an explosion of gas, the force of the blast closes it against 
 its frame or seating, and prevents a communication with other districts. 
 The blast being over, the weight of the valve allows it to return to its 
 normal position. 
 
 Set. To fix in place a prop or sprag. 
 
 Set Hammer. The flat-faced hammer held on hot iron by a blacksmith when 
 shaping or smoothing a surface by aid of his striker's sledge. 
 
 Set of Timber. The timbers which compose any framing, whether used in 
 a shaft, slope, level, or gangway. Thus, the four pieces forming a single 
 course in the curbing of a shaft, or the three or four pieces forming 
 the legs and collar, and sometimes the sill of an entry framing are 
 together called a set of timber, or timber set. 
 
 Shackle. A U-shaped link in a chain closed by a pin; when the latter is with- 
 drawn the chain is severed at that point. 
 
 Shaft. A vertical or highly inclined pit or hole made through strata, through 
 which the product of the mine is hoisted, and through which the ventila- 
 tion is passed either into or out of the mine. A shaft sunk from one 
 seam to another is called a "blind shaft." 
 
 Shaft Pillar. Solid material left unworked beneath buildings and around 
 the shaft, to support them against subsidence. 
 
 Shaking Screen or Shaker. A flat screen, often inclined, which is given an 
 oscillatory motion and is used for sizing coal. 
 
 Shale. (1) Strictly speaking, all argillaceous strata that split up or peel off 
 in thin laminae. (2) A laminated and stratified sedimentary deposit of 
 clay, often impregnated with bituminous matter. 
 
 Shank. The body portion of any tool, up from its cutting edge or bit. 
 
 Shearing. Cutting a vertical groove in a coal face or breast. The cutting of 
 a "fast end" of coal. 
 
 Shear Legs. A high wooden frame placed over an engine or pumping shaft 
 fitted with small pulleys and rope for lifting heavy weights. 
 
 Shears, or Sheers (English). Two tall poles, with their feet some distance 
 apart and their tops fastened together, for supporting hoisting tackle. 
 
 Shear Zone. Hogback. 
 
 Sheave. A wheel with a grooved circumference over which a rope is passed 
 either for the transmission of power or for winding 'or hauling. 
 
 Sheet Pump. See Sludger. 
 
 Sheets. Coarse cloth curtains or screens for directing the ventilating current 
 underground. 
 
 Shelly. A name applied to coal that has been so crushed and fractured that 
 it easily breaks up into small pieces. The term is also applied to a lami- 
 nated roof that sounds hollow and breaks into thin layers of slate or 
 shale. 
 
 Shet (Staffordshire) .- Fallen roof of coal mine. 
 
 Sheth. An old term denoting a district of about eight or nine adjacent 
 bords. Thus, a "sheth of bords," or a "sheth of pillars." 
 
 Shift. (1) The number of hours worked without change. (2) A gang or 
 force of workmen employed at one time upon any work, as the day shift, 
 or the night shift. 
 
 Sheading (Cornish) . Prospecting. 
 
 Shoe. (1) A steel or iron guide piece fixed to the ends or sides of cages, to 
 fit or run on the conductors. (2) The lower capping of any post or pile, 
 
A GLOSSARY OF MINING TERMS 1139 
 
 to protect its end while driving. (3) A wooden or sheet-iron frame or 
 muff arranged at the bottom of a shaft while sinking through quicksand, 
 to prevent the inflow of sand while inserting the shaft lining. 
 
 Shoot, Chute, Shute. An inclined or vertical trough or pipe for conveying 
 materials from a higher to a lower level. 
 
 Shoot. To break rock or coal by means of explosives. 
 
 Shooting. Blasting in a mine. 
 
 Shore (English). A studdle or thrusting stay. 
 
 Shore Up. To stay, prop up, or support by braces. 
 
 Shot. (1) A charge or blast. (2) The firing of a blast. (3) Injured by a 
 blast. 
 
 Shot Firer. See Shot Lighter. 
 
 Shot Hole. The bore hole in which an explosive substance is placed for 
 blasting. 
 
 Shot Lighter, or Shot Firer. A man specially appointed by the manager of 
 the mine to fire off every shot in a certain district, if, after he has 
 examined the immediate neighborhood'of the shot, he finds it free from 
 gas, and otherwise safe. 
 
 Show. When the flame of a safety lamp becomes elongated or unsteady, 
 owing to the presence of firedamp in the air, it is said to show. 
 
 Showing. The first appearance of float, indicating the approach to an out- 
 cropping vein or seam. Blossom. 
 
 Shroud. A housing or jacket. 
 
 Shute. See Chute, Shoot, and Schute. 
 
 Shutter. (1) A movable sliding door, fitted within the outer casing of a 
 Guibal or other closed fan, for regulating the size of the opening from 
 the fan, to suit the ventilation and secure economical working of the 
 machine. (2) A slide covering the opening in a door or brattice, and 
 forming a regulator for the proportionate division of the air current 
 between two or more districts of a mine. 
 
 Siddle. Inclination. 
 
 Side. (1) The more or less vertical face or wall of coal or goaf forming one 
 side of an underground working place. (2) Rib. (3) A district. 
 
 Side Chain. A chain hooked on to the sides of cars running on an incline or 
 along a gangway, to keep the cars together in case the coupling breaks. 
 
 Siding. A short piece of track parallel to the main track, to serve as a pass- 
 ing place. 
 
 Siding Over. A short road driven in a pillar in a headwise direction. 
 
 Sight. (1) A bearing or angle taken with a compass or transit when making 
 a survey. (2) Any established point of a survey. 
 
 Sights. Bobs or weighted strings hung from two or more established points 
 in the roof of a room or entry, to give direction to the men driving the 
 entry or room. 
 
 Sill. (1) The floor piece of a timber set, or that on which the track rests; 
 the base of any framing or structure. (2) The floor of a seam. 
 
 Sing. The noise made by a feeder of gas issuing from the coal. 
 
 Singing Coal. Coal from which gas is issuing with a hissing sound. 
 
 Singing Lamp. A safety lamp, which, when placed in an atmosphere of 
 explosive gas, gives out a peculiar sound or note, the strength of the 
 note varying in proportion to the percentage of firedamp present. 
 
 Single-Entry System. A system of opening a mine by driving a single entry 
 only, in place of a pjair of entries. The air current returns along the 
 face of the rooms, which must be kept open. 
 
 Single-Intake Fan. A ventilating fan that takes or receives its air upon one 
 side only. 
 
 Single-Rope Haulage. A system of underground haulage in which a single 
 'rope is used, the empty trip running in by gravity. This is engine-plane 
 haulage. 
 
 Sink. To excavate a shaft or slope; to bore or put down a bore hole. 
 
 Sinker. A man who works at the bottom of a shaft or face of a slope during 
 the course of sinking. 
 
 Sinker Bar. In rope drilling, a heavy bar attached above the jars, to give 
 force to the up stroke, so as to dislodge the bit in the hole. 
 
 Sinking. The process of excavating a shaft or slope or boring a hole. 
 
 Siphon. A simple, effective, and economical mode of conveying water over 
 a hill whose height is not greater than what the atmospheric pressure 
 will raise the water. Its form is that of an iron pipe, bent like an in- 
 
J140 A GLOSSARY OF MINING TERMS 
 
 verted U ; the vertical height between the surface of the water in the 
 
 upper basin and the top of the hill is called the lift of the siphon: while 
 
 the vertical height between the surfaces of the water in the upper and 
 
 lower basins is called the fall of the siphon. 
 Sirdar. A foreman. 
 Sizing. To sort minerals into sizes. 
 Skew Back. The beveled member from which an arch springs, and upon which 
 
 it rests. 
 
 Skids. Slides upon which heavy bodies are slid from place to place. 
 Skip. (1) A mine car. (2) A car for hoisting out of a slope. (3) A thin 
 
 slice taken off from a breast or pillar or rib along its entire length or 
 
 part of its length. 
 Skit (Cornish). A pump. 
 Slab. Split pieces of timber from 2 in. to 3 in. thick, 4 ft. to 6 ft. long, and 
 
 7 in. to 14 in. wide, placed behind sets or frames of timber in shafts or 
 
 levels. 
 Slack. (1) Fine coal that will pass through the smallest sized screen. The 
 
 fine coal and dust resulting from the handling of coal, and the disinte- 
 gration of soft coal. (2) The process by which lignite disintegrates 
 
 when exposed to the air and weather. 
 Slant. (1) An underground roadway driven at an angle between the full 
 
 rise or dip of the seam and the strike or level. (2) Any inclined road 
 
 in a seam. 
 Slant Chutes. Chutes driven diagonally across a pillar, to connect a breast 
 
 manway with a manway chute. 
 Slate. (1) A hardened clay having a peculiar cleavage. (2) About coal 
 
 mines, slate is any shale accompanying the coal, also sometimes applied 
 
 to bony coal. 
 Slate Chute. (1) A chute for conveying slate or bony coal to a pocket from 
 
 which it is loaded into "dumpers." (2) A chute driven through slate. 
 Slate Picker. (1) A man or boy that picks the slate or bone from coal. (2) 
 
 A mechanical contrivance for separating slate and coal. 
 Sleek (Derbyshire). Mud in a mine. 
 Sled. A drag used to convey coal along the face to the road head where it is 
 
 loaded, or to the chute. 
 Sledge. A heavy double-handed hammer. 
 
 Sleeper (English). The foundation pieces or cross- ties on which rails rest. 
 Sleeve. A hollow cylinder usually fitting over two pieces, to hold them to- 
 gether. 
 
 Slickensides. Polished surfaces of vein walls. 
 Slide. Loose deposit covering the outcrop of a seam. 
 Slides. See Guides. 
 Sliding Scale. A mode of regulating the wages paid workingmen by taking 
 
 as a basis for calculation the market price of coal, the wages rising and 
 
 falling with the state of trade. 
 Sliding Wind Bore (English). The bottom pipe 9r suction piece of a sinking 
 
 set of pumps having a lining made to slide like a telescope within it, to 
 
 give length without altering the adjustment of the whole column of pipes. 
 Slime, Sludge. The pulp or fine mud from a drill hole. 
 Slings. Pieces of ropes or cnains to be put around stones, etc., for raising 
 
 them. 
 Slip. (1) A fault. (2) A smooth joint or crack where the strata have 
 
 moved upon each other. 
 Slip Cleavage. Microscopic folding and fracture accompanied by slippage; 
 
 quarrymen's "false cleavage." 
 
 Slit. A short heading put through to connect two other headings. 
 Slitter. See Pick. 
 Slope. A plane or inclined roadway, usually driven in the seam from the 
 
 surface. A rock slope is a slope driven across the strata, to connect two 
 
 seams; or a slope opening driven from the surface, to reach a seam below 
 
 that does not outcrop at an accessible point. 
 Sludge. See Slime. 
 Sludger, Sludge Pump. A cylinder having an upward opening valve at the 
 
 bottom, which is lowered into a bore hole, to pump out the sludge or 
 
 fine rock resulting from drillings. 
 Sluice. Any overflow channel. 
 Sluice Head, or Head (Australia and New Zealand). A supply of 1 cu. ft. of 
 
 water per second, regardless of the head, pressure, or size of orifice. 
 
A GLOSSARY OF MINING TERMS 1141 
 
 Small Bee Slack. 
 
 Smift, Snift. A bit of touch paper, touch wood, etc., attached by a bit of clay 
 or grease to the outside end of the train of gunpowder when blasting 
 
 Smut (Staffordshire). Soft, bad coal. 
 
 Snore, Snore Piece. The hole in the lower part of a sinking or Cornish pump 
 through which water enters. 
 
 Snub or Snubbing. (1) To undercut by means of explosives or otherwise. 
 (2) To lower, as a car, by a turn of a rope around a post. 
 
 Soapstone. A term incorrectly applied by the miner to any soft, unctuous 
 rock. 
 
 Socavon (Mexican). A mining tunnel; an adit. Socavon d kilo de veto. A 
 drift tunnel. Socavon crucero. A crosscut tunnel or adit. 
 
 Socket. (1) The innermost end of a shot hole, not blown away after firing. 
 (2) A wrought-iron contrivance by means of which a wire rope is se- 
 curely attached to a chain or block. 
 
 Sole, Sole Plate. A piece of timber set underneath a prop. 
 
 Sollar. (1) A wooden platform fixed in a shaft, for the ladders to rest on. (2) 
 A division of the air compartment in a drift or slope. 
 
 Sondear (Mexican). To bore for prospecting purposes. 
 
 Sondeo (Mexican). A boring for prospecting purposes. 
 
 Soplete (Mexican). A blowpipe. 
 
 Sorting. Separating valuable from worthless material. 
 
 Sounding. (1) Knocking on a roof to see whether it is sound or safe to 
 work under. (2) Rapping on a pillar so that a person on the other side 
 of it may be signaled to, or to enable him to estimate its width. 
 
 Sow. (1) A tool used for sharpening drills. (2) Iron deposits at the bottom 
 of furnaces. 
 
 Spad. A horseshoe nail with a hole in the head, or a similar device for 
 driving into the mine timbers, or into a wooden plug fitted into the roof, 
 to mark a survey station. 
 
 Spall. To break up rocks with a large hammer, for hand sorting. 
 
 Spalls. The chips and other waste material cut from a block of stone in 
 process of dressing. 
 
 Spar. A name given to certain white quartz-like minerals, e.g., calcspar, 
 feldspar, fluorspar. 
 
 Spears. Pump-rods. 
 
 Specimen. A picked piece of mineral.. 
 
 Spelter. The commercial name for zinc. 
 
 Spent Shot. A blast hole that has been fired, but has not done its work. 
 
 Spiders. See Drum Rings. 
 
 Spiegeleisen. Manganiferous white cast iron. 
 
 Spiking Curbs. A light ring of wood to which planks are spiked when plank 
 tubbing is used. 
 
 Spiles (Cornish). A temporary lagging* driven ahead on levels in loose 
 ground. Short pieces of planking sharpened flatways, and used for 
 driving into watery strata as sheath piling, to assist in checking the 
 flow; used much in sinking through quicksands. 
 
 Spiling. A process of timbering through soft ground. 
 
 Spiral. A spiral coal chute which mechanically separates the slate from the 
 coal. 
 
 Spiral Drum. See Conical Drum. 
 
 Splint, or Splent. A hard, high volatile coal, producing a white ash, inter- 
 mediate between cannel and bituminous coal. 
 
 Split. (1) To divide an air current into two or more separate currents. (2) 
 Any division or branch of the ventilating current. (3) The workings 
 ventilated by that branch. (4) Any member of a coal bed split by 
 thick partings into two or more seams. (5) A bench separated by a con- 
 siderable interval from the other benches of a coal bed. 
 
 Spoil. Debris from a coal mine. 
 
 Spoon. A slender iron rod with a cup-shaped projection at right angles to 
 the rod, used for scraping drillings out of a bore hole. 
 
 Spout. A short underground passage connecting a main road with an air- 
 course. 
 
 Sprag. (1) A short wooden prop set in a slanting position for keeping up 
 the coal during the operation of holing. (2) A short round piece of hard 
 wood, pointed at both ends, to act as a brake when placed between the 
 spokes of mine-car wheels. (3) The horizontal member of a square set 
 of timber running longitudinally with the deposit. 
 
1142 A GLOSSARY OF MINING TERMS 
 
 Spragger. One who attends to the spragging of cars. 
 
 Sprag Road. A mine road having such a sharp grade that sprags are needed 
 
 to control the speed of the cars. 
 
 Spreader. A timber stretched across a shaft or stope. 
 
 Spring Beams. Two short parallel timber beams, built with a Cornish pump- 
 ing engine house, nearly on a level with the engine beam, for catching 
 
 the beam, etc., and preventing a smash in case of a breakdown. 
 Spring Latch. The latch or tongue of an automatic switch, operated by a 
 
 spring pole at the side of the track. 
 Spring Pole. An elastic wooden pole from which boring rods are suspended. 
 
 Used also to operate a spring latch. 
 Sprocket Wheel (English). Rag wheel. A wheel with teeth or pins which 
 
 engage the links of a chain. 
 Spur. (1) A short ridge or offsetting pointed branch from a main ridge or 
 
 mountain. (2) A short branch or feeder from the main lode of a vein. 
 
 (3) A branch road. 
 
 Square Set. A variety of timbering for large excavations. 
 Squealer. A shot which breaks the coal only enough to allow the gases of 
 
 detonition to escape with a whistling or squealing sound; also called a 
 
 whistler. 
 
 Squeeze. See Creep. 
 
 Squib. A straw, rush, paper, or quill tube filled with a priming of gun- 
 powder, with a slow match on one end. 
 Stage. A platform on which mine cars stand. 
 Stage Pumping. Draining a mine by means of two or more pumps placed at 
 
 different levels, each of which raises the water to the next pump above, 
 
 or to the surface. 
 Stage Working. A system of working minerals by removing the strata above 
 
 the beds, after which the various beds are removed in steps or stages. 
 Staging. A temporary flooring or scaffold, or platform. 
 Stalactites. Icicle-shaped formations of mineral matter depending from roof 
 
 strata. 
 Stalagmites. Accumulations of mineral matter that form on the floor, caused 
 
 by the continual dripping of water impregnated with mineral matter. 
 Stall. A narrow breast, or chamber. 
 Stall Gate. A road along which the mineral worked in a stall is conveyed to 
 
 the main road. 
 
 Stanchion. A vertical prop or strut. 
 Standage. Pump reservoir. 
 
 Standing. Not at work, not going forwards, idle. 
 
 Standing Gas. A body of firedamp known to exist in a mine, but not in cir- 
 culation; sometimes fenced off. 
 
 Standing Sett (English). A fixed lift of pumps in a sinking set. 
 Staple. (1) A shallow pit within a mine. (2) An underground shaft. 
 Starter. A man who ascends a chute to the battery and starts the coal to 
 
 running. 
 
 Starved (English). When a pump is choked at the brass holes. 
 Station. A flat or convenient resting place in a shaft or level. 
 Stave. A ladder step. 
 
 Stay (English). Props, struts, or ties for keeping anything in its place. 
 Steamboat Coal. In anthracite only, coal small enough to pass through bars 
 
 set 6 to 8 in. apart, but too large to pass through bars from 85 to 5 in. 
 
 Comparatively few collieries make steamboat coal except to fill special 
 
 contracts or orders. 
 
 Steam Coal. A hard, free-burning, non-caking coal. 
 Steam Jet. A system of ventilating a mine by means of a number of jets of 
 
 steam, at high pressure, kept constantly blowing off from a series of pipes 
 
 in the bottom of the upcast shaft. 
 Steel Mill. An apparatus for obtaining light in a fiery mine. It consisted 
 
 of a revolving steel wheel, to which a piece of flint was held, to produce 
 
 Steel Needle. An instrument used in preparing blasting holes, before the 
 
 safety fuse was invented. 
 
 Steening, or Steining. The brick or stone lining of a shaft. 
 Stemmer. A copper or wooden bar used for stemming. 
 Stemming. (1) Fine shale or dirt put into a shot hole after the powder, and 
 
 rammed hard. (2) Tamping a shot. 
 Step (English). (1) The cavity in a piece for receiving the pivot of an 
 
A GLOSSARY OF MINING TERMS 1143 
 
 upright shaft, or the end of an upright piece. (2) The shearing in a 
 coal face. 
 
 Stint. The amount of work to be done by a man in a specified time. 
 
 Stitch. To fasten a timber by toe nailing. 
 
 Stobb. A long steel wedge used in bringing down coal after it has been holed. 
 
 Stomp. A short wooden plug fixed in the roof of a level, to serve as a bench 
 mark for surveys. 
 
 Stone Coal. Anthracite; also other hard varieties of coal. 
 
 Stone Head. A heading or gangway driven in stone. A tunnel. 
 
 Stone Tubbing. Water-tight stone walling of a shaft cemented at the back. 
 
 Stook. A pillar of coal about 4 yd. square, being the last portion of a full- 
 sized pillar to be worked away in bord-and-pillar workings. 
 
 Stook-and-Feather. A wedge for breaking down coal, worked by hydraulic 
 power, the pressure being applied at the extreme inner end of the drilled 
 
 Stoop. A pillar of coal. 
 
 Stoop-and-Room. A system of working coal very similar to pillar-and-stall. 
 
 Slop. Any cleat or beam to check the descent of a cage, car, pump rods, etc. 
 
 Slope. (1) To excavate mineral in a series of steps. (2) A place in a mine 
 that is worked by stoping. 
 
 Sloping. Working out mineral between two levels or on the surface, by 
 stopes or steps. Stoping Overhand. Mining a stope upwards, the flight 
 of steps being inverted. Stoping Underhand. Mining a stppe downwards 
 in such a series that it presents the appearance of a flight of steps. 
 
 Stopping. An air-tight wall built across any passageway in a mine. 
 
 Stove Coal. In anthracite only; two sizes of stove coal are made, large and 
 small: large stove, known as No. 3, passes through a 2i-in. to 2-in. mesh 
 and over a IJ-in. to 1^-in. mesh; small stove, known as No. 4, passes 
 through a l|-in. to If-in. mesh and over a U-in. to 1-in. mesh. Only 
 one size of stove coal is now usually made. It passes through a 2-in. 
 square mesh and over If -in. square mesh. 
 
 Stove Up, or Slaved. Upset. When a rod of iron heated at one end is ham- 
 mered endwise the diameter of that end is enlarged, and it is said to be 
 upset or stove up. " 
 
 Stow~ To pack away rubbish into goaves or old workings. 
 
 Stowce. (1) Windlass. (2) Landmarks. 
 
 Stowing. The debris of a vein thrown back of a miner and which supports 
 the roof or hanging wall of the excavation. 
 
 Straight Ends and Walls. A system of working coal somewhat similar to 
 bord-and-pillar. Straight ends are headings from 4 ft. 6 in. to 6 ft. in 
 width. Walls are pillars 30 ft. wide. 
 
 Straight Work. A system of getting coal by headings or narrow work. 
 
 Stroke. A slightly inclined table for separating heavier minerals from 
 lighter ones. 
 
 Stratification. Arrangement in layers. 
 
 Stratum (plural, strata). A layer or bed of rocks, or other deposit. 
 
 Streak. The color of the mark made when a mineral is scratched against a 
 white surface. 
 
 Strett. The system of getting coal by headings or narrow work. See Bord- 
 and-Pillar. 
 
 Strike (of a seam or vein). The intersection of an inclined seam or a vein 
 with a horizontal plane. A level course in the seam. The direction of 
 strike is always at right angles to the direction of the dip of the seam. 
 
 Strike Joints. Joints or cleavages that are parallel to the strike of the seam. 
 
 Striking Deal. Planks fixed in a sloping direction just within the mouth ot 
 a shaft, to guide the tub to the surface. 
 
 Stringer (English). Any longitudinal timber or beam. 
 
 StringpumpA. system of pumping whereby the motion of the engine is 
 transmitted to the pump by timbers or stringers bolted together. . 
 
 String Rods. A line of surface rods connected rigidly for the transmission 
 of power; used for operating small pumps in adjoining shatts tn 
 central station. . ... ... . 
 
 Strip. (i) To remove the overlying strata of a bed or vein. (2) Mining a 
 deposit by first takirTf off the overlying material. 
 
 Strut (English) A prop to sustain compression, whether vertical or inclined. 
 
 Struve Ventilator. A pneumatic ventilating apparatus consisting of two 
 vessel-like gas holders, which are moved up and down m a tank 01 
 water. By this means, the air is sucked out of the mine as required. 
 
1144 A GLOSSARY OF MINING TERMS 
 
 Studdle. A piece of squared timber placed vertically between two sets of 
 
 timber in a shaft. 
 
 Stull. A post for supporting the wall or roof in a mine; a prop timber. 
 Stump. The pillar between the gangway and each room turned off the gang- 
 way. Sometimes the entry pillars are called stumps. 
 Stumping. A kind of pillar-and-stall plan of getting coal. 
 Stup. Powdered coke 9r coal mixed with clay. 
 Sturt. A tribute bargain profitable to the miner. 
 Stuttle, or Sprag. The horizontal member of a square set of timber running 
 
 longitudinally with the deposit. 
 Stythe. Carbonic-acid gas (blackdamp). 
 Sucker Rod. The pump rod of an oil or artesian well. 
 Suction Pump (English). A pump wherein, by the movement of the piston, 
 
 water is drawn up into the vacuum caused. 
 Sulphur. (1) One of the elements. (2) Iron pyrites?. 
 Sulphur et. See Sulphide. 
 
 Sulphide. A combination of sulphur and a base. 
 Sump, or Sumpt.A. catch basin into which the drainage of a mine flows and 
 
 from which it is pumped to the surface. 
 Sumping, or Sumping Cut. Forcing the cutter bar of a coal cutter into or 
 
 under the coal. 
 
 Surface Deposits. Those that are exposed and can be mined from the surface. 
 Swab Stick. A short wooden rod, bruised into a kind of stumpy brush at one. 
 
 end, for cleaning out a drill hole. 
 
 Swally, or Swelly. A trough, or syncline, in a coal seam. 
 Swamp. A depression or natural hollow in a seam, a basin. 
 Sweeping Table. A stationary buddle. 
 Sweet. Free from deleterious gases. 
 Swing. The arc or curve described by the point of an instrument, such as a 
 
 pick or hammer, when being used. 
 Switch. (1) The movable tongue or rail by which a train is diverted from 
 
 one track to another. (2) The junction of two tracks. (3) An pa- 
 
 paratus for changing the course of or interrupting an electrical current. 
 Switchboard. A board where several electrical wires terminate, and where, 
 
 by means of switches, connection may be established between any of 
 
 these wires and the main wire. 
 Synclinal Axis. The line or course of a syncline. 
 Syncline. The point or axis of a basin toward which the strata upon either 
 
 side dip. An inverted anticline. A basin. 
 Systematic Timbering. Placing mine timbers according to a predetermined 
 
 plan, regardless of roof conditions. 
 
 Tackle (English). (1) Ropes, chain, detaching hooks, cages, and all other 
 apparatus for raising coal or ore in shafts. (2) Any rope for hoisting, 
 as a tackle rope, block and tackle, etc. 
 
 Tail-Back. When the firedamp ignites and the flame is elongated or creeps 
 backwards against the current of air, it is said to tail-back. 
 
 Tailing. The blossom; the outcrop or smut. 
 
 Tailngs. The refuse from a jig. 
 
 Tail-Pipe. The suction pipe of a pump. 
 
 Tailrace. The channel along which water flows after it has done its work. 
 
 Tail-Rope. (1) In a tail-rope system of haulage, the rope that is used to 
 draw the empties back into the mine. (2) A wire rope attached beneath 
 cages, as a balance. 
 
 Tail-Rope System of Haulage. A haulage system in which the full trip is 
 drawn out by the main rope and the empty trip is drawn in by the tail- 
 rope, these ropes being attached to the opposite ends of the trip. 
 
 Tail-Sheave. The sheave at the inbye end of any haulage system. See Turn 
 Pulley. 
 
 Take the Air. (1) To measure the ventilating current. (2) Applied to a 
 ventilating fan as working well, or working poorly. 
 
 Taladro (Mexican). A drill for mechanical or mining purposes. Taladrar. 
 To bore or drill. 
 
 Tally. (1) A mark or number placed by the mine? on every car of coal sent 
 out of his place, usually a tin ticket. By counting these, a tally is made 
 of all the cars of coal he sends out. (2) Any numbering, or counting, 
 or memorandum, as a tally sheet. 
 
 Tamp. To fill a bore hole, after inserting the charge, with some substance 
 
A GLOSSARY OF MINING TERMS 1145 
 
 which is rammed hard as it is put into the hole. Vertical holes are often 
 
 tamped with water, when blasting with dynamite. 
 Tamping. The process of stemming or filling a bore hole. 
 Tamping Bar. A. copper-tipped bar, for ramming the tamping or stemming. 
 Tanates (Mexican). Leather, hide, or jute bags, to carry ore or waste rock 
 
 within or out of a mine. Tanatero. A laborer or bag carrier. 
 Tap. (1) To cut or bore into old workings, for the purpose of liberating ac- 
 cumulations of gas or water. (2) To pierce or open any gas or water 
 
 feeder. (3) To win coal in a new district. 
 Tapextle (Mexican). A working platform or stage built up in a stope or any- 
 where m a mine; a landing place between two flights of ladders. 
 Teem. To pour or tip. 
 
 Teeming Trough. A trough into which the water from a mine is pumped. 
 Telegraph.- A sheet-iron trough-shaped chute, for conveying coal or slate 
 
 from the screens to the pockets, or boilers. 
 Temper. (1) To change the hardness of metals by first heating and then 
 
 plunging them into water, oil, etc. (2) To mix mortar, or to prepare 
 
 clay for bricks, etc. 
 Tempering. The act of reheating and properly cooling a bar of metal to any 
 
 desired degree of hardness. 
 Temper Screw. In rope drilling, a screw for gradually lowering the clamped 
 
 (upper) end of the rope as the hole is deepened. 
 Tenon. A projecting tongue fitting into a corresponding cavity called a 
 
 mortise. 
 Tequio (Mexican). A task set for a drillman or for any laborer in a mine, to 
 
 be regarded as a day's work. 
 Terrace. A raised level bank, such as river terraces, lake terraces, etc. 
 Terrero (Mexican). The dump of a mine. 
 
 Test. A trial of an engine, fan, or other appliance or substance. 
 Theodolite. An instrument used in surveying, for taking both vertical and 
 
 horizontal angular measurements. An -engineer's large transit, with 
 
 attachments. 
 Thill. See Floor. 
 Thimble. (1) A short piece of tube slid over another piece, to strengthen a 
 
 joint, etc. (2) An iron ring with a groove around it on the outside, used 
 
 as an eye when a rope is doubled about it. 
 Thirl. See Crosscut. 
 Through-and-Through. A system of getting bituminous coal, without regard 
 
 to the size of the lump. 
 Throw. (1) A fault of dislocation. (2) The vertical distance between the 
 
 two ends of a faulted bed of coal. 
 Thrown. Faulted; broken by a fault. 
 Thrust. Creep or squeeze due to excessive weight, hard floor, and too small 
 
 pillars. 
 
 Thurl (Staffordshire). To cut through from one working into another. 
 Tie- Back. (1) A beam serving a purpose similar to a fend-off beam, but 
 
 fixed at the opposite side of the shaft or inclined road. (2) The wire 
 
 ropes or stayrods which are sometimes used on the side of the tower 
 
 opposite the hoisting engine, in place of or to reenforce the engine braces. 
 Tiff. Calcite or carbonate of lime. 
 Timber. (1) Props, bars, collars, legs, laggings, etc. (2) To set or place 
 
 timber in a mine or shaft. 
 
 Timberer, Timberman. A man who sets timber. 
 Time. (1) Hours of work performed by workmen. (2) To count the 
 
 strokes of a pump or revolutions of an engine or fan. 
 Tin-Can Safely Lamp. A Dayy lamp placed inside a tin can or cylinder 
 
 having a glass in front, air holes near the bottom, and open-topped, 
 
 making the lamp safer in a rapid current of air. 
 Tip. A dump. See Tipper, or Tipple. 
 Tipper, Tipple, or Tippler. An apparatus for emptying cars of coal or ore, 
 
 by tipping or turning them upside down, and then bringing them back 
 
 to original position, with a minimum of manual labor. 
 Tipple. The dump trestle and tracks at the mouth of a shaft or slope, where 
 
 the output of a mine is dumped, screened, and loaded. 
 Tiro (Mexican). A mining shaft. Tiro Vertical. A. vertical shaft. 
 Token. (1) A piece of leather or metal stamped with the hewer s or putter s 
 
 number or distinctive mark, and fastened to the tub he is filling 01 
 
 putting. 
 
1146 A GLOSSARY OF MINING TERMS 
 
 Ton. A measure of weight. Long ton is 2,240 lb.; short ton is 2,000 lb.; 
 metric ton is 1,000 kilograms = 2,204.6 lb. 
 
 Top. m See Roof. (2) Top of a shaft; surface over a mine. 
 
 Topit. A kind of brace head screwed to the top of boring rods, when with- 
 drawing them from the hole. 
 
 Topping. The coal on a car above the t6p of the car box. 
 
 Track. Railways or tramways. 
 
 Tracking. Wooden rails. 
 
 Train Boy. A boy that rides on a trip, to attend to rope attachments, signal 
 in case of derailment of cars, etc. Trip rider. 
 
 Train, or Trip. The cars taken at one time by mules, or by any motor, or 
 run at one time on a slope, plane, or sprag road, always together. 
 
 Tram. A mine car, or the track on which it rums. 
 
 Trammer. One who pushes cars along the track. " "' 
 
 Tramroad. A mine track or railroad. 
 
 Tram Rope. A hauling rope, to which the cars are attached by a clip or 
 chain, either singly or in trips. 
 
 Tramway. A small, roughly constructed track for running wagons or trucks 
 on. 
 
 Transfer Carriage. Movable platform or truck used to transfer mine cars 
 from one track to another. 
 
 Transome (English). A heavy wooden bed or supporting piece. 
 
 Trap. (1) A steep heading along which men travel. (2) A fault of dislo- 
 cation. (3) An eruptive rock. (4) A dangerous place. (5) To tend 
 door. 
 
 Trjap Dike. A fault (not necessarily accompanied by displacement of strata) 
 in which the spaces between the fractured edges of the beds are filled up 
 by a thick wall of igneous rock. 
 
 Trap Door. A small door, kept locked, fixed in a stoping, for giving access 
 to firemen and certain others to the return airways, dams, or other un- 
 used portions of the mine'. 
 
 Trapper. A boy employed underground to tend doors. 
 
 Traveling Road. An underground passage or way used expressly, though 
 not always exclusively, for men to travel along to and from their work- 
 ing places. 
 
 Treenail. A long wooden pin for securing planks or beams together. 
 
 Trend. The course of a vein, fault, or other feature. 
 
 Tribute. A method of working mines by contract, whereby the miners 
 receive a certain share of the products won. Tributers. Miners paid 
 by results. 
 
 Trig. A sprag used to block or stop a wheel or any machinery. 
 
 Trip. The mine cars in one train or set. See Train. 
 
 Triple-Entry System. A system of opening a mine by driving three parallel 
 entries for the main entries. 
 
 Triturate. To grind or pulverize. 
 
 Trolley. (1) A small four-wheeled truck, used for carrying the ore bucket 
 underground. (2) An electric locomotive. (3) The arm of a loco- 
 motive or other machine that conducts the electric current from the wire 
 above the track to the machine. 
 
 Trompe. An apparatus for producing ventilation by the fall of water down 
 a shaft. 
 
 Trouble. A dislocation or fault; any irregularity in the bed. 
 
 Trough Fault. A wedge-shaped fault, or, more correctly, a mass of rock, 
 coal, etc.; let down in between two faults, which faults, however, are 
 not necessarily of equal throw. 
 
 Troughs, or Thirling. A passage cut through a pillar to connect two rooms. 
 
 Truck. Used synonymously with Barney. 
 
 Truck System. Paying miners in food instead of money. 
 
 Trunnions. Cylindrical projections or journals, attached to the sides of a 
 vessel, so that it can rotate in a vertical plane. 
 
 Trying the Lamp. The examination of the flame of a safety lamp for the 
 purpose of forming a judgment as to the quantity of firedamp mixed 
 with the air. 
 
 Tub. (1) A mine car. (2) An iron or wooden barrel used in a shaft, for 
 hoisting material. 
 
 Tubbing. Cast iron, and sometimes timber, lining or "walling of a circular shaft. 
 
 Tubbing Wedges. Small wooden wedges hammered between the joints of 
 tubbing plates. 
 
A GLOSSARY OF MINING TERMS 1147 
 
 Tubing. Iron pipes or tubes used for lining bore holes, to prevent caving. 
 Tunnel. A horizontal passage driven across the measures and open to day at 
 
 both ends; applied also to such passages open to day at only one end, or 
 
 not open to day at either end. 
 furbary. A peat bog. 
 Turbine. (1) A rapidly revolving waterwheel, impelled by the pressure of 
 
 water upon blades. (2) A similar type of power generator propelled by 
 
 steam or air. 
 Turn. (1) The hours during which coal, etc., is being raised from the mine. 
 
 (2) See Shift. (3) To open rooms, headings, or chutes off from an entry 
 
 or gangway. (4) The number of cars allowed each miner. 
 Turnout. A siding or passing on any tram or haulage road. 
 Turn Pulley. A sheave fixed at the inside end of an endless- or tail-rope 
 
 haulage plane, around which the rope returns. See Tail-Sheave. 
 Turntable. A revolving platform on which cars or locomotives are turned 
 
 around. 
 
 Tut Work. Breaking ground at so much per foot or fathom. 
 Tuyere. The tubes through which air is forced into a furnace. 
 Two-Throw. When, in sinking, a depth of about 12 ft. has been reached, and 
 
 the d6bris has to be raised to the surface by two lifts or throws with the 
 
 shovel, one man working on staging above another. 
 Unconformability. When one layer of rock, resting on another layer, does 
 
 not correspond in its angle of bedding. 
 
 Undercast, An air-course carried under another air-course or roadway. 
 Underclay. A bed of fireclay or other less clayey stratum, lying immediately 
 
 beneath a seam of coal. 
 Undercut. To remove a small portion of the bottom of the bed or the under- 
 
 clay, so that the mass of coal or mineral can be wedged or blasted down. 
 Underhand Sloping. See Sloping Underhand. 
 Underhand Work. Picking or drilling downwards. 
 Underholing, Undermining. To mine out a portion of the bottom of a seam 
 
 or the underclay, by pick or powder, thus leaving the top unsupported 
 
 and ready to be blown down by shots, broken down by wedges, or mined 
 
 with a pick or bar. 
 Underlie, or Underlay. The inclination of a stratum at right angles to its 
 
 course or strike; the true dip. 
 Underviewer, or Underlooker. An inside foreman. 
 Unwater. To drain or pump the water from a mine or shaft. 
 Upcast. The shaft through which the return air ascends. 
 Upraise. An auxiliary shaft, a mill hole, or heading carried from one level up 
 
 toward another. 
 
 Upthrow. A fault in which the displacement has been upward. 
 Vapor (Mexican). Steam; heated and stinking gas sometimes found in 
 
 mines, which causes candles to burn dimly and go out. 
 Vein. See Lode. Often applied incorrectly to a seam or bed of coal or other 
 
 mineral. 
 
 Vena (Mexican). A thin vein, not over 3 in. thick a knife-blade vein. 
 Vend (North of England). Total sales of coal from a mine. 
 Vent, or Vent Hole. (1) A small passage made with a needle through the 
 
 tamping, which is used for admitting a squib, to enable the charge to be 
 
 lighted. (2) Any opening made into a confined space. 
 Ventilating Column. See Motive Column. 
 Ventilating Pressure. The total pressure or force required to overcome the 
 
 friction of the air in mines; the unit of ventilating pressure or pressure 
 
 per sq. ft. of area multiplied by the area of the airway. 
 Ventilation. Circulation. The atmospheric air circulating in a mine. 
 Ventilator. Any means or apparatus for producing a current of air in a mine 
 
 or other airway. 
 
 Vestry (North of England). A refuse. 
 Viewer. The general manager or mining engineer of one or more collieries, 
 
 who has control of the whole of the underground works, and also gen- 
 erally of those on the surface. 
 Vug, or Vugh (Cornish). A cavity in the rock. 
 Wagon. A mine car. 
 Wagon Breast. A breast in which the mine cars are taken up to the working 
 
 face. 
 Wailing. Picking stones and dirt from among coals. 
 
1148 A GLOSSARY OF MINING TERMS 
 
 Wale (North of England). Hand-dressing coal. 
 
 Walking Beam. See Working Beam. 
 
 Wall. (1) The face of a longwall working or breast. (2) A rib'of solid coal 
 between two breasts. (3) A crosscut driven between bords. 
 
 Walling. See Steening. 
 
 Walling Cribs. Oak cribs or curbs upon which walling is built. 
 
 Walling Stage. A movable wooden scaffold suspended from a crab on the 
 surface, upon which the workmen stand when walling or lining a shaft. 
 
 Wall Plates. The two longest pieces of timber in a set used ina rectangular 
 shaft. 
 
 Warners. Apparatus consisting of a variety of delicately constructed 
 machines, actuated by chemical, physical, electrical, and mechanical 
 properties, for indicating the presence of small quantities of firedamp in 
 the mines. At present, most of these ingenious contrivances are more 
 suited to the laboratory than for practical application underground. 
 
 Warning Lamp. A safety lamp fitted with certain delicate apparatus, for 
 indicating very small proportions of firedamp in the atmosphere* of a 
 mine. As small a quantity as 3 % can be determined by this means. 
 
 Wash. Drift, clay, stones, etc., overlying the strata. 
 
 Washer. A jig. 
 
 Wash Fault. A portion of a seam of coal replaced by shale or sandstone. 
 
 Washing Apparatus, or Washery. (1) Machinery and appliances erected on 
 the surface at a colliery, often in connection with coke ovens, for extract- 
 ing, by washing with water, the impurities mixed with the coal dust or 
 small slack. (2) Machinery for removing impurities from small sizes of 
 anthracite coal. 
 
 Washout. The erosion of an appreciable extent of a coal seam by aqueous 
 agency. 
 
 Waste. (1) See Goaf. (2) Very small coal or slack. (3) The portion of a 
 mine occupied by the return airways. (4) Also used to denote the 
 spaces between the pack walls in the gob of longwall working. (5) 
 Refuse material. 
 
 Waste Gate (English). A door for regulating discharge of surplus water. 
 
 Water Blast. The sudden escape of air pent up in rise workings, under con- 
 siderable pressure from a head of water that has accumulated in a 
 connecting shaft. 
 
 Water Cartridge. A waterproof cartridge surrounded by an outer case. The 
 space between being filled with water, which is employed to destroy the 
 name produced when the shot is fired, thereby lessening the chance of an 
 explosion should gas be present in the place. 
 
 Water Gauge. An instrument for measuring the pressure per square foot 
 producing ventilation in a mine. 
 
 Water Hammer. The hammering noise caused by the intermittent escape of 
 gas through water in pipes. 
 
 Water-Jacket. A jacket filled with water, to keep cool a cylinder or furnace. 
 
 Water Level. An underground passage or heading driven very nearly dead 
 level or with sufficient grade only to drain off the water. 
 
 Water Right. The privilege of taking a certain quantity of water from a 
 watercourse. 
 
 Watershed. The elevated land or ridge that divides drainage areas. 
 
 Waterwheel (English). Overshot, undershot, breast wheels, etc. A wheel 
 provided with buckets, which is set in motion by the weight or impact 
 of a stream of water. 
 
 Weather. To crumble by exposure to the atmosphere. 
 
 Weather Door. See Trap Door. 
 
 Web. The face of a longwall stall in course of being holed and broken down 
 for removal. The length of breast or face brought down by one mining. 
 
 Wedging. The material, moss or wood, used to render the shaft lining tight. 
 
 Wedging Crib. A curb or crib of wood or cast iron wedged tightly in place 
 and packed, in order to form a water-tight joint and upon which tubbing 
 is built. 
 
 Wedging Down. Breaking down the coal at the face with hammers and 
 wedges instead of by blasting. 
 
 Weigh Bridge (English). A platform large enough to carry a wagon, resting 
 on a series of levers, by means of which heavy bodies are weighed. 
 
 Weize. A band or ring of spun yarn, rope, rubber, lead, etc., put in between 
 the flanges of pipes before bolting them together, in order to make a 
 water-tight joint; a gasket. 
 
.4 GLOSSARY OF MINING TERMS 1149 
 
 Well. A sump, or a branch from the sump. 
 Whim. A winding drum worked by a horse. 
 Whim Shaft. A shaft through which coal, ore, water, etc., are raised from a 
 
 mine by means of a whim. 
 Whin. A hard, compact rock. 
 Whin Dike. A fault or fissure filled with whin and the debris of other rocks, 
 
 sometimes accompanied by a dislocation of the strata. 
 Whip. A hoisting appliance consisting of a pulley supporting the hoisting 
 
 rope to which the horse is directly attached. 
 Whitedamp. Carbonic oxide (CO). A gas found in coal mines, generally 
 
 where ventilation is slack. A product of slow combustion in a limited 
 
 supply of air. It burns and will support combustion. It is extremely 
 
 poisonous. 
 
 Whole Working. The first working of a seam, which divi'des it into pillars. 
 Wild Rock. Any rock not fit tor commercial slate. 
 Win. To sink a shaft or slope, or drive a drift to a workable seam of mineral 
 
 in such a manner as to permit its being successfully worked. 
 Winch, or Windlass. A hoisting machine consisting of a horizontal drum 
 
 operated by crank-arm and manual labor. 
 Wind Bore (England). The bottom or suction pipe of a lift of pumps, which 
 
 has suitable brass holes or perforations for suction of water or air. 
 Wind Gauge. An anemometer for testing the velocity of air in mines. 
 Winding. The operation of raising or hauling the product of a mine by 
 
 means of an engine and ropes. 
 Winding Engines. Hoisting or haulage engines. 
 Wind Method. A system of separating coal into various sizes, and extracting 
 
 the dirt from it, which in principle depends on the specific gravity or 
 
 size of the coal and the strength of the current of air. 
 Wind Sail. The top part of canvas piping, which is used for conveying air 
 
 down shallow shafts. 
 Wing Bore. A side or flank bore hole. 
 Wings. See Rests and Keeps. 
 Winning. A sinking shaft, a new coal, ironstone, clay, shale, or other mine 
 
 of stratified material. A working place in a mine. 
 
 Winse. 'Interior shaft connecting levels, sometimes used as an ore chute. 
 Won. Proved, sunk to, and tested. 
 Work. (1) To mine. (2) Applied to mine working when affected by 
 
 squeeze or creep. 
 
 Workable. Any seam that can be profitably mined. 
 Worked Out. When all available mineral has been extracted from a mine it 
 
 is worked out. 
 
 Working. Applied to mine workings when squeezing. 
 Working Barrel. The water cylinder of a pump. 
 Working Beam (English). A beam having a vertical motion on a rock shaft 
 
 at its center, one end being connected with the piston rod and the other 
 
 with a crank or pump rod, etc. 
 
 Working Cost. The total cost of producing the mineral. 
 Working Face. See Face. 
 Working Home Getting or working out a seam of coal, etc., from the 
 
 boundary or far end of the mine toward the shaft bottom. 
 Working on Air. A pump works on air when air is sucked up with the water. 
 Working Out. Working outwards or in the direction of the boundaries of 
 
 the colliery. 
 
 Working Place. The actual place in a mine at which the coal is being mined. 
 Workings. The openings of a colliery, including all roads, ways, levels, dips, 
 
 airways, etc. 
 
 Wrought Iron. Iron in its minimum state of carbunzation. 
 Wythern (Wales). Lode. 
 Xacal (Mexican). A miner's cabin; a storehouse for mining goods; a shaft 
 
 house. 
 
 Yardage, Yard Work. Price paid per yard for cutting coal. 
 Yard Price. Various prices, per yard driven (in addition to the tonnage 
 
 prices), paid for roads of certain widths and driven in certain directions. 
 Yield. The proportion of a seam sent to market. 
 Zone. In coal-mining phraseology this word means a certain series of coal 
 
 seams with their accompanying shales, etc., which contain, for example, 
 
 much firedamp, called a fiery zone, or, if much water, a watery zone. 
 
INDEX 
 
 Abbreviations, mathematical, 18 
 
 surveyor's, 89 
 
 weights and measures, 1-17 
 Abel, Prof., 853, 948 
 Absolute zero, 353 
 Abutments of dams, 328 
 Accidents, 969, 975 
 Acetylene, 871 
 
 lamps, 900 
 
 Acid waters, pumps for, 346 
 Afterdamp, 869 
 
 Aggregates in concrete work, 206 
 Air, atmospheric, 845 
 
 compressed, 474-484 
 
 diffusion compared to gases, 843 
 
 humidity, 843 
 
 mine, 846 
 
 psychrometers or hygrometers, 
 844 
 
 required for combustion of 
 gases, 447 
 
 standard, 935 
 
 weight and volume, 447, 841, 
 
 842 
 
 Air-lift pumps, 349 
 Aitkin's gas indicator, 894 
 Alabama methods of working mines, 
 
 632 
 
 Alaskan coals, analyses, 390 
 Alcohol as fuel, 536 
 Alkalies, effect on concrete, 210 
 Allis-Chalmers Co., 251 
 Almy boilers, 416 
 
 Altitude, determination of, in sur- 
 veying, 105 
 
 effect on boiling point of water, 
 
 363 
 
 Aluminum compared to copper, 490, 
 491 
 
 strength of, 170 
 American Blower Co., 933 
 American Chemical Society, 378 
 American Institute of Electrical 
 
 Engineers, 755 
 American Medical Association, 853, 
 
 855 
 
 American Safety Lamp Co., 878 
 American Society of Civil Engineers: 
 
 report on concrete, 207 
 
 tests of cement, 198 
 American Society of Mechanical 
 
 Engineers, 423, 431, 433 
 American Steel and Wire Co., 738 
 American Well Works, 554 
 American wire gauge, 490 
 Ammonium nitrate, 667 
 Anaconda Copper Mining Co., 725, 
 
 Analyses of coals, 378-391 
 Andre's rule for shaft pillars, 697 
 Angle of friction, 160 
 Angles, geometrical construction of, 
 39 
 
 latitudes and departure, tables, 
 1074 
 
 logarithmic tables, 1009 
 
 logarithms of trigonometric 
 functions, 1028 
 
 method of laying off, 9 
 
 of repose, tables, 160, 161, 162 
 
 sines and cosines of, 989, 991 
 
 tangents and cotangents, 1000 
 
 traverse tables, 1073 
 Angular measure, 9 
 Annealed copper wire, properties of, 
 
 489 
 
 Ansell's indicator, 893 
 Anthracite coal, 371 
 
 change to wood, 368 
 
 compressive strength, 694 
 
 crushing strength, 694 
 
 handling, 962 
 
 preparation of, 958 
 
 pressure against vertical walls, 
 
 table. 966 
 
 Apothecaries' weight, 4 
 Apparatus for mine rescue, 986 
 Arc, geometrical construction of, 40 
 
 time equivalent, 10 
 Areas, tables, 1081, 1097 ' 
 Arithmetic, 19-36 
 Arithmetical progression, 24 
 Artificial respiration, 970, 987 
 Ashworth-Hepplewhite-Gray lamp, 
 
 876, 877, 888 
 
 Asphyxiation, recovery from, 987 
 Astronomical time in surveying, 100 
 Atkinson, J. J., 909 
 Atomic weights of elements, 833 
 Australian woods, weight, 281 
 Avogadro's law, 836 
 A/pirdupois weight, 5 
 Axis of symmetry, 155 
 Axle and wheel, 150 
 
 oil, 168 
 Axles, coefficients of friction, 162 
 
 Babcock and Wilcox, 366, 397, 416 
 Baker, 863 
 
 Baldwin Locomotive Works. 759 
 Ball bearing on mine-car wheels, 166 
 Bamford, Roy, 310 
 Barker, 870 
 Barometers, 839 
 
 Barometric elevations, table, 142 
 leveling, 140 
 
 1151 
 
1152 
 
 INDEX 
 
 Batteries, electric, 514 
 Baum6 hydrometer, 537 
 Beams, 174 
 
 deflection formulas, 179 
 
 designing of, 176 
 
 external sheer and bending 
 moment, table, 175, 177 
 
 iron and steel, 187 
 
 modulus of rupture, 178 
 
 problems in strength, 184 
 
 stiffness, 178 
 
 table of safe loads, 186 
 Beard, T. J., 910, 920, 942, 943 
 Beard-Mackie sight indicator, 894 
 Bearing values of rivets, table, 173, 
 
 174 
 
 Beau de Rochas, 532 
 Belting in power transmission, 272 
 Belt pulleys, 271 
 Bending moment of a beam, table, 
 
 175, 177 
 
 Bethellizing timber, 724 
 Bickford's fuse, 676 
 Biram's ventilator, 131 
 Bitumen, prospecting for, 557 
 Bituminous coal, 372 
 
 preparation of, 959 
 
 pressure against vertical 
 
 walls, 965 
 
 Black Diamond culm plant, 702 
 Blackdamp, 851, 869 
 Blair, 855, 862 
 Blasting, 638, 667-691 
 Blossburg, coal region, 618 
 Blow-offs, boiler, 416, 417 
 Board measure, 302 
 Boilers. 406-454 
 
 air required, 451 
 
 blowing down, 438 
 
 blow-9ffs, 416, 417 
 
 capacity water and steam, 443 
 
 care of, 438 
 
 chimneys, 446 
 
 chimneys, erection, 452 
 
 cleaning, 438 
 
 connecting, 434 
 
 connection of steam gauge, 416 
 
 coverings for pipes, 419 
 
 durability, 443 - .3T,-*. 
 
 efficiency, 433 
 
 equalizing feed, 435 
 
 explosion, liability to, 442 
 
 feeding and feedwater, 422 
 
 feed pumps, 335, 438 
 
 feedwater, factors of evapora- 
 tion, 432 
 
 feedwater, heating, 430 
 
 feedwater, purification, 428 
 
 feedwater, testing, 428 
 
 filling, 433 
 
 fire, cleaning of, 435 
 
 firing, 438 
 
 firing with solid fuel, 435 
 
 fittings, 414 
 
 fittings inspection, 441 
 
 foaming, 437, 439 
 
 fuels, temperature of ignition, 
 448 
 
 furnace fittings, 417 
 
 Boilers, fusible plugs, 415, 438 
 
 gauges, 438 
 
 grates, 417 
 
 heating surface, ratio of horse- 
 power, 444, 445 
 
 horsepower, standard of, 431 
 
 impurities in feedwater, 425 
 
 incrustation and corrosion, 424 
 
 injectors, 422 
 
 inspection, 439 
 
 loss of heat from pipes, table, 
 420 
 
 management, 433 
 of fires, 434 
 
 overheating of plates, 427 
 
 oxygen and air required for 
 combustion, 448 
 
 piping, 412 
 
 priming, 436 
 
 production and measurement 
 of draft, 451, 453 
 
 products of combustion, 446 
 
 repairs, 443 
 
 safety valves, 414, 438 
 valves, inspection, 441 
 
 scale, 425 . 
 
 scale-forming substances and 
 remedies, 427 
 
 selection of, 441 
 
 shutting down, 437 
 
 size of chimneys and horsepower 
 of boilers, 454 
 
 starting up, 437 
 
 steam, 406 
 
 stokers, 418 
 
 table of work, 445 
 
 temperature of fire, 449 
 of ignition, 448 
 
 trials, 430 
 
 tubes, weight, 297 
 
 uniform steam pressure, 436 
 
 water circulation, 444 
 level, 436, 438 
 required, table, 423 
 
 weight of air, water vapor and 
 
 saturated mixtures, 447 
 Bolt heads, proportions, 300 
 
 weight, 292 
 Bolts, weights, 299 
 Bowron, Chas. E. f 776 
 Box regulators, 919, 920 
 Boyle's law, 475, 840 
 Brackett, F. E., 350 
 Brass sheets, weights, 293 
 Brass, strength of, 170 
 Breathing apparatus, 986 
 Brick, size and strength, 236 
 
 masonry piers, 235 
 Brickwork, measures of, 6 
 Bridge wall of a furnace, 417 
 Bridges, suspension, ropes for, 243, 
 
 248 
 
 Briggs, 882 
 Briggs' wire loop, 894 
 Briqueting fuel, 967 
 Briquets, cement, 200 
 British thermal unit, 353 
 British Westinghouse Co., 743 
 Broockmann, Dr., 808 
 
INDEX 
 
 1153 
 
 Broderick & Bascom Rope Co., 237 
 
 Bronze, strength of, 170 
 
 Brown, Col. D. P., 637 
 
 Brown, Thomas J., 402 
 
 Brown & Sharpe Gauge, 291, 293, 
 
 490 
 
 Brownhoist, 966 
 Brunck, Dr., 862, 863, 870 
 Buckets, coal, 580, 963 
 Building materials, weight, 283, 
 
 284 
 
 Bunsen Coal Co., 738 
 Burnettizing timber, 724 
 Burr, W. A., 316 
 Burrell, G. A., 866, 868 
 By-product gas, 401 
 
 Cables for suspension bridges, 248 
 
 strength of, 183 
 Cableways, 242, 258 
 Cahall boilers, 416 
 Calorie, 354 
 
 Calorific value of fuel oil, 396 
 Calumet & Hecla Mining Co., 475 
 Calyx drilling, 556 
 Cambria Steel Co., .293 
 Campbell, Dr. M. R., 372, 373 
 Campbell, J. R., 857 
 Canadian coals, analyses, 388 
 Canaries, effect of afterdamp on, 857 
 Cantilever, 174 
 
 Capacity, metric measures of, 12 
 Capell ventilator, 933 
 Carbon as fuel, 365 
 
 dioxide, 848 
 
 heat and products of combus- 
 tion, 449 
 
 in coal, 369, 371 
 
 monoxide, 852 
 Carbureters, 541 
 Carnegie Steel Co., Ltd., 299, 730, 
 
 764, 766 
 
 Cartridges, hydraulic, 686 
 Cast-iron pipe, weight, 294 
 Catlett, Charles, 370 
 Ceag electric lamp, 897 
 Cement testing. 195 
 
 boiling test, 197 
 
 fineness, 203 
 
 machines for testing, 200 
 
 measurements of expansion, 196 
 
 natural and slag cements, 204 
 
 normal tests, 196 
 
 primary tests, 196 
 
 results of tensile strength tests, 
 201 
 
 sampling, 195 
 
 sand for mortar tests, 199 
 
 secondary tests, 202 
 
 soundness, 196 
 
 specific gravity, 203 
 
 steam test, 197 
 
 tensile strength, 198 
 
 time of setting, 202 
 Cementing materials, 187 
 
 injection in mine shafts, 591 
 
 mortars, 191, 193 
 
 requirements for, 205 
 
 specifications, 204 
 
 73 
 
 Cements, 188 
 Center of gravity, 155 
 Centigrade thermometers and Fahr- 
 enheit compared, 355 
 Central Coal Basin rule for shaft 
 
 pillars, 698 
 Centrifugal fans, 931 
 
 pumps, 343 
 Chain machines, 645 
 Chain, surveyor's, 65 
 Chains, -strength of, 183 
 Chamberlain, Rollin T., 852, 859, 
 
 864-871 
 
 Chance, E. M., 849 
 Charcoal-iron ropes, 237 
 Charles' law, 840 
 Chemistry of gases, 831 
 Chesneau lamps, 875, 890 
 Chester, Thomas, 933 
 Chimneys of boilers, 446 
 combustion rate, 453 
 erection, 452 
 production and measurement 
 
 of draft, 451, 453 
 size and horsepower of boilers, 
 
 454 
 
 Christian, L. A., 484 
 Chutes, coal, 962 
 Circles, 48 
 
 circumferences and areas, tables, 
 
 1097 
 
 Circular curves in railroad survey- 
 ing, 109 
 measure, 9 
 segments, 49 
 Circumferences and areas, tables, 
 
 1081, 1097 
 
 Circumferential stress, 174 
 Clanny, Dr. W. R., 874, 876 
 Clanny lamp, 880, 883, 886 
 Clark, D. K., 290 
 Clearance of steam engines, 454 
 Clearfield coal region, 616 
 Cleats, 614 
 Clement, J. P., 850 
 Climax boilers, 416 
 Clinometer, surveyor's, 67 
 Clinton wire cloth, 218 
 Closed work in mines, 606 
 Clowes, 847, 850, 855, 856, 862, 864, 
 
 893 
 
 Clowes' hydrogen lamp, 889, 983 
 Coal, Alaskan, analyses, 390 
 
 American, analyses, table, 382- 
 
 385, 387 
 
 analyses of typical, 381 
 reports of. 379 
 proximate, 378 
 
 anthracite, see Anthracite Coal, 
 as fuel, 368-394 
 ash, 379 
 bituminous, see Bituminous 
 
 Coal. 
 
 blacksmith coals, 374 
 breakers of reinforced concrete, 
 
 227 
 
 calorific power, 392 
 Canadian, analyses, 388 
 cannel, 378 
 
1154 
 
 INDEX 
 
 Coal chutes, 962 
 
 classification and localities, 370 
 coke, yield of, 376 
 coking, 374 
 constituents, 368 
 cost of unloading, 966 
 crushing and compressive 
 
 strength of anthracites, 694 
 cubic contents of 2000 pounds, 
 
 968 
 
 cubic feet in one ton, 290 
 domestic, 373 
 Dulong's formula, 394 
 dust explosions, 901 
 fat and dry, 378 
 firedamp from analyses of, 864 
 fixed carbon, 379 
 foreign, analyses, 391 
 formations, 550 
 free-burning, 378 
 gas, analyses, 402, 403 
 gas coals, 373 
 heating value, determination of, 
 
 392, 394 
 
 heating values, table, 382-385 
 Kent's method, 392, 393, 394 
 lands, diagram for reporting, 
 
 560 
 
 lignite, 373 
 Lord and Haas' method, 392, 
 
 393, 394 
 
 mines, see Mines. 
 
 moisture, 379 
 
 non-coking, 378 
 
 Pennsylvania anthracite, analy- 
 ses, 386 
 
 pillars in mines, 692 
 
 Pish el's test for coking qualities, 
 
 377 
 
 pockets 9f concrete, 229 
 preparation of, 949-968 
 products of combustion, 446 
 proximate analysis, 378 
 sampling for analysis, 378 
 
 in prospecting, 559 
 seams, horizontal, contents of, 
 
 289 
 
 semianthracite, 372 
 semibituminous, 372 
 sizes of prepared anthracite, 289 
 smithing, 374 
 
 specific gravity, tables, 286, 288 
 splint, 378 
 
 spontaneous ignition, 948 
 steam coal, 374 
 storage, 949 
 sub-bituminous, 372 
 sulphur analysis, 379 
 temperature of ignition, 448 
 value as fuel compared with 
 
 oil, 397 
 volatile combustible matter, 
 
 379 
 
 washers, 953 
 
 weight equivalent to wood, 366 
 weights and measurements, 
 table, 287, 288 
 
 of English and French, 290 
 Coefficient of elasticity, 171 
 
 Coefficient of friction, 159 
 
 Coefficients, in power transmission, 
 265 
 
 Coins, United States and foreign, 16, 
 18 
 
 Coke-oven gas, 402 
 
 Coke ovens, 566 
 
 Coking coals, 374 
 
 Pishel's test, 377 
 
 Coleman shaft, 350 
 
 Colorado Fuel and Iron Co., 903 
 
 Columns, strength, table, 180, 181 
 wooden, formula, 182 
 
 Combined stresses, 182 
 
 Combustion of fuels, 363 
 of gases, 447 
 
 Compass, surveyor's, 60-62 
 
 Composition of forces, 153 
 
 Compressed air, 474-484 
 
 classification of compressors, 
 
 474 
 
 compressors, design of, 483 
 for haulage plants, 803 
 installation, 483 
 operation of, 484 
 construction of compressors, 
 
 475 
 efficiencies of compressors at 
 
 different altitudes, 476 
 explosions, avoiding, 483 
 friction in pipes, 482 
 haulage locomotives, 798 
 hoisting engines, 741 
 horsepower necessary for com- 
 pressors, 807 
 
 locomotive storage tanks, 803 
 losses in transmission, 478-482 
 pipe for haulage plants, 805 
 pipes for transmission, 476 
 rating of compressors, 475 
 theory of, 475 
 transmission of air in pipes, 476 
 
 Compressibility of liquids, 307 
 
 Compressive stress, 169 
 
 Compressors, see Compressed Air. 
 
 Concrete, 187-233 
 
 aggregates used, 206 
 
 cementing materials, 187 
 
 crushing strength, 212 
 
 dams, 331 
 
 destructive agencies, 209 
 
 expansion and contraction, 211 
 
 fire, effect of, 210 
 
 Fuller's rule for quantities, 212 
 
 joining old with new, 213 
 
 measuring ingredients, methods 
 
 of, 211 
 
 mine shaft lining, 737 
 mine water, effect of, 210 
 mixing, 212 
 plain, 206 
 proportioning of ingredients, 
 
 207, 208 
 
 report of Joint Committee, 207 
 retempering, 213 
 steel reinforcement, 214 
 strength of, table, 207, 208 
 thermal changes, effect of, 211 
 vibration, effect of, 211 
 
INDEX 
 
 1155 
 
 Concrete, water used, 209 
 
 weight of ingredients, 207 
 working at freezing and high 
 
 temperatures, 213 
 working stresses and strength 
 
 values, 211 
 Concrete, reinforced, 214 
 
 areas and weights of bars, 
 
 table, 216 
 
 braces for wall forms, 223 
 clamping devices and plank 
 
 holders, 223 
 coal breakers, 227 
 coal pockets, 229 
 conduits, 226 
 floor-systems, 218, 220 
 form work, construction and 
 
 finish, 220, 221 
 hooped columns, 214 
 materials and kinds of bars, 
 
 217 
 members to resist lines of 
 
 failure, 215 
 mixers, 223 
 parts of steel floor-system, 
 
 214 
 principles of construction, 
 
 214 
 
 retaining walls, 226 
 shaft lining, 230 
 tank tower construction, 223 
 uses in engineering, 223 
 wall forms, 221,222 _ 
 Condensers for steam engines, 459 
 Conducting power of substances, 421 
 Conduction of heat, 359 
 Conductors of electricity, 488 
 Conduits of reinforced concrete, 226 
 Cone, 53 
 
 Conical drums, 745 
 Connecticut River rule, 302 
 Connellsville, Pa., method of mining, 
 
 635 
 
 Connor, Eli T., 705 
 Considere, 211 
 Construction, concrete, 214 
 geometrical, 38 
 masonry, 234 
 Continental Coke Co., 402 
 Conversion factors of liquids, 314 
 
 of metric system, 13 
 Copper, compared to aluminum, 
 
 490, 491 
 
 sheets, weights, 293 
 strength of, 170 
 Coquillon's gas indicator, 892 
 Cord, dimensions of, 6 
 Corliss engines, 333 
 
 starting and stopping, 461 
 Corliss-valve hoisting engine, 740 
 
 Cornish pumps, 333 
 Corrosion of boil 
 
 Corrosion of boilers, 424 
 
 of metal reinforcement in con- 
 
 crete, 209 
 
 Cosines, tables of, 989, 991 
 Cotangents, tables of, 989, 1000 
 Coxe, E. B., 950 
 Coxe Bros. & Co., 287 
 Cox's formula, 323 
 
 Crawford and McCrimmon, 941 
 
 Crude oil, 395 
 
 Crushing machinery, 949 
 
 Cube root, 27, 1081 
 
 Cubes of numbers, tables, 1081 
 
 Cubic measures, 6 
 
 Culm, flushing of, 702 
 
 Cuninghame-Cadbury indicator, 
 
 894 
 
 Cunningham, W. H., 734 
 Currency, United States and foreign 
 
 systems, 16, 17 
 Current motors, 332 
 Curtis turbine, 469, 470 
 Curves in railroad surveying, 109 
 Cylinder oil. 168 
 
 Cylinder ratios of steam engines, 458 
 Cylinders, 53 
 
 contents, 295 
 Cylindrical rings, 52 
 
 sheets, strength of, 174 
 
 Dams, abutments and discharge 
 gates, 328 
 
 earth, 329 
 
 in mines, 327 
 
 masonry and concrete, 331 
 
 outside of mines, 328 
 
 pressure against, 304 
 
 refuse, 331 
 
 spillways or waste ways, 329 
 
 stone, 329 
 
 wing, 331 
 
 wooden, 328 
 
 D'Arcy's formula, 320, 322, 477 
 Davis, investing atoms of latent 
 
 heat, 362 
 
 Davis, James B., 703, 705 
 Davis, W. W., 168 
 Davy lamp, 880, 883, 884 
 Davy, Sir Humphrey, 874, 876 
 Dawson, Thomas W., 982 
 Dead plate of a boiler, 418 
 Decimal fractions, 20 
 
 gauge, 292 
 
 Decimals, tables, 2, 4, 5 
 Deformation, definition, 171 
 Delabeche & Playfair, 290 
 De Laval steam turbine, 469, 471, 
 
 472 
 
 Demanet, 862 
 Departures, tables, 1074 
 Designing of beams, 176 
 Despritz system of hoisting, 750 
 Diamond drill, 555 
 Direct stress, 171, 172 
 Discounts, definition, 23 
 Displacement of a ship, 7 
 Ditches, water, 315, 316 
 Division by logarithms, 33 
 Dodson culm plant, 702 
 Dominion Iron and Steel Co., 401 
 Double shear, 174 
 Doyle's rule, 302 
 Drainage of shafts, 596 
 Drilling in prospecting, 554 
 Dron's rule for shaft pillars, 698 
 Drouain, 856 
 Dry measure, 7 
 
1156 
 
 INDEX 
 
 Dudley, C. B., 378 
 Dulong's formula, 394, 396 
 Durability of stone, 236 
 Dynamite, charging and firing, 680 
 
 composition of, 668 
 
 thawing, 673 
 Dynamos, 497 
 
 Earth, coefficients of friction, 161 
 
 specific gravity, table, 276 
 Earthwork in railroad surveying, 115 
 Eavenson, Howard N. t 402 
 Economic-type boilers, 416 
 Edison electric cell, 516 
 Elastic limit, 172 
 Elasticity, modulus of, 171 
 Electric current for pumping water, 
 
 342 
 
 hoisting engines, 742 
 safety lamps, 896 
 Electric-locomotive haulage, 815- 
 
 831 
 advantages and disadvantages, 
 
 815 
 alter nating-current locomotives, 
 
 830 
 
 bonding, 818 
 
 cable-reel locomotives, 826 
 capacity of locomotives, 824 
 construction of motors, 822 
 crab locomotives, 827 
 direct-current locomotives, 822 
 feeders, 819 
 
 rack-rail locomotives, 827 
 resistance of steel rails, 817 
 sizes of locomotives, rails and 
 
 bonds, 818 
 
 sizes of wires, table, 821 
 storage-battery locomotives, 
 
 830 
 
 tandem locomotives, 826 
 troubles, 828 
 wiring, 816 
 Electrical shock, protecting men 
 
 from, 980 
 treatment for, 972 
 Electricity, 484-531 
 
 alternating-current dynamos, 
 
 506 
 
 alternating-current motors, 508 
 alternators, 506 
 aluminum and copper mines 
 
 compared, 490, 491 
 aluminum cables, breaking 
 
 strength, 491 
 annealed copper wire, 490 
 annunciator system, 517 
 arc lamps, 495 
 armature faults, 528 
 armature, heating of, 524 
 batteries, 514 
 bearings, heating of, 524 
 bell wiring, 516 
 brush faults, 523 
 calculation of wires for trans- 
 mission, 492 
 circuits, 486 
 commutator faults, 524 
 compound-wound dynamos, 501 
 
 Electricity, conductors, 488 
 
 conductors for electric haulage 
 
 plants, 496 
 
 connections for continuous-cur- 
 rent motors, 504 
 copper cables, breaking 
 
 strength, 491 
 
 copper cables, capacity, 490 
 current estimates, 494 
 current required for direct-cur- 
 rent motors, 496 
 direct-current circuits, calcula- 
 tion of wires, 492 
 direct-current dynamos, 497 
 direct-current motors, 501 
 dynamo, failure to generate, 527 
 dynamos and motors, 497 
 dynamos, electromotive force 
 
 generated, 500 
 
 dynamos, field excitation, 500 
 electric power, 485 
 electrical expressions and their 
 
 equivalents, 486 
 electromotive force, 485 
 electromotive force generated 
 
 by dynamos, 500 
 field coils, heating of, 524" 
 field excitation of dynamos, 500 
 firing explosives by, 681 
 heating of armature, field coil, 
 
 and bearings, 524 
 incandescent lamps, 494 
 induction motors, 508 
 induction motors, installation 
 
 and care, 511 
 insulated wires, 494 
 motors, 495 
 
 multiphase alternators, 507 
 noise, 525 
 Ohm's law, 485 
 regulation of speed of motors, 
 
 526 
 
 residual magnetism, 527 
 resistance,_485 
 resistance in series and multiple, 
 
 488 
 
 resistance of conductors, esti- 
 mation of, 491 
 rules for handling, 529 
 series-wound dynamos, 500 
 shunt- wound dynamos, 501 
 signaling, 514 
 sparking at brushes, 523 
 speed regulation of motors, 503 
 strength of current, 484 
 synchronous motors, 508 
 transformers, 513 
 troubles with dynamo and 
 
 motor, 523 
 
 weather-proof line wire, 494 
 wire gauze, 490 
 wiring, 488 
 Electrolysis of concrete structures, 
 
 209 
 
 Elements, atomic weights and sym- 
 bols, 833 
 
 of mechanics, 149 
 Elevators, water, 349 
 Ellipse, construction of, 42 
 
INDEX 
 
 1157 
 
 Ellipse, perimeter of, 50 
 Eloin lamp, 876, 877 
 Emery, Charles E., 421 
 Endless-rope haulage system, 785 
 Engineers' Club, Scranton, 694 
 Engineers, stationary, rules for, 473 
 Engine management, 460 
 
 oil, 168, 169 
 Engines, endless-rope haulage, 787 
 
 haulage motor gasoline, 540 
 
 internal combustion, 532-548 
 
 stationary gas, 540 
 
 steam, 454 
 
 English coal, weights of, 290 
 Entries in mines, 607 
 Equations, solution by logarithms, 
 
 36 
 
 Equilibrium of liquids, 303 
 Equivalent orifice, 910 
 Eschka's method of analyzing coal, 
 
 379 
 
 Ethane, 870 
 Ethylene, 871 
 Euler's formula, 180, 182 
 Evan Thomas lamp, 886 
 Evans, .869 
 Evolution by Ipgarithms, 34 
 
 mathematical, 26 
 Examples, see Problems. 
 Excavations, supporting, 692-738 
 Expansion by heat, 354 
 Explosives and blasting, 667-691 
 
 amount and kind, 690 
 
 analyses of mine air after blast- 
 ing, 670 
 
 black powder, sizes of grains, 
 667 
 
 blasting definitions, 687 
 
 boiler, 442 
 
 caps, 677 
 
 care of, 673 
 
 charging and firing black pow- 
 der, 678 
 
 charging and firing dynamite, 
 680 
 
 detonators, 677 
 
 dynamites, composition of, 668 
 
 effect of free faces in mining, 
 688 
 
 electric detonators, 677 
 
 firing, 676, 679 
 
 firing by electricity, 681 
 
 for coal mines, 672 
 
 for rock work, 668 
 
 fuse, 676 
 
 handling, 674 
 
 high explosives, 667, 669 
 
 hydraulic cartridge, 686 
 
 in mines, 900 
 
 lime cartridges, 687 
 
 low explosives, 667 
 
 permissible, 672 
 
 precautions when tamping, 680 
 
 rjroduction of carbon mon- 
 oxide, 852 
 
 products of combustion, 670 
 
 reversing air current, 985 
 
 rules of Bureau of Mines for 
 handling, 675 
 
 Explosives and blasting, squibs, 676 
 storing, 673 
 
 strength, comparative, 670 
 substitutes for blasting in dry 
 
 mines, 685 
 
 thawing dynamite, 673 
 water cartridge, 687 
 wedging down coal, 685 
 
 External shear of beams, table, 175, 
 177 
 
 Eytelwein's formula, 321 
 
 Factor of safety, 172 
 
 Fahrenheit thermometers and Centi- 
 grade compared, 355 
 Fairbanks Company, 200 
 Fairmount Coal Co., 776 
 Falling bodies, velocity, 153 
 Fanning, J. T., 306 
 Fanning's tables, 322 
 Fans, 929-944 
 
 Biram's ventilator, 931 
 
 blades, 943 
 
 capacities, 941 
 
 Capell ventilator, 933 
 
 centrifugal, 930 
 
 construction, 942 
 
 diameter and speed, 934, 942 
 
 disk type, 929 
 
 equivalent orifice, 935 
 
 evase stack, 934 
 
 exhaust, 930 
 
 force fans and blowers, 930 
 
 Guibal ventilator, 932 
 
 inlet velocity, 935 
 
 manometrical efficiency, 942 
 
 mechanical efficiency, 942 
 
 motors, 934, 944 
 
 Murgue's formula, 936 
 
 Murphy ventilator, 933 
 
 Nasmyth, 931 
 
 position, 941 
 
 ratings, table, 938-940 
 
 reversible, 936 
 
 Schiele ventilator, 932 
 
 Sirocco fan, 933 
 
 size of orifice, 942 
 
 spiral casing, 944 
 
 standard air, 935 
 
 Sullivan fans, 936, 937 
 
 tests, 944 
 
 vacuum and plenum systems, 
 930 
 
 Waddle ventilator, 932 
 Fathom, 1 
 
 Feedwater of boilers, 422 
 Fire, effect of, on concrete, 210 
 
 temperature of, 449 
 Firedamp, 859, 864 
 
 whistle, 895 
 Fires in boilers, 434 
 
 in mines, 945-949 
 First aid, 969-975 
 Flapping of belts,. 274 
 Flue dust, briqueting, 968 
 Flumes, 318 
 
 Forbes' gas indicator, 895 
 Forces, composition and resolution 
 of, 153 
 
1158 
 
 INDEX 
 
 Forces, moments of, 154 
 
 Form work for reinforced concrete, 
 
 220 
 
 Formulas, mathematical, 20 
 Foster's rule for shaft pillars, 697 
 Fractions, arithmetical and decimal, 
 
 19, 20 
 
 Fraser & Chalmers, 251, 252 
 French coal, weights of, 290 
 French Coal Commission, 448 
 Frick, H. C., Coke Co., 230, 604, 
 
 708, 738, 982 
 Friction, angle of, 160 
 
 coefficient of, 159 
 
 definition, 159 
 
 in haulage, 758 
 
 mine cars, 163 
 
 reduction by lubrication, 166 
 
 resistance of shafting, 162 
 
 rolling, table, 160, 162 
 
 tables of coefficients and angles 
 of repose, 160-162 
 
 tests on mine-car wheels, tables, 
 
 164, 165 
 
 Fuel oils, 537; see also Petroleum. 
 Fuels, 365-406 
 
 air required for combustion, 451 
 
 alcohol, 536 
 
 briqueting, 967 
 
 carbon, 365 
 
 coal, 368 
 
 coking C9als, 374 
 
 combustion of, 363 
 
 gas engine, 536 
 
 gaseous, 398 
 
 gasoline, 536 
 
 hydrogen, 365 
 
 kerosene, 537 
 
 liquid, comparative value, 537 
 
 peat, 367 
 
 petroleum, 395 
 
 temperature of ignition, 448 
 
 wood, 365 
 Fuller, W. B., 212 
 Functions, trigonometric, of angles, 
 
 55 
 
 Fundamental relations in trigo- 
 nometry, 55 
 Furnace fittings, 417 
 
 mine, 927 
 Fuse, 676 
 Fusible plugs, 415, 438 
 
 Galloway, G., 736 
 
 Garforth, Sir William, 877 
 Garforth-Walker gas indicator, 893 
 Gas, coal, analyses, 402, 403 
 
 engine fuels, 536 
 
 indicators, 891 
 
 natural, 400 
 
 natural, prospecting for, 557 
 
 producers, 404, 405 
 
 water, 403 
 Gases, acetylene, 871 
 
 afterdamp, 869 
 
 analyses and heating values 
 398, 399 
 
 as fuels, 398" 
 
 atmospheric pressure, 838 
 
 Gases, atomic weights, 833 
 
 Avogadro's law, 836 
 
 barometers, 839 
 
 blackdamp, 851 
 
 blast-furnace, 398 
 
 by-product, 401 
 
 carbon dioxide, 848 
 
 carbon monoxide, 852 
 
 chemical reactions, weights and 
 volumes of gases, 834, 835 
 
 chemistry of, 831 
 
 coke oven, 402 
 
 density, 836 
 
 diffusion of, 842 
 
 ethylene, 871 
 
 explosibility, relative, 863 
 
 fire damp, 864 
 
 heating value at" 32 F., 400 
 
 hydrogen, 871 
 
 hydrogen sulphide, 871 
 
 methane, 850, 859 
 
 mine, 845 
 
 molecular weights, 834 
 
 nitric oxide, 872 
 
 nitrogen, 848 
 
 nitrogen dioxide, 872 
 
 occluded, 860 
 
 occlusion and transpiration, 843 
 
 olefin, 871 
 
 oxygen, 846 
 
 oxygen and air required for 
 combustion, 447 
 
 paraffin, 870 
 
 percentage composition, 834 
 
 physics of, 836 
 
 rarer mine gases, 870 
 
 specific gravity, 277, 837 
 
 specific heats, 361 
 
 sulphur dioxide, 872 
 
 symbols of elements, 833 
 
 temperature of ignition, 448 
 
 volume, temperature, pressure, 
 etc., relations, 840 
 
 volumes when burned in air, 
 835 
 
 weight and volume of air and 
 
 gases, 841 
 Gasoline, as fuel, 536 
 
 engines, 532 
 
 hoisting engines, 741 
 
 locomotives for haulage plants, 
 
 807 
 
 Gates, dam, 328 
 Gauges, tables of, 291, 292 
 Gay-Lussac's law, 475, 840 
 Geological chart for. United States. 
 551 
 
 maps, construction of, 557 
 Geometrical construction, 38 
 
 progression, 25 
 Geometry, 36-43 
 
 in railroad surveys, 109 
 Geordie lamps, 886 
 George's Creek coal district, 617 
 Gilberton water shaft, 350 
 Glossary of mining terms, 1101 
 
 of wire-rope terms, 262 
 Gobert system of freezing, 591 
 Gordon electric cells, 516 
 
INDEX 
 
 1159 
 
 Gottlieb's values for woods as fuel 
 
 365, 366 
 
 Gould, E. Sherman, 320 
 Gow, Alex M., 483 
 Gradient, hydraulic, 320 
 Grady, P. A., 811 
 Graham, 854 
 Graham's law, 842 
 Grates, boiler, 417 
 Gravity, center of, 155 
 Great Britain, currency, 16 
 
 weights and measures, 15 
 Griffith, William, 705 
 Grouting, 194 
 Guibal, 862 
 
 ventilator, 932 
 Gyration, radius of, 158 
 
 Haas, 848, 853, 856, 861 
 Haas' formula, 392, 393, 394 
 Haddock, 733 
 Hailwood lamp, 888 
 
 locks for lamps, 879 
 Halberstadt, Dr. G. H., 969 
 Haldane, Dr., 846, 849-851, 854 
 
 858, 869, 872-874 
 Hall, Clarence, 872 
 Hamilt9n Coal Co., 260 
 Hardy indicator, 895 
 Harger, 870 
 
 Hauger gas-signaling apparatus, 896 
 Haulage, 758-831 
 
 animal haulage, 775 
 
 calculations for jig planes, 784 
 
 calculations for low- and high- 
 speed, endless-rope engines, 
 971 
 
 calculations for self-acting in- 
 clines, 781 
 
 comparison of endless- and tail- 
 rope systems, 794 
 
 comparison of gasoline and other 
 motors, 810 
 
 compressed-air haulage, 798 
 
 cost of gasoline-locomotive 
 haulage, 809 
 
 cost of mule haulage, 777 
 
 curvature, 759, 763 
 
 diamond switch, 773 
 
 electric-locomotive, 815 
 
 endless-rope, 785 
 
 engine planes, 785 
 
 engines for tail-rope system, 793 
 
 entry switches, 770 
 
 friction, 758 
 
 frogs, 771 
 
 gasoline-motor, 807 
 
 gauge of track, 765 
 
 grade equivalents, table, 761 
 
 grade resistance, 760 
 
 grades and their effects, 781 
 
 grips and grip cars, 788 
 
 high speed endless-rope haul- 
 age, 790 
 
 inertia, 762 
 
 jig planes, 783 
 
 mules, 775 
 
 overhead endless-rope haulage, 
 790 
 
 Haulage, rail elevation, 764 
 
 rails, weight of, 766 
 
 resistances, 758 
 
 room and branch switches, 771 
 
 safe grade for mules, 778 
 
 self-acting inclines, 778 
 
 side-entry, 789 
 
 slopes and engine planes, 784 
 
 spikes for rails, 769 
 
 steam-locomotive haulage, 795 
 
 table of rails and accessories, 
 764, 766, 768 
 
 tail-rope system, 792 
 
 ties, 768, 770 
 
 track laying, notes, 773 
 
 tracks on inclines, 779 
 
 trackwork, 762 
 
 weight of rails for track, 768 
 Hawksley's formula, 321 
 Hawsers, 243, 250 
 Hazard Manufacturing Co., 237 
 Hazleton boilers, 416 
 Heading machines, 647 
 Heat, 352-364 
 
 absolute zero, 353 
 
 boiling point of water at vari- 
 9113 altitudes, 363 
 
 British thermal unit, 353 
 
 calorie, 354 
 
 coefficients of linear expansion, 
 359 
 
 combustion of fuels, 363 
 
 conducting power of materials, 
 421 
 
 conduction of, 359 
 
 effect of, on concrete, 211 
 
 equivalence of units, 354 
 
 expansion by, 354 
 
 mechanical equivalent of heat, 
 354 
 
 melting points and latent heat 
 of fusion of metals, 362 
 
 of burning carbon, 449 
 
 radiation of, 359 
 
 sensible and latent, 361 
 
 specific, 360 
 
 thermometers, 352 
 Heberle gate, 955 
 Heine boilers, 416 
 Hemp rope for power transmission, 
 
 Hewitt, William, 251, 253, 264 
 Hillebrand, W. F., 378 
 Hoisting, 739-758 
 
 balanced, 744 
 
 calculations for first-motion 
 engines, 751 
 
 calculations for second-motion 
 engines, 757 
 
 compressed-air engines, 741 
 
 conical drums, 745 
 
 Despritz system, 750 
 
 electric engines, 742 
 
 engines, 739, 740 
 
 first-motion engines, 741 
 
 flat ropes and reels, 746 
 
 forces and moments, 755 
 
 gasoline engines, 741 
 
 hand- and horsepower hoists, 739 
 
1160 
 
 INDEX 
 
 Hoisting, hydraulic engines, 742 
 
 Koepe system, 748 
 
 Monopol system, 751 
 
 reels, 746 
 
 ropes, 239 
 
 second-motion engines, 740 
 
 steam-power engines, 740 
 
 tail-rope balancing, 745 
 
 Whiting system, 749 
 Honeycombing of boiler plates, 
 
 426 
 
 Hood, O. P., 811, 813 
 Horsepower, compressed air require- 
 ment, 807 
 
 definition, 153 
 
 of a stream, 331 
 
 of belts, 273 
 
 of hoisting engines, 754 
 
 of Manila ropes, 269 
 
 of steam engines, 456 
 
 required to raise water, table, 
 339 
 
 standard of boiler, 431 
 
 transmission by shafting, 271 
 
 transmission by wire rope, 266, 
 
 267 
 
 Hughes, H. W. 775, 875, 881 
 Hughes, Thomas E., 254 
 Hughes's rule for shaft pillars, 698 
 Humidifying air current in mines, 
 
 902 
 
 Humphrey, H. A., 398 
 Hunt, C. W., 486 
 Hunt, C. W., Co., 967 
 Hutchinson, 869 
 Hyatt bar for reinforced concrete, 
 
 217 
 
 Hydrated lime, 188 
 Hydraulic coal classifiers, 953 
 
 gradient, 320 
 
 hoisting engines, 742 
 
 limes, 188 
 Hydraulics, 307-352 
 
 conversion factors, 314 
 
 definitions, 307 
 
 discharge of water, table, 311 
 
 flow of water in open channels, 
 315 
 
 flow through pipes, 320 
 
 flumes, 318 
 
 formulas for velocity, 321 
 
 gauging by weirs, 312-314 
 
 gauging water, 309 
 
 horsepower required to raise 
 water, table, 339 
 
 irrigation quantity, tables, 330 
 
 mine dams, 327 
 
 outside dams, 328 
 
 pump machinery, 333 
 
 reservoirs, 327 
 
 tunnels, 319 
 
 water elevators, 349 
 
 water power, 331 
 
 See also Water. 
 Hydrogen, 871 
 
 as fuel, 365 
 
 sulphide, 871 
 Hydrostatics, 303 
 Hygrometers, 844, 904 
 
 Ignition, temperature of, 448 
 
 Ilgner system, 742 
 Imperial measure, 15 
 Inclined plane, power required to 
 hoist on, 151 
 
 stress in hoisting ropes on, 
 
 254 
 
 Incrustation on boilers, 424 
 Indian woods, weight, 282 
 Indiana coal mining, 618 
 Indicators, gas, 891 
 Inertia, moments of, 157 
 Injectors for boiler feeding, 422 
 Injuries, treatment of, 969 
 Institution of Civil Engineers of 
 
 Great Britain, 398 
 Instruments, care of surveyor's, 92 
 leveling, 73 
 
 surveyor's, 60-67 
 Interest on money, computing, 23 
 Internal-combustion engines, 532- 
 548 
 
 at mines, 538 
 
 back firing, 547 
 
 carbureter troubles, 548 
 
 carbureters, 541 
 
 compression troubles, 548 
 
 engine starters, 545 
 
 four-cycle engines, 532, 533 
 
 fuels, 536 
 
 gasoline-engine cycles, 532 
 
 ignition, 542 
 
 misfiring, 547 
 
 operation, 545 
 
 preignition, 548 
 
 spark plugs, 544 
 
 starting the engine, 545 
 
 stationary gas engines, 540 
 
 stopping the engine, 545 
 
 troubles and remedies, 547 
 
 two-cycle engines, 533, 534 
 International Bureau of Weights 
 
 and Measures, 11 
 Interstitial currents, 956 
 Involution, 25 
 
 by logarithms, 34 
 Iowa coal mining, 618 
 Iron, strength of, 170 
 
 plates, weights, 293 
 
 wrought, weight, 293, 298, 301 
 Irrigation quantity, tables, 330 
 
 Jeffrey-Robinson coal washer, 953 
 
 Jet pump, 349 
 
 Jig planes, 783 
 
 Johnson, A. L., 217 
 
 Johnson, W. R., 288 
 
 Joule's investigations, 354 
 
 Kahn trussed bar for reinforced 
 concrete, 218, 226 
 
 Kehley's Run Colliery, 327 
 
 Kent's method of determining heat- 
 ing value of coal, 392-394 
 
 Kentucky Mining Institute, 731 
 
 Kerosene as fuel, 537 
 
 as remover of scale on boilers, 
 425 
 
INDEX 
 
 1161 
 
 Kind-Chaudron system of shaft 
 
 sinking, 592 
 Kinetic energy, 153 
 King, A. J., 811, 813, 866, 871 
 Knight bucket impact wheel, 475 
 Koehler, 862 
 
 Koepe system of hoisting, 748 
 Koppers' regenerative ovens, 401 
 Kutter's formula, 317, 321 
 
 Lacing of power belts, 274 
 
 Laminations of boiler plates, 426 
 Lamps, 874-891 
 
 acetylene, 900 
 
 Ashworth-Hepplewhite- Gray 
 lamp, 888 
 
 bonnets, 876 
 
 bull's eye, 887 
 
 cap electric lamps, 898 
 
 Chesneau lamp, 875, 890 
 
 circulation of air, 877 
 
 Clanny lamp, 880, 883, 886 
 
 cleaning, 883 
 
 Clowes' hydrogen lamp, 889, 983 
 
 Davy lamp, 880, 883, 884 
 
 deflector, 887 
 
 design, 875 
 
 electric, 896 
 
 Evan Thomas lamp, 886 
 
 failure of lamps, 884 
 
 gas indicators and signaling 
 devices, 891 
 
 gauzes, 875 
 
 Geordie lamps, 886 
 
 glasses, 876 
 
 Hailwood lamp, 888 
 
 height of gas cap, 882 
 
 igniters, 878 
 
 illuminating power, 880 
 
 locks, 878 
 
 Marsaut lamp, 874-876, 880, 
 887 
 
 Mauchline lamp, 887 
 
 Mueseler lamp, 877, 887 
 
 multiple gauzes, 876 
 
 oils, 879 
 
 Pieler lamp, 890 
 
 principle and origin, 874 
 
 protector lamp, 888 
 
 specifications, 875 
 
 Stephenson lamp, 880, 886 
 
 Stokes' alcohol lamp, 889 
 
 Stuchlick acetylene lamp, 891 
 
 testing fpr gas, 882 
 
 testing for methane, 881 
 
 Tombelaine acetylene lamp, 891 
 
 wicks, 877 
 
 Wolf lamp, 876, 878, 880, 888 
 Lang lay ropes, 238, 242 
 Latitude, determination of, in sur- 
 veying, 105 
 
 and departures, tables, 1074 
 Law of mechanics, 149 
 Lay of wire ropes, 238 
 Lead, strength of, 170 
 League, length of, 1 
 Le Chatelier, 805 
 
 flask, 204 
 
 gas indicator, 892 
 
 Leclanche' cell, 514 
 
 Lehigh and Wilkes-Barre Coal Co., 
 
 604, 734 
 
 Lehigh Valley Coal Co., 735 
 Lehmann, 872 
 
 Leschen & Sons Rope Co., 237 
 Leveling, 73-76 
 
 barometric, 140 
 Lever safety valve, 414 
 Levers, 149 
 Lewes, Prof., 948 
 Libin gas indicator, 893 
 Lime mortars, 191 
 Limes, 188 
 Line shafting, 270 
 Linear measures, 1 
 Link-Belt Engineering Co., 237, 269, 
 
 962, 968 
 Lippman system of shaft sinking, 
 
 593 
 
 Liquid measure, 7, 8 
 Liquids, comparative value as fuel, 
 537 
 
 compressibility, 307 
 
 equilibrium, 303 
 
 pressure, 303-306 
 
 specific gravity, 277, 538 
 
 specific heats, 361 
 Liveing gas indicator, 892 
 Locomotive boilers, inspection, 441 
 Locomotives, electric, for haulage, 
 815 
 
 for mine haulage, 795 
 
 gasoline, 807 
 Logarithmic tables, 1009 
 Logarithms, 29-36 
 
 of trigo nometric functions, 
 
 table, 1028 
 
 Longitude and time, 10 
 Longwall system of mining, 652-666 
 
 advantages and disadvantages, 
 654 
 
 buildings, pack walls, and stow- 
 ing, 666 
 
 control of roof pressure, 665 
 
 in contiguous seams, 664 
 
 in flat seams, 655 
 
 in inclined thick seams, 664 
 
 in panels, 661 
 
 in pitching seams, 657 
 
 in thick seams, 663 
 
 labor and trade conditions, 654 
 
 rectangular long wall, 656 
 
 roadways, 665 
 
 roof pressure, 653 
 
 Scotch or Illinois plan, 655 
 
 starting workings, 664 
 
 surface damage, water, gas, etc., 
 654 
 
 timbering the face, 666 
 
 waste, 653 
 Lord and Haas' method, 392, 393, 
 
 394 
 
 Lord, N. W., 400 
 Lovatt, A. L., 788 
 Low gas-signaling apparatus, 896 
 Lubricant tests, 168 
 Lubricants, best for different pur- 
 poses, 169 
 
1162 INDEX 
 
 Lubrication, 166 
 
 of wire ropes, 257 
 Lucas, F. E., 401 
 Lungmotor, 987 
 
 McCutcheon gas indicator, 893 
 McDonald, W. Va., coal, 380 
 McKibben, Frank P., 705 
 McMyler dump, 967 
 MacGeorge, E. F., 555 
 Machine mining, 644 
 Machinery, crushing, 950 
 
 elementary forms, 149 
 Manila ropes, horsepower of, 269 
 Mapping, in surveying, 95 
 Maps, geological, 557 
 Mariotte's law, 840 
 Marks' investigations, 362 
 Marsaut lamp, 874-876, 880, 887 
 Marsh gas, 859 
 Marcus screen, 960 
 Martin, R. D., 402 
 Masonry, 234-236 
 
 absorptive power of stone, 230 
 
 brick, 236 
 
 crushing strength of stones and 
 piers, 235 
 
 dams, 331 
 
 durability of stone, 236 
 
 materials, coefficients of fric- 
 tion and angles of repose, 
 160 
 
 measures of, 6 
 
 safe-bearing values of materials, 
 234 
 
 strength of stone, 234 
 
 supports for excavations, 735 
 Massachusetts Institute of Technol- 
 ogy, 421 
 Materials, properties of, 275 
 
 strength of, tables, 169, 170, 
 
 171 
 
 Mathematics, 18-59 
 Mauchline lamp, 887 
 Measure, angular, 8 
 
 board, 302 
 
 brickwork, 6 
 
 circular, 9 
 
 conversion factors, metric and 
 United States, 13, 14 
 
 displacement of ships, 7 
 
 dry, 7 
 
 Great Britain, 15 
 
 linear, 1 
 
 liquid, 7 
 
 masonry, 6 
 
 metric system, 10 
 
 square, 3 
 
 surface, 3 
 
 surveyor's linear, 1 
 
 surveyor's square, 3 
 
 timber, 301 
 
 time, 10 
 
 tonnage of ships, 7 
 
 volume, 6 
 
 water, volumes and weights, 8 
 
 weight, 3 
 Measurements of boiler tubes, 297 
 
 of coal, 287, 288 
 
 Mechanical powers, 149 
 Mechanics, 149-169 
 
 center of gravity, 155 
 
 composition and resolution of 
 forces, 153 
 
 elements, 149 
 
 falling bodies, 153 
 
 friction, 159 
 
 moment of inertia, 157 
 
 moments of forces, 154 
 
 radius of gyration, 158 
 
 section modulus and moment of 
 resistance, 159 
 
 work, 153 
 Mensuration of solids, 50-54 
 
 of surfaces, 43-50 
 
 Meridian, determination of, in sur- 
 veying, 99 
 Merivale's rule for shaft pillars, 
 
 697 
 
 Metals, melting points and latent 
 heat of fusion, 362 
 
 relative heat conductivities, 359 
 
 specific gravity, table, 277 
 
 strength, 170, 296 
 
 weight, table, 278 
 Methane, 850, 859 
 Methods of mining, 604-666 
 
 Alabama methods, 631 
 
 battery breasts, 626 
 
 blasting after undercutting, 642 
 
 Brown's method, 637 
 
 buggy breasts, 622 
 
 chutes, 623 
 
 cleats, 614 
 
 closed work, 606 
 
 Connellsville, Pa., method, 635 
 
 contiguous seams, 629 
 
 double-chute rooms, 625 
 
 drawing pillars, 648 
 entries, 607 
 
 flat seams, 616 
 inclined seams, 626 
 longwall w 9 rk, 644, 652-666 
 machine mining, 644 
 mining and blasting coal, 638 
 New Castle, Col., method, 631 
 open work, 604 
 panel system, 637 
 pillar-and-stall systems, 634 
 pillar drawing, 648 
 pitching seams, 619 
 roof slip, 616 
 
 room-and-pillar systems, 607 
 rooms, 611 
 
 shooting off the solid, 638 
 single-chute rooms, 624 
 small seams, 621 
 steam-shovel mines, 605 
 Tesla, Cal., method, <632 
 thick and gaseous seams* 620 
 thick non-gaseous seams, 621 
 undercutting and solid shooting, 
 
 643 
 Williams, J. L., method, 636 
 
 Metric system, 10 
 
 conversion factors, 13 
 
 Mice, effect of afterdamp on, 857 
 
 Midvalley Coal Co., 810 
 
INDEX 
 
 1163 
 
 Vline laws of Pennsylvania, 906, 918 
 Mine-rescue apparatus, 986 
 
 work. 984 
 Mine safety, 975-989 
 
 mismanipulation of controlling 
 devices, 980 
 
 premium system and company 
 rules, 976 
 
 protecting from electricity, 980 
 
 safeguarding machinery, 978 
 
 safety practices of Prick Coke 
 Co., 982 
 
 supervision, 975 
 Vline surveying, laying out sharp 
 
 curves, 133 
 
 shafts and slopes, 77-82 
 underground, 83-92 
 Vf ine timbering, 707-730 
 longwalfface, 666 
 Vline water, effect of, on concrete, 
 
 210 
 
 Minerals, specific gravity, table, 276 
 Vliner's inch, 309 
 Vlines, accidents, 969, 975 
 
 air, 846 
 
 air affected by gasoline locomo- 
 tives, 811, 812 
 
 air after blasting, analyses, 670 
 
 air, humidity of, 843 
 
 batteries for signaling, 514 
 
 blasting, 687 
 
 blasting, substitutes for, 685 
 
 cars, friction, 163-166 
 
 coal-bearing formations, 550 
 
 compressed-air locomotives, 798 
 
 dams, 327, 337 
 
 drainage of shafts, 596 
 
 effect of free faces, 688 
 
 electric-locomotive haulage, 815 
 
 entries, 607 
 
 explosive condition, 900 
 
 explosives and blasting, 672 
 
 fires, 945-949 
 
 flushing of culm, 702 
 
 furnace construction, 927 
 
 gases, 845 
 
 gasoline-motor haulage, 807 
 
 haulage, 758-831 
 
 heat and humidity, effect on 
 miners, 873 
 
 hoisting, 739-758 
 
 induction motors, 509 
 
 internal combustion engines, 
 538 
 
 lamp houses, 884, 899 
 
 lamp stations, 602 
 
 machinery, lubrication, 166 
 
 methods of working, 604-666 
 
 mules, 775 
 
 opening a mine, 563-604 
 
 plan arrangement, 925 
 
 prospecting, 549 
 
 pump machinery, 333 
 
 pumps, electrically driven, 343 
 
 pumps for acid waters, 346 
 
 refuse dams, 331 
 
 reporting on coal lands, dia- 
 gram, 560 
 
 rooms, 611 
 
 Mines, sampling and estimating 
 amount of mineral available, 
 559 
 
 sampling coal for analysis, 378 
 
 shaft bottoms, 599 
 
 shaft lining of concrete, 230 
 
 shafts, 578-596 
 
 slope bottoms, 596 
 
 slopes, 575 
 
 stables, 601 
 
 steam l9comotives, 795 
 
 supporting excavations, 692- 
 738 
 
 surf ace tracks, 603 
 
 telephone system, 521 
 
 trackwork, 762 
 
 tunnels, 509 
 
 ventilation, 831-945 
 
 water buckets, 350 
 
 water elevators, 349 
 
 wedging down coal, 685 
 
 wire ropes, use of, 237 
 Mining engineering rule for shaft 
 pillars, 697 
 
 machines, 644 
 
 methods, 604-666 
 
 terms, glossary, 1101 
 Mixers for concrete, 223 
 Modulus of elasticity, 171 
 
 of rupture, 178 
 
 of rupture of stone, 234 
 
 section, 159 
 
 Molecular weights of elements, 834 
 Moment of resistance, 159 
 
 of beams, 176 
 Moments of forces, 154 
 
 of inertia, 157 
 Monetary systems, 16, 17 
 Monopol system of hoisting, 751 
 Moore, Edwin A., 401 
 Mooring lines, 250 
 Morin's experiments, 720 
 Mortars, 191-205 
 
 adhesion, 194 
 
 cement, 191 
 
 composition in brick piers, 235 
 
 compressive strength, 193 
 
 grouting, 194 
 
 laying in freezing weather, 194 
 
 lime. 191 
 
 materials required, 192 
 
 percentage of water for sand, 
 199 
 
 properties of cement, 193 
 
 sand for tests, 199 
 
 retempering, 194 
 
 shrinkage, 194 
 
 tensile strength, 193 
 Motors, current, 332 
 
 electric, 497 
 
 Mueseler lamp, 877, 887 
 Mules for mine haulage, 775, 809 
 Multiplication by logarithms, 32 
 Murgue, M. D., 910, 936, 942 
 Murphy ventilator, 933 
 
 Nails, size and weight, 299 
 
 Nasmith, 854 
 Nasmyth fan, 931 
 
1164 
 
 INDEX 
 
 Natural cement, 188, 189 
 
 sines and cosines, tables, 991 
 tangents and cotangents, tables, 
 1000 
 
 Neville's formula, 321 
 
 New Castle, Col., method of work- 
 ing mines, 631 
 
 New England Gas and Coke Co., 
 Everett, Mass., 399, 401 
 
 Nitric oxide, 872 
 
 Nitrogen, 848 
 dioxide, 872 
 
 Nitroglycerin, 667 
 
 Nolten, G., 555 
 
 Norris, R. Van A., 163, 944 
 
 Nova Scotia Steel and Coal Co., 402 
 
 Noyes, W. A., 378 
 
 Numbers, squares and cubes of, 
 tables, 1081 
 
 Nuts, iron, weights, 292 
 proportion, 300 
 
 Ohio State University, 392 
 
 Ohm's law, 485 
 
 Oiling of mine cars, 163 
 
 of mine machinery, 166 
 Oils, for safety lamps, 879 
 
 fuel or compound, 537 
 
 tests, 168 
 Opening a mine, 563-604 
 
 coke ovens, 566 
 
 cost of opening and production, 
 564 
 
 drifts, 568 
 
 engine and pump room, 602 
 
 grades, 565 
 
 location of opening, 567 
 
 locatio.n of surface plant, 565 
 
 mining plant, 566 
 
 mining village, 566 
 
 rock tunnels, 571 
 
 safety appliances, 575 
 
 shafts, 578-596 
 
 sidings, 565 
 
 slope and shaft bottoms, 596 
 
 slopes, 575 
 
 stables,601 
 
 surface tracks for slopes and 
 shafts, 603 
 
 tracks on bottom of slopes and 
 shafts, 596, 599 
 
 tunnels, 569 
 Open work in mines, 604 
 Ormsbee, J. J., 954 
 Orvitz, 870 
 
 Otto cycle engines, 532 
 Oxygen, 846 
 
 required for combustion of 
 gases, 447 
 
 Pamely's rule for shaft pillars, 697 
 
 Panel system of mining, 637 
 Parallelogram of forces, 154 
 Parallelograms, 44 
 Parallelepipeds, 52 
 Parr, 870 
 
 Paul, J. W., 875, 883 
 Peat as fuel, 367 
 Pdclet, 421 
 
 Pelton bucket impact wheel, 475 
 Pelton Water Wheel Co., 322 
 Pennsylvania anthracite coals, an- 
 alyses, 386 
 
 Pennsylvania Coal Co., 229 
 Pennsylvania Gas Coal Co., 403 
 Pennsylvania R. R. Co., 288 
 Percentage, 22 
 Perch, dimensions of, 1, 3, 6 
 Percy, Dr., 948 
 Pescheux gas-signaling apparatus, 
 
 896 
 Petroleum as fuel, 395 
 
 advantages and disadvantages, 
 397 
 
 calorific value, 396 
 
 composition of crude, 395 
 
 flash point and firing point, 395 
 
 prospecting for, 557 
 
 ultimate analysis, 396 
 
 value as fuel compared to coal, 
 
 397 
 
 Pfeiffer, G. W., 900 
 Philadelphia & Reading Coal & Iron 
 
 Co., 350, 603, 725, 727, 969 
 Philippine woods, weight, 281 
 Phosphorus in coal, 370 
 Physics of gases, 836 
 Pick machines, 644 
 Picric acid, 667 
 Pieler lamp, 890 
 Piers, stone masonry, 235 
 Piez, 967 
 Pillar-and-stall systems of mining, 
 
 634 
 
 Pillar drawing, 648 
 Pine Hill coal breaker, 227 
 Pins, surveyor's, 66 
 Pipes, cast-iron, weight, 294 
 
 C9ntents, 295 
 
 dimensions of iron welded, 296 
 
 thickness for heads and pres- 
 sures, 306 
 
 water, friction in, 323 
 
 wood, 306, 307 
 Piping for compressed air, 476 
 
 of boilers, 412 
 
 Pishel's test for coking coal, 377 
 Piston speed for steam engines, 458 
 Pittsburg coal region, 616 
 Plane, inclined, power required on, 
 
 151 
 
 Plane trigonometry, 54-59 
 Plotain, 856 
 Plow-steel ropes, 238 
 Plymouth Coal Co., 733 
 Poetsch system of freezing, 591 
 Polaris, observation of, in surveying, 
 
 101-105 
 Polygons, 45 
 Polyhedrons, 50 
 Porter, 870 
 
 Porter, H. K., Company, 799, 801 
 Portland cement, 188, 189, 195, 204 
 Power, definition, 153 
 
 pumps, 341 
 Power transmission, 264-275 
 
 belt pulleys. 271 
 
 belting, 272 
 
INDEX 
 
 1165 
 
 Power transmission, constants for 
 ropes on different materials, 
 267 
 
 diameters of sheaves, table, 
 266 
 
 distance between bearings of 
 shafts, 270 
 
 flapping of belts, 275 
 
 formula of horsepower trans- 
 mitted, 266 
 
 Jiemp rope, 268 
 
 horsepower transmitted by 
 shafting, table, 271 
 
 horsepower transmitted uy steel 
 rope, 267 
 
 line shafting, 270 
 
 manila ropes, 269 
 
 sheaves, 266 
 
 value of coefficients, table, 
 
 265 
 
 Powers of numbers, 26 
 Preparation of coal, 949-968 
 
 anthracite, preparation of, 958 
 
 bituminous, preparation of, 959 
 
 briqueting, 967 
 
 buckets, 963 
 
 chutes, 962 
 
 corrugated rolls, 950 
 
 cost of unloading, 966 
 
 cracking rolls, 949 
 
 crushing machinery, 949 
 
 disintegrating rolls and pul- 
 verizers, 950 
 
 hammers, 950 
 
 handling of material, 962 
 
 hydraulic classifiers, 953 
 
 interstitial currents, 956 
 
 jigs, 954 
 
 removal of sulphur from coal, 
 957 
 
 screens, 951 
 
 sizing and classifying appa- 
 ratus, 951 
 
 tipple design, 962 
 Pressure of liquids, 303-306 
 Priestly, 849 
 Prismoids, 50 
 
 Problems: air compressors, volume, 
 476 
 
 air current, division, 919 
 
 air current, measurement, 908, 
 912, 917 
 
 air current regulators, 920, 921 
 
 air supply, in combustion, 451 
 
 angle of repose, 160 
 
 angles, latitude and departure, 
 1073 
 
 area of wire, 490 
 
 barometric leveling, 141 
 
 belting, horsepower of, 273 
 
 bending moment of a beam, 176 
 
 boiler efficiency, 433 
 
 boiler feedwater, factor of evap- 
 oration, 433 
 
 boiler feedwater, purification, 
 429 
 
 boiler heating surface, 445 
 
 boiler horsepower and evapora- 
 tion, 431 
 
 Problems: cantilever beam, reaction. 
 
 175 
 
 center of gravity, 156 
 chimney, height and draft, 452, 
 
 453 
 
 coefficient of friction, 159 
 combustion, air required for, 448 
 compressed air storage tanks, 
 
 804, 805 
 compressors for haulage plants, 
 
 806 
 
 cost of opening a mine, 564 
 designing of beams, 178 
 electric current estimates, 495 
 electric current, etc., 485 
 electric current feeders, 497 
 electric-locomotive feeders, 820, 
 
 821 
 
 electric resistance, 488 
 electric wire, resistance, 491 
 electricity, transmission, 493 
 gas required to displace coal, 
 
 400 
 
 gases, chemical reactions, 835 
 gases, ^percentage composition, 
 
 834 
 
 gases, volume, weight, tempera- 
 ture, etc., 840, 841 
 gases, volumes when burned, 836 
 gases, weight, volume, and loss 
 
 in boilers, 446 
 geometrical, 38-43 
 haulage on inclines, 782, 784 
 head of water, 322 
 hoisting, conical drum for, 745 
 hoisting engines, calculations 
 
 for, 754, 758 
 
 hoisting, rope and reel, 747 
 horsepower of haulage engines, 
 
 791, 792 
 
 horsepower of water, 153 
 horsepower required on in- 
 clined plane, 151 _ 
 humidity of mine air, 844 
 inertia, moment of, 158 
 kinetic energy of water, 153 
 levers and power, 1.50 
 logarithmic, 30-36 
 mathematical, 22-29 
 measuring concrete materials, 
 
 212 
 
 mensuration, 46-48 
 mine entries, 611 
 mine locomotive power, 797, 798 
 mine pillars, 696 
 mine shaft timbering, 715 
 mine shaft tubbing, 737 
 mine shafts, size, 579 
 moment of resistance, 159 
 mortar materials, 192, 199 
 power transmission, 268, 269 
 pressure of liquids, 304 
 pulleys in power transmission, 
 
 272 
 pump and horsepower required 
 
 to raise water, 338 
 radius of gyration, 158 
 resistance to haulage, 759, 760, 
 
 761, 762 
 
1166 
 
 INDEX 
 
 Problems: rope-size for hoisting, 245 
 safety valve, weight for, 414 
 sand, percentage of voids in, 
 
 190 
 
 screw, weight raised by, 151 
 section modulus, 159 
 sines of angles, 990 
 siphon discharge, 352 
 solar observations in surveying, 
 
 105 
 
 specific gravity, 275 
 specific heats, 361 
 steam engines, cooling water 
 
 for condenser, 460 
 steam engines, cut off and ex- 
 pansions, 455 
 
 steam engines, horsepower, 457 
 steam engines, injection water 
 
 for condensers, 460 
 steam engines, mean effective 
 
 pressure, 456 
 
 steam engines, piston speed, 458 
 steam pipe, elbows, 412 
 steam pressure, 408, 409 
 steam, quality of, 410 
 stiffness of beams, 178 
 strength of beams and props, 
 
 184 
 
 strength of columns, 181 
 strength of pipes, 174 
 stress, 172 
 surveying, 144-148 
 surveying shafts, 78-80 
 temperature of fire, 450 
 temperature stress, 174 
 ties for mine tracks, 770 
 timber measures, 302 
 time and longitude, 101 
 track curvature, 763 
 trigonometric, 58, 59 
 ventilating pressure, 928 
 water, conversion into steam, 
 
 362 
 
 water velocity, 307, 308 
 wirfe ropes, bending stress, 251 
 Producer gas, 404 
 Progression, arithmetical, 24 
 
 geometrical, 25 
 Prony's formula, 321 
 Properties of materials, 275 \ 
 Proportion, mathematical, 21 
 Props, strength of, 184 
 Prospecting, 549-563 
 
 bore-hole records, 558 
 coal-bearing formations, 550 
 construction of geological maps 
 
 and cross-sections, 557 
 diagram for reporting on coal 
 
 lands, 560 
 dip and strike, 558 
 drilling, 553 
 earth augers, 553 
 exploration by drilling or bore 
 
 holes, 553 
 for petroleum, natural gas, and 
 
 bitumen, 557 
 outfit, 549 
 percussion drills, 554 
 plan of operations, 549 
 
 Prospecting, sampling and estimat- 
 ing amount of mineral, 559 
 Protector lamp, 888 
 Psychrometers, 844 
 Pulley, belt, for power transmission, 
 271 
 
 element of machinery, 152 
 Pulmotor, 989 
 Pulsometer, 349 
 Pump machinery, 333-352 
 
 air-lift, 349 
 
 amount of water raised by 
 single-acting lift pump, 340 
 
 boiler feed-pumps, 335 
 
 capacity, table, 336, 340 
 
 centrifugal, 343 
 
 Cornish pumps, 333 
 
 depth of suction, 338 
 
 discharge at various piston 
 speeds, 344 
 
 electric current consumed for 
 pumping water, 342 
 
 electrically driven, in mines, 
 343 
 
 for acid waters, 346 
 
 foundations, 346 
 
 horsepower required, 336 
 
 jet pump, 349 
 
 management, 346 
 
 packing, 333 
 
 piston speed, 335 
 
 power, 341, 342 
 
 power, electrically driven, 342 
 
 ratio of areas to diameters of 
 cylinders, 336, 337 
 
 ratio of steam and water 
 cylinders, 335 
 
 simple and duplex pumps, 333 
 
 sinking pumps, 346 
 
 speed of water through, 334 
 
 stations, 346 
 
 vacuum, 349 
 
 valves, 341 
 Puzzolan cement, 188 
 Pyramids, 53 
 
 Quin, Robert A., 289 
 
 Radiation of heat, 359 
 
 Radii and deflection, table, 111 
 
 Radius of gyration, 158 
 
 Railroad surveying, 109 
 
 Rails, table 9f, 764, 766, 768 
 
 Ralph's gas indicator, 893 
 
 Ramsay, Sir William, 845 
 
 Ramsey, Robert, 604 
 
 Rankine's formula, 180 \ 
 
 Rjiteau turbine, 409, 470 
 
 Ratio, 21 
 
 Reactions of beams, 175 
 
 Reciprocals, 23 
 
 Recovery work, 985 
 
 Refraction, table, 107 
 
 Refuse dams, 331 
 
 Regulators of air current, 919, 920 
 
 Reinforced concrete, 214 
 
 Repose, angle of, 160 
 
 Rescue work, 984 
 
INDEX 
 
 1167 
 
 Reservoirs, 327 
 Resistance, moment of, 159 
 Resolution of forces, 153, 154 
 Resultant of forces, 153 
 Resuscitation apparatus, 987 
 Reversing air current, 985 
 Reynoldsville coal region, 617 
 Richards, Frank, formula, 477 
 Richards, Prof. R. H., 955, 956 
 Right angles, 9 
 Rings, 49 
 
 cylindrical, 52 
 Risdon Iron Works, 309 
 Rittinger, 955 
 Rivets, shearing and bearing values, 
 
 table, 173 
 Roadway, surface, rolling friction 
 
 for, 162 
 
 Roane Iron Co., 809 
 Robb-Mumford boilers, 416 
 Rock tunnels, 571 
 Roebling's line wire, 494 
 Roebling's Sons Co., John A., 237, 
 
 245, 264, 266, 291 
 Roller bearings on mine-car wheels, 
 
 166 
 
 Rolling friction, table, 160, 162 
 Root, cube, 27, 1081 
 
 fourth and fifth, 28 
 
 method of extracting, 29 
 
 square, 26, 1081 
 Rope, glossary of terms, 262 
 
 hemp, 268 
 
 manila, 269 
 
 steel, 237 
 
 strength of, 183 
 
 wire, 237 
 
 Roper's safety-valve rules, 414 
 Rupture, modulus of, 178 
 
 Safety devices, 575, 982 
 
 factor of, 172 
 
 lamps, 874-891 
 
 valves, 414 
 Salt, W. G., 788 
 Sand for mortar tests, 199 
 
 used in cements, 189-191 
 Scale of tenths of a foot, 2 
 Scale, on boilers, 425 
 Schiele ventilator, 932 
 Schmidt, E. C., 759 
 Scholz, 873 
 Schondorff, 805 
 Scotch boilers, 416 
 
 longwall system of mining, 
 
 655 
 
 Screens, coal, 951 
 Screw, element of machinery, 151 
 
 threads, proportions, 300 
 Screws, wood, 298 
 Scribner's rule, 302 
 Seale ropes, 240, 242, 244 
 Sea-water, effect on concrete, 210 
 Section modulus, 159 
 Sectors, 49 
 
 Sederholm, E. T., 251, 252 
 Segments, circular, 49 
 
 spherical, 52 
 Self rescuer, 987 
 
 Settling factors for minerals in 
 
 water, 956 
 
 Sewell seam coal, 380 
 Shade Coal Mining Co., 810 
 Shaf er resuscitation method, 970, 987 
 Shafting, frictional resistance of, 162 
 
 line, 270 
 Shafts, bottoms, 599 
 
 buckets, 580 
 
 cementation process, 591 
 
 compartments, 578 
 
 construction of, 578-596 
 
 covering, 582 
 
 data, table, 576, 577 
 
 drainage and pumping, 596 
 
 draining the ground, 586 
 
 enlarging and deepening, 593 
 
 freezing processes, 591 
 
 Kind-Chaudron system, 592 
 
 lining of concrete, 230 
 
 Lippman system, 593 
 
 long-hole method, 585 
 
 pneumatic process, 590 
 
 shoes for shaft sinking, 588 
 
 sinking head frame, 581 
 
 sinking through firm ground, 
 . 5 83 
 
 sinking through running ground, 
 586 
 
 sinking tools, 580 
 
 size, 578 
 
 surveying, 77 
 
 Triger method, 590 
 
 upraising, 594 
 
 ventilation and lighting, 583 
 Shaw gas-testing machines, 895 
 Shearing stress, 171 
 
 values of rivets, table, 173 
 Sheaves for wire rope transmission, 
 
 266 
 
 Sheet-metal gauges, 291 
 Shipping, measures used in, 7 
 Shoes for shaft sinking, 590 
 Signs, mathematical, 18 
 
 trigonometric, 55 
 Simon's method, 856 
 Simple stress, 171, 172 
 Sines, tables of, 989, 991 
 Single shear, 172 
 Sinking mine shafts, 583 
 Siphons, 351 
 Sirocco fan, 933 
 Slope bottoms, 596 
 Slopes in mines, 575 
 
 surveying, 82 
 Sluice head of water, 310 
 
 Smith, Joseph, 877 
 Solar observation, 
 
 in surveying, 105 
 Solid shooting, 638 
 Solids, center of gravity, 156 
 
 mensuration of, 50-54 
 
 specific heats, 360 
 Southern Coal and Coke Co., 809 
 Spark plugs of eng-ines, 544 
 Specific gravity, 275 
 
 cement, 203 
 
 coal, tables, 286, 288 
 
 dry woods, 278 
 
 gases and vapors, table, 277 
 
1168 
 
 ' INDEX 
 
 Specific gravity, liquids, 277 
 
 metals, table, 277 
 
 minerals and earth, table, 276 
 
 miscellaneous, 278 
 Specific heat, 360 
 Specification for cement, 204 
 Sphere, 51 
 Spherical segments, 52 
 
 zcfties, 52 
 
 Spikes, size and weight, 299 
 Spillways of dams, 329 
 Splicing wire rope, 255, 256 
 Splitting of air current, 918, 922 
 Spontaneous combustion, 948 
 Spring Valley Coal Co., 735 
 Square measure, 3 
 
 root, 26, 1081 
 
 Squares of numbers, tables, 1081 ' 
 Squibs, 676 
 Stadia surveying, 134 
 Stag Canon Fuel Company, 684, 
 
 Stag Canon Mines, 402 
 
 Stanley header, 647 
 
 Stassart, 880, 881 
 
 Stationary engineers, rules for, 473 
 
 Steam, flow of, 410 
 
 pipes, covering for, 419 
 pipes for engines, 412 
 quality, 410 
 resistance of elbows and valves, 
 
 411 
 
 saturated, properties, 406, 407 
 superheated, 409 
 weight delivered, table, 411 
 Steam engines, 454-474 
 
 area of piston rod, allowance 
 
 for, 458 
 clearance, 454 
 comparison with turbines, 
 
 469 
 compound slide-valve engine, 
 
 462 
 
 condensers, 459 
 condensing slide-valve en- 
 gine, 461 
 Corliss engine, compound, 
 
 461, 463 
 cut-off, 455 
 cylinder ratios, 458 
 engine management, 460 
 faulty bearings, 463 
 faulty brasses, 466 
 faulty oiling, 467 
 grit in bearings, 468 
 hoisting engines, 740 
 horsepower, 456 
 hot bearings, 465 
 improper valve setting, 464 
 jet condenser, 460 
 mean effective pressure, 455 
 mechanical efficiency, 458 
 non-condensing slide-valve 
 
 engine, 461 
 
 oil and grease cups, 461 
 piston speed, 458 
 pounding of engines, 463 
 priming, 464 
 ratio of expansion, 455 
 
 Steam engines, requirements, 454 
 reversal of pressure, 464 
 rules for stationary engineers, 
 
 starting and stopping, 460 
 
 stating sizes, 457 
 
 surface condensers, 459 
 warming up, 460 
 Steam-shovel mines, 605 
 Steam turbines, 469 
 
 care of gears in DeLaval 
 turbines, 472 
 
 comparison with engines, 469 
 
 consumption of steam, 469 
 
 economy, 472 
 
 finding horsepower, 470 
 
 operation, 471 
 
 troubles, 470 
 
 types, 469 
 
 Stearns, Irving A., 288 
 Steavenson, A. L., 895 
 Steel plates, weights, 293 
 
 reinforcement of concrete, 214 
 
 rope, see Wire Ropes. 
 
 strength of, 170 
 
 supports for excavations, 730 
 
 tape, surveyor's, 66 
 Stephenson, George, 874, 876 
 Stephenson lamp, 880, 886 
 Stirling boilers, 416 
 Stirling, Paul, 958 
 Stokers, mechanical, 418 
 Stokes' alcohol lamp, 889 
 Stone, absorptive power, 236 
 
 crushing strength, 234, 235 
 
 durability, 236 
 
 in masonry, 234 
 Straight line formula, 180 
 Strain, 171 
 Strength of materials, 169-187 
 
 beams, table, 174, 186, 187 
 
 brick in masonry, 236 
 
 cement briquets, 201 
 
 cement mortars, 193 
 
 cement, table, 208 
 
 chains, 183 
 
 columns, 180 
 
 cylindrical shells and pipes, 
 174 
 
 metals, 170, 296 
 
 ropes, 183 
 
 seasoned timber, 184 
 
 stone in masonry, 234 
 
 tables, 170, 171, 181, 186 
 
 wire ropes, 246-249 
 
 wood, 171 
 Stress, combined, 182 
 
 definition, 169 
 
 direct, formulas, 172 
 
 of concrete, 211 
 
 on wire rope, 251 
 
 Stromberg-C a rlson Tele phone 
 Manufacturing Company, 
 521 
 
 Stuchlick acetylene safety lamp, 891 
 Suction lift of pumps, 338 
 Sullivan fans, 936, 937 
 Sullivan pressed-steel plank holder, 
 223 
 
INDEX 
 
 1169 
 
 Sulphur dioxide, 872 
 
 in coal, 370 
 
 Sun, parallax in altitude, table, 106 
 Supporting excavations, 692-738 
 
 advantages of steel timbering, 
 735 
 
 barrier pillars, table, 699, 700 
 
 built-up packs and cribs, 705 
 
 chain pillars, 699 
 
 coal pillars, 692 
 
 cost of steel and wood timber- 
 ing, 733 
 
 dry filling, strength, 706 
 
 entry pillars, 697 
 
 flat seams, 707 
 
 flushing of culm, 702 
 
 masonry shaft lining, 735 
 
 packs and cribs, 705 
 
 pillars in inclined seams, 698 
 
 pitching seams, 712 
 
 reserve pillars, 699 
 
 room pillars, 695 
 
 shaft linings, 735 
 
 shaft pillars, rules, 697 
 
 slope pillars, 696 
 
 squeeze and creep, 701 
 
 steel and masonry supports, 730 
 
 steel gangway timbers, 732 
 
 timbering with wood, 707 
 
 tubbing, 736 
 
 weight on pillars, 696 
 Surface measures, 3 
 Surfaces, mensuration of, 43-50 
 Surveying, 60-148 
 
 abbreviations, 89 
 
 barometric leveling, 140 
 
 care of instruments, 92 
 
 chain, steel tape, and pins, 65 
 
 circular curves, 109 
 
 clinometer, 67 
 
 compass, 60 
 
 cost of railroad work, 119 
 
 curved railroad tracks, 124 
 
 curves in a mine, laying out, 133 
 
 determination by observing 
 Polaris, 101 
 
 determination of latitude and 
 corrections for altitude, 105 
 
 determination of meridian, 99 
 
 errors in closure, 94 
 
 field notes for curves, 115 
 
 instruments, 60-67 
 
 leveling, 73, 90 
 
 mine corps, 92 
 
 mine surveys, 83 
 
 note taking, 88 
 
 outside surveys, 68 
 
 pitching work, 90 
 
 Polaris, observation of, 101-105 
 
 problems, 144 
 
 radii and deflections, table, 111 
 
 railroad location, 119 
 
 railroad surveys, 109 
 
 shafts, 77 
 
 slopes, 82 
 
 solar observation, 105 
 
 stadia surveys, 134 
 
 time, 100 
 
 transit, 62 
 
 Surveying, transit surveying, 67 
 traversing and mapping, 93 
 underground surveys, 83 
 Surveyor's linear measure, 1 
 
 square measure, 3 
 Suspension bridges, ropes for, 243, 
 
 ^48 
 Susquehanna Coal Co., 163, 288, 
 
 289, 735 
 
 Swan gas indicator, 893 
 Swedish wire rope, 237 
 Swoboda, H. O., 897 
 Sykes, Wilfred, 755 
 Sylvester resuscitation method, 971, 
 
 987 
 
 Tangents, tables of, 989, 1000 
 
 Tank tower of reinforced concrete, 
 223 
 
 Taylor coal breaker, 227, 229 
 
 Taylor, W. Purves, 211 
 
 Telephone system in mines, 521 
 
 Temperature of fire, 449 
 stress, 174 
 
 Temple Iron Co., 737 
 
 Tennessee Coal, Iron & Railroad 
 Co., 725, 738 
 
 Tensile stress, 169 
 
 Tesla, CaL, method of working 
 mines, 632 
 
 Tests of cement, 195 
 of lubricants, 169 
 of mine-car wheels, 163 
 
 Thermometers, 352 
 
 Fahrenheit and Centigrade 
 compared, 355 
 
 Thompson, Prof, G. R., 882 
 
 Thurston, 169 
 
 Tiller rope, 244 
 
 Timber measure, 301 
 
 table of constants for, 184 
 weight, 283 
 
 Timbering in mines, 707-730 
 bad roofs, 709 
 choice of timber, 707 
 cost compared with steel, 733 
 cost of preservation, methods, 
 
 725, 726 
 
 cutting and storing timber, 722 
 destructive agencies, 723 
 durabilityof treated timber, 727 
 economy in use of treated tim- 
 ber, 728 
 
 entry timbering, 710, 713 
 four-stick sets, 711 
 framing timbers, 720 
 in flat seams, 707, 710 
 in loose dry material, 716 
 in pitching seams, 712, 713 
 in rock, 715 
 in swelling ground, 717 
 in wet ground or quicksand, 717 
 joints, 721 
 
 limiting angle of resistance, 720 
 longwall face, 666 
 open-tank treatment, 724 
 placing sets, 720 
 preservation, 723 
 pressure treatment, 724 
 
1170 
 
 INDEX 
 
 Timbering in mines, props, 707 
 
 room timbering, 707, 712 
 
 shaft timbering, 715 
 
 square frame at foot of shaft, 
 718 
 
 square-set timbering, 718 
 
 supporting face while under- 
 cutting, 710 
 
 systematic timbering, 708 
 
 three-stick sets, 711, 714 
 
 two-stick sets, 710, 713 
 
 undersetting of props, 712 
 Time, 100 
 
 measure of, 10 
 Tin, strength of, 170 
 Tombelaine acetylene lamp, 891 
 Ton, cubic measurement, 6 
 
 long, 6 
 
 shipping, 7 
 
 short, 5 
 
 Tonnage of ships, 7 
 Torricelli vacuum, 839 
 Trackwork in mines, 762 
 Tracks, shaft bottoms, 599, 601 
 
 slope bottoms, 596 
 
 surface tracks, 603 
 Trade discount denned, 23 
 Tramways, 260 
 
 cables, 249 
 
 ropes for, 242 
 Transformers, electric, 513 
 Transit, surveyor's, 62-65, 67-73 
 Transmission of power, 264-275 
 
 of pressure through water, 305 
 Trapeziums, 45 
 Trapezoids, 44 
 Traverse tables, 1073 
 Traversing in surveying, 93 
 Treatment of injured persons, 969 
 Trenton Iron Co., 237, 251, 264, 
 
 291 
 Triangles, 43 
 
 solution of, 56 
 
 Triger method of sinking shafts, 590 
 Trigonometric functions, table of 
 logarithms of, 1028 
 
 leveling, 76 
 
 tables, 989 
 
 Trigonometry, plane, 54-59 
 Troy weight, 4 
 Tubes, boiler, 297 
 Tunnels for water, 319 
 
 mine, 569 
 
 Turbines, steam, 469 
 Turf as fuel, 367 
 Turquand's gas indicator, 892 
 
 Ultimate strength of flexure, 178 
 
 of materials, 172 
 Unit stress, 169 
 United-Otto ovens, 401 
 United States, currency, 16 
 
 measures, conversion factors to 
 
 metric, 13-15 
 United States Bureau of Mines, 286, 
 
 386, 672, 675, 681, 847, 848 
 
 851, 853, 857, 862, 868, 897, 
 
 900, 902, 984 
 United States Coal & Coke Co., 976 
 
 United States Coast and Geodetic 
 
 Survey, 11 
 
 United States Forest Service, 724 
 United States Geological Survey, 
 
 382, 387, 390, 404 
 United States Steamboat Inspection 
 
 Service, 414 
 United States Testing Board on 
 
 strength of cables, 183 
 Upham, C. C., 957 
 
 Vacuum pump, 349 
 Vaporizer, 541 
 Vapors, specific gravity, 277 
 Velocity of falling bodies, 153 
 Ventilation of mines, 831-945 
 
 acetylene, 871 
 
 afterdamp, 869 
 
 air columns, 927 
 
 air current, reversing, 985 
 
 ascensional, 925 
 
 atmospheric and mine air, 845 
 
 blackdamp, 851 
 
 box regulators, 919, 920 
 
 carbon dioxide, 848 
 
 carbon monoxide, 852 
 
 centrifugal fans, 931 
 
 coal dust in mine workings, 901 
 
 conducting air currents, 944 
 
 current produced by ventila- 
 tors, 916 
 
 derangement of ventilating cur- 
 rent, 901 
 
 distribution of air, 917 
 
 door regulator, 920 
 
 effect of heat and humidity on 
 miners, 873 
 
 elements in ventilation, 907 
 
 elements in ventilation, varia- 
 tion of, 915 
 
 equivalent orifice, 910, 935 
 
 ethylene, 871 
 
 explosive conditions in mines, 
 900 
 
 fan ratings, table, 938-940 
 
 fans, 929 
 
 fire damp, 864 
 
 friction of air, 909 
 
 furnace, 927 
 
 gas indicators and signaling 
 devices, 891 
 
 gases, chemistry of, 831 
 
 gases, volumes when burned in 
 air, 835 
 
 humidifying the air current, 
 902 
 
 hydrogen, 871 
 
 hydrogen sulphide, 871 
 
 influence of seasons, 926 
 
 measurement of currents, 907 
 
 mechanical ventilators, 929, 942 
 
 methane, 850, 859 
 
 mice and canaries as test of 
 aftermath, 857 
 
 mine gas, 845 
 
 mine plan, 925 
 
 mine resistance, 907, 909 
 
 natural, 925 
 
 nitric oxide, 872 
 
INDEX 
 
 1171 
 
 Ventilation, nitrogen, 848 
 
 nitrogen dioxide, 872 
 
 olefin gases, 871 
 
 oxygen, 846 
 
 paraffin gases, 870 
 
 physics of gases, 836 
 
 plenum system, 930 
 
 potential factor of a mine, 910 
 
 quantity of air required, 906 
 
 rarer mine gases, 870 
 
 rise and dip workings, 926 
 
 safety lamps, 874 
 
 shafts, 583 
 
 splitting of air current, 918, 922 
 
 sulphur dioxide, 872 
 
 vacuum system, 930 
 
 water gauge, 908, 911 
 Vernier, -of compass, 62 
 
 of transit, 63 
 
 Vertical curves in railway survey- 
 ing, 122 
 
 Vicat needle, 202 
 Volume, measure of, 6 
 
 metric measures of, 12 
 
 Wabner, 854, 861, 862, 868 
 Waddle ventilator, 932 
 Walker, S. F., 893 
 Walls, retaining, of concrete, 226 
 Ward, 169 
 
 Wardle's rule for shaft pillars, 697 
 Washers, iron, weight, 292 
 Wasteways of dams, 329 
 Water, boiling point affected by 
 altitude, 363 
 
 buckets, in mines, 350 
 
 channels, character of, 317 
 
 contraction and discharge co- 
 efficients, 308 
 
 conversion factors, 314 
 
 dams, 327, 328 
 
 delivering to boilers by in- 
 jectors, 422 
 
 discharge, table, 311 
 
 ditches, 315, 316 
 
 electric current for pumping, 
 342 
 
 elevators, 349 
 
 flow in brooks and rivers, 317 
 
 flow in open channels, 315 
 
 flow in pipes by diameters, 
 table, 324 
 
 flow through flumes, 319 
 
 flumes, 318 
 
 friction in pipes, 323 
 
 gas, 403 
 
 gauges, 908, 911 
 
 gauging, 309 
 
 irrigation quantity, tables, 330 
 
 loss of head by friction, 322, 325 
 
 measures of, 8 
 
 measuring flow in channels, 317 
 
 metric equivalents of volume, 
 weight and capacity, 12 
 
 mine dams, 327 
 
 miner's inch, 310 
 
 outside dams, 328 
 
 pressure, 304, 305 
 
 quantities delivered, table, 323 
 
 Water, resistance of soils to erosion 
 by, 316 
 
 safe bottom'and mean velocities, 
 315 ' 
 
 sluice head, 310 
 
 specific heat at various tempera- 
 tures, 360 
 
 speed through pump machinery, 
 334 
 
 thickness of pipes, 306 
 
 tunnels, 319 
 
 velocity, 307, 308 
 
 weirs, 312-314 
 Waterbury Co., 237 
 Waterfall, power of, 332 
 Water-power, 331 
 
 current motors, 332 
 
 efficiency of, 331 
 
 utilizing a waterfall, 332 
 Watertown Arsenal tests, 206 
 Watteyne, 880, 881 
 Webster gas indicator, 893 
 Wedge, element of machinery, 151 
 
 form of a trapezoid, 53 
 Weight, air, 841 
 air in boilers, 447 
 
 boiler tubes, 297 
 
 bolts, 299 
 
 building materials, 283, 284 
 
 cast-iron pipe, 294 
 
 cements, 189 
 
 coal, American, 287, 288 
 
 coal, English and French, 290 
 
 dry woods, 279-282 
 
 gases, 841 
 
 iron boltheads, nuts and wash- 
 ers, 292 
 
 measures of, 3 
 
 metals, 278 
 
 metric measures of, 12 
 
 miscellaneous materials, 284 
 
 of substances, 278 . 
 
 rails and accessories, 764, 766, 
 768 
 
 sheets and plates of steel, iron, 
 etc., 293 
 
 spikes and nails, 299 
 
 timbers, American, 283 
 
 water vapor, table, 447 
 
 wood as to fuel values, 366 
 Weights and measures, 1-17 
 Weir, gauging by, 312-314 
 Weisbach's formula, 322 
 Wellman-Seaver-M organ water 
 
 hoist, 350 
 
 West Kentucky Coal Co., 734 
 West Virginia Coal Mining Insti- 
 tute, 811 
 
 West Virginia coal region, 617 
 Western Electric Company, 521 
 Western Society of Engineers, 401 
 Westinghouse Airbrake Co., 401 
 Westinghouse-Parsons turbine, 469, 
 
 470 
 
 Westinghouse steam engines, 457 
 Westmoreland Coal Co., 403 
 Wheel and axle, 150 
 Wheels used in waterfalls, 332 
 Whitedamp, 852 
 
1172 
 
 INDEX 
 
 Whiting system of hoisting, 749 
 Wilcox, Babcock and, 367, 397, 416 
 Williams, J. L., method of mining, 
 
 636 
 
 Williams' methanometer, 894 
 Williams steam engine, 457 
 Windlass, 150, 739 
 Wing dams, 331 
 
 Wire, annealed copper, properties^ 
 489 
 
 gauge, 291, 490 
 Wire ropes, 237-261 
 
 bending stress, 251 
 
 cables for bridges, 248 
 
 cableways, 242, 258 
 
 calculations, 251 
 
 care of, 255 
 
 cast-steel, for inclines, life of, 
 254, 255 
 
 construction, 238 
 
 derrick ropes, 243 
 
 drums and fastenings, 244 
 
 effect of sheaves on life, 254 
 
 flat ropes, 241 
 
 flattened strand ropes, 240, 
 242 
 
 glossary of rope terms, 262 
 
 haulage ropes, 241 
 
 hawsers, 243, 250 
 
 hoisting ropes, 239 
 
 horsepower transmitted by 
 steel rope, 268 
 
 inspection of, 257 
 
 iron hoisting ropes, life of, 
 255 
 
 lay of ropes, 238 
 
 life pf, for hoisting, 254, 255 
 
 lubrication of, 257 
 
 materials, 237 
 
 mooring lines, 250 
 
 non-spinning, 240 
 
 power transmission by, 264 
 
 proper working load, 253 
 
 round, 239 
 
 Wire ropes, running rope, 250 
 scale ropes, 240, 242, 244 
 sizes and strength, tables, 245 
 
 -250 
 
 sockets, 244 
 splicing, 255, 256 
 starting stress, 253, 254 
 stress on planes, 254 
 suspension bridges, 243, 248 
 tables of sizes, strengths, etc. 
 
 245-250 
 taper ropes, 241 
 tiller rope, 244 
 tramway cables, 249 
 tramways, 260 
 wear of, 257 
 working load, 251 
 See also Power Transmission. 
 
 Wolf lamp, 876, 878, 880, 888 
 
 Wood, as fuel, 365 , 
 
 Australian, weight, 281 
 changed to anthracite, 368 
 coal equivalents by weight, 366 
 composition and calorific value, 
 
 366 
 
 crushing loads, 185 
 Indian, weight, 282 
 Philippine, weight, 281 
 screws, diameters, 298 
 specific gravity, 278 
 strength of, 171, 184 
 timbers, American, weight, 283 
 weight of dry, 279 
 weights by fuel values, 366 
 
 Wooden pipe, 306, 307 
 
 Woodworth, R. B., 731 
 
 Work, definition, 153 
 
 Working a mine, methods, 604-666 
 stress, 172 
 
 Wrought iron, weight, 293, 298, 301 
 
 Zero, absolute, 353 
 
 Zinc, strength of, 170 
 Zones, spherical, 52 
 
THE BUYERS' MANUAL 
 
 LINK-BELT 
 
 MACHINERY 
 
 for the handling and preparation of coal at the mine includes: 
 
 Tipples, Car Hauls, Retarding Conveyors, Coal Washeries, 
 Coal Driers, Mine Cages, Car Dumps, Weigh Boxes, Load- 
 ing Booms ; Shaking Screens, Picking Tables, Coal Chutes. 
 Rescreening Plants, Revolving Screens, Conveying and Ele- 
 vating Machinery. Anthracite Coal Handling Machinery. 
 
 Power House Machinery, Peck Carriers (Pivoted Overlap- 
 ping Bucket Carriers), Undercut Gates, Feeders, Clutches, 
 Belt Conveyors, Link-Belt Silent Chain, Crushers, Loco- 
 motive Cranes. 
 
 We design as well as build complete machinery for the hand- 
 ling and preparation of coal at the mine. Submit your 
 problems to us for solution. We make no charge for advice, 
 layouts or estimates. Catalogs on request. 
 
 LINK-BELT COMPANY 
 
 PHILADELPHIA CHICAGO INDIANAPOLIS 
 
THE BUYERS' MANUAL 
 
 <TJEffUMi Power Pumps 
 
 .^^^^^^^i^^ 
 Save Time, Space and Fuel 
 
 They need so little attention, they 
 are almost automatic. Only an 
 occasional oiling is required. 
 Their construction permits their 
 use where the head-room is ex- 
 tremely limited. 
 
 Their operating cost is usually 
 about one-third of the direct act- 
 ing steam pump, doing the same 
 kind of work. 
 
 Thirty-five years of pump build- 
 ing experience is behind them. 
 
 Fig. 716, with Motor 
 
 Drive. 
 
 May be used as a gather- 
 ing or sump pump. Capa- 
 cities from 30 to 215 gal- 
 lons per minute. One of 
 many Deming Pumps of 
 this type. 
 
 THE DEMING COMPANY 
 
 SALEM, OHIO U. S. A. 
 
 HAND AND POWER PUMPS FOR ALL USES 
 
 General Distributing Houses: 
 
 CHICAGO: Henion & Hubbell 
 PITTSBURGH: Harris Pump & Supply Co. 
 
 Agencies in All Principal Cities 
 
THE BUYERS' MANUAL 
 
 pOR use as sump or gathering 
 
 pumps; for boiler feeding; for 
 
 general water supply of all kinds, 
 
 POWER PUMPS 
 
 are the most economical pumping 
 
 units. Hundreds of letters in our 
 
 files, from users, will testify to these 
 
 statements. 
 
 If interested in any kind of a pump- 
 
 ing problem for deep or shallow 
 
 wells, put it up to us first. 
 
 Fig. 50, Motor Driven 
 Triplex Power Pump. 
 Made in many sizes. Capa- 
 cities from 300 to 60,000 
 gallons per hour. Com- 
 plete line of Deming Trip- 
 lex Pumps shown in 
 Catalogue "J". 
 
 THE DEMING COMPANY 
 
 SALEM, QHIO U. S. A. 
 
 HAND AND POWER PUMPS FOR ALL USES 
 
 General Distributing Houses: 
 
 NEW YORK: Ralph B. Carter Co. 
 BUFFALO: Root, Neal & Co. 
 
 Agencies in All Principal Cities 
 
THE BUYERS' MANUAL 
 
 Multi-Blade Mine 
 Ventilating Fans 
 
 have the three all important features 
 
 RELIABILITY 
 DURABILITY and EFFICIENCY 
 
 Technical information regarding these fans may be 
 had by request to our Mine Fan Engineering De- 
 partment. 
 
 Include Catalogue No. 303 in your request, 
 
 AMERICAN BLOWER COMPANY 
 
 DETROIT, MICHIGAN, U. S. A. 
 
 CANADIAN SIROCCO COMPANY, Ltd.. WINDSOR, ONT. 
 MANUFACTURERS FOR CANADA 
 
 Double Inlet 
 Sirocco Mine 
 Ventilating 
 Fan Wheel , 
 having been rigidly 
 constructed, perfect- 
 ly balanced and 
 thoroughly inspect- 
 ed, is ready for 
 shipment. 
 
THE BUYERS' MANUAL 
 
 As your first step toward 
 
 f NATIONAL" Preparedness 
 
 Send for a copy of 
 
 "NATIONAL" BULLETIN 
 
 No. 11 
 History, Characteristics 
 
 and 
 
 The Advantages of'NA TIONAL" Pipe 
 
 Look for the Name 
 
 
 On Every Length 
 
 NATIONAL TUBE COMPANY 
 
 General Sales Offices: FRICK BUILDING, PITTSBURGH, PA. 
 
 DISTRICT SALES OFFICES: 
 
 Atlanta, Boston, Chicago, Denver, Kansas City, New Orleans, New York 
 Omaha. Philadelphia, Pittsburgh. Salt Lake City. St. Louis. St Paul 
 
 PACIFIC COAST REPRESENTATIVES; U. S. Steel Products Company. 
 San Francisco Los Angeles Portland Seattle 
 
 EXPORT REPRESENTATIVES U. S. Steel Products Company. 
 New York City 
 
THE BUYERS' MANUAL 
 
 L 
 
 XPLOSIVE 
 
 For Blasting Coal and Ore Are 
 
 the Products of Over A 
 
 Century's Experience 
 
 I^OR COAL MINING in gaseous and dusty 
 mines, our "permissibles" are extensively 
 used to the entire satisfaction of miners and 
 operators. 
 
 MONOBEL and CARBONITE 
 
 are our "permissibles" and are subjected to the severest 
 tests in our own galleries before submission to the Bureau 
 of Mines for approval. We make twelve kinds a wide 
 range which assures the selection of a "permissible" ex- 
 actly suited to local mine conditions. FREE booklet 
 "PERMISSIBLE EXPLOSIVES" gives a complete de- 
 scription of these "safety-first" blasting agencies. 
 
 BLASTING POWDERS 
 
 we make contain the best of materials thoroughly in- 
 corporated, and made into seven standard granulations 
 to meet all the requirements of blasting coal and ore. 
 
 FOR ORE MINING 
 
 in the open or in mines, we have an assortment of 
 Gelatins, Extra and Straight Dynamites scientifically and 
 expressly made for blasting ore in the most practical, 
 expeditious and economical manner. 
 
 Descriptive Booklets iiving detailed information about DU PONT EXPLOSIVES 
 and practical instruction to prospective users will be sent free to applicants. 
 
 E. I. DU POINT DE NEMOURS & CO. 
 
 POWDER MAKERS SINCE 1802 
 
 WILMINGTON, DELAWARE 
 
THE BUYERS' MANUAL 
 
 B<SjfP|J) C 
 LASTING SUPPLIEU 
 
 Ensure Maximum. Efficiency 
 of Explosives 
 
 THE complete detonation of explosives is 
 largely dependent on the efficiency of the 
 detonators employed. 
 
 DU PONT DETONATORS 
 
 Whether the charges are exploded by electric blasting 
 caps or with blasting caps and fuse, use a detonator of 
 Du Pont manufacture. 
 
 Years of field experience enable us to produce detonators 
 capable of delivering the necessary shock to ensure com- 
 plete detonation and consequent efficiency of explosives. 
 
 DU PONT BLASTING MACHINES 
 
 for the generation of electricity for firing electric blasting 
 caps are practical in design, compact in form and posi- 
 tive in action. 
 
 GALVANOMETERS and RHEOSTATS 
 
 are blasting machine accessories for determining the con- 
 dition of the blasting circuit and the assurance that the 
 blasting machine is up to its capacity. 
 
 OTHER BLASTING SUPPLIES 
 
 consisting of connecting and leading wire, thawing ket- 
 tles, cap crimpers, blasting mats, tamping bags and fuse 
 can be used with the same assurance of entire satisfaction. 
 
 Get the maximum efficiency out of your explosives by detonating them with the 
 requisite Du Pont BLASTING SUPPLIES. 
 
 E. I. DU PONT DE NEMOURS & CO. 
 
 POWDER MAKERS SINCE 1802 
 
 WILMINGTON, DELAWARE 
 
THE BUYERS' MANUAL 
 
 WHY YOU SHOULD USE 
 
 Williams Crushers is, first because they are 
 of proven merit, they are adaptable to all 
 kinds of crushing, coarse or fine, for stoker 
 or chain grate coal, for bee-hive or by-product 
 oven coal, for low-grade ore, or for grinding 
 coal for burning in suspension. They are 
 adjustable for any size crushing desired, and 
 are made in capacities to suit any and all 
 requirements. 
 
 WILLIAMS 
 COAL CRUSHERS 
 
 will solve your crushing problems ; space will 
 not permit us to enumerate here their nu- 
 merous superior features. To get full details 
 write for catalog No. 75. 
 
 THE WILLIAMS PATENT 
 CRUSHER AND PULVERIZER CO. 
 
 Works: Gen. Sales Dept. 
 
 ST. LOUIS, MO. Old Colony Bldg., CHICAGO, ILL. 
 
THE BUYERS' MANUAL 
 
 PHILLIPS 
 
 MINE CAR TRUCKS 
 
 Excel in Efficiency 
 
 Either oil or semi-fluid grease can be used as 
 a lubricant in the Phillips Open-Cap Wheel. 
 With the latter, as high as 27 months' 
 service has been had from .one lubrication. 
 The wheels and boxes do not wear large in 
 the bore, and equipment which has been in 
 service for over 8 years shows no perceptible 
 wear internally. Boxes cannot shift or axles 
 get out of alignment, and the wheels are true 
 to gauge at all times. Many concerns use 
 this Truck exclusively on account of its 
 easy-running qualities, and the economies it 
 effects in repair bills and lubricant. 
 
 For guarantee and further information write 
 
 PHILLIPS MINE & MILL SUPPLY CO. 
 
 BUILDERS OF MINE CARS AND TRUCKS- 
 MINE CAR WHEELS SCREENING EQUIP- 
 MENTSPHILLIPS AUTOMATIC CAR DUMPS 
 
 PITTSBURGH, PA. U. S. A. 
 
10 
 
 THE BUYERS' MANUAL 
 
 There are 150 grades and kinds of 
 Atlas Blasting Explosives, each differ- 
 ing in some important property from 
 the other. Our catalogue describes 
 them in a general way but if you want 
 to know which one has those proper- 
 ties that make it the most efficient and 
 economical for your work, write our 
 blasting department. 
 
 ATLAS POWDER CO. 
 
 WILMINGTON, DEL. 
 
 Catalog on Request 
 
 WILLIAMSPORT WIRE ROPE CO. 
 Williamsport, Pa. 
 
THE BUYERS' MANUAL 
 
 11 
 
 GOODMAN 
 
 Coal Mining 
 Machines 
 
 MANY 
 TYPES 
 
 Breast Machines, Straightface Machines 
 
 Shortwall Machines, Longwall Machines 
 
 Direct or Alternating Current, Compressed Air 
 
 Electric Mine Locomotives 
 
 All Sizes 
 
 GATHERING AND MAIN HAULAGE 
 
 SINGLE-MOTOR AND TWO-MOTOR TYPES 
 
 TROLLEY AND STORAGE BATTERY 
 
 A Locomotive for Every Mine Service 
 
 Write for Descriptive Bulletins 
 
 GOODMAN MANUFACTURING CO. 
 
 NEW YORK 
 PITTSBURGH 
 CINCINNATI 
 CHARLESTON, W. VA. 
 
 CHICAGO 
 
 ILLINOIS 
 
 BIRMINGHAM 
 ST. LOUIS 
 DENVER 
 SEATTLE 
 
12 THE BUYERS' MANUAL 
 
 Wyoming Automatic Eliminator 
 
 To keep steam dry even under 
 the most unusual conditions 
 that's the work the W y o m i n g 
 Eliminator does. It is 
 
 "The Watch Dog of the Steam" 
 
 Four baffle plates keep the steam 
 dry. No chance for moisture to get 
 back into steam; vertical corruga- 
 tions prevent moisture from being 
 brushed off the plates. 
 This is one reason why 73 per cent of the 
 largest coal companies use Wyoming 
 Eliminators. 
 
 Ask for full information 
 Also get our quotations on 
 
 Steam Traps; Boiler Gauge Cocks; 
 Cylinder Drip Cocks; Brake Valves 
 and Gauge Cocks for Mine Locomo- 
 tives; Shaft Couplings for Breaker 
 Shafts. 
 
 W. H. Nicholson & Co. 
 
 Wilkes-Barre, Pa. 
 
 SPECIAL 
 MINING MACHINERY 
 
 We have the very latest word in 
 
 Conveyor and Elevator Chains, Car Hauls 
 Par risk Flexible Arm Shaking Screens 
 Simplex Jigs, Vigilant Jig Plungers 
 Lloyd Compound Gear Driven Rolls 
 Hollow Ground Roll Teeth 
 
 Consult us before closing your designs and specifications for ma- 
 chinery to be used in the mining and preparation of coal. 
 
 WILMOT ENGINEERING CO. 
 
 HAZLETON, PA. Works WHITE HAVEN, PA. 
 
THE BUYERS' MANUAL 13 
 
 "Hendrick" 
 
 Perforated Screens 
 
 for all purposes Special Improved Types 
 
 FOR 
 
 CLEANING 
 
 COAL 
 AND COKE 
 
 Our Patent Flanged 
 Lip Screen. 
 
 This screen does the final 
 cleaning of coal and coke 
 at the loading pockets and 
 on shaking screens. It does 
 the work. 
 
 Write for Bulletin 
 No. 27 
 
 "HENDRICK" 
 Manganese Bronze Screens 
 
 have been resisting the action of sulphurous 
 mine waters for over 25 years 
 
 ELEVATOR BUCKETS, FLIGHTS AND TROUGH 
 GENERAL SHEET AND PLATE WORK 
 
 Ask for Catalogue 
 
 HENDRICK MANUFACTURING CO. 
 
 CARBONDALE, PA. 
 
14 THE BUYERS' MANUAL 
 
 GENUINE 
 ARMSTRONG STOCKS & DIES 
 
 FOR THREADING PIPE OR BOLTS 
 MALLEABLE IRON HINGED PIPE VISES 
 
 PIPE CUTTERS 
 PIPE THREADING MACHINES 
 
 MANUFACTURED BY 
 
 THE ARMSTRONG M'FG. CO. 
 
 336 KNOWLTON ST., BRIDGEPORT, CONN. 
 
 NEW YORK 248 Canal Street 
 
 WATER SOFTENERS 
 FILTERS, PURIFIERS 
 
 FOR 
 
 Prevention of Scale Deposits, Mud or 
 Corrosion in Boilers, Tubes or Pipes 
 and for the Purification and Filtration 
 of Water Supplies for any Purpose, 
 Designed and Installed Anywhere by 
 
 AMERICAN WATER SOFTENER CO. 
 
 1011 Chestnut Street PHILADELPHIA 
 
THE BUYERS' MANUAL 15 
 
 HOCKENSMITH 
 WHEEL & MINE CAR CO. 
 
 (Pittsburg District.) Penns Station, Pa. 
 
 MANUFACTURERS OF 
 
 Chilled Annealed] Self-Oiling 
 
 Mine Car Wheels) Roller Bearing 
 
 ANGLE BAR TRUCKS 
 
 The Truck for Severe Service 
 
 MINE CARS 
 
 Steel Composite Wood 
 
 Awarded Gold Medal Panama-Pacific Exposition for 
 Mine Cars, Wheels and Oiling System. 
 
 Cast Iron Pipe Frogs 
 
 Turnouts Mine Car Hitchings 
 Motor Wheels 
 
 Our Engineering Department is prepared to 
 co-operate with you in the design of any equip- 
 ment manufactured by us. 
 
 Catalogue upon request 
 
16 
 
 THE BUYERS' MANUAL 
 
 The Practical 
 the Mechanical 
 Side of Coal Mining 
 
 The Library of Coal Mining and Engineering is gradually 
 and surely establishing itself as the one library on the sub- 
 ject which fills the needs of that great body of men, the men 
 who are perfecting their knowledge of the practical side of 
 coal mining, as a means of climbing to the higher positions 
 in the industry. 
 
 It is gradually and surely establishing a precedent in self- 
 help mining literature, covering as it does the entire opera- 
 tion, from surveying, shaft and drift opening, mechanical 
 equipment and operation, to the chemical analysis of the 
 output. 
 
 Price $16, payable $2 per month. Write for free 
 examination. 
 
 McGraw-Hill Book Co., Inc., 239 West 39th Street, New York 
 
THE BUYERS' MANUAL 17 
 
 Copper and Iron 
 
 Wire 
 
 Exploders 
 
 And 
 
 Blasting Supplies 
 
 Star Electric Fuze Works 
 
 WILKES-BARRE PENNA. 
 
 New Books on Coal and Coke 
 Wagner Coal and Coke 
 
 By FREDERICK H. WAGNER, Member American Gas 
 Institute; Franklin Institute. 431 pages, 6x9, 
 137 illustrations, $4.00 (173) net, postpaid. 
 
 A complete treatise, prepared to give the student of coal gas produc- 
 tion data in concise form covering the various systems of coal 
 carbonization. 
 
 Wagner Coal Gas Residuals 
 
 By FREDERICK H. WAGNER. 176 pages, 6x9, 
 
 illustrated, $2.00 (8/4) net, postpaid. 
 
 A complete treatise giving the modern methods of securing the resid- 
 uals pertaining to the carbonization of coal. 
 
 Somermeier Coal 
 
 Its Composition, Analysis, Utilization and Valuation. 
 By E. E. SOMERMEIER, Professor of Metallurgy, 
 Ohio State University. 175 pages, 6 x 9, illus- 
 trated, $2.00 (8/4) net, postpaid. 
 
 Designed to increase the knowledge of the properties and utilization 
 of coal. 
 
 McGraw-Hill Book Company, Inc. 
 239 West 39th Street NEW YORK 
 
18 THE BUYERS' MANUAL 
 
 VULCAN SAFETY 
 
 QUALITY FIRST 
 
 FLEXIBILITY 
 OF CONTROL 
 
 is one of the biggest reasons for the continued 
 popularity of the large Vulcan steam hoisting 
 engine. The thousands of mine cars that are 
 moved at high speeds, without accident each 
 year, are proof that the many installations of 
 
 VULCAN 
 
 HOISTING ENGINES 
 
 have that flexibility of control, together with 
 the proper design and materials, that insure a 
 safe and economical investment. Write now 
 for full information and photos of big and 
 little Vulcans in service. 
 
 VULCAN IRON WORKS 
 
 WILKES-BARRE :: PENNSYLVANIA 
 
 NEW YORK CHICAGO 
 
 30 Church Street 913 McCormick Building 
 
HIGH 
 OUTPUT EFFICIENCY 
 
 is one of the strong points of most electrically- 
 driven machinery, and this is due partly to 
 transmission without heavy power loss, eco- 
 nomical use of power, and concentrative 
 designs that mean low maintenance. 
 
 VULCAN 
 ELECTRIC HOISTS 
 
 are showing high output efficiency throughout 
 the mining regions, and have an enviable 
 record for continued safe and efficient opera- 
 tion. Write for the names of electric hoist 
 users and the wide range of types and sizes. 
 
 VULCAN IRON WORKS 
 
 WILKES-BARRE :: PENNSYLVANIA 
 
 NEW YORK CHICAGO 
 
 30 Church Street 913 McCormick Building 
 
20 
 
 THE BUYERS' MANUAL 
 
 PENNSYLVANIA CRUSHER CO. 
 
 Stephen Oirard BW'g., PHILADELPHIA, PA. 
 
 NEW YORK PITTSBURGH 
 
 50 Church Street Peoples Bank Bld'g. 
 
 COAL CRUSHING & CLEANING MACHINERY FOR BY- 
 PRODUCT COKE PLANTS, SWINGHAMMER CRUSH- 
 ERS, BRADFORD COAL CLEANERS, SINGLE ROLL 
 CRUSHERS, DELAMATER "SINK & FLOAT" TESTERS. 
 
 "PENNSYLVANIA" SWING-HAMMER CRUSHERS 
 
 Extensively used for pulverizing Bituminous Coals in By- 
 Product and Bee-Hive Coking Plants, for crushing Cement 
 
 Rock and Lime- 
 stones in Cement 
 Mills, for Lime, 
 Shales, Bone and a 
 multitude of other 
 materials. 
 
 Main frame fabri- 
 cated Steel practically 
 immunefrom breakage. 
 Removable Steel Wear 
 Liners, Ball & Socket 
 Bearings, 6, 8 and 10 
 rows of Hammers, large 
 diameter Steel Discs, 
 (Patented) quick adjustable Grind- 
 
 ing Cage. Built in Capacities 3 tons to 400 tons hourly. By weight 
 the "Pennsylvania" is more than 90 % Steel. 
 
 "PENNSYLVANIA" BRADFORD COAL CLEANERS 
 For Power Houses, By-Product Coke Plants, etc. 
 
 In addition to its advantages as a Crusher, this machine has the re- 
 markable ability to automatically remove impurities, slate, bone, sul- 
 phur balls or binder from 
 bituminous steam and cok- 
 ing coals, thereby reducing 
 the objectionable ash and 
 sulphur. 
 
 Used extensively in pre- 
 
 paring R.O.M. coals in By- 
 Prod 
 
 uct Coking plants and 
 for Bee- Hive Ovens. 
 
 In connection with its 
 crushing and cleaning func- 
 tions for R.O.M. coal for 
 large Power Houses, the 
 "Pennsylvania" Bradford 
 is most efficient in remov- 
 ing stray iron, coupling 
 pins, mine props and all 
 sorts of impedimenta that 
 damage Conveyors, Stokers and other Power House machinery. 
 
 For Stoker feed it Crushes R.O.M. with I ess fines than Rolls. 
 
 Absolutely automatic in operation, low horse power, runs 12 to 15 
 R.P.M., requires no labor to operate other than occasional oiling. 
 Practically "fool-proof." 
 
 Several "Pennsylvania" Bradfords are successfully operating in 
 Coal Washers. 
 
 (Patented) 
 
MINERAL TESHNDLOGY LIBRARY 
 
 UNIVERSITY OF CALIFORNIA 
 BERKELEY 
 
 Return to desk from which bor 
 This book is DUE on the last date sta 
 
 NOV 2 7 1950 
 
 LD 21-100m-9,'48(B399sl6)476 
 
394012 
 
 UNIVERSITY OF CALIFORNIA LIBRARY