Mch. dept. - -eering Library INDUSTRIAL ENGINEERING PART ONE INDUSTRIAL ENGINEERING A HANDBOOK OF USEFUL INFORMATION FOR MANAGERS, ENGINEERS, SUPERINTENDENTS, DESIGN- ERS, DRAFTSMEN AND OTHERS ENGAGED IN CONSTRUCTIVE WORK BY WILLIAM M. BARR Author of "Pumping Machinery," "Boilers and Furnaces," etc. PART I NEW YORK W. M. BARR COMPANY, INC. 116 WEST 39TH STREET 1918 Engineering Library Copyright, 1918 by WILLIAM M. BARE COMPOSITION, ELECTROTYPING AND PRINTING BY PUBLISHERS PRINTING COMPANY, NEW YORK CITY PREFACE IN the preparation of this handbook the writer attempts a systematic arrangement of a considerable volume of useful information for engineers, much of which has not been readily accessible to the public. The collection includes separate specifications relating to the chemical and physical properties of practically all of the materials entering into engineering work for the U. S. Government. The importance and economic value of the data thus presented will be recognized by manufacturers and engineers engaged in Government work not only, but this value extends into every department in industrial engineering. The usefulness of this handbook will not rest so much upon the extent of the compila- tion as upon the practical nature of the data presented ; a feature made possible through the free use of working drawings contributed for insertion in these pages. Selections from these drawings appear throughout the entire work in carefully prepared illustrations accompanied in most cases by tables of working dimensions; these cover a wider range of detail than is common in books of this class. It has been the constant aim of the writer that such data shall be so complete that principal dimensions given in any table may, with suitable adaptations, be used directly in the preparation of shop drawings, and without the labor of recalculating. Correct proportions, in series, cannot be had by selecting PH acceptable detail and making one of its dimensions a unit, and then assigning proportional values to the other dimensions, except within very narrow limits. Suppose a series of strap joints as in the table, page 601; diameters ranging from a 3-inch to a 12-inch pin; the writer's method is to complete two designs similar in detail, one for the smallest and the other for the largest diameter of pin, then measuring the proportional differences graphically obtained for intermediate sizes. There are numerous machine details which are now designed to be complete in themselves, and with very slight changes made to fit into any machine where such a detail is demanded; many examples of this kind are included in this work; in all cases the nature of the design and the properties of materials entering into it are fully con- sidered and the proportions fixed once for all. Pulleys are a familiar example; they are designed for single or double belts, as also double extra heavy for very severe service, but once designed and patterns made, no further changes occur; the pulley becomes one of many units in a plant requiring no further attention on the part of the designer than the mere selection of size and strength. So-called empiricism, or the reliance on direct observation and experience to the exclusion of theories, or assumed principles in machine design, if it ever existed, is no longer in use; many of the so-called empirical or practical rules are in reality founded upon carefully conducted experiments, or the result of long and methodical observation in the working of machines, the ultimate proportions being fixed to safely carry the load regardless of conventional factors of safety; the latter are not believed to be "factors of ignorance" so much as they are generous allowances made to withstand the effect of forces too complex to be dealt with mathematically or physically. Rigidity depends largely upon the form and details of construction. The chemical and physical properties of any material used in engineering is now known with precision. The data relating to strength of materials in this work are wholly those obtained by direct experimept, mainly in testing machines owned and operated by the U. S. Government. There will be noticed throughout the book a general tendency toward steam-engine details, due in large measure to the writer's long familiarity with that subject. Two satisfactory types of steam-engines are now in use the modern locomotive engine and [v] PREFACE the triple expansion marine engine; both of these use steam pressures, seldom less than 165 pounds per square inch. In locomotive design the present proportions are the outcome of a practical acquaintance with the success or failure of each and every detail, covering experiences hi thousands of locomotives with every peculiarity of design, operating on road-beds of every conceivable variety, often under conditions that would seem to invite failure, and through it all the locomotive stands the test with an economic margin that invites confidence and places upon its design and proportions the seal of approval. Similarly the success of the modern triple expansion marine steam-engine, the designs for which are based upon accurate knowledge of the strength and elasticity of materials employed, to which is added an increment in size, based upon experience, to resist stresses occurring at irregular intervals with a suddenness that would seem to imperil the safety of the engine; the proportioning of parts that will completely absorb such shocks without harm and without stoppage in service, is one of the results of thorough technical training supplemented by experiences which can only be had at sea. There has been no attempt in fact, the writer disavows any intention of making this a text-book in engineering. The designs illustrated and accompanied by tables of working dimensions are based mainly upon marine and railroad practice, than which no severer working tests occur; the proportions given have long since passed the experi- mental stage and are known to be ample for the controlling unit, in any given case. Machine design in its narrowest applications is all that is attempted in this work; it has been his opinion throughout that the theory of machines, applied kinematics or machines considered as modifying motion, applied dynamics or machines considered as modifying both motion and force, are subjects requiring special mathematical treats ment, and therefore foreign to the present purpose: he contents himself with the simple presentation of some acceptable details in machine construction. The writer is under obligations to many professional friends contributing and assisting in the selection of material for these pages. His thanks are especially due officials of the Navy Department, the Bureau of Mines, the Bureau of Standards, Examiners in several of the Departments in the U. S. Patent Office; for courtesies in the Library of Congress, the Smithsonian Institution, etc. Extended use has been made of official reports on materials forming the basis of engineering specifications now used in Government contracts, especially those relating to the Navy. Free use has also been made of the Records of Tests made at the Watertown Arsenal, the Wash- ington Navy Yard, and other Governmental Laboratories. In this connection it will be understood that the official reports and specifications appearing in this book are for the information of the reader, and not herein officially published. As to the apparent exclusion of excellent work done by several Societies in Testing Materials, as well as to results of tests made public by railroads, steel works, forges, foundries, and other industrial plants, it occurs only through lack of space; preference is given the Government Specifications based upon extended chemical and physical investigations because, as presented, they are more or less mandatory in their application. Free use has been made of Valuable contributions to the various engineering societies, magazines, and trade papers covering almost every department of technology. The writer's collection of such material is large, and as most of the papers have been pre- pared by experts their value is correspondingly great; the collection thus serves to sup- plement some of the more recent books authoritatively. With the development of the subjects selected for this book it has become necessary to divide the work into two parts. The present volume, Part I, deals mostly with the chemical and physical properties of the materials used in engineering, particularly such as are called for in Government specifications; these specifications are so numerous and conform so minutely to the official terms, that the space occupied by them is more than double that originally assigned. This has been the case in other sections as well, but the expansion of the work is believed to be wholly in the interest of and will prove doubly useful to, the reader. Part II is in active preparation for early publication. The long delay after the preliminary announcement regarding its preparation for early publication has been due to the industrial changes which have taken place through- [vi]. PREFACE out our country because of the European War, an occurrence which has made neces- sary many changes in the book, including the rearrangement and rewriting of whole sections, the preparation of new drawings, the calculating of new tables, all of which has taken much time, but it has greatly increased the value and importance of the book. Complete accuracy is not expected in a work involving so much detail as does this, and the writer can only say with respect to this detail that the present work represents an extended and thoroughly earnest effort on his part to secure perfectly reliable ma- terial, arranging it in convenient sequence, presenting it in clearly printed pages and carefully indexing the whole for ready reference. WILLIAM M- BARE. NEW YORK, September, 1918. [vii] CONTENTS SECTION 1 UNITS AND STANDARDS Unit of Time Standard of Length Unit of Mass C. G. S. System Me- chanical and Geometrical Quantities Units of Measurement and De- rived Units in use in Great Britain and the United States Fundamental and Derived Units of Length, Mass, Time, and Temperature Geometric and Dynamic Units Air as a Standard Water as a Standard Physical Constants of Metals Melting Points of Chemical Elements Specific Gravity of Metals, Minerals, and other substances Horsepower Kilowatt as a Unit of Power Table of Horsepowers to Kilowatts Table of Kilowatts to Horsepowers 1-38 SECTION 2 WEIGHTS AND MEASURES Measures of Length Measures of Surface Measures of Volume Measures of Capacity Avoirdupois Weight Troy Weight Apothecaries' Weights and Measures United States Money Value of Foreign Coins in United States Money Measures of Time Longitude and Time Compared Metric System of Weights and Measures Tables for Interconversion of Metric and United States Weights and Measures Table of Admiralty Knots to Statute Miles and Kilometers Tables: Pounds per Square Inch to Kilograms per Square Centimeter; Cubic Feet per Second to Cubic Meters per Second. Tables: Wire Gauges in use in the United States United States Standard Gauge for Sheet and Plate Iron and Steel Legal Weights (in pounds) per Bushel of Various Commodities 39- SECTION 3 MENSURATION AND MECHANICAL TABLES Mensuration of Surfaces Table of Useful Functions of Pi (TT) Tables: Diame- ter, Circumference, Area of Circles, and Side of Equal Square Diameters and Areas of Circles, with Squares, Cubes, Square and Cube Roots Reciprocals of Numbers Lengths of Circular Arcs Areas of Circular Segments Area of an Irregular Figure Plane Trigonometry Trigono- metrical Formulae Sines, Cosines, Tangents, Cotangents, Secants, and Cosecants of Angles to 90 Logarithmic Sines-, Cosines, Tangents, and Cotangents of Angles from to 90. Mensuration of Solids Logarithms of Numbers 89-197 [ix] CONTENTS SECTION 4 PROPERTIES OF SOME MATERIALS USED IN ENGINEERING Acetylene Acids Air Alcohol Alkalis Alloys Aluminum Amalgams Ammonia Antimony Arsenic Asbestos Austenite Barium Bessemer Steel, Acid and Basic Bismuth Blister Steel Borax Boron Cadmium Calcium Carbon Cementite Chromium Cobalt Copper Crucible Steel Ferrite Gold Graphite Harvey Steel Hydrogen Ingot Iron Iridium Iron Lead Lithium Magnesia Magnesite Magnesium Manga- nese Martensite Mercury Molybdenum Nickel Nitrogen Open-Hearth Steel, Acid and Basic Talbot Process Oxides Oxygen Pearlite Phosphorus Platinum Potassium Semi-Steel Silica Silicon Silver Sodium Tin Steel Steel Castings Sulphur Tantalum Titanium Tungsten Vanadium Wulf en- ite Zinc. Alloy Steels: Simple Tungsten Steel Simple Chromium Steel Maganese Steel Simple Nickel Steels Properties of Ordinary Nickel Steel Nickel-Chromium Steels Mayari Steel Silicon Steels High-Speed Tool Steels Stellite Chromium-Vanadium Steels Heat Treatment of Alloy Steels Heat Treatment of High Speed Tools Theory of High Speed Steels. Navy Department Requirements for Steel Plates, Shapes, and Bars Rivet Steel Steel Castings Wrought Iron Steel Forgings Reinforcement Steel for Concrete Hull Plating Boiler Plates Special Treatment Steel Plates for Protective Hull Plating Drill Rod Steel Hot Rolled or Forged Carbon Steel for use by the Naval Gun Factory Cold-Rolled and Cold-Drawn Machinery Steel, Rods and Bars Extra Soft Steel for use as a Wrought Iron Substitute Steel Rods and Bars for Stanchions, Da- vits, and Drop and Miscellaneous Forgings Spring Steel Tool Steel. Fire Clays and Fire Bricks: Nature of Refractory Clays Effect of the Acces- sory Constituents of Fire Clays upon the Softening Temperatures, such as Quartz, Alumina, Iron Oxide, Feldspar, Mica, Lime Effect of Fluxes upon Refractoriness Load Tests of Fire Brick Effect of Chemical Composition Fire Brick and Clay Analysis Chemical Formulae Results of Physical Tests at 1,300 C, and with a load of 75 pounds per square inch Influence of Cold-Crushing Strength. Structural Timbers Used hi Engineering: Southern Yellow Pines: Longleaf Pine, Shortleaf Pine, Loblolly Pine Timbers of the Pacific Coast: Doug- las Fir, Western Hemlock, Western Larch, Redwood Timbers of the New England and Lake States: Norway Pine, Tamarack, Spruce Timber Tests 199-302 SECTION 5 %. STEEL BARS, PLATES, SHAPES, BOLTS, RIVETS Requirements for Navy Department: Physical and Chemical Properties of Boiler Plates Steel Plates for Hulls and Hull Construction Steel Shapes for Hulls and Hull Construction Black and Galvanized Sheet Steel Corrugated Galvanized Sheet Steel Floor Plates Terneplate Roofing Tin Standard Steel Hull Rivets and Rivet Rods Specifications for Manufactured Rivets Small Rivets for Sheet Metal Work Tables: Weight of Rectangular Steel Plates Weight of Circular Steel Plates- Weight of Square and Round Steel Bars Strength of Round Steel Bars. [x] CONTENTS Screw Threads: Franklin Institute Standard; United States Standard; Table of U. S. Standard Bolts and Nuts from Y inch to 12 inches Maximum Working Load for Tabular Tensile Strength Weight of Hexagon Bolt- Heads and Nuts Round Slotted Nuts, U. S. N. Box Wrenches, U. S. N. Lock Nuts and Split Pins, U. S. N. Spring-Cotters, U. S. N. Acme Thread Screws, U. S. N. Square Thread Screws, U. S. N. Multiple Thread Screws Buttress Thread Screws Knuckle Thread Screws Sharp V-Thread Screws S. A. E. Standard Screws Whitworth Standard Screws British Association Standard Thread International Standard Screw Threads (System International) Castle Nuts Cap Nuts Com- mercial Steel Bolts and Nuts for U. S. N. Bolts and Nuts, U. S. Standard, Weight per 100 -Machinery Bolts and Nuts and Material for the same, U. S. N. Iron Bolts and Nuts, U. S. N. Deck Bolts and Nuts, U. S. N. Holding Down Bolts for Gun Mounts, Torpedo Tubes, and Turret Tracks, U. S. N. Bolts of Steel or Composition Metals, and Nuts of Iron, Steel, or Composition Metals Studs and Nuts and Bars for Bolts and Nuts, U. S. N. Standard Taper Bolts and Reamers Machine Bolts, Manufacturer's Standard Bolts of Uniform Strength Collar Screws Set Screws Cap Screws Studs Hook Bolts Coach Screws Bolt Head Dimensions Upset Bolt Ends Turnbuckles Sleeve Nuts Washers Foundation Bolts Eye Bolt Heads Eye Bolt Pins Eye Bolts for Flanges Bolt Ends with Slot and Cotter Bolt End with Slot, Gib and Key Wrenches, Open End Box Wrenches, Socket Wrenches Spikes ..'...- .. .303-420 SECTION 6 GENERAL SPECIFICATIONS FOR INSPECTION OF MATERIAL. NAVY DEPARTMENT General Quality Chemical Properties Analysis by Manufacturer Analysis by Government Physical Tests and Test Pieces Pulling Speed Types of Test Pieces Standard Size for Test Pieces Standard Size for Test Pieces for Boiler Plates and Steam Pipes Length of Test Pieces Flaws in Text Pieces Bending Test Pieces Special Heat Treatment Material Exempt from Tests All Material Subject to Inspection Annealing Weights Methods of Checking Contractors' and other Orders for In- spection of Material Material which is to be Inspected without Instruc- tions Inspection During Manufacture^ 'Contractors to Supply Blue Prints Information to be Furnished by the Manufacturer Shipment of Material Invoices to be prepared by Manufacturers Inspection Stamps Sealing of Cars Acceptance of Material Rejection at Destination. General Specifications for Inspection of Rubber Material, Navy Department: Temperature of Room Tests of Adhesion of Rubber Parts to Cotton or Fabric Parts Apparatus Preparation of Test Pieces Tests of Rubber Parts Making of the Measurements; Taking of Time; Elongation Tensile Strength Pressure Tests Composition: Friction, Material, Sample for Chemical Analysis Average Reading to be based on at least Four Determinations Rejections and Replacements Testing Me- chanical Rubber Goods, Bureau of Standards: Source of Crude Rubber Vulcanizing Rubber Substitutes Reclaimed Rubber Manufacture Breaking Down and Washing Drying Compounding and Mixing Sheeting Friction Cutting the Canvas Rubber Hose: Tubes and Covers; Making up the Hose, Vulcanizing, Cotton Rubber-lined Hose, Braided Hose with Rubber Tube and Cover Rubber Belting Me-r chanical Rubber Goods Physical Testing of Rubber: Tension Test, [xi] CONTENTS Recovery, Friction, Steam Pressure, Packing, Tires, Tension Test, Test Piece; Influence of Speed on Tensile Strength and Elongation; Influence of Temperature on Strength, Elongation, and Recovery; Influence of Cross Section on Tensile Strength and Elongation; Influence of the Direction in which Specimens are cut on Strength, Elongation, and Recovery; Influence of Previous Stretching on Strength, Elongation, and Recovery; Influence of the Form of Test Specimen on the Results of Tension Tests Friction Test Hydraulic Pressure Test The Chemistry of Rubber 421-442 SECTION 7 IRON AND STEEL CASTINGS Foundry Pig Iron: Carbon, Silicon, Manganese, Spiegeleisen, Ferromanganese, Silicon-Spiegel, Oxygen and Manganese, Sulphur, Phosphorus Grading Pig Iron Analysis of Standard Pig Iron Foundry Pig Iron for U. S. N.: Grades, Chemical Requirements, Purpose for which used, Sampling, Method of Analysis, Penalties, Locality, Sow Iron Chemical Changes in the Cupola: Foundry Coke, Calorific Value of Coke, Excess of Air, Temperature of Escaping Gases, Slag, Flux, Limestone, Fluorspar, Fuel Efficiency of the Cupola Furnace Iron Castings for U. S. N.: Physical Properties, Grades, Tensile Strength, Transverse Breaking Load, Pur- poses for which Intended, Hardness, Quality of Material, Tests, Finish- Malleable Cast Iron: Composition and Structure, Manganese, Phos- phorus, Silicon, Open-Hearth Furnace, Cupola Furnace, Annealing Specifications: Chemical Properties, Physical Properties, Test Lugs, Annealing, Finish Malleable Iron Castings for U. S. N.: Open-Hearth or Air-Furance, Physical and Chemical Properties, Freedom from Defects, to have Sufficient Anneal, Test Bars, Appearance after Machining, Pipe Flanges Semi-Steel Castings: Chemical Composition, Physical Prop- erties Steel Castings: Specifications for Steel Castings Three Classes: Hard, Medium, Soft Physical Properties of Each Steel Castings for U. S. N.: Process of Manufacture, Chemical and Physical Properties, Classification on Special, A, B, and C Classes, Physical Properties of Each: Treatment (a) All Castings shall be Annealed, (b) Additional or Subse- quent Treatment, (c) Castings treated without consent of the Inspector, (d) Cleaning Test Specimens Rejection after Delivery Percussive Test Surface Inspection Welding, when permitted Chemical Analy- sis Casting Record Annealing Record Ordnance Castings. Plum- bago for U. S. N. Foundry use: Volatile Matter, Ash, Graphite Carbon; for Foreign Shipment (U. S. N.), for Domestic Shipment (U. S. N.).. . .443^64 SECTION 8 IRON AND STEEL FORCINGS. CARBON AND HIGH-SPEED STEELS. HEAT TREATMENT Wrought Iron : Chemistry, Analysis of Pig and Wrought Irons, Wrought Iron and Steel, Texture of Wrought Iron, Malleability, Tensile Strength, Duc- tility, Elastic Limit, Safe Load, Compression, Welding, Stiffening, An- nealing, Effect of Low Temperature' Wrought Iron for Blacksmith use, U. S. N.: Process of Manufacture, Physical and Chemical Requirement, Tests, Nick Test, Drift Test, Completed Forgings, Special Grade of Wrought Iron, Physical and Chemical Requirements, Blacksmith Grade, Elongation Steel Forgings for Hulls, Engines, and Ordnance, U. S. N.: Material, Process, Discard, Surface and other Defects, Chemical and [xii] CONTENTS Physical Properties, Nickel Steel, Physical Test Specimens, Longitudinal Test Specimens, Transverse Test Specimens, Individual Tests, (a) Gen- eral, (b) Special, Test by Lot, List of Forgings Covered by the Foregoing General Requirements, Testing Miscellaneous Bars, Treatment of Forg- ings, Treatment of Hollow Forgings, Additional Heat Treatment Ingots, Slabs, Blooms, and Billets for U. S. N. : Line between Blooms and Billets Ingots, Slabs, Blooms, and Billets to be forged or rolled will require tests only of finished objects. Physical and Chemical Requirements for Blooms and Billets for Reforging General Requirements for Engine Forgings, U. S. N.: Treatment, Kind of Ingot, Test Pieces for Line, Thrust, and Propeller Shafts, Test Pieces for Crank Shafts, Test Pieces for Reverse Shafts Engine Forgings: Furnace, Size of Ingot, Defects, Piping, Segregation Reheating the Ingot Recalescence Forging Hollow Forgings Bell's Steam Hammer Heat Treatment of Carbon Steel : Carbon and Iron, Molecular Structure, Tempering and Annealing, Elements other than Carbon, Carbon Theory of Hardening Steel Solu- tion Theory-^-Allotropic Theory of Hardening Sorbite Heating Carbon Steel Three Factors in Heating Steel: Neutral Atmosphere, Uniformity in Heating, Temperature of the Furnace Carbon Tool Steel and Heat Treatment: Color Scale Indicating Temper of Carbon Steel Tools Furnaces: Tool Tempering Furnace Muffle Furnace Oven Furnace Oil Furnace Gas Furnace Flameless Combustion Furnace Electric Heating Furnace Heating Baths: The Lead Bath Cyanide of Potas- sium Bath Barium Chloride Bath Disadvantages of Barium Chloride Bath Hardening and Tempering High-Speed Steel Tools Electric Hardening Colors of Heated Steel Quenching Baths: Water, Brine, Oil, Tallow, Air Quenching Quenching and Hardening High-Speed Steel: Mushet's Self -hardening Steel; Heating and Hardening the Later High- speed Tool Steels; Double Hardening. Annealing Mild Steel Composi- tion and Heat Treatment of Carbon Steel other than Tool Steels: Compo- sition, Characteristics and Uses, Heat Treatment Hardening of Carbon and Low-Tungsten Steels: Hardening Temperatures, Change Point, Length of Time of Heating, Previous Annealing, Heating in Two Furnaces, Change of Length in Hardening, Miscellaneous Results, Effect of Tem- pering, Tensile Strength Composition and Heat Treatment of Carbon and Alloy Steels: Composition, Characteristics and Uses, Heat Treatment, Chrome-Nickel Steel, Chrome- Vanadium Steel Case-Hardening: Metals to be Case-Hardened, Mild Steel, Nickel Steel, Chrome Steel Carbur- izing Materials: Bone, Charred Leather, Cyanides, Effect of Nitrogen, Carburizing Gas, Method of Case-Hardening, Heating, Case-Hardening Temperatures, Quenching, Cooling and Reheating Case-Hardening Mixture Cyanide Process of Case Hardening Case Hardening for Colors 465-504 SECTION 9 NON-FERROUS METALS AND ALLOYS Non-Ferrous Metals Copper Group: Copper, Mercury, Lead, Bismuth Tin Group: Tin, Antimony, Arsenic Iron Group: Iron, Ferro-Mangan- ese, Manganese, Nickel, Cobalt Zinc Group: Zinc, Cadmium, Mag- nesium, Aluminum Alkaline-Earthy Metals: Calcium, Barium, Strontium Alkali Metals: Sodium, Potassium Non-Metals: Boron, Carbon, Hydrogen, Lime, Nitrogen, Oxygen, Phosphorus, Calcium Sulphate, Silicon, Sulphur Non-Ferrous Alloys: Physical Properties, Chemical Nature of Alloys, Specific Gravity, Fusibility, Liquation, Specific Heat, Eutectic Alloys, Occulsion, Oxygen, Deoxodizing Copper [xiii] CONTENTS Porosity of Brass Castings Fluxes used in Melting Non-Ferrous Metals Aluminum Alloys Amalgams. Chemical and Physical Requirements for use in U. S. Navy: Ingot Copper Copper Sheets, Plates, Rods, Bars, and Shapes Sheet Copper for Sheathing Bottoms of Wooden Craft Refined Copper for use in making Cartridge Cases Silicon Copper Phosphor Copper Ingot Tin Phosphor Tin Slab Zinc Rolled Zinc Plates Zinc for Boilers, Salt- Water Piping, Etc. Pig Lead Ingot Aluminum Gun Metal Valve Bronze Journal Bronze Torpedo Bronze Manganese Bronze Phos- phor Bronze Castings; Rolled or Drawn Bars Vanadium Bronze Rolled Bronze Plates Monel Metal Castings; Sheets, Plates, Rods, Bars. Benedict Nickel German Silver Inspection of Copper, Brass, and Bronze Standard Requirements for Alloys of Copper, Tin, and Zinc Seamless Brass Pipe Naval Brass Castings Rolled Naval Brass Sheets, Plates, Rods, Bars, Shapes Muntz Metal Castings Muntz Metal Sheets, Plates, Rods, Bars, and Shapes Commercial Brass: Castings, Rods, Bars, Shapes, Sheets, Plates, Piping Brass Castings for Electrical Appliances Anti-Friction Metal Castings Solder: Spelter, Half-and Half Crucibles Kroeschell-Schwartz Crucible Furnace Composition of Some Alloys used in Engineering; An Alphabetically Arranged List of 100 Alloys Covering all the Ordinary and most of the Special Needs of the Engineer Notes on Metals 505-568 SECTION 10 MACHINE DETAILS, PRINCIPALLY THOSE RELATING TO STEAM ENGINES Keyways and Keys: Proportions Length of Key Square Sunk Key Spe- cial Keys Gib Head Key, Table Sliding Key, Table Maximum Load on Key Double Keys, Table to 24 in. Shaft Kennedy Double Key, Table Peters' Double Key, Table to 12-in. Shaft Keys for Screw Propellers Bolt End with Collar and Cotter, Table Bolt End for Rigid Frame Connection, Table Valve Rod End with Bushing, Table Valve Rod End with Coupling, Table Valve Rod End, Boxes with Key Adjust- ment, Table Valve Rod Knuckle, Table Strap Joint with Gun-Metal Body and Steel Strap, Table Rod Coupling with Collar and Cotter, Table Rod Coupling with Single Taper Socket, Table Rod Coupling with Two Abutting Ends and Cotter, Table Rod Coupling with Two Taper Ends and Cotter, Table Screw Coupling, Adjustable, Table- Cranks, Cast Iron, Table Crank Pins, Table to 12-in. Diam. Connect- ing Rod Box Stub End with Wedge Adjustment for Crank Pin, 1 to 6-in. Pin, Table Connecting Rod Stub End with Strap Joint, Gib and Key, 1 to 6-in. Diam., Two Designs, Two Tables Connecting Rod Stub End for Crank Pin, with Bolted Strap, Wedge Block and Key, Table to 3-inch Pin Another Design continuing Proportions up to 12-inch Crank Pin! Connecting Rod Stub End for Crank Pin, Two Designs, Forked Pattern with Back Block, Adjusting Wedge and Liner, Both Sizes for 3 to 8-inch Crank Pin, Two Tables 569-607 INDEX.. ....609-619 PART II In Preparation for Early Publication CONTENTS ION 11. MACHINE TOOLS. 12. RIVETING AND FLANGING. 13. BOILER DESIGN CONSTRUCTION DETAILS. 14. BOILERS AND FURNACES CHIMNEYS. 15. HEAT AND STEAM. 16. FUEL AND COMBUSTION. 17. STEAM ENGINES. 18. STEAM TURBINES. 19. CONDENSING APPARATUS. 20. FRICTION AND LUBRICATION. 21. MEASURING AND RECORDING INSTRUMENTS. 22. WROUGHT PIPES AND TUBES WELDED AND RIVETED. 23. BRASS, COPPER, AND LEAD PIPES. 24. PIPE FITTINGS VALVES TRAPS. 25. INSULATING MATERIALS PACKINGS. 26. EVAPORATING AND DISTILLING APPARATUS. 27. GASES, PROPERTIES OF GASOLENE INDUSTRIAL ALCOHOL. 28. GAS PRODUCERS AND GAS ENGINES GASOLENE ENGINES. 29. OIL AND OIL ENGINES. 30. SHAFTING PULLEYS BEARINGS COUPLINGS. 31. POWER TRANSMISSION BELTS ROPES GEARS. 32. SCREW PROPELLERS PADDLE WHEELS. 33. FEED WATER PURIFICATION AND HEATING. 34. WATER WHEELS TURBINES. 35. PUMPING MACHINERY. 36. CAST-IRON PIPES VALVES HYDRANTS. 37. HYDRAULIC MACHINES. 38. COMPRESSED AIR. 39. HEATING AND VENTILATING. 40. PLUMBING FIXTURES. 41. REFRIGERATING MACHINERY. 42. HOISTING AND CONVEYING MACHINERY. 43. COAL HANDLING AND STORAGE. 44. FOUNDATIONS. 45. CONCRETE CEMENT MORTARS. 46. INDUSTRIAL RAILWAYS. 47. CHAINS ANCHORS HEMP ROPES WIRE ROPES. 48. CORROSION PROTECTIVE COATINGS PAINTS. 49. FIRE PROTECTION. 50. ELECTRICAL MACHINERY. xv INDUSTRIAL ENGINEERING SECTION I UNITS AND STANDARDS A unit is an acknowledged or standardized quantity in terms of which other quantities may be measured, results recorded, comparisons made, and measurements executed in experimental demonstration. The fundamental units in terms of which every measurement must be executed are those of Time, Space, and Mass. Time. Standards of time are derived from the revolution of the earth about its axis, which has an inclination of about 23 28' from a perpendicular to its plane. The motion of its rotation is from west to east. The Mean Solar Day is the mean interval which elapses between the sun's crossing the meridian, or being situated directly south of a place, and the next occasion on which it crosses that line. Be- sides rotating on its own axis, the earth describes- an ellipse around the sun; the effect of these combined movements is to alter the length of the solar day, a variation occurs throughout the year of from 14 ^ minutes fast to 16% minutes slow. A mean solar day is the average or mean of all the solar days in a year; it is divided into 24 hours, each hour into 60 minutes and each minute into 60 seconds; therefore, one second represents 24 X 60 X 60 = 86400 part of a solar day; the usual sub- division of seconds is decimal. The Unit of Time in engineering is one second of mean solar time. For con- venience, other and larger units are often used, such as revolutions per minute, miles per hour, and so forth. Space is a necessary representation which serves for the foundation of all ex- ternal intuitions. It is not a conception which has been derived from outward experiences. We can never imagine the non-existence of space, though we may easily enough think that no objects are found in it. Intuition lies at the root of all our conceptions of space. We can only represent to ourselves one space and that an infinite given quantity; when we talk of divers spaces, we mean only parts of one and the same space. We conceive of space as having three dimensions, within which are contained all objects which can appear to us externally. Geometry is a science which determines the property of space synthetically. When a single point moves it describes a line and the shortest distance between two points is a straight line; a representation of space in one direction. Points are conceived of as having position without magnitude, and lines as having length without breadth or thickness. A straight line may be divided into any number of shorter lines and one of these may be chosen as a unit by which other lines may be measured in terms of that unit. Standard of Length. The British standard yard is defined by law as " the distance between the centers of the transverse lines in the two gold plugs in the bronze bar deposited in the office of the Exchequer " at the temperature of 62 F. An authorized copy of this standard is deposited at Washington. This standard yard has been subdivided into three equal parts, one of which is called a foot; and into 36 equal parts, one of which is called an inch. The Metric System is based upon an authorized standard of length called a meter, which consists in that distance, at the temperature of melting ice, between the ends of a platinum rod preserved in the French Archives, Paris. An authorized copy of this standard meter has been deposited at Washington. The metric system of measurement of length is decimal. [1] UNITS AND STANDARDS The equivalent length of a meter in British measurements as adopted by the United States is as follows: Meter = 39 . 37000 inches, or .............. 1 inch = . 02540 meter. = 3.28083 feet, or ........... . _____ 1 foot = . 30480 meter. = 1.09361 yards, or ........... ---- 1 yard = 0.91440 meter. Mass. The mass of a body is the quantity of matter which it contains; it must be carefully distinguished from weight. Mass is a constant quantity, whilst weight varies with the force of gravity which produces it. Weight varies with the latitude, being greatest at the poles and least at the equator; weight varies with different elevations above the level of the sea, but the mass of a body is its own property, it is the same under all circumstances, it is unaffected by change of latitude or by altitude. We are accustomed in commercial transactions to employ mass in terms of weight, and correctly as according to Newton's Law of Gravitation, which tells us that in any locality whatever the weights of bodies are equal if their masses are equal. The earth's attraction for a body free to fall in a vacuum is subject to a constant downward acceleration of about 32.2 feet per second, at the level of the sea, latitude of London, but it is not the same at all points of the earth's surface. Inasmuch as gravity varies less than one-half per cent, within the latitudes covered by engineering practice, weights need not ordinarily be corrected for locations approximating the level of sea; but for height much above the sea level, such as mountains, the lesser weight of the atmosphere or barometric changes must be taken into account. The Unit of Mass in use by English and American engineers is the British standard pound avoirdupois, an arbitrary standard consisting of a certain piece of platinum deposited in the office of the Exchequer, an authorized copy of which is preserved at Washington. This standard pound contains 7,000 grains, a grain being the smallest unit employed in British weight. When used for comparing or verifying other standards, it is directed to be used when the thermometer is 62 F., and the barometer at 30 inches. Then = =217.39! grains. g oZ.Z An avoirdupois ounce = 437.5 grains. 437 5 Then oi>7 onV = 2 . 01 = the British unit of force Poundal, equivalent to one- J17 . o91 half ounce nearly. This unit of force does not in any way depend on local variations in the force of gravity. For all practical purposes, the engineer's Unit of Force is the avoirdupois pound. A pound-mass equal to 32.2 British Units of Force. The French standard of weight is the Kilogram (= 1000 grams), made of platinum, and preserved at the Archives in Paris. This standard is intended to have the same weight as a cubic decimeter of water at the temperature of its maxi- mum density that is, 3* .9 C. A gram is equal to the 1000th part of a kilogram or the mass of one cubic centi- meter of water at the temperature of its maximum density. The gram is chosen as a unit in the C.G.S. System. C. G. S. SYSTEM The fundamental units in this system, recommended by the British Association and accepted as the standards of references throughout the scientific world, are: a definite length, centimeter (C); a definite mass, gram (G); a definite interval of time, second (S). These standards of length, mass, and time are permanent and do not change with lapse of time. [2] G. G. S. SYSTEM The reason for selecting the centimeter and the gram, rather than the meter and the gram, is that since a gram of water has a volume of approximately one cubic centi- meter, the selection of the centimeter makes the density of water unity; whereas the selection of the meter would make it a million, and the density of a substance would be a million times its specific gravity, instead of being identical with its gravity, as in the C. G. S. System. The adoption of one common scale for all quantities involves the frequent use of very large and very small numbers. Such numbers are most conveniently written by expressing them as the product of two factors, one of which is a power of 10, and it is usually advantageous to effect the resolution in such a way that the exponent of the power of 10 shall be characteristic of the logarithm of this number. Thus: 3,240,000,000 will be written 3.24 X 10 9 , and 0.00000324 will be written 3.24 X 10-6. The value of the meter in British inches, adopted by the Bureau International des Poids et Mesures, is 39.3699. This makes 1 yard = 91.4404 centimeters. 1 foot = 30.4801 centimeters. 1 inch = 2.5400 centimeters. The standard pound = 453.59 grams, which gives 1 kilogram = 2.20463 pounds. This is in practical correspondence with the units legalized in the United States. By Act of Congress, July 28, 1866, the legal equivalent of 1 meter - 39.37 inches. This makes 1 yard = 91.4402 centimeters. 1 foot = 30.4801 centimeters. 1 inch = 2.54001 centimeters. A variation from the International Metric System so slight as to make little difference whether American or European units or products are employed. MECHANICAL AND GEOMETRICAL QUANTITIES The fundamental units are abbreviated thus: L = length, M = mass, T = time. Example, Area = L 2 , Volume = L 3 , Velocity = , Acceleration = , Momentum = ~~^T) Density = , density being defined as mass per unit volume. Force = , since a force is measured by the momentum which it generates per unit of time, and is therefore the quotient of momentum by time. Or, since a force is measured by the product of a mass by the acceleration generated in this mass. Work = , being the product of force and distance. Kinetic Energy = - being half the product of mass by the square of velocity. The constant factor y% can be omitted, as not affecting dimensions. Torque, or Moment of Couple = ~-, being the product of a force by a length. The Dimensions of Angle, when measured by rr are zero. The same angle will radius be denoted by the same number whatever be the unit of length employed. In fact, arc L we have - = - = L . radius L The work done by a torque in turning a body through any angle is the product of [3] C. G. S. SYSTEM the torque by the angle. The identity of dimensions between work and torque is thus verified. Angular Velocity = . Angular Acceleration = . Moment of Inertia = M L 2 . Angular Momentum = Moment of Momentum = , being the product of mo- ment of inertia by angular velocity, or the product of momentum by length. Intensity of pressure; or intensity of stress generally, being a force per unit of area, . , ,. . force ., M is of dimensions , that is, -. area ' L T 2 Intensity of force of attraction at a point, often called simply force at a point, being force per unit of attracted mass, is of dimensions or . It is numerically equal to the acceleration which it generates, and has accordingly the dimensions of acceleration. Curvature (of a curve) = , being the angle turned by the tangent per unit distance Li travelled along the curve. Tortuosity = , being the angle turned by the osculating plane per unit distance Li travelled along the curve. J. D. Everett. C. G. S. MECHANICAL UNITS Value of g. Velocity is the rate of motion. It is either uniform or variable. When variable, the rate at which it changes is called acceleration if the velocity is increasing, and retardation if it is diminishing. The C. G. S. unit of acceleration is the accelera- tion of a body whose velocity increases in every second by the C. G. S. unit of velocity namely, by a centimeter per second. The apparent acceleration of a body falling freely under the action of gravity in vacuo is denoted by g. The value of g in C. G. S. units is about 978 at the equator, about 983 at the poles, and about 981 at Paris or London. The value at sea level and latitude 45 employed by the Bureau of Standards is g = 980.665 dynes. Unit of Force. The C. G. S. unit of force is called the dyne. It is the force which, acting upon a gram of matter for a second, generates a velocity of a centimeter per second. The dyne is about 1.02 times the weight of a milligram at any part of the earth's surface; and the megadyne is about 1.02 times the weight of a kilogram. The force represented by the weight of a gram varies from place to place. To com- pute its amount in dynes at any place where g is known, observe that a mass of one gram falls in vacuo with acceleration g. The weight (when weight means force) of one gram is therefore g dynes, and the weight of m grams is m g dynes. The weight of a gram at any part of the earth's surface is about 980 dynes. Force is said to be expressed in gravitation measure when it is expressed as equal to the weight of a given mass. Such specification is inexact unless the value of g is also given. For purposes of accuracy it must always be remembered that the pound, the gram, etc., are, strictly speaking, units of mass. Poundal. The name poundal has been given to the unit force based on the pound, foot, and second; that is, the force which, acting on a pound for a second, generates a velocity of a foot per second. It is of the weight of a pound, g denoting the accelera- [4] C. G. S. SYSTEM tion due to gravity expressed in foot-second units, which is about 32.2 feet per second, at the level of the sea, latitude of London. To compare the poundal with the dyne, let x denote the number of dynes in a poundal; we then have _ gm. cm. _ Ib. ft. sec 2 sec 2 x = J*L. 1*1= 453.59 X 30.4801 = 13,825. gm. cm. Unit of Momentum is the momentum of a gram moving with the velocity of a centimeter per second. Unit of Work. The C. G. S. unit of work is called the erg. It is the amount of work done by a dyne working through a distance of a centimeter. The gram-centi- meter is about 980 ergs. The kilogrammeter is about 98,000,000 ergs. Unit of Energy. The C. G. S. unit of energy is also the erg, energy being measured by the amount of work which it represents. Unit of Power. The C. G. S. unit of power is the power of doing work at the rate of one erg per second; and the power of an engine, under given conditions of working, can be specified in ergs per second. Gravitation Units of Work. Work, like force, is often expressed in gravitation measures, such as the foot, pound and kilogrammeter, these varying with locality, being proportional to the value of g. 1 gram-centimeter = g ergs. 1 kilogrammeter = 100,000 g ergs. 1 foot-poundal = 453.59 X (30.4801) 2 = 421,401 ergs. 1 foot-pound = 13,823 gram-centims., which, if g = 981 = 1.356 X 10 7 ergs. 1 joule = 10 7 ergs. Work-rate, or Activity. The time rate of doing work in the C. G. S. System is one erg per second. A horsepower is defined as 550 foot-pounds per second. This is 7.46 X 10 9 ergs per second. A cheval is defined as 75 kilogrammeters per second. This is 7.36 X 10 9 ergs per second. The value of g = 981. Watt. A work-rate of 10 7 C. G. S. is called a watt, and 1,000 watts make a kilowatt. 1 watt = 10 7 ergs per second = .00134 horsepower = .737 foot-pounds per second = .1019 kilogrammeters per second. 1 kilowatt = 1.34 horsepower. 1 horsepower = 550 foot-pounds per second = 76.0 kilogrammeters per second = 746 watts = 1.01385 cheval = .746 kilowatt. 1 cheval = 75 kilogrammeters per second = 542.48 foot-pounds per second = 736 watts = .9863 horsepower = .736 kilowatt. Calorie. Engineers commonly reckon the heat value of fuels in terms of kilogram- calories. The kilogram calorie represents the energy required to raise the temperature of one kilogram of cold water one degree Centigrade; this is equivalent to raising one kilogram to a height of about 427 meters. The kilogram-calorie is sometimes called the kilogram-degree, as well as the major calorie. The heat unit employed in physical and chemical laboratories is a metric unit also called a calorie; it is the heat required to raise the temperature of a gram of cold water one degree Centigrade. This is the gram-degree or minor calorie. In the C. G. S. System the primary unit of heat in calorimetry is the erg. In this system the unit of force is called the dyne; the force which, acting upon a gram for a second, generates a velocity of a centimeter per second. This work unit is called a dyne-centimeter, which, for convenience, has been shortened to erg. Since the erg is a very small unit of work, the joule = 10 7 ergs is often used. But it is the practice to employ a secondary rather than the primary unit of heat, and this unit is called a therm. It has the same value as the gram-degree, or the minor calorie, given above. The kilogram-degree, or major calorie, is equal to 1,000 therms. The pound-degree Cent, is 453.6 therms, and the pound-degree Fahr. is 252.0 therms. The ratio of the secondary to the primary unit of heat is commonly called the [5] BRITISH THERMAL UNIT " mechanical equivalent of heat," quite often "Joule's equivalent," and is denoted by the symbol J. It is the number of .units of work required to raise the temperature of unit mass of water 1. In the C. G. S. System it is the number of ergs in a therm. The following values of J will be useful for reference. Taking g as 981, 1 kilogram-degree = 1000 therms. = 426.5 kilogrammeters. 1 pound-degree Cent. = 453.6 therms. = 1399.4 foot-pounds. 1 pound-degree Fahr. = 252.0 therms. = 777.4 foot-pounds. Taking g as 981.2, its value at Greenwich, these values of J are changed to 426.42, 1399.1, 777.3. At Edinburgh, taking g as 981.6, they will be 426.67, 1399.9, 777.7 In latitude 45, taking g as 980.62, they will be 426.67, 1399.9, 777.7. Unit of Heat. The British thermal unit of heat (B.t.u.) is the amount of heat required to raise the temperature of 1 Ib. of water 1 Fahr. when at or near its greatest density (39.1 F.). This is sometimes called the pound-degree Fahrenheit unit. In the pound-degree Centigrade unit the avoirdupois pound and the Centigrade scale of temperature are used. The mechanical equivalent of heat as experimentally determined by Joule was found to equal 772 foot-pounds for one degree Fahr., or 1,390 foot-pounds for a degree Cent., communicated to one pound of water at its greatest density. In honor of Joule, the mechanical equivalent of heat is usually denoted by the letter J. Recent investigations by Rowland and others have led to the conclusion that 778 is a more nearly correct value (about f of 1 per cent greater) and that 1 B.t.u. = 778 foot-pounds = J. In engineering calculations, the former equivalent gives oo ooo 1 horsepower = ' = 42.74 thermal units. The later equivalent gives DO OOO 1 horsepower = ' = 42.42 thermal units. 77o UNITS OF MEASUREMENT AND DERIVED UNITS IN USE IN GREAT BRITAIN AND THE UNITED STATES The fundamental units of length and mass employed in engineering work are not commonly those of the C. G. S. System. In the United States the same units are employed as in Great Britain; the unit of length being the yard, or, for convenience, a subdivision of the yard as foot or inch. The unit of mass is the avoirdupois pound. The unit of tune is the second. The folio whig dimensional formulae are from the Smithsonian Physical Tables. Derived Units. Units of quantities depending on powers greater than unity of the fundamental length, mass and time units, or on combinations of different powers of these units, are called " derived units." Thus, the units of area and volume are respectively the area of a square whose side is the units of length and the volume of a cube whose edge is the unit of length. Suppose that the area of a surface is expressed in terms of the foot as fundamental unit, and we wish to find the area-number when the yard is taken as fundamental unit. The yard is three times as long as the foot, and therefore the area of a square whose side is a yard is 3 X 3 times as great as that whose side is a foot: Dimensional Formulae. It is convenient to adopt symbols for the ratio of length units, mass units and time units, and adhere to their use throughout, and to what [6] FUNDAMENTAL AND DERIVED UNITS follows the small letters I, m, t, will be used for these ratios. These letters will always represent simple numbers, but the magnitude of the number will depend upon the relative magnitude of the units, the ratio of which they represent. When the values of the numbers represented by I, m, t, are known, and the powers of I, m, t, involved in any particular are also known, the factor for transformation is at once obtained. Conversion Factors. In order to determine the symbolic expression for the con- version factor for any physical quantity, it is sufficient to determine the degree to which the quantities, length, mass and time are involved in the quantity. Thus, a velocity is expressed by the ratio of the number representing a length to that repre- senting an interval of time, or , an acceleration by a velocity-number divided by an interval of a time-number, or , and so on, and the corresponding ratios of units must, therefore, enter to precisely the same degree. The factors would thus be for the above cases, and . Equations of the form above given for velocity and ac- t t celeration which show the dimensions of the quantity in terms of the fundamental units are called " dimensional equations." Area. The unit of area is the square the side of which is measured by the unit of length. The area of a surface is therefore expressed as S = CL 2 , where C is a constant depending on the shape of the boundary of the surface and L a linear dimension. For example, if the surface be a square and L be the length of a side, C is unity. If the boundary be a circle and L be a diameter, C = , and so on. The dimensional formula is thus L 2 , and the conversion factor Z 2 . Volume. The unit of volume is the volume of a cube the edge of which is measured by the unit of length. The volume of a body is therefore expressed a? V = CL 3 where, as before, C is a constant depending on the slope of the boundary. The dimensional formula is L 3 and the conversion factor is Z 3 . Density. The density of a substance is the quantity of matter in the unit of volume. M The dimension formula is therefore or M L~ 3 , and conversion factor ra Z~ 3 . NOTE. The specific gravity of a body is the ratio of its density to the density of a standard substance. The dimension formula and conversion factor are therefore both unity. Velocity. The velocity of a body at any instant is given by the equation v = -r-=, or velocity is the ratio of a length-number to a time-number. The dimensional formula L T - J , and conversion factor It" 1 . Angle. Angle is measured by the ratio of the length of an arc to the length of the radius of the arc. The dimension formula and the conversion factor are therefore both unity. Angular Velocity. Angular velocity is the ratio of the magnitude of the angle described in an interval of time to the length of the interval. The dimension formula is therefore T" 1 , and the conversion factor is t~ l . dv Linear Acceleration. Acceleration is the rate of change of velocity or a = 7-. The at dimension formula is therefore VT" 1 or LT~ 2 , and the conversion factor is lt~ z . Angular Acceleration. Angular acceleration is the rate of change of angular velocity. The dimensional formula is thus or T~ 2 , and the conver- sion factor is t ~ 2 . Solid Angle. A solid angle is measured by the ratio of the surface of the portion m FUNDAMENTAL AND DERIVED UNITS of a sphere inclosed by the conical surface forming the angle to the square of radius of the radius of the spherical surface, the center of the sphere being at the vertex of the cone. The dimensional formula is therefore or 1, and hence the conversion factor is also 1. Curvature. Curvature is measured by the rate of change of direction of the curve with reference to distance measured along the curve as independent variable. The dimension formula is therefore : - - or L"" 1 , and the conversion factor is Z" 1 . length Tortuosity. Tortuosity is measured by the rate of rotation of the tangent plane round the tangent, to the curve of reference when length along the curve is independent variable. The dimension formula is therefore . or L" 1 , and the conversion length factor is l~ l . Specific Curvature of a Surface. This was denned by Gauss to be at any point of the surface, the ratio of the solid angle enclosed by a surface formed by moving a normal to the surface round the periphery of a small area containing the point, to the magnitude of the area. The dimensional formula is therefore - ; - or L~ 2 . and the con- surface version factor is l~\ Momentum. This is the quantity of motion in the Newtonian sense, and is, at any instant, measured by the product of the mass-number and the velocity-number for the body. Thus, the dimension formula is M V or M L T -1 and the conversion factor mlt~ l . The Moment of Momentum. The moment of momentum of a body with reference to a point is the product of its momentum-number and the number expressing the distance of its line of motion from the point. The dimensional formula is thus M L 2 T - * and hence the conversion factor is m P t~ l . Moment of Inertia. The moment of inertia of a body round any axis is expressed by the formula S m r 2 , where m is the mass of any particle of the body and r its distance from the axis. The dimension formula for the sum is clearly the same as for each element and hence is M L 2 . The conversion factor is therefore m I 2 . Angular Momentum. The angular momentum of a body round any axis is the product of the numbers expressing the moment of inertia and the angular velocity of the body. The dimensional formula and the conversion factor are therefore the same as for moment of momentum given above. Force. A force is measured by the rate of change of momentum it is capable of producing. The dimension formulae for force and " time-rate of change of momentum" are therefore the same and are expressed by ratio of momentum-number to time- number or M L T~ 2 . The conversion factor is thus ml t~ z . NOTE. When mass is expressed in pounds, length in feet, and tune in seconds, the unit of force is called the poundal. When grams, centimeters, and seconds are the corresponding units, the unit of force is called the dyne. Moment of a Couple, Torque or Twisting Motive. These are different names for a quantity which can be expressed as the product of two numbers representing a force and a length. The dimension formula is therefore FL or M L 2 T~ 2 , and the con- version factor is m I 2 t~ 2 . Intensity of a Stress. The intensity of a stress is the ratio of a number expressing the total stress to the number expressing the area over which the stress is distributed. The dimensional formula is thus F L~ 2 or M L -1 T~ 2 , and the conversion factor isml-H-*. Intensity of Attraction, or " Force at a Point." This is the force of attraction per unit mass on a body placed at the point, and the dimensional formula is therefore F M" 1 or LT~ 2 , the same as acceleration. The conversion factors for acceleration therefore apply. [8] FUNDAMENTAL AND DERIVED UNITS Absolute Force of a Center of Attraction, or " Strength of a Center." This is the intensity of force at unit distance from the center and is, therefore, the force per unit- mass at any point multiplied by the square of the distance from the center. The dimensional formula thus becomes FL 2 M" 1 or L 3 T~ 2 . The conversion factor is therefore l*t~ 2 . Modulus of Elasticity. A modulus of elasticity is the ratio of stress intensity to percentage strain. The dimension of percentage strain is a length divided by a length, and is therefore unity. Hence the dimensional formula of a modulus of elasticity is the same as that of stress intensity, or M L~ 1 T~ 2 , and the conversion factor is thus also ml~ l t~ 2 . Work and Energy. When the point of application of a force acting on a body moves in the direction of the force, work is done by the force, and the amount is measured by the product of the force and displacement number. The dimensional formula is therefore FL or M L 2 T~ 2 . The work done by the force either produces a change in the velocity of the body, or a change of shape or configuration of the body, or both. In the first case it produces a change of kinetic energy, in the second a change of potential energy. The dimension formulae of energy and work representing quantities of the same kind are identical and the conversion factor for both is m I 2 <" 2 . Resilience. This is the work done per unit-volume of a body in distorting it to the elastic limit, or in producing rupture. The dimension formula is therefore M L 2 X-2 L~3 or M L" 1 T~ 2 , and the conversion factor is m l~ l t~*. Power, or Activity. Power or, as it is now very commonly called, activity is dw defined as the time-rate of doing work, or, if W represents work and P power, P = - . d t The dimensional formula is therefore W T - l or M L 2 T ~ 3 and the conversion factor m I 2 t ~ 3 , or for problems in gravitation-units, more conveniently / It ~ l , where / stands for force factor. EXAMPLE 1. Find the number of gram- centimeters in one foot-pound. Here the units of force are the attraction of the earth on the pound and the gram of matter, and the conversion factor is / 1, where / is 453.59 and I is 30.48. Hence the number is 453.59 X 30.48 = 13,825. NOTE. It is important to remember that in problems like that here given the terms "pound " or "gram" refer to force and not to mass. 2. If gravity produces an acceleration of 32.2 feet per second per second, how many watts are required to make one horse-power? One horse-power is 550 foot-pounds per second, or 550 X 32.2 = 17,710 foot- poundals per second. One watt is 10 7 ergs per second, that is, 10 7 dyne- centimeters per second. The conversion factor is ml 2 t~ 3 , where m = 453.59, I = 30.48, and t = 1, and the result has to be divided by 10 7 , the number of dyne-centimeters per second in the watt. Hence, 17,710 mPt~ 3 -;- 10 7 = 17,710 X 453.59 X 30.48 2 -f- 10 7 = 746.3. 3. How many gram-centimeters per second correspond to 33,000 foot-pounds per minute? The conversion factor suitable for this case is fl t -1 , where / is 453.59, I is 30.48, and t is 60. Hence, 33,000 It-* = 33,000 X 453.59 X 30.48 + 60 = 7,604,000, nearly. HEAT UNITS If heat be measured in dynamical units its dimensions are the same as those of energy, namely, ML 2 T~ 2 . The most common measurements, however, are made in thermal units, that is, in terms of the amount of heat required to raise the temperature of unit mass of water one degree of temperature at some stated temperature. This method of measurement involves the unit of mass and some unit of temperature, and hence if we denote temperature-numbers by 9 and their conversion factors by d, the dimensional formula and conversion factor for quantity of heat will be M9 and mO respectively. The relative amount of heat compared with water as standard substance [9] FUNDAMENTAL AND DERIVED UNITS required to raise unit mass of different substances one degree in temperature is called their specific heat and is a simple number. Unit volume is sometimes used instead of unit mass in the measurement of heat, the units being then called thermometric units. The dimensional formula is in that case changed by the substitution of volume for mass and becomes L 3 6, and here the conversion factor is to be calculated from the formula 1*6. Coefficient of Expansion. The coefficient of expansion of a substance is equal to the ratio of the change of length per unit length (linear) or change of volume per unit volume (voluminal) to the change of temperature. These ratios are simple numbers, and the change of temperature is inversely as the magnitude of the unit of tempera- ture. Hence, the dimensional and conversion-factor formulae are 9 1 d~ l . Conductivity, or Specific Conductance. This is the quantity of heat transmitted per unit 01 time per unit of surface per unit of temperature gradient. The equation TT for conductivity is therefore with H as quantity of heat K = L 2 T and the dimensional L formula = T-TT> which gives m I ~ 1 1 ~ l for conversion factor. 9 L 1 LI In thermometric units the formula becomes L 2 T ~ *, which properly represents diffusivity . In dynamical units H becomes M L 2 T ~~ 2 and the formula changes to M L T - 3 *. The conversion factors obtained from these are I 2 1 ~ 1 and mlt" 3 6~ 1 respectively. Similarly, for emission and absorption we have: Emissivity and Immissivity. These are the quantities of heat given off by or taken in by the body per unit of time per unit of surface per unit difference of tem- perature between the surface and the surrounding medium. We thus get the equation EL 2 9T = H = M9. The dimensional formula for E is therefore M L~ 2 T~ l , and conversion factor ml~ z t~ l . In thermometric units by substituting I* for m the factor becomes I t~ l , and in dynamical units m t~ s 0~ l . Thermal Capacity. This is the product of the number for mass and the specific heat, and hence the dimensional formula and conversion factor are simply M and m. Latent Heat. Latent heat is the ratio of the number representing the quantity of heat required to change the state of a body to the number representing the quantity of M 9 matter in the body. The dimensional formula is therefore, or 9, and hence the conversion factor is simply the ratio of the temperature units or 6. In dynamical units the factor isl*t-*. NOTE. When 9 is given the dimension formula L 2 T~ 2 , the formulae in thermal and dynamical units are always identical. The thermometric units practically suppress mass. Joule's Equivalent. Joule's dynamical equivalent is connected with quantity of heat by the equation ML2T- 2 = JHorJM8. This gives for the dimensional formula of J the expression L 2 T~ 2 9. The conver- sion factor is thus represented by Z* 1~ 2 0. When heat is measured in dynamical units J is a simple number. Entropy. The entropy of a body is directly proportional to the quantity of heat it contains and inversely proportional to its temperature. The dimensional formula is ivr 9 thus - or M, and the conversion factor is m. When heat is measured in dynamical 9 units the factor ismPt~ z 6~ l . EXAMPLE. Find the relation between the British thermal unit, the calorie and the therm. Neglecting the variation of the specific heat of water with temperature, or defining all the units for the same temperature of the standard substance, we have the following definitions: The British thermal unit is the quantity of heat required to raise the [10] FUNDAMENTAL AND DERIVED UNITS temperature of one pound of water 1 F. The calorie is the quantity of heat required to raise the temperature of one kilogram of water 1~ O. The therm is the quantity of heat required to raise the temperature of one gram of water 1 C. Hence: To find the number of calories in one British thermal unit, we have ra = .45399 and 8 = ; m 6 = .45399 X = .25199. y To find the number of therms in a calorie, m = 1,000 and = 1; .". m = 1,000. It follows at once that the number of therms in one British thermal unit is 1,000 X .25199 = 251.99. If Joule's equivalent be 776 foot-pounds per pound of water per degree Fahr., what will be its value in gravitation units when the meter, the kilogram and the degree Cent, are units? The conversion factor in this case is v It t ~ 2 6 _ or 1 0, where I = .3048 and = 1.8; ' :. 776 X .3048 X 1.8 = 425.7. If Joule's equivalent be 24,832 foot-poundals when the degree Fahr. is unit of temperature, what will be its value when kilogrammeter-second and degree-Centigrade units are used? The conversion factor is Z 2 ~ 2 0, where I = .3048, t = 1, and 6 = 1.8; .'. 24,832 Xl 2 t~ 2 6 = 24,832 X .3048 2 X 1.8 = 4,152.5. In gravitation units this would give ' ' = 423.3. 9.ol FUNDAMENTAL AND DERIVED UNITS OF LENGTH, MASS, TIME, AND TEMPERATURE Fundamental: Length ......... Symbol: L ...... Conversion factor: I Mass .................... M ..................... m Time ____ ... ............. T ...................... t Temperature ............. ...................... 6 GEOMETRIC AND DYNAMIC UNITS Derived: Area .............. ........... . . .Conversion factor: P Volume ......................................... . I 3 Angle ............................................ Solid Angle ................ .... _____ ......... ..... . Curvature ............ .............. .............. ~ l Tortuosity ..... .- ....... . ............ ............. Specific Curvature of a Surface ..................... - 2 Angular Velocity .................................. Angular Acceleration ..... ....... ........ ............ It ~ 2 Linear Velocity. . . ........ ......; ........... ..... . I t~ l Linear Acceleration ............................... .. lt~ z Density ................................. . . . ...... m l~ 3 Moment of inertia ...... ................. ......... m P Intensity of attraction, or " force at a point " . . . ..... It-* Absolute force of a center of attraction, or "strength of a center" ..... ................. . ........ ..... I 3 1 ~ 2 Momentum ......................... ... .......... mlt~ l Moment of momentum, or angular momentum ........ m Z 2 t~ l Force ............................................ ml t~ 2 Moment of a couple, or torque ...................... mPt~ 2 Intensity of stress ................................. ml~ l t~ 2 Modulus of elasticity ....................... ........ ml~ 1 t~ 2 Work and energy ...... ........................... m I' 2 1 ~ 2 Resilience ............... . ........................ m l~ l t~ 2 Power, or activity ................................. m I 2 1 ~ 3 111] UNITED STATES UNITS AND STANDARDS HEAT UNITS Derived: Quantity of heat (thermal units) . . .Conversion factor: m Quantity of heat (thermometric units) ............... p Q Quantity of heat (dynamical units) .................. mPt~ z Coefficient of thermal expansion .................... Q - 1 Conductivity (thermal units) ....................... ml~ l t~ l Conductivity (thermometric units), or diffusivity ...... I 2 t~ l Conductivity (dynamical units) .................. m 1 1~ 3 1 Emissivity and imissivity (thermal units) ............ ml- 2 t~ l Emissivity and imissivity (thermodynamic units) ...... lt~ l Emissivity and imissivity (dynamical units) .......... mt~ 3 0~ l Thermal capacity ................................. m Latent heat (thermal units) ........................ Latent heat (dynamical units) ...................... l z t~ 2 Joule's equivalent ................................. p t ~ 2 Entropy (heat measured in thermal units) ............ m Entropy (heat measured in dynamical units) ......... UNITED STATES UNITS AND STANDARDS The weights and measures in common use in the United States are an inheritance from the Colonial period, therefore in substantial agreement with those of Great Britain; certain variations occur such as the gallon and the bushel, which will be explained further on. Conformably to a resolution passed by the U. S. Senate in 1830, the Secretary of the Treasury ordered a comparison of the weights and measures in use at the principal custom houses to be made, and appointed F. R. Hassler, Superintendent of the U. S. Coast Survey, to make the investigation and report. A preliminary report was made in 1831, followed by a more complete report the year following. As was anticipated, large discrepancies were found, but the average value of the different denominations agreed fairly well with those in use in Great Britain at the time of the American Revolution. Mr. Hassler was instructed to correct this irregularity by the construction of uniform weights and measures for the customs service. With the exception of the troy pound-weight, Congress had legalized no system of units of weights and measures. The avoirdupois pound adopted by Mr. Hassler as the standard for the Treasury Department was derived from the troy pound of the U. S. Mint according to the equiv- alent 1 avoirdupois pound equals - 1 - pounds troy. This was the accepted relation 5,7oO in this country as well as in England. The standard yard of 36 inches, copied from the English yard, was incorporated as the standard unit of length. Two units of capacity, the wine gallon of 231 cubic inches and the Winchester bushel of 2,150.42 cubic inches, were adopted because they represented more closely than any other English standards the average capacity measures in use in the United States at the date of Mr. Hassler's investigation. These were the fundamental standards adopted upon the recommendation of Mr. Hassler by the U. S. Treasury Department, and to which the weights and measures for the customs service were made to conform. AIR AS A STANDARD The atmosphere varies in density from practically nothing, where it shades off into space, to that produced by a pressure of 14.7 Ibs. at the level of the sea, which we call atmospheric pressure. The height of the atmosphere has never been measured, but observations of the duration of twilight, which is due to reflection from particles of dust and air, give about 50 miles as the limit. [12J AIR AS A STANDARD 1 atmosphere 1 pound per square inch 1 pound pressure per sq. in. 1 pound pressure per sq. in. 1 Ib. pressure per sq. in. 32 F. F. = 1 Ib. pressure per sq. in. 62' 1 atmosphere 32 F. 1 inch height of mercury 1 atmosphere 62 F. inch height of mercury atmosphere pound per square foot pound pressure per sq. ft. pound pressure per sq. ft. 1 pound pressure per sq. ft. = 1 atmosphere 1 foot height of water at 62 F. 1 atmosphere 1 foot height of water at 32 Ah-, dry and pure, 32 F. 32 F. 32 F. 62 F. 62 F. 62 F. 1 atmosphere at 32 F. F. 1 atmosphere 1 short ton per square foot 1 atmosphere 1 long ton per square foot 14.697 pounds per square inch (14.7). .0680 atmosphere. 27.72 inches or 2.31 feet high of water at 62 F. 1891 feet high of air of uniform density at sea level and 62 F. 2.035 inches high of mercury or 51.7 milli- meters. 2.04 inches high of mercury. 29.921 incLes high of mercury. .0334 atmosphere, 32 F. 30 inches high of mercury. .0333 atmosphere, 62 F. 2116.35 pounds per square foot. .000473 atmosphere. .1925 inches high of water at 62 F. 13.13 feet high of air of uniform density at sea level and 32 F. .0141 inch or .359 millimeter of mercury at sea level and 32 F. At 62 F. the height is .01417 inch. = 33.947 feet of water in height at 62 F. = .0294 atmosphere. 33.901 feet high of water at 32 F. = .0295 atmosphere. = 1.0000 specific gravity. = .080728 weight in pounds, 1 cubic foot. = 12.387 vol. of 1 pound in cubic feet. .94263 specific gravity 32 = 1.000. .076097 weight of 1 cu. ft. pounds. = 13.141 vol. of 1 pound in cubic feet. = 27801 feet or 5.265 miles high of uniform dens- ity, equal to that of air at the level of the sea. = 1.0582 short tons per square foot. .945 atmosphere. .945 long tons per square foot. 1.0584 atmosphere. Weight of air compared with water at the level of the sea = Water at 32 F. = 773.2 times the weight of air at 32 F. 39 1 = 773.27 times the weight of air at 32 62 = 772.4 times the weight of air at 32 62 = 819.4 times the weight of air at 62 52 3 = 820.0 times the weight of air at 62 Weight in pounds of 1 cubic foot of air containing a standard amount of carbonic acid. English Board of Trade, Standards Department. Condition of Air Temperatures in Degrees Fahrenheit 32 62 80 Dry air. . . . .08098 .08093 .08080 .07632 .07596 .07578 .07377 .07313 .07281 Ordinary air Moist air (saturation (saturation = f) = 1) The standard amount of carbonic acid mentioned above is 6 volumes of carbonic acid to 10,000 volumes of air. [13] AIR AS A STANDARD Metric Measurements 1 atmosphere = 10332.9 kilograms per square meter. 1 kilogram per square meter .000097 atmosphere. 1 atmosphere = 760.0000 millimeters of mercury. 1 millimeter of mercury .001316 atmosphere. 1 atmosphere = 10.333 meters high of water. 1 meter high of water .0969 atmosphere. 1 atmosphere = 1.033 kilograms per square centimeter. 1 kilogram per square centimeter = .969 atmosphere. 1 atmosphere 1.013 megadynes per square centimeter. 1 megadyne per square centimeter = .9872 atmosphere. One liter of air, under one atmosphere of 760 millimeters, at Centigrade, at sea level, weighs 1.293 grams, or 19.955 grains. The collected data for dry air as given in C. G. S. System by Professor Everett is: Expansion from to 100 C. at constant pressure as .... 1 to 1.367 Specific heat at constant pressure 0.238 Specific heat at constant volume 0.170 Pressure-height at C. about 7.99 X 10 5 cm., or about. . 26210.000 ft. Standard barometric column, 76 cm 29.922 ins. Standard pressure = 1033.3 grams per square centimeter, or 14.7 pounds per square inch, or 2117.0 pounds per square foot, or 1.0136 X 10 6 dynes per square centimeter. Standard density, at C. = 0.001293 gram per cubic centimeter. or 0.0807 prunds per cubic foot. Standard bulkiness 773.0 cubic centimeters per gram, or 12.39 cubic foot per pound. Specific Heat of Air. The specific heat of air is the ratio of the amount of heat required to raise the temperature of one pound of air through one degree at 32 F. Air, in common with other gases, has two specific heats: (1) Specific heat at constant pres- sure; the application of heat to air expands it: if the air is free to expand, work is done in heating the air and in overcoming the external pressure of the atmosphere; (2) if the air is confined so that its volume cannot change and heat is applied, the effect is rise in temperature, and this is called specific heat at constant volume. The former requires more hea than the latter because external work is performed in addition to the rise in temperature. When air is heated at constant volume, only internal work is done. Regnault found the specific heat at constant pressure to be .2375 water = 1. Then, one cubic foot of air at 32 F. = .08098 pound, the reciprocal of which = 12.3487 cubic feet under one atmosphere of pressure and 32 F. The specific heat of air at constant volume = .1689. Ratio of the specific heats of air: Constant pressure, .2375 _ Constant volume, .1689 " which agrees with the values obtained indirectly from the velocity of sound. Assum- ing that the value 332 meters (1089 feet) per second is good for the velocity of sound, the ratio of the specific heats must pe near to 1.4063. According to the Smithsonian Physical Tables, 1.4065 may be taken as fairly representing our present knowledge of the subject. [14] CONVERSION FACTORS FOR WATER WATER AS A STANDARD Reduction factors: 1 cubic foot of water at 4 C., or 39 2 F. = 62.4 pounds. 1 cubic inch of water = 0.0361111 pounds. 1 cubic centimeter of water at 4 C. = 1 gram. Reciprocal 1 gram of water = 15.432356 grains 0.0647989 =; 0.811532 U. S. Apoth. scruples 1 .232237 = . 270511 U. S. Apoth. dram 3 . 696707 = 0.0610234 cubic inch 16.387163 = 0.0352740 ounce, av 28.349492 = . 0338138 U. S. liquid ounce 29 . 573724 = 0.0321507 ounce, troy 31 . 103521 = 0.00267923 pound, troy. . 373.241566 = 0.00220462 pound, av : . . . 453.592428 WATER AS A STANDARD Reciprocal 1 cubic inch of water = 252.777778 grains 0.00395604 = 16.387163 grams 0.0610234 = 0.577778 ounce, av 1.730769 = 0.554113 U. S. liquid ounce 1 .804688 = 0.526620 ounce, troy 1 .898901 = 0.043885 pound, troy 22.786814 = 0.036111 pound, av 27.692307 = 0.034632 U. S. liquid pint 28.875000 = 0.0288326 English pint 34.683000 = 0.017316 U. S. liquid quart 57.750000 = 0.0163872 liter 61.023378 = 0.0163872 kilogram 61 .023378 = 0.0144163 English quart 69 .366000 = 0.004329 U. S. gallon 231 .000000 = 0.00360408 English gallon 277.463000 = 0.0005787 cubic foot 1728.000000 WATER AS A STANDARD Reciprocal 1 pound of water = 453 .592428 grams 0.00220462 = 27.692307 cubic inches 0.0361111 = 15 .344695 U. S. liquid ounces 0.0651691 = 1 .215278 pounds, troy 0.822857 = 0.959041 U. S. liquid pint 1 .042708 = 0.798440 English pint : 1 .252442 = 0.479520 U. S. liquid quart 2.085417 = 0.453592 liter 2.204622 = 0.453592 kilogram 2.204622 = 0.399220 English quart 2 .504883 = 0.119880 U. S. gallon 8.341667 = 0.0998054 English gallon 10.019497 = 0.0160256 cubic foot^x 62 .400000 = 0.000593542 cubic yard. . . .v. .v. 1684.800000 = 0.00050000 short ton 2000.000000 = . 000453592 cubic meter . 2204 . 622341 = 0.000453592 metric ton 2204.622341 = 0.00044643 long ton 2240.000000 [15] CONVERSION FACTORS FOR WATER WATER AS A STANDARD Reciprocal 1 liter of water = 61 .023378 cubic inches 0.0163872 = 2 . 679228 pounds, troy . 373242 = 2. 204622 pounds, av 0.453592 = 2.113364 U. S. liquid pints 0.473179 = 1 .759464 English pints 0.568354 = 1 .056681 U. S. liquid quarts 0.946359 = 1.000000 kilogram 1.000000 = 0.879732 English quart 1 . 136708 = 0.264170 U. S. gallon 3.785434 = 0.219933 English gallon 4.546831 = 0.0353145 cubic foot 28.317016 = 0.00130793 cubic yard 764.559444 = 0.00110231 short ton 907 . 184872 = 0.00100000 metric ton 1000.000000 = 0.00098421 long ton 1016.047057 WATER AS A STANDARD United States GaUons Reciprocal 1 gallon of water = 231 .000000 cubic inches 0.004329 = 10. 137461 pounds, troy. . 0.098644 = 8.341667 pounds, av 0. 119880 = 8.000000 U. S. liquid pints 0.125000 = 6.660324 English pints 0. 150143 = 4.000000 U. S. liquid quarts 0.250000 = 3.785434 liters 0.264170 = 3.785434 kilograms ' 0.264170 = 3.330162 English quarts 0.300286 = 0.832543 English gallon 1.201139 = 0.133681 cubic foot 7.480519 = 0.00495113 cubic yard 201 .974025 = 0.00417083 short ton 239.760231 = 0.00372396 long ton 268.531457 = 0.00378543 cubic meter 264. 170467 = 0.00378543 metric ton 264. 170467 WATER AS A STANDARD Imperial Gallon of Great Britain Reciprocal 1 gallon of water = 277.463000 cubic inches 0.00360408 = 12. 176472 pounds, troy 0.0821256 = 10.019497 pounds, av 0.0998054 = 9.609108 U. S. liquid pints 0. 104068 = 8.000000 English pints 0. 125000 = 4.804554 U. S. liquid quarts 0.208136 = 4.546831 liters 0.219933 = 4.546831 kilograms .219933 = 4.000000 English quarts 0.250000 = 1 .201139 U. S. gallons. . 0.832543 = 0.160569 cubic foot 6.227843 = 0.0059470 cubic yard 168.152150 = 0.00500975 short ton 199.610819 = 0.00454477 metric ton 220.033235 = 0.00447299 long ton 223.564117 [161 CONVERSION FACTORS FOR WATER WATER AS A STANDARD Reciprocal 1 cubic foot of water = 1728.000000 cubic inches 0.000578704 = 75.833333 pounds, troy 0.0131868 = 62.400000 pounds, av . 0.0160256 = 59.844047 U. S. liquid pints 0.0167101 = 49.822679 English pints 0.0200712 = 29.922112 U. S. liquid quarts 0.0334201 = 28.317016 liters 0.0353145 = 28.317016 kilograms 0.353145 = 24.911340 English quarts 0.0401424 7.480495 U. S. gallons 0. 133681 6.227857 English gaUons 0.160569 0.370370 cubic yard 27.000000 0.031200 short ton 32.051282 0.0283170 cubic meters* 35.314455 0.0283042 metric ton 35.330486 0.0278571 long ton 35.897436 This line and the one following show the relation of a cubic foot to a cubic meter figured in feet and inches, also the relation of a cubic foot of water = 1728 cubic inches weighing 62.4 pounds to a metric ton. The figures should in both cases be alike, the difference is due to the cumulative effect of unending decimals. In the case of the metric ton we have the fractions: 1 meter = 3.280833333 feet, and 1 kilogram = 2.204- 622341 pounds. Without attempting to adjust fractional differences, the recognized metric ton = 2204 . 622341 pounds is here employed. WATER AS A STANDARD Reciprocal 1 cubic yard of water = 1684.800000 pounds 0.000593485 = 764.212640 liters 0.000130854 = 201 .974025 U. S. gallons 0.00495113 = 168. 152150 English gallons 0.00594700 = 27.000000 cubic feet 0.0370370 .842400 short tons 1.187085 = .764213 metric ton 1 .308536 .752143 long ton 1 .329534 WATER AS A STANDARD 1 cubic meter of water at 4 C. = 1 metric ton Reciprocal 1 cubic meter of water = 2204.622341 pounds 0.000453592 = 1000.000000 liters 0.001000000 = 1000.000000 kilograms 0.001000000 = 264.170467 U. S. gallons 0.00378543 = 219.933389 English gallons 0.00454683 = 35.314455 cubic feet 0.0283170 1 .307943 cubic yards 0.764560 1.102311 short tons 0.907185 1.000000 metric ton 1.000000 = ' 0.984206 long ton 1.0160471 [17] CONVERSION FACTORS FOR WATER WATER AS A STANDARD Reciprocal 1 short ton of water = 2000.000000 pounds 0.0005000 = 907.184872 liters 0.00110231 = 907. 184872 kilograms 0.00110231 = 239.760231 U. S. gallons 0.00417083 = 199.610819 English gallons 0.00500975 = 32.051283 cubic feet 0.031200 1 . 187085 cubic yards 0.842400 0.892858 long ton 1 . 120000 . 907185 metric ton . . . 1 . 10231 1 WATER AS A STANDARD Reciprocal 1 long ton of water = 2240.000000 pounds 0.000446429 = 1016.047057 liters 0.00098421 = 1016.047057 kilograms 0.00098421 = 268.531457 U. S. gallons 0.00372396 = 223.564117 English gallons 0.00447299 = 35.897436 cubic feet 0.0278571 1 .329535 cubic yards 0.752143 1 . 120000 short tons 0.892858 1.016047 metric tons . . 0.984206 [18] PROPERTIES OF METALS PHYSICAL CONSTANTS OF METALS Metal. Symbol. Atomic Weight. Atomic Volume. Specific Gravity. Specific Heat. Melt- ing Point. C. Coefficient of Linear Expansion. Thermal Conduc- tivity in cal. cm. sees. Electrical Conduc- tivity. Ag.=100. Aluminium . Al 27'1 10-6 2-56 0-218 657 0-0000231 0-502 57-3 Antimony Sb 120-2 17-9 6-71 0-051 630- 0-0000105 0-042 4-6 Arsenic . As 75-0 13-2 5-67 0-081 450 0-0000055 , . 47 Barium . Ba 137-4 36-3 3-78 0-047 850 . . . . 13 Bismuth . Bi 208-0 21-2 9-80 0-031 266 0-0000162 0-019 1-3 Cadmium Cd 112-4 13-2 8-60 0-056 322 0-0000306 0-219 147 Caesium . Cs 132-8 71-1 1-87 0-048 26 .. 37 Calcium . Ca 40-1 25-5 1-57 0-170 780 . . 22-1 Cerium . Ce 140-2 21-0 6'68 0-045 623 % . . Chromium Cr 52-0 7-7 6-80 0*120 1482 ff .. Cobalt . Co 59-0 6-9 8*50 0-103 1464 0-00*00123 . . 15-6 Columbian! . Cb 93-5 7'4 1270 0-071 >t tm Copper . Cu 63-6 71 8-93 0-093 1084 0-0000167 0-924 94 : Gallium . Ga 699 11-8 5-90 0-079 30 . . . . (ilucinum Gl 91 4'7 1-93 0-621 .. Gold Au 197-2 10-2 19-32 0-031 1065 0-0000144 0-700 66-8 Indium . In 114-8 15-5 7-42 0-057 155 0-0000417 , . 16-5 Iridium . Ir 1931 8-6 22-42 0-033 1950 0-0000070 Iron Fe 55-8 7-1 7-8G 0-110 1505 0-0000121 0-147 16 : 2 Lanthanum . La 1390 22-4 6*20 0'045 810 , < .. Lead Pb 2071 18-2 11-37 0-031 327 0-0000292 0-084 7'2 Lithium . Li 6-9 13-0 0-54 0-941 186 17-5 Magnesium . Mg 24-3 14-0 1-74 0-250 633 0-0000269 0-343 337 Manganese . Mn 64-9 6-9 8' 00 0'120 1207 . . . . Mercury . Hg 200-6 14-7 13-59 0-032 -39 0-0000610 0-020 1-6 Molybdenum . Mo 96-0 11-2 8-60 0-072 2500 Nickel . Hi 58-7 6-7 8-80 0-108 1427 0-0000127 0-141 21-2 Osmium Os 1909 8-5 22-48 0-031 2500 0-0000065 15-5 Palladium Pd 1067 9-3 11-50 0-059 1535 0-0000117 0-168 145 Platinum Pt 195-2 9-1 21-50 0-032 1710 0-0000089 0-1G6 13-4 Potassium K 39-1 45-5 0-86 0-170 62 0-0000841 .. 80-8 Rhodium Rh 102-9 8-5 12-10 0-058 1660 0-0000085 . . Rubidium Rb 85-5 65-9 1-53 0-077 38 .. .. Ruthenium . Ru 101-7 8-3 12-26 0-061 1800 0-0000096 Silver Ag 107-9 10-2 10-53 0-056 961 0-0000192 0-993 lOO'O Sodium . Na 23-0 23-8 0'97 0-290 95 0-0000710 0-365 37'3 Stro'ntium Sr 87-6 34-5 2-54 t 800 6-7 Taritalum Ta 181-5 16-7 10-80 0-036 2910 0-0000079 . . 8-9 Tellurium Te 127-5 20-4 625 0-049 440 0-0000167 . . 6-8 Thallium Tl 204-0 17-2 11-85 0-033 303 0-0000302 .. 8'3 Thorium Th 232-4 20-9 11 10 0-028 , . . .. Tin Sn 119-0 16-3 7'2'J 0-055 232 0-0000223 0-155 ii-3 Titanium Ti 48-1 9-9 4-87 0-130 .. Tungsten W 184-0 9-6 1910 0-034 3100 .. i : 7 Uranium u 238-5 12-8 18-70 0-028 . . .. Vanadium V 510 9'3 5-50 0-125 1680 .. Yttrium . Yt 89-0 23-4 3-80 . . .. tf Zinc Zn 65-4 9-1 7-15 0-094 419 0-0000291 0-269. 25-2 Zirconium Zr 90-6 21'8 4-15 0*066 1500 v [19] CHEMICAL ELEMENTS MELTING POINTS OF THE CHEMICAL ELEMENTS BUREAU OF STANDARDS Element P C Element P C Helium Hydrogen Neon <-456 -434 423 <-271 -259 -253? Praseodymium. Germanium. . . SILVER. . 1725 1756 1761 940? 958 960 5 Fluorine 369 223 Glucinum. . >AK Oxygen. -360 -218 ? Nitrogen 346 210 GOLD 1945.5 1063.0 Argon 306 188 COPPER 1981 5 1083 Krypton 272 169 Manganese. . 2237 1225 Xenon 220 140 Yttrium ? Chlorine 150 5 101 5 | 2370- Samarium. . . . 1 1300-1400 MERCURY . . . Bromine - 37.7 + 18 9 38.7 7 3 Scandium ( 2550 ? Caesium. . 79 26 Silicon 2588 1420 Gallium 86 30 NICKEL 2646 1452 Rubidium. 100 38 Cobalt 2714 1490 Phosphorus. . . . Potassium 111.4 144 44 62.3 Chromium. . . . IRON 2750 2768 1510 1520 Sodium 207 5 97 5 PALLADIUM. 2820 1549 Iodine. 236 5 113 5 Zirconium 3100 1700? fSi 235.0 112.8 Thorium. f >3090 >1700 Sulphur j Sn 246 . 6 [Sui 244 2 119.2 106 8 Vanadium { 3270 > 1800? Selenium 422-428 217-220 Ytterbium. ? TIN 449.4 231.9 Titanium 3450 1900? Bismuth 520 271 Rhodium 3525 1940 Thallium CADMIUM.... LEAD 576 609.6 621.1 302 320.9 327 4 Ruthenium. . . . Columbium (Niobium) . . >3550 4000 >1950 2200? ZINC 786 9 419 4 ( 4000- ] Tellurium. . . 846 452 Boron 4500 2200-2500 ANTIMONY... Cerium. . 1166 1184 630.0 640 Iridium Uranium. 4170 2300? ? Magnesium. . . . ALUMINIUM 1204 1217 7 651 658 7 Molybdenum . . Osmium 4500 4900 2500? 2700? Calcium .... 1490 810 Tantalum 5160 2850 Lanthanum .... Strontium. 1490 810? >Ca6500 3000 Neodymium. . . . Arsenic 1544 1560 840? 850? Carbon for !p= 1 At. >3600 forp = lAt. Barium. . 1560 850 The values of the melting points used by the Bureau of Standards as standard tem- peratures for the calibration of thermometers and pyrometers are indicated in capitals. The other values have been assigned after a careful survey of all the available data. As nearly as may be, all values, in particular the standard points, have been reduced to a common scale, the thermodynamic scale. For high temperatures, and for use with optical pyrometers, this scale is satisfied very exactly by taking c 2 = 14,500 in the formula for Wien's law connecting I, monochromatic luminous intensity of wave length A, and T, absolute temperature: log I/I. = Ci A log e (1/T 2 1/T). For all purposes, except the most accurate investigations, the thermodynamic scale is identical with any of the gas scales. [20] SPECIFIC GRAVITY OF METALS WEIGHT AND SPECIFIC GRAVITY OF METALS Metal Specific Gravity WEIGHT Metal Specific Gravity WEIGHT Cu. In. Cu. Ft. Cu. In. Cu. Ft. Aluminum Antimony 2. 56 to 2.80 6. 70 to 6.72 3. 75 to 4.00 9. 70 to 9.90 8. 54 to 8.67 1.88 to 1.90 1.58 6. 62 to 6.72 6. 52 to 6.73 8. 50 to 9.10 7.10to 7.40 8. 80 to 8.95 6.54 5.93 5.46 1.86 to 2.06 19. 26 to 19. 34 7. 27 to 7.42 21. 78 to 22. 42 7.21 7.77 7.8 to 7.9 6. 05 to 6.16 11. 34 to 11.36 .097 .242 .140 .354 .311 .068 .057 .241 .239 .318 .262 .321 .236 .214 .197 .071 .697 .266 .798 .260 .280 .284 .220 .410 167 418 242 612 537 118 99 416 414 549 452 554 408 370 341 122 1,204 459 1,379 450 485 490 381 708 Lithium Magnesium .... Manganese .... Mercury 0.59 1.69 to 1.75 6. 86 to 8.03 13.596 8. 40 to 8.60 8.9 to 9.2 21. 40 to 22. 40 11.0 to 12.0 21. 20 to 21. 70 0.85 to 0.88 11. 00 to 12. 10 11. 00 to 11.40 10. 40 to 10.57 0.97 to 0.99 2.50to 2.58 11.8 to 11. 9 7. 29 to 7.30 5.30 9.4 to 10.1 19.12 18. 33 to 18.65 7.04to 7.16 7.19 4.14 .021 .062 .269 .491 .307 .327 .791 .416 .774 .031 .417 .405 .378 .035 .091 .428 .263 .192 .352 .690 .668 .256 .260 .149 37 107 465 848 530 565 1,366 718 1,338 54 721 699 654 61 158 739 455 331 608 1,193 1,154 443 449 258 Barium Bismuth C admium Molybdenum. . . Nickel CsBsium Calcium Osmium C6rium PaUadium Chromium Platinum . . Cobalt Potassium Rhodium Columbium Copper Ruthenium. . . . Silver Didymium Gallium Sodium Strontium Germanium Glucinium Thallium Gold Tin . ... Indium Iridium Titanium Thorium Iron cast Tungsten ...... Uranium Iron, wrought. . . Iron (steel) Lanthanum Lead Zinc, cast Zinc, wrought . . Zirconium WEIGHT AND SPECIFIC GRAVITY OF VARIOUS SUBSTANCES Substance Specific Gravity WEIGHT Substance Specific Gravity WEIGHT Cu. In. Cu. Ft. Cu. In. Cu. Ft. Alabaster 2.76 1.72 1.31 4.50 2.90 2.55 2.20 1.75 1.90 2.51 .100 .062 .042 .163 .105 .092 .079 .063 .069 .091 172 107 82 281 181 159 137 109 119 157 Clay 1.92 2.26 1.60 2.10 4.20 2.90 1.60 1.40 1.90 2.55 .069 .082 .058 .076 .152 .105 .058 .050 .069 .092 120 141 100 131 262 181 100 87 119 159 Alum . . Concrete, stone Concrete, cinder. . . Concrete, slag Copper ore Asphaltum Barytes Basalt Bauxite . Dolomite Earth, argillaceous. Earth, light vege . . Earth, potters' .... Feldspar Bluestone Borax Brick. . . . Chalk, air-dried [21 SPECIFIC GRAVITY OF MINERALS WEIGHT AND SPECIFIC GRAVITY OF VARIOUS SUBSTANCES (Con/.) Substance Specific Gravity WEIGHT Substance Specific Gravity WEIGHT Cu. In. Cu. Ft. Cu. In. Cu. Ft. Flint . 2.63 2.50 2.60 2.66 2.93 2.20 .095 .090 .094 .096 .106 .079 .056 .064 .108 .072 .108 .032 .187 .137 .184 .100 .082 .269 .100 .097 .103 .095 .150 .108 .097 .063 .100 .060 .059 .032 .027 .017 164 156 162 166 183 137 95 110 187 125 187 56 324 237 318 172 141 465 172 168 178 165 259 187 168 109 172 103 102 56 47 29 Phosphate rock. . . . Phosphorus 3.20 1.80 1.09 2.31 2.75 1.38 2.90 2.18 .64 2.66 2.65 1.92 2.30 2.30 2.30 2.80 2.60 2.80 2.73 .116 .065 .039 .083 .100 .050 .105 .079 .023 .096 .095 .069 .083 .057 .064 .068 .083 .083 .101 .094 .101 .098 200 112 68 144 172 86 181 136 40 166 165 120 144 98 110 118 144 144 175 162 175 170 10 50 168 125 168 75 119 418 170 253 Glass, common . . Glass, flint Pitch Granite, gneiss Porcelain Granite, gray Porphyry Graphite Portland cmt., loose Portland cmt., set . Potash Gravel, loose Gravel, packed Greenstone s'oo 2.00 3.00 .90 5.20 3.80 5.09 2.75 2.26 7.45 2.75 2.69 2.86 2.65 4.15 3.00 2.70 1.75 2.75 1.65 1.63 .89 .76 .46 Pumice Gypsum Quartz Hornblende Rock crystal Ice melting Salt, common solid Salt rock Iron ore, hematite Iron ore, limonite Iron ore, maepietic Sand, dry, loose. . . Sand, packed Sand, wet Sandstone Iron slag Lava. . Lead ore Schist, rough Schist, slate. . Lime, loose Limestone carboniferous Limestone, magnesian . . Limestone, marble . . . Serpentine Shale, slate Slate Manganese ore Snow, loose . . Magnesite Snow, compact .... Soapstone, talc. . . . Sulphur Talc, steatite Tar, bituminous . . . Tile . . . 2.70 2.00 2.70 1.20 1.90 6.70 2.72 4.05 !097 .072 .097 .043 .069 .242 .098 .146 Marble Marl Mica Mortar Mud Paraffine . . Tin ore Peat, dense Trap Peat, fibrous Zinc ore WEIGHT AND SPECIFIC GRAVITY OF AMERICAN COALS Specific Gravity Pounds Cubic Foot Anthracite, Lehigh Co., Pa 1.57 1.36 1.40 1.41 98 85 87 88 Anthracite, Carbon Co Pa Semi- Anthracite, Wilkesbarre, Pa Semi-Bituminous Cumberland Md [22] SPECIFIC GRAVITY OF COALS AND WOOD WEIGHT AND SPECIFIC GRAVITY OF AMERICAN COALS (Cont.) Specilc Gravity Pounds Cubic Foot Semi-Bituminous, Blossburg, Pa .32 82 Bituminous Pennsylvania 35 84 Block Coal Indiana 29 80 Brown Coal Kentucky .17 73 Caking Coal short flame 33 83 Caking Coal long flame . .30 81 Caking Coal gas .29 80 Cannel Coal Indiana 1 23 77 Coke Connellsville. 1.28 80 Coke, loose per cubic foot 50 Lignite Kentucky ^ 1 20 75 Lignite Texas . 1.23 77 Lignite, Colorado 1.28 80 Peat light fibrous . . 20 Peat dense . . . . 41 Peat, comoressed. hard . . 75 WEIGHT AND SPECIFIC GRAVITY OF VARIOUS KINDS OF WOOD Wood Specific Gravity WEIGHT Wood Specific Gravity WEIGHT Cubic Inch Cubic Foot Cubic Inch Cubic Foot Apple Ash .75 .74 .46 .80 .64 .38 .51 .78 .66 .24 .48 1.21 .58 .54 .83 .51 .99 .53 .75 .53 1.25 .46 .71 .027 .027 .017 .029 .023 .014 .019 .028 .024 .009 .017 .044 .021 .020 .030 .019 .036 .019 .027 .019 .045 .017 .025 47 46 29 50 40 24 32 49 41 15 30 76 36 34 52 32 62 33 47 33 78 29 44 Mahogany, Hond. Mahogany, Spa. . Maple .56 .85 .69 .64 .95 .74 .62 .75 .61 .54 .83 .48 .42 .48 .48 .42 .51 .50 .72 .77 .98 .67 .50 .020 .031 .025 .023 .034 .027 .023 .027 .022 .020 .030 .017 .015 .017 .017 .015 .019 .018 .026 .028 .035 . .024 .018 35 53 43 40 59 46 39 47 38 34 52 30 26 30 30 26 32 31 45 48 61 42 31 Basswood Beech.. Oak, red Birch Oak, live Butternut Oak, white . . Cedar Pine, loblolly Pine, long leaf . . . Pine, Norway. . . . Pine, Oregon .... Pine, pitch Cherry Chestnut Cork Cvoress . Ebony Elm. . . Pine, red Pine, white Pine, yellow Poplar Fir, Douglas. . . Gum, blue. . . r . Gum, red Redwood, Cal. . . Spruce Gum, water. . . . Hemlock Hickory Sycamore Tamarack Larch . . Teak, Indian .... Teak, African. . . . Walnut Lignum vitae. . . Linden Locust Willow NOTE. Weights are approximate only. Green timber may have as much as 50% moisture. Well- seasoned, air-dried timber may have 15 to 20% moisture. [23] SPECIFIC GRAVITY OF LIQUIDS AND GASES WEIGHT AND SPECIFIC GRAVITY OF VARIOUS LIQUIDS Liquid I?: WEIGHT Liquid G p r ; WEIGHT U.S. Gal. Cu. In. Cu. Ft. U.S. Gal. Cu. In. Cu. Ft. Acetone 0.792 1.207 1.519 1.800 .811 .802 .793 .792 .830 .808 .899 3.187 .960 1.293 1.480 .736 1.260 .840 .665 1.495 1.600 .996 6.55 10.03 12.70 14.97 6.82 6.68 6.55 6.55 6.95 6.68 7.49 26.60 8.02 10.88 12.30 6.15 10.56 6.95 5.48 12.43 13.37 8.34 .028 .043 .055 .065 .030 .029 .028 .028 .030 .029 .032 .115 .035 .047 .053 .027 .046 .030 .024 .054 .058 .036 49 75 95 112 51 50 49 49 52 50 56 199 60 81 92 46 79 52 41 93 100 62 Oil, castor Oil, cocoanut .... .969 .925 .926 1.070 .920 .942 .913 918 8.02 7.75 7.75 8.96 7.62 7.89 7.62 7.62 7.49 7.09 7.75 7.62 8.02 7.62 7.22 7.35 6.68 6.68 8.56 10.16 7.22 8.34 .035 .034 .034 .039 .033 .034 .033 .033 .032 .031 .034 .033 .035 .033 .031 .032 .029 .029 .037 .044 .031 .036 60 58 58 67 57 59 57 57 56 53 58 57 60 57 54 55 50 50 64.3 76 54 62.4 Acid, hydrochloric . . . Acid, nitric Oil, cottonseed Oil, creosote Oil, lard Acid, sulphuric Alcohol, amyl Alcohol, butyl Oil, linseed Oil, mineral (lub.).. Oil olive Alcohol, ethyl Alcohol, methyl. . . Alcohol, octyl Oil, palm Oil pine .905 .855 .924 .914 .955 .920 .873 .878 .800 .800 1.025 1.210 .858 1.000 Alcohol, propyl. . Benzine . . Oil, poppy Oil rapeseed Bromine Carbolic acid Oil, resin Oil, whale Carbon disulphide. . . Chloroform Oil, turpentine Ether Oil, petroleum Oil, petr. (light) . . . Pyroligneous acid. . Sea water Glycerine Naphtha (wood) 'Naphtha (petroleum). Nitroglycol . Soda lye Nitroglycerin Toluene \Vater pure Oil, anise-seed WEIGHT AND SPECIFIC GRAVITY OF VARIOUS GASES Gases I?: WEIGHT Gases 1?: WEIGHT Cu. Ft. Cu. Ft. perLb. Cu. Ft. Cu. Ft. per Lb. Ah- (32 F.) Acetylene C2H2 1.000 .898 .592 1.529 .967 2.422 .967 .400 .0807 .0724 .0478 .1234 .0780 .1955 .0780 .0323 12.387 13.812 20.921 8.104 12.821 5.115 12.821 30.960 Gas natural .475 .069 .559 .971 1.039 1.527 1.106 2.247 .0383 :0056 .0451 .0784 .0838 .1232 .0893 .1813 26.110 178.571 22.173 12.755 11.933 8.117 11.198 5.516 H y drogen Ammonia, NHa Marsh gas, CH Carbon dioxide, CO 2 . . Carbon monoxide, CO. Chlorine, C1 2 O Nitrogen Nitric oxide, NO Nitrous oxide, N 2 O. . . Oxygen Ethylene, C 2 H 4 . . . Gas, illuminating Sulphur dioxide, SO 2 . [24] HORSEPOWER AS A UNIT OF POWER HORSEPOWER BUREAU OF STANDARDS James Watt, the inventor of the modern steam engine, adopted the term "horse- power" as a unit for expressing the power of his steam engines, and defined its value in gravitational units, viz., foot-pounds per minute. The value was derived from experi- ments made about the year 1775. Some heavy horses of Barclay & Perkins's brewery, London, were caused to raise a weight from the bottom of a deep well by pulling horizontally on a rope passing over a pulley. It was found that a horse could raise a weight of 100 pounds while walking at the rate of 2.5 miles per hour. This is equivalent to 22,000 foot-pounds per minute. Watt added 50 per cent to this value, giving 33,000 foot-pounds per minute, or 550 foot-pounds per second. The addition of 50 per cent was an allowance made for friction, so that a purchaser of one of his engines might have no ground for complaint. The figure thus arrived at by Watt is admitted to be in excess of the power of an average horse for continuous work, and is probably at least twice the power of the average horse working six hours per day. Since the time of Watt, his value has been in general use in England and the United States, and 550 foot-pounds per second is known as the English horsepower. The Pound as a Unit of Force has generally been used as a "gravitational" unit, the characteristic of the gravitational units being that their magnitudes vary with locality as g varies. Thus, a pound force is equal to the force of gravity on a pound mass at any place where measurements happen to be made. The one advantage of the gravitational system is that a given mass exerts the same number of pounds of force no matter what its location. But by this mode of definition the magnitude of the pound force is not constant, as it varies with g. A few writers, on the other hand, have defined the pound force as a fixed unit, taking it as equal to the force of gravity on a pound mass at some one particular place e. g., Paris, or 45 latitude and sea level thus destroying the gravitational character of the unit. The unit of force can be made definite and fixed, however, without abolishing the gravitational system. This is done by recognizing the difference between the absolute and the gravitational pound by the use of the terms "standard" and "local," re- spectively. The principle involved is that contained in the definition of "standard weight" by the International Conference on Weights and Measures in 1901. The statement by the conference is given herewith: The term weight designates a quantity of the same nature as a force; the weight of a body is the product of the mass of that body, by the acceleration of gravity; in particular, the standard weight of a body is the product of the mass of that body by the standard acceleration of gravity. The number adopted in the International Service of Weights and Measures for the value of the standard acceleration of gravity is 980.665 centimeters per second (Proces- Verbaux des Seances, Comite International des Poids et Mesures, p. 172, 1901). By analogy with "standard weight," the "standard pound force" may be defined as equal to the force of gravity on a pound mass at a place where g has the standard value, 980.665 centimeters per second per second or 32.1740 feet per second per second. Likewise the "local pound force" in any given locality may be defined as equal to the force of gravity on a pound mass in that given locality. The Standard Value of g, 980.665 centimeters per second per second, was originally intended to represent the latitude of 45 and sea level. It has been widely used as a standard value for barometric reductions, etc., since 1901, and there is no reason why it should not continue in use as a standard value, although the accepted theoretical value for 45 and sea level is now a few parts in 100,000 different. The value, 980.665, is the result of a calculation made by the International Committee on Weights and Measures (Proces-Verbaux des Seances, p. 165, 1901) from Defforges' absolute deter- mination (Ibid., p. 181, 1891; Memorial du Depdt General de la Guerre 15, (1), 1894) of g at the International Bureau in 1888. In calculating the equivalent of the horsepower in various units for different latitudes, the following formula is used: g = 978.038 (1 + 0.005302 sin 2 ? 0.000007 sin 2 2^), [25] ENGLISH AND AMERICAN HORSEPOWER where ^ is the latitude. This formula is accepted by the United States Coast and Geodetic Survey, and is the result of observations all over the United States with Hayford's corrections for "isostatic compensation." It is referred to the absolute determination of g at Potsdam about 1900. TABLE 1 VARIOUS VALUES ADOPTED FOB THE HORSEPOWER [Foot-pounds given in terms of the local foot and pound] Foot- Pounds per Second English Horse- power Kilogram- meters per Second Authority* England and United States 550 1 0000 76 041 v Austria (old) . 430 1 0010 76 119 H Switzerland 500 9863 75 000 A Sweden . 600 9856 74 943 N Russia 550 1 0000 76 041 N Prussia . . 480 9906 75 325 H Saxony 530 9869 75 045 H Baden 500 9863 75 000 jj Wurtemburg. 525 9890 75 204 H Bavaria 460 9888 75 190 K Modern Germany Austria 9863 75 000 v France Italy, etc *V=various. H=Des Ingenieurs Taschenbuch-HUtte II (Berlin, 1902). A=F. Autenheimer, Mechanische Arbeit (Stuttgart, 1871), p. 15. N =J. W. Nystrom, Elements of Mechanics (Philadelphia, 1875), p. 63. K=Karnarsch und Heeren's Technisches Worterbuch VI (1883), p. 637; and Alexander's Weights and Measures (Baltimore, 1850). After the metric system had come into use in France, Germany and Austria the values of the horsepower in the various countries were reduced to kilogrammeters per second, with the results shown in the table. The values range from 75 to 76 kilogram- meters per second, averaging only a little more than 75. Hence, this round value, 75, has been adopted generally on the Continent as the value of the horsepower. The English value, 550 foot-pounds per second, is, however, equivalent to 76.041 kilogrammeters per second, and hence it is that there is a difference of nearly 1.5 per cent between the value generally used in English and American practice and that used in continental practice. Reduced to watts, the English horsepower is generally taken as 746 watts, although the precise equivalent, in watts, of 550 foot-pounds per second depends on the acceleration of gravity, and hence on the latitude and altitude. TABLE 2 VALUE OF THE ENGLISH AND AMERICAN HORSEPOWER (746 WATTS) IN LOCAL FOOT- POUNDS PER SECOND AT VARIOUS LATITUDES AND ALTITUDES LATITUDE Altitude (Equator) 30 45 60 90 (Pole) Sea level 551 70 550.97 550.24 549.52 548.79 5000 feet 551 86 551 13 550 41 549.68 548.95 10,000 feet 552.03 551.30 550.57 549.85 549.12 AV/j \J\J\J IV/dJ ....* / J . \J*J *J*J J. . *J\J W\J . *J I f_^JCcf - <--* U^fiS . I *- The foregoing table may be put in the following approximate form for ease of remembering. [26] CONTINENTAL HORSEPOWER TABLE 3 ENGLISH AND AMERICAN HORSEPOWER (746 WATTS) AT VARIOUS LATITUDES Latitude Local Foot- Pounds per Second (Approx.) 90 pole 549 50 London 550 (39 W^ashington) ' . (550.5) 30 New Orleans 551 0, equator . 552 The value of the English horsepower may also be given in metric units for various latitudes and altitudes, as follows: TABLE 4 VALUE OF THE ENGLISH AND AMERICAN HORSEPOWER (746 WATTS) IN LOCAL KILO- GRAMMETERS PER SECOND AT VARIOUS LATITUDES AND ALTITUDES LATITUDE Equator 30 45 60 90 (Pole) Sea level 76 . 275 76 . 175 76.074 75.973 75.873 1500 meters (= 5000 feet approximately) 76 . 297 76 . 197 76 . 096 75.995 75.895 3000 meters (= 10,000 feet approximately) 76.320 76 . 220 76.119 76 . 018 75.918 By interpolation one can take out of these tables the proper value of the horse- power in gravitation measure (either foot-pounds or kilogrammeters per second) for any latitude and altitude. Continental Horsepower. It is unfortunate that the value of the horsepower on the Continent of Europe was not taken as 76 kilogrammeters per second instead of 75, in order that it might agree with the English value, as was originally intended. It is perhaps unlikely that a change of 76 could now be made, or that an agreement could be reached by which the continental and the English horsepower would correspond to the same number of watts. It is to some extent customary for continental writers to distinguish the two horsepowers by the words "English" and "metric." The Bureau calls the latter the "continental horsepower." German writers speak of the "Englische Pf erdestarke " and the "metrische Pf er- destarke." The term " Pf erdestarke " is now the preferred name for the horsepower in Germany, the old term " Pf erdekraf t " being unsuitable because "Kraft" means "force." In France, the old term " f orce-de-cheval " has been given up for " cheval-vapeur." Poncelet. There is another unit of power which has been used in Europe, the "poncelet," or 100 kilogrammeters per second. This unit was named in honor of Jean Victor Poncelet, who introduced the teaching of kinematics at the Sorbonne in 1838. This unit was adopted in France shortly before 1846. It was adopted as a unit of power in 1889 by the "Congres international de mcanique appliquee." Its use is still per- mitted in the electrical regulations issued by the "Association alsacienne des Pro- prie"taires d'Appareils a Vapeur." It has not, however, been much used in practice. This is probably due in part to the fact that the horsepower had so firm a hold as the unit of power, and in part to the very near equivalence of the poncelet to the kilowatt. The poncelet is open to the same objection as the horsepower when the latter is rigidly defined as a certain number of foot-pounds or kilogrammeters per second, viz., that the power it represents varies from place to place. [27] HORSEPOWER AN UNSUITABLE UNIT Equivalents of the Continental Horsepower. The continental horsepower is generally given either as 75 kilogrammeters per second or as 736 watts. These two equivalents are independent definitions and are likely to cause confusion unless one of them is assigned to some definite place on the earth's surface. The unit, to be definite, should represent the same rate of work at all places. The continental horsepower, then, should be taken as 736 watts, which is equivalent to 75 local kilogrammeters per second at latitude 52 30', or Berlin. The number of kilogrammeters per second expressing this amount of power will be smaller than 75 at more northern latitudes and larger at lower latitudes. The values at various latitudes at sea level are given in Table 5 : TABLE 5 CONTINENTAL HORSEPOWER (736 WATTS) IN LOCAL KILOGRAMMETERS PER SECOND LATITUDE Altitude Equator 30 45 60 90 (Pole) Sea level . . . 75 253 75 153 75 054 74 955 74 856 1500 meters 3000 meters 75.275 75 297 75.175 75 197 75.076 75 098 74.977 74 999 74.878 74 900 Horsepower an Unsuitable Unit. On account of the variation with g, and because the equivalents of the horsepower are not decimal multiples of any of the fundamental units, and, further, because its definition and value are different on the Continent of Europe from its definition and value in England and America, it has long been felt that the horsepower is an unsuitable unit for many purposes. Modern engineering practice is constantly tending away from the horsepower and toward the watt and kilowatt. In Germany, it has been proposed to call the kilowatt "Neupferd" (new horsepower), to make its use appeal more strongly to those who have become firmly attached to the horsepower. The objection to the horsepower has been particularly strong in electrical engineering. The International Congress of Electricians at Paris, in 1889, recommended that the power of machines be expressed in kilowatts instead of in horsepower. A more definite and powerful action with a view to the elimination of the horsepower was taken by the International Electro-technical Commission at Turin, Italy, in 1911. This body, com- posed of the representatives of great electrical interests all over the world, recommended that in all countries electrical machinery, including motors, be rated in kilowatts only. Kilowatt as the Unit of Power. It is considered desirable that the watt and kilo- watt be used as the units of power, whenever possible, for all kinds of scientific, en- gineering, and other work. It is not unlikely that the unit of horsepower will ultimately go out of use. In the meantime, however, it is desirable that its definition be uniform. If the horsepower is to represent the same amount of power at different places, its relation to the watt must be a constant number, and the number of local foot-pounds or kilogram- meters per second which it represents must vary from place to place. Table 2 and others of this circular show clearly this variation with locality. It might be feared that some confusion could arise because of the independent definitions of the mechanical watt and the "international" electrical watt. The watt and kilowatt are defined primarily in purely mechanical terms, and not electrically at all. That they have been used mainly in electrotechnical work is merely accidental, and is due to the fact that they are metric units and so fit in naturally with the metric units in which all electrical quantities are universally expressed. Any kind of power may properly be measured in kilowatts. For example, in the case of the hydraulic power furnished by a flowing stream, the power is given in kilowatts by multiplying 0.163 into the product of the head in meters by the flow in cubic meters per minute; the power is likewise given in kilowatts by multiplying 0.000188 into the product of the head in feet by the flow in gallons per minute. The watt is defined directly in terms of the fundamental -units of mass, length, and time, in the "meter-kilogram-second" system, thus: "The watt is the power developed by the action, with a velocity of 1 meter per second, of a force capable of giving to a mass of 1 kilogram in one second a velocity [28] KILOWATT AS THE UNIT OF POWER of 1 meter per second." The "international watt," however, is defined in terms of concrete electrical standards, which electrical standards represent practically, as nearly as the limitations of experiment allow, the absolute electrical quantities in terms of their theoretical relations to length, mass, and time. The international watt thus defined is the closest concrete realization of the theoretical absolute or mechanical watt which we have. We cannot at the present time say whether the international watt is greater or less than the absolute or mechanical watt, but the difference is probably not greater than a few parts in 10,000. Consequently, there is in reality no confusion between the mechanical watt and the international electrical watt. It is recommended that engineering societies and other interests concerned recognize the value of the "English and American horsepower" as 746 watts (or 550 foot-pounds per second at 50 latitude and sea level, approximately the latitude of London), em- ploying Table 2 to obtain the value in foot-pounds per second at other places. It is likewise recommended that the value of the "continental horsepower" be taken uni- formly as 736 watts (or 75 kilogrammeters per second at latitude 52 30', the latitude of Berlin), and that the value in kilogrammeters per second at other places be obtained from such a table as Table 5. It is probably not generally known that these values were adopted by a committee of the British Association for the Advancement of Science in 1873. This was a com- mittee which recommende4 the C. G. S. System, and on it were Sir W. Thomson, Carey Foster, Clerk Maxwell, J. D. Everett, and others (B. A. Report, 1873, p. 222). The committee in its report said: "One horsepower is about three-fourths of an erg-ten per second. More nearly, it is 7.46 erg-nines per second; and one force-de-cheval is 7.36 erg-nines per second." (One erg-nine = 100 watts.) The Standards Committee of the American Institute of Electrical Engineers adopted, on May 16, 1911, the following rule, which was inserted in the Standardization Rules of the Institute: In view of the fact that a horsepower defined as 550 foot-pounds per second repre- sents a power which varies slightly with the latitude and altitude (from 743.3 to 747.6 watts), and also in view of the fact that different authorities differ as to the precise value of the horsepower in watts, the standards committee has adopted 746 watts as the value of the horsepower. The number of foot-pounds per second to be taken as one horsepower is, therefore, such a value at any given place as is equivalent to 746 watts; the number varies from 552 to 549 foot-pounds per second, being 550 at 50 latitude (London), and 550.5 at Washington. The Standards Committee, however, recommends that the kilowatt instead of the horsepower be used generally as the unit of power. The same value, 746 watts, is used by the Bureau of Standards as the exact equivalent of the English and American horsepower. The Bureau recommends the use, whenever possible, of the kilowatt instead of the horsepower. HORSEPOWERS TO KILOWATTS Reduction factor: 1 horsepower = 0.746 kilowatts Horse- Kilo- powers watts Horse- Kilo- powera watts Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts 10= 7.460 20= 14.920 30= 22.380 40= 29.840 50=- 37.300 1= 0.746 1 8.206 1 15.666 1 23.126 1 30.586 1 38.046 2 1.492 2 8.952 2 16.412 2 23.872 2 31.332 2 38.792 3 2.238 3 9.698 3 17.158 3 24.618 3 32.078 3 39.538 4 2.984 4 10.444 4 17.904 4 25.364 4 32.824 4 40.284 5 3.730 5 11.190 5 18.650 5 26.110 5 33.570 5 41.030 6 4.476 6 11.936 6 19.396 6 26.856 6 34.316 6 41.776 7 5.222 7 12.682 7 20.142 7 27.602 7 35.062 7 42.522 8 5.968 8 13.428 8 20.888 8 28.348 8 35.808 8 43.268 9 6.714 9 14 . 174 9 21.634 9 29.094 9 36.554 9 44.014 [29] HORSEPOWERS TO KILOWATTS HORSEPOWERS TO KILOWATTS Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- Horse- Kilo- Horse- Kilo- powers watts powers watts powers watts Horse- Kilo- powers watts 60=44.760 1 45.506 2 46.252 3 46.998 4 47.744 100= 74.60 1 75.35 2 76.09 3 76.84 4 77.58 140 = 104.44 1 105 . 19 2 105.93 3 106.68 4 107.42 180.= 134. 28 1 135.03 2 135.77 3 136.52 4 137.26 220 = 164.12 1 164.87 2 165.61 3 166.36 4 167.10 260 = 193.96 1 194.71 2 195.45 3 196.20 4 196.94 5 48.490 6 49.236 7 49.982 8 50.728 9 51.474 5 78.33 6 79.08 7 79.82 8 80.57 9 81.31 5 108.17 6 108.92 7 109.66 8 110.41 9 111.15 5 138.01 6 138.76 7 139.50 8 140.25 9 140.99 5 167.85 6 168.60 7 169.34 8 170.09 9 170.83 5 197.69 6 198.44 7 199.18 8 199.93 9 200.67 70 = 52.220 1 52.966 2 53.712 3 54.458 4 55.204 110= 82.06 1 82.81 2 83.55 3 84.30 4 85.04 150 = 111.90 1 112.65 2 113.39 3 114.14 4 114.88 190 = 141.74 1 142.49 2 143.23 3 143.98 4 144.72 230 = 171.58 1 172.33 2 173.07 3 173.82 4 174.56 270 = 201.42 1 202.17 2 202.91 3 203.66 4 204.40 5 55.950 6 56.696 7 57.442 8 58.188 9 58.934 5 85.79 6 86.54 7 87.28 8 88.03 9 88.77 5 115.63 6 116.38 7 117.12 8 117.87 9 118.61 5 145.47 6 146.22 7 146.96 8 147.71 9 148.45 5 175.31 6 176.06 7 176.80 8 177.55 9 178.29 5 205.15 6 205.90 7 206.64 8 207.39 9 208.13 80 = 59.680 1 60.426 2 61.172 3 61.918 4 62.664 120= 89.52 1 90.27 2 91.01 3 91.76 4 92.50 160 = 119.36 1 120.11 2 120.85 3 121.60 4 122.34 200 = 149.20 1 149.95 2 150.69 3 151.44 4 152.18 240 = 179.04 1 179.79 2 180.53 3 181.28 4 182.02 280 = 208.88 1 209.63 2 210.37 3 211.12 4 211.86 5 63.410 6 64.156 7 64.902 8 65.648 9 66.394 5 93.25 6 94.00 7 94.74 8 95.49 9 96.23 5 123.09 6 123.84 7 124.58 8 125.33 9 126.07 5 152.93 6 153.68 7 154.42 8 155.17 9 155.91 5 182.77 6 183.52 7 184.26 8 185.01 9 185.75 5 212.61 6 213.36 7 214.10 8 214.85 9 215.59 90=67.140 1 67.886 2 68.632 3 69.378 4 70.124 130= 96.98 1 97.73 2 98.47 3 99.22 4 99.96 170 = 126.82 1 127.57 2 128.31 3 129.06. 4 129.80 210 = 156.66 1 157.41 2 158.15 3 158.90 4 159.64 250 = 186.50 1 187.25 2 187.99 3 188.74 4 189.48 290 = 216.34 1 217.09 2 217.83 3 218.58 4 219.32 5 70.870 6 71.616 7 72.362 8 73.108 9 73.854 5 100.71 6 101.46 7 102.20 8 102.95 9 103.69 5 130.55 6 131.30 7 132.04 8 132.79 9 133.53 5 160.39 5 190.23 6 161.14 6 190.98 7 161.88 7 191.72 8 162.63 8 192.47 9 163.37 9 193.21 5 220.07 6 220.82 7 221.56 8 222.31 9 223.05 [30] HORSEPOWERS TO KILOWATTS HORSEPOWERS TO KILOWATTS Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts 300 = 223.80 1 224.55 2 225.29 3 226.04 4 226.78 340 = 253.64 1 254.39 2 255.13 3 255.88 4 256.62 380 = 283.48 1 284.23 2 284.97 3 285.72 4 286.46 420 = 313.32 1 314.07 2 314.81 3 315.56 4 316.30 460 = 343.16 1 343.91 2 344.65 3 345.40 4 346.14 500 = 373.00 1 373.75 2 374.49 3 375.24 4 375.98 5 227.53 6 228.28 7 229.02 8 229.77 9 230.51 5 257.37 6 258.12 7 258.86 8 259.61 9 260.35 5 287.21 6 287.96 7 288.70 8 289.45 9 290.19 5 317.05 6 317.80 7 318.54 8 319.29 9 320.03 5 346.89 6 347.64 7 348.38 8 349.13 9 349.87 5 376.73 6 377.48 7 378.22 8 378.97 9 379.71 310=231.26 1 232.01 2 232.75 3 233.50 4 234.24 350 = 261.10 1 261.85 2 262.59 3 263.34 4 264.08 390 = 290.94 1 291.69 2 292.43 3 293.18 4 293.92 430 = 320.78 1 321.53 2 322.27 3 323.02 4 323.76 470 = 350.62 1 351.37 2 352.11 3 352.86 4 353.60 510 = 380.46 1 381.21 2 381.95 3 382.70 4 383.44 5 234.99 6 235.74 7 236.48 8 237.23 9 237.97 5 264.83 6 265.58 7 266.32 8 267.07 9 267.81 5 294.67 6 295.42 7 296.16 8 296.91 9 297.65 5 324.51 6 325.26 7 326.00 8 326.75 9 327.49 5 354.35 6 355.10 7 355.84 8 356.59 9 357.33 5 384.19 6 384.94 7 385.68 8 386.43 9 387.17 320 = 238.72 1 239.47 2 240.21 3 240.96 4 241.70 360= 268.56 1 269.31 2 270.05 3 270.80 4 271.54 400 = 298.40 1 299.15 2 299.89 3 300.64 4 301.38 440 = 328.24 1 328.99 2 329.73 3 330.48 4 331.22 480= 358.08 1 358.83 2 359.57 3 360.32 4 361.06 520=387.92 1 388.67 2 389.41 3 390.16 4 390.90 5 242.45 6 243.20 7 243.94 8 244.69 9 245.43 5 272.29 6 273.04 7 273.78 8 274.53 9 275.27 5 302.13 6 302.88 7 303.62 8 304.37 9 305.11 5 331.97 6 332.72 7 333.46 8 334.21 9 334.95 5 361 81 6 362.56 7 363.30 8 364.05 9 364.79 5 391.65 6 392.40 7 393.14 8 393.89 9 394.63 330=246.18 1 246.93 2 247.67 3 248.42 4 249.16 370= 276.02 1 276.77 2 277.51 3 278.26 4 279.00 410=305.86 1 306.61 2 307.35 3 308.10 4 308.84 450 = 335.70 1 336.45 2 337.19 3 337.94 4 338.68 490= 365.54 1 366.29 2 367.03 3 367.78 4 368.52 530 = 395.38 1 396.13 2 396.87 3 397.62 4 398.36 5 249.91 6 250.66 7 251.40 8 252.15 9 252.89 5 279.75 6 280.50 7 281.24 8 281.99 9 282.73 5 309.59 6 310.34 7 311.08 8 311.83 9 312.57 5 339.43 6 340.18 7 340.92 8 341.67 9 342.41 5 369.27 6 370.02 7 370.76 8 371.51 9 372.25 5 399.11 6 399.86 7 400.60 8 401.35 9 402.09 [31] HORSEPOWERS TO KILOWATTS HORSEPOWERS TO KILOWATTS Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts 540=402.84 1 403.59 2 404.33 3 405.08 4 405.82 580=432.68 1 433.43 2 434.17 3 434.92 4 435.66 620=462.52 1 463.27 2 464.01 3 464.76 4 465.50 660 = 492.36 1 493.11 2 493.85 3 494.60 4 495.34 700=522.20 1 522.95 2 523.69 3 524.44 4 525.18 740 = 552.04 1 552.79 2 553.53 3 554.28 4 555.02 5 406.57 6 407.32 7 408.06 8 408.81 9 409.55 5 436.41 6 437.16 7 437.90 8 438.65 9 439.39 5 466.25 6 467.00 7" 467.74 8 468.49 9 469.23 5 496.09 6 496.84 7 497.58 8 498.33 9 499.07 5 525.93 6 526.68 7 527.42 8 528.17 9 528.91 5 555.77 6 556.52 7 557.26 8 558.01 9 558.75 550 = 410.30 1 411.05 2 411.79 3 412.54 4 413.28 590=440.14 1 440.89 2 441.63 3 442.38 4 443.12 630=469.98 1 470.73 2 471.47 3 472 22 4 472.96 670=499.82 1 500.57 2 501.31 3 502.06 4 502.80 710 = 529.66 1 530.41 2 531.15 3 531.90 4 532.64 750 = 559.50 1 560.25 2 560.99 3 561.74 4 562.48 5 414.03 6 414.78 7 415.52 8 416.27 9 417.01 5 443.87 6 444.62 7 445.36 8 446.11 9 446.85 5 473.71 6 474.46 7 475.20 8 475.95 9 476.69 5 503.55 6 504.30 7 505.04 8 505.79 9 506.53 5 533.39 6 534.14 7 534.88 8 535.63 9 536.37 5 563.23 6 563.98 7 564.72 8 565.47 9 566.21 560=417.76 1 418.51 2 419.25 3 419.99 4 420.74 600= 447.60 1 448.35 2 449.09 3 449.84 4 450.58 640 = 477.44 1 478.19 2 478.93 3 479.68 4 480.42 680=507.28 1 508.03 2 508.77 3 509.52 4 510.26 720= 537.12 1 537.87 2 538.61 3 539.36 4 540.10 760 = 566.96 1 567.71 2 568.45 3 569.20 4 569.94 5 421.49 6 422.42 7 422.98 8 423.73 9 424.47 5 451.33 6 452.08 7 452 '.82 8 453.57 9 454.31 5 481.17 6 481.92 7 482.66 8 483.41 9 484.15 5 511.01 6 511.76 7 512.50 8 513.25 9 513.99 5 540.85 6 541.60 7 542.34 8 543.09 9 543.83 5 570.69 6 571.44 7 572.18 8 572.93 9 573.67 570=425.22 1 425.97 2 426.71 3 427.46 4 428.20 610= 455.06 1 455.81 2 456.55 3 457.30 4 458.04 650=484.90 1 485.65 2 486.39 3 487.14 4 487.88 690=514.74 1 515.49 2 516.23 3 516.98 4 517.72 730= 544.58 1 545.33 2 546.07 3 546.82 4 547.56 770 = 574.42 1 575.17 2 575.91 3 576.66 4 577.40 5 428.95 6 429.70 7 430.44 8 431.19 9 431.93 5 458.79 6 459.54 7 460.28 8 461.03 9 461.77 5 488.63 6 489.38 7 490.12 8 490.87 9 491.61 5 518.47 6 519.22 7 519.96 8 520.71 9 521.45 5 548.31 6 549.06 7 549.80 8 550.55 9 551.29 5 578.15 6 578.90 7 579.64 8 580.39 9 581.13 [32] HORSEPOWERS TO KILOWATTS HORSEPOWERS TO KILOWATTS Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts Horse- Kilo- powers watts 780 = 581.88 1 582.63 2 583.37 3 584.12 4 584.86 820 = 611.72 1 612.47 2 613.21 3 613.96 4 614.70 860=641.56 1 642.31 2 643.05 3 643.80 4 644.54 900 = 671.40 1 672.15 2 672.89 3 673.64 4 674.38 940 = 701.24 1 701.99 2 702.73 3 703.48 4 704.22 980 = 731.08 1 731.83 2 732.57 3 733.32 4 734.06 5 585.61 6 586.36 7 587.10 8 587.85 9 588.59 5 615.45 6 616.20 7 616.94 8 617.69 9 618.43 5 645.29 6 646.04 7 646.78 8 647.53 9 648.27 5 675.13 6 675.88 7 676.62 8 677.37 9 678.11 5 704.97 6 705.72 7 706.46 8 707.21 9 707.95 5 734.81 6 735.56 7 736.30 8 737.05 9 737.79 790=589.34 1 590.09 2 590.83 3 591.58 4 592.32 830=619.18 1 619.93 2 620.67 3 621.42 4 622.16 870=649.02 1 649.77 2 650.51 3 651.26 4 652.00 910=678.86 1 679.61 2 680.35 3 681.10 4 681.84 950 = 708.70 1 709.45 2 710.19 3 710.94 4 711.68 990=738.54 1 739.29 2 740.03 3 740.78 4 741.52 5 593.07 6 593.82 7 594.56 8 595.31 9 596.05 5 622.91 6 623.66 7 624.40 8 625.15 9 625.89 5 652.75 6 653.50 7 654.24 8 654.99 9 655.73 5 682.59 6 683.34 7 684.08 8 684.83 9 685.57 5 712.43 6 713.18 7 713.92 8 714.67 9 715.41 5 742.27 6 743.02 7 743.76 8 744.51 9 745.25 800=596.80 1 597.55 2 598.29 3 599.04 4 599.78 840= 626.64 1 627.39 2 628.13 3 628.88 4 629.62 880 = 656.48 1 657.23 2 657.97 3 658.72 4 659.46 920=686.32 1 687.07 2 687.81 3 688.56 4 689.30 960=716.16 1 716.91 2 717.65 3 718.40 4 719.14 1000= 746 2000 = 1492 3000 = 2238 4000=2984 5000=3730 5 600.53 6 601.28 7 602.02 8 602.77 9 603.51 5 630.37 6 631.12 7 631.86 8 632.61 9 633.35 5 660.21 6 660.96 7 661.70 8 662.45 9 663.19 5 690.05 6 690.80 7 691.54 8 692.29 9 693.03 5 719.89 6 720.64 7 721.38 8 722.13 9 722.87 6000=4476 7000 = 5222 8000=5968 9000=6714 10000=7460 810=604.26 1 605.01 2 605.75 3 606.50 4 607.24 850= 634.10 1 634.85 2 635.59 3 636.34 4 637.08 890=663.94 1 664.69 2 665.43 3 666.18 4 666.92 930=693.78 1 694.53 2 695.27 3 696.02 4 696.76 970=723.62 1 724.37 2 725.11 3 725.86 4 726.60 5 607.99 6 608.74 7 609.48 8 610.23 9 610.97 5 637.83 6 638.58 7 639.32 8 640.07 9 640.81 5 667.67 6 668.42 7 669.16 8 669.91 9 670.65 5 697.51 6 698.26 7 699.00 8 699.75 9 700.49 5 727.35 6 728.10 7 728.84 8 729.59 9 730.33 [33] KILOWATTS TO HORSEPOWERS KILOWATTS TO HORSEPOWERS Reduction factor: 1 kilowatt = 1.3404826 horsepower Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers 1 1.34 2 2.68 3 4.02 4 5.36 40= 53.62 1 54.96 2 56.30 3 57.64 4 58.98 80= 107.24 1 108.58 2 109.92 3 111.26 4 112.60 120= 160.86 1 162.20 2 163.54 3 164.88 4 166.22 160= 214.48 1 215.82 2 217.16 3 218.50 4 219.84 200= 268.10 1 269.44 2 270.78 3 272.12 4 273.46 5 6.70 6 8.04 7 9.38 8 10.72 9 12.06 5 60.32 6 61.66 7 63.00 8 64.34 9 65.68 5 113.94 6 115.28 7 116.62 8 117.96 9 119.30 5 167.56 6 168.90 7 170.24 8 171.58 9 172.92 5 221.18 6 222.52 7 223.86 8 225.20 9 226.54 5 274.80 6 276.14 7 277.48 8 278.82 9 280.16 10= 13.40 1 14.75 2 16.09 3 17.43 4 18.77 50= 67.02 1 68.36 2 69.71 3 71.05 4 72.39 90= 120.64 1 121.98 2 123.32 3 124.66 4 126.01 130= 174.26 1 175.60 2 176.94 3 178.28 4 179.62 170= 227.88 1 229.22 2 230.56 3 231.90 4 233.24 210= 281.50 1 282.84 2 284.18 3 285.52 4 286.86 5 20.11 6 21.45 7 22.79 8 24.13 9 25.47 5 73.73 6 75.07 7 76.41 8 77.75 9 79.09 5 127.35 6 128.69 7 130.03 8 131.37 9 132.71 5 180.97 6 182.31 7 183.65 8 184.99 9 186.33 5 234.58 6 235.92 7 237.27 8 238.61 9 239.95 5 288.20 6 289.54 7 290.88 8 292.23 9 293.57 20= 26.80 1 28.15 2 29.49 3 30.83 4 32. 17 60= 80.43 1 81.77 2 83.11 3 84.45 4 - 85.79 100= 134.05 1 135.39 2 136.73 3 138.07 4 139.41 140= 187.67 1 189.01 2 190.35 3 191.69 4 193.03 180= 241.29 1 242.63 2 243.97 3 245.31 4 246.65 220= 294.91 1 296.25 2 297.59 3 298.93 4 300.27 5 33.51 6 34.85 7 36.19 8 37.53 9 38.87 5 87.13 6 88.47 7 89.81 8 91.15 9 92.49 5 140.75 6 142.09 7 143.43 8 144.77 9 146.11 5 194.37 6 195.71 7 197.05 8 198.39 9 199.73 5 247.99 6 249.33 7 250.67 8 252.01 9 253.35 5 301.61 6 302.95 7 304.29 8 305.63 9 306.97 30= 40.21 1 41.55 2 42.90 3 44.24 4 45.58 70= 93.83 1 95.17 2 96.51 3 97.86 4 99.20 110= 147.45 1 148.79 2 150.13 3 151.47 4 152.82 150= 201.07 1 202.41 2 203.75 3 205.09 4 206.43 190= 254.69 1 256.03 2 257.37 3 258.71 4 260.05 230= 308.31 1 309.65 2 310.99 3 312.33 4 313.67 5 46.92 6 48.26 7 49.60 8 50.94 9 52.28 5 100.54 6 101.88 7 103.22 8 104.56 9 105.90 5 154.16 6 155.50 7 156.84 8 158.18 9 159.52 5 207.77 6 209.12 7 210.46 8 211.80 9 213.14 5 261.39 6 262.73 7 264.08 8 265.42 9 266.76 5 315.01 6 316.35 7 317.69 8 319.03 9 320.38 [34] KILOWATTS TO HORSEPOWERS KILOWATTS TO HORSEPOWERS Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers 240= 321.72 1 323.06 2 324.40 3 325.74 4 327.08 280= 375.34 1 376.68 2 378.02 3 379.36 4 380.70 320= 428.95 1 430.29 2 431.64 3 432.98 4 434.32 360= 482.57 1 483.91 2 485.25 3 486.60 4 487.94 400= 536.19 1 537.53 2 538.87 3 540.21 4 541.55 440= 589.81 1 591.15 2 592.49 3 593.83 4 595.17 5 328.42 6 329.76 7 331.10 8 332.44 9 333.78 5 382.04 6 383.38 7 384.72 8 386.06 9 387.40 5 435.66 6 437.00 7 438.34 8 439.68 9 441.02 5 489.28 6 490.62 7 491.96 8 493.30 9 494.64 5 542.90 6 544.24 7 545.58 8 546.92 9 548.26 5 596.51 6 597.86 7 599.20 8 600.54 9 601.88 250= 335.12 1 336.46 2 337.80 3 339 . 14 4 340.48 290= 388.74 1 390.08 2 391.42 3 392.76 4 394.10 330= 442.36 1 443.70 2 445.04 3 446.38 4 447.72 370= 495.98 1 497.32 2 498.66 3 500.00 4 501.34 410^= 549.60 1 550.94 2 552.28 3 553.62 4 554.96 450= 603.22 1 604.56 2 605.90 3 607.24 4 608.58 5 341.82 6 343.16 7 344.50 8 345.84 9 347.18 5 395.44 6 396.78 7 398.12 8 399.46 9 400.80 5 449.06 6 450.40 7 451.74 8 453.08 9. 454.42 5 502.68 6 504.02 7 505.36 8 506.70 9 508.04 5 556.30 6 557.64 7 558.98 8 560.32 9 561.66 5 609.92 6 611.26 7 612.60 8 613.94 9 615.28 260= 348.53 1 349.87 2 351.21 3 352.55 4 353.89 300= 402.14 1 403.49 2 404.83 3 406.17 4 407.51 340= 455.76 1 457.10 2 458.45 3 459.79 4 461.13 380= 509.38 1 510.72 2 512.06 3 513.40 4 514.75 420= 563.00 1 564.34 2 565.68 3 567.02 4 568.36 460= 616.62 1 617.96 2 619.30 3 620.64 4 621.98 5 355 . 23 6 356.57 7 357.91 8 359.25 9 360.59 5 408.85 6 410.19 7 411.53 8 412.87 9 414.21 5 462.47 6 463.81 7 465.15 8 466.49 9 467.83 5 516.09 6 517.43 7 518.77 8 520.11 9 521.45 5 569.71 6 571.05 7 572.39 8 573.73 9 575.07 5 623.32 6 624.66 7 626.01 8 627.35 9 628.69 270= 361.93 1 363 . 27 2 364.61 3 365.95 4 367.29 310= 415.55 1 416.89 2 418.23 3 419.57 4 420.91 350= 469.17 1 470.51 2 471.85 3 473.19 4 474.53 390= 522.79 1 524.13 2 525.47 3 526.81 4 528.15 430= 576.41 1 577.75 2 579.09 3 580.43 4 581.77 470= 630.03 1 631.37 2 632.71 3 634.05 4 635.39 5 368.63 6 369.97 7 371.31 8 372.65 9 373.99 5 422.25 6 423.59 7 424.93 8 426.27 9 427.61 5 475.87 6 477.21 7 478.55 8 479.89 9 481.23 5 529.49 6 530.83 7 532.17 8 533.51 9 534.85 5 583.11 6 584.45 7 585.79 8' 587.13 9 588.47 5 636.73 6 638.07 7 639.41 8 640.75 9 642.09 [35] KILOWATTS TO HORSEPOWERS KILOWATTS TO HORSEPOWERS Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- Watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers 480= 643.43 1 644.77 2 646.11 3 647.45 4 648.79 520= 697.05 1 698.39 2 699.73 3 701.07 4 702.41 560= 750.67 1 752.01 2 753.35 3 754.69 4 756.03 600= 804.29 1 805.63 2 806.97 3 808.31 4 809.65 640= 857.91 1 859.25 2 860.59 3 861.93 4 863.27 680= 911.53 1 912.87 2 914.21 3 915.55 4 916.89 5 650. 13 6 651.47 7 652.82 8 654.16 9 655.50 5 703.75 6 705.09 7 706.43 8 707.77 9 709.12 5 757.37 6 758.71 7 760.05 8 761.39 9 762.73 5 810.99 6 812.33 7 813.67 8 815.01 9 816.35 5 864.61 6 865.95 7 867.29 8 868.63 9 869.97 5 918.23 6 919.57 7 920.91 8 922.25 9 923.59 490= 656.84 1 658.18 2 659.52 3 660.86 4 662.20 530= 710.46 1 711.80 2 713.14 3 714.48 4 715.82 570= 764.08 1 765.42 2 766.76 3 768.10 4 769.44 610= 817.69 1 819.03 2 820.38 3 821.72 4 823.06 650= 871.31 1 872.65 2 873.99 3 875.34 4 876.68 690= 924.93 1 926.27 2 927.61 3 928.95 4 930.29 5 663.54 6 664.88 7 666.22 8 667.56 9 668.90 5 717.16 6 718.50 7 719.84 8 721.18 9 722.52 5 770.78 6 772.12 7 773.46 8 774.80 9 776.14 5 824.40 6 825.74 7 827.08 8 828.42 9 829.76 5 878.02 6 879.36 7 880.70 8 882.04 9 883.38 5 931.64 6 932.98 7 934.32 8 935.66 9 937.00 500= 670.24 1 671.58 2 672.92 3 674.26 4 675.60 540= 723.86 1 725.20 2 726.54 3 727.88 4 729.22 580= 777.48 1 778.82 2 780.16 3 781.50 4 782.84 620= 831.10 1 832.44 2 833.78 3 835.12 4 836.46 660= 884.72 . 1 886.06 2 887.40 3 888.74 4 890.08 700= 938.34 1 939.68 2 941.02 3 942.36 4 943.70 5 676.94 6 678.28 7 679.62 8 680.97 9 682.31 5 730.56 6 731.90 7 733.24 8 734.58 9 735.92 5 784.18 6 785.52 7 786.86 8 788.20 9 789.54 5 837.80 6 839.14 7 840.48 8 841.82 9 843.16 5 891.42 6 892.76 7 894.10 8 895.44 9 896.78 5 945.04 6 946.38 7 947.72 8 949.06 9 950.40 510= 683.65 1 684.99 2 686.33 3 687.67 4 689.01 550= 737.27 1 738.61 2 739.95 3 741.29 4 742.63 590= 790.88 1 792.23 2 793.57 3 794.91 4 796.25 630= 844.50 1 845.84 2 847.19 3 848.53 4 849.87 670= 898.12 1 899.46 2 900.80 3 902.14 4 903.49 710= 951.74 1 953.08 2 954.42 3 955.76 4 957.10 5 690.35 6 691.69 7 693.03 8 694.37 9 695.71 5 743.97 6 745.31 7 746.65 8 747.99 9 749.33 5 797.59 6 798.93 7 800.27 8 801.61 9 802.95 5 851.21 6 852.55 7 853.89 8 855 . 23 9 856.57 5 904.83 6 906.17 7 907.51 8 908.85 9 910.19 5 958.45 6 959.79 7 961.13 8 962.47 9 963.81 [36] KILOWATTS TO HORSEPOWERS KILOWATTS TO HORSEPOWERS Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers 720= 965.15 1 966.49 2 967.83 3 969.17 4 970.51 760 = 1018.77 1 1020. 10 2 1021.45 3 1022.79 4 1024.13 800 = 1072.39 1 1073.73 2 1075.07 3 1076.41 4 1077.75 840 = 1126.01 1 1127.35 2 1128.69 3 1130.03 4 1131.37 880=1179.62 1 1180.97 2 1182.31 3 1183.65 4 1184.99 920 = 1233.24 1 1234.58 2 1235.92 3 1237.27 4 1238.61 5 971.85 6 973.19 7 974.53 8 975.87 9 977.21 5 1025.47 6 1026.81 7 1028.15 8 1029.49 9 1030.83 5 1079.09 6 1080.43 7 1081.77 8 1083.11 9 1084.45 5 1132.71 6 1134.05 7 1135.39 8 1136.73 9 1138.07 5 1186.33 6 1187.67 7 1189.01 8 1190.35 9 1191.69 5 1239.95 6 1241.29 7 1242.63 8 1243.97 9 1245.31 730= 978.55 1 979.89 2 981.23 3 982.57 4 983.91 770 = 1032.17 1 1033.51 2 1034.85 3 1036.19 4 1037.53 810 = 1085.79 1 1087.13 2 1088.47 3 1089.81 4 1091.15 850 = 1139.41 1 1140.75 2 1142.09 3 1143.43 4 1144.77 890 = 1193.03 1 1194.37 2 1195.71 3 1197.05 4 1198.39 930 = 1246.65 1 1247.99 2 1249.33 3 1250.67 4 1252.01 5 985.25 6 986.60 7 987.94 8 989.28 9 990.62 5 1038.87 6 1040.21 7 1041.55 8 1042.90 9 1044.24 5 1092.49 6 1093.83 7 1095.17 8 1096.51 9 1097.86 5 1146.11 6 1147.45 7 1148.79 8 1150.13 9 1151.47 5 1199.73 6 1201.07 7 1202.41 8 1203.75 9 1205.09 5 1253.35 6 1254.69 7 1256.03 8 1257.37 9 1258.71 740= 991.96 1 993.30 2 994.64 3 995.98 4 997.32 780 = 1045.58 1 1046.92 2 1048.26 3 1049.60 4 1050.94 820 = 1099.20 1 1100.54 2 1101.88 3 1103.22 4 1104.56 860 = 1152.82 1 1154.16 2 1155.50 3 1156.84 4 1158.18 900 = 1206.43 1 1207.77 2 1209.12 3 1210.46 4 1211.80 940 = 1260.05 1 1261.39 2 1262.73 3 1264.08 4 1265.42 5 998.66 6 1000.00 7 1001.34 8 1002.68 9 1004.02 5 1052.28 6 1053.62 7 1054.96 8 1056.30 9 1057.64 5 1105.90 6 1107.24 7 1108.58 8 1109.92 9 1111.26 5 1159.52 6 1160.86 7 1162.20 8 1163.54 9 1164.88 5 1213.14 6 1214.48 7 1215.82 8 1217.16 9 1218.50 5 1266.76 6 1268.10 7 1269.44 8 1270.78 9 1272.12 750 = 1005.36 1 1006.70 2 1008.04 3 1009.38 4 1010.72 790 = 1058.98 1 1060.32 2 1061.66 3 1063.00 4 1064.34 830 = 1112.60 1 1113.94 2 1115.28 3 1116.62 4 1117.96 870 = 1166.22 1 1167.56 2 1168.90 3 1170.24 4 1171.58 910 = 1219.84 1 1221.18 2 1222.52 3 1223.86 4 1225.20 950 = 1273.46 1 1274.80 2 1276.14 3 1277.48 4 1278.82 5 1012.06 6 1013.40 7 1014.75 8 1016.09 9 1017.43 5 1085.68 6 1057.02 7 1088.36 8 1069.71 9 1071.05 5 1119.30 6 1120.64 7 1121.98 8 1123.32 9 1124.66 5 1172.92 6 1174.26 7 1175.60 8 1176.94 9 1178.28 5 1226.54 6 1227.88 7 1229.22 8 1230.56 9 1231.90 5 1280. 16 6 1281.50 7 1282.84 8 1284.18 9 1285.52 [37] KILOWATTS TO HORSEPOWERS KILOWATTS TO HORSEPOWERS Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers Kilo- Horse- watts powers 960 = 1286.86 970 = 1300.27 980 = 1313.67 990 = 1327.08 1000= 1340 1 1288.20 1 1301.61 1 1315.01 1 1328.42 1 2000= 2681 2 1289.54 2 1302.95 2 1316.35 2 1329.76 3000= 4021 3 1290.88 3 1304.29 3 1317.69 3 1331.10 4000= 5362 4 1292.23 4 1305.63 4 1319.03 4 1332.44 5000= 6702 5 1293.57 5 1306.97 5 1320.38 5 1333.78 6000= 8043 6 1294.91 6 1308.31 6 1321.72 6 1335.12 7000= 9383 7 1296.25 7 1309.65 7 1323.06 7 1336.46 8000 = 10723 8 1297.59 8 1310.99 8 1324.40 8 1337.80 9000 = 12064 9 1298.93 9 1312.33 9 1325.74 9 1339.14 10000 = 13405 [38] SECTION 2 WEIGHTS AND MEASURES MEASURES OF LENGTH Line Measurement is used in measuring distances. Any convenient unit may be employed, as inch, foot, yard or mile. The standard unit of length is the yard. In 1813 Mr. Hassler obtained for the use of the United States Coast Survey a standard brass bar 82 inches long, graduated by Troughton, of London. The gradua- tions of this bar were accepted as corresponding at the temperature of 62 F. to the standard yard of Great Britain. The standard yard adopted by the United States Treasury Department was the 36 inches between the 27th and the 63d inches of the above 82-inch bar. LINEAR MEASURE 12 inches = 1 foot mi. rd. yd. ft. in. 3 feet = 1 yard 1 = 320 = 1,760 = 5,280 = 63,360 5| yards = 1 rod 1 = 51 = m = 198 320 rods = 1 mile 1=3= 36 The symbols: ' for feet and " for inches are used in dimensioning drawings, often in books, and in correspondence. EXAMPLE. 18' 7" = 18 feet 7 inches. The foot is commonly divided for civil engineers into tenths and hundredths of a foot. At the United States Custom Houses, the yard is divided into tenths and hundredths. A mile of 5,280 ft. is called a statute mile. It is the legal mile of the United States and Great Britain. Surveyors' Linear Measure is used in measuring land. The unit of this measure is Gunter's chain, 66 feet or 4 rods in length, having 100 links, each joined to the adja- cent one by three smaller links. A square chain is one-tenth of an acre, or 10,000 square links. LAND MEASURES 100 links = 1 chain mi. ch. ft. 1. in. 80 chains = 1 mile 1 = 80 = 5,280 = 8,000 = 63,360 1 = 66 = 100 = 792 66 = 1 = 7.92 25 links = 1 rod 1 furlong = mile City surveyors and civil engineers commonly use steel tapes 100 feet long, the feet divided into tenths and hundredths. OTHER LINEAR DIMENSIONS IN USE 1 hand = 4 inches. Used in measuring the heights of horses. 1 fathom = 6 feet. Used principally in nautical measurements; depth of water, length of rope, etc. It approximates the thousandth part of a nautical mile. 1 cable = 120 fathoms, or 720 feet; commonly written cable-length. 1 knot = 1 nautical mile. = 1 Admiralty knot = 6080 feet per hour. NOTE. A knot is a velocity, not a length. It is used to express the speed of a ship at sea. EXAMPLE. 15 knots per hour. [39] WEIGHTS AND MEASURES 1 geographical mile = 1.1515 statute miles; variously estimated from 6,075 to 6,080 ft. = 1 minute of longitude at the equator. = 1/60 degree of latitude. 1 measured mile = English Admiralty " measured mile" is 6,080 feet; used to ascertain the speed of ships. 1 league = 3 nautical miles. 1 degree = 60 geographical miles; variously estimated from 69.21 to 69.29 statute miles. = 1/360 part of the earth's circumference. MEASURE OF SURFACE A linear unit squared is a corresponding square unit in determining the areas of surfaces. The side of the square may be an inch, foot, yard, or any other convenient unit. SUPERFICIAL MEASURE 144 square inches = 1 square foot it* square mciies = i square loot 9 square feet = 1 square yard 30 j square yards = 1 square rod 160 square rods = 1 square acre 640 acres = 1 square mile 1 rood = j acre. With the exception of the acre, the above units of superficial square measure are derived from the corresponding units of linear measure. A square inch is the area of a rectangle the side of which is one inch. A circular inch is the area of a circle one inch in diameter = 0.7854 square inch. One square inch = 1.2732 circular inches. One square foot = 144 square inches = 183.35 circular inches. Slate and other roofing is often reckoned by the square, meaning 100 square feet of surface. Plastering and painting are commonly reckoned by the square yard. SURVEYOR'S SQUARE MEASURE 625 square links = 1 square rod 16 square rods = 1 square chain 10,000 square links = 1 square chain 10 square chains = 1 acre 640 acres = 1 square mile 36 square miles = 1 township An acre is 208.71 feet square = 43,560 square feet. This is the common unit of land measure. The public lands of the United States are divided by north and south meridianal lines crossed by others at right angles forming Townships of six miles square. Townships are sub-divided into Sections one mile square. A section one mile square contains 640 acres. It is divided into half-sections of 320 acres; quarter-sections of 160 acres; half-quarter sections of 80 acres; and quarter- quarter sections of 40 acres. Board Measure is used in measuring lumber. The unit is 1 square foot of surface by 1 inch in thickness, or iV of a cubic foot. Unless otherwise stated, boards less than an inch thick are reckoned as if they were of that thickness. Boards over an inch thick are reduced to the inch standard; that is, for 1^-inch boards add j to the surface measure, for 1^-inch boards add to the surface measure, and so on for any thickness. All sawed timber is measured by board measure. 1,000 feet board measure = 83.33 cubic feet. [40] WEIGHTS AND MEASURES MEASURES OF VOLUME Cubic measure applies to measurement in the three dimensions of length, breadth, and depth or thickness. Any convenient linear unit may be employed because quan- tities are always expressed in cubes of fixed linear measurement, as cubic inch, cubic foot, or cubic yard. SOLID OR CUBIC MEASURE 1,728 cubic inches 1 cubic foot 27 cubic feet = 1 cubic yard 128 cubic feet = 1 cord 24f cubic feet = 1 perch A perch of masonry is 16| feet long, 1 feet thick, and 1 foot high = 24| cubic feet. A cord of wood is 8 feet long, 4 feet wide, and 4 feet high = 128 cubic feet. Timber measured in bulk and not to be computed in cubic feet is reduced to board measure, that is, in terms of square feet of surface by 1 inch in thickness. MEASURES OF CAPACITY The United States gallon corresponds to the British wine gallon of 1707, which was abolished in 1824, when the Imperial gallon, containing 10 pounds of water, was made the British standard. This latter measure is not in use in this country. The unit of liquid measure in the United States is the wine gallon of 231 cubic inches. TABLE gal. qt. pt. gi. 4 gills = 1 pint 1 = 4 = 8 = 32 2 pints = 1 quart 1=2=8 4 quarts = 1 gallon 1=4 1 gallon of pure water at 62 F. = 8.34 poiihds. 1 cubic foot of water contains 7.48 gallons. Barrels are not uniform in capacity, ranging from 31? to 50 gallons. Their capacity is found by gauging, actual measurement, or by weight. Hogshead = 2 barrels. Actual capacity must be determined by gauging or other measurement. The British Imperial Gallon is defined as the volume of 10 pounds weight of pure distilled water at the temperature of 62 F., the height of the barometer being 30 inches. There is no legal equivalent of the gallon expressed in cubic inches. Until the year 1890 it was usual to take 277.274 cubic inches as the equivalent of the gallon, but from very careful experiments by Mr. H. J. Chaney, recorded in the Philosophical Trans- actions of the Royal Society for 1892, the weight of a cubic inch of water was determined as 252.286 grains, from which the volume of the gallon is computed to be 277.463 cubic inches. An Imperial gallon = 1.20114 United States gallons. A United States gallon =231 cubic inches = .83254 Imperial gallon. DRY MEASURE Dry Measure is used in measuring grain, fruits, etc. The unit in the United States is the Winchester bushel = 2,150.42 cubic inches = 1.244 cubic feet. TABLE bu. pk. qt. pt. 2 pints = 1 quart 1 = 4 = 32 = 64 8 quarts = 1 peck 1 = 8 = 16 4 pecks = 1 bushel 1 bushel = 2,150.42 -;- 231 = 9.30 wine gallons [41] WEIGHTS, AND MEASURES The above is what is known as the struck bushel or the bushel measure even full. The heaped bushel is about one-quarter more, the cone being about 6 inches high. A bushel measure is 18 niches diameter by 8 inches deep. The U. S. Standard Bushel was fixed at 2,150.42 cubic inches. This is the same as the Winchester bushel, now abolished in the British system, substituting therefor as the legal bushel one containing 8 Imperial gallons, equivalent to 2,219.704 cubic inches or 1.284 cubic feet. It will be seen that neither the gallon nor the bushel adopted by the U. S. Treasury Department is in accord with the British standards. Grain in bulk is sold by weight. Commercial usage has established an equivalent number of pounds per bushel for the various kinds of grain as well as for other com- modities shipped in bulk; these equivalent weights have been generally legalized throughout the United States. AVOIRDUPOIS WEIGHT Commercial weights are always in terms of the Avoirdupois standard. Troy weights are reserved for gold, silver, and precious stones. Apothecaries' weight is employed when compounding medicine. The unit of Avoirdupois weight is the pound containing 7,000 Troy grains. Table of Tons of 2,000 Pounds Also known as Short or Net Tons ton cwt. Ib. oz. 16 ounces < = 1 pound 1 = 20 = 2,000 = 32,000 100 pounds = 1 hundredweight 1 = 100 = 1,600 20 hundredweights = 1 ton 1 = 16 The ounce is divided into halves and quarters. The ton of 2,000 pounds is the standard ton of commerce. Table of Tons of 2,240 Pounds Also known as Long or Gross Tons ton cwt. Ib. oz. 16 ounces = 1 pound , -" 1 = 20 = 2,240 = 35,840 112 pounds = 1 hundredweight 1 = 112 = 1,792 20 hundredweights = 1 ton 1 = 16 One quarter = 28 pounds The ton of 2,240 pounds is used for weighing ores, pig iron, steel rails, etc. It is used in U. S. Custom Houses for estimating ocean freights. It is the standard ton of Great Britain. One shipping ton (for measuring cargo) = 40 cubic feet. In England, one shipping ton (for measuring cargo) = 42 cubic feet. TROY WEIGHT The Troy Pound was the first standard to be adopted by Congress and put into practical use. It was the legalization of a certain brass Troy-pound-weight procured by the Minister of the United States at London, in the year 1827, for the use of the Mint, and now hi the custody of the U. S. Mint at Philadelphia. This is the standard Troy pound, comformably to which the U. S. coinage is regulated. It is an exact copy of the Imperial Troy pound of Great Britain. Troy weight is used chiefly in the weighing of gold, silver, and articles of jewelry. The unit of weight is the Troy pound. [42] WEIGHTS AND MEASURES Table Ib. oz. pwt. gr. 24 grains = 1 pennyweight 1 = 12 = 240 = 5,760 20 pennyweights = 1 ounce 1 = 20 = 480 12 ounces = 1 pound Carat is a term employed to express the commercial fineness of gold. An ounce is divided into 24 equal parts, one of which is called a carat. Pure gold is 24 carats fine; 18-carat gold is 18 parts pure gold and 6 parts alloy. A Carat Weight when employed to weigh diamonds = 3.2 Troy grains. The International 200-milligram carat went into effect in the United States, July 1, 1913, as the standard for weighing all kinds of gems and precious stones. By com- parison, 1 milligram = .0154 Troy grains. Then .0154 X 200 = 3.08 Troy grains. APOTHECARIES' WEIGHT The ounce in Apothecaries' weight is the same as the Troy ounce but differently divided. The grain and the pound are the same as the Troy standards. There does not appear to be a standard unit in Apothecaries' weight, but from the fact that it is used in compounding medicines in small quantities, the ounce (Troy) would appear to be a convenient one inasmuch as chemicals for industrial use, when sold in large quantities, are commonly by Avoirdupois weight. Table Ib. 5 5 9 gr. 20 grains = 1 scruple. . . sc. or 9 1 = 12 = 96 = 288 = 5,760 3 scruples = 1 dram. . . .dr. or 5 1 = 8 = 24 = 480 8 drams = 1 ounce. ... oz. or 5 1=3= 60 12 ounces = 1 pound. . . .Ib. or Ib The symbols always precede the number, thus: 54, 52, 91=4 oz., 2 dr., 1 scruple. Apothecaries' Fluid Measure Used by physicians when prescribing and by apothecaries in compounding liquid medicines. The gallon is the standard wine gallon of 231 cubic inches, of which the pint is one- eighth. Table Cong.O. f 5 f 5 m 60 minims (m) =1 fluid drachm. f 5 1 = 8 = 128 = 1,024 = 61,440 8 fluid drachms = 1 fluid ounce., .f 5 1 = 16 = 128 = 7,680 16 fluid ounces = 1 pint O. 1 = 8 = 480 8 pints = 1 gallon Cong. 1 = 60 Cong., Latin Congius, gallon; O., Latin octavius, one-eighth. Medical Signs and Abbreviations ^ (Lat. Recipe), take; aa, of each; Ib, pound; 5, ounce; 5, drachm; 3, scruple; TIL, minim, or drop; O or o, pint; f 5j fluid ounce; f 5, fluid drachm; as, 5 ss, half an ounce; 5 i, one ounce; 5 iss, one ounce and a half; 5 ij, two ounces; gr., grain; Q. S., as much as sufficient; Ft. Mist., let a mixture be made; Ft. Haust., let a draught be made; Ad., add to; Ad lib., at pleasure; Aq., water; M., mix; Mac., macerate; Pulv., powder; Pil., pill; Solv., dissolve; St., let it stand; Sum., to be taken; D., dose; Dil., dilute; Filt., filter; Lot., a wash; Garg., a gargle; Hor. Decub., at bedtime; Inject., injection; Gtt., drops; ss, one-half; Ess., essence. The symbols always precede the numbers to which they refer. The International Metric System has practically displaced the above system in laboratory work as well as in compounding medicines, [43] MEASURES OF TIME UNITED STATES MONEY The legal currency of the United States is based on the gold standard. Coins are of gold, silver, nickel, and copper. Authorized paper money includes gold certificates, silver certificates, United States notes, Treasury notes of 1890, and National bank notes. The unit of value is the gold dollar of 25.8 grains. Table E. $ d. c. m. 10 mills = 1 cent 1 = 10 10 cents = 1 dime 1 = 10 = 100 10 dimes = 1 dollar 1 = 10 = 100 = 1,000 10 dollars = 1 eagle 1 = 10 = 100 = 1,000 = 10,000 Gold coins are 90 per cent gold and 10 per cent alloy, consisting of silver and copper. Denominations, $20, $10, $5, $2.50. Silver coins are 90 per cent silver and 10 per cent copper alloy. Standard silver dollar weighs 412.5 grains. Ratio to gold 15.988 to 1. Coinage ceased in 1905. Subsidiary silver coins weigh 385.8 grains to the dollar. Ratio to gold 14.953 to 1. Denominations, 50 cents, 25 cents, 10 cents. Legal tender, not to exceed $10. Re- deemable in " lawful money " at the Treasury in sums or multiples of $20. Minor coins now consist of the 5-cent and the 1-cent pieces only. The 5-cent piece weighs 77.16 grains. Alloy consists of 75 per cent copper and 25 per cent nickel. The 1-cent piece weighs 48 grains. Alloy consists of 95 per cent copper and 5 per cent tin and zinc. They are legal tender not to exceed 25 cents. Redeemable in " lawful money " at the Treasury in sums or multiples of $20. " Lawful money " includes gold coin, silver dollars, United States notes, and Treasury notes. United States notes (greenbacks) are by regulation receivable for customs so long as they continue redeemable in coin. Treasury notes were issued for purchase of silver bullion which was coined into dollars, wherewith the notes are being redeemed. MEASURES OF TIME A solar day is the period of one revolution of the earth around its axis in reference to the sun. It is divided into 24 hours, in two periods of 12 hours each; from 12 o'clock noon or meridian to 12 o'clock midnight, and from midnight to noon. The change in the name and number of days and months in the civil calendar occurs at midnight. Table day hr. min. sec. 60 seconds = 1 minute 1 = 24 = 1,440 = 86,400 60 minutes = 1 hour 1 = 60 = 3,600 24 hours = 1 day 1 = 60 7 days = 1 week 365 days = 1 calendar year The length of the solar year is 365 days, 5 hr., 48 min., nearly. A calendar year of 365 days is nearly one-fourth of a day too short, for which one day is added to the month of February every four years, called leap-year. But this addition makes one day too much in every 128.866 years, which error is corrected every fourth century, which can be divided by four without a remainder. Thus, 1884 was leap-year, but not 1900, this omission of one leap-year in every four centuries being necessary to correct the error above referred to. A sidereal day differs from a solar day in taking no account of the sun, but record- ing that interval of time between the appearance of a fixed star in the meridian and again returning to the same star the night immediately following. This interval of [44] UNITED STATES MONEY EQUIVALENTS VALUE OF FOREIGN COINS IN UNITED STATES MONEY Country Standard Monetary Unit Value in U.S. Gold Dollar Remarks (a) Argentina . Austria- Hungary . Belgium. . . Bolivia. . . . Brazil British Col- onies in Australia & Africa. . Canada. . . Cent. Ameri- can States: B.Hond's. CostaRica Guat'ala . Honduras Nicaragua Salvador . Chile China Gold... Gold... Gold(b) Gold... Gold... Gold... Gold... Gold... Gold... Silver. . Silver. . Peso Crown Franc $0.9648 .2026 .1930 .3893 .5462 4.8665 1.0000 1.0000 .4653 .3537 .3537 1.0000 .3537 .3650 .5296 .5899 .5780 1.0000 1.0000 .2680 .4867 4.9431 .1930 .1930 .2382 4.8665 .1930 .9647 .3244 Currency: depreciated paper, convertible at 44 per cent of face value. Member of Latin Union; gold is the actual standard. 12^ bolivianos equal 1 pound sterling. Currency: Government paper. Exchange rate about $0.25 to the milreis. Currency: inconvertible paper, exchange rate 40 pesos = $1.00. Currency: bank notes. Currency: convertible into silver on de- mand. Currency: inconvertible paper; exchange rate approximately, $0.14. Currency: inconvertible paper; exchange rate, approximately, $105 paper to $1 gold. The actual standard is the British pound sterling, which is legal tender for 97 % piasters. Member of Latin Union; gold is the actual standard. Member of Latin Union; gold is the actual standard. Currency: inconvertible paper; exchange rate, approximately, $0.16. (15 rupees equal 1 pound sterling.) Boliviano .... \lilreis Pound sterling Dollar Dollar Colon Peso Peso Gold. . . Silver . Cordoba Peso Gold. . . Silver. . Gold... Gold. Peso ^ C Shanghai 8 ] Haikwan "* [Canton.. Dollar Colombia. . Cuba Peso Denmark. . Ecuador. . . Egypt.... Finland . . . France. . . . Germany. . Gt. Britain Greece Hayti India ..... Gold... Gold. . . Gold... Gold... Gold(b) Gold... Gold. . . Gold(b) Gold... Gold. . . Crown Sucre Pound (100 pi- asters) Mark Franc Mark. . Pound sterling Drachma Gourde ...... Rupee ... . (a) The exchange rates shown under this heading are recent quotations and given as an indication of the values of currencies which are fluctuating in their relation to the legal standard. They are not to take. the place of the Consular certificate where it is available, (b) And silver. [45] UNITED STATES MONEY EQUIVALENTS VALUE OF FOREIGN COINS IN UNITED STATES MONEY (Cont.) Country Standard Monetary Unit Value in U.S. Gold Dollar Remarks (a) Italy Japan. Gold(b) Gold. Lira .... .1930 .4985 1.0000 .4985 .4020 1.0139 .2680 1.0000 .3537 .1700 4.8665 .5000 1.0806 .1930 .5146 1.0000 .1930 .3709 .1930 .5678 .2680 .1930 .0440 1.0342 .1930 Member of Latin Union; gold is the actual standard. Currency: depreciated silver token coins; customs duties are collected in gold. Mexican exchange rate fluctuating, ap- proximately, $0.15. Currency: depreciated paper; exchange rate 1.550 per cent. This is the value of the gold kran. Cur- rency is silver circulating above its me- tallic value; exchange value of silver kran, approximately, $0.0875. Currency: inconvertible paper; exchange rate, approximately, $0.70}^. Valuation is for the gold peseta; currency is silver circulating above its metallic value; exchange value, approximately, $0.20. Member Latin Union; gold is actual stand- ard. 100 piasters equal to the Turkish . Yen Liberia. . . . Mexico Netherlands. Newfound- land Norway. . . Panama . . . Paraguay. . Persia Peru Philippine Islands. . . Portugal. . . Roumania. Russia . . . . Santo Dom Serbia Siam. . . . Gold... Gold... Gold... Gold... Gold... Gold... Silver. . Dollar Peso Florin Dollar Crown Balboa Peso Gold(b) Gold. . . Gold. . . Gold... Gold... Kran Libra Peso Escudo Leu Gold... Gold... Gold... Gold. Ruble....... Dollar Dinar. Tical Spain Gold(b) Gold. . . Gold... Gold... Gold... Gold Peseta Straits Set'm'ts.. Sweden. . . Switzerl'd . Turkey.... Uruguay . Dollar Crown Franc .... Piaster Peso Venezuela . Gold... Bolivar (a) The exchange rates shown under this heading are recent quotations and given as an indication of the values of currencies which are fluctuating in their relation to the legal standard. They are not to take the place of the Consular certificate where it is available, (b) And silver. time is divided into 24 hours continuously beginning at 1 p. M. and not into two periods of 12 hours each. Let there be two clocks, one regulated for mean solar time, indicating 24 hours from meridian to meridian of a fixed star; the latter clock will indicate only 23 hr., 56 min., 4 sec., of mean solar time; the fixed star passing the meridian 3 min., 56 sec., earlier every day. A sidereal year is the time which elapses during a complete revolution of the earth around the sun, measured by the recurrence of the same fixed star selected at the begin- ning of the observation; it is 365 days, 6 hrs., 9 min., 9.3145 sec. of mean solar time. [46] MEASURES OF TIME SS5S32 |g883 O rH Cl CO ^ b- b- b- b- b- CO cO cO CO CO >O CO b 00 OS r^ t^ t^ t> t>. CO CO CO CO CO I s * 00 OS O* *H 00 00 00 OS OS cO cO cO cO cO 3S OS O rH d rf( to to O gggg ggg rH Cq CO CO co CO Tt< to CO b- 00 cO cO cO cO cO O5 O i-l CO CO CO CO CO CO CO CO 00 OS O rH - !> OO OO 00 iO iO O iO to 28 i t"- OO O5 O i-H rf< O b 00 OS O rH 00 O5 O i-H i-t rH ^-H - rH 00 O5 to CO t^- 00 O5 w w eo co co rH OO OS O rH O b* 00 Os CD CO CO CO CO rH d CO Tt< IO COt>-OOOS CO CO CO CO CO CO CO CO CO 22 g 2S 22 22 SS SS CO CO CO CO CO CO CO T-I (M CO rj< to S S S S 2 CO CO CO CO CO COt-OOOSO i-ldCO-^to COI>OOOSO rH(NCO^to TH rHrHrHrHrH rHrHrHrHd ddddd to co i> oo CO CO CO CO CO CO CO CO l>- 00 OS OrH(MCO^ tOCOi>OOOS cococococo cococococo CO CO .CO CO to co i> oo IIS Os Os OS Os Os Os Os OS to to to to OOOSOrHdCO co co co co co co co co co co ^^ ^^ ^< ^^ (NCOrt-OOOSQi-( (NCO^tOCO oooooooooo ooooooosos ososososos o O rH rH rH (N (M (N CO ^ to CO iO iO to to to totOtocOcO COCOCOCOCO l>OOO5OrH (NCOrt^tOCO l>-OOOSOrH 1 2Q r i (: 2 f 2'^! ocob-ooos OrHl>I>l>. b-b-b-b-t>. OOOOOOOOOO OOOOOOOOOOOS I ^??3^^ &%%$3 3 b-OOOSOrH C^ICO^tOCO b-OOOS Tfl^T^iOtO tototOtOtO tototo Ct rH (M CO r < to CO t- oo os o rH rH 00 OS O rH (M CO T H to co t>. 00 05 A 19| 19A m 19A 19f ISA 19| 19A 19f 19H 19f 19B 191 19M 20 20^ 201 20A 20i 20A 20f 20^ 18.688 18.750 18.813 18.875 18.938 474.7 476.3 477.8 479.4 481.0 482.6 484.2 485.8 487.4 489.0 490.5 492.1 493.7 495.3 496.9 498.5 500.1 501.7 503.2 404.8 506.4 508.0 509.6 511.2 512.8 514.4 515.9 517.5 519.1 21A 21f 21A 21f 21H 21f 21H 211 21M 22 22^ 22i 22^ 221 22A 22f 22^ 22* 22^ 22f 22^ 22f 22M 221 22H 23 23A 231 23A 23i 23A 23| 23A 23J 23& 23f 23H 23| 23H 231 23M 24 24^ 241 24^ 21.438 21.500 21.563 21.625 21.688 21.750 21.813 21.875 21.938 544.5 546.1 447.7 549.3 550.9 552.5 554.0 555.6 557.2 558.8 560.4 562.0 563.6 565.2 566.7 568.3 569.9 571.5 573.1 574.7 576.3 577.9 579.4 581.0 582.6 584.2 585.8 587.4 589.0 590.6 592.1 593.7 595.3 596.9 598.5 600.1 601.7 603.3 604.8 606.4 608.0 609.6 611.2 612.8 614.4 16.063 16.125 16.188 16.250 16.313 16.375 16.438 16.500 16.563 16.625 16.688 16.750 16.813 16.875 16.938 19.063 19.125 19.188 19.250 19.313 19.375 19.438 19.500 19.563 19.625 19.688 19.750 19.813 19.875 19.938 22.063 22.125 22.188 22.250 22.313 22.375 22.438 22.500 22.563 22.625 22.688 22.750 22.813 22.875 22.938 17.063 17.125 17.188 17.250 17.313 17.375 17.438 17.500 17.563 17.625 17.688 17.750 17.813 17.875 17.938 20.063 20.125 20.188 20.250 20.313 20.375 20.438 23.063 23 . 125 23.188 23.250 23.313 23.375 23.438 23.500 23.563 23.625 23.688 23.750 23.813 23.875 23.938 20 '20& 20f 20H 20| 20M 201 20i 21 21A aij 21A 21* 21A 21f 20.500 20.563 20.625 20.688 20.750 20.813 20.875 20.938 520.7 522.3 523.9 525.5 527.1 528.6 530.2 531.8 533.4 535.0 536.6 538.2 539.8 541.3 542.9 18.063 18.125 18.188 18.250 18.313 18.375 18.438 18.500 18.563 18.625 21.063 21.125 21.188 21.250 21.313 21.375 24.063 24.125 24.188 [57] INCHES AND FRACTIONS TO MILLIMETERS LENGTHS. INCHES AND FRACTIONS TO MILLIMETERS (Cord.) IN CHB3 Milli- IN CHES Milli- IN( :HES Milli- Fractions Decimals meters Fractions Decimals meters Fractions Decimals meters 241 24.250 616.0 27& 27.063 687.4 291 29.875 758.8 24& 24.313 617.5 27i 27.125 689.0 29H 29.938 760.4 241 24.375 619.1 27 A 27 . 188 690.6 30 762.0 w 8 24 24.438 620.7 Arf * 16 271 27.250 692.2 30^ 30.063 763.6 24* 24.500 622.3 27A 27.313 693.7 30| 30.125 765.2 24& 24.563 623.9 27| 27.375 695.3 30^ ,30.188 766.8 24f 24.625 625.5 27& 27.438 696.9 301 30.250 768.4 24H 24.688 627.1 27* 27.500 698.5 30& 30.313 769.9 24f 24.750 628.7 27& 27.563 700.1 30| 30.375 771.5 24H 24.813 630.2 27f 27.625 701.7 30^ 30.438 773.1 341 24.875 631.8 27H 27.678 703.3 30* 30.500 774.7 24H 24.938 633.4 27| 27.750 704.9 30& 30.563 776.3 25 635.0 27 U 27.813 706.4 301 30.625 777.9 25^ 25.063 636.6 ** 1 $ 271 27.875 708.0 w 8 30H 30.688 779.5 25| 25.125 638.2 27H 27.938 709.6 30| 30.750 781.1 25A 25.188 639.8 28 711.2 30H 30.813 782.6 251 25.250 641.4 28^ 28.063 712.8 301 30.875 784.2 25& 25.313 642.9 28| 28.125 714.4 30H 30.938 785.8 251 25.375 644.5 28A 28.188 716.0 31 787.4 ,*rf_r 5 25& 25.438 646.1 *j<*j 16 281 28.250 717.6 31A 31.063 789.0 25* 25.500 647.7 28& 28.313 719.1 3U 31.125 790.6 25& 25.563 649.3 28f 28.375 720.7 31& 31.188 792.2 25f 25.625 650.9 28& 28.438 722.3 311 31.250 793.8 25H 25.688 652.5 28* 28.500 723.9 31A 31.313 795.3 25| 25.750 654.1 28& 28.563 725.5 31f 31.375 796.9 25H 25.813 655.5 28f 28.625 727.1 31& 31.438 798.5 25f 25.875 657.2 28H 28.688 728.7 31* 31.500 800.1 25H 25.938 658.8 28| 28.750 730.3 31A 31.563 801.7 26 660.4 28M 28.813 731.8 31f 31.625 803.3 26& 26.063 662.0 281 28.875 733.4 31H 31.688 804.9 26| 26.125 663.6 28H 28.938 735.0 31f 31.750 806.5 26A 26.188 665.2 29 736.6 31H 31.813 808.0 A^VF 1$ 261 26.250 666.8 29& 29.063 738.2 *^ 1 6 311 31.875 809.6 26& 26.313 668.3 29i 29.125 739.8 31H 31.938 811.2 261 26 . 375 669.9 29 A- 29.188 741.4 32 812.8 Mpg 26& 26.438 671.5 ^^ 16 291 29.250 743.0 32^ 32.063 814.4 26* 26.500 673.1 29& 29.313 744.5 32* 32.125 816.0 26& 26.563 674.7 29f 29.375 746.1 32^ 32.188 817.6 26f 26.625 676.3 29& 29.438 747.7 321 32.250 819.2 26H 26.688 677.9 29* 29.500 749.3 32^ 32.313 820.7 26f 26.750 679.5 29& 29.563 750.9 32| 32.375 822.3 26H 26.813 681.0 29f 29.625 752.5 32^ 32.438 823.9 261 26.875 682.6 29H 29.688 754.1 32* 32.500 825.5 26M 26.938 684.2 29f 29.750 755.7 32& 32.563 827.1 27 685.8 29 H 29.813 757.2 32f 32.625 828.7 1 6 [58] INCHES AND FRACTIONS TO MILLIMETERS LENGTHS. INCHES AND FRACTIONS TO MILLIMETERS (Con/.) INCHES Milli- meters INCHES Milli- meters INCHES Milli- meters Fractions Decimals Fractions Decimals Fractions Decimals 32H 32.688 830.3 35^ 35.188 893.8 37H 37.688 957.3 32f 32.750 831.9 351 35.250 895.4 37f 37.750 958.9 32H 32.813 833.4 35& 35.313 896.9 37M 37.813 960.4 32| 32.875 835.0 35| 35.375 898.5 871 37.875 962.0 32f| 32.938 836.6 35& 35.438 900.1 8TH 37.938 963.6 33 838.2 354 35.500 901.7 38 965.2 33^ 33.063 839.8 *-"-*2 35& 35.563 903.3 38^ 38.063 966.8 33i 33.125 841.4 35f 35.625 904.9 38i 38.125 968.4 33& 33.188 843.0 35H 35.688 906.5 38A 38.188 790.0 331 33.250 844.5 35| 35.750 908.1 381 38.250 971.6 33& 33.313 846.1 35ff 35.813 909.6 38 A 38.313 973.1 33| 33.375 847.7 35| 35.875 911.2 38| 38.375 974.7 33^ 33.438 849.3 35U 35.938 912.8 38& 38.438 976.3 331 33.500 850.9 36 914.4 384 38.500 977.9 uu 2 33& 33.563 852.5 36^ 36.063 916.0 VF-*2 38& 38.563 979.5 33| 33.625 854.1 36i 36.125 917.6 38f 38.625 981.1 33H 33.688 855.7 36^ 36.188 919.2 38H 38.688 982.7 33| 33.750 857.3 361 36.250 920.8 38f 38.750 984.3 33H 33.813 858.8 36& 36.313 922.3 38H 38.813 985.8 33| 33.875 860.4 36| 36.375 923.9 38f 38.875 987.4 33H 33.938 862.0 36^ 36.438 925.5 38H 38.938 989.0 34 863.6 364 36 . 500 927.1 39 990.6 34^ 34.063 865.2 <-*v/2 36& 36.563 928.7 39^ 39.063 992.2 34i 34.125 866.8 36f 36.625 930.3 39i 39.125 993.8 34& 34.188 868.4 36H 36.688 931.9 39& 39.188 995.4 341 34.250 870.0 36| 36.750 933.5 391 39.250 997.0 34^ 34.313 871.5 36H 36.813 935.0 39& 39.313 998.5 34f 34.375 873.1 36| 36.875 936.6 39| 39.375 1000.1 34& 34.438 874.7 36M 36.938 938.2 39& 39.438 1001.7 344 34.500 876.3 37 939.8 39| 39.500 1003.3 v-r --2 34& 34.563 877.9 37& 37.063 941.4 39A 39.563 1004.9 34| 34.625 879.5 37| 37.125 943.0 39f 39.625 1006.5 34H 34.688 881.1 37^ 37.188 944.6 39H 39.688 1008.1 34| 34.750 882.7 371 37.250 946.2 39f 39.750 1009.7 34ff 34.813 884.2 37^ 37.313 947.7 39H 39.813 1011.2 34| 34.875 885.8 37| 37.375 949.3 39| 39.875 1012.8 34H 34.938 887.4 37ft 37.438 950.9 39H 39.938 1014.4 35 889.0 374 37.500 952.5 40 1016.0 35^ 35:063 890.6 *** * 37^ 37.563 954.1 35i 35.125 892.2 37f 37.625 955.7 [59] MILLIMETERS TO INCHES LENGTHS. MILLIMETERS TO INCHES. FROM 1 TO 1,000 UNITS Reduction factor: 1 millimeter = 0.03937 inch Mflli- Milli- Milli- Milli- Milli- Milli- meters Ins. meters Ins. meters Ins. meters Ins. meters Ins. meters Ins. Milli- Milli- meters Ins. meters Ins. 5 1.77 90 = 3.54 5 5.32 180 = 7.09 5 8.86 ! 270 =10.63 5 12.40 1 = .039 6 1.81 1 3.58 6 5.35 1 7.13 6 8.90 1 10.67 6 12.44 2 .079 7 1.85 2 3.62 7 5.39 2 7.17 7 8.94 2 10.71 7 12.48 3 .118 8 1.89 3 3.66 8 5.43 3 7.20 8 8.98 3 10.75 8 12.52 4 .157 9 1.93 4 3.70 9 5.47 4 7.24 9 9.02 4 10.79! 9 12.56 5 .197 50 = 1.97 5 3.74 140 = 5.51 5 7.28 230 = 9.06 5 10.83^20 =12.60 6 .236 1 2.01 6 3.78 1 5.55 6 7.32 1 9.09 6 10.87! 1 12.64 7 .276 2 2.05 7 3.82 2 5.59 7 7.36 2 9.13 7 10.91! 2 12.68 8 .315 3 2.09 8 3.86 3 5.63 8 7.40 3 9.17 8 10.94 3 12.72 9 .354 4 2.13 9 3.90 4 5.67 9 7.44 4 9.21 9 10.98 4 12.76 10 = .394 5 '2.17 100 = 3.94 5 5.71 190 = 7.48 5 9.25J280 =11.02 ! 5 12.80 1 .433 6 2.20 1 3.98 6 5.75 1 7.52 6 9.29 1 11.06; 6 12.83 2 .472 7 2.24 2 4.02 7 5.79 2 7.56 7 9.33 2 11.10; 7 12.87 3 .512 8 2.28 3 4.06 8 5.83 3 7.60 8 9.37 3 11.14| 8 12.91 4 .551 9 2.32 4 4.09 9 5.87 4 7.64 9 9.41 4 11.18 9 12.95 5 .591 60 = 2.36 5 4.13 150 = 5.91 5 7.68 240 = 9.45 5 11.22 330 =12.99 6 .630 1 2.40 6 4.17 1 5.95 6 7.72 1 9.49 6 11.26 1 13.03 7 .669 2 2.44 7 4.21 2 5.98 7 7.76 2 9.53 7 11.30 2 13.07 8 .709 3 2.48 8 4.25 3 6.02 8 7.80 3 9.57 8 11.34 3 13.11 9 .748 4 2.52 9 4.29 4 6.06 9 7.83 4 9.61 9 11.38 4 13.15 20 = .79 5 2.56 110 = 4.33 5 6.10 200 = 7.87 5 9.65 290 =11.42 5 13.19 1 .83 6 2.60 1 4.37 6 6.14 1 7.91: 6 9.69 1 11.46 6 13.23 2 .87 7 2.64 2 4.41 7 6.18 2 7.95 7 9.72 2 11.50 7 13.27 3 .91 8 2.68 3 4.45 8 6.22 3 7.99 8 9.76 3 11.54 8 13.31 4 .94 9 2.72 4 4.49 9 6.26 4 8.03 9 9.80 4 11.57 9 13.35 5 .98 70 = 2.76 5 4.53 160 = 6.30 5 8.07 250 = 9.84 5 11.61 340 =13.39 6 .02 1 2.80 6 4.57 1 6.34 6 8.11 1 9.88 6 11.65 1 13.43 7 .06 2 2.83 7 4.61 2 6.38 7 8.15 2 9.92 7 11.69 2 13.46 8 .10 3 2.87 8 4.65 3 6.42 8 8.19 3 9.96 8 11.73 3 13.50 9 .14 4 2.91 9 4.69 4 6.46 9 8.23 4 10.00 9 11.77 4 13.54 30 = .18 5 2.95 120 = 4.72 5 6.50 210 = 8.27 5 13.04300 =11.81 5 13.58 1 .22 6 2.99 1 4.76 6 6.54 1 8.31 6 10.08 1 11.85 6 13.62 2 .26 7 3.03 2 4.80 7 6.57 2 8.3 7 10.12 2 11.89 7 13.66 3 .30 8 3.07 3 4.84 8 6.61 3 8.39 8 10.16 3 11.93! 8 13.70 4 .34 9 3.11 4 4.88 9 6.65 4 8.43 9 10.20 4 11.97 9 13.74 5 1.38 80 = 3.15 5 4.92 170 = 6.69 5 8.46260 =10.24 5 12.01350 =13.78 6 1.42 1 3.19 6 4.96 1 6.73 6 8.50: 1 10.28 6 12.05 1 13.82 7 1.46 2 3.23! 7 5.00 2 6.77 7 8.54 2 10.31 7 12.09 2 13.86 8 1.50 3 3.27 8 5.04 3 6.81 8 8.58 3 10.35 8 12.13 3 13.90 9 1.54 4 3.31 9 5.08 4 6.85 9 8.62 4 10.39 9 12.17 4 13.94 40 = 1.57 5 3.35 139 = 5.12 5 6.89 220 = 8.66 5 10.43310 =12.20 5 13.98 1 1.61 6 3.39 1 5.16 6 6.93 1 8.70 6 10.47 1 12.24 6 14.02 2 1.65 7 3.43 2 5.20 7 697 2 8.74 7 10.51 2 12.28 7 14.06 3 1.69 8 3.46 3 5.24 8 7.01 3 8.78 8 10.55 3 12.32 8 14.09 4 1.73 9 3.50 4 5.28 9 7.05 4 8.82 9 10.59 4 12.36 9 14.13 [60] MILLIMETERS TO INCHES LENGTHS. MILLIMETERS TO INCHES (Cont.) Milli- meters Ins. Milli- meters Ins. Milli- meters Ins. Milli- meters Ins. Milli- meters Ins. Milli- meters Ins. Milli- Milli- meters Ins. meters Ins. 360 =14.17 5 15.94 450 =17.72 5 19.49 540 =21.26 5 23.03 630 =24.80 5 26.57 1 14.21 6 15.98 1 17.76 6 19.53 1 21.30 6 23.07 1 24.84 6 26.61 2 14.25 7 16.02 2 17.80 7 19.57 2 21.34 7 23.11 2 24.88 7 26.65 3 14.29 8 16.06 3 17.83 8 19.61 3 21.38 8 23.15 3 24.92 8 26.69 4 14.33 9 16.10 4 17.87 9 19.65 4 21.42 9 23.19 4 24.96 9 26.73 5 14.37 410 =16.14 5 17.91 500 =19.69 5 21.46 590 =23.23 5 25.00 680 =26.77 6 14.41 1 16.18 6 17.95 1 19.72 6 21.50 1 23.27 6 25.04 1 26.81 7 14.45 2 16.22 7 17.99 2 19.76 7 21.54 2 23.31 7 25.08 2 26.85 8 14.49 3 16.26 8 18.03 3 . 19.80 8 21.57 3 23.35 8 25.12 3 26.89 9 14.53 4 16.30 9 18.07 4 19.84 9 21.61 4 23.39 9 25.16 4 26.93 370 =14.57 5 16.34 460 =18.11 5 19.88 550 =21.65 5 23.43 640 =25.20 5 26.97 1 14.61 6 16.38 1 18.15 6 19.92 1 21.69 6 23.46 1 25.24 6 27.01 2 14.65 7 16.42 2 18.19 7 19.96 2 21.73 7 23.50 2 25.28 7 27.05 3 14.69 8 16.46 3 18.23 8 20.00 3 21.77 8 23.54 3 25.31 8 27.09 4 14.72 9 16.50 4 18.27 9 20.04 4 21.81 9 23.58 4 25.35 9 27.13 5 14.76 420 =16.54 5 18.31 510 =20.08 5 21.85 600 =23.62 5 25.39 690 =27.17 6 14.80 1 16.57 6 18.35 1 20.12 6 21.89 1 23.66 6 25.43 1 27.20 7 14.84 2 16.61 7 18.39 2 20.16 7 21.93 2 23.70 7 25.47 2 27.24 8 14.88 3 16.65 8 18.43 3 20.20 8 21.97 3 23.74 8 25.51 3 27.28 9 14.92 4 16.69 9 18.46 4 20.24 9 22.01 4 23.78 9 25.55 4 27.32 380 =14.96 5 16.73 470 =18.50 5 20.28 560 =22.05 5 23.82 650 =25.59 5 27.36 1 15.00 6 16.77 1 18.54 6 20.31 1 22.09 6 23.86 1 25.63 6 27.40 2 15.04 7 16.81 2 18.58 7 20.35 2 22.13 7 23.90 2 25.67 7 27.44 3 15.08 8 16.85 3 18.62 8 20.39 3 22.17 8 23.94 3 25.71 8 27.48 4 15.12 9 16.89 4 18.66 9 20.43 4 22.20 9 23.98 4 25.75 9 27.52 5 15.16 430 =16.93 5 18.70 520 =20.47 5 22.24 610 =24.02 5 25.79 700 =27.56 6 15.20 1 16.97 6 18.74 1 20.51 6 22.28 1 24.06 6 25.83 1 27.60 7 15.24 2 17.01 7 18.78 2 20.55 7 22.32 2 24.09 7 25.87 2 27.64 8 15.28 3 17.05 8 18.82 3 20.59 8 22.36 3 24.13 8 25.91 3 27.68 9 15.31 4 17.09 9 18.86 4 20.63 9 22.40 4 24.17 9 25.94 4 27.72 390 =15.35 5 17.13 480 =18.90 5 20.67 570 =22.44 5 24.21 660 =25.98 5 27.76 1 15.39 6 17.17 1 18.94 6 20.71 1 22.48 6 24.25 1 26.02 6 27.80 2 15.43 7 17.20 2 18.98 7 20.75 2 22.52 7 24.29 2 26.06 7 27.83 3 15.47 8 17.24 3 19.02 8 20.79 3 22.56 8 24.33 3 26.10 8 27.87 4 15.51 9 17.28 4 19.06 9 20.83 4 22.60 9 24.37 4 26.14 9 27.91 5 15.55 440 =17.32 5 19.09 530 =20.87 5 22.64 620 =24.41 5 26.18 710 =27.95 6 15.59 1 17.36 6 19.13 1 20.91 6 22.68 1 24.45 6 26.22 1 27.99 7 15.63 2 17.40 7 19.17 2 20.94 7 22.72 2 24.49 7 26.26 2 28.03 8 15.67 3 17.44 8 19.21 3 20.98 8 22.76 S 3 24.53 8 26.30 3 28.07 9 15.71 4 17.48 9 19.25 4 21.02 9 22.80 4 24.57 9 26.34 4 28.11 400 =15.75 5 17.52 490 =19.29 5 21.06 580 =22.83 5 24.61 670 =26.38 5 28.15 1 15.79 6 17.56 1 19.33 6 21.10 1 22.87 6 24.65 1 26.42 6 28.19 2 15.83 7 17.60 2 19.37 7 21.14 2 22.91 7 24.68 2 26.46 7 28.23 3 15.87 8 17.64 3 19.41 8 21.18 3 22.95 8 24.72 3 26.50 8 28.27 4 15.91 9 17.68 4 19.45 9 21.22 4 22.99 9 24.76 4 26.54 9 28.31 [611 MILLIMETERS TO INCHES LENGTHS. MILLIMETERS TO INCHES (Cont.) Milli- meters Ins. Milli- meters Ins. Milli- meters Ins. Milli- meters Ins. Milli- meters Ins. Milli- meters Ins. Milli- meters Ins. Milli- meters Ins. 720 =28.35 5 29.72 790 =31.10 5 32.48 860 =33.86 5 35.24 930 =36.61 5 37.99 1 28.39 6 29.76 1 31.14 6 32.52 1 33.90 6 35.28 1 36.65 6 38.03 2 28.43 7 29.80 2 31.18 7 32.56 2 33.94 7 35.31 2 36.69 7 38.07 3 28.46 8 29.84 3 31.22 8 32.60 3 33.98 8 35.35 3 36.73 8 38.11 4 28.50 9 29.88 4 31.26 9 32.64 4 34.02 9 35.39 4 36.77 9 38.15 5 28.54 760 =29.92 5 31.30 830 =32.68 5 34.06 900 =35.43 5 36.81 970=38.19 6 28.58 1 29.96 6 31.34 1 32.72 6 34.09 1 35.47 6 36.85 1 38.23 7 28.62 2 30.00 7 31.38 2 32.76 7 34.13 2 35.51 7 36.89 2 38.27 8 28.66 3 30.04 8 31.42 3 32.80 8 34.17 3 35.55 8 36.93 3 38.31 9 28.70 4 30.08 9 31.46 4 32.83 9 34.21 4 35.59 9 36.97 4 38.35 730 =28.74 5 30.12 800 =31.50 5 32.87 870 =34.25 5 35.63 940 =37.01 5 38.39 1 28.78 6 30.16 1 31.54 6 32.91 1 34.29 6 35.67 1 37.05 6 38.43 2 28.82 7 30.20 2 31.57 7 32.95 2 34.33 7 35.71 2 37.09 . 7 38.46 3 28.86 8 30.24 3 31.61 8 32.99 3 34.37 8 35.75 3 37.13 8 38.50 4 28.90 9 30.28 4 31.65 9 33.03 4 34.41 9 35.79 4 37.17 9 38.54 5 28.94 770 =30.31 5 31.69 840 =33.07 5 34.45 910 =35.83 5 37.20 980=38.58 6 28.98 1 30.35 6 31.73 1 33.11 6 34.49 1 35.87 6 37.24 1 38.62 7 29.02 2 30.39 7 31.77 2 33.15 7 34.53 2 35.91 7 37.28 2 38.66 8 29.06 3 30.43 8 31.81 3 33.19 8 34.57 3 35.94 8 37.32 3 38.70 9 29.09 4 30.47 9 31.85 4 33.23 9 34.61 4 35.98 9 37.36 4 38.74 740 =29.13 5 30.51 810 =31.89 5 33.27 880 =34.65 5 36.02 950 =37.40 5 38.78 1 29.17 6 30.55 1 31.93 6 33.31 1 34.68 6 36.06 1 37.44 6 38.82 2 29.21 -7 30.59 2 31.97 7 33.25 2 34.72 7 36.10 2 37.48 7 38.86 3 29.25 8 30.63 3 32.01 8 33.39 3 34.76 8 36.14 3 37.52 8 38.90 4 29.29 9 30.67 4 32.05 9 33.43 4 34.80 9 36.18 4 37.56 9 38.94 5 29.33 780 =30.71 5 32.09 850 =33.46 5 34.84 920 =36.22 5 37.60 990=38.98 6 29.37 1 39.75 6 32.13 1 33.50 6 34.88 1 36.26 6 37.64 1 39.02 7 29'. 41 2 30.79 7 32.17 2 33.54 7 34.92 2 36.30 7 37.68 2 39.06 8 29.45 3 30.83 8 32.20 3 33.58 8 34.96 3 36.34 8 37.72 3 39.09 9 29.49 4 30.87 9 32.24 4 33.62 9 35.00 4 36.38 9 37.76 4 39.13 750 =29.53 5 30.91 820 =32.28 5 33.66 890 =35.04 5 36.42 960 =37.80 5 39.17 1 29.57 6 30.94 1 32.32 6 33.70 1 35.08 6 36.46 1 37.83 6 39.21 2 29.61 7 30.98 2 32.36 7 33.74 2 35.12 7 36.50 2 37.87 7 39.25 3 29.65 8 31.02 3 32.40 8 33.78 3 35.16 8 36.54 3 37.91 8 39.29 4 29.68 9 31.06 4 32.44 9 33.82 4 35.20 9 36.57 7.95 9 39.33 1000 39.37 1000 millimeters = 1 meter =39.37 inches = 3.28 feet = 1.09 yards. [62] CUSTOMARY TO METRIC UNITS COMPARISON OF CUSTOMARY AND METFJC UNITS FROM 1 TO 10 Reduction factors: 1 meter = 39.37 inches 1 inch = 25 . 4001 millimeters LENGTHS Inches Millimeters Ins. Centimeters Feet Meters U.S.Yds. Meters U.S. Miles. Kilom. 0.039 = 1 .079=2 .118 = 3 .157=4 .197 = 5 0.394= 1 .787= 2 1 = 2.540 1.181= 3 1.575= 4 1 =0.305 2 = .610 3 = .914 3.281 = 1 4 =1.219 1 =0.914 1.094 = 1 2 =1.829 2.187=2 3 =2.743 0.621= 1 1 = 1.609 1.243= 2 1.864= 3 2 = 3.219 .236 = 6 .276 = 7 .315=8 .354=9 1.969= 5 2 = 5.080 2.362= 6 2.756= 7 5 =1.524 6 =1.829 6.562 = 2 7 =2.134 3.281=3 4 =3.658 4.374=4 5 =4.572 2.485= 4 3 = 4.828 3.107= 5 3.728= 6 1= 25.400 2= 50.800 3= 76.200 4 = 101.600 5 = 127.000 3 = 7.620 3.150= 8 3.543= 9 4 =10.160 5 =12.700 8 =2.438 9 =2.743 9.843=3 13.123=4 16.404=5 5.468 = 5 6 =5.486 6.562 = 6 7 =6.401 7.655 = 7 4 = 6.437 4.350= 7 4.971= 8 5 = 8.047 5.592= 9 6 = 152.400 7 = 177.800 8=203.200 9=228.600 6 =15.240 7 =17.780 8 =20.320 9 =22.860 19.685=6 22.966 = 7 26.247=8 29.528 = 9 8 =7.315 8.749=8 9 =8.230 9.843=9 6 = 9.656 7 =11.265 8 =12.875 9 =14.484 COMPARISON OF CUSTOMARY AND METRIC UNITS FROM 1 TO 10 Reduction factors: 1 sq. meter = 1 . 196 sq. yard 1 sq. yard = 1 sq. meter = 10 . 764 sq. foot 1 sq. foot = 1 sq. centimeter = 0.155 sq. inch 1 sq. inch 0.836 sq. meter 0. 0929 sq. meter 6 . 452 sq. centimeter 1 sq. centimeter = 0.155 sq. inch 1 sq. inch = 6.452 sq. centimeter 1 sq. millimeter = 0.00155 sq. inch 1 sq. inch = 645.16 sq. millimeter AREAS Square Inches Square Millimeters Square Square Inches Centimeters Square Feet Square Meters Square Square Yards Meters Square Square Mil^s Kilometers 0.002 = 1 0.155= 1 1 =0.093 1 =0.836 0.386= 1 .003 = 2 .310= 2 2 = .186 1.196 = 1 .772= 2 .005 = 3 .465= 3 3 = .279 2 =1.672 1 = 2.59 .006 = 4 .620= 4 4 = .372 2.392=2 1.158= 3 .008 = 5 .775= 5 5 = .465 3 =2.508 1.544= 4 .009 = 6 .930= 6 6 = .557 3.588 = 3 1.931= 5 .011 = 7 1 = 6.452 7 = .650 4 =3.345 2 = 5.18 .012 = '8 1.085= 7 8 = .743 4.784=4 2.317= 6 .014 = 9 1.240= 8 9 = .836 5 =4.181 2.703= 7 [63] CUSTOMARY TO METRIC UNITS COMPARISON OF CUSTOMARY AND METRIC UNITS FROM 1 TO AREAS (Cont.) Square Square Inches Millimeters Square Square Inches Centimeters Square Square Feet Meters Square Square Yards Meters Square Square Miles Kilometers 1 = 645.16 2 = 1290.33 3 = 1935.49 4 = 2580.65 5 = 3225.81 1.395 = 9 2 = 12.903 3 = 19.355 4 = 25.807 5 = 32.258 10.764 = 1 21.528 = 2 32.292 = 3 43.055 = 4 53.819 = 5 5.980 = 5 6 =5.017 7 =5.853 7.176 = 6 8 =6.689 3 = 7.77 3.089= 8 3.475= 9 4 =10.36 5 =12.95 6 = 3870.98 7 = 4516.14 8 = 5161.30 9 = 5806.46 6 = 38.710 7 = 45.161 8 = 51.613 9 = 58.065 64.583 = 6 75.347 = 7 86.111 = 8 96.875 = 9 8.372 = 7 9 =7.525 9.568=8 10.764 = 9 6 =15.54 7 =18.13 8 =20.72 9 =23.31 COMPARISON OF CUSTOMARY AND METRIC UNITS FROM 1 TO 10 Reduction factors: 1 cu. meter = 1.308 1 cu. meter = 35.314 1 cu. centimeter = 0.061 cu. yd cu. ft. cu. HI. 1 cu. millimeter = 0.000061 cu. in. 1 cu. yd. = 0. 765 cu. meter 1 cu. ft. = 0. 028 cu. meter 1 cu. in. = 16.387 cu. centimeters 1 cu. in. = 16.387 cu. millimeters VOLUMES Cubic Cubic Inches Millimeters Cubic Cubic Inches Centimeters Cubic Cubic Feet Meters Cubic Cubic Yards Meters Acres Hectares .000061=1 0.061 = 1 1=0.028 1 =0.765 1 =0.405 .000122 = 2 .122 = 2 2= .057 1.308 = 1 2 = .809 .000183=3 .183=3 3= .085 2 =1.529 2.471 = 1 .000244=4 .244 = 4 4= .113 2.616=2 3 =1.214 .000305 = 5 .305=5 5= .142 3 =2.294 4 =1.619 .000366 = 6 .366 = 6 6= .170 3.924=3 4.942 = 2 .000427 = 7 .427=7 7= .198 4 =3.058 5 =2.023 .000488=8 .488=8 8= .227 5 =3.823 6 =2.428 .000549=9 .549 = 9 9= .255 5. 232 ='4 7 =2.833 1= 16387 . 1= 16.387 35.314 = 1 6 =4.587 7.413=3 2= 32774 2= 32.774 70.629 = 2 6.540 =5 8 =3.238 3= 49162 3= 49.162 105.943=3 7 =5.352 9 =3.642 4= 65549 4= 65.549 141.258=4 7.848 =6 9.884 = 4 5= 81936 5= 81.936 176.572=5 8 =6.117 12.355=5 6= 98323 6= 98.323 211.887=6 9 =6.881 14.826=6 7 = 114710 7 = 114.710 247.201=7 9.156 =7 17.297 = 7 8 = 131097 8 = 131.097 282.516=8 110.464 =8 19.768 = 8 9 = 147485 9 = 147.485 317.830 = 9 11.772 =9 22.239 = 9 AREAS Continued [64] CUSTOMARY TO METRIC UNITS COMPARISON OF CUSTOMARY AND METRIC UNITS FROM 1 TO 10 Reduction factors are as given in first line of each measure CAPACITIES U. S. Milli- Liquid liters Ounces (cc.) U. S. Milli- Apoth liters Drams (cc.) U. S. Milli- Apoth, liters Scruples (cc.) U.S. Liquid Liters Quarts U.S. Liquid Gallons Liters 0.03381=1 0.2705= 1 0.8115= 1 1 =0.94636 0.26417 = 1 .068 = 2 .541 = 2 1 = 1.2322 1.057 = 1 .528 = 2 .101 =3 .812 = 3 1.623 = 2 2 =1.893 .793 = 3 .135 = 4. 1 = 3.6967 2 = 2.465 2.113=2 1 = 3.78543 .169 =5 1.082 = 4 2.435 = 3 3 =2.839 1.057, = 4 .203 =6 1.353 = 5 3 = 3.697 3.170 = 3 1.321 = 5 .237 = 7 1.623 = 6 3.246 = 4 4 =3.785 1.585 = 6 .271 =8 1.894 = 7 4 = 4.929 4.227=4 1.849 rj .304 =9 2 = 7.393 4.058 = 5 5 =4.732 2 = 7.571 1= 29.574 2.164 = 8 4.869 = 6 5.283=5 2.113 o 2= 59.147 2.435 = 9 5 = 6.161 6 =5.678 2.378 = 9 3= 88.721 3 =11.090 5.681 = 7 6.340 = 6 3 = 11.356 4 = 118.295 4 =14.787 6 = 7.393 7 =6.625 4 = 15.142 5 = 147.869 5 =18.484 6.492 = 8 7.397=7 5 = 18.927 6 = 177.442 6 =22.180 7 = 8.626 8 =7.571 6 =22.713 7=207.016 7 =25.877 7.304 = 9 8.453=8 7 = 26.498 8 = 236.590 8 =29.574 8 = 9.858 9 =8.517 8 = 30.283 9 = 266.163 9 =33.270 9 =11.090 9.510=9 9 = 34.069 COMPARISON OF CUSTOMARY AND METRIC UNITS FROM 1 TO 10 CAPACITIES (Cont.) U.S. Dry Liters Quarts "- U. S. Deka- Pecks liters U. S. Hecto- Bushels liters U. S. Hectoliters Bushels per per Acre Hectare 0.9081=1 0.11351= 1 1 =0.8810 1 =0.35239 1 =0.87078 1 =1.1012 .227 = 2 1.1351 = 1 2 = .705 1.14840 = 1 1.816 =2 .341 = 3 2 =1.762 2.838 = 1 2 =1.742 2 =2.203 .454 = 4 2.270 =2 3 =1.057 2.967 =2 2.724 =3 .568 = 5 3 =2.643 4 =1.410 3 =2.612 3 =3.304 .681 = 6 3.405 =3 5 =1.762 3.445 =3 3.632 =4 .795 = 7 4 =3.524 5.675=2 4 =3.483 4 =4.405 .908 = 8 4.540 =4 6 =2.114 4.594 =4 4.540 =5 1 = 8.810 5 =4.405 7 =2.467 5 =4.354 5 =5.506 1.022 = 9 5.676 =5 8 =2.819 5.742 =5 5.449 =6 2 =17.620 6 =5.286 8.513=3 6 =5.225 6 =6.607 3 =26.429 6.811 =6 9 =3.172 6.890 =6 6.357 =7 4 =35.239 7 =6.167 11.351=4 7 =6.095 7 =7.709 5 =44.049 7.946 =7 14.189=5 8 =6.966 7.265 =8 6 =52.859 8 =7.048 17.026=6 8.039 =7 8 =8.810 7 =61.669 9 =7.929 19.864 = 7 9 =7.837 8.173 =9 8 =70.479 9.081 =8 22.702=8 9.187 =8 9 =9.911 9 79.288 10.216 =9 25.540 = 9 10.336 =9 [65] CUSTOMARY TO METRIC UNITS COMPARISON OF CUSTOMARY AND METRIC UNITS FROM 1 TO 10 Reduction factors are as given in first line of each measure MASSES Grains Grains Avoir- dupois Grams Ounces Su^ces Grams Avoir- dupois Pounds Kilograms Troy Pounds Kilograms 1=0.06480 0.03527 = 1 0.03215 = 1 1 =0.45359 1 =0.37324 2 = .130 .071 =2 .064 =2 2 = .907 2 = .746 3= .194 .106 =3 .096 =3 2.20462 = 1 2.67923 = 1 4= .259 .141 =4 .129 =4 3 = 1.361 3 = 1.120 5= .324 .176 =5 .161 =5 4 = 1.814 4 = 1.493 6= .389 .212 =6 .193 =6 4.409 =2 5 = 1.866 7 = .454 .247 =7 .225 =7 5 =2.268 5.358 = 2 8= .518 .282 =8 .257 =8 6 =2.722 6 =2.239 9= .583 .317 =9 .289 =9 6.614 =3 7 =2.613 15.4324 = 1 1= 28.3495 1= 31.10348 7 =3.175 8 =2.986 30.865 =2 2= 56.699 2= 62.207 8 =3.629 8.038 = 3 46.297 =3 3= 85.049 3= 93.310 8.818 =4 9 =3.359 61.729 =4 4 = 113.398 4 = 124.414 9 =4.082 10.717 =4 77.162 =5 5 = 141.748 5 = 155.517 11.023 = 5 13.396 = 5 92.594 =6 6 = 170.098 6 = 186.621 13.228 = 6 16.075 =6 108.027 =7 7 = 198.447 7 = 217.724 15.432 = 7 18.755 =7 123.459 =8 8=226.796 8=248.828 17.637 =8 21.434 =8 138.891 =9 9 = 255.146 9=279.931 19.842 = 9 24.113 =9 [66] CUSTOMARY TO METRIC UNITS COMPARISON OF THE VARIOUS TONS AND POUNDS IN USE IN THE UNITED STATES. FROM i TO 10 UNITS. LONO TONS. SHORT TONS. METRIC TONS. KILOGRAMS. AVOIRDUPOIS POUNDS. TROT POUNDS. .00036735 .00041143 .00037324 .37324 .822857 1 .00044643 .00050000 .00045359 .45369 1 1.21528 .00073469 .00082286 .00074648 .74648 1.64571 2 .00089286 .00100000 .00090718 .90718 2 2.43066 .00098421 .00110231 .00100000 1 2.20462 2.67923 .00110204 .00123429 .00111973 .11973 2.46857 3 .00133929 .00150000 .00136078 .36078 3 3.64683 .00146939 .00164571 .00149297 .49297 3. 29143 4 .00178571 .00200000 .00181437 .81437 4 4.86111 .00183673 .00205714 .00186621 .86621 4. 11429 5 .00196841 .00220462 .00200000 2 4.40924 6.35846 .00220408 .00246857 .00223945 2.23945 4.93714 6 .00223214 .00250000 .00226796 2.26796 5 b. 07639 .00257143 .00288000 .00261269 2.61269 6.76000 7 .00267857 .00300000 .00272165 2.72155 6 7.29167 .00293878 .00329143 .00298593 2.98593 6.58286 8 .00295262 .00330693 .00300000 3 6.61387 8.03769 .00312500 .00350000 .00317515 3. 17515 7 8.50694 .00330612 .00370286 .00335918 3.35918 7.40571 9 .00357143 .00400000 .00362874 3. 62874 8 9.72222 .00393683 .00440924 .00400000 4 8.81849 10.71691 .00401786 .00450000 .00408233 4.08233 9 10.93750 .00492103 .00551156 .00500000 5 11.0231 13.39614 .00590524 .00661387 .00600000 6 13.2277 16.0763T .00688944 .00771618 .00780000 7 15.4324 18.75460 .00787365 .00881849 .00800000 8 17.6370 21.43383 .00885786 .00992080 .0090000 9 19.8416 24. 11306 .89287 1 .90718 907.18 2,000.00 2,430.66 .98421 1:10231 1 1,000.00 2,204.62 2,679.23 1 1.12000 1.01605 1,016.05 2,240.00 2,722.22 1.78571 2 1.81437 1,814.37 4,000.00 4,861.11 1.96841 2.20462 2 2,000.00 4,409.24 6,358.46 2 2.24000 2.03209 2,032.09 4,480.00 6,444.44 2.67857 3 2.72155 2,721.55 JB.000.00 7,291.67 2.95262 3.30693 3 3,000.00 '6,613.87 8,037.69 3 3.36000 3.04814 3,048.14 6,720.00 8,166.67 3.57143 4 3. 62874 3,628.74 8,000.00 9,722.22 3.93683 4.40924 4 4,000.00 8,818.49 10,716.91 4 4.48000 4.06419 4,064.19 8,960.00 10,888.89 4.46429 5 4.53592 4,536.92 10,000.00 12,152.78 4.92103 6.51156 5 6,000.00 11,023.11 13, 3%. 14 5 6.60000 5.08024 6,080.24 11,200.00 13,611.11 6.35714 6 6.44311 6,443.11 12,000.00 14,683.33 6.90524 6.61387 6 6,000.00 13,227.73 16,075.37 6 6.72000 6.09628 6,096.28 13,440.00 16,333.33 6.25000 1 6.35029 6,350.29 14,000.00 17,013.89 6.88944 7.71618 7 7,000.00 15,432.36 18,764.60 7.14286 7.84000 8 7.11232 7.25748 7,112.32 7,257.48 15,680.00 16,000.00 19,065.66 19,444.44 7.87365 8.81849 8 8,000.00 17,636.98 21,433.83 8 8.96000 8. 12838 8,128.38 17,920.00 21,777.78 8.03571 9 8. 16466 8,164.66 18,000.00 21,876.00 8.85786 9.92080 9 9,000.00 19,841.60 24,113.06 9 10.08000 9. 14442 9,144.42 20,160.00 24,600.00 ISSUED BY THE BUREAU OF STANDARDS [67] ADMIRALTY KNOTS TO STATUTE MILES AND KILOMETERS LENGTHS. ADMIRALTY KNOTS TO STATUTE MILES AND KILOMETERS Conversion factors: 1 Admiralty knot = 6080 feet 1 statute mile = 5280 feet 1 kilometer = 3280.833 feet statute mile = Admiralty knot X 1. 151515 kilometer = Admiralty knot X 1.8531877 Knots Hour Miles Kilo- meters SPEED Knots per Hour Miles Kilo- meters SPEED Feet per Minute Feet per Second Feet per Minute Feet per Second 1 1.152 1.853 101.3 1.69 9% 11.227 18.069 988. 16.47 IH 1.439 2.316 126.7 2.11 10 11.515 18.532 1013.3 16.89 VA 1.727 2.780 152.0 2.53 10% 11.803 18.995 1038.7 17.31 IX 2.015 3.243 177.3 2.96 10^ 12.091 19.458 1064. 17.73 2 2.303 3.706 202.7 3.38 10% 12.379 19.922 1089.3 18.16 2% 2.591 4.170 228. 3.80 11 12.667 20.385 1114.7 18.58 VA 2.879 4.633 253.3 4.22 11% 12.955 20.848 1140. 19.00 2% 3.167 5.096 278.7 4.64 ny 2 ;3.242 21.312 1165.3 19.42 3 3.455 5.560 304. 5.07 11% 13.530 21.775 1190.7 19.84 3% 3.742 6.023 329.3 5.49 12 13.818 22.238 1216. 20.27 &A 4.030 6.486 354.7 5.91 12% 14.106 22.702 1241.3 20.69 3% 4.318 6.949 380. 6.33 12^ 14.394 23.165 1266.7 21.11 4 4.606 7.413 405.3 6.76 12% 14.682 23.628 1292. 21.53 4% 4.894 7.876 430.7 7.18 13 14.970 24.091 1317.3 21.96 4H- 5.182 8.339 456. 7.60 13% 15.258 24.555 1342.7 22.38 4% 5.470 8.803 481.3 8.02 13H 15.545 25.018 1368. 22.80 5 5.758 9.266 506.7 8.44 13% 15.833 25.481 1393.3 23.22 5% 6.045 9.729 532. 8.87 14 16.121 25.945 1418.7 23.64 5 1 A 6.333 10.193 557.3 9.29 14% 16.409 26.408 1444. 24.07 5% 6.621 10.656 582.7 9.71 UM 16 697 26.871 1469.3 24.49 6 6.909 11.119 608. 10.13 14% 16.985 27.335 1494.7 24.91 6% 7.197 11.582 633.3 10.56 15 17.273 27.798 1520. 25.33 Q 1 A 7.485 12.046 658.7 10.98 15% 17.561 28.261 1545.3 25.76 6% 7.773 12.509 684. 11.40 15^ 17.848 28.724 1570.7 26.18 7 8.061 12.972 709.3 11.82 15% 18.136 29.18S 1596. 26.60 7% 8.348 13.436 734.7 12.24 16 18.424 29.651 1621.3 27.02 ? 1 A 8.636 13.899 760. 12.67 16% 18.712 30.114 1646.7 27.44 7%- 8.924 14.362 785.3 13.09 16M 19.000 30.578 1672. 27.87 8 9.212 14.826 810.7 13.51 16% 19.288 31.041 1697.3 28.29 8% 9.500 15.289 836. 13.93 17 19.576 31.504 1722.7 28.71 m 9.788 15^752 861.3 14.36 17% 19.864 31.967 1748. 29.13 8% 10.076 16.215 886.7 14.78 V 1 A 20.152 32.431 1773.3 29.56 9 10.364 16.679 912. 15.20 17% 20.439 32.894 1798.7 29.98 9% 10.652 17.142 937.3 15.62 18 20.727 33.357 1824. 30.40 9^ 10.939 17.605 962.7 16.04 18% 21.015 33.821 1849.3 30.82 [68] ADMIRALTY KNOTS TO STATUTE MILES AND KILOMETERS LENGTHS. ADMIRALTY KNOTS TO STATUTE MILES AND KILOMETERS (Cont.) Knots per Hour Miles Kilo- meters SPEED Knots Hour Miles Kilo- meters SPEED Feet per Minute Feet per Second Feet per Minute Feet per Second 18H 21.303 34.284 1874.7 31.24 29^ 33.970 54.669 2989.3 49.82 18% 21.591 34.747 1900. 31.67 29% 34.258 55.132 3014.7 50.24 19 21.879 35.211 1925.3 32.09 30 34.545 55.596 3040. 50.67 19% 22.167 35.674 1950.7 32.51 30M 34.833 56.059 3065.3 51.09 19H 22.455 36.137 1976. 32.93 30^ 35.121 56.522 3090.7 51.51 19% 22.742 36.600 2001.3 33.36 30^ 35.409 56.986 3116. 51.93 20 23.030 37.064 2026.7 33.78 31 35.697 57.449 3141.3 52.36 20M 23.318 37.527 2052. 34.20 31% 35.985 57.912 3166.7 52.78 20^ 23.606 37.990 2077.3 34.62 31H 36.273 58.375 3192. 53.20 20% 23.894 38.454 2102.7 35.04 31% 36.561 58.839 32_7.3 53.62 21 24.182 38.917 2128. 35.47 32 36.848 59.302 3242.7 54.04 21% 24.470 39.380 2153.3 35.89 32M 37.136 59.765 3268. 54.47 21^ 24.758 39.844 2178.7 36.31 32^ 37.424 60.229 3293.3 54.89 21% 25.045 40.307 2204. 36.73 32M 37.712 60.692 3318.7 55.31 22 25.333 40.770 2229.3 37.16 33 38.000 61 . 155 3344. 55.73 22M 25.621 41.233 2254.7 37.58 33M 38.288 61.618 3369.3 56.16 22^ 25.909 41.697 2280. 38.00 33^ 38.576 62.082 3394.7 56.58 22M 26.197 42.160 2305.3 38.42 33% 38.864 62.545 3420. 57.00 23 26.485 42.623 2330.7 38.84 34 39.152 63.008 3445.3 57.42 23M 26.773 43.087 2356. 39.27 34M 39.439 63.472 3470.7 57.84 23^ 27.061 43.550 2381.3 39.69 34^ 39.727 63.935 3496. 58.27 23^ 27.348 44.013 2406.7 40.11 34^ 40.015 64.398 3521.3 58.69 24 27.636 44.477 2432. 40.53 35 40.303 64.862 3546.7 59.11 24^ 27.924 44.940 2457.3 40.96 35^ 40.591 65.325 3572. 59.53 24^ 28.212 45.403 2482.7 41.38 35^ 40.879 65.788 3597.3 59.96 24% 28.500 45.866 2508. 41.80 35% 41.167 66.251 3622.7 60.38 25 28.788 46.330 2533.3 42.22 36 41.455 66.715 3648. 60.80 25M 29.076 46.793 2558.7 42.64 36M 41.742 67.178 3673.3 61.22 25H 29.364 47.256 2584. 43.07 36^ 42.030 67.641 3698.7 61.64 25% 29.652 47.720 2609.3 43.49 36^ 42.318 68.105 3724. 62.07 26 29.939 48.183 2634.7 43.91 37 42.606 68.568 3749.3 62.49 26M 30.227 48.646 2660. 44.33 37K 42.894 69.031 3774.7 62.91 26^ 30.515 49.109 2685.3 44.76 37^ 43 . 182 69.495 3800. 63.33 26M 30.803 49.573 2710.7 45.18 37M 43.470 69.958 3825.3 63.76 27 31.091 50.036 2736. 45.60 38 43.758 70.421 3850.7 64.18 27M 31.379 50.499 2761.3 46.02 38M 44.045 70.884 3876. 64.60 27^ 31.667 50.963 2786.7 46.44 38^ 44.333 71.348 3901.3 65.02 27^ 31.955 51.426 2812. 46.87 38% 44.621 71.811 3926.7 65.44 28 32.242 51.889 2837.3 47.29 39 44.909 72.274 3S52. 65.87 28M 32.530 52.353 2862.7 47.71 39^ 45.197 72.738 3977.3 66.29 28^ 32.818 52.815 2888. 48.13 39^ 45.485 73.201 4002.7 66.71 28% 33.106 53.279 2913.3 48.56 39M 45.773 73.664 4028. 67.13 29 33.394 53.742 2938.7 48.98 40 46.061 74.128 4053.3 67.56 29M 33.682 54.206 2964. 49.40 [69] PRESSURES, POUNDS TO KILOGRAMS PRESSURES. POUNDS PER SQUARE INCH TO KILOGRAMS PER SQUARE CENTIMETER Conversion factor : 1 pound per square inch = . 0703027 kilograms per square centimeter Pounds Kilograms per per Sq. In. Sq. Cm. Pounds Kilograms per per Sq. In. Sq. Cm. Pounds Kilograms per per Sq. In. Sq. Cm. Pounds Kilograms per per Sq. In. Sq. Cm. 40 = 2.812 80 = 5.624 120 = 8.436 1 = .0703 1 = 2.882 1 = 5.695 1 = 8.507 2 = .1406 2 = 2.953 2 = 5.765 2 = 8.577 3 = .2109 3 = 3.023 3 = 5.835 3 = 8.647 4 = .2812 4 = 3.093 4 = 5.905 4 = 8.718 5 = .3515 5 = 3.164 5 = 5.976 5 = 8.788 6 = .4218 6 = 3.234 6 = 6.046 6 = 8.858 7 = .4921 7 = 3.304 7 = 6.116 7 = 8.928 8 = .5624 8 = 3.375 8 = 6.187 8 = 8.999 9 = .6327 9 = 3.445 9 = 6.257 9 = 9.069 10 = .703 50 = 3.515 90 = 6.327 130 = 9.139 1 = .773 1 = 3.585 1 = 6.398 1 = 9.210 2 = .844 2 = 3.656 2 = 6.468 2 = 9.280 3 = .914 3 = 3.726 3 = 6.538 3 = 9.350 4 = .984 4 = 6.608 4 = 9.421 4 = 3.796 5 = 1.055 5 = 3.867 5 = 6.679 5 = 9.491 6 = 1.125 6 = 3.937 6 = 6.749 6 = 9.561 7 = 1.195 7 = 4.007 7 = 6.819 7 = 9.631 8 - 1.265 8 = 4.078 8 = 6.890 8 = 9.702 9 = 1.336 9 = 4.148 9 = 6.960 9 = 9.772 20 = 1.406 60 = 4.218 100 = 7.030 140 = 9.842 1 = 1.476 1 = 4.288 1 = 7.101 1 = 9.913 2 = 1.547 2 = 4.359 2 = 7.171 2 = 9.983 3 = 1.617 3 = 4.429 3 = 7.241 3 = 10.053 4 = 1.687 4 = 4.499 4 = 7.311 4 = 10.124 5 = 1.758 5 = 4.570 5 = 7.382 5 = 10.194 6 = 1.828 6 = 4.640 6 = 7.452 6 = 10.264 7 = 1.898 7 = 4.710 7 = 7.522 7 = 10.334 8 = 1.968 8 = 4.781 8 = 7.593 8 = 10.405 9 = 2.039 9 = 4.851 9 = 7.663 9 = 10.475 30 = 2.109 70 = 4.921 110 = 7.733 150 = 10.545 1 = 2.179 1 = 4.991 1 = 7.804 1 = 10.616 2 = 2.250 2 = 5.062 2 = 7.874 2 = 10.686 3 = 2.320 3 = 5.132 3 = 7.944 3 = 10.756 4 = 2.390 4 = 5.202 4 = 8.015 4 = 10.827 5 = 2.461 5 = 5.273 5 = 8.085 5 = 10.897 6 = 2.531 6 = 5.343 6 = 8.155 6 = 10.967 7 = 2.601 7 = 5.413 7 = 8.225 7 = 11.038 8 = 2.672 8 = 5.484 8 = 8.296 8 = 11.108 9 * 2.742 9 = 5.554 9 = 8.366 9 = 11.178 [70] PRESSURES, POUNDS TO KILOGRAMS PRESSURES. POUNDS PER SQUARE INCH TO KILOGRAMS PER SQUARE CENTIMETER (Cont.) Pounds Kilograms per per Sq. In. Sq. Cm. Pounds Kilograms per per Sq. In. Sq. Cm. Pounds -Kilograms per per Sq. In. Sq. Cm. Pounds Kilograms per per Sq. In. Sq. Cm. 160 = 11.248 1 = 11.319 2 = 11.389 3 = 11.459 4 = 11.530 200 = 14.061 1 = 14.131 2 = 14.201 3 = 14.271 4 = 14.342 240 = 16.873 1=16.943 2 = 17.013 3 = 17.084 4 = 17.154 280= 19.685 1= 19.755 2= 19.825 3= 19.896 4= 19.966 5 = 11.600 6 = 11.670 7 = 11.741 8 = 11.811 9 = 11.881 5 = 14.412 6 = 14.482 7 = 14.553 8 = 14.623 9 = 14.693 5 = 17.224 6 = 17.294 7 = 17.365 8 = 17.435 9 = 17.505 5= 20.036 6= 20.107 7= 20.177 8= 20.247 9= 20.317 170 = 11.951 1 = 12.022 2 = 12.092 3 = 12.162 4 = 12.233 210 = 14.764 1=14.834 2 = 14.904 3 = 14.974 4 = 15.045 250 = 17.576 1=17.646 2 = 17.716 3 = 17.787 4 = 17.857 290= 20.388 1= 20.458 2= 20.528 3= 20.599 4= 20.669 5 = 12.303 6 = 12.373 7 = 12.444 8 = 12.514 9 = 12.584 5 = 15.115 6 = 15.185 7 = 15.256 8 = 15.326 9 = 15.396 5 = 17.927 6 = 17.997 7 = 18.068 8 = 18.138 9 = 18.208 5= 20.739 6= 20.810 7= 20.880 8= 20.950 9= 21.021 180 = 12.654 1=12.725 2 = 12.795 3 = 12.865 4 = 12.936 220 = 15.467 1 = 15.537 2 = 15.607 3 = 15.678 4 = 15.748 260 = 18.279 1=18.349 2 = 18.419 3 = 18.490 4 = 18.560 300= 21.091 400= 28.121 500= 35.151 600= 42.182 700= 49.212 5 = 13.006 6 = 13.076 7 = 13.147 8 = 13.217 9 = 13.287 5 = 15.818 6 = 15.888 7 = 15.959 8 = 16.029 9 = 16.099 5 = 18.630 6 = 18.701 7 = 18.771 8 = 18.841 9 = 18.911 800= 56.242 900= 63.272 1000= 70.303 1100= 77.333 1200= 84.363 190 = 13.358 1 = 13.428 2 = 13.498 3 = 13.568 4 = 13.639 230 = 16.170 1 = 16.240 2 = 16.310 3 = 16.381 4 = 16.451 270 = 18.982 1=19.052 2 = 19.122 3 = 19.193 4 = 19.263 1300= 91.393 1400= 98.424 1500 = 105.454 1600 = 112.484 1700 = 119.515 5 = 13.709 6 = 13.779 7 = 13.850 8 = 13.920 9 = 13.990 5 = 16.521 6 = 16.591 7 = 16.662 8 = 16.732 9 = 16.802 5 = 19.333 6 = 19.404 7 = 19.474 8 = 19.544 9 = 19.614 1800 = 126.545 1900 = 133.575 2000 = 140.605 2100 = 147.636 2200 = 154.666 [71] SPEED OR FLOW, CUBIC FEET TO CUBIC METERS SPEED OR FLOW. CUBIC FEET PER SECOND TO CUBIC METERS PER SECOND Reduction factor: 1 cubic foot per second = 0.0283170 cubic meter per second Cubic Feet per Second Cubic Meters per Second Cubic Cubic Feet Meters per per Second Second Cubic Cubic Feet Meters per per Second Second Cubic Cubic Feet Meters per per Second Second Cubic Cubic Feet Meters per per Second Second 40= 1.133 80=2.265 300= 8.495 700= 19.822 1 = .028 1= 1.161 1=2.294 310= 8.778 710= 20.105 2 = .057 2= 1.189 2=2.322 320= 9.061 720= 20.388 3 = .085 3= .218- 3=2.350 330= 9.345 730= 20.671 4 = .113 4= .246 4=2.379 340= 9.628 740= 20.955 5 = .142 5= .274 5=2.407 350= 9.911 750= 21.238 6 = .170 6= .303 6 = 2.435 360 = 10.194 760= 21.521 7 = .198 7= .331 7=2.464 370 = 10.477 770= 21.804 8 = .227 8= .359 8=2.492 380 = 10.760 780= 22.087 9 = .255 9= .388 9=2.520 390 = 11.044 790= 22.370 10 = .283 50= .416 90 = 2.549 400 = 11.327 800= 22.654 1 = .311 1= .444 1=2.577 410 = 11.610 810= 22.937 2 = .340 2= 1.472 2 = 2.605 420 = 11.893 820= 23.220 3 = .368 3= 1.500 3 = 2.633 430 = 12.176 830= 23.503 4 = .396 4= 1.529 4=2.662 440 = 12.459 840= 23.786 5 = .425 5= 1.557 5 = 2.690 450 = 12.743 850= 24.069 6 = .453 6= 1.5S6 6 = 2.718 460 = 13.026 860= 24.353 7 = .481 7= 1.614 7=2.747 470 = 13.309 870= 24.636 8 = .510 8= 1.642 8=2.775 480 = 13.592 880= 24.919 9 = .538 9= 1.671 9 = 2.803 490 = 13.875 890= 25.202 20 = .566 60= 1.699 100=2.832 500 = 14.159 900= 25.485 1 = .595 1= 1.727 110 = 3.115 510 = 14.442 910= 25.768 2 = .623 2= 1.756 120 = 3.398 520 = 14.725 920= 26.052 3 = .651 3= 1.784 130=3.681 530 = 15.008 930= 26.335 4 = .680 4= 1.812 140 = 3.964 540 = 15.291 940= 26.618 5 = .708 5= 1.841 150=4.248 550 = 15.574 950= 26.901 6 = .736 6= 1.869 160=4.531 560 = 15.858 960= 27.184 7 = .765 7= 1.897 170=4.814 570 = 16.141 970= 27.467 .793 8= 1.926 180 = 5.097 580 = 16.424 980= 27.751 9 = .821 9= 1.954 190 = 5.380 590 = 16.707 990= 28.034 30 = .850 70= 1.982 200 = 5.663 600 = 16.990 1000= 28.317 1 = .878 1= 2.011 210 = 5.947 610 = 17.273 2000= 56.634 2 = .906 2= 2.039 220=6.230 620 = 17.557 3000= 84.951 3 = .934 3= 2.067 230 = 6.513 630 = 17.840 4000 = 113.268 4 = .963 4= 2.095 240 = 6.796 640 = 18.123 5000 = 141.585 5 = .991 5= 2.124 250 = 7.079 650 = 18.406 6 = 1.019 6= 2.152 260 = 7.362 660 = 18.689 7 = 1.048 7= 2.180 270 = 7.646 670 = 18.972 8 = 1.076 8= 2.209 280 = 7.929 680 = 19.256 9 = 1.104 9= 2.237 290 = 8.212 690 = 19.539 [72] CHARACTERISTICS OF WIRE GAUGES WIRE GAUGES BUREAU OF STANDARDS Wire gauges are in use now less than formerly, two only are used extensively in this country, viz., the "American Wire Gauge" (Brown & Sharpe) and the "Steel Wire Gauge" (variously called the Washburn & Moen, Roebling, and American Steel & Wire Company's). Three other gauges are still used to some extent, viz., the Bir- mingham Wire Gauge (Stubs), the Old English Wire Gauge (London), and the Stubs' Steel Wire Gauge. There are in addition certain special gauges, such as the Music Wire Gauge, the drill and screw gauges, and the United States Standard Sheet-Metal Gauge. In England one wire gauge has been made legal and is in use generally, viz., the "Standard Wire Gauge." The diameters of the six general wire gauges mentioned are given in mils in Table 4, and in millimeters in. Table 5. In Germany, France, Austria, Italy, and other continental countries practically no wire gauge is used; size of wires is specified directly by the diameter in millimeters. This system is sometimes called the "millimeter wire gauge." The American Wire Gauge was devised by J. R. Brown, one of the founders of the Brown & Sharpe Manufacturing Co., in 1857. It speedily superseded the Birmingham Wire Gauge in this country, which was then in general use. It is, perhaps, more gener- ally known by the name " Brown & Sharpe Gauge," but this name is not the one pre- ferred by the Brown & Sharpe Co. In their catalogues they regularly refer to the gauge as the "American Standard Wire Gauge." The word "Standard" is probably not a good one to retain in the name of this gauge, since it is not the standard gauge for all metals in the United States; and, further, since it is not a legalized gauge, as are the (British) Standard Wire Gauge and the United States Standard Sheet-Metal Gauge. The abbreviation for the name of this ga*uge has usually been written "A. W. G." The American Wire Gauge is now used for more metals than any other in this country, and is practically the only gauge used for copper and aluminum wire, and in general for wire used in electrical work. It is the only wire gauge now in use whose successive sizes are determined by a simple mathematical law. Characteristics of the American Wire Gauge. The gauge is formed by the spec- ification of two diameters and the law that a given number of intermediate diameters are formed by geometrical progression. Thus, the diameter of No. 0000 is defined as 0.4600 inch and of No. 36 as 0.0050 inch. There are 38 sizes between these two, hence the ratio of any diameter to the diameter of the 39 / 4600 39 next greater number = \l '- = \/92 = 1.122 932 2. The square of this ratio = \ .0050 1.2610. The sixth power of the ratio, i.e., the ratio of any diameter to the diameter of the sixth greater number = 2.0050. The law of geometrical progression on which the gauge is based may be expressed in either of the three following manners: (1) the ratio of any diameter to the next smaller is a constant number; (2) the difference between any two successive diameters is a constant per cent of the smaller of the two diameters; (3) the difference between any two successive diameters is a constant ratio times the next smaller difference between two successive diameters. The " Steel Wire Gauge " is the same gauge which has been known by the names of Washburn & Moen gauge and American Steel & Wire Co.'s gauge. This gauge also, with a number of its sizes rounded off to thousandths of an inch, has been known as the Roebling gauge. The gauge was established by Ichabod Washburn about the year 1830, and was named after the Washburn & Moen Manufacturing Co. This company is no longer in existence, having been merged into the American Steel & Wire Co. The latter company continued the use of the Washburn & Moen Gauge for steel wire, giving it the name "American Steel & Wire Co.'s gauge." The company specifies all steel wire by this gauge, and states that it is used for fully 85 per cent of the total [73] WIRE GAUGES production of steel wire. This gauge was also formerly used by the John A. Roebling's Sons Co., who named it the Roebling gauge, as mentioned above. However, the Roebling company, who are engaged in the production of wire for electrical purposes, now prefer to use the American Wire Gauge. The name "Steel Wire Gauge" was suggested by the Bureau of Standards, in its correspondence with various companies, and it met with practically unanimous ap- proval. It was necessary to decide upon a name for this gauge, and the three names which have been used for it in the past were all open to the objection that they were the names of particular companies. These companies have accepted the new name. The abbreviations of the name of the gauge should be "Stl. W. G.," to distinguish it from "S. W. G." the abbreviation for the (British) Standard Wire Gauge. When it is necessary to distinguish the name of this gauge from others which may be used for steel wire, e.g., the (British) Standard Wire Gauge, it may be called the United States Steel Wire Gauge. Decimal Measurement. The trend of practice in the gaging of materials is increas- ingly toward the direct specification of the dimensions in decimal fractions of an inch, without use of gauge numbers. This has been, for a number of years, the practice of some of the large electrical and manufacturing companies of this country. The United States Navy Department also, hi June, 1911, ordered that all diameters and thicknesses of materials be specified directly in decimal fractions of an inch, omitting all reference to gauge numbers. The War Department, in December, 1911, issued a similar order, for all wires. The American Society for Testing Materials, in their Specifications for Cop- per Wire, recommend that diameters instead of gauge numbers be used. This is sim- ilar to the practice on the Continent of Europe, where sizes of wire are specified directly by the diameters in millimeters. The practice of specifying the diameters themselves and omitting gauge numbers has the advantages that it avoids possible confusion with other gauge systems and states an actual property of the wire directly. Stock Sizes of Wire. When gauge numbers are not used, it is necessary that a cer- tain set of stock sizes be considered standard, so that the manufacturers would not be required to keep in stock an unduly large number of different sizes of wire. The large companies who have ceased to use gauge numbers have recognized this, having taken as standard the American Wire Gauge sizes, to the nearest mil, for the larger diam- eters and to a tenth of a mil for the smaller. (See list of sizes, Table IV.) These sizes were adopted, in December, 1911, by the United States War Department for all wires. It seems likely that this system of sizes, based on the American Wire Gauge, will be perpetuated. Micrometer Gauges. The objection is often raised that the use of diameters re- quires the employment of a micrometer; and that the wire gauge as an instrument marked in gauge numbers is a very rapid means of handling wires and is indispensable for use by unskilled workmen. However, the use of the wire gauge as an instrument is consistent with the practice of specifying the diameters directly, provided the wire gauge is marked in mils. Wire gauges marked both in the A. W. G. numbers and in thousandths of an inch can be obtained from the manufacturers. One thus reads off directly from the wire gauge 81 mil, 64 mil, etc., just as he would No. 12, No. 14, etc. (Of course, the diameters in millimeters could be marked on the gauge for those who prefer the metric system.) It should not be forgotten, however, that a wire gauge gradually wears with use, and that for accurate work a micrometer should always be used. Birmingham Wire Gauge. Of the three wire gauges which have remained in use but are now nearly obsolete, the one most frequently mentioned is the Birmingham, sometimes called the Stubs' Wire Gauge. Its numbers were based upon the reduction of size made in practice by drawing wire from rolled rod. Thus, rod was called No. 0, first drawing No. 1, and so on. Its gradations of size are very irregular, as shown in the table of "Wire Gauges in Use in the United States," given on the page following; by simply comparing the several decimal equivalents of the Birmingham gauge with the equivalents of the American, or Brown & Sharpe gauge, as they appear directly opposite in the first column of the table. The Birmingham gauge is typical of most wire gauges, and the irregularity of its steps is shown in marked contrast to the [74] WIRE GAUGES regularity of the steps of the American Wire Gauge. The Birmingham gauge was used extensively both in Great Britain and in the United States for many years. It has been superseded, however, and is now nearly obsolete. The principal outstanding exception to the abandonment of the Birmingham gauge is that the Treasury Department, with certain legislative sanction, still specifies the Birmingham gauge for use in the collection of duty on imports of wire. This gauge was prescribed by the Treasury Department in 1875, after it had been ascertained that it was the standard gauge "not only throughout the United States, but the world." This reason for the use of this gauge does not now exist, inasmuch as the gauge is now used very little in the United States, and even less in other countries, but the Treasury De- partment considers that it can not change its practice, since legislative approval has been given the Birmingham gauge by the tariff acts with a provision for assessment of duty according to gauge numbers, and further since a change would alter the rate of duty on certain sizes of wire. These facts have been brought to the attention of the congressional committees which have charge of tariff legislation, and it is possible that when the tariff act is next amended the gauge numbers will be stricken out and the diameters themselves specified. The Stubs' Steel Wire Gauge has a somewhat limited use for tool steel wire and drill rods. This gauge should not be confused with the Birmingham, which is some- times known as Stubs' Iron Wire Gauge. English Standard. The "Standard Wire Gauge," otherwise known as the New British Standard, the English Legal Standard, or the Imperial Wire Gauge, is the legal standard of Great Britain for all wires, as fixed by order in Council, August 23, 1883. It was constructed by modifying the Birmingham Wire Gauge, so that the differences between successive diameters were the same for short ranges, i.e., so that a graph rep- resenting the diameters consists of a series of a few straight lines. WIRE GAUGES IN USE IN THE UNITED STATES Dimensions are hi decimal parts of an inch Steel Wire Gauge Number of "Wire American Birmingh'm rvr Q-HiKcx* Washburn & Moen British Imperial Wire Stubs' Qfo^l United States Gauge & Sharpe or otuos Iron Wire Roebling Gauge Ot-661 Wire Standard for Plate American S. W. G. Steel & ^ . Wire Co. 0000000 .4900 .500 .500 000000 .58000 .4615 .464 .... .46875 00000 .51650 .... .4305 .432 .... .4375 0000 .46000 .454 .3938 .400 .40625 000 .40964 .425 .3625 .372 .... .375 00 .36480 .38 .3310 .348 .34375 .32486 .34 .3065 .324 .3125 1 .28930 .3 .2830 .300 !227 .28125 2 .25763 .284 .2625 .276 .219 .265625 3 .22942 .259 .2437 .252 .212 .25 4 .20431 .238 .2253 .232 .207 .234375 5 .18194 .22 .2070 .212 .204 .21875 6 .16202 .203 .1920 .192 .201 .203125 7 .14428 .18 .1770 .176 .199 .1875 8 .12849 .165 .1620 .160 .197 .171875 9 .11443 .148 .1483 .144 .194 . 15625 [75] WIRE GAUGES , WIRE GAUGES IN USE IN THE UNITED STATES (Cont., Number of Wire American or Brown & Sharpe Birmingh'm or Stubs' Iron Wire Steel Wire Gauge British Imperial Wire Stubs' United States for Plate Washburn & Moen Roebling S. W. G. American Steel & Wire Co. 10 . 101897 .134 .1350 .128 .191 . 140625 11 .090742 .12 .1205 .116 .188 .125 12 .080808 .109 .1055 .104 .185 . 109375 13 .071961 .095 .0915 .092 .182 .09375 14 .064084 .083 .0800 .080 .180 .078125 15 .057068 .072 .0720 .072 .178 .0703125 16 .050821 .065 .0625 .064 .175 .0625 17 .045257 .058 .0540 .056 .172 .05625 18 .040303 .049 .0475 .048 .168 .05 19 .035890 .042 .0410 .040 .164 .04375 20 .031961 .035 .0348 .036 .161 .0375 21 .028462 .032 .03175 .032 .157 .034375 22 .025347 .028 .0286 .028 .155 .03125 23 .022571 .025 .0258 .024 .153 .028125 24 .020101 .022 .0230 .022 .151 .025 25 .017900 .02 .0204 .020 .148 .021875 26 .015941 .018 .0181 .018 .146 .01875 27 .014195 .016 .0173 .0164 .143 .0171875 28 .012641 .014 .0162 .0149 .139 .015625 29 .011257 .013 .0150 .0136 .134 .0140625 30 .010025 .012 .0140 .0124 .127 .0125 31 .008928 .01 .0132 .0116 .120 .0109375 32 .007950 .009 .0128 .0108 .115 .01015625 33 .007080 .008 .0118 .0100 .112 .009375 34 .006304 .007 .0104 .0092 .110 .00859375 35 .005614 .005 .0095 .0084 .108 .0078125 36 .005000 .004 .0090 .0076 .106 .00703125 37 .004453 .... .0085 .0068 .103 .006640625 38 .003965 .0080 .0060 .101 .00625 39 40 .003531 .003144 .... .0075 .0070 .0052 .0048 .099 .097 NOTE. Reference to Tables 4 and 5, page 69, are Copper Wire Tables issued by the Bureau of Standards. These tables will be found in the Electrical Section of this book. When it is remembered that a mil is a unit of length used in measuring the diameter of wire equal to one thousandth of an inch, it is only necessary when diameters are given in decimal parts of an inch to move the decimal point to correspond, thus, reading across the table given above: No. 1 American wire gauge is .28930 inch diameter, or 289 mils. No. 1 Birmingham gauge = .3 inch diameter, or 300 mils. No. 1 Steel wire gauge = .2830 inch diameter, or 283 mils. ,76] U. S. STANDARD GAUGE FOR SHEET IRON AND STEEL U. S. STANDARD GAUGE FOR SHEET AND PLATE IRON AND STEEL Be it enacted by the Senate and House of Representatives of the United States of America in Congress assembled, That for the purpose of securing uniformity, the fol- lowing is established as the only standard gauge for sheet and olate iron and steel in the United States of America, namely: Number of Gauge Approxi- mate Thickness, in Frac- tions of an Inch Approximate Thickness, in Decimal Parts of an Inch Approximate Thickness, in Milli- meters Weight per Square Foot, in Ounces Avoir- dupois Weight per Square Foot, in Pounds Avoir- dupois Weight per Square Foot, in Kilo- grams Weight per Square Meter, in Kilo- grams Weight per Square Meter, in Pounds Avoir- dupois 0000000 1-2 .5 12.7 320 20.00 9.072 97.65 215.28 000000 15-32 .46875 11.90625 300 18.75 8.505 91.55 201.82 00000 7-16 .4375 11.1125 280 17.50 7.983 85.44 188.37 0000 13-32 .40625 10.31875 260 16.25 7.371 79.33 174.91 000 3-8 .375 9.525 240 15 6.804 73.24 161.46 00 11-32 .34375 8.73125 220 13.75 6.237 67,13 148.00 5-16 .3125 7.9375 200 12.50 5.67 61.03 134.55 1 9-32 .28125 7.14375 180 11.25 5.103 54.93 121.09 2 17-64 .265625 6.746875 170 10.625 4.819 51.88 114.37 3 w .25 6.35 160 10 4.536 48.82 107.64 4 15-64 ,234375 5.953125 150 9.375 4.252 45.77 100.91 5 7-32 .21875 5.55625 140 8.75 3.969 42.72 94.18 6 13-64 .203125 5.159375 130 8.125 3.685 39.67 87.45 7 3-16 .1875 4 . 7625 120 7.5 3.402 36.62 80.72 8 11-64 .171875 4.365625 110 6.875 3.118 33.57 74.00 9 5-32 .15625 3.96875 100 6.25 2.835 30.52 67.27 10 9-64 .140625 3.571875 90 5.625 2.552 27.46 60.55 11 i-8 .125 3.175 80 5 2.268 24.41 53.82 12 7-64 . 109375 2.778125 70 4.375 1.984 21.36 47.09 13 3-32 .09375 2.38125 60 3.75 1.701 18.31 40.36 14 5-64 .078125 1.984375 50 3.125 1.417 15.26 33.64 15 9-128 .0703125 1.7859375 45 2.8125 1.276 13.73 30.27 16 1-16 .0625 1.5875 40 2.5 1.134 12.21 26.91 17 9-160 .05625 1.42875 36 2.25 1.021 10.99 24.22 18 1-20 .05 1.27 32 2 .9072 9.765 21.53 19 7-160 .04375 1.11125 28 1.75 .7988 8.544 18.84 20 3-80 .0375 .9525 24 1.50 .6804 7.324 16.15 21 11-320 .034375 .873125 22 1.375 .6237 6.713 14.80 22 1-32 .03125 .793750 20 1.25 .567 6.103 13.46 23 9-320 .028125 .714375 18 1.125 .5103 5.493 12.ll 24 1-40 .025 .635 16 1 .4536 4.882 10.76 25 7-320 .021875 .555625 14 .875 .3969 4.272 9.42 26 3-160 .01875 .47625 12 .75 .3402 3.662 8.07 27 11-640 .0171875 .4365625 11 .6875 .3119 3.357 7.40 28 1-64 .015625 .396875 10 .625 .2835 3.052 6.73 [77] U. S. STANDARD GAUGE FOR SHEET IRON AND STEEL U. S. STANDARD GAUGE FOR SHEET AND PLATE IRON AND STEEL (Cont.) Number of Gauge Approxi- mate Thickness, in Frac- tions of an Inch Approximate Thickness, in Decimal Parts of an Inch Approximate Thickness, in Milli- meters Weight per Square Foot, in Ounces Avoir- dupois Weight per Square Foot, in Pounds Avofr- dupois Weight per Square Foot, in Kilo- grams Weight per Square Meter, in Kilo- grams Weight per Square Meter, in Pounds Avoir- dupois 29 9-640 .0140625 .3571875 9 .5625 .2551 2.746 6.05 30 1-80 .0125 .3175 8 .5 .2268 2.441 5.38 31 7-640 .0109375 .2778125 7 .4375 .1984 2.136 4.7i 32 13-1280 .01015625 .25796875 6^ .40625 .1843 1.983 4.37 33 3-320 .009375 .238125 6 .375 .1701 1.831 4.04 34 11-1280 .00859375 .21828125 5H .34375 .1559 1.678 3.70 35 5-640 .0078125 .1984375 5 .3125 1.417 1.526 3.36 36 9-1280 .00703125 . 17859375 4K .28125 .1276 1.373 3.03 37 17-2560 .006640625 . 168671875 4M .265625 .1205 1.297 2.87 38 1-160 .00625 .15875 4 .25 .1134 1.221 2.69 And on and after July 1, 1893, the same and no other shall be used in determining duties and taxes levied by the United States of America on sheet and plate iron and steel. But this act shall not be construed to increase duties upon any articles which may be imported. SEC. 2. That the Secretary of the Treasury is authorized and required to prepare suitable standards in accordance herewith. SEC. 3. That in the practical use and application of the standard gauge hereby established a variation of 2^ per cent either way may be allowed. Approved, March 3, 1893. NOTE. A variation of 2| per cent either way is permitted, so that the excessive number of decimal places in the "approximate" equivalents is undue refinement for the practical purposes for which the act was established. Moreover, the values in some cases are beyond the limits of measurement of the highest precision. For these reasons and greater convenience in use, the figures not usually required in view of the tolerance are printed in smaller type. S. W. STRATTON, . Director Bureau of Standards. [78] LEGAL WEIGHTS OF VARIOUS COMMODITIES LEGAL WEIGHTS (IN POUNDS) PER BUSHEL OF VARIOUS COMMODITIES BUREAU OF STANDARDS I. Introduction. The legal weights per bushel of various commodities, as given in the following tables, have been fixed by national legislation mainly for customs pur- poses or by the State legislatures for purposes of commerce within the States. In many cases these weights differ considerably in the different States, and in the cases of only a few commodities, such as wheat, oats, and pease, are the legal weights uniform through- out the entire country. It should not be assumed that the legal weights herein given represent a volume e.qual to the bushel of 2,150.42 cubic inches (United States bushel). On account of the variations in the densities of commodities in different localities and in different seasons, it is impossible to fix with any degree of certainty the weight of a given volume. The best that could be done would be to give the average of all localities for a number of years. Inasmuch, however, as the weight of a given volume of any commodity, such as potatoes, apples, coal, corn, etc., can only be approximately fixed, it is important in transactions involving such measures that it be distinctly understood which bushel is meant, viz., the volume of 2,150.42 cubic inches or a certain number of pounds called a bushel, which might be quite a different amount. On account of the impossibility of reconciling these two definitions of the bushel, it is recommended that all sales be made by weight, as is now the practice in wheat transactions. II. Commodities for Which Bushel Weights Have Been Adopted in But One or Two States Alsike (or Swedish) seed, 60 pounds (Md. and Okla.). Beggarweed seed, 62 pounds (Fla.). Bermuda grass seed, 40 pounds (Okla.). Blackberries, 30 pounds (Iowa) ; 48 pounds (Tenn.); dried, 28 pounds (Term.). Blueberries, 42 pounds (Minn.). Bromus inermus, 14 pounds (N. Dak.). Burr clover, in hulls, 8 pounds (N. C.). Cabbage, 50 pounds (Tenn.). Canary seed, 60 pounds (Tenn.); 50 pounds (Iowa). Cantaloupe melon, 50 pounds (Tenn.). Caster seed, 50 pounds (Md.). Cement, 80 pounds (Tenn.). Cherries, 40 pounds (Iowa) ; with stems, 56 pounds (Tenn.); without stems, 64 pounds (Tenn.). Chufa, 54 pounds (Fla.). Cotton seed, staple, 42 pounds (S. C.). Culm, 80 pounds (Md.). Currants, 40 pounds (Iowa and Minn.). Feed, 50 pounds (Mass.). Fescue, seed of all the, except the tall and meadow fescue, 14 pounds (N. C.). Fescue, tall and meadow fescue seed, 24 pounds (N. C.). Grapes, 40 pounds (Iowa) ; with stems, 48 pounds (Tenn.); without stems, 60 pounds (Tenn.). Guavas, 54 pounds (Fla.). Hominy, 60 pounds (Ohio); 62 pounds (Tenn.). Horseradish, 50 pounds (Tenn.). Italian rye-grass seed, 20 pounds (Tenn.). Japan clover in hulls, 25 pounds (N. C.). Johnson grass, 28 pounds (Ark.); 25 pounds (N. C.). Kale, 30 pounds (Tenn.). Land plaster, 100 pounds (Tenn.). Lentils, 60 pounds (N. C.). Lucerne, 60 pounds (N. C.). Lupines, 60 pounds (N. C.). Meadow seed, tall, 14 pounds (N. C.). Meal (?), 46 pounds (Ala.); unbolted, 48 pounds (Ala.). Middlings, fine, 40 pounds (Ind.); coarse middlings, 30 pounds (Ind.). [791 LEGAL WEIGHTS OF VARIOUS COMMODITIES Millet, Japanese barnyard, 35 pounds (Mass, and N. H.). Mustard, 30 pounds (Tenn.). Mustard seed, 58 pounds (N. C.). Oat grass seed, 14 pounds (N. C.). Plums, 40 pounds (Fla.); 64 pounds (Tenn.); dried, 28 pounds (Mich.). Prunes, dried, 28 pounds (Idaho); green, 45 pounds (Idaho). Radish seed, 50 pounds (Iowa). Raspberries, 32 pounds (Iowa and Kan.); 48 pounds (Tenn.). Rhubarb, 50 pounds (Tenn.). Sage, 4 pounds (Tenn.). Salads, 30 pounds (Tenn.). Sand, 130 pounds (Iowa). Seed of brome grasses, 14 pounds (N. C.). Spinach, 30 pounds (Tenn.). Strawberries, 32 pounds (Iowa); 48 pounds (Tenn.). Sugar cane seed (amber), 57 pounds (N. J.). Sunflower seed, 24 pounds (N. C.). Teosinte, 59 pounds (N. C.). Velvet grass seed, 7 pounds (Tenn.). Vetches, 60 pounds (N. C.). In the following pages is given an alphabetical list of commodities for which legal weights (in pounds) per bushel have been more generally adopted by States. Special explanations or conditions affecting the definition are printed in foot-notes to these tables. LEGAL WEIGHTS PER BUSHEL OF COMMODITIES III. Commodities for which bushel weights have been more widely adopted. u. s... Ala | Alfalfa Seed Apples jj Beans ! 3 1 c Buckwheat a o Clover Seed Coal o. i Q m ii I 1 1 | te 90 80 1 .1 Stone Coal 48 47 45 48 50 60 2 55 2 60 50 4? 24 Ariz . . . Ark ... Cal . . . 3 50 24 14 20 48 52 40 52 48 60 80 80 Colo . . . Conn 48 25 48 48 60 60 4 60 14 20 50 20 20 60 60 Del D. C. Fla.... Ga . 3 48 24 24 48 47 48 6 60 6 60 48 20 720 14 ... 52 60 80 Hawaii . Idaho 19 ... 111 24 25 24 24 24 48 48 48 48 47 48 48 6 60 60 8 60 60 6 60 46 46 46 ' 46 56 56 14 14 14 9 14 14 20 20 20 20 50 52 50 52 50 56 50 50 20 60 60 60 60 60 80 80 80 80 76 Ind Iowa. . . Kans . . Ky. . 60 60 48 3 48 76 76 76 La Me.... ... 44 60 60 48 "iH [80] LEGAL WEIGHTS OF VARIOUS COMMODITIES LEGAL WEIGHTS PER BUSHEL OF COMMODITIES III. Commodities for which bushel weights have been more widely adopted. Cont. 3 Apples | Beans i Blue-grass Seed \\ la PQ w 1 f Carrots Charcoal Clover Seed Coal i t < 09 1 i Q I PQ Castor Beans (Shelled) 1 o 1 Bituminous Coal ? Md... Mass . . Mich . . Minn. . Miss. . . 60 48 48 3 50 48 45 3 48 * 48 48 50 28 25 22 28 26 24 24 24 25 25 48 48 48 48 48 4S 48 48 48 48 48 60 "60 60 60 6 60 12 60 60 6 60 60 2 11 60 10 50 46 12 46 46 46 46 60 50 50 56 60 60 14 14 14 14 14 14 14 9 20 20 50 50 20 60 60 60 60 60 60 60 60 60 60 64 80 48 48 80 ... 80 20 20 20 20 20 20 57 50 48 52 52 52 50 48 50 45 50 50 50 50 50 20 80 76 80 80 Mo.... Mont. . Nebr . . Nev. . . N. H 60 60 N.J.... N Mex N. Y 48 3 48 50 50 48 45 25 24 24 28 48 48 48 48 48 46 47 48 60 13 60 60 60 60 20 20 46 30 48 50 42 50 52 4? 50 50 50 60 60 . 60 N. C. . . N. Dak. Ohio.. . Okla... Oreg. 60 60 *46 46 60 56 60 14 14 80 80 80 60 60 60 60 60 80 20 30 Pa 48 14 15 18 20 16 75 80 76 R. I. .. S. C . ... 48 25 60 46 50 20 48 50 S. Dak. 48 48 48 60 12 n 60 6 60 46 60 50 14 20 20 20 30 42 42 50 42 60 18 60 60 80 80 80 Tenn . . Tex ... 3 50 45 24 28 50 22 22 Ut-ah. Vt Va.... Wash.. W. Va. Wis.... ... 46 3 45 50 28* 28 25 25 48 48 48 48 48 62 6 60 60 60 60 14 .... 48 52 4? 50 60 60 60 60 60 80 80 5? ... 50 20 50 50 Wyo... 1 Not defined. 2 Small white beans, 60 pounds. 3 Green apples. 4 Sugar beets and mangel-wurzeU > Shelled beans, 60 pounds; velvet beans, 78 pounds. White beans. ? Wheat bran. s Green unshelled beans, 56 pounds. s English blue-grass seed, 22 pounds; native blue- grass seed, 14 pounds. 10 Also castor seed. 11 Soy beans, 58 pounds. 12 Green unshelled beans, 30 pounds. 13 Soy beans. 14 Commercially dry, for all hard woods. 15 Fifteen pounds commercially dry, for all soft woods. 18 Standard weight in borough of Greensburg. " Dried beans. 18 Red and white. ' Idaho law repealed in 1905. [81 LEGAL WEIGHTS OF VARIOUS COMMODITIES LEGAL WEIGHTS PER BUSHEL OF COMMODITIES III. Commodities for which bushel weights have been more widely adopted. Cord. Corn" Corn Meal Cotton Seed Flaxseed (Linseed) (Plastering) Hair Hemp Seed Herds Grass Hungarian Grass Seed || Indian Corn or Maize I 1 U *g S-S J* SI I 1 Shelled Corn 1 Q II I s il -1 ^ 6 SS wO Upland Cotton Seed u. s Ala 56 48 56 70 75 56 32 Ariz 54 Ark 70 74 56 48 33| 56 Cal 52 56 56 56 Colo .... 70 50 50 44 Conn 44 30 55 45 Del 44 48 D C Fla 70 56 56 48 48 32 30 46 Ga 70 56 8 44 Hawaii. . . 56 Idaho 16 111 70 2 4 70 5 70 75 56 56 56 56 56 48 50 50 56 8 44 44 Ind Iowa Kans Ky La . 38 3 50 7 70 56 56 56 56 56 6 8 8 44 44 44 ... 50 50 50 .... 50 Me 8 50 11 44 44 50 44 44 44 44 48 45 45 45 45 50 50 48 50 48 50 50 50 10 56 "56 56 Md 4 70 56 9 50 56 56 56 56 56 56 56 48 50 50 48 50 50 50 48 50 56 Mass. 44 30 55 56 6 8 8 Mich.... Minn 4 70 70 72 70 Miss 44 48 32 33 56 56 56 56 56 56 Mo Mont .... 70 70 ... ... Nebr . . Nev 6 70 ... ... N. H 9 50 N. J 55 N Mex N. Y 50 48 ... 30 44 44 30 55 55 56 44 45 ... 56 56 N. C 70 70 68 70 N. Dak. 72 56 56 56 Ohio Okla..... 40 56 44 50 50 32 ... 56 44 56 56 Oree Pa 40 58 '821 LEGAL WEIGHTS OF VARIOUS COMMODITIES LEGAL WEIGHTS PER BUSHEL OF COMMODITIES III. Commodities for which bushel weights have been more widely adopted. Cont. s Corn" Corn Meal 1 Cotton Seed | (Plastering) Hair i a Herds Grass o bfl'S 3C/2 . S 2 S ^"S II Corn in Ear, Unhusked 1 Corn Meal 1 II GO g Corn Meal Unbolted Cotton Seed 1 Sea Island Cotton Seed 5 tj-j p R. I S. C 40 70 56 50 "48 48 48 12 30 44 30 56 44 ... 50 S. Dak... 70 70 70 13 74 72 56 56 56 56 Tenn Tex . . 40 50 48 28 32 56 56 8 44 \\ v 48 48 Utah Vt 45 56 56 Va 70 56 50 32 56 56 8 44 12 48 Wash.... W. Va. . . Wis ... 56 56 50 44 30 56 8 44 48 56 Wyo 1 Not denned. 2 Corn in ear, 70 pounds until Dec. 1 next after grown; 68 pounds thereafter. 3 Sweet corn. 4 In the cob. 5 Indian corn in ear. 8 Unwashed plastering hair, 8 pounds: washed plas- tering hair, 4 pounds. 7 Corn in ear, from Nov. 1 to May 1 following, 70 pounds, 68 pounds from May 1 to Nov. 1. 8 Indian-corn meal. 9 Cracked corn, w Shelled. 11 Standard weight bushel corn meal, bolted or un- unbolted, 48 pounds. 12 Except the seed of long staple cotton, of which the weight shall be 42 pounds. 13 Green unshelled corn, 100 pounds. 14 See also " Popcorn," "Indian corn," and corn." Idaho law repealed in 1905. Kaffir [83] LEGAL WEIGHTS OF VARIOUS COMMODITIES LEGAL WEIGHTS III. Commodities for which bushel PER BUSHEL OF COMMODITIES weights have been more widely adopted. Cont. Li me 1 Peache s 1 1 a Unslaked Lime 75 3 S m o Onions 1 Orchard Grass S 1 o . PH 1 Dried Peaches, Unpeeled Peanuts (or " Gi Peas")* ! I u. s 34 3?, 60 Ala 32 38 33 fio Ariz .... 32 Ark 50 3?, 57 14 33 33 60 Cal 32 Colo 80 32 57 Conn 70 32 52 45 33 33 60 Del D.C Fla 50 32 56 2 54 33 22 60 Ga 80 32 57 38 33 *25 60 Hawaii 32 Idaho 29 .... Ill 80 38 32 57 33 Ind.... 4 35 50 3? 48 14 33 55 33 Iowa 80 50 32 57 14 32 42 48 33 20 Kans. . 80 32 50 32 57 52 48 33 7 go Ky La ... 35 50 8 32 57 14 39 *24 60 Me 32 52 45 60 Md 80 4 34 10 50 11 32 57 14 12 40 22 13 60 Mass. . . 70 32 52 45 48 33 14 20 58 60 Mich 70 50 32 54 14 33 28 60 Minn . . 80 48 32 52 14 42 15 28 60 Miss Mo 80 38 38 50 50 32 32 57 57 14 36 44 48 33 33 *24 48 60 17 60 Mont 80 30 32 57 50 45 60 Nebr. . 80 30 50 32 57 39 33 60 Nev N. H 70 32 50 32 32 57 52 50 45 48 48 15 33 5 33 14 20 58 7 60 60 N. J 30 57 50 33 33 60 N. Mex 60 N. Y 70 32 57 33 N. C 50 32 57 14 22 60 N. Dak . . . 80 50 32 52 60 Ohio 70 34 50 32 55 48 33 60 Okla Oreg 80 38 50 32 32 57 14 36 44 48 28 33 22 48 45 60 Pa 32 50 [84] LEGAL WEIGHTS OF VARIOUS COMMODITIES LEGAL WEIGHTS PER BUSHEL OF COMMODITIES III. Commodities for which bushel weights have been more widely adopted. Cont. Lime s 3 1 o Onions 1 o 1 Osage Orange Seed .& Peaches O k Pears 1 j 1 Unslaked Lime Peaches 1 Dried Peaches, Peeled Dried Peaches, Unpeeled R. I S. C 70 38 50 32 50 50 48 33 3 60 S. Dak.... Tenn . Tex 80 19 80 20 50 50 32 32 32 52 21 56 57 2*56 60 60 14 33 50 23 50 50 26 28 23 Utah Vt 38 50 50 32 30 32 32 32 52 57 14 34 60 25 60 Va Wash 80 .... 40 28 33 33 32 22 3 45 W Va 26 34 Wis 70 80 57 44 60 Wyo 1 Not denned. 2 Green peaches, s Green. 4 Malt rye. 6 Top sets; bottom sets 32 pounds, s Shelled, 56 pounds. 7 Shelled, dry. 8 Strike measure. 9 Bottom onion sets. 10 German and American. 11 Shelled. 12 Peaches (peeled) ; unpeeled 32 pounds. 13 Cowpeas. 14 Roasted; green 22 pounds. 16 Not stated whether peeled or unpeeled. 16 Top onion sets. 17 Including split peas. In the ear. 19 Slaked lime, 40 pounds. 20 German, Missouri, and Tennessee millet seeds. 21 Matured onions. 22 Bottom onion sets, 32 pounds. 23 Matured. 24 Matured pears, 56 pounds; dried pears, 26 pounds. 25 Black-eyed pease. 26 Barley malt. 27 Includes "Rice corn." 28 " Rive corn." 29 Idaho law repealed in 1905. [85] LEGAL WEIGHTS OF VARIOUS COMMODITIES LEGAL WEIGHTS PER BUSHEL OF COMMODITIES III. Commodities for which bushel weights have been more widely adopted. Cont* Pot atoes i Salt I Sweet Potatoes White Potatoes Quinces I 1 1 8 S ja Rutabagas I 1 V a a OT Fine Salt Coarse Salt 1 Timothy Seed Tomatoes .1 H w U.S. . . 60 56 60 Ala "55 60 56 55 60 Ariz 56 60 Ark 60 50 14 56 50 50 60 57 60 Cal 54 60 Colo 60 56 80 45 60 Conn 60 54 45 60 50 56 50 70 60 Del 60 D.C. 60 Fla 60 60 48 56 60 56 54 60 Ga 55 60 43 56 45 55 60 Hawaii. . 56 60 Idaho 8 111 50 60 56 55 50 45 55 60 Ind .... 60 55 56 50 45 55 60 Iowa 60 46 48 50 14 50 56 80 2 50 45 50 55 60 Kans .... 60 50 56 80 50 45 56 55 60 Ky 6 60 55 56 50 55 45 60 60 La . . 56 60 Me 60 60 50 50 60 70 60 Md 60 60 50 3 14 56 56 70 50 45 60 60 60 Mass Mich 60 54 56 60 48 4 14 45 ... 50 56 56 56 50 70 45 45 56 55 58 60 60 Minn 55 60 50 4 14 5? 56 57 45 60 Miss 60 60 56 50 4?, 45 55 60 \ Mo 56 60 4 14 50 56 50 42 45 45 60 Mont 60 56 50 45 50 60 Nebr 50 60 56 50 50 45 55 60 Nev 60 50 56 SO 50 45 56 56 60 N H 6 60 54 48 50 56 50 70 45 56 55 60 N. J 54 60 56 45 60 N Mex N. Y . 54 60 45 50 56 56 70 45 60 N.C N. Dak 6 56 56 46 60 60 50 4 14 44 56 56 80 50 45 45 50 60 60 60 Ohio 6 60 50 56 45 56 60 60 Okla 55 60 50 4 14 50 56 SO 50 45 45 60 60 Oree 60 56 60 Pa 56 56 6 62 85 60 [86] LEGAL WEIGHTS OF VARIOUS COMMODITIES LEGAL WEIGHTS PER BUSHEL OF COMMODITIES III. Commodities for which bushel weights have been more widely adopted. Cont. Pol atoe B Salt Potatoes 1 I w White Potatoes '3 cy Rape Seed Red Top S Rutabagas Rye Meal 1 1 Fine Salt Coarse Salt Sorghum Seed Timothy Seed Tomatoes t I 1 R. I 54 60 50 56 50 70 45 56 50 60 S. C _ S. Dak 46 60 56 SO 42 60 60 Tenn 50 60 18 4 14 56 50 50 45 56 50 60 Tex 55 60 56 50 45 55 55 60 Utah Vt 60 56 70 45 60 7 60 Va ... . 56 56 12 56 50 45 55 60 Wash 60 56 60 W. Va 60 56 45 60 Wis Wyo 60 54 ... 50 45 56 50 56 50 70 45 ... 42 60 1 Not denned. 2 Sorghum saccharatum seed. 3 Red top grass seed (chaff) ; fancy 32 pounds. < Seed. 5 Irish potatoes. 6 Ground salt, 70 pounds. 7 India wheat, 46 pounds. s Idaho law repealed in 1905. [87] SECTION 3 MENSURATION AND MATHEMATICAL TABLES MENSURATION OF SURFACES To Find the Area of a Parallelogram ; whether it be a square, a rectangle, a rhombus, or a rhomboid. Rule: Multiply the length by the height; or, multiply the product of two contiguous sides by the natural sine of the included angle. NOTE. The perpendicular height of the parallelo- gram is equal to the area divided by the base. The area of a parallelogram which is not right angled can be converted into a rectangle by cutting off a triangle at one end and putting it on the other. Its area is the length multiplied into the breadth measured perpendicularly, or, as it is commonly stated, Area = base X altitude. To Find the Area of a Triangle. Rule: Multiply the base by the perpen- dicular height and take half the product. Or, multiply half the product of \ two contiguous sides by the natural sine of the included angle. NOTE. A triangle is half a parallelogram of the same base and altitude. The perpendicular height of the triangle is equal to twice the area divided by the base. To Find the Area of a Triangle Whose Three Sides Only Are Given. Rule 1. From half the sum of the three sides subtract each side severally. Multiply half the sum and the three remainders continually together, and the square root of the product will be the area required. Rule 2. Any two sides of a triangle being multiplied together and the product again by half the natural sine of their included angle will give the area of the triangle. That is, AC multiplied by CB X natural sine of the angle C = twice area. Any Two Sides of a Right Angle Triangle Being Given to Find the Third Side. Rule 1. When the two legs are given to find the hypotenuse. Add the square of one of the legs to the square of the other, and the square root of the sum will be equal to the hypotenuse. Rule 2. When the hypotenuse and one of the legs are given to find the other leg. From the square of the hypotenuse take the square of the given leg, and the ~~ B square root of the remainder will be equal to the other leg. To Find the Area of a Trapezium. Rule: Multiply the diagonal by the sum of the two perpendiculars falling upon it from the opposite angles, and half the product will be the area. [89] MENSURATION NOTE. If the trapezium can be inscribed in a circle; that is, if the sum of two of its opposite angles is equal to two right angles, or 180, the area may be found thus: Rule: From half the sum of the four sides sub- tract each side severally; then multiply the four remainders continually together, and the square root of the product will be the area. To Find the Area of a Trapezoid, or a Quad- rangle, Two of Whose Opposite Sides Are Parallel. Rule: Multiply the sum of the parallel sides by the perpendicular distance between them, and half the product will be the area. To Find the Area of a Regular Polygon. Rule: Multiply half the perimeter of the figure by the perpendicular falling from its center upon one of the sides, and the product will be the area. NOTE. Every regular polygon is composed of as many equal triangles as it has sides, consequently the area of one of those triangles being multiplied by the number of sides must give the area of the whole figure. To Find the Area of a Regular Polygon When the Side Only Is Given. Rule: Multiply the square of the side of the polygon by the number standing opposite its name in the following table and the product will be the area. NOTE. The multipliers in the table are the areas of the polygon to which they belong when the side is unity or one. The table is formed by trigonometry, thus: As radius = 1 : tang. Z O B P : : BP (f ) : P O = BPXtang. ZOPB radius Whence O P X B P = tang. Z O B P = area of the O B P X number of sides = tabular number, or the area = tang. ZOBP: tang. A A B; and of the polygon. The angle O B P, together with its tangent, for any polygon of not more than twelve sides is shown hi the following table: No. of Sides Names Multipliers Angle OBP Tangents 3 4 Trigon or equil. A Tetragon or square 0.433013- 1 000000+ 30 45 .57735+ = W3 1 00000+ =1X1 5 Pentagon 1 720477+ 54 1 37638+ = V1 + H5 6 Hexagon 2 598076+ 60 1 73205+ = V3 7 Heptagon . . . . ; 3.633912+ 64 2.07652 + 8 Octagon 4 828427+ 67f 2 41421+ = 1 + V2 9 Nonagon 6 181824+ 701 2.74747+ 10 Decagon . . 7 694209 72 3 07768+ = V5+2V5 11 Undecagon 9 365640 73tV 3.40568+ 12 Duodecagon 11.196152+ 75 3.73205+ = 2+V3 To Find the Area of Any Polygon. Rule: Divide the polygon into triangles and trapezoids by drawing diagonals' find the area of these as above shown, fo** the area. [90] MENSURATION To Find the Area of Any Quadrilateral Figure. Rule: Divide the quadrilateral into two triangles; the sum of the areas of the triangles is the area. Or, multiply half the product of the two diagonals by the natural sine of the angle of their intersection. NOTE. As the diagonal of a square and a rhombus intersect at right angles (the natural sine of which is 1), half the product of their diagonals is the area. To Find the Area of an Irregular Polygon or Figure of Any Number of Sides. Rule : Divide the figure into triangles and trapeziums, and find the area of each separately. Add these areas together and the sum will be the area of the whole polygon. CIRCLES The proportion of the diameter of a circle to its circumference has never yet been exactly ascertained. Nor can a square or any other right lined figure be found that shall be equal to a given circle. Though the relation between the diameter and circumference cannot be accurately expressed in known numbers, it may yet be approximated to any assigned degree of exactness. Van Ceulen, a Dutchman, in his book, "De Circulo et Adscriptis" showed that if the diameter of a circle was 1, the circumference would be 3.141592653589793 and so on to thirty-six places of decimals. This is commonly abbreviated as 1 to 3.1416. When the diameter = 1, the area is equal to .785398+, commonly abbreviated to .7854. In these ratios, the diameter and circumference are taken lineally and the area superficially. If the diameter is in inches, the circumference will be in lineal inches, the area in square inches. The circumference of a circle is commonly signified by the Greek letter TT, which indicates the length of the circumference when the diameter is 1. D = diameter of circle, TT = circumference of circle, A = area of circle, A = D 2 = .7854 D 2 . =^--= 1.1284 VA If the diameter be multiplied or divided by any number, the area must be multiplied or divided by the square of that number. Thus: Diameter = nD. Area = n 2 A. Diameter = . n Area = . The Diameter of a Circle Being Given to Find the Circumference; or, the circum- ference being given to find the diameter. Rule: Multiply the diameter by 3.1416, and the product will be the circumference, or, divide the cir- cumference by 3.1416, and the quotient will be the diameter. NOTE. 1. As 7 is to 22, so is the diameter to the circumfer- ence; or, as 22 is to 7, so is the circumference to the diameter. 2. As 113 is to 355, so is the diameter to the circumference; or, as 355 is to 113, so is the circumference to the diameter. To Find the Area of a Circle. Rule 1. Multiply half the circumference by half the diameter, and the product will be the area. Or, taKe one-fourth the product of the whole circumference and diameter. NOTE. A circle may be considered as a regular polygon of an infinite number of sides, the circumference being equal to the perimeter, and the radius to the perpendicular. But the area of a regular polygon is equal to half the [91] MENSURATION perimeter multiplied by the perpendicular, and consequently the area of a circle is equal to half the circumference multiplied by the radius, or half the diameter. Rule 2. Multiply the square of the diameter by .7854, and the product will be the area; or, multiply the square of the circumference by .07958, and the product will be the area. NOTE. All circles are to each other as the squares of their diameters. The following proportions are those of Metius and Archimedes: As 452 : 355 :: square of the diameter : area. As 14 : 11 :: square of the diameter : area. If the circumference be given instead of the diameter, the area may be found as follows: The square of the circumference X .07958 = area. As 88 : 7 : : square of the circumference : area. As 1420 : 113 :: square of the circumference : area. The following table will show most of the useful problems relating to the circle and its equal or inscribed square: Diameter X .8862 = side of an equal square. Circumference X .2821 = side of an equal square. Diameter X .7071 = side of an inscribed square. Circumference X .2251 = side of the inscribed square. Area X .6366 = side of the inscribed square. Side of a square X 1.4142 = diameter of its circumscribing circle. Side of a square X 4.443 = circumference of its circumscribing circle. Side of a square X 1.128 = diameter of an equal circle. Side of a square X 3.545 = circumference of an equal circle. Radius X 6.2832 = circumference. Circumference X .3183 = diameter. Circumference = 3.5449 A/area of a cirde. Diameter = 1.1283 Varea of a circle. Length of arc = number of degrees X .0175 radius, arc of 1 to radius 1 = 0.017453. arc of 1' to radius 1 = 0.000291. arc of 1" to radius 1 = 0.00000485. Degrees in arc whose length = radius = 57 .2958. [921 MENSURATION USEFUL FUNCTIONS OF ir = ratio of circumference to diameter = 3.1415926536 N 2N 3N 4N 5N 6N 7N 8N 9N v = 3.1416 6.2832 9.4248 12.5664 15.7080 18.8496 21.9911 25.1327 28.2743 -= 1.5708 3.1416 4.7124 6.2832 7.8540 9.4248 10.9956 12.5664 14.1372 -~= 1.0472 2.0944 3.1416 4.1888 5.2360 6.2832 7.3304 8.3776 9.4248 -f-= .7854 1.5708 2.3562 3.1416 3.9270 4.7124 5.4978 6.2832 7.0686 1T= .5236 1.0472 1.5708 2.0944 2.6180 3.1416 3.6652 4.1888 4.7124 -= .4488 .8976 1.3464 1.7952 2.2440 2.6928 3.1416 3.5904 4.0392 ~j- = .1963 .3927 .5890 .7854 .9817 1 . 1781 1.3744 1.5708 1.7671 -j= .1309 .2618 .3927 .5236 .6545 .7854 .9163 1.0472 1.1781 7T .1964 .2945 .3927 .4909 .5890 .6872 .7854 .8836 iio= - 0175 .0349 .0524 .0698 .0873 .1047 .1222 1396 .1571 7T 2 = 9.8696 19.7392 29.6088 39.4784 49.3480 59.2176 69.0872 78.9568 88.8264 7T 3 = 31.0063 -= .3183 -~= .1013 -~= .0323 62.0126 .6366 .2026 .0645 93.0188 .9549 .3040 .0968 124.0251 1.2732 .4053 .1290 155.0314 1.5915 .5066 .1613 186.0377 1.9099 .6079 .1935 217.0439 2.2282 .7092 .2258 248.0502 2.5465 .8106 .2580 279.0565 2.8648 .9119 .2903 V^= 1.7725 V~r= 1.4646 3.5449 2.9292 5.3174 4.3938 7.0898 5.8584 8.8623 7.3230 10.6347 8.7876 12.4072 10.2521 14.1796 11.7167 15.9521 13.1813 Jl= .5642 1 . 1284 1.6926 2.2568 2.8209 3.3851 3.9493 4.5135 5.0777 3^= .6828 1.3656 2.0484 2.7311 3.4139 4.0967 4.7795 5.4623 6.1451 Log TT = . 4971499 .9943 1.4915 1.9886 2.4857 2.9829 3.4800 3.9772 4.4743 [93] CIRCLES DIAMETER, CIRCUMFERENCE, AREA CIRCLES DIAMETER, CIRCUMFERENCE, AREA, AND SIDE OF EQUAL SQUARE FROM 1 TO 120 Diameter Circum- ference Area Side of Equal Square . (Square Root of Area) Diameter Circum- ference Area Side of Equal Square (Square Root of Area) 3 9.4248 7.0686 2.6586 A .1963 .00307 .0553 3& 9.6211 7.3662 2.7140 H .3927 .01227 .1107 3K 9.8175 7.6699 2.7694 A .5890 .02761 .1661 3A 10.014 7.9798 2.8248 M .7854 .04909 .2215 3M 10.210 8.2957 2.8801 A .9817 .07670 .2770 3A 10.406 8.6180 2.9355 H 1.1781 .1104 .3323 3K 10.6C2 8.9462 2.9909 A 1.3744 .1503 .3877 3^ 10.799 9.2807 3.0463 1 A 1.5708 .1963 .4431 3M 10.995 9.6211 3.1017 & 1.7771 .2485 .4984 3& 11.191 9.9680 3.1571 1.9635 .3068 .5539 3K 11.388 10.320 3.2124 tt 2.1598 .3712 .6092 3H 11.584 10.679 3.2678 3 /* 2.3562 .4417 .6646 3M 11.781 11.044 3.3232 H 2.5525 .5185 .7200 3H 11.977 11.416 3.3786 K 2.7489 .6013 .7754 3K 12.173 11.793 3.4340 if 2.9452 .6903 .8308 3H 12.369 12.177 3.4894 i 3.1416 .7854 .8862 4 12.566 12.566 3.5448 iA 3.3379 .8866 .9416 4^ 12.762 12.962 3.6002 IK 3.5343 .9940 .9969 4K 12.959 13.364 3.6555 1ft 3.7306 .1075 1.0524 4& 13.155 13.772 3.7109 iM 3.9270 .2271 1.1017 4M 13.351 14.186 3.7663 1A 4.1233 .3530 1.1631 4A 13.547 14.606 3.8217 iK 4.3197 .4848 1.2185 4K 13.744 15.033 3.8771 iA 4.5160 .6229 1.2739 4^ 13.940 15.465 3.9325 l 4.7124 1.7671 1.3293 4K 14.137 15.904 3.9880 *A 4.9087 1.9175 1.3847 4& 14.333 16.349 4.0434 if* 5.1051 2.0739 1.4401 4K 14.529 16.800 4.0987 ltt 5.3014 2.2365 .4955 4H 14.725 17.257 4.1541 iK 5.4978 2.4052 .5508 4M 14.922 17.720 4.2095 lit 5.6941 2.5800 .6062 4H 15.119 18.190 4.2648 IK 5.8905 2.7611 .6616 4K 15.315 18.665 4.3202 m 6.0868 2.9483 .7170 4M 15.511 19.147 4.3756 2 6.2832 3.1416 1.7724 5 15.708 19.635 4.4310 2A 6.4795 3.3380 1.8278 5^ 15.904 20.129 4.4864 2K 6.6759 3.5465 1.8831 5K 16.100 20.629 4.5417 2A 6.8722 3.7584 1.9385 5& 16.296 21 . 135 4.5971 2M 7.0686 3.9760 1.9939 5M 16.493 21.647 4.6525 2& 7.2649 4.2000 2.0493 5A 16.689 22.166 4.7079 2K 7.4613 4.4302 2.1047 5K 16.886 22.690 4.7633 2& 7.6576 4.6664 2.1601 5^ 17.082 23.221 4.8187 2K 7.8540 4.9087 2.2155 5K 17.278 23.758 4.8741 2& 8.0503 5.1573 2.2709 5& 17.474 24.301 4.9295 2K 8.2467 5.4119 2.3262 5K 17.671 24.850 4.9848 2H 8.4430 5.6723 2.3816 5H 17.867 25.406 5.0402 2M 8.6394 5.9395 2.4370 5M 18.064 25.967 5.0956 2H 8.8357 6.2126 2.4924 5H 18.231 26.535 5.1510 2K 9.0321 6.4918 2.5478 5K 18.457 27.108 5.2064 2H 9.2284 6.7772 2.6032 5H 18.653 27.688 5.2618 [94 CIRCLES DIAMETER, CIRCUMFERENCE, AREA CIRCLES DIAMETER, CIRCUMFERENCE, AREA, ETC. (Cont.) Diame- ter Circum- ference Area Side of Equal Square (Square Root of Area) Diameter Circum- ference Area Side of Equal Square (Square Root of Area) 6 18.849 28.274 5.3172 H^ 36.128 103.869 10.191 Q l /s 19.242 29.464 5.4280 11^ 36.521 106.139 10.302 VA 19.635 30.679 5.5388 11% 36.913 108.434 10.413 W/8 20.027 31.919 5.6495 W/s 37.306 110.753 10.523 V/2 20.420 33.183 5.7603 Q 5 /8 20.813 34.471 5.8711 12 37.699 113.097 10.634 6% 21.205 35.784 5.9819 12^ 38.091 115.466 10.745 V/8 21.598 37.122 6.0927 12^ 38.484 117.859 10.856 12^ 38.877 120.276 10.966 7 21.991 38.484 6.2034 12^ 39.270 122.718 11.077 7 l /8 22.383 39.871 6.3142 12% 39.662 125.184 11.188 7% 22.776 41.282 6.4350 12% 40.055 127.676 11.299 1H 23.169 42.718 6.5358 12ft 40.448 130.192 11.409 7H 23.562 44.178 6.6465 1Y* 23.954 45.663 6.7573 13 40.840 132.732 11.520 1% 24.347 47.173 6.8681 13H 41.233 135.297 11.631 1% 24.740 48.707 6.9789 I3H 41.626 137.886 11.742 13% 42.018 140.500 11.853 8 25.132 50.265 7.0897 133^ 42.411 143.139 11.963 8^ 25.515 51.848 7.2005 13% 42.804 145.802 12.074 8% 25.918 53.456 7.3112 13% 43.197 148.489 12.185 m 26.310 55.088 7.4220 13% 43.589 151.201 12.296 V/2 26.703 56.745 7.5328 8% 27.096 58.426 7.6436 14 43.982 153.938 12.406 8% 27.489 60.132 7.7544 14% 44.375 156.699 12.517 S 7 /8 27.881 61.862 7.8651 14% 44.767 159.485 12.628 14% 45.160 162.295 12.739 9 28.274 63.617 7.9760 14% 45.553 165.130 12.850 9H 28.667 65.396 8.0866 14% 45.945 167.989 12.960 9% 29.059 67.200 8.1974 14% 46.338 170.873 13.071 9% 29.452 69.029 8.3081 14% 46.731 173.872 13.182 9^ 29.845 70.882 8.4190 9% 30.237 72.759 8.5297 15 47.124 176.715 13.293 9% 30.630 74.662 8.6405 15% 47.516 179.672 13.403 $ 7 /8 31.023 76.588 8.7513 15% 47.909 182.654 13.514 15% 48.302 185.661 13.625 10 31.416 78.540 8.8620 15% 48.694 188.692 13.736 10% 31.808 80.515 8.9728 15% 49.087 191.748 13.847 10% 32.201 82.516 9.0836 15% 49.480 194.828 13.957 10% 32.594 84.540 9.1943 15% 49.872 197.933 14.068 10% 32.986 86.590 9.3051 10% 33.379 88.664 9.4159 16 50.265 201.062 14.179 10% 33.772 90.762 9.5267 16% 50.658 204.216 14.290 10K 34.164 92.885 9.6375 16% 51.051 207.394 14.400 16% 51.443 210.597 14.511 11 34.557 95.033 9.7482 16% 51.836 213.825 14.622 11H 34.950 97.205 9.8590 16% 52.229 217.077 14.732 11% 35.343 99.402 9.9698 16% 52.621 220.353 14.843 11% 35.735 101.623 10.080 16% 53.014 223.654 14.954 [95] CIRCLES DIAMETER, CIRCUMFERENCE, AREA CIRCLES DIAMETER, CIRCUMFERENCE,. AREA, ETC. (Cont.) Diameter Circum- ference Area Side of Equal Square (Square Root of Area) Diameter Circum- ference Area Side of Equal Square (Square Root of Area) 17 53.407 226.980 15.065 22% 70.686 397.608 19.939 WH 53.799 230.330 15.176 22% 71.078 402.038 20.050 17H 54.192 233.705 15.286 22% 71.471 406.493 20.161 17% 54.585 237.104 15.397 22y 8 71.864 410.972 20.271 17H 54.978 240.528 15.508 i7H 55.370 243.977 15.619 23 72.256 415.476 20.382 im 55.763 247.450 15.730 23% 72.649 420.004 20.493 17% 56.156 250.947 15.840 23% 73.042 424.557 20.604 23% 73.434 429.135 20.715 18 56.548 254.469 15.951 23% 73.827 433.731 20.825 18% 56.941 258.016 16.062 23% 74.220 438.363 20.936 mi 57.334 261.587 16.173 23% 74.613 443.014 21.047 18% 57.726 265.182 16.283 23% 75.005 447.699 21.158 18^ 58.119 268.803 16.394 1SH 58.512 272.447 16.505 24 75.398 452.390 21.268 18% 58.905 276.117 16.616 24% 75.791 457.115 21.379 18% 59.297 279.811 16.727 24% 76.183 461.864 21.490 24% 76.576 46'6.638 21.601 19 59.690 283.529 16.837 24H 76.969 471.436 21.712 19% 60.083 287.272 16.948 24% 77.361 476.259 21.822 19% 60.475 291.039 17.060 24% 77.754 481 . 106 21.933 19% 60.868 294.831 17.170 24% 78.147 485.978 22.044 19% 61.261 298.648 17.280 19% 61.653 302.489 17.391 25 78.540 490.875 22.155 19% 62.046 306.355 17.502 25% 78.932 495.796 22.265 19% 62.439 310.245 17.613 25% 79.325 500.741 22.376 25% 79.718 505.711 22.487 20 62.832 314.160 17.724 25^ 80.110 510.706 22.598 20% 63.224 318.099 17.834 25% 80.503 515.725 22.709 20% 63.617 322.063 17.945 25% 80.896 520.769 22.819 20% 64.010 326.051 18.056 25% 81.288 525.837 22.930 20% 64.402 330.064 18.167 20% 64.795 334.101 18.277 26 81.681 530.930 23.041 20% 65.188 338.163 18.388 26% 82.074 536.047 23.152 20% 65.580 342.250 18.499 26% 82.467 541 . 189 23.262 26% 82.859 546.356 23.373 21 65.973 346.361 18.610 26^ 83.252 551.547 23.484 21% 66.366 350.497 18.721 26% 83.645 556.762 23.595 21M 66.759 354.657 18.831 26% 84.037 562.002 23.708 21H 67.151 358.841 18.942 26% 84.430 567.267 23.816 21H 67.544 363.051 19.053 21% 67.937 367.284 19.164 27 84.823 572.556 23.927 21% 68.329 371.543 19.274 27% 85.215 577.870 24.038 21% 68.722 375.826 19.385 27% 85.608 583.208 24.149 27% 86.001 588.571 24.259 22 69.115 380.133 19.496 27^ 86.394 593.958 24.370 22% 69.507 384.465 19.607 27% 86.786 599.370 24.481 22% 69.900 388.822 19.718 27% 87.179 604.807 24.592 22% 70.293 393.203 19.828 27% 87.572 610.268 24.703 [96] CIRCLES DIAMETER, CIRCUMFERENCE, AREA CIRCLES DIAMETER, CIRCUMFERENCE, AREA, ETC. (Cont.) : Diameter Circum- ference Area Side of Equal Square (Square Root of Area) Diameter Circum- ference Area Side of Equal Square (Square Root of Area) 28 87.964 615.753 ' 24.813 33% 105.243 881.41 29.687 28 y 8 88.357 621.263 24.924 33% 105.636 888.00 29.798 28% 88.750 626.798 25.035 33% 106.029 894.61 29.909 28% 89.142 632.357 25.146 33% 106.421 901.25 30.020 28% 89.535 637.941 25.256 28% 89.928 643.594 25.367 34 106.814 907.92 30.131 28% 90.321 649.182 25.478 34% 107.207 914.61 30.241 28% 90.713 654.839 25.589 34% 107.599 921.32 30.352 34% 107.992 928.06 30.463 29 91.106 660.521 25.699 34% 108.385 934.82 30.574 29% 91.499 666.227 25.810 34% 108.777 941.60 30.684 29% 91.891 671.958 25.921 34% 109.170 948.41 30.795 29% 92.284 677.714 26.032 34% 109.563 955.25 30.906 29% 92.677 683.494 26.143 29% 93.069 689.298 26.253 35 109.956 962.11 31.017 29% 93.462 695.128 26.364 35% 110.348 968.99 31 . 128 29% 93.855 700.981 26.478 35% 110.741 975.90 31.238 35% 111.134 982.84 31.349 30 94.248 706.860 26.586 35% 111.526 989.80 31.460 30% 94.640 712.762 26.696 35% 111.919- 996.78 31.571 30% 95.033 718.690 26.807 35% 112.312 1003.78 31.681 30% 95.426 724.641 26.918 35% 112.704 1010.82 31.792 30^ 95.818 730.618 27.029 30% 96.211 736.619 27.139 36 113.097 1017.87 31.903 30% 96.604 742.644 27.250 36% 113.490 1024.95 32.014 30% 96.996 748.694 27.361 36% 113.883 1032.06 32.124 36% 114.275 1039.19 32.235 31 97.389 754.769 27.472 36% 114.668 1046.35 32.349 31% 97.782 760.868 27.583 36% 115.061 1053.52 32.457 31M 98.175 766.992 27.693 36% 115.453 1060.73 32.567 31K 98.567 773.140 27.804 36% 115.846 1067.95 32.678 31H 98.968 779.313 27.915 31% 99.353 785.510 28.026 37 116.239 1075.21 32.789 31% 99.745 791.732 28.136 37% 116.631 1082.48 32.900 31% 100.138 797.978 28.247 37% 117.024 1089.79 33.011 37% 117.417 1097.11 33.021 32 100.531 804.249 28.358 37% 117.810 1104.46 33.232 32% 100.924 810.545 28.469 37% 118.202 1111.84 33.343 32% 101.316 816.865 28.580 37% 118.595 1119.24 33.454 32% 101.709 823.209 28.691 37% 118.988 1126.66 33.564 32% 102.102 829.578 28.801 32% 102.494 835.972 28.912 38 119.380 1134.11 33.675 32% 102.887 842.390 29.023 38% 119.773 1141.59 33.786 32% 103.280 848.833 29.133 38% 120.166 1149.08 33.897 ' 38% 120.558 1156.61 34.008 33 103.672 855.30 29.244 38% 120.951 1164.15 34.118 33% 104.055 861 . 79 29.355 38% 121.344 1171.73 34.229 33% 104.458 868.30 29.466 38% 121.737 1179.32 34.340 33% 104.850 874.84 29.577 38% 122.129 1186.94 34.451 [97] CIRCLES DIAMETER, CIRCUMFERENCE, AREA CIRCLES DIAMETER, CIRCUMFERENCE, AREA, ETC. (Cont,) Diameter Circum- ference Area Side of Equal Square (Square Root of Area) Diameter Circum- ference Area Side of Equal Square (Square Root of Area) 39 122.522 1194.59 34.561 44% 139.801 1555.28 39.436 39% 122.915 1202.26 34.672 44% 140.193 1564.03 39.546 39M 123.307 1209.95 34.783 44% 140.586 1572.81 39.657 39% 123.700 1217.67 34.894 44% 140.979 1581.61 39.768 39% 124.093 1225.42 35.005 39% 124.485 1233.18 35.115 45 141.372 1590.43 39.879 39% 124.878 1240.98 35.226 45% 141.764 1599.28 39.989 39% 125.271 1248.79 35.337 45K 142.157 1608.15 40.110 45^ 142.550 1617.04 40.211 40 125.664 1256.64 35.448 45^ 142.942 1625.97 40.322 40% 126.056 1264.50 35.558 45% 143.335 1634.92 40.432 40% 126.449 1272.39 35.669 45M 143.728 1643.89 40.543 40% 126.842 1280.31 35.780 45^ 144.120 1652.88 40.654 40% 127.234 1288.25 35.891 40% 127.627 1296.21 36.002 46 144.513 1661.90 40.765 40% 128.020 1304.20 36.112 46K 144.906 1670.95 40.876 40% 128.412 1312.21 36.223 46M 145.299 1680.01 40.986 46% 145.691 1689.10 41.097 41 128.805 1320.25 36.334 46^ 146.084 1698.23 41.208 41% 129.198 1328.32 36.445 46% 146.477 1707.37 41.319 41% 129.591 1336.40 36.555 46M 146.869 1716.54 41.429 41% 129.983 1344.51 36.666 46% 147.262 1725.73 41.540 41% 130.376 1352.65 36.777 41% 130.769 1360.81 36.888 47 147.655 1734.94 41.651 41% 131.161 1369.00 36.999 47% 148.047 1744.18 41.762 41% 131.554 1377.21 37.109 47M 148.440 1753.45 41.873 47% 148.833 1762.73 41.983 42 131.947 1385.44 37.220 47% 149.226 1772.05 42.094 42% 132.339 1393.70 37.331 47% 149.618 1781.39 42.205 42% 132.732 1401.98 37.442 47% 150.011 1790.76 42.316 42% 133.125 1410.29 37.552 47% 150.404 1800.14 42.427 42% 133.518 1418.62 37.663 42% 133.910 1426.98 37.774 48 150.796 1809.56 42.537 42% 134.303 1435.36 37.885 48% 151.189 1818.99 42.648 42% 134.696 1443.77 37.996 48M 151.582 1828.46 42.759 48% 151.974 1837.93 42.870 43 135.088 1452.20 38.106 48% 152.367 1847.45 42.980 43% 135.481 1460.65 38.217 48% 152.760 1856.99 43.091 43% 135.874 1469.13 38.328 48% 153.153 1866.55 43.202 43% 136.266 1477.63 38.439 48% 153.545 1876.13 43.313 43% 136.659 1486.17 38.549 43% 137.052 1494.72 38.660 49 153.938 1885.74 43.423 43% 137.445 1503.30 38.771 49% 154.331 1895.37 43.534 43% 137.837 1511.90 38.882 49M 154.723 1905.03 43.645 49% 155.116 1914.70 43.756 44 138.230 1520.53 38.993 49% 155.509 1924.42 43.867 44% 138.623 1529.18 39.103 49% 155.901 1934.15 43.977 44% 139.015 1537.86 39.214 49% 156.294 1943.91 44.088 44% 139.408 1546.55 39.325 49% 156.687 1953.69 44.199 [98] CIRCLES DIAMETER, CIRCUMFERENCE, AREA CIRCLES DIAMETER, CIRCUMFERENCE, AREA, ETC. (Coni.) Diameter Circum- ference Area Side of Equal Square (Square Root of Area) Diameter Circum- [; ference Area Side of Equal Square (Square Root of Area) 50 157.080 1963.50 44.310 60 188.496 2827.44 53.172 50% 157.865 1983.18 44.531 60% 189.281 2851.05 53.393 50^ 158.650 2002.96 44.753 60^ 190.066 2874.76 53.615 ' 50% 159.436 2022.84 44.974 60% 190.852' 2898.56 53.836 51 160.221 2042.82 45.196 61 191.637 2922.47 54.048 51% 161.007 2062.90 45.417 61% 192.423 2946.47 54.279 5iy 2 161.792 2083.07 45.639 61H 193.208 2970.57 54.501 51% 162.577 2103.35 45.861 MX 193.993. 2994.77 54.723 52 163.363 2123.72 46.082 62 194.779 3019.07 54.944 52% 164.148 2144.19 46.304 62% 195.564 3043.47 55.166 52^ 164.934 2164.75 46.525 62^ 196.350 3067.96 55.387 52% 165.719 2185.42 46.747 62% 197.135 3092.56 55.609 53 166.504 2206.18 46.968 63 197.920 3117.25 55.830 53% 167.290 2227.05 47.190 63% 198.706 3142.04 56.052 53^ 168.075 2248.01 47.411 63^ 199.491 3166.92 56.273 53% 168.861 2269.06 47.633 63% 200.277 3191.91 56.495 54 169.646 2290.22 47.854 64 201.062 3216.99 56.716 54% 170.431 2311.48 48.076 64% 201.847 3242.17 56.938 54^ 171.217 2332.83 48.298 64^ 202.633 3267.46 57.159 54% 172.002 2354.28 48.519 64% 203.418 3292.83 57.381 55 172.788 2375.83 48.741 65 204.204 3318.31 57.603 55% 173.573 2397.48 48.962 65M 204.989 3343.88 57.824 55^ 174.358 2419.22 49.184 65^ 205.774 3369.56 58.046 55% 175.144 2441.07 49.405 65% 206.560 3395.33 58.267 56 175.929 2463.01 49.627 66 207.345 3421.20 58.489 56% 176.715 2485.05 49.848 66M 208.131 3447.16 58.710 56^ 177.500 2507.19 50.070 66^ 208.916 3473.23 58.932 56% 178.285 2529.42 50.291 66% 209.701 3499.39 59.154 57 179.071 2551.76 50.513 67 210.487 3525.66 59.375 57% 179.856 2574.19 50.735 67% 211.272 3552.01 59.597 57^ 180.642 2596.72 50.956 67^ 212.058 3578.47 59.818 57% 181.427 2619.35 51.178 67% 212.843 3605.03 60.040 58 182.212 2642.08 51.399 68 213.628 3631.68 60.261 58% 182.998 2664.91 51.621 68% 214.414 3658.44 60.483 58^ 183.783 2687.83 51.842 68^ 215.199 3685.29 60.704 58% 184.569 2710.85 52.064 68% 215.985 3712.24 60.926 59 185.354 2733.97 52.285 69 216.770 3739.28 61 . 147 59% 186.139 2757.19 52.507 69% 217.555 3766.43 61.369 59H 186.925 2780.51 52.729 69^ 218.341 3793.67 61.591 59% 187.710 2803.92 52.950 69% 219.126 3821.02 61.812 [99] CIRCLES DIAMETER, CIRCUMFERENCE, AREA CIRCLES DIAMETER, CIRCUMFERENCE, AREA, ETC. (Cont.) Diameter Circum- ference Area Side of Equal Square (Square Root of Area) Diameter Circum- ference Area Side of Equal Square (Square Root of Area) 70 219.912 3848.46 62.034 80 251.328 5026.56 70.896 70% 220.697 3875.99 62.255 80% 252.113 5058.00 71.118 70^ 221.482 3903.63 62.477 80^ 252.898 5089.58 71.339 70% 222.268 3931.36 62.698 80% 253.683 5121.22 71.561 71 223.053 3959.20 62.920 81 254.469 5153.00 71 . 782 71 % 223.839 3987.13 63.141 81 % 255.254 5184.84 72.004 ny 2 224.624 4015.16 63.363 81^ 256.040 5216.82 72 . 225 71% 225.409 4043.28 63.545 81% 256.825 5248.84 72.447 72 226.195 4071.51 63.806 82 257.611 5281.02 72.668 72% 226.980 4099.83 64.028 82% 258.396 5313.28 72.890 72H 227.766 4128.25 64.249 82^ 259.182 5345.62 73.111 72% 228.551 4156.77 64.471 82% 259.967 5378.04 73.333 73 229.336 4185.39 64.692 83 260.752 5410.62 73.554 73% 230.122 4214.11 64.914 83% 261.537 5443.24 73.776 73^ 230.907 4242.92 65.135 83^ 262.323 5476.00 73.997 73% 231.693 4271.83 65.357 83% 263.108 5508.84 74.219 74 232.478 4300.85 65.578 84 263.894 5541.78 74.440 74% 233.263 4329.95 65.800 84^ 264.679 5574.80 74.662 74^ 234.049 4359.16 66.022 84^ 265.465 5607.95 74.884 74% 234.834 4388.47 66.243 84% 266.250 5641 . 16 75.106 75 235.620 4417.87 66.465 85 267.036 5674.51 75.327 75% 236.405 4447.37 66.686 85M 267.821 5707.92 75.549 75^ 237.190 4476.97 66.908 85^ 268.606 5741.47 75.770 75% 237.976 4506.67 67.129 85% 269.392 5775.09 75.992 76 238.761 4536.47 67.351 86 270.177 5808.81 76.213 76% 239.547 4566.36 67.572 86M 270.962 5842.60 76.435 76^ 240.332 4596.35 67.794 86^ 271.748 5876.55 76.656 76% 241.117 4626.44 68.016 86% 272.533 5910.52 76.878 77 241.903 4656.63 68.237 87 273.319 5944.69 77.099 77% 242.688 4686.92 68.459 87% 274.104 5978.88 77.321 77^ 243.474 4717.30 68.680 87^ 274.890 6013.21 77.542 77% 244.259 4747.79 68.902 87% 275.675 6047.60 77.764 78 245.044 4778.37 69.123 88 276.460 6082.13 77.985 78% 245.830 4809.05 69.345 88% 277.245 6116.72 78.207 78^ 246.615 4839.83 69.566 88^ 278.031 6151.44 78.428 78% 247.401 4870.70 69.788 88% 278.816 6186.20 78.650 79 248.186 4901.68 70.009 89 279.602 6221.15 78.871 79% 248.971 4932.75 70.231 89% 280.387 6256.12 79.093 79^ 249.757 4963.92 70.453 89^ 281 . 173 6291.25 79.315 79% 250.542 4995.19 70.674 89% 281.958 6326.44 79.537 100] CIRCLES DIAMETER, CIRCUMFERENCE *A jtEA i CIRCLES DIAMETER, CIRCUMFERENCE, AREA, ETC. (Cont.) Side of Side of Equal Equal Diameter Circum- ference Area Square (Square Diameter Circum- ference Area Square (Square Root Root of Area) of Area) 90 282.744 6361.74 79.758 101 317.301 8011.84 89.509 90% 283.529 6399.12 79.980 101** 318.872 8091.36 89.952 90** 90% 284.314 285.099 6432.62 6468.16 80.201 80.423 102 102** 320.442 322.014 8171.28 8251.60 90.395 90.838 91 285.885 6503.89 80.644 103 323.584 8332.29 91.282 91% 286.670 6539.68 80.866 103*6 325.154 8413.40 91.725 91** 287.456 6573.56 81.087 91% 288.242 6611.52 81.308 104 326.726 8494.87 92.168 104** 328.296 8576.76 92.611 92 92% 92** 289.027 289.812 290.598 6647.62 6683.80 6720.07 81.530 81.752 81.973 105 105** 329.867 331.438 8659.01 8741.68 93.054 93.497 92% 291.383 6756.40 82.195 106 333.009 8824.73 93.940 106** 334.580 8908.20 94.383 93 292.168 6792.92 82.416 93% 292.953 6829.48 82.638 107 336.150 8992.02 94.826 293.739 6866.16 82.859 107** 337.722 9076.24 95.269 93% 294.524 6882.92 83.081 108 339.292 9160.88 95.713 94 295.310 6939.79 83.302 108** 340.862 9245.92 96.156 94% 296.095 6976.72 83.524 109 342.434 9331.32 96.599 94^ 296.881 7013.81 83.746 109** 344.004 9417.12 97.042 94% 297.666 7050.92 83.968 110 345.575 9503.32 97.485 95 298.452 7088.23 84.189 110** 347.146 9589.92 97.928 95% 95** 95% 299.237 300.022 300.807 7125.56 7163.04 7200.56 84.411 84.632 84.854 111 HI** 348.717 350.288 9676.89 9764.28 98.371 98.815 96 96% 301.593 302.378 7238.24 7275.96 85.077 85.299 112 112** 351.858 353.430 9852.03 9940.20 99.258 99.701 96** 302.164 7313.84 85.520 113 355.000 10028.75 100.144 96% 303.948 7351.82 85.742 113*^ 356.570 10117.68 100.587 97 304.734 7389.80 85.963 114 358.142 10207.03 101.031 97% 305.520 7427.96 86.185 114** 359.712 10296.76 101.474 97** 97% 306.306 307.090 7474.20 7504.52 86.407 86.628 115 361.283 362.854 10386.89 10477.40 101.917 102.360 98 98% 98** 307.876 308.662 309.446 7452.96 7581.48 7620,12 86.850 87.072 87.293 116 116** 364.425 365.996 10568.32 10659.64 102.803 103.247 98% 310.232 7658.80 87.515 117 367.566 10751.32 103.690 117** 369.138 10843.40 104.133 99 311.018 7697.68 87.736 99% 311.802 7736.60 87.958 118 370.708 10935.88 104.576 99** 312.588 7775.64 88.180 118** 372.278 11028.76 105.019 99% 313.374 7814.76 88.401 119 373.849 11122.02 105.463 100 314.159 7854.00 88.623 119*6 375.420 11215.68 105.906 100** 315.730 7932.72 89.066 120 376.991 11309.73 106.350 [101 GIRDLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS OF CIRCLES, SQUARES, CUBES, SQUARE AND CUBE ROOTS FROM 1 TO 1,000 Number or Diameter Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 1 3.1416 0.7854 1 1 1.000 1.000 1.000000 2 6.28 3.14 4 8 1.414 .259 .500000 3 9.42 7.07 9 27 1.732 .442 .333333 4 12.57 12.57 16 64 2.000 .587 .250000 5 15.71 19.63 25 125 2.236 .709 .200000 6 18.85 28.27 36 216 2.449 .817 .166667 7 21.99 38.48 49 343 2.645 .912 .142857 8 25.13 50.26 64 512 2.828 2.000 .125000 9 28.27 63.61 81 729 3.000 2.080 .111111 10 31.42 78.54 100 1,000 3.162 2.154 .100000 11 34.55 95.03 121 1,331 3.316 2.223 .090909 12 37.69 113.09 144 1,728 3.464 2.289 .083333 13 40.84 132.73 169 2,197 3.605 2.351 .076923 14 43.98 153:93 196 2,744 3.741 2.410 .071429 15 47.12 173.71 225 3,375 3.872 2.466 .066667 16 50.26 201.06 256 4,096 4.000 2.519 .062500 17 53.40 226.98 289 4,913 4.123 2.571 .058824 18 56.54 254.46 324 5,832 4.232 2.620 .055556 19 59.69 283.52 361 6,859 4.358 2.668 .052632 20 62.83 314.15 400 8,000 4.472 2.714 .050000 21 65.97 346.36 441 9,261 4.582 2.758 .047619 22 69.11 380.13 484 10,648 4.690 2.802 .045455 23 72.25 415.47 529 12,167 4.795 2.843 .043478 24 75.39 452.38 576 13,824 4.898 2.884 .041667 25 78.54 490.87 625 15,625 5.000 2.924 .040000 26 81.68 530.02 676 17,576 5.099 2.962 .038462 27 84.82 572.55 729 19,683 5.196 3.000 .037037 28 87.96 615.75 784 21,952 5.291 3.036 .035714 29 91.10 660.52 841 24,389 5.385 3.072 .034483 30 94.24 706.85 900 27,000 5.477 3.107 .033333 31 97.38 754.76 961 29,791 5.567 3.141 .032258 32 100.53 804.24 1,024 32,768 5.656 3.174 .031250 33 103.67 855.29 1,089 35,937 5.744 3.207 .030303 34 106.81 907.92 1,156 39,304 5.830 3.239 .029412 35 109.95 962.11 1,225 42,875 5.916 3.271 .028571 36 113.09 1017.87 1,296 46,656 6.000 3.301 .027778 37 116.23 1075.21 1,369 50,653 6.082 3.332 .027027 38 119.38 1134.11 ,444 54,872 6.164 3.361 .026316 39 122.52 1194.59 ,521 59,319 6.244 3.391 .025641 40 125.66 1256.63 ,600 64,000 6.324 3.419 .025000 41 128.80 1320.25 ,681 68,921 6.403 3.448 .024390 42 131.94 1385.44 ,764 74,088 6.480 3.476 .023810 43 135.08 1452.20 ,849 79,507 6.557 3.503 .023256 44 138.23 1520.52 ,936 85,184 6.633 3.530 .022727 45 141.37 1590.43 2,025 91,215 6.708 3.556 .022222 [102] CIRCLES AREAS, SQUARES, CUBES, ETC, NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) M 1 s Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 46 144.51 1661.90 2,116 97,336 6.782 3.583 .021739 47 147.65 1734.94 2,209 103,823 6.855 3.608 .021277 48 150.79 1809.55 2,304 110,592 6.928 3.634 .020833 49 153.93 1885.74 2,401 117,649 7.000 3.659 .020408 50 157. Q8 1963.49 2,500 125,000 7.071 3.684 .020000 51 160.22 2042.82 2,601 132,651 7.141 3.708 .019608 52 163.36 2123.71 2,704 140,608 7.211 3.732 .019231 53 166.50 2206.18 2,809 148,877 7.280 3.756 .018868 54 169.64 2290.21 2,916 157,464 7.348 3.779 .018519 55 172.78 2375.82 3,025 166,375 7.416 3.802 .018182 56 175.92 2463.09 3,136 175,616 7.483 3.825 .017857 57 179.07 2551.75 3,249 185,193 7.549 3.848 .017544 58 182.21 2642.08 3,364 195,112 7.615 3.870 .017241 59 185.35 2733.97 3,481 205,379 7.681 3.892 .016949 60 188.49 2827.43 3,600 216,000 7.745 3.914 .016667 61 191.63 2922.46 3,721 226,981 7.810 3.936 .016393 62 194.77 3019.07 3,844 238,328 7.874 3.957 .016129 63 197.92 3117.24 3,969 250,047 7.937 3.979 .015873 64 201.06 3216.99 4,096 262,144 8.000 4.000 .015625 65 204.20 3318.30 4,225 274,625 8.062 4.020 .015385 66 207.34 3421.18 4,356 287,496 8.124 4.041 .015152 67 210.48 3525.65 4,489 300,763 8.185 4.061 .014925 68 213.62 3631.68 4,624 314,432 8.246 4.081 .014706 69 216.77 3739.28 4,761 328,509 8.306 4.101 .014493 70 219.91 3848.45 4,900 343,000 8.366 4.121 .014286 71 223.05 3959.19 5,041 357,911 8.426 4.140 .014085 72 226.19 4071.50 5,184 373,248 8.485 4.160 .013889 73 229.33 4185.38 5,329 389,017 8.544 4.179 .013699 74 232.47 4300.84 5,476 405,224 8.602 4.198 .013514 75 235.61 4417.86 5,625 421,875 8.660 4.217 .013333 76 238.76 4536.45 5,776 438,976 8.717 4.235 .013158 77 241.90 4656.62 5,929 456,533 8.744 4.254 .012987 78 245.04 4778.36 6,084 474,552 8.831 4.272 .012821 79 248.18 4901.66 6,241 493,039 8.888 4.290 .012658 80 251.32 5026.54 6,400 512,000 8.944 4.308 .012500 81 254.46 5153.00 6,561 531,441 9.000 4.326 .012346 82 257.61 5281.01 6,724 551,368 9.055 4.344 .012195 83 260.75 5410.59 6,889 571,787 9.110 4.362 .012048 84 263.89 5541.77 7,056 592,704 9.165 4.379 .011905 85 267.03 5674.50 7,225 614,125 9.219 4.396 .011765 86 270.17 5808.80 7,396 636,056 9.273 4.414 .011628 87 273.31 5944.67 7,569 658,503 9.327 4.431 .011494 88 276.46 6082.11 7,744 681,472 9.380 4.447 .011364 89 279.60 6221 . 13 7,921 704,969 9.433 4.461 .011236 90 282.74 6361.72 8,100 729,000 9.486 4.481 .011111 [103] CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) Number or Diameter Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 91 285.88 6503.87 8,281 753,571 9.539 4.497 .010989 92 289.02 6647.61 8,464 778,688 9.591 4.514 .010870 93 292.16 6792.90 8,649 804,357 9.643 4.530 .010753 94 295.31 6939.78 8,836 830,584 9.695 4.546 .010638 95 298.45 7088.21 9,025 857,375 9.746 4.562 .010526 96 301.59 7238.23 9,216 884,736 9.797 4.578 .010417 97 304.73 7389.81 9,409 912,673 9.848 4.594 .010309 98 307.87 7542.96 9,604 941,192 9.899 4.610 .010204 99 311.01 7697.68 9,801 970,299 9.949 4.626 .010101 100 314.15 7853.97 10,000 1,000,000 10.000 4.641 .010000 101 317.30 8011.86 10,201 1,030,301 10.049 4.657 .009901 102 320.41 8171.30 10,404 1,061,208 10.099 4.672 .009804 103 323.58 8332.30 10,609 ,092,727 10.148 4.687 .009709 104 326.72 8494.88 10,816 ,124,864 10.198 4.702 .009615 105 329.86 8659.03 11,025 ,157,625 10.246 4.717 .009524 106 333.00 8824.75 11,236 ,191,016 10.295 4.732 .009434 107 336.15 8992.04 11,449 ,225,043 10.344 4.747 .009346 108 339.29 9160.90 11,664 ,259,712 10.392 4.762 .009259 109 342.43 9331.33 11,881 ,295,029 10.440 4.776 .009174 110 345.57 9503.34 12,100 1,331,000 10.488 4.791 .009091 111 348.71 9676.91 12,321 1,367,631 10.535 4.805 .009009 112 351.85 9852.05 12,544 1,404,928 10.583 4.820 .008929 113 355.01 10028.77 12,759 1,442,897 10.630 4.834 .008850 114 358.14 10207.05 12,996 1,481,544 10.677 4.848 .008772 115 361.28 10386.91 13,225 1,520,875 10.723 4.862 .008696 116 364.42 10568.34 13,456 1,560,896 10.770 4.876 .008621 117 367.56 10751.34 13,689 1,601,613 10.816 4.890 .008547 118 370.70 10935.90 13,924 1,643,032 10.862 4.904 .008475 119 373.81 11122.04 14,161 1,685,159 10.908 4.918 .008403 120 376.99 11309.76 14,400 1,728,000 10.954 4.932 .008333 121 380.13 11499.04 14,641 1,771,561 11.000 4.946 .008264 122 383.27 11689.89 14,884 1,815,848 11.045 4.959 .008197 123 386.41 11882.31 15,129 1,860,867 11.090 4.973 .008130 124 389.55 12076.31 15,376 1,906,624 11.135 4.986 .008065 125 392.70 12271.87 15,625 1,953,125 11.180 5.000 .008000 126 395.84 12469.01 15,876 2,000,376 11.224 5.013 .007937 127 398.98 12667.71 16,129 2,048,383 11.269 5.026 .007874 128 402.12 12867.99 16,384 2,097,152 11.313 5.039 .007c?13 129 405.26 13069.84 16,641 2,146,689 11.357 5.052 .007752 130 408.10 13273.26 16,900 2,197,000 11.401 5.065 .007692 131 411.54 13478.24 17,161 2,248,091 11.445 5.078 .007634 132 414.69 13694.80 17,424 2,299,968 11.489 5.091 .007576 133 417.83 13892.94 17,689 2,352,637 11.532 5.104 .007519 134 420.97 14102.64 17.956 2,406,104 11.575 5.117 .007463 135 424.11 14313.91 18^225 2,460,375 11.618 5.129 .007407 [104] CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) Number or Diameter ' Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 136 427.25 14526.75 18,496 2,515,456 11.661 5.142 .007353 137 430.39 14741.17 18,769 2,571,353 11.704 5.155 .007299 138 433.54 14957.15 19,044 2,620,872 11.747 5.167 .007246 139 436.68 15174.71 19,321 2,685,619 11.789 5.180 .007194 140 439.82 15393.84 19,600 2,744,000 11.832 5.192 .007143 141 442.96 15614.53 19,881 2,803,221 11.874 5.204 .007092 142 446.10 15836.80 20,164 2,863,288 11.916 5.217 .007042 143 449.24 16060. 541 1699.60 229871.65 292,681 158,340,421 23.259 8.148 .001848 542 1702.74 230722.24 293,764 159,220,088 23.281 8.153 .001845 543 1705.88 231574.40 294,849 160,103,007 23.302 8.158 .001842 544 1709.03 232428.13 295,936 160,989,184 23.324 8.163 .001838 545 1712.17 233283.43 297,025 161,878,625 23.345 8.168 .001835 546 1715.31 234140.30 298,116 162,771,336 23.367 8.173 .001832 547 1718.45 234998.74 299,209 163,667,323 23.388 8.178 .001828 548 1721.59 235858.76 300,304 164,566,592 23.409 8.183 .001825 549 1724.73 236720.34 301,401 165,469,149 23.431 8.188 .001821 550 1727.88 237583.50 302,500 166,375,000 23.452 8.193 .001818 551 1731.02 238448.22 303,601 167,284,151 23.473 8.198 .001815 552 1734.16 239314.52 304,704 168,196,608 23.495 8.203 .001812 553 1737.30 240182.38 305,809 169,112,377 23.516 8.208 .001808 554 1740.44 241051.82 306,916 170,031,464 23.537 8.213 .001805 555 1743.58 241922.83 308,025 170,953,875 23.558 8.218 .001802 556 1746.72 242795.41 309,136 171,879,616 23.579 8.223 .001799 557 1749.77 243669.56 310,249 172,808,693 23.601 8.228 .001795 558 1753.09 244545.28 311,364 173,741,112 23.622 8.233 .001792 559 1756.15 245422.57 312,481 174,676,879 23.643 8.238 .001789 560 1759.29 246301.44 313,600 175,616,000 23.664 8.242 .001786 561 1762.43 247181.87 314,721 176,558,481 23.685 8.247 .001783 562 1765.57 248063.87 315,844 177,504,328 23.706 8.252 .001779 563 1768.72 248947.45 316,969 178,453,547 23.728 8.257 .001776 564 1771.86 249832.59 318,096 179,406,144 23.749 8.262 .001773 565 1775.00 250719.31 319,225 180,362,125 23.769 8.267 .001770 566 1778.14 251607.60 320,356 181,321,496 23.791 8.272 .001767 567 1781.28 252497.36 321,489 182,284,263 23.812 8.277 .001764 568 1784.42 253388.88 322,624 183,250,432 23.833 8.282 .001761 569 1787.57 254281.88 323,761 184,220,009 23.854 8.286 .001757 570 1790.71 255176.64 24,900 185,193,000 23.875 8.291 .001754 571 1793.85 256072.60 326,041 186,169,411 23.896 8.296 .001751 572 1796.99 256970.31 327,184 187,149,248 23.916 8.301 .001748 573 1800.13 257869.59 328,329 188,132,517 23.937 8.306 .001745 574 1803.27 258770.45 329,476 189,119,224 23.958 8.311 .001742 575 1806.42 259672.87 330,625 190,109,375 23.979 8.315 .001739 576 1809.56 260576.87 331,776 191,102,976 24.000 8.320 .001736 577 1812.80 261482.43 332,929 192,100,033 24.021 8.325 .001733 578 1815.84 262388.57 334,084 193,100,552 24.042 8.330 .001730 579 1818.98 263298.28 335,241 194,104,539 24.062 8.335 .001727 580 1822.12 264208.56 336,400 195,112,000 24.083 8.339 .001724 581 1825.26 265120.46 337,561 196,122,941 24.104 8.344 .001721 582 1828.41 266033.82 338,724 197,137,368 24.125 8.349 .001718 583 1831.55 266948.82 339,889 198,155,287 24.145 8.354 .001715 584 1834.69 267865.38 341,056 199,176,704 24.166 8.359 .001712 585 1837.83 268783.57 342,225 200,201,625 24.187 8.363 .001709 [114] CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) 1 1 * s Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 586 1840.97 269703.21 343,396 201,230,056 24.207 8.368 .001706 587 1844.11 270624.49 344,569 202,262,003 24.228 8.373 .001704 588 1847.26 271547.33 345,744 203,297,472 24.249 8.378 .001701 589 1850.40 272471.75 346,921 204,336,469 24.269 8.382 .001698 590 1853.54 273397.74 348,100 205,379,000 24.289 8.387 .001695 591 1856.68 274325.29 349,281 206,425,071 24.310 8.392 .001692 592 1859.82 27 5254 .42 350,464 207,474,688 24.331 8.397 .001689 593 1862.96 276185.12 351,649 208,527,857 24.351 8.401 .001686 594 1866.11 277117.39 352,836 209,584,584 24.372 8.406 .001684 595 1869.25 278051.23 354,025 210,644,875 24.393 8.411 .001681 596 1872.39 278986.64 355,216 211,708,736 24.413 8.415 .001678 597 1875.53 279923.62 356,409 212,776,173 24.433 8.420 .001675 598 1878.67 280862.18 357,604 213,847,192 24.454 8.425 .001672 599 1881.81 281802.30 358,801 214,921,799 24.474 8.429 .001669 600 1884.96 282744.00 360,000 216,000,000 24.495 8.434 .001667 601 1888.10 283687.26 361,201 217,081,801 24.515 8.439 .001664 602 1891.24 284632.10 362,404 218,167,208 24.536 8.444 .001661 603 1894.38 285578.50 363,609 219,256,227 24.556 8.448 .001658 604 1897.52 286526.48 364,816 220,348,864 24.576 8.453 .001656 605 1900.66 287476.03 366,025 221,445,125 24.597 8.458 .001653 606 1903.80 288426.15 367,236 222,545,016 24.617 8.462 .001650 607 1906.. 95 289379.84 368,449 223,648,543 24.637 8.467 .001647 608 1910.09 290334.10 369,664 224,755,712 24.658 8.472 .001645 609 1913.23 291289.93 370,881 225,886,529 24.678 8.476 .001642 610 1916.37 292247.34 372,100 226,981,000 24.698 8.481 .001639 611 1919.51 293206.31 373,321 228,099,131 24.718 8.485 .001637 612 1922.65 294166.85 374,544 229,220,928 24.739 8.490 .001634 613 1925.80 295128.97 375,769 230,346,397 24.758 8.495 .001631 614 1928.94 296092.65 376,996 231,475,544 24.779 8.499 .001629 615 1932.08 297057.91 378,225 232,608,375 24.799 8.504 .001626 616 1935.22 298024.74 379,456 233,744,896 24.819 8.509 .001623 617 1938.36 298993.14 380,689 234,885,113 24.839 8.513 .001621 618 1941.50 299963.00 381,924 236,029,032 24.859 8.518 .001618 619 1944.65 300934.64 383,161 237,176,659 24.879 8.522 .001616 620 1947.79 301907.76 384,400 238,628,000 24.899 8.527 .001613 621 1950.93 302882.44 385,641 239,483,061 24.919 8.532 .001610 622 1954.07 303858.69 386,884 240,641,848 24.939 8.536 .001608 623 1957.21 304836.51 388,129 241,804,367 24.959 8.541 .001605 624 1960.35 305815.91 389,376 242,970,624 24.980 8.545 .001603 625 1963.50 306796.87 390,625 244,140,625 25.000 8.549 .001600 626 1966.64 307779.41 391,876 245,314,376 25.019 8.554 .001597 627 1969.78 308763.41 393,129 246,491,883 25.040 8.559 .001595 628 1972.92 309749.19 394,384 247,673,152 25.059 8.563 .001592 629 1976.06 310736.44 395,641 248,858,189 25.079 8.568 .001590 630 1979.20 311725.26 396,900 250,047,000 25.099 8.573 .001587 [115] CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) Number || or Diameter] Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 631 1982.34 312715.64 398,161 251,239,591 25.119 ^8.577 .001585 632 1985.49 313707.58 399,424 252,435,968 25.139 8.582 .001582 633 1988.63 314701.14 400,689 253,636,137 25.159 8.586 .001580 634 1991 . 77 315696.64 401,956 254,840,104 25.179 8.591 .001577 635 1994.91 316692.91 403,225 256,047,875 25.199 8.595 .001575 636 1998.05 317691 . 15 404,496 257,259,456 25.219 8.599 .001572 637 2001.19 318690.97 405,769 258,474,853 25.239 8.604 .001570 638 2004.34 319692.35 407,044 259,694,072 25.259 8.609 .001567 639 2007.48 320695.31 408,321 260,917,119 25.278 8.613 .001565 640 2010.62 321699.84 409,600 262,144,000 25.298 8.618 .001563 641 2013.76 322705.93 410,881 263,374,721 25.318 8.622 .001560 642 2016.90 323713.60 412,164 264,609,288 25.338 8.627 .001558 643 2020.04 324722.84 413,449 265,847,707 25.357 8.631 .001555 644 2023.19 325733.65 414,736 267,089,984 25.377 8.636 .001553 645 2026.33 326746.03 416,025 268,836,125 25.397 8.640 .001550 646 2029.47 327759.98 417,316 269,586,136 25.416 8.644 .001548 647 2032.61 328775.50 418,609 270,840,023 25.436 8.649 .001546 648 2035.76 329792.60 419,904 272,097,792 25.456 8.653 .001543 649 2038.89 330811.26 421,201 273,359,449 25.475 8.658 .001541 650 2042.04 331831 . 50 422,500 274,625,000 25.495 8.662 .001538 651 2045.18 332853.40 423,801 275,894,451 25.515 8.667 .001536 652 2048.32 333876.68 425,104 277,167,808 25.534 8.671 .001534 653 2051.46 334901.62 426,409 278,445,077 25.554 8.676 .001531 654 2054.60 335928.14 427,716 279,726,264 25.573 8.680 .001529 655 2057.74 336956.23 429,025 281,011,375 25.593 8.684 .001527 656 2060.88 337985.89 .430,336 282,800,416 25.612 8.689 .001524 657 2064.03 339017.12 431,649 283,593,393 25.632 8.693 .001522 658 2067.17 340049.92 432,964 284,890,312 25.651 8.698 .001520 659 2070.31 341084.29 434,281 286,191,179 25.671 8.702 .001517 660 2073.45 342120.24 435,600 287,496,000 25.690 8.706 .001515 661 2076.59 343157.75 436,921 288,804,781 25.710 8.711 .001513 662 2079.73 344196.33 438,244 290,117,528 25.720 8.715 .001511 663 2082.88 345237.49 439,569 291,434,247 25.749 8.719 .001508 664 2086.02 346279.71 440,896 292,754,944 25.768 8.724 .001506 665 2089.16 347323.51 442,225 294,079,625 25.787 8.728 .001504 666 2092.30 348368.88 443,556 295,408,296 25.807 8.733 .001502 667 2095.44 349416.40 444,889 296,740,963 25.826 8.737 .001499 668 2098.58 350464.32 446,224 298,077,632 25.846 8.742 .001497 669 2101.73 351514.30 447,561 299,418,309 25.865 8.746 .001495 670 2104.87 352566.06 448,900 300,763,000 25.884 8.750 .001493 671 2108.01 353619.28 450,241 302,111,711 25.904 8.753 .001490 672 2111.15 354674.07 451,584 303,464,448 25.923 8.759 .001488 673 2114.29 355730.43 452,929 304,821,217 25.942 8.763 .001486 674 2117.43 356788.37 454,276 306,182,024 25.961 8.768 .001484 675 2120.58 357847.87 455,625 307,546,875 25.981 8.772 .001481 [116] CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) Number II or Diameter Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 676 2123.72 358908.95 456,976 308,915,776 26.000 8.776 .001479 677 2126.86 359971.59 458,329 310,288,733 26.019 8.781 .001477 678 2130.00 361035.81 459,684 311,665,752 26.038 8.785 .001475 679 2133.14 362101.60 461,041 313,046,839 26.058 8.789 .001473 680 2136.28 363168.96 462,400 314,432,000 26.077 8.794 .001471 681 2139.42 364237.88 463,761 315,821,241 26.096 8.798 .001468 682 2142.57 365308.38 465,124 317,214,568 26.115 8.802 .001466 683 2145.71 366380.40 466,489 318,611,987 26.134 8.807 .001464 684 2148.85 367454.10 467,856 320,013,504 26.153 8.811 .001462 685 2151.99 368529.31 469,225 321,419,125 26.172 8.815 .001460 686 2155.13 369600.60 470,596 322,828,856 26.192 8.819 .001458 687 2158.27 370684.45 471,969 324,242,703 26.211 8.824 .001456 688 2161.42 371764.37 473,344 325,660,672 26.229 8.828 .001453 689 2164.56 372845.87 474,721 327,082,769 26.249 8.832 .001451 690 2167.70 373928.94 476,100 328,509,000 26.268 8.836 .011449 691 2170.84 375013.57 477,481 329,939,371 26.287 8.841 .001447 692 2173.98 376099 . 78 478,864 331,373,888 26.306 8.845 .001445 693 2177.12 377187.56 480,249 332,812,557 26.325 8.849 .001443 694 2180.27 378276.91 481,636 334,255,384 26.344 8.853 .001441 695 2183.41 379367.83 483,025 335,702,375 26.363 8.858 .001439 696 2186.55 380460.32 484,416 337,153,536 26.382 8.862 .001437 697 2189.69 381554.38 485,809 338,608,873 26.401 8.866 .001435 698 2192.83 382650.02 487,204 340,068,392 26.419 8.870 .001433 699 2195.97 383747.22 488,601 341,532,099 26.439 8.875 .001431 700 2199.12 384846.00 490,000 343,000,000 26.457 8.879 .001429 701 2202.26 385949.52 491,401 344,472,101 26.476 8.883 .001427 702 2205.40 387048.26 492,804 345,948,088 26.495 8.887 .001425 703 2208.54 388151.74 494,209 347,428,927 26.514 8.892 .001422 704 2211.68 389256.80 495,616 348,913,664 26.533 8.896 .001420 705 2214.82 390363.43 497,025 350,402,625 26.552 8.900 .001418 706 2217.96 391471.63 498,436 351,895,816 26.571 8.904 .001416 707 2221.11 392581.40 499,849 353,393,243 26.589 8.908 .001414 708 2224.25 393692.74 501,264 354,894,912 26.608 8.913 .001412 709 2227.39 394805.65 502,681 356,400,829 26,627 8.917 .001410 710 2230.53 395920.14 504,100 357,911,000 26.644 8.921 .001408 711 2233.67 397036.19 505,521 359,425,431 26.664 8.925 .001406 712 2236.81 398151.81 506,944 360,944,128 26.683 8.929 .001404 713 2239.96 399273.01 508,369 362,467,097 26.702 8.934 .001403 714 2243.10 400393.73 509,796 363,994,344 26.721 8.938 .001401 715 2246.24 401516.11 511,225 365,525,875 26.739 8.942 .001399 716 2249.38 402640.02 512,656 367,061,696 r 26.758 8.946 .001397 717 2252.52 403765.50 514,089 368,601,813 26.777 8.950 .001395 718 2255.66 404892.54 515,524 370,146,232 26.795 8.954 .001393 719 2258.81 406021 . 16 516,961 371,694,959 26.814 8.959 .001391 720 2261.95 407151.36 518,400 373,248,000 26.833 8.963 .001389 [117] CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cant.) Number 1 { Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 721 2265.09 408283.32 519,841 374,805,361 26.851 8.967 .001387 722 2268.23 409416.45 521,284 376,367,048 26.870 8.971 .001385 723 2271.37 410551.25 522,729 377,933,067 26.889 8.975 .001383 724 2274.51 411687.93 524,176 379,503,424 26.907 8.979 .001381 725 2277.66 412825.87 525,625 381,078,125 26.926 8.983 .001379 726 2280.80 413965.24 527,076 382,657,176 26.944 8.988 .001377 727 2283.94 415106.06 528,529 384,240,583 26.963 8.992 .001376 728 2287.08 416249.43 529,984 385,828,352 26.991 8.996 .001374 729 2290.22 417393.76 531,441 387,420,489 27.000 9.000 .001372 730 2293.36 418539.66 532,900 389,017,000 27.018 9.004 .001370 731 2296.50 419687.12 534,361 390,617,891 27.037 9.008 .001368 732 2299.65 420836.14 535,824 392,223,168 27.055 9.012 .001366 733 2302.79 421986.78 537,289 393,832,837 27.074 9.016 .001364 734 2305.93 423138.96 538,756 395,446,904 27.092 9.020 .001362 735 2309.07 424292.71 540,225 397,065,375 27.111 9.023 .001361 736 2312.21 425442.03 541,696 398,688,256 27.129 9.029 .001359 737 2315.35 426604.93 543,169 400,315,553 27.148 9.033 .001357 738 2318.50 427763.39 544,644 401,947,272 27.166 9.037 .001355 739 2321.64 428923.43 546,121 403,583,419 27.184 9.041 .001353 740 2324.78 430085.04 547,600 405,224,000 27.203 9.045 .001351 741 2327.92 431248.21 549,081 406,869,021 27.221 9.049 .001350 742 2331.06 432412.96 550,564 408,518,488 27.239 9.053 .001348 743 2334.20 433579.28 552,049 410,172,407 27.258 9.057 .001346 744 2337.35 434747.17 553,536 411,830,784 27.276 9.061 .001344 745 2340.49 435916.63 555,025 413,493,625 27.295 9.065 .001342 746 2343.63 437087.66 556,516 415,160,936 27.313 9.069 .001340 747 2346.77 438260.26 558,009 416,832,723 27.331 9.073 .001339 748 2349.91 439434.48 559,504 418,508,992 27.349 9.077 .001337 749 2353.05 440610.18 561,001 420,189,749 27.368- 9.081 .001335 750 2356.20 441787.50 562,500 421,875,000 27.386 - 9.086 .001333 751 2359.34 442966.38 564,001 423,564,751 27.404 9.089 .001332 752 2362.48 444146.84 565,504 424,525,900 27.423 9.094 .001330 753 2365.62 445328.86 567,009 426,957,777 27.441 9.098 .001328 754 2368.76 446512.46 568,516 428,661,064 27.459 9.102 .001326 755 2371.90 447697.63 570,025 430,368,875 27.477 9.106 .001325 756 2375.04 448884.37 571,536 432,081,216 27.495 9.109 .001323 757 2378.19 450072.68 573,049 433,798,093 27.514 9.114 .001321 758 2381.33 451262.56 574,564 435,519,512 27.532 9.118 .001319 759 2384.47 452454.01 576,081 437,245,479 27.549 9.122 .001318 760 2387.61 453647.04 577,600 438,976,000 27.568 9.126 .001316 761 2390.75 454841.63 579,121 440,711,081 27.586 9.129 .001314 762 2393.89 456037.87 580,644 442,450,728 27.604 9.134 .001312 763 2397.04 457235.53 582,169 444,194,947 27.622 9.138 .001311 764 2400.18 458435.83 583,696 445,943,744 27.640 9.142 .001309 765 2403.32 459635.71 585,225 447,697,125 27.659 9.146 .001307 [118] CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) Numberl or Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 766 2406.46 460838.16 586,756 449,455,096 27.677 9.149 .001305 767 2409.60 462042.18 588,289 451,217,663 27.695 9.154 .001304 768 2412.74 463247.76 589,824 452,984,832 27.713 9.158 .001302 769 2415.98 464454.92 591,361 454,756,609 27.731 9.162 .001300 770 2419.03 465663.66 592,900 456,533,000 27.749 9.166 .001299 771 2422.17 466873.96 594,441 458,314,011 27.767 9.169 .001297 772 2425.31 468085.83 595,984 460,099,648 27.785 9.173 .001295 773 2428.45 469299.27 597,529 461,889,917 27.803 9.177 .001294 774 2431.59 470514.29 599,076 463,684,824 27.821 9.181 .001292 775 2434.74 471730.87 600,625 465,484,375 27.839 9.185 .001290 776 2437.88 472949.03 602,176 467,288,576 27.857 9.189 .001289 777 2441.02 474168.75 603,729 469,097,433 27.875 9.193 .001287 778 2444.16 475396.05 605,284 470,910,952 27.893 9.197 .001285 779 2447.40 476612.92 606,841 472,729,139 27.910 9.201 .001284 780 2450.44 477837.36 608,400 474,552,000 27.928 9.205 .001282 781 2453.58 479063.36 609,961 476,379,541 27.946 9.209 .001280 782 2456.73 480290.94 611,524 478,211,768 27.964 9.213 .001279 783 2459.87 481520.10 613,089 480,048,687 27.982 9.217 .001277 784 2463.01 482750.82 614,656 481,890,304 28.000 9.221 .001276 785 2466.15 483983.11 616,225 483,736,025 28.017 9.225 .001274 786 2469.29 485216.97 617,796 485,587,656 28.036 9.229 .001272 787 2472.43 486452.41 619,369 487,443,403 28.053 9.233 .001271 788 2475.48 487689.73 620,944 489,303,872 28.071 9.237 .001269 789 2478.72 488927.99 622,521 491,169,069 28.089 9.240 .001267 790 2481.86 490168.14 624,100 493,039,000 28.107 9.244 .001266 791 2485.00 491409.85 625,681 494,913,671 28.125 9.248 .001264 792 2488.14 492653 . 14 627,264 496,793,088 28.142 9.252 .001263 793 2491.28 493898.20 628,849 498,677,257 28.160 9.256 .001261 794 2494.43 495144.43 630,436 500,566,184 28.178 9.260 .001259 795 2497.57 496392.43 632,025 502,459,875 28.196 9.264 .001258 796 2500.71 497648.40 633,616 504,358,336 28.213 9.268 .001256 797 2503.85 498893.14 635,209 506,261,573 28.231 9.271 .001255 798 2506.99 500145.86 636,804 508,169,592 28.249 9.275 .001253 799 2510.13 501400.14 638,401 510,082,399 28.266 9.279 .001251 800 2513.28 502656.00 640,000 512,000,000 28.284 9.283 .001250 801 2516.42 503913.42 641,601 513,922,401 28.302 9.287 .001248 802 2519.56 505172.43 643,204 515,849,608 28.319 9.291 .001247 803 2522.70 506432.98 644,809 517,781,627 28.337 9.295 .001245 804 2525.84 507655.52 646,416 519,718,464 28.355 9.299 .001244 805 2528.98 508958.83 648,025 521,660,125 28.372 9.302 .001242 806 2532.12 510224.11 649,636 523,606,616 28.390 9.306 .001241 807 2535.27 511490.96 651,249 525,557,943 28.408 9.310 -.001239 808 2538.41 512759.38 652,864 527,514,112 28.425 9.314 .001238 809 2541.55 514029.37 654,481 529,474,129 28.443 9.318 .001236 810 2544.09 515300.94 656,100 531,441,000 28.460 9.321 .001235 119] CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) 1 Number II or | Diameter Circum- ference Circular . Area Square Cube Square Root Cube Root Reciprocal 811 2547.83 516574.07 657,721 533,411,731 28.478 9.325 .001233 812 2550.97 517848.77 659,344 535,387,328 28.496 9.329 .001232 813 2554.12 519125.05 660,969 537,366,797 28.513 9.333 .001230 814 2557.26 520402.85 662,596 539,353,144 28.531 9.337 .001229 815 2560.40 521682.31 664,225 541,343,375 28.548 9.341 .001227 816 2563.54 522663.30 665,856 543,338,496 28.566 9.345 .001225 817 2566.68 524245.86 667,489 545,338,513 28.583 9.348 .001224 818 2569.82 525529.98 669,124 547,343,432 28.601 9.352 .001222 819 2572.97 526815.68 670,761 549,353,259 28.618 9.356 .001221 820 2576.11 528102.96 672,400 551,368,000 28.636 9.360 .001220 821 2579.25 529391.80 674,041 553,387,661 28.653 9.364 .001218 822 2582.39 530682.21 675,684 555,412,248 28.670 9.367 .001217 823 2585.53 531974.39 677,329 557,441,767 28.688 9.371 .001215 824 2588.64 533267.75 678,976 559,476,224 28.705 9.375 .001214 825 2591.82 534562.87 680,625 561,515,625 28.723 9.379 .001212 826 2594.96 535859.57 682,276 563,559,976 28.740 9.383 .001211 827 2598.10 537159.83 683,929 565,609,283 28.758 9.386 .001209 828 2601.24 538457.62 685,584 567,663,552 28.775 9.390 .001208 829 2604.38 539759.08 687,241 569,722,789 28.792 9.394 .001206 830 2607.52 541062.06 688,900 571,787,000 28.810 9.398 .001205 831 2610.66 542366.60 690,561 573,856,191 28.827 9.401 .001203 832 2613.81 543672.72 692,224 575,930,368 28.844 9.405 .001202 833 2616.95 544980.52 693,889 578,009,537 28.862 9.409 .001200 834 2620.09 546289.68 695,556 580,093,704 28.879 9.413 .001199 835 2623.23 547600.51 697,225 582,182,875 28.896 9.417 .001198 836 2626.37 548912.91 698,896 584,277,056 28.914 9.420 .001196 837 2629.51 550226.89 700,569 586,376,253 28.931 9.424 .001195 838 2632.64 551542.43 702,244 588,480,472 28.948 9.428 .001193 839 2635.80 552859.58 703,921 590,589,719 28.965 9.432 .001192 840 2638.94 554178.24 705,600 592,704,000 28.983 9.435 .001190 841 2642.08 555498.49 707,281 594,823,321 29.000 9.439 .001189 842 2645.22 556820.32 708,964 596,947,688 29.017 9.443 .001188 843 2648.35 558143.72 710,649 599,077,107 29.034 9.447 .001186 844 2651.51 559468.69 712,336 601,211,584 29.052 9.450 .001185 845 2654.65 560795.23 714,025 603,351,125 29.069 9.454 .001183 846 2657.79 562123.34 715,716 605,495,736 29.086 9.458 .001182 847 2660.93 563456.82 717,409 607,645,423 29.103 9.461 .001181 848 2664.07 564784.28 719,104 609,800,192 29.120 9.465 .001179 849 2667.21 566117.10 720,801 611,960,049 29.138 9.469 .001178 850 2670.36 567451.59 722,500 614,125,000 29.155 9.473 .001176 851 2673.50 568787.46 724,201 616,295,051 29.172 9.476 .001175 852 2Q76.64 570125.00 725,904 618,470,208 29.189 9.480 .001174 853 2679.78 571464.10 727,609 620,650,477 29.206 9.483 .001172 854 2682.92 572804.78 729,316 622.835,864 29.223 9.487 .001171 855 2686.06 574147.03 731,025 625,026,374 29.240 9.491 .001170 120] CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) Number 1 1 or Diameter Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 856 2689.20 575490.85 732,736 627,222,016 29.257 9.495 .001168 857 2692.35 576836.24 734,449 629,422,793 29.274 9.499 .001167 858 2695.49 578183.20 736,164 631,628,712 29.292 9.502 .001166 859 2698.63 579531.73 737,881 633,839,779 29.309 9.506 .001164 860 2701.77 580881.84 739,600 636,056,000 29.326 9.509 .001163 861 2704.91 582233.51 741,321 638,277,381 29.343 9.513 .001161 862 2708.05 583586.75 743,044 640,503,928 29.360 9.517 .001160 863 2711.20 584941 . 57 744,769 642,735,647 29.377 9.520 .001159 864 2714.34 586297.95 746,496 644,972,544 29.394 9.524 .001157 865 2717.48 587655.91 748,225 647,214,625 29.411 9.528 .001156 866 2720.66 589015.41 749,956 649,461,896 29.428 9.532 .001155 867 2723.76 590376.54 751,689 651,714,363 29.445 9.535 .001153 868 2726.90 591739.20 753,424 653,972,032 29.462 9.539 .001152 869 2730.05 593103.44 755,161 656,234,909 29.479 9.543 .001151 870 2733.19 594469.26 756,900 658,503,000 29.496 9.546 .001149 871 2736.33 595836.44 758,641 660,776,311 29.513 9.550 .001148 872 2739.87 597205.59 760,384 663,054,848 29.529 9.554 .001147 873 2742.61 598576.91 762,129 665,338,617 29.546 9.557 .001145 874 2745.75 599948.21 763,876 667,627,624 29.563 9.561 .001144 875 2748.90 601321.87 765,625 669,921,875 29.580 9.565 .001143 876 2752.04 602697.11 767,376 672,221,376 29.597 9.568 .001142 877 2755.18 604073.91 769,129 674,526,133 29.614 9.572 .001140 878 2758.32 605451.49 770,884 676,836,152 29.631 9.575 .001139 879 2761.46 606832.24 772,641 679,151,439 29.648 9.579 .001138 880 2764.60 608213.76 774,400 681,472,000 29.665 9.583 .001136 881 2767.74 609596.84 776,161 683,797,841 29.682 9.586 .001135 882 2770.89 610981.50 777,924 686,128,968 29.698 9.590 .001134 883 2774.03 612367.74 779,689 688,465,387 29.715 9.594 .001133 884 2777.17 613755.54 781,456 690,807,104 29.732 9.597 .001131 885 2780.31 615144.91 783,225 693,154,125 29.749 9.601 .001130 886 2783.45 616535.85 784,996 695,506,456 29.766 9.604 .001129 887 2786.59 617928.37 786,769 697,864,103 29.782 9.608 .001127 888 2789.75 619322.45 788,544 700,227,072 29.799 9.612 .001126 889 2792.88 620718.11 790,321 702,595,369 29.816 9.615 .001125 890 2796.02 622115.34 792,100 704,969,000 29.833 9.619 .001124 891 2799.16 623514.13 793,881 707,347,971 29.850 9.623 .001122 892 2802.30 624914.50 795,664 709,732,288 29.866 9.626 .001121 893 2805.44 626316.44 797,449 712,121,957 29.883 9.630 .001120 894 2808.59 627719.95 799,236 714,516,984 29.900 9.633 .001119 895 2811.73 629120.35 801,025 716,917,375 29.916 9.637 .001118 896 2814.87 630531.68 802,816 719,323,136 29.933 9.640 .001116 897 2818.82 631939.90 804,609 721,734,273 29.950 9.644 .001115 898 2821.15 633349.70 806,404 724,150,792 29.967 9.648 .001114 899 2824.29 634768.13 808,201 726,572,699 29.983 9.651 .001112 900 2827.44 636174.00 810,000 729,000,000 30.000 9.655 .001111 121 CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) Number II or Diameter Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 901 2830.58 637588.50 811,804 731,432,701 30.017 9.658 .001110 902 2833.72 639004.58 813,604 733,870,808 30.033 9.662 .001109 903 2836.86 640422.22 815,409 736,314,327 30.050 9.666 .001107 904 2840.00 641841.44 817,216 738,763,264 30.066 9.669 .001106 905 2843.14 643262.23 819,025 741,217,625 30.083 9.673 .001105 906 2846.28 644684.74 820,836 7^3,677,416 30.100 9.676 .001104 907 2849.43 646108.52 822,649 746,142,643 30.116 9.680 .001103 908 2852.57 647534.02 824,464 748,613,312 30.133 9.683 .001101 909 2855.71 648961.09 826,281 751,089,429 30.150 9.687 .001100 910 2858.85 650389.74 828,100 753,571,000 30.163 9.690 .001099 911 2861.99 651819.95 829,921 756,058,031 30.183 9.694 .001098 912 2865.13 653251.73 831,744 758,550,528 30.199 9.698 .001096 913 2868.29 654689.09 833,569 761,048,497 30.216 9.701 .001095 914 2871.42 656120.81 835,396 763,551,944 30.232 9.705 .001094 915 2874.56 657556.51 837,225 766,060,874 30.249 9.708 .001093 916 2877.70 658994.58 839,056 768,575,296 30.265 9.712 .001092 917 2880.84 660432.22 840,880 771,095,213 30.282 9.715 .001091 918 2883.98 661875.42 842,724 773,620,632 30.298 9.718 .001089 919 2887.13 663318.20 844,561 776,151,559 30.315 9.722 .001088 .920 2890.27 664762.56 846,400 778,688,000 30.331 9.726 .001087 921 2893.41 666208.48 848,241 781,229,961 30.348 9.729 .001086 922 2896.55 667655.97 850,084 783,777,448 30.364 9.733 .001085 923 2899.69 669101.61 851,929 786,330,467 30.381 9.736 .001083 924 2902.83 670555.67 853,776 788,889,024 30.397 9.740 . 101082 925 2905.98 672007.87 855,625 791,453,125 30.414 9.743 .001081 926 2909.12 673461.65 857,476 794,022,776 30.430 9.747 .001080 927 2912.26 674916.99 859,329 796,597,983 30.447 9.750 .001079 928 2915.40 676373.91 861,184 799,178,752 30.463 9.754 .001078 929 2918.54 677832.40 863,041 801,765,089 30.479 9.757 .001076 930 2921.68 679292.46 864,900 804,357,000 30.496 9.761 .001075 931 2924.82 680754.08 866,761 806,954,491 30.512 9.764 .001074 932 2927.97 682217.30 868,624 809,557,568 30.529 9.768 .001073 933 2931.11 683682.06 870,489 812,166,237 30.545 9.771 .001072 934 2934.25 685148.40 872,356 814,780,504 30.561 9.775 .001071 935 2937.39 686616.31 874,225 817,400,375 30.578 9.778 .001070 936 2940.53 688085.79 876,096 820,025,856 30.594 9.783 .001068 937 2943.67 689556.85 877,969 822,656,953 30.610 9.785 .001067 938 2946.82 691029.47 879,844 825,293,672 30.627 9.789 .001066 939 2949.96 692503.67 881,721 827,936,019 30.643 9.792 .001065 940 2953.10 693979.44 883,600 830,584,000 30.659 9.796 .001064 941 2956.24 695456.77 885,481 833,237,621 30.676 9.799 .001063 942 2959.38 696935.68 887,364 835,896,888 30.692 9.803 .001062 943 2962.43 698416.14 889,249 838,561,807 30.708 9.806 .001060 944 2965.67 699898.21 891,136 841,232,384 30.724 9.810 .001059 945 2968.81 701381.83 893,025 843,908,625 30.741 9.813 .001058 [122] CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) I_J Circum- ference Circular Area Square C-ibe Square Root Cube Root Reciprocal 946 2971.95 702867.02 894,916 846,590,536 30.757 9.817 .001057 947 2975.09 704350.25 896,809 849,278,123 30.773 9.820 .001056 948 2978.23 705841.80 898,704 851,971,392 30.790 9.823 .001055 949 2981.37 707332.02 900,601 854,670,349 30.806 9.827 .001054 950 2984.52 708023.50 902,500 857,375,000 30.822 9.830 .001053 951 2987.66 710316.54 904,401 860,085,351 30.838 9.834 .001052 952 2990.72 711811.16 906,304 862,801,408 30.854 9.837 .001050 953 2993.94 713307.34 908,209 865,523,177 30.871 9.841 .001049 954 2997.08 714805.10 910,116 868,250,664 30.887 9.844 .001048 955 3000.22 716304.43 912,025 870,983,875 30.903 9.848 .001047 956 3003.36 717805.33 913,936 873,722,816 30.919 9.851 .001046 957 3006.51 719307.80 915,849 876,467,493 30.935 9.854 .001045 958 3009.65 720811.84 917,764 879,217,912 30.951 9.858 .001044 959 3012.79 722317.45 919,681 881,974,079 30.968 9.861 .001043 960 3015.90 723824.64 921,600 884,736,000 30.984 9.865 .001042 961 3019.07 725333.39 923,521 887,503,681 31.000 9.868 .001041 962 3022.21 726843.71 925,444 890,277,128 31.016 9.872 .001040 963 3025.36 728355.61 927,369 893,056,347 31.032 9.875 .001038 964 3028.50 729869.07 929,296 895,841,344 31.048 9.878 .001037 965 3031.64 731384.11 931,225 898,632,125 31.064 9.881 .001036 966 3034.78 732900.72 933,156 901,428,696 31.080 9.885 .001035 967 3037.92 734418.90 935,089 904,231,063 31.097 9.889 .001034 968 3041.06 735938.64 937,024 907,039,232 31.113 9.892 .001033 969 3044.21 737459.96 938,961 909,853,209 31.129 9.895 .001032 970 3047.35 738982.86 940,900 912,673,000 31.145 9.899 .001031 971 3050.49 740507.32 942,841 915,498,611 31.161 9.902 .001030 972 3053.63 742033.35 944,784 918,330,048 31.177 9.906 .001029 973 3056.77 743560.95 946,729 921,167,317 31.193 9.909 .001028 974 3059.91 745090.13 948,676 924,010,424 31.209 9.912 .001027 975 3063.06 746620.87 950,625 926,859,375 31.225 9.916 .001026 976 3066.20 748153.19 952,576 929,714,176 31.241 9.919 .001025 977 3069.36 749687.07 954,529 932,574,833 31.257 9.923 .001024 978 3072.48 751222.53 856,484 935,441,352 31.273 9.926 .001022 979 3075.62 752759.56 958,441 938,313,739 31.289 9.929 .001021 980 3078.76 754298.16 960,400 941,192,000 31.305 9.933 .001020 981 3081.90 755838.32 962,361 944,076,141 31.321 9.936 .001019 982 3085.05 757380.06 964,324 946,966,168 31.337 9.940 .001018 983 3088.19 758923.38 966,289 949,862,087 31.353 9.943 .001017 984 3091.33 760468.26 968,256 952,763,904 31.369 9.946 .001016 985 3094.47 762014.71 970,225 955,671,625 31.385 9.950 .001015 986 3097.61 733562.73 972,196 958,585,256 31.401 9.953 .001014 987 3100.75 765119.33 974,169 961,504,803 31.416 9.956 .001013 988 3103.96 766663.49 976,144 964,430,272 31.432 9.960 .001012 989 3107.04 768216.23 978,121 967,361,669 31.448 9.963 .001011 990 3110.18 769770.54 980,100 970,299,000 31.464 9.966 .001010 [123] CIRCLES AREAS, SQUARES, CUBES, ETC. NUMBERS, DIAMETERS AND AREAS, ETC. (Cont.) Number II or Diameter Circum- ference Circular Area Square Cube Square Root Cube Root Reciprocal 991 3113.32 771326.41 982,081 973,242,271 31.480 9.970 .001009 992 3116.46 772883.86 984,064 976,191,488 31.496 9.973 .001008 993 3119.60 774442.88 986,049 979,146,657 31.512 9.977 .001007 994 3122.75 776003.47 988,036 982,107,784 31.528 9.980 .001006 995 3125.89 777565.63 990,025 985,074,875 31.544 9.983 .001005 996 3129.03 779129.36 992,016 988,047,936 31.559 9.987 .001004 997 3132.17 780694.66 994,009 991,026,973 31.575 9.990 .001003 998 3135.11 782261.54 996,004 994,011,992 31.591 9.993 .001002 999 3138.45 783829.98 998,001 997,002,999 31.607 9.997 .001001 1,000 3141.60 785400.00 1,000,000 1,000,000,000 31.623 10.000 .001000 To Find the Length of Any Arc of a Circle. Rule 1. When the chord of the arc and the versed sine of half the arc are given. To fifteen times the square of the chord, add thirty-three times the square of the versed sine, and reserve the number. To the square of the chord, add four times the square of the versed sine, and the square root of the sum will be twice the chord of half the arc. Multiply twice the chord of half the arc by ten times the square of the versed sine, divide the product by the re- serve number, and add the quotient to twice the chord of half the arc : the sum will be the length of the arc very nearly. When the Chord of the Arc and Chord of Half the Arc are Given. From the square of the chord of half the arc subtract the square of half the chord of the arc, the re- mainder will be the square of the versed sine; then proceed as above. Rule 2. When the Diameter and the Versed Sine of Half the Arc Are Given. From sixty times the diameter subtract twenty-seven times the versed sine, and reserve the number. Multiply the diameter by the versed sine, and the square root of the product will be the chord of half the arc. Multiply twice the chord of half the arc by ten times the versed sine, divide the product by the reserve number, and add the quotient to twice the chord of half the arc; the sum will be the length of the arc very nearly. NOTE. 1. When the diameter and chord of the arc are given, the versed sine may be found thus: From the square of the diameter subtract the square of the chord, and extract the square root of the remainder. Subtract this root from the diameter and half the remainder will give the versed sine of half the arc. 2. The square of the chord of half the arc being divided by the diameter will give the versed sine, or being divided by the versed sine will give the diameter. 3. The length of the arc may also be found by multi- plying together the number of degrees it contains, the radius and the number .01745329. To Find the Area of a Sector of a Circle. Rule: Multi- ply half the length of the arc of the sector by the radius. Or, multiply the number of the degrees in the arc by the square of the radius, and by .008727. NOTE. If the diameter or radius is not given, add the [124] MENSURATION square of half the chord of the arc to the square of the versed sine of half the arc; this sum being divided by the versed sine will give the diameter. To Find the Area of a Segment of a Circle. Rule 1 : Find the area of the sector which has the same arc as the segment; also the area of the triangle formed by the radial sides of the sector and the chord of the arc; the difference or the sum of these areas will be the area of the segment, according as it is less or greater than a semicircle. NOTE. The difference between the versed sine and radius, multiplied by half the chord of the arc, will give the area of the triangle. ' * x * % !'''' \ Rule 2. Divide the height, or versed sine, by the diame- ***TQ' ter, and find the quotient in the table of versed sines. / Multiply the number on the right hand of the versed ^ / sines by the square of the diameter, and the product will \ / be the area. N ^--J ~*' NOTE 1. When the quotient arising from the versed sine E~ divided by the diameter has a remainder or fraction after the third place of decimals; having taken the area answering to the first three figures subtract it from the next following area, multiply the remainder by the said fraction, and add the product to the first area: the sum will be the area for the whole quotient. NOTE 2. The table to which this rule refers is formed of the areas of the segments of a circle whose diameter is 1; and which is supposed to be divided by perpendicular chords into 1000 equal parts. The rule depends upon this property that the versed sine of similar segments are as the diameters of the circles to which they belong, and the area of those segments as the squares of the diameter; which may be thus demonstrated: Let A D B A and adb a be any two similar segments, cut off from the similar sectors A D B C A and adb ca, by the chords A B and a b, and let the perpendicular C D bisect them. Then by similar triangles, DB: db :: B C : 6 c and DB: db :: ~Dm:dn', whence, by equality, Bc:6c::Dw:dn, or2BC:26c::Dm:dw. LENGTHS OF CIRCULAR ARCS FROM 1 TO 180 Given the Degrees. Radius = 1 In this table, the lengths of circular arcs are given proportionately to that of radius = 1, as determined by the following formula: Length of arc = ' X radius X number of degrees. The numbers of degrees in the arc are given in the first column, and the length of the arc, as compared with the radius, is given decimally in the second column. To use this table: Find the proportional length of the arc corresponding to the degrees in the arc, and multiply it by the actual length of the radius; the product is the length of the arc. Example: Required the length of a circular arc corresponding to 62, the radius = 36. From the table, 62 = 1.0821. Then 1.0821 X 36 = 38.9556, the required length. [125] LENGTHS OF CIRCULAR ARCS LENGTHS OP CIRCULAB ARCS FROM 1 TO 180. GIVEN THE DEGREES. Radius = 1. Degrees Length Degrees Length Degrees Length Degrees Length 1 .0174 46 .8028 91 .5882 136 2.3736 2 .0349 47 .8203 92 .6057 137 2.3911 3 .0524 48 .8377 93 .6231 138 2.4085 4 .0698 49 .8552 94 .6406 139 2.4260 5 .0873 50 .8727 95 .6581 140 2.4435 6 .0147 51 .8901 96 .6755 141 2.4609 7 .0222 52 .9076 97 .6930 142 2.4784 8 .0396 53 .9250 98 .7104 143 2.4958 9 .0571 54 .9424 99 .7279 144 2.5133 10 .1745 55 .9599 100 .7453 145 2.5307 11 .1920 56 .9774 101 .7628 146 2.5482 12 .2094 57 .9948 102 .7802 147 2.5656 13 .2269 58 1.0123 103 .7977 148 2.5831 14 .2443 59 1.0297 104 .8151 149 2.6005 15 .2618 60 1.0472 105 .8326 150 2.6180 16 .2792 61 1.0646 106 .8500 151 2.6354 17 .2967 62 1.0821 107 .8675 152 2.6529 18 .3141 63 .0995 108 .8849 153 2.6703 19 .3316 64 .1170 109 .9024 154 2.6878 20 .3491 65 .1345 110 .9199 155 2.7053 21 .3665 66 .1519 111 .9373 156 2.7227 22 .3840 67 .1694 112 .9548 157 2.7402 23 .4014 68 .1868 113 .9722 158 2.7576 24 .4189 69 .2043 114 .9897 159 2.7751 25 .4363 70 .2217 115 2.0071 160 2.7925 26 .4538 71 .2392 116 2.0246 161 2.8100 27 .4712 72 .2566 117 2.0420 162 2.8274 28 .4887 73 .2741 118 2.0595 163 2.8449 29 .5061 74 .2915 119 2.0769 164 2.8623 30 .5236 75 .3090 120 2.0944 165 2.8798 31 .5410 76 .3264 121 2.1118 166 2.8972 32 .5585 77 .3439 122 2.1293 167 2.9147 33 .5759 78 .3613 123 2.1467 168 2.9321 34 .5934 79 .3788 124 2.1642 169 2.9496 35 .6109 80 .3963 125 2.1817 170 2.9670 36 .6283 81 .4137 126 2.1991 171 2.9845 37 .6458 82 .4312 127 2.2166 172 3.0020 38 .6632 83 .4486 128 2.2304 173 3.0194 39 .6807 84 .4661 129 2.2515 174 3.0369 40 .6981 85 1.4835 130 2.2689 175 3.0543 41 .7156 86 1.5010 131 2.2864 176 3.0718 42 .7330 87 1.5184 132 2.3038 177 3.0892 43 .7505 88 1.5359 133 2.3213 178 3.1067 44 .7679 89 1.5533 134 2.3387 179 3.1241 45 .7854 90 1.5708 135 2.3562 180 3.1416 [126] LENGTHS OF CIRCULAR ARCS LENGTHS OF CIRCULAR ARCS, UP TO A SEMICIRCLE Given the Height. Chord = 1 In this table the chord is taken = 1, and the rise or height of the arc, expressed decimally as compared with the chord, is given in the first column. The length of the arc relatively to the chord is given in the second column. To use this table, divide the height of the arc by the chord for the proportional height of the arc, which find in the first column of the table. The proportional length of the arc corresponding to it, being multiplied by the actual length of the chord, gives the actual length of the arc. NOTE. The length of an arc of a circle may be found nearly thus: Subtract the chord of the whole arc from eight times the chord of half the arc, one-third of the remainder is the length nearly. LENGTHS OF CIRCULAR ARCS, UP TO A SEMICIRCLE. GIVEN THE HEIGHT. Chord = 1. Height Length Height Length Height Length Height Length .100 1.02645 .101 .02698 .131 1.04515 .161 1.06775 .191 .09461 .102 .02752 .132 1.04584 .162 1.06858 .192 .09557 .103 .02806 .133 1.04652 .163 1.06941 .193 .09654 .104 .02860 .134 1.04722 .164 1.07025 .194 .09752 .105 .02914 .135 1.04792 .165 1.07109 .195 .09850 .106 .02970 .136 1.04862 .166 1.07194 .196 1.09949 .107 .03026 .137 1.04932 .167 1.07279 .197 1.10048 .108 .03082 .138 1.05003 .168 1.07365 .198 1.10147 .109 .03139 .139 1.05075 .169 1.07451 .199 1.10247 .110 .03196 .140 1.05147 .170 1.07537 .200 1.10348 .111 .03254 .141 1.05220 .171 1.07624 .201 1.10447 .112 .03312 .142 1.05293 .172 1.07711 .202 1.10548 .113 .03371 .143 .05367 .173 1.07799 .203 1.10650 .114 .03430 .144 .05441 .174 1.07888 .204 1.10752 .115 .03490 .145 .05516 .175 1.07977 .205 1.10855 .116 .03551 .146 .05591 .176 1.08066 .206 .10958 .117 .03611 .147 .05667 .177 1.08156 .207 .11062 .118 .03672 .148 .05743 .178 1.08246 .208 .11165 .119 .03734 .149 .05819 .179 1.08337 .209 . 11269 .120 .03797 .150 1.05896 .180 1.08428 .210 .11374 .121 .03860 .151 1.05973 .181 1.08519 .211 1.11479 .122 .03923 .152 1.06051 .182 1.08611 .212 1.11584 .123 .03987 .153 1.06130 .183 1.08704 .213 1.11692 .124 .04051 .154 1.06209 .184 1.08797 .214 1.11796 .125 .04116 .155 1.06288 .185 1.08890 .215 1.11904 .126 .04181 .156 1.06368 .186 1.08984 .216 1.12011 .127 .04247 .157 1.06449 .187 1.09079 .217 1.12118 .128 .04313 .158 1.06530 .188 1.09174 .218 1.12225 .129 .04380 .159 1.06611 .189 \ 1.09269 .219 1 . 12334 .130 1.04447 , .160 1.06693 .190 j 1.09365 .220 1.12445 127] LENGTHS OF CIRCULAR ARCS LENGTHS OF CIRCULAR ARCS (Cont.) Height Length Height Length Height Length Height Length .221 1.12556 .266 .17912 .311 1.24070 .356 .30954 .222 1.12663 .267 .18040 .312 1.24216 .357 .31115 .223 1.12774 .268 . 18162 .313 1.24360 .358 .31276 .224 1.12885 .269 .18294 .314 1.24506 .359 .31437 .225 1.12997 .270 .18428 .315 1.24654 .360 .31599 .226 .13108 .271 . 18557 .316 1.24801 .361 .31761 .227 .13219 .272 .18688 .317 1.24946 .362 .31923 .228 .13331 .273 1 . 18819 .318 1.25095 .363 .32086 .229 .13444 .274 1.18969 .319 1.25243 .364 .32249 .230 .13557 .275 1.19082 .320 1.25391 .365 .32413 .231 1 . 13671 .276 1 . 19214 .321 1.25539 .366 .32577 .232 1.13786 .277 1.19345 .322 1.25686 .367 .32741 .233 1.13903 .278 1.19477 .323 1.25836 .368 .32905 .234 1.14020 .279 1.19610 .324 1.25987 .369 .33069 .235 1.14136 .280 1.19743 .325 1.26137 .370 .33234 .236 1 . 14247 .281 1.19887 .326 1.26286 .371 .33399 .237 1.14363 .282 1.20011 .327 1.26437 .372 .33564 .238 . 14480 .283 1.20146 .328 1.26588 .373 .33730 .239 .14597 .284 1.20282 .329 1.26740 .374 .33896 .240 .14714 .285 1.20419 .330 1.26892 .375 .34063 .241 .14831 .286 1.20558 .331 1.27044 .376 .34229 .242 .14949 .287 1.20696 .332 1.27196 .377 .34396 .243 .15067 .288 1.20828 .333 1.27349 .378 .34563 .244 .15186 .289 1.20967 .334 .27502 .379 .34731 .245 .15308 .290 1.21202 .335 .27656 .380 1.34899 .246 .15429 .291 1.21239 .336 .27810 .381 1.35068 .247 .15549 .292 1.21381 .337 .27864 .382 1.35237 .248 .15670 .293 .21520 .338 .28118 .383 1.35406 .249 . 15791 .294 .21658 .339 .28273 .384 1.35575 .250 .15912 .295 .21794 .340 .28428 .385 1.35744 .251 .16033 .296 .21926 .341 .28583 .386 1.35914 .252 .16157 .297 .22061 .342 .28739 .387 1.36084 .253 . 16279 .298 .22203 .343 .28895 .388 1.36254 .254 .16402 .299 .22347 .344 .29052 .389 1.36425 .255 1.16526 .300 .22495 .345 1.29209 .390 1.36586 .256 1.16649 .301 .22635 .346 1.29366 .391 .36767 .257 1.16774 .302 .22776 .347 1.29523 .392 .36939 .258 1 . 16899 .303 1.22918 .348 1.29681 .393 .37111 .259 1.17024 .304 1.23061 .349 1.29839 .394 .37283 .260 1.17150 [305 1.23205 .350 1.29997 .395 .37455 .261 1.17275 .306 1.23349 .351 1.30156 .396 1.37628 .262 1.17401 .307 1.23494 .352 1.30315 .397 1.37801 .263 1 . 17527 .308 1.23636 .353 1.30474 .398 1.37974 .264 1.17655 .309 1.23780 .354 1.30634 .399 1.38148 .265 1.17784 .310 1.23925 .355 1.30794 .400 1.38322 [128] AREAS OF CIRCULAR SEGMENTS LENGTHS OP CIRCULAR ARCS (Cont.) Height Length Height Length Height Length Height Length .401 1.38496 .426 1.42945 .451 1.47565 .476 1.52346 .402 1.38671 .427 1.43127 .452 1.47753 .477 1.52541 .403 1.38846 .428 1.43309 .453 .47942 .478 1.52736 .404 1.39021 .429 1.43491 .454 .48131 .479 1.52931 .405 1.39196 .430 1.43673 .455 .48320 .480 1.53126 .406 1.39372 .431 1.43856 .456 .48509 .481 1.53322 .407 1.39548 .432 1.44039 .457 .48699 .482 1.53518 .408 1.39724 .433 1.44222 .458 .48889 .483 1.53714 .409 1.39900 .434 1.44405 .459 .49079 .484 1.53910 .410 1.40077 .435 1.44589 .460 .49269 .485 1.54106 .411 .40254 .436 1.44773 .461 1.49460 .486 1.54302 .412 .40432 .437 1.44957 .462 1.49651 .487 1.54499 .413 .40610 .438 1.45142 .463 1.49842 .488 1.54696 .414 .40788 .439 1.45327 .464 1.50033 .489 1.54893 .415 .40966 .440 1.45512 .465 1.50224 .490 1.55090 .416 .41145 .441 1.45697 .466 1.50416 .491 1.55288 .417 .41324 .442 1.45883 .467 1.50608 .492 1.55486 .418 .41503 .443 1.46069 .468 1.50800 .493 1.55685 .419 1.41682 .444 1.46255 .469 1.50992 .494 1.55854 .420 1.41861 .445 1.46441 .470 1.51185 .495 1.56083 .421 1.42041 .446 1.46628 .471 1.51378 .496 1.56282 .422 1.42222 .447 1.46815 .472 1.51571 .497 1.56481 .423 1.42402 .448 1.47002 .473 1.51764 .498 1.56680 .424 1.42583 .449 1.47189 .474 1.51958 .499 1.56879 .425 1.42764 .450 1.47377 .475 1.52152 .500 1.57079 AREAS OF CIRCULAR SEGMENTS The areas of circular segments are given, in proportional superficial measure, the diameter of the circle of which the segment forms a portion being = 1. The height of the segment, expressed decimally in proportion to the diameter, is given in the first column, and the relative area in the second column. To use the table, divide the height by the diameter, find the quotient in the table, and multiply the corresponding area by the square of the actual length of the diameter; the product will be the actual area. AREAS OF CIRCULAR SEGMENTS, UP TO A SEMICIRCLE Diameter of Circle = 1 Height Area Height Area Height Area Height Area .001 .00004 .006 .00062 .011 .00153 .016 .00268 .002 .00012 .007 .00078 .012 .00175 .017 .00294 .003 .00022 .008 .00095 .013 .00197 .018 .00320 .004 .00034 .009 .00114 .014 .00220 .019 .00347 .005 .00047 .010 .00133 .015 .00244 .020 .00375 129] AREAS OF CIRCULAR SEGMENTS AREAS OF CIRCULAR SEGMENTS (Cont.) Height Area Height Area Height Area Height Area .021 .00403 .066 .02215 .111 .04763 .156 .07819 .022 .00432 .067 .02265 .112 .04826 .157 .07892 .023 .00461 .068 .02315 .113 .04889 .158 .07965 .024 .00492 .069 .02366 .114 .04953 .159 .08038 .025 .00523 .070 .02417 .115 .05016 .160 .08111 .026 .00555 .071 .02468 .116 .05080 .161 .08185 .027 .00587 .072 .02520 .117 .05145 .162 .08258 .028 .00619 .073 .02571 .118 .05209 .163 .08332 .029' .00653 .074 .02624 .119 .05274 .164 .08406 .030 .00687 .075 .02676 .120 .05338 .165 .08480 .031 .00721 .076 .02729 .121 .05404 .166 .08554 .032 .00756 .077 .02782 .122 .05469 .167 .08629 .033 .00792 .078 .02836 .123 .05535 .168 .08704 .034 .00828 .079 .02889 .124 .05600 .169 .08778 .035 .00864 .080 .02943 .125 .05666 .170 .08854 .036 .00901 .081 .02997 .126 .05733 .171 .08929 .037 .00939 .082 .03053 .127 .05799 .172 .09004 .038 .00977 .083 .03108 .128 .05866 .173 .09080 .039 .01015 .084 .03163 .129 .05933 .174 .09155 .040 .01054 .085 .03219 .130 .06000 .175 .09231 .041 .01093 .086 .03275 .131 .06067 .176 .09307 .042 .01133 .087 .03331 .132 .06135 .177 .09383 .043 .01173 .088 .03385 .133 .06203 .178 .09460 .044 .01214 .089 .03444 .134 .06271 .179 .09537 .045 .01255 .090 .03501 .135 .06339 .180 .09613 .046 .01297 .091 .03538 .136 .06407 .181 .09690 .047 .01340 .092 .03616 .137 .06476 .182 .09767 .048 .01382 .093 .03674 .138 .06545 .183 .09845 .049 .01425 .094 .03732 .139 .06614 .184 .09922 .050 .01468 .095 .03790 .140 .06683 .185 .10000 .051 .01512 .096 .03850 .141 .06753 .186 .10077 .052 .01556 .097 .03909 .142 .06822 .187 .10153 .053 .01601 .098 .03968 .143 .06892 .188 .10233 .054 .01646 .099 .04028 .144 .06963 .189 .10317 .055 .01691 .100 .04087 .145 .07033 .190 .10390 .056 .01737 .101 .04148 .146 .07103 .191 .10469 .057 .01783 .102 .04208 .147 .07174 .192 .10547 .058 .01830 .103 .04269 .148 .07245 .193 .10626 .059 .01877 .104 .04330 .149 .07316 .194 .10705 .060 .01924 .105 .04391 .150 .07387 .195 .10784 .061 .01972 .106 .04452 .151 .07459 .196 .10864 .062 .02020 .107 .04514 .152 .07530 .197 .10943 .063 .02068 .108 .04576 .153 .07603 .198 .11023 .064 .02117 .109 .04638 .154 .07675 .199 .11102 .065 .02166 .110 .04701 .155 .07747 .200 .11182 [130] AREAS OF CIRCULAR SEGMENTS AREAS OF CIRCULAR SEGMENTS (Cont.) Height Area Height Area Height Area Height Area .201 .11262 .246 .15009 .291 .18996 .336 .23169 .202 .11343 .247 .15096 .292 .19086 .337 .23263 .203 .11423 .248 .15182 .293 .19177 .338 .23358 .204 .11504 .249 .15268 .294 .19268 .339 .23453 .205 .11584 .250 .15355 .295 .19360 .340 .23547 .206 .11665 .251 .15442 .296 .19451 .341 .23642 .207 .11746 .252 .15528 .297 .19543 .342 .23737 .208 .11827 .253 .15615 .298 .19634 .343 .23832 .209 .11908 .254 .15702 .299 .19725 .344 .23927 .210 .11990 .255 .15789 .300 .19817 .345 .24025 .211 .12071 .256 .15876 .301 .19908 .346 .24117 .212 .12153 .257 .15964 .302 .20000 .347 .24212 .213 .12235 .258 .16051 .303 .20092 .348 .24307 .214 .12317 .259 .16139 .304 .20184 .349 .24403 .215 .12399 .260 .16226 .305 .20276 .350 .24498 .216 .12481 .261 .16314 .306 .20368 .351 .24593 .217 .12563 .262 .16402 .307 .20460 .352 .24689 .218 .12646 .263 .16490 .308 .20553 .353 .24784 .219 .12729 .264 .16578 .309 .20645 .354 .24880 .220 .12811 .265 .16666 .310 .20738 .355 .24976 .221 .12894 .266 .16755 .311 .20830 .356 .25071 .222 .12977 .267 .16843 .312 .20923 .357 .25167 .223 .13060 .268 .16932 .313 .21015 .358 .25263 .224 .13144 .269 .17020 .314 .21108 .359 .25359 .225 .13227 .270 .17109 .315 .21201 .360 .25455 .226 .13311 .271 .17198 .316 .21294 .361 .25551 .227 .13395 .272 .17287 .317 .21387 .362 .25647 .228 .13478 .273 .17376 .318 .21480 .363 .25743 .229 .13562 .274 .17465 .319 .21573 .364 .25839 .230 .13646 .275 .17554 .320 .21667 .365 .25936 .231 .13731 .276 .17644 .321 .21760 .366 .26032 .232 .13815 .277 .17733 .322 .21853 .367 .26128 .233 .13899 .278 .17823 .323 .21947 .368 .26225 .234 .13984 .279 .17912 .324 .22040 .369 .26321 .235 .14069 .280 .18002 .325 .22134 .370 .26418 .236 .14154 .281- .18092 .326 .22228 .371 .26514 .237 .14239 .282 .18182 .327 .22322 .372 .26611 .238 .14324 .283 .18272 .328 .22415 .373 .26708 .239 .14409 .284 .18362 .329 .22509 .374 .26805 .240 .14494 .285 .18452 .330 .22603 .375 .26901 .241 . 14580 .286 .18542 .331 .22697 .376 .26998 .242 .14665 .287 .18633 .332 .22792 .377 .27095 .243 .14752 .288 .18723 .333 .22886 .378 .27192 .244 .14837 .289 .18814 .334 .22980 .379 .27289 .245 .14923 .290 .18905 .335 .23074 .380 .27386 [131 AREAS OF CIRCULAR SEGMENTS AREAS OF CIRCULAR SEGMENTS (Cont.) Height Area Height Area Height Area Height Area .381 .27483 .406 .29926 .431 .32392 .462 .35474 .382 .27580 .407 .30024 .432 .32491 .464 .35673 .383 .27678 .408 .30122 .433 .32590 .466 .35873 .384 .27775 .409 .30220 .434 .32689 .468 .36072 .385 .27872 .410 .30319 .435 .32788 .470 .36272 .386 .27969 .411 .30417 .436 .32887 .471 .36371 .387 .28070 .412 .30516 .437 .32987 .473 .36571 .388 .28164 .413 .30614 .438 .33086 .475 .36771 .389 .28262 .414 .30712 .439 .33185 .477 .36971 .390 .28359 .415 .30811 .440 .33284 .479 .37170 .391 .28457 .416 .30910 .441 .33384 .482 .37470 .392 .28554 .417 .31008 .442 .33483 .484 .37670 .393 .28652 .418 .31107 .443 .33582 .486 .37870 .394 .28750 .419 .31205 .444 .33682 .488 .38070 .395 .28848 .420 .31304 .445 .33781 .490 .38270 .396 .28945 .421 .31403 .446 .33880 .491 .38370 .397 .29043 .422 .31502 .447 .33980 .492 .38470 .398 .29141 .423 .31600 .448 .34079 .493 .38570 .399 .29239 .424 .31699 .449 .34179 .494 .38670 .400 .29337 .425 .31798 .450 .34278 .495 .38770 .401 .29435 .426 .31897 .451 .34378 .496 .38870 .402 .29533 .427 .31996 .453 .34577 .497 .38970 .403 .29631 .428 .32095 .455 .34776 .498 .39070 .404 .29729 .429 .32194 .457 .34975 .499 .39170 .405 .29827 .430 .32293 .459 .35175 .500 .39270 To Find the Area of a Ring Included Between the Circumferences of Two Concen- tric Circles. Rule 1. The difference between the areas of two circles will be the area of the ring. Or, multiply the sum of the diameters by their difference, and by .7854. Rule 2. Multiply half the sum of the circumferences by half the difference of the diameter, and the product will be the area. This rule will also serve for any part of the ring, using half the sum of the inter- cepted arc for half the sum of the circumference. [132] MENSURATION To Find the Length of the Whole Arc of a Cycloid. Rule: Multiply the diameter of the generating circle by 4. To Find the Area of a Cycloid. Rule: Multiply the area of the generating circle by 3. To Find the Area of a Parabola. Rule: Multiply the base by the height; two- thirds of the product is the area. To Find the Length of an Arc of a Parabola, cut off by a double ordinate to the axis. Rule: To the square of the ordinate add four- fifths of the square of the abscissa; twice the square root of the sum is the length nearly. NOTE. This rule is an approximation which applies to those cases only in which the abscissa does not exceed half the ordinate. To Find the Circumference of an Ellipse. Multiply the square root of half the sum of the squares of the two axes by 3.1416. To Find the Area of an Ellipse. Multiply the product of the two axes by .7854. NOTE. The area of an ellipse is equal to the area of a circle of which the diameter is a mean proportional between the two axes. To Find the Area of an Elliptic Segment, the base of which is parallel to either axis of the ellipse. Rule: Divide the height of the segment by the axis of which it is a part, and find the area of a circular segment as given in the table relating to circular segments, of which the height is equal to this quotient; multiply the area thus found by the two axes of the ellipse successively ; the product is the area. To Describe an Elliptic Figure, When One Diameter A B is given: Divide A B into four equal parts. From C and D, with radius C A, or D B, de- scribe circles touching each other in E. From C and D, with radius C D, describe arcs cutting each other in F G. Draw lines G C, G D, F C, F D, and produce them until they cut the circles in H IJ and K. From F and G, with radius F K or G I, draw arcs uniting H with I and J with K, which will complete the figure. [133] MENSURATION To Describe an Ellipse with Arcs of Three Radii. On the transverse axis A B draw the rectangle B G, on the height O C; to the diagonal AC draw the perpendicular G H D; set off O K equal to O C, and describe a semi-circle on A K, and produce O C to L; set off O M equal to C L, and on D describe an arc with radius DM; on A, with radius O L, cut this arc at a. Thus the five centers D, a, 6, H, H' are found, from which the arcs are described to form the ellipse. NOTE. This process works well for nearly all proportions of ellipses. It is em- ployed in striking out vaults, stone bridges, etc. To Find the Length of an Arc of a Hyperbola, beginning at the vertex. Rule 1. To nineteen times the transverse axis add twenty-one times the parameter to this axis, and multiply the sum by the quotient of the abscissa divided by the transverse. 2. To nine times the transverse add twenty-one times the parameter, and multiply the sum by the quotient of the abscissa divided by the transverse,. 3. To each of these products add fifteen times the pa- rameter and then, as the latter sum : is to the former sum : : so is the ordinate : to the length of the arc, nearly. To Find the Area of a Hyperbola. Rule: To the product of the transverse and abscissa add five-sevenths of the square of the abscissa, and multiply the square root of the sum by 21; to this product add four times the square root of the product of the transverse and abscissa; multiply the sum by four times the product of the conjugate and abscissa, and divide by seventy-five times the trans- verse. The quotient is the area nearly. To Find the Areas of Lunes, or the spaces between the intersecting arcs of two eccentric circles. Rule: Find the areas of the two segments from which the lune is formed, and their difference will be the area required. NOTE. A lune is a space included between the arcs of two unequal circles inter- secting each other in two points, and having their centers on the same side of the straight line which joins these points of intersection. The lune was the first curvilinear space that was shown to be exactly equal to a [134] MENSURATION rectilinear one, and this was first effected by Hippocrates. The following property is one of the most curious: If A B C be a right-angled triangle, and semicircles be described on the three sides as diameters, then will the said triangle be equal to the two lunes D and F taken together. For the semicircles described on A C and B C = the one described on A B, from each take the segments cut off by A C and B C, then will the lune A F C E and B D C G = the triangle A C B. AREA OF AN IRREGULAR FIGURE The area of an irregular figure, as D E C B, in which the base is a straight line, and the perpendiculars at D and E also straight lines, the line B C, being an irregular I i i fc line, may be obtained by dividing the base line into a number of equal parts as indi- cated by full lines, and erecting an ordinate in each as shown by .dotted lines. The length of each ordinate is to be carefully measured and all are added together; the sum so obtained is divided by the number of ordinates; the quotient is the mean height, D F. Draw F G parallel to D E. Produce D B to F, and E C to G. The parallelogram D E F G is equal in area to the irregular figure: then Area' = Base X Height. Case 2. A Non-Symmetrical Figure. When the area is not symmetrical about a line, the figure should be enclosed by drawing a base line and erecting perpendiculars, each touching the projecting curves at that side. Draw A B parallel to C D; this line must also touch the highest curve at the top of the figure. The parallelogram A B C D is thus formed around the figure. The base C D is to be divided into any number of equal parts, and in the center of each draw ordinates, efgh, etc. Measure the ordinates, add them together, and divide the sum by the number of ordinates, the quotient will be the equivalent height for a parallelogram of which' the base is C D. Simpson's Rule. Divide the base line A B into a number of equal parts. This ensures that the number of ordinates is an odd number. Draw the ordinates from the base line to the boundary line. [135] TRIGONOMETRY Add together the first and last ordinates and call the sum A. Add together the even ordinates and call that sum B. Add together the odd ordinates, except the first and last, and call the sum C. Let D be the common distance, then A + 4B -f 2C x D = Area of Figure. 3 Rule: Add together the extreme ordinates, four times the sum of the even ordinates, and twice the sum of the odd ordinates (omitting the first and the last). Multiply the result by one-third the common interval between the consecutive ordinates. The end ordinates, as c and fc, may both be zero, as in the illustration, the curve commencing from the base line A B. In this case A is zero, and the above rule expressed as formula becomes, Area = - (O + 4 B = 2 C), o in which S denotes the common distance or space between the ordinates. PLANE TRIGONOMETRY The circumference of a circle is supposed to be divided into 360 or divisions, and as the total angularity about the center is equal to four right angles, each right angle contains 90 degrees, or 90, and half a right angle contains 45. Each degree is divided into 60 minutes, or 60'; and, for the sake of \still further minuteness of measurement, each c./,^,/ minute is divided into 60 seconds, or 60". In ~~! a whole circle there are, therefore, 360 X 60 X 60 = 1,296,000 seconds. The annexed diagram exemplifies the relative positions of the sine, cosine, versed sine, tangent, cotangent, secant, and cosecant of an angle. It may be stated, generally, that the correlated quantities, name- ly, the cosine, cotangent, and cosecant of an angle, are the sine, tangent, and secant, re- spectively, of the complement of the given angle, thecomplement being the difference between the given angle and a right angle. The supplement of an angle is the amount by which it is less than two right angles. When the sines and cosines of angles have been calculated (by means of formulas which it is not necessary here to particularize) the tangents, cotangents, secants, and cosecants are deduced from them according to the following relations: rad 2 rad 2 rad 2 rad X sin tan = ; cotan tan rad 2 sec = ; cosec cos sin For these the values will be amplified in tabular form. A triangle consists of three sides and three angles. When any three of these are given, including a side, the other three may be found by calculation : Case 1. When a side and its opposite angle are two of the given parts. Rule 1. To find a side, work the following proportion: as the sine of the angle opposite the given side is to the sine of the angle opposite the required side, so is the given side to the required side. [136] TRIGONOMETRY Rule 2. To find an angle: as the side opposite to the given angle is to the side opposite to the required angle, so is the sine of the given angle to the sine of the required angle. Rule 3. In a right-angled triangle, when the angies and one side next the right angle are given, to find the other side: as radius is to the tangent of the angle adjacent to the given side, so is this side to the other side. Case 2. When two sides and the included angle are given. Rule 4. To find the other side: as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference add this half difference to the half sum to find the greater angle, and subtract the half difference from the half sum to find the less angle. The other side may then be found by Rule 1. Rule 5. When the sides of a right-angled triangle are given, to find the angles: as one side is to the other side, so is the radius to the tangent of the angle adjacent to the first side. Case 3. When the three sides are given. Rule 6. To find an angle. Subtract the sum of the logarithms of the sides- which contain the required angle from 20, and to the remainder add the logarithm of half the sum of the three sides, and that of the difference between this half sum and the side opposite to the required angle. Half the sum of these three logarithms will be the logarithmic cosine of half the required angle. The other angles may be found by Rule 1. Rule 7. Subtract the sum of the logarithms of the two sides which contain the required angle from 20, and to the remainder add the logarithms of the differences between these two sides and half the sum of the three sides. Half the result will be the logarithmic sine of half the required angle. NOTE. In all ordinary cases either of these rules gives sufficiently accurate results. It is recommended that Rule 6 should be used when the required angle exceeds 90; and Rule 7 when it is less than 90. TRIGONOMETRICAL FORMULA The diagram shows the different trigonometrical expressions in terms of the angle A. In the following formulae Radius = 1. Complement of an angle = its difference from 90. Supplement of an angle = its difference from 180. sin = = - = V (1 cos 2 ) cosec cot sin 1 tan = = cos cot sec = V rad 2 + tan 2 = = -7 cos sin cos = V (1 sin 2 ) = - - = sin X cot = tan sec cos 1 1 cot = -r- = . cosec = -r- sin tan sin [137] TRIGONOMETRY versin = rad cos coversin = rad sin rad = tan X cot = V sin 2 + cos 2 Solution of Right-Angled Triangles. hyp 2 = base 2 + perp 2 base 2 = (hyp + perp) X (hyp - perp) perp 2 = (hyp + base) X (hyp - base) A sin cos tana=A cosec a = A seca=lf cot a = - A. A cosb=- b = 90 - a A = B tan a A = C sin a B = C cos a = A cot a = V (C + A) (C - A) C = + B 2 = sin a cos a Solution of Oblique- Angled Triangles. Value of any side C is: C = C = A sin c _ B sin c _ A sin a sin b cos b + sin b cot c B = A cos b + A cos a -f- sin a cot c C = V A 2 + B 2 - 2 A B cos c = B cos a + B sin a cot b Value of any angle a is: A sin c A sin b sui a = sin (b + c) sin a = sin b cos c -f cos b sin c. cos a = sin b sin c cos b cos c. cos a tan a C 2 + B 2 - A 2 2BC A sin c A sin b B A cos c ~ C A cos b [138] SINES, COSINES, TANGENTS, ETC. SINES, COSINES, TANGENTS, COTANGENTS, SECANTS, AND COSECANTS OF ANGLES FROM TO 90 This table is constructed for angles of from to 90, advancing by 10', or one-sixth of a degree. The length of the radius is equal to 1, and forms the basis for the relative lengths given in the table, and which are given to six places of decimals. Each entry in the table has a duplicate significance, being the sine, tangent, or secant of one angle, and at the same time the cosine, cotangent, or cosecant of its complement. For this reason, and for the sake of compactness, the headings of the columns are reversed at the foot; so that the upper headings are correct for the angles named in the left-hand margin of the table, and the lower headings for those named in the right-hand margin. To Find the Sine, or Other Element, to Odd Minutes. Divide the difference between the sines, etc., of the two angles greater and less than the given angle, in the same proportion that the given angle divides the difference of the two angles, and add one of the parts to the sine next it. By an inverse process the angle may be found for any given sine, etc., not found in the table. SINES, COSINES, TANGENTS, COTANGENTS, SECANTS AND COSECANTS FOR ANGLES TO 90 Advancing by 10' or one-sixth of a Degree. Radius = 1 Angle Sine Cosecant Tangent- Cotangent Secant Cosine 0' .000000 Infinite .000000 Infinite 1.00000 1.000000 90 0' 10 .002909 343.77516 .002909 343.77371 1.00000 .999996 50 20 .005818 171.88831 .005818 171.88540 1.00002 .999983 40 30 .008727 114.59301 .008727 114.58865 1.00004 .999962 30 40 .011635 85.945609 .011636 85.939791 1.00007 .999932 20 50 .014544 68.757360 .014545 68.750087 1.00011 .999894 10 1 0' .017452 57.298688 .017455 57.289962 .00015 .999848 89 0' 10 .020361 49.114062 .020365 49.103881 .00021 .999793 50 20 .023269 42.975713 .023275 42.964077 .00027 .999729 40 30 .026177 38.201550 .026186 38.188459 .00034 .999657 30 40 .029085 34.382316 .029097 34.367771 .00042 .999577 20 50 .031992 31.257577 .032009 31.241577 .00051 .999488 10 2 0' .034899 28.653708 .034921 28.636253 .00061 .999391 88 V 10 .037806 26.450510 .037834 26.431600 .00072 .999285 50 20 .040713 24.562123 .040747 24.541758 1.00083 .999171 40 30 .043619 22.925586 .043661 22.903766 1.00095 .999048 30 40 .046525 21.493676 .046576 21.470401 1.00108 .998917 '20 50 .049431 20.230284 .049491 20.205553 1.00122 .998778 10 3 0' .052336 19.107323 .052408 19.081137 1.00137 .998630 87 0', 10 .055241 18.102619 .055325 18.074977 1.00153 .998473 50 20 .058145 17.198434 .058243 17.169337 1.00169 .998308 40 30 .061049 16.380408 .061163 16.349855 1.00187 .998135 30 40 .063952 15.636793 .064083 15.604784 1.00205 .997857 20 50 .066854 14.957882 .067004 14.924417 1.00224 .997763 10 Cosine Secant Cotangent Tangent Cosecant Sine Angle [139] SINES, COSINES, TANGENTS, ETC. SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Cosecant Tangent Cotangent Secant Cosine 4 0' .069756 14.335587 .069927 14.300666 1.00244 .997564 86 0' 10 .072658 13.763115 .072851 13.726738 1.00265 .997357 50 20 .075559 13.234717 .075776 13 . 196888 1.00287 .997141 40 30 .078459 12.745495 .078702 12.706205 1.00309 .996917 30 40 .081359 12.291252 .081629 12.2505505 1.00333 . 996685 20 50 .084258 11.868370 .084558 11.826167 1.00357 .996444 10 5 0' .087156 11.473713 .087489 11.430052 1.00382 .996195 85 0' 10 .090053 11.104549 .090421 11.059431 1.00408 .995937 50 20 .092950 10.758488 .093354 10.711913 1.00435 .995671 40 30 .095846 10.433431 .096289 10.385397 1.00463 .995396 30 40 .098741 10.127522 .099226 10.078031 1.00491 .995113 20 50 .101635 9.8391227 . 102164 9.7881732 1.00521 .994822 10 6 0' . 104528 9.5667722 . 105104 9.5143645 1.00551 .994522 84 0' 10 . 107421 9.3091699 . 108046 9.2553035 1.00582 .994214 50 20 .110313 9.0651512 .110990 9.0098261 1.00614 .993897 40 30 .113203 8.8336715 .113936 8.7768874 1.00647 .993572 30 40 .116093 8.6137901 .116883 8.5555468 1.00681 .993238 20 50 .118982 8.4045586 .119833 8.3449558 1.00715 .992896 10 7 0' . 121869 8.2055090 . 122785 8.1443464 1.00751 .992546 83 0' 10 . 124756 8.0156450 .125738 7.9530224 1.00787 .992187 50 20 .127642 7.8344335 . 128694 7.7703506 1.00825 .991820 40 30 . 130526 7.6612976 . 131653 7.5957541 1.00863 .991445 30 40 .133410 7.4957100 . 134613 7.4287064 1.00902 .991061 20 50 . 136292 7.3371909 .137576 7.2687255 1.00942 .990669 10 8 0' . 139173 7.1852965 . 140541 7.1153697 1.00983 .990268 82 0' 10 .142053 7.0396220 . 143508 6.9682335 1.01024 .989859 50 20 . 144932 6.8997942 . 146478 6.8269437 1.01067 .989442 40 30 .147809 6.7654691 . 149451 6.6911562 1.01111 .989016 30 40 .150686 6.6363293 . 152426 6.5605538 1.01155 .988582 20 50 .153561 6.5120812 . 155404 6.4348428 1.01200 .988139 10 9 0' .156434 6.3924532 . 158384 6.3137515 1.01247 .987688 81 0' 10 . 159307 6.2771933 . 161368 6.1970279 1.01294 .987229 50 20 . 162178 6.1660674 . 164354 6.0844381 1.01332 .986762 40 30 . 165048 6.0588980 . 167343 5.9757644 1.01391 .986286 30 40 . 167916 5.9553625 . 170334 5.8708042 1.01440- .985801 20 50 .170783 5.8553921 . 173329 5.7693688 1.01491 .985309 10 10 0' .173648 5.7587705 . 176327 5.6712818 1.01543 .984808 80 0' 10 .176512 5.6653331 . 179328 5.5763786 1.01595 .984298 50 20 . 179375 5.5749258 .182332 5.4845052 1.01649 .983781 40 30 .182236 5.4874043 . 185339 5.3955172 1.01703 .983255 30 40 . 185095 5.4026333 . 188359 5.3092793 1.01758 .982721 20 50 .187953 5.3204860 .191363 5.2256647 1.01815 .982178 10 Cosine Secant Cotangent Tangent Cosecant Sine Angle 140] SINES, COSINES, TANGENTS, ETC. SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Cosecant Tangent Cotangent Secant Cosine 11 0' . 190809 5.2408431 . 194380 5.1445540 .01872 .981627 79 0' 10 . 193664 5.1635924 . 197401 5.0658352 .01930 .981068 50 20 .196517 5.0886284 .200425 4.9894027 .01989 .980500 40 30 . 199368 5.0158317 .203452 4.9151570 .02049 .979925 30 40 .202218 4.9451687 .206483 4.8430045 .02110 .979341 20 50 .205065 4.8764907 .209518 4.7728568 .02171 .978748 10 12 0' .207912 4.8097343 .212557 4.7046301 .02234 .978148 78 0' 10 .210756 4.7448206 .215599 4.6382457 .02298 .977539 50 20 .213599 4.6816748 .218645 4.5736287 .02362 .976921 40 30 .216440 4.6202263 .221695 4.5107085 .02428 .976296 30 40 .219279 4.5604080 .224748 4.4494181 .02494 .975662 20 50 .222116 4.5021565 .227806 4.3896940 .02562 .975020 10 13 0' .224951 4.4454115 .230868 4.3314759 .02630 .974370 77 0' 10 .227784 4.3901158 .233934 4.2747066 .02700 .973712 50 20 .230616 4.3362150 .237004 4.2193318 .02770 .973045 40 30 .233445 4.2836576 .240079 4.1652998 .02842 .972370 30 40 .236273 4.2323943 .243158 4.1125614 .02914 .971687 20 50 .239098 4.1823785 .246241 4.0610700 .02987 .970995 10 14 0' .241922 4.1335655 .249328 4.0107809 1.03061 .970296 76 0' 10 .244743 4.0859130 .252420 3.9616518 1.03137 .969588 50 20 .247563 4.0393804 .255517 3.9136420 1.03213 .968872 40 30 .250380 3.9939292 .258618 3.8667131 1.03290 . 968148 30 40 .253195 3.9495224 .261723 3.8208281 1.03363 .967415 20 50 .256008 3.9061250 .264834 3.7759519 1.03447 .966675 10 15 0' .258819 3.8637033 .267949 3.7320508 1.03528 .965926 75 0' 10 .261628 3.8222251 .271069 3.6890927 1.03609 .965169 50 20 .264434 3.7816596 .274195 3.6470467 1.03691 .964404 40 30 .267238 3.7419775 .277325 3.6058835 1.03774 . 963630 30 40 .270040 3.7031506 .280460 3.5655749 1.03858 .962849 20 50 .272840 3.6651518 .283600 3.5260938 1.03944 .962059 10 16 0' .275637 3.6279553 .286745 3.4874144 .04030 .961262 74 0' 10 .278432 3 . 5915363 .289896 3.4495120 .04117 .960456 50 20 .281225 3.5558710 .293052 3.4123626 .04206 .959642 40 30 .284015 3 . 5209365 .296214 3.3759434 .04295 .958820 30 40 .286803 3.4867110 .299380 3.3402326 .04385 .957990 20 50 .289589 3.4531735 .302553 3.3052091 .04477 .957151 10 17 0' .292372 3.4203036 .305731 3.2708526 .04569 .956305 73 0' 10 .295152 3.3880820 .308914 3.2371438 .04663 .955450 50 20 .297930 3.3564900 .312104 3.2040638 .04757 .954588 40 30 .300706 3.3255095 .315299 3.1715948 1.04853 .953717 30 40 .303479 3.2951234 .318500 3.1397194 1.04950 .952838 20 50 .306249 3.2653149 .321707 3.1084210 1.05047 .951951 10 Cosine Secant Cotangent Tangent Cosecant Sine Angle 141 SINES, COSINES, TANGENTS, ETC. SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Cosecant Tangent Cotangent Secant Cosine 18 0' .309017 3.2360680 .324920 3.0776835 1.05146 .951057 72 0' 10 .311782 3.2073673 .328139 3.0474915 1.05246 .950154 50 20 .314545 3.1791978 .331364 3.0178301 1.05347 .949243 40 30 .317305 3.1515453 .334595 2.9886850 1.05449 .948324 30 40 .320062 3.1243959 .337833 2.9600422 1.05552 .947397 20 50 .322816 3.0977363 .341077 2.9318885 1.05657 .946462 10 19 0' .325568 3.0715535 .344328 2.9042109 1.05762 .945519 71 0' 10 .328317 3.0458352 .347585 2.8769970 1.05869 .944568 50 20 .331063 3.0205693 .350848 2.8502349 1.05976 .943609 40 30 .333807 2.9957443 .354119 2.8239129 1.06085 .942641 30 40 .336547 2.9713490 .357396 2.7980198 1.06195 .941666 20 50 .339285 2.9473724 .360680 2.7725448 1.06306 .940684 10 20 0' .342020 2.9238044 .363970 2.7474774 1.06418 .939693 70 0' 10 .344752 2.9006346 .367268 2.7228076 .06531 .938694 50 20 .347481 2.8778532 .370573 2.6985254 .06645 .937687 40 30 .350207 2.8554510 .373885 2.6746215 .06761 .936672 30 40 .352931 2.8334185 .377204 2.6510867 .06878 .935650 20 50 .355651 2.8117471 .380530 2.6279121 .06995 .934619 10 21 0' .358368 2.7904281 .383864 2.6050891 .07115 .933580 69 0' 10 .361082 2.7694532 .387205 2.5826094 .07235 .932534 50 20 .363793 2.7488144 .390554 2.5604649 .07356 .931480 40 30 .366501 2.7285038 .393911 2.5386479 .07479 .930418 30 40 .369206 2.7085139 .397275 2.5171507 .07602 .929348 20 50 .371908 2.6888374 .400647 2.4959661 .07727 .928270 10 22 0' .374607 2.6694672 .404026 2.4750869 .07853 .927184 68 0' 10 .377302 2.6503962 .407414 2.4545061 .07981 .926090 50 20 .379994 2.6316180 .410810 2.4342172 .08109 .924989 40 30 .382683 2.6131259 .414214 2.4142136 .08239 .923880 30 40 .385369 2.5949137 .417626 2/3944889 .08370 .922762 20 50 .388052 2.5769753 .421046 2.3750372 .08503 .921638 10 23 0' .390731 2.5593047 .424475 2.3558524 .08636 .920505 67 0' 10 .393407 2.5418961 .427912 2.3369287 .08771 .919364 50 20 .396080 2.5247440 .431358 2.3182606 .08907 .918216 40 30 .398749 2.5078428 .434812 2.2998425 .09044 .917060 30 40 .401415 2.4911874 .438276 2.2816693 .09183 .915896 20 50 .404078 2.4747726 .441748 2.2637357 .09323 .914725 10 24 O 7 .406737 2.4585933 .445229 2.2460368 1.09464 .913545 66 0' 10 .409392 2.4426448 .448719 2.2285676 1.09606 .912358 50 20 .412045 2.4269222 .452218 2.2113234 1.09750 .911164 40 30 .414693 2.4114210 .455726 2.1942997 1.09895 .909961 30 40 .417338 2.3961367 .459244 2.1774920 1 . 10041 .908751 20 50 .419980 2.3810650 .462771 2.1608958 1 . 10189 .907533 10 Cosine Secant Cotangent Tangent Cosecant Sine Angle 142] SINES, COSINES, TANGENTS, ETC. SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Cosecant Tangent Cotangent Secant Cosine 25 0' .422618 2.3662016 .466308 2.1445069 1 . 10338 .906308 65 0' 10 .425253 2.3515424 .469854 2.1283213 1.10488 .905075 50 20 .427884 2.3370833 .473410 2.1123348 1.10640 .903834 40 30 .430511 2.3228205 .476976 2.0965436 1.10793 .902585 30 40 .433135 2.3087501 .480551 2.0809438 1.10947 .901329 20 50 .435755 2.2948685 .484137 2.0655318 1.11103 .900065 10 26 0' .438371 2.2811720 .487733 2.0503038 1.11260 .898794 64 0' 10 .440984 2.2676571 .491339 2.0352565 1.11419 .897515 50 20 .443593 2.2543204 .494955 2.0203862 1.11579 .896229 40 30 .446198 2.2411585 .498582 2.0056897 1.11740 .894934 30 40 .448799 2.2281681 .502219 .9911637 1.11903 .893633 20 50 .451397 2.2153460 .505867 .9768050 1.12067 .892323 10 27 0' .453990 2.2026893 .509525 .9626105 1.12233 .891007 63 0' 10 .456580 2.1901947 .513195 .9485772 1.12400 .889682 50 20 .459166 2.1778595 .516876 .9347020 1.12568 .888350 40 30 .461749 2.1656806 .520567 1.9209821 1 . 12738 .887011 30 40 .464327 2.1536553 .524270 1.9074147 1.12910 .885664 20 50 .466901 2.1417808 .527984 1.8939971 1.13083 .884309 10 28 0' .469472 2.1300545 .531709 1.8807265 1.13257 .882948 62 0' 10 .472038 2.1184737 .535547 1.8676003 1.13433 .881578 50 20 .474600 2.1070359 .539195 1.8546159 1 . 13610 .880201 40 30 .477159 2.0957385 .542956 1.8417409 1.13789 .878817 30 40 .479713 2.0845792 .546728 1.8290628 1.13970 .877425 20 50 .482263 2.0735556 .550515 1.8164892 1 . 14152 .876026 10 29 0' .484810 2.0626653 .554309 1.8040478 1 . 14335 .874620 61 0' 10 .487352 2.0519061 .558118 1.7917362 1.14521 .873206 50 20 .489890 2.0412757 .561939 1.7795524 1.14707 .871784 40 30 .492424 2.0307720 .565773 1.7674940 1 . 14896 .870356 30 40 .494953 2.0203929 .569619 1.7555590 1.15085 .868920 20 50 .497479 2.0101362 .573478 1.7437453 1.15277 .867476 10 30 0' .500000 2.0000000 .577350 1.7320508 1.15470 .866025 60 0' 10 .502517 1.9899822 .581235 1.7204736 1 . 15665 .864567 50 20 .505030 1.9800810 .585134 1.7090116 1 . 15861 .863102 40 30 .507538 1.9702944 .589045 1.6976631 . 16059 .861629 30 40 .510043 1.9606206 .592970 1.6864261 . 16259 .860149 20 50 .512543 1.9510577 .596908 1.6752988 . 16460 .858662 10 31 0' .515038 1.9416040 .600861 1.6642795 .16663 .857167 59 0' 10 .517529 1.9322578 .604827 1.6533663 .16868 .855665 50 20 .520016 1.9230173 .608807 1.6425576 . 17075 .854156 40 30 .522499 1.9138809 .612801 1.6318517 . 17283 .852640 30 40 .524977 1.9048469 .616809 1.6212469 . 17493 .851117 20 50 .527450 1.8959138 .620832 1.6107417 . 17704 .849586 10 Cosine Secant Cotangent Tangent Cosecant Sine Angle 143 n SINES, COSINES, TANGENTS, ETC. SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Cosecant Tangent Cotangent Secant Cosine 32 0' .529919 1.8870799 .624869 1.6003345 1 . 17918 .848048 58 0' 10 .532384 1.8783438 .628921 1.5900238 1.18133 .846503 50 20 .534844 1.8697040 .632988 1.5798079 1.18350 .844951 40 30 .537300 1.8611590 .637079 1.5696856 1 . 18569 .843391 30 40 . 539751 1.8527073 .641167 1.5596552 1 . 18790 .841825 20 50 .542197 1.8443476 .645280 1.5497155 1 . 19012 .840251 10 33 0' .544639 1.8360785 .649408 . 5398650 1 . 19236. .838671 57 0' 10 .547076 1.8278985 .653531 .5301025 1 . 19463 .837083 50 20 .549509 1.8198065 .657710 .5204261 1 . 19691 .835488 40 30 .551937 1.8118010 .661886 .5108352 1 . 19920 .833886 30 40 .554360 1.8038809 .666077 .5013282 1.20152 .832277 20 50 .556779 1.7960449 .670285 .4919039 1.20386 .830661 10 34 0' .559193 1.7882916 .674509 .4825610 .20622 .829038 56 0' 10 .561602 1.7806201 .678749 .4732983 .20859 .827407 50 20 .564007 1.7730290 .683007 .4641147 .21099 .825770 40 30 .566406 1.7655173 .687281 .4550090 .21341 .824126 30 40 .568801 1.7580837 .691573 .4459801 .21584 .822475 20 50 .571191 1.7507273 .695881 .4370268 .21830 .820817 10 35 0' .573576 1.7434468 .700208 .4281480 .22077 .819152 55 0' 10 .575957 1.7362413 . 704552 .4193427 .22327 .817480 50 20 .578332 1.7291096 .708913 .4106098 1.22579 .815801 40 30 .580703 1.7220508 .713293 .4019483 1.22833 .814116 30 40 .583069 1.7150639 .717691 .3933571 1.23089 .812423 20 50 .585429 1.7081478 .722108 .3848355 1.23347 .810723 10 36 0' .587785 .7013016 .726543 .3763810 1.23607 .809017 54 0' 10 .590136 .6945244 .730996 .3679959 1.23869 .807304 50 20 .592482 .6878151 .735469 .3596764 1.24134 .805584 40 30 .594823 .6811730 .739961 .3514224 1.24400 .803857 30 40 .597159 .6745970 .744472 .3432331 1.24669 .802123 20 50 .599489 .6680864 .749003 .3351075 1.24940 .800383 10 37 0' .601815 .6616401 .753554 .3270448 1.25214 .798636 53 0' 10 .604136 .6552575 .758125 .3190441 1.25489 .796882 50 20 .606451 .6489376 .762716 .3111046 1 . 25767 .795121 40 30 .608761 .6426796 .767627 .3032254 1.26047 .793353 30 40 .611067 .6364828 .771959 .2954057 1.26330 .791579 20 50 .613367 .6303462 .776612 .2876447 1.26615 .789798 10 38 0' .615661 1.6242692 .781286 .2799416 1.26902 .788011 52 0' 10 .617951 1.6182510 .785981 .2722957 1.27191 .786217 50 20 .620235 1.6122908 .790698 .2647062 1.27483 .784416 40 30 .622515 1.6063879 .795436 .2571723 1.27778 .782608 30 40 .624789 1.6005416 .800196 .2496933 1.28075 .780794 20 50 .627057 1.5947511 .804080 .2422685 1.28374 .778973 10 Cosine Secant Cotangent Tangent Cosecant Sine Angle [144] SINES, COSINES, TANGENTS, ETC. SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Cosecant Tangent Cotangent Secant Cosine 39 0' .629320 1.5890157 .809784 1.2348972 .28676 .777146 51 0' 10 .631578 1.5833318 .814612 1.2275786 .28980 .775312 50 20 .633831 1.5777077 .819463 1.2203121 .29287 .773472 40 30 .636078 1.5721337 .824336 1.2130970 .29597 .771625 30 40 .638320 1.5666121 .829234 1.2059327 .29909 .769771 20 50 .640557 1.5611424 .834155 1.1988184 .30223 .767911 10 40 0' .642788 1.5557238 .839100 1 . 1917536 1.30541 .766044 50 0' 10 .645013 1.5503558 .844069 1.1847376 1.30861 .764171 50 20 .647233 1.5450378 .849062 1.1777698 1.31183 .762292 40 30 .649448 1.5397690 .854081 1 . 1708496 1.31509 .760406 30 40 .651657 1.5345491 .859124 1.1639763 1.31837 .758514 20 50 .653861 1.5293773 .864193 1.1571495 1.32168 .756615 10 41 0' .656059 1.5242531 .869287 .1503684 1 . 32501 .754710 49 0' 10 .658252 1.5191759 .874407 . 1436326 1.32838 .752798 50 20 .660439 1.5141452 .879553 . 1369414 1.33177 .750880 40 30 .662620 1.5091605 .884725 . 1302944 .33519 .748956 30 40 .664796 1.5042211 .889924 . 1236909 .33864 .747025 20 50 .666966 1.4993267 .895151 .1171305 .34212 .745088 10 42 0' .669131 1.4944765 .900404 1.1106125 .34563 .743145 48 0' 10 .671289 1.4896703 .905685 1 . 1041365 .34917 .741195 50 20 .673443 1.4849073 .910994 1.0977020 1.35274 .739239 40 30 .675590 1.4801872 .916331 1.0913085 1.35634 .737277 30 40 .677732 1.4755095 .921697 1.0849554 1.35997 .735309 20 50 .679868 1.4708736 .927091 1.0786423 1.36363 .733335 10 43 0' .681998 .4662792 .932515 .0723687 1.36733 .731354 47 0' 10 .684123 .4617257 .937968 .0661341 .37105 .729367 50 20 .686242 .4572127 .943451 .0599381 .37481 .727374 40 30 .688355 .4527397 .948965 .0537801 .37860 .725374 30 40 .690462 .4483063 .954508 .0476598 .38242 .723369 20 50 .692563 1.4439120 .960083 .0415767 .38628 .721357 10 44 0' .694658 1.4395565 .965689 1.0355303 .39016 .719340 46 0' 10 .696748 1.4352393 .971326 1.0295203 .39409 .717316 50 20 .698832 1.4309602 .976996 1.0235461 1.39804 .715286 40 30 .700909 1.4267182 .982697 1.0176074 1.40203 .713251 30 40 .702981 1.4225134 .988432 1.0117088 1.40606 .711209 20 50 .705047 1.4183454 .994199 1.0058348 1.41012 .709161 10 45 0' .707107 1.4142136 1.000000 1.0000000 1.41421 .707107 45 -0' Cosine Secant Cotangent Tangent Cosecant Sine Angle [145] LOGARITHMIC SINES, COSINES, TANGENTS, ETC. LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS OF ANGLES FROM TO 90 -This table is constructed similarly to the table of natural sines, etc., preceding. To avoid the use of logarithms with negative indices, the radius is assumed, instead of being equal to 1, to be equal to 10 10 , or 10,000,000,000; consequently, the logarithm of the radius = 10 log 10 = 10. Whence, if to log sine of any angle, when calculated for a radius = 1, there be added 10, the sum will be the log sine of that angle for a radius = 10 10 . For example, to find the logarithmic sine of the angle 15 50': Nat. sine 15 50' = .272840; its log = 1.435908 add = 10 Logarithmic sine of 15 50' = 9.435908 When the logarithmic sines and cosines have been found in this manner, the loga- rithmic tangents, cotangents, secants, and cosecants are found from those by addition or subtraction, according to the correlations of the trigonometrical elements already given, and here repeated in logarithmic form: log tan = 10 + log sin log cosin log cotan = 20 log tan log sec =20 log cosin log cosec = 20 log sin To Find the Logarithmic Sine, Tangent, etc., of Any Angle. When the number of degrees is less than 45, find the degrees and minutes in the left-hand column headed angle, and under the heading sine or tangent, etc., as required, the logarithm is found in a line with the angle. When the number of degrees is above 45, and less than 90, find the degrees and minutes in the right-hand column headed angle, and in the same line, above the title at the foot of the page, sine or tangent, etc., find the logarithm in a line with the angle. When the number of degrees is between 90 and 180, take their supplement to 180; when between 180 and 270, diminish them by 180; and when between 270 and 360, take their complement to 360, and find the logarithm of the remainder as before. If the exact number of minutes is not found in the table, the logarithm of the nearest tabular angle is to be taken and increased or diminished, as the case may be, by the due proportion of the difference of the logarithms of the angles greater and less than the given angle. [146] LOGARITHMIC SINES, COSINES, TANGENTS, ETC. LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS OF ANGLES FROM TO 90 Advancing by 10', or one-sixth of a Degree Angle Sine Tangent Cotangent Cosine 0.000000 0.000000 Infinite 10.000000 90 10' 7.463726 7.463727 12.536273 9.999998 50' 20 7.764754 7.764761 12.235239 9.999993 40 30 7.940842 7.940858 12.059142 9.999983 30 40 8.065776 8.065806 11.934194 9.999971 20 50 8.162681 8.162727 11.837273 9.999954 10 1 8.241855 8.241921 11.758079 9.999934 89 10' 8.308794 8.308884 11.691116 9.999910 50' 20 8.366777 8.366895 11.633105 9.999882 40 30 8.417919 8.418068 11.581932 9.999851 30 40 8.463665 8.463849 11.536151 9.999816 20 50 8.505045 8.505267 11.494733 9.999778 10 2 8.542819 8.543084 11.456916 9.999735 88 10' 8.577566 8.577877 11.422123 9.999689 50' 20 8.609734 8.610094 11.389906 9.999640 40 30 8.639680 8.640093 11.359907 9.999586 30 40 8.667689 8.668160 11.331840 9.999529 20 50 8.693998 8.694529 11.305471 9.999469 10 3 8.718800 8.719396 11.280604 9.999404 87 10' 8.742259 8.742922 11.257078 9.999336 50' 20 8.764511 8.765246 11.234754 9.999265 40 30 8.785675 8.786486 11.213514 9.999189 30 40 8.805852 8.806742 11.193258 9.999110 20 50 8.825130 8.826103 11.173897 9.999027 10 4 8.843585 8.844644 11.155356 9.998941 86 10' 8.861283 8.862433 11.137567 9.998851 50' 20 8.878285 8.879529 11.120471 9.998757 40 30 8.894643 8.895984 11.104016 9.998659 30 40 8.910404 8.911846 11.088154 9.998558 20 50 8.925609 8.927156 11.072844 9.998453 10 5 8.940296 8.941952 11.058048 9.998344 85 10' 8.954499 8.956267 11.043733 9.998232 50' 20 8.968249 8.970133 11.029867 9.998116 40 30 8.981573 8.983577 11.016423 9.997996 30 40 8.994497 8.996624 11.003376 9.997872 20 50 9.007044 9.009298 10.990702 9.997745 10 6 9.019235 9.021620 10.978380 9.997614 84 10' 9.031089 9.033609 10.966391 9.997480 50' 20 9.042625 9.045284 10.954716 9.997341 40 30 9.053859 9.056659 10.943341 9.997199 30 40 9.064806 9.067752 10.932248 9.997053 20 50 9.075480 9.078576 10.921424 9.996904 10 Cosine Cotangent Tangent Sine Angle [147] LOGARITHMIC 'SINES, COSINES, TANGENTS, ETC LOGARITHMIC SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Tangent Cotangent Cosine 7 9.085894 9.089144 10.910856 9.996751 83 10' 9.096062 9.099468 10.900532 9.996594 50' 20 9.105992 9.109559 10.890441 9.996433 40 30 9.115698 9.119429 10.880571 9.996269 30 40 9.125187 9.129087 10.870913 9.996100 20 50 9.134470 9.138542 10.861458 9.995928 10 8 9.143555 9.147803 10.852197 9.995753 82 10' 9.152451 9.156877 10.843123 9.995573 50' 20 9.161164 9.165774 10.834226 9.995390 40 30 9.169702 9.174499 10.825501 9.995203 30 40 9.178072 9.183059 10.816941 9.995013 20 50 9.186280 9.191462 10.808538 9.994818 10 9 9.194332 9.199713 10.800287 9.994620 81 10' 9.202234 9.207817 10.792183 9.994418 50' 20 9.209992 9.215780 10.784220 9.994212 40 30 9.217609 9.223607 10.776393 9.994003 30 40 9.225092 9.231302 10.768698 9.993789 20 50 9.232444 9.238872 10.761128 9.993572 10 10 9.239670 9.246319 10.753681 9.993351 80 10' 9.246775 9.253648 10.746352 9.993127 50' 20 9.253761 9.260863 10.739137 9.992898 40 30 9.260633 9.267967 10.732033 9.992666 30 40 9.267395 9.274964 10.725036 9.992430 20 50 9.274049 9.281858 10.718142 9.992190 10 11 9.280599 9.288652 10.711348 9.991947 79 10' 9.287048 9.295349 10.704651 9.991699 50' 20 9.293399 9.301951 10.698049 9.991448 40 30 9.299655 9.308463 10.691537 9.991193 30 40 9.305819 9.314885 10.685115 9.990934 20 50 9.311893 9.321222 10.678778 9.990671 10 12 9.317879 9.327475 10.672525 9.990404 78 10' 9.323780 9.333646 10.666354 9.990134 50' 20 9.329599 9.339739 10.660261 9.989860 40 30 9.335337 9.345755 10.654245 9.989582 30 40 9.340996 9.351697 10.648303 9.989300 20 50 9.346779 9.357566 10.642434 9.989014 10 13 9.352088 9.363364 10.636636 9.988724 77 10' 9.357524 9.369094 10.630906 9.988430 50' 20 9.362889 9.374756 10.625244 9.988133 40 30 9.368185 9.380354 10.619646 9.987832 30 40 9.373414 9.385888 10.614112 9.987526 20 50 9.378577 9.391360 10.608640 9.987217 10 Cosine Cotangent Tangent Sine Angle 148] LOGARITHMIC SINES, COSINES, TANGENTS, ETC. LOGARITHMIC SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Tangent Cotangent Cosine 14 9.383675 9.396771 10.603229 9.986904 76 10' 9.388711 9.402124 10.597876 9.986587 50' 20 9.393685 9.407419 10.592581 9.986266 40 30 9.398600 9.412658 10.587342 9.985942 30 40 9.403455 9.417842 10.582158 9.985613 20 50 9.408254 9.422974 10.577026 9.985280 10 15 9.412996 9.428052 10.571948 9.984944 75 10' 9.417684 9.433080 10.566920 9.984603 50' 20 9.422318 9.438059 10.561941 9.984259 40 30 9.426899 9.442988 10.557012 9.983911 30 40 9.431429 9.447870 10.552130 9.983558 20 50 9.435908 9.452706 10.547294 9.983202 10 16 9.440338 9.457496 10.542504 9.982842 74 10' 9.444720 9.462242 10.537758 9.982477 50' 20 9.449054 9.466945 10.533055 9.982109 40 30 9.453342 9.471605 10.528395 9.981737 30 40 9.457584 9.476223 10.523777 9.981361 20 50 9.461782 9.480801 10.519199 9.980981 10 17 9.465935 9.485339 10.514661 9.980596 73 10' 9.470046 9.489838 10.510162 9.980208 50' 20 9.474115 9.494299 10.505701 9.979816 40 30 9.478142 9.498722 10.501278 9.979420 30 40 9.482128 9.503109 10.496891 9.979019 20 50 9.486075 9.507460 10.492540 9.978615 10 18 9.489982 9.511776 10.488224 9.978206 72 10' 9.493851 9.516057 10.483943 9.977794 50' 20 9.497682 9.520305 10.479695 9.977377 40 30 9.501476 9.524520 10.475480 9.976957 30 40 9.505234 9.528702 10.471298 9.976532 20 50 9.508956 9.532853 10.467147 9.976103 10 19 9.512642 9.536972 10.463028 9.975670 71 10' 9.516294 9.541061 10.458939 9.975233 50' 20 9.519911 9.545119 10.454881 9.974792 40 30 9.523495 9.549149 10.450851 9.974347 30 40 9.527046 9.553149 10.446851 9.973897 20 50 9 . 530565 9.557121 10.442879 9.973444 10 20 9.534052 9.561066 10.438934 9.972986 70 10' 9.537507 9.564983 10.435017 9.972524 50' 20 9.540931 9.568873 10.431127 9.972058 40 30 9.544325 9.572738 10.427262 9.971588 30 40 9.547689 9.576576 10.423424 9.971113 20 50 9.551024 9.580389 10.419611 9.970635 10 Cosine Cotangent Tangent Sine Angle 149] LOGARITHMIC SINES, COSINES, TANGENTS, ETC. LOGARITHMIC SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Tangent Cotangent Cosine 21 9.554329 9.584177 10.415823 9.970152 69 10' 9.557606 9.587941 10.412059 9.969665 50' 20 9.560855 9.591681 10.408319 9.969173 40 30 9.564075 9.595398 10.404602 9.968678 30 40 9.567269 9.599091 10.400909 9.968178 20 50 9.570435 9.602761 10.397239 9.967674 10 22 9.573575 9.606410 10.393590 9.967166 68 10' 9.576689 9.610036 10.389964 9.966653 50 20 9.579777 9.613641 10.386359 9.966136 40 30 9.582840 9.617224 10.382776 9.965615 30 40 9.585877 9.620787 10.379213 9.965090 20 50 9.588890 9.624330 10.375670 9.964560 10 23 9.591878 9.627852 10.372148 9.964026 67 10' 9.594842 9.631355 10.368645 9.963488 50' 20 9.597783 9.634838 10.365162 9.962945 40 30 9.600700 9.638302 10.361698 9.962398 30 40 9.603594 9.641747 10.358253 9.961846 20 50 9.606465 9.645174 10.354826 9.961290 10 24 9.609313 9.648583 10.351417 9.960730 66 10' 9.612140 9.651974 10.348026 9.960165 50' 20 9.614944 9.655348 10.344652 9.959596 40 30 9.617727 9.658704 10.341296 9.959023 30 40 9.620488 9.662043 10.337957 9.958445 20 50 9.623229 9.665366 10.334634 9.957863 10 25 9.625948 9.668673 10.331328 9.957276 65 10' 9.628647 9.671963 10.328037 9.956684 50' 20 9.631326 9.675237 10.324763 9.956089 40 30 9.633984 9.678496 10.321504 9.955488 30 40 9.636623 9.681740 10.318260 9.954883 20 50 9.639242 9.684968 10.315032 9.954274 10 26 9.641842 9.688182 10.311818 9.953660 64 10' 9.644423 9.691381 10.308619 9.953042 50' 20 9.646984 9.694566 10.305434 9.952419 40 30 9.649527 9.697736 10.302264 9.951791 30 40 9.652052 9.700893 10.299107 9.951159 20 50 9.654558 9.704036 10.295964 9.950522 10 27 9.657047 9.707166 10.292834 9.949881 63 10' 9.659517 9.710282 10.289718 9.949235 50' 20 9.661970 9.713386 10.286614 9.948584 40 30 9.664406 9.716477 10.283523 9.947929 30 40 9.666824 9.719555 10.280445 9.947269 20 50 9.669225 9.722621 10.277379 9.946604 10 Cosine Cotangent Tangent Sine Angle 11501 LOGARITHMIC SINES, COSINES, TANGENTS, ETC. LOGARITHMIC SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Tangent Cotangent Cosine 28 9.671609 9.725674 10.274326 9.945935 62 10' 9.673977 9.728716 10.271284 9.945261 50' 20 9.676328 9.731746 10.268254 9.944582 40 30 9.678663 9.734764 10.265236 9.943899 30 40 9.680982 9.737771 10.262229 9.943210 20 50 9.683284 9.740767 10.259233 9.942517 10 29 9.685571 9.743752 10.256248 9.941819 61 10' 9.687843 9.746726 10.253274 9.941117 50' 20 9.690098 9.749689 10.250311 9.940409 40 30 9.692339 9.752642 10.247358 9.939697 30 40 9.694564 9.755585 10.244415 9.938980 20 50 9.696775 9.758517 10.241483 9.938258 10 30 9.698970 9.761439 10.238561 9.937531 60 10' 9.701151 9.764352 10.235648 9.936799 50' 20 9.703317 9.767255 10.232745 9.936062 40 30 9.705469 9.770148 10.229852 9.935320 30 40 9.707606 9.773033 10.226967 9.934574 20 50 9.709730 9.775908 10.224092 9.933822 10 31 9.711839 9.778774 10.221226 9.933066 59 10' 9.713935 9.781631 10.218369 9.932304 50' 20 9.716017 9.784479 10.215521 9.931537 40 30 9.718085 9.787319 10.212681 9.930766 30 40 9.720140 9.790151 10.209849 9.929989 20 50 9.722181 9.792974 10.207026 9.929207 10 32 9.724210 9.795789 10.204211 9.928420 58 10' 9.726225 9.798596 10.201404 9.927629 50' 20 9.728227 9.801396 10.198604 9.926831 40 30 9.730217 9.804187 10.195813 9.926029 30 40 9.732193 9.806971 10.193029 9.925222 20 50 9.734147 9.809748 10.190252 9.924409 10 33 9.736109 9.812517 10.187483 9.923591 57 10' 9.738048 9.815280 10.184720 9.922768 50' 20 9.739975 9.818035 10.181965 9.921940 40 30 9.741889 9.820783 10.179217 9.921107 30 40 9.743792 9.823524 10.176476 9.920268 20 50 9.745683 9.826259 10.173741 9.919424 10 34 9.747562 9.828987 10.171013 9.918574 56 10' 9.749429 9.831709 10.168291 9.917719 50' 20 9.751284 9.834425 10.165575 9.916859 40 30 9.753128 9.837134 10.162866 9.915994 30 40 9.754960 9.839838 10.160162 9.915123 20 50 9.756782 9.842535 10.157465 9.914246 10 Cosine Cotangent Tangent Sine Angle [151] LOGARITHMIC SINES, COSINES, TANGENTS, ETC. LOGARITHMIC SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Tangent Cotangent Cosine 35 9.758591 9.845227 10.154773 9.913365 55 10' 9.760390 9.847913 10.152087 9.912477 50' 20 9.762177 9.850593 10.149407 9.911584 40 30 9.763954 9.853268 10.146732 9.910686 30 40 9.765720 9.855938 10.144062 9.909782 20 50 9.767475 9.858602 10.141398 9.908873 10 36 9.769219 9.861261 10.138739 9.907958 54 10' 9.770952 9.863915 10.136085 9.907037 50' 20 9.772675 9.866564 10.133436 9.906111 40 30 9.774388 9.869209 10.130791 9.905179 30 40 9.776090 9.871849 10.128151 9.904241 20 50 9.777781 9.874474 10.125516 9.903298 10 37 9.779463 9.877114 10.122886 9.902349 53 10' 9.781134 9.879741 10.120259 9.901394 50' 20 9.782796 9.882363 10.117637 9.900433 40 30 9.784447 9.884980 10.115020 9.899467 30 40 9.786089 9.887594 10.112406 9.898494 20 50 9.787720 9.890204 10.109796 9.897516 10 38 9.789342 9.892810 10.107190 9.896532 52 10' 9.790854 9.895412 10.104588 9.895542 50' 20 9.792557 9.898010 10.101990 9.894546 40 30 9.794150 9.900605 10.099395 9.893344 30 40 9.795733 9.903197 10.096803 9.892536 20 50 9.797307 9.905785 10.094215 9.891523 10 39 9.798872 9.908369 10.091631 9.890503 51 10' 9.800427 9.910951 10.089049 9.889477 50' 20 9.801973 9.913529 10.086471 9.888444 40 30 9.803511 9.916104 10.083896 9.887406 30 40 9.805039 9.918677 10.081323 9.886362 20 50 9.806557 9.921247 10.078753 9.885311 10 40 9.808067 9.923814 10.076186 9.884254 50 10' 9.809569 9.926378 10.073622 9.883191 50' 20 9.811061 9.928940 10.071060 9.882121 40 30 9.812544 9.931499 10.068501 9.881046 30 40 9.814019 9.934056 10.065944 9.879963 20 50 9.815485 9.936611 10.063389 9.878875 10 41 9.816943 9.939163 10.060837 9.877780 49 10' 9.818392 9.941713 10.058287 9.876678 50' 20 9.819832 9.944262 10.055738 9.875571 40 30 9.821265 9.946808 10.053192 9.874456 30 40 9.822688 9.949353 10.050647 9.873335 20 50 9.824104 9.951896 10.048104 9.872208 10 Cosine Cotangent Tangent Sine Angle [152] LOGARITHMIC SINES, COSINES, TANGENTS, ETC. LOGARITHMIC SINES, COSINES, TANGENTS, ETC. (Cont.) Angle Sine Tangent Cotangent Cosine 42 9.825511 9.954437 10.045563 9.871073 48 10' 9.826910 9.956977 10.043023 9.869933 50' 20 9.828301 9.959516 10.040484 9.868785 40 30 9.829683 9.962052 10.037948 9.867631 30 40 9.831058 9.964588 10.035412 9.866470 20 50 9.83242S 9.967123 10.032877 9.865302 10 43 9.833783 9.969656 10.030344 9.864127 47 10' 9.835134 9.972188 10.027812 9.862946 50' 20 9.836477 9.974720 10.025280 9.861758 40 30 9.837812 9.977250 10.022750 9.860562 30 40 9.839140 9.979780 10.020220 9.859360 20 50 9.840459 9.982309 10.017691 9.858151 10 44 9.841771 9.984837 10.015163 9.856934 46 10' 9.843076 9.987365 10.012635 9.855711 50' 20 9.844372 9.989893 10.010107 9.854480 40 30 9.845662 9.992420 10.007580 9.853242 30 40 9.846944 9.994947 10.005053 9.851997 20 50 9.848218 9.997473 10.002527 9.850745 10 45 9.849485 10.000000 10.000000 9.849485 45 Cosine Cotangent Tangent Sine Angle MENSURATION OF SOLIDS To Find the Solidity of a Cube. Rule: Multiply the side of the cube by itself and that product again by the side. NOTE. The surface of the cube is equal to six times the square of its side. To Find the Solidity of a Parallelepipedon. Rule: Multiply the length by the breadth and that product by the depth or altitude. NOTE. The surface of the parallelepipedon is equal to the sum of the areas of each of its sides or ends. To Find the Solidity of a Prism. Rule: Multiply the area of the base into the perpendicular height of the prism. NOTE. The surface of a prism is equal to the sum of the areas of the two ends and each of its sides. [153] MENSURATION To Find the Convex Surface of a Cylinder. Rule: Multiply the circumference of the base by the height of the cylinder. NOTE. If twice the area of either of the ends be added to the convex surface, it will give the whole surface of the cylinder. To Find the Solidity of a Cylinder. Rule: Multiply the area of the base by the perpendicular height. NOTE. The four following cases contain all the rules for finding the superfices and solidities of cylindric ungulas. Case 1. When the Section is Parallel to the Axis of the Cylinder. Rule 1. Multiply the length of the arc line of the base by the height of the cylinder, the product will be the curve surface. Rule 2. Multiply the area of the base by the height of the cylinder, the product will be the solidity. Case 2. When the Section Passes Obliquely Through the Opposite Sides of the Cylinder. Rule 1. Multiply the circumference of the base of the cy Under by half the sum of the greatest and least lengths of the ungula, the product will be the curve surface. Rule 2. Multiply the area of the base of the cylinder by half the sum of the greatest and least lengths of the ungula, the product will be the solidity. H Case 3. When the Section Passes Through the Base of the Cylinder, and One of its Sides. -Rule 1. Multiply the sine of half the arc of the base by the diameter of the cylinder, and from this product subtract the product of the arc and cosine. Rule 2. Multiply the difference thus found, by the quotient of the height divided by the versed sine, the product will be the curve surface. [1541 MENSURATION Rule 3. From two-thirds of the cube of the right sine of half the arc of the base, subtract the product of the area of the base and the cosine of the said half arc. Multiply the difference thus found by the quotient arising from the height divided by the versed sine, the product will be the solidity. Case 4. When the Section Passes Obliquely Through Both Ends of the Cylinder. Rule 1. Conceive the section to be continued till it meets the side of the cylinder produced; then as the difference of the versed sine of half the arcs of the two ends of the ungula is to the versed sine of half the arc of the less end, so is the height of the cylinder to the part of the side produced. Rule 2. Find the surface of each of the ungulas, thus formed, by Case 3, and their difference will be the surface required. Rule 3. In like manner find the solidi- ties of each of the ungulas, and their difference will be the solidity required. To Find the Convex Surface of a Cone. Rule: Multiply the circumference of the base by the slant height, or the length of the sides of the cone, and half the product will be the surface required. To get the complete surface of the above cone the area of the base must be added. The Convex Surface of a Cone is a Sector of a Circle. To construct such a sector: Let the circumference of the base of the cone be divided into any number of equal parts. Then with A C as a radius describe the arc C E. Set off as many equal spaces on C E as are contained in the circumference of the base of the cone. Draw C A and E A, the sector will equal the convex surface of the cone. To Find the Convex Surface of the Frustum of a Cone. Rule : Multiply the sum [155] MENSURATION of the perimeters of the two ends by the slant height of the frustum, half the product will be the surface required. To Find the Solidity of a Cone. Rule: Multiply the area of the base by one- third of the perpendicular height of the cone, the product will be the solidity. To Find the Solidity of a Frustum of a Cone. Rule: For the frustum of a cone, the diameters, or circumferences, of the two ends and the height being given. Add together the square of the diameter of the greater end, the square of the diameter of the less ends, and the product of the two diameters; multiply the sum by .7854, and the product by the height; one-third of the last product will be the solidity. Or, add together the square of the circumference of the greater end, the square of the circumference of the less end, and the product of the two cir- cumferences; multiply the sum by .07958, and the product by the height; one-third of the last product will be the solidity. To Find the Surface of a Pyramid. Rule: Multiply the perimeter of the base by the length of the side, or slant height of the pyramid, and half the product will be the surface required. NOTE. By slant height is meant the distance Q O at the center of one of the slant sides. The development of the side would be a triangle A O D of which Q O is the height. To Develop the Convex Surface of a Pyramid. In this case hexagonal. The pyramid BAG stands upon a hexagonal base, shown below it. With A C as a radius, draw an arc, and from a central point as at G, with one of the sides of the hexagonal base as a unit, measure off three lengths to B, and three lengths to D. Draw B A and D A, also draw through the intermediate points E, F, G, H, I, radial lines meeting in A. Draw the perimeter lines D E, E F, F G, etc., to B. This diagram represents the convex surface of the pyramid. To Find the Surface of the Frustum of a Pyramid. Rule: Multiply the sum of the perimeters of the ends by the slant height, and half the product will be the surface required. Demonstration: Let A B, a 6, represent one of the sides of the frustum of the pyramid, having the height Q t. By construction draw the diagonal A b, dividing the figure into two triangles. Let a g be drawn perpendicular to A 6, and B / perpendicular to A 6. Then the triangle A a b = % (A 6 X a g\ and the triangle AB6 = HA6XB/). The area of the four-sided figure A a 6 B equals the area of the two triangles into [156] MENSURATION which the figure was divided by the line A 6; therefore the area of a trapezium may be found by multiplying the sum of the parallel sides by half the perpendicular distance between them. To Find the Solidity of a Pyramid. Rule: Multiply the area of the base by one- third of the perpendicular height. Let A B represent one edge of a cube, and lines be drawn from each of the four corners of the base A, B, C, D, to the center of the cube, a square pyramid will be formed, the base of which will be equal to the base of the cube, and its height equal to one-half the height of the cube. A cube consists of six sides, therefore a cube will contain six such pyramids; hence the volume of the pyramid is one-sixth that of the cube. Inasmuch as the pyramid is only one-half the height of the cube, two such pyramids can be contained within it to equal the same height; hence the volume of any pyramid is equal to f (area of base X height). To Find the Solidity of a Frustum of a Pyramid Whose Sides Are Regular Poly- gons. Add together the square of a side of the greater end, and the square of a side of the less end, and the product of these two sides; multiply the sum by the proper number in the table under " To find the area of a regular polygon, when the side only is given," and the product by the height; one-third of the last product will be the solidity. NOTE. When the ends of the pyramids are not regular polygons, add together the areas of the two ends and the square root of their product; multiply the sum by the height, and one-third of the product will be the solidity. To Find the Solidity of a Wedge. Rule: Add twice the length of the base to the length of the edge, and reserve the number. Multiply the height of the wedge by the breadth of the base, and this product by the reserved number; one-sixth of the last product will be the solidity. NOTE. When the length of the base is equal to half of the wedge, the wedge is evidently equal to half a prism of the same base and altitude, [157] MENSURATION To Find the Solidity of a Prismoid. Rule: To the sum of the areas of the two ends, add four times the area of a section parallel to and equally distant from both ends, and this last sum multiplied by one-sixth of the height will give the solidity. NOTE. The length of the middle of the rectangle is equal to half the sum of the length of the rectangle of the two ends, and its breadth equal to half the sum of the breadths of those rectangles. To Find the Convex Surface of a Sphere. Rule: Multiply the diameter of the sphere by its circumference, the product will be the convex superfices required. NOTE. The curve surface of any zone or segment will also be found by multiplying its height by the whole circumference of the sphere. Cor. 1. The surface of a sphere is also equal to the curve surface of its circumscribing cylinder. Cor. 2. The surface of a sphere is also equal to four times the area of a great circle of it. Lunar Surface. To find the lunar surface included between two great circles of the sphere. Rule: Multiply the diameter into the breadth of the surface in the middle, the product will be the superfices required. Or, as one right angle is to the great circle of the sphere, so is the angle made by the two great circles to the surface included by them. Spherical Triangle. To find the area of a spherical triangle, or the surf ace included by the intercepting arcs, of three great circles of the sphere. Rule: As two right angles, or 180, is to a great circle of the sphere, so is the excess of the three angles above two right angles to the area of a triangle. To Find the Solidity of a Sphere. Rule: Multiply the cube of a diameter by .5236, the product will be the solidity. Cor. A sphere is equal to two-thirds of its circumscribing cylinder. A cone, hemisphere, and cylinder of the same base and altitude are to each other J, J, and 1; or, as 1, 2, and 3. All spheres are to each other as the cubes of their diam- [158] MENSURATION eters. For cylinders of the same altitude are to each other as the cubes of their diam- eters; and a sphere is two-thirds of a cy Under whose diameter and altitude are equal to the diameter of the sphere. To Find the Solidity of the Segment of a Sphere. Rule: To three times the square of the radius of its base add the square of its height; and this sum multipUed by the height, and the product again by .5236, will give the soUdity. Or, From three times the diameter of the sphere subtract twice the height of the seg- ment, multiply by the square of the height, and that product by .5236; the last product will be the soUdity. To Find the Solidity of a Frustum or Zone of a Sphere. Rule: To the sum of the squares of the radii of the two ends, add one-third of the square of their distance, or of the breadth of the zone, and this sum multipUed by the said breadth, and the product again by 1.5708, will give the soUdity. To Find the Solidity of a Spheroid. Rule: Multiply the square of the revolving axe by the fixed axe, and this product again by .5236, and it will given the solidity required. Where note that .5236 = of 3.1416. To Find the Content of the Middle Frustum of a Spheroid, Its Length, the Middle Diameter, and That of Either of the Ends Being Given. Case 1. When the Ends are Circular, or Parallel to the Revolving Axis. Rule: To twice the square of the middle diameter, add the square of the diameter of either of the ends, and this sum multiplied by the length of the frustum, and the product again by .2618, will give the solidity. Where note that .2618 = & of 3.1416. Case 2. When the Ends are Elliptical or Perpendicular to the Revolving Axis. Rule 1. Multiply twice the transverse diameter of the middle section by its conjugate diameter, and to this product add the product of the transverse and conjugate diameters of either of the ends. 2. Multiply the sum thus found by the distance of the ends or the height of the frustum, and the product again by .2618, and it will give the solidity required. To Find the Solidity of the Segment of a Spheroid. Case 1. When the Base is Parallel to the Revolving Axis. [159] MENSURATION Rule 1. Divide the square of the revolving axis by the square of the fixed axe, and multiply the quotient by the difference between three times the fixed axe and twice the height of the segment. 2. Multiply the product, thus found, by the square of the height of the segment, and this product again by .5236, and it will give the solidity required. Case 2. When the Base is Perpendicular to the Revolving Axis. Rule 1. Divide the fixed axe by the revolving axe, and multiply the quotient by the difference between three times the revolving axe and twice the height of the segment. 2. Multiply the product, thus found, by the square of the height of the segment, and this prociuct again by .5236, and it wiU give the solidity required. To Find the Solidity of a Parabolic Conoid. Rule: Multiply the area of the base by half the altitude, and the product will be the content. NOTE. The parabolic conoid = \ its circumscribing cylinder. The rule given above will hold for any segment of the paraboloid, whether the base be perpendicular or oblique to the axe of the solid. To find the Solidity of the Frustum of a Paraboloid, When Its Ends are Perpen- dicular to the Axe of the Solid. Rule: Multiply the sum of the squares of the diameters cf the two ends by the height of the frustum, and the product again by .3927, and it will give the solidity. To Find the Solidity of an Hyperboloid. Rule: To the square of the radius of the [160] MENSURATION base add the square of the middle diameter between the base and the vertex; and this sum multiplied by the altitude, and the product again by .5236 will give the solidity. To Find the Solidity of the Frustum of an Hyperbolic Conoid. Rule: Add together the squares of the greatest and least semi-diameters, and the square of the whole diameter hi the middle, then this sum being multiplied by the altitude, and the product again by .5236 will give the solidity. NOTE. The content of any spindle formed by the revolution of a conic section about its axis may be found by the following rule: Add together the squares of the greatest and least diameters, and square of double the diameter in the middle between the two, and this sum multiplied by the length, and the product again by .1309 will give the solidity. And the rule will never deviate much from the truth when the figure revolves about any other line which is not the axis. REGULAR BODIES The whole number of regular bodies which can possibly be formed is five: 1. The tetrahedron, or regular pyramid, which has four triangular faces. 2. The hexahedron, or cube, which has six square faces. 3. The octahedron, which has eight triangular faces. 4. The dodecahedron, which has twelve pentagonal faces. 5. The icosahedron, which has twenty triangular faces. NOTE. There are only three kinds of equilateral and equiangular plane figures which, when joined together, will form a solid angle, and these are triangles, squares, or pentagons; and there are no more than five different solids, given above, which are bounded by equilateral and equiangular plane figures. Tetrahedron. The solid angles of a tetrahedron are formed by three equilateral plane triangles, and the solid is bounded by four equal and equilateral plane triangles, therefore, it is a pyramid. Hexahedron. The solid angles of a hexahedron are formed by three equal squares, and the solid is bounded by six equal squares, therefore, it is a cube. Octahedron. The solid angles of an octa- hedron are formed by four equal and equi- lateral plane triangles, and the solid is bounded by eight equal and equilateral plane triangles; consequently it is formed by two equal square pyramids joined together at their bases, the sides whereof are equilateral triangles. Dodecahedron. The solid angles of a do- decahedron are formed by three equal, equilateral, and equiangular pentagons; and the solid is bounded by twelve equal, equilateral and equiangular pentagons. This solid may be con- ceived to consist of twelve equal pentagonal pyramids, whose vertices meet in the center of a sphere circumscribing it. [161] W\A MENSURATION Icosahedron. The solid angles of an icosahedron are formed by five equal and equilateral plane triangles, and the solid is bounded by twenty equal and equilateral plane triangles. The solid may be conceived to consist of twenty equal triangular pyramids, whose vertices meet in the center of a sphere circumscribing it. To Find the Solidity of a Tetrahedron. Rule: Multiply one-twelfth of the cube of the linear side by the square root of 2, and the product will be the solidity. To Find the Solidity of a Hexahedron. Rule: Multiply the side of the cube by itself, and that product again by the side, and it will give the solidity required. NOTE. When the number denoting the length of the edge of the cube is known, the volume is obtained by cubing the given number. The converse operation, i. e., given the volume to find the length of an edge, re- quires the extraction of the cube root. To Find the Solidity of an Octahedron. Rule: Multiply one-third of the cube of the linear side by the square root of 2, the product will be the solidity. To Find the Solidity of a Dodecahedron. Rule: To twenty-one times the square root of 5, add 47, and divide the sum by 40; then the square root of the quotient being multiplied by five times the cube of the linear side will give the solidity required. To Find the Solidity of a Icosahedron. Rule: To three times the square root of 5 add 7, and divide the sum by 2; then the square root of this quotient being multiplied by five-sixths of the cube of the linear side will give the solidity required. [102] MENSURATION That is, S 3 X V (7 + solidity when S is = to the linear side. NOTE. The superfices and solidity of any of the five regular bodies may be found as follows: Rule 1. Multiply the tabular area by the square of the linear edge, and the product will be the superfices. 2. Multiply the tabular solidity by the cube of the linear edge, and the product will be the solidity. SURFACES AND SOLIDITIES OF THE REGULAR BODIES No. of Sides Names Surfaces Solidities 4 Tetrahedron 1 73205 0.11785 6 Hexahedron 6.00000 1.00000 8 Octahedron 3 46410 47140 12 Dodecahedron . .... 20 64578 7.66312 20 Icosahedron 8.66025 2.18169 CYLINDRIC RINGS To Find the Convex Superfices of a Cylindric Ring. Rule: To the thickness of the ring add the inner diameter, and this sum being multiplied by the thickness and the product again by 9.8696 will give the superfices required. NOTE. A solid ring of this kind is only a bent cylinder, and therefore the rules for obtaining its superfices or solidity are the same as those already given. For, let A c be any section of the solid per- pendicular to its axis o n, and then A c X 3.1416 = circumference of that section, and A c + cd (on) X . ...... 3.1416 = length of the axis on. 1WHI 1111311113 To Find the Solidity of a Cylindric Ring. Rule 1. To the thickness of the ring add the inner diame- ter, and this sum being multiplied by the square of half the thickness and the product again by 9.8696 will give the solidity. Hule 2. Add together the inner diameter and the thickness of the ring for a mean diameter. Multiply the mean diameter by 3.1416, and the product by the area of the cross-section of the ring will give the solidity. LOGARITHMS OF NUMBERS Logarithms are useful in shortening and facilitating the arithmetical operations of multiplication and division. The sum of the logarithms of two numbers is the logarithm of the product of those numbers; and since logarithms are the indices of powers of the same basis, the difference of the logarithms of two numbers is the logarithm of the quotient; also the multiple of the logarithm of a number is the logarithm of the power of that number, and a fraction of the logarithm of a number is the logarithm of the corresponding root. Hence, a complete table of logarithms would enable one to perform multiplication by addition, division by subtraction, involution by multi- plication, and evolution by division. There are two systems of logarithms in use: The common system, in which the base is 10, and the Naperian system, in which the base (denoted by e) is 2.718281828. Naperian logarithms are also called natural, but commonly hyperbolic logarithms. [163] LOGARITHMS OF NUMBERS The common system of logarithms is generally referred to as the Briggs' system, after their inventor. In this system the logarithm of every number between 1 and 10 is some number between and 1, that is, it is a fractional number. As all numbers are to be regarded as powers of 10, we have 10 = 1, and is the logarithm of 1 10 1 = 10, and 1 is the logarithm of 10 10 2 = 100, and 2 is the logarithm of 100 10 3 = 1000, and 3 is the logarithm of 1000 10 4 = 10000, and 4 is the logarithm of 10000 The logarithm, therefore, of every number between 10 and 100 is some number between 1 and 2, that is, it is 1+ a fraction; similarly, every number between 100 and 1000 is some number between 2 and 3, that is, 2+ a fraction. This principle is extended to fractions by means of negative exponents, thus lO i =o.l, and 1 is the logarithm of 0. 1 10 2 =0.01, and 2 is the logarithm of 0.01 10 3 = 0.001, and 3 is the logarithm of 0.001 10-4 = 0.0001, and -4 is the logarithm of 0.0001 The logarithm of every number between 1 and 0.1 is some number between and 1, *or may be represented by 1+ a fraction; the logarithm of every number be- tween 0.1 and .01 is some number between 1 and 2, or may be represented by 2 + a fraction, and so on. The negative sign is commonly placed over the figure, 2" rather than 2. Writing the minus sign over the characteristic, and not before it, indicates that the characteristic only is 'negative, and not the whole expression. The Logarithm of a Number Consists of Two Parts, an integral part and a fractional part. The integral part is called the characteristic, and the fractional part the mantissa. The Characteristic of the Logarithm of any number greater than unity is one less than the number of integral figures in the given number. Thus, the logarithm of 385 is 2+ a fraction; that is the characteristic of the logarithm of 385 is one less than the number of integral figures, or 2. The characteristic of the logarithm of a decimal fraction is a negative number, and is equal to the number of places by which its first significant figure is removed from the place of units. Thus, the logarithm of .0047 is 3+ a fraction; that is, the char- acteristic of the logarithm is 3 (3 ), the first significant figure 4 being removed three paces from the unit. To Add Two Negative Characteristics, take their sum and make it negative. Thus 5+2 = 7. To Add a Positive to a Negative Characteristic, take their difference and make its sign the sign- of the greater; thus, 3 + 5 =2, and 3+5 = 2. To Subtract a Negative Characteristic^ changejts sign _to plus and proceed as in addition; thus, 4-3 = 4 + 3=7, and 4-3 = 4 + 3 = 1. To Subtract a Positive Characteristic^change rts sign to minus and proceed as in addition; thus, 4-3 = 4+3=1, and 4-3 =4+3 = 7. To Multiply a Negative Characteristic, multiply as if positive and make the product negative; thus, 2X3=6. The Mantissa of a logarithm is its decimal part. The mantissa is always positive, the minus sign being usually written over the characteristic and not before it, to in- dicate that the characteristic only and not the whole expression is negative; thus, 1.4084604 stands for -1+ .4084604. Multiplication. The logarithm of the product of two or more factors is equal to the sum of the logarithm of those factors. If it is required to multiply two or more numbers by each other, we have only to add their logarithms: the sum will be the logarithm of their product. Then look in the table for the number answering to that logarithm and obtain the required product. Division. The logarithm of the quotient of one number divided by another is equal to the difference of the logarithm of those numbers. If it is required to divide one number by another, we have only to subtract the logarithm of the divisor from that of the dividend; the difference will be the logarithm of the quotient. [164J LOGARITHMS OF NUMBERS The Decimal Part of the Logarithm of any number is the same as that of the number multiplied or divided by 10, 100, 1000, etc. That is, if any number be multiplied or divided by 10, its logarithm will be increased or diminished by 1; and as this is an integer, it will only change the characteristic of the logarithm, without affecting the decimal part. Thus, -the logarithm of 47,630 = 4.677881 4,763 = 3.677881 476.3 = 2.677881 47.63 = 1.677881 4.763 = 0.677881 .4763 = L677881 .04763 =2.677881 .004763 = 3.677881 To Divide a Logarithm Having a Negative Characteristic. If the characteristic is divisible by the divisor without a remainder, write _the quotient with a negative sign and divide the decimal part in the usual way; 6.458938 -=- 2 = 3.229469. If the characteristic is not divisible by the divisor without a remainder, add such a negative number to it as will make it divisible without a remainder and prefix an equal positive number to the decimal part of the logarithm, then divide the increased negative char- acteristic and the other part of the logarithm separately; thus 7.135718 -r- 3 = (2+7+2.135718) ^ 3 = (9 + 2.135718) -=-!} = 3.711906. To Find the Logarithm of a Vulgar Fraction. Reduce the vulgar fraction to a deci- mal, and find its logarithm; or, since the value of a fraction is equal to the quotient of the numerator divided by the denominator, we may subtract the logarithm of the denominator from that of the numerator; the difference will be the logarithm of the fraction. Involution by Logarithm. On the principle that the logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power, we have the following rule. Multiply the logarithm of the number by the exponent of the power required. Example, required the square of 428: The logarithm of 428 is 2.631444 2 Square 183184, log 5 .262888 It should be remembered, that what is carried from the decimal part of the logarithm, is positive, whether the characteristic is positive or negative. Example, required the cube of .07654: Cube, .0004484, log 4.651664 Evolution by Logarithm. The logarithm of any root of a number is equal to the logarithm of that number divided by the index of the root. To extract the root of a number by logarithm we have the following rule: Divide the logarithm of the number by the index of the root required. Example, required the cube root of 482.38. The logarithm of 482.38 is 2.683389. Dividing by 3, we have 0.894463 which corresponds to 7.842, which is the root required. When the characteristic of the logarithm is negative, and is not divisible by the given divisor, we may increase the characteristic by any number which will make it exactly divisible, provided we prefix an equal positive number to the decimal part of the logarithm. Example, required the seventh root of 0.005846. [165] LOGARITHMS OF NUMBERS The logarithm of 0.005846 is 3~.766859, which may be written 1 + 4.766859. To Find the Reciprocal of a Number. Subtract the decimal part of the logarithm of the number from 0.000000; add 1 to the index of the logarithm, and change the sign of the index. This completes the logarithm of the reciprocal. Example, to find the reciprocal of 230: 0.000000 Log 230 = 2.361728 3.638272 = log 0.004348 the reciprocal. Inversely, to find the reciprocal of the decimal .00438 : 0.000000 Log .004348 = 3.638272 2.361728 = log 230 the reciprocal. TO FIND THE LOGARITHM OF A NUMBER BY THE TABLES To find the logarithm of a number containing one or two digits, look for the number in the preliminary table, which gives all numbers from 1 to 100; the logarithm will be found in the adjoining column. For example, required the logarithm of 84. In the preliminary table, opposite 84, is 1.924279, which includes the integer. Or, annex a cipher to it, making the number 840 and find that number hi the larger table; opposite will be the decimal .924279, to which is to be prefixed the integer 1, included hi the pre- liminary table. As 84 was multiplied by 10, the base of the system, the decimal was not changed, nor would it have been if multiplied by 100, 1000, or any other multiple of 10. The logarithm of any number between 100 and 10000 can be found in the larger table by locating the number, if less than 1000, in column N; the logarithm will be in the adjoining column under O. If the number be over 1000 and less than 10000, say 6849, find the first three of the numbers (684) in column N; in the adjoining column will be found .83, which is to be prefixed to the figures 5627, found on the same line under heading 9; the mantissa of logarithm is .835627, to which must be added the integer 3, then 3.835627 is the logarithm of 6849. To fine the logarithm of a number consisting of five or more digits, find the logarithm for the first four as above; multiply the difference, in column D, by the remaining digits, and divide by 10, if there be only one digit more, or by 100, if there be two more, and so on; add the quotient to the logarithm for the first four. The sum is the decimal part of the required logarithm, to which the index is to be prefixed. For example, take 3.1416. The logarithm of 3141 is .497068, decimal part; and the difference 138 times 6 -^ 10 = 83, is to be added, thus 0.497068 83 Making the complete logarithm 0.497151 To Find the Number Corresponding to a Given Logarithm, look for the logarithm without the index. If it be found exactly, or within two or three units of the right-hand digit, then the first three figures of the indicated number will be found in the number column, in a line with the logarithm, and the fourth figure at the top or the foot of the column containing the logarithm. Annex the fourth figure to the first three, and place the decimal point in its proper position, on the principles already explained. If the given logarithm differs by more than two or three units from the nearest in the table, find the number for the next less tabulated logarithm, which will give the first four digits of the required number. To find the fifth and sixth digit, subtract the tabulated logarithm from the given logarithm, add two ciphers and divide by the difference found in column D, opposite the logarithm. Annex the quotient to the four [166] LOGARITHMS OF NUMBERS digits already found, and place the decimal point. For example, to find the number represented by the logarithm 2.564732: 2.564732 given logarithm, Logarithm 367.0 = 2.564666 nearest less .056 D 118)6600(56 nearly 590 367.056 700 708 showing that the required number is 367.056. LOGARITHMS OF NUMBERS From 1 to 1000 No. Log. No. Log. No. Log. No. Log. - 1 0.000000 26 .414973 51 1.707570 76 1.880814 . .,2 0.301030 27 .431364 52 1.716003 77 1.886491 3 0.477121 28 .447158 53 1.724276 78 1.892095 4 0.602060 29 .462398 54 1.732394 79 1.897627 5 0.698970 30 .477121 55 1.740363 80 1.903090 6 0.778151 31 1.491362 56 .748188 81 1.908485 ii,7 0.845098 32 1.505150 57 .755875 82 1.913814 ;-s 0.903090 33 1.518514 58 .763428 83 1.919078 9 0.954243 34 1.531479 59 .770852 84 1.924279 10 1.000000 35 1.544068 60 .778151 85 1.929419 11 .041393 36 1.556303 61 1.785330 86 .934498 12 .079181 37 1.568202 62 1.792392 87 .939519 13 .113943 38 1.579784 63 1.799341 88 .944483 14 . 146128 39 1.591065 64 1.806180 89 .949390 15 . 176091 40 1.602060 65 1.812913 90 .954243 16 1.204120 41 .612784 66 1.819544 91 1.959041 17 1.230449 42 .623249 67 1.826075 92 1.963788 18 1.255273 43 .633468 68 1.832509 93 1.968483 19 1.278754 44 .643453 69 1.838849 94 1.973128 20 1.301030 45 .653213 70 1.845098 95 1.977724 21 .322219 46 .662758 71 1.851258 96 1.982271 22 .342423 47 .672098 72 1.857332 97 1.986772 23 .361728 48 .681241 73 1.863323 98 1.991226 24 .380211 49 .690196 74 1.869232 99 1.995635 25 .397940 50 .698970 75 1.875061 100 2.000000 [167] LOGARITHMS OF NUMBERS LOGARITHMS OF NUMBERS FROM 1 TO 1000 (Cont.) N i 2 3 4 5 6 7 8 9 D 100 101 102 00- 00- 00- 0000 4321 8600 0434 4751 9026 0868 5181 9451 1301 5609 9876 1734 6038 2166 6466 2598 6894 3029 7321 3461 7748 3891 8174 432 428 4?5 102 01- 0300 0724 1147 1570 1993 2415 424 103 104 01- 01- 2837 7033 3259 7451 3680 7868 4100 8284 4521 8700 4940 9116 5360 9532 5779 9947 6197 6616 420 417 104 02- 0361 0775 416 105 106 107 02- 02- 02- 1189 5306 9384 1603 5715 9789 2016 6125 2428 6533 2841 6942 3252 7350 3664 7757 4075 8164 4486 8571 4896 8978 412 408 405 107 108 109 03- 03- 03- 3424 7426 3826 7825 0195 4227 8223 0600 4628 8620 1004 5029 9017 1408 5430 9414 1812 5830 9811 2216 6230 2619 6629 3021 7028 404 400 398 109 04- 0207 0602 0998 397 110 111 112 04- 04- 04- 1393 5323 9218 1787 5714 9606 2182 6105 9993 2576 6495 2969 6885 3362 7275 3755 7664 4148 8053 4540 8442 4932 8830 393 389 388 11? 05- 0380 0766 1153 1538 1924 2309 2694 386 113 114 114 05- 05- 06- 3078 6905 3463 7286 3846 7666 4230 8046 4613 8426 4996 8805 5378 9185 5760 9563 6142 9942 6524 0320 383 383 37Q 115 116 117 06- 06- 06- 0698 4458 8186 1075 4832 8557 1452 5206 8927 1829 5580 9298 2206 5953 9668 2582 6326 2958 6699 3333 7071 3709 7443 4083 7815 376 373 380 117 07- 0038 0407 0776 1145 1514 370 118 119 120 07- 07- 07- 1882 5547 9181 2250 5912 9543 2617 6276 9904 2985 6640 3352 7004 3718 7368 4085 7731 4451 8094 4816 8457 5182 8819 366 363 36? 1?0 08- 0266 0626 0987 1347 1707 2067 2426 360 121 122 123 08- 08- 08- 2785 6360 9905 3144 6716 3503 7071 3861 7426 4219 7781 4576 8136 4934 8490 5291 8845 5647 9198 6004 9552 357 355 355 123 124 125 125 09- 09- 09- 10- 3422 6910 0258 3772 7257 0611 4122 7604 0963 4471 7951 1315 4820 8298 1667 5169 8644 2018 5518 8990 2370 5866 9335 2721 6215 9681 3071 6562 0026 353 349 348 346 126 127 128 128 10- 10- 10- 11- 0371 3804 7210 0715 4146 7549 1059 4487 7888 1403 4828 8227 1747 5169 8565 2091 5510 8903 2434 5851 9241 2777 6191 9579 3119 6531 9916 3462 6871 0253 343 341 338 337 129 130 131 131 11- 11- 11- 12- 0590 3943 7271 0926 4277 7603 1263 4611 7934 1599 4944 8265 1934 5278 8595 2270 5611 8926 2605 5943 9256 2940 6276 9586 3275 6608 9915 3609 6940 0245 335 333 331 330 N o 1 2 3 4 5 6 7 8 9 D [168] LOGARITHMS OF NUMBERS LOGARITHMS OF NUMBERS FROM 1 TO 1000 (ConO N 1 2 3 4 5 6 7 8 9 D 132 12- 0574 0903 1231 1560 1888 2216 2544 2871 3198 3525 328 133 12- 3852 4178 4504 4830 5156 5481 5806 6131 6456 6781 325 134 12- 7105 7429 7753 8076 8399 8722 9045 9368 9690 .... 323 134 13- 0012 323 135 13- 0334 0655 0977 1298 1619 1939 2260 2580 2900 3219 321 136 13- 3539 3858 4177 4496 4814 5133 5451 5769 6086 6403 318 137 13- 6721 7037 7354 7671 7987 8303 8618 8934 9249 9564 316 138 13- 9879 315 138 14- 0194 0508 0822 1136 1450 1763 2076 2389 2702 314 139 14- 3015 3327 3639 3951 4263 4574 4885 5196 5507 5818 311 140 14- 6128 6438 6748 7058 7367 7676 7985 8294 8603 8911 309 141 14- 9219 9527 9835 308 141 15- 0142 0449 0756 1063 1370 1676 1982 307 142 15- 2288 2594 2900 3205 3510 3815 4120 4424 4728 5032 305 143 15- 5336 5640 5943 6246 6549 6852 7154 7457 7759 8061 303 144 15- 8362 8664 8965 9266 9567 9868 302 144 16- 0168 0469 0769 1068 301 145 16- 1368 1667 1967 2266 2564 2863 3161 3460 3758 4055 299 146 16- 4353 4650 4947 5244 5541 5838 6134 6430 6726 7022 297 147 16- 7317 7613 7908 8203 8497 8792 9086 9380 9674 9968 295 148 17- 0262 0555 0848 1141 1434 1726 2019 2311 2603 2895 293 149 17- 3186 3478 3769 4060 4351 4641 4932 5222 5512 5802 291 150 17- 6091 6381 6670 6959 7248 7536 7825 8113 8401 8689 289 151 17- 8977 9264 9552 9839 287 151 18- 0126 0413 0699 0986 1272 1558 287 152 18- 1844 2129 2415 2700 2985 3270 3555 3839 4123 4407 285 153 18- 4691 4975 5259 5542 5825 6108 6391 6674 6956 7239 283 154 1&- 7521 7803 8084 8366 8647 8928 9209 9490 9771 281 154 19- 0051 281 155 19- 0332 0612 0892 1171 1451 1730 2010 2289 2567 2846 279 156 19- 3125 3403 3681 3959 4237 4514 4792 5069 5346 5623 278 157 19- 5900 6176 6453 6729 7005 7281 7556 7832 8107 8382 276 158 19- 8657 8932 9206 9481 9755 275 158 20- 0029 0303 0577 0850 1124 274 159 20- 1397 1670 1943 2216 2488 2761 3033 3305 3577 3848 272 160 20- 4120 4391 4663 4934 5204 5475 5746 6016 6286 6556 271 161 20- 6826 7096 7365 7634 7904 8173 8441 8710 8979 9247 269 162 20- 9515 9783 .... .... 268 162 21- .... 0051 0319 0586 0853 1121 1388 1654 1921 267 163 21- 2188 2454 2720 2986 3252 3518 3783 4049 4314 4579 266 164 21- 4844 5109 5373 5638 5902 6166 6430 6694 6957 7221 264 165 21- 7484 7747 8010 8273 8536 8798 9060 9323 9585 9846 262 166 22- 0108 0370 0631 0892 1153 1414 1675 1936 2196 2456 261 N 1 2 3 4 5 6 7 8 9 D [169] LOGARITHMS OF NUMBERS LOGABITHMS OF NUMBERS FROM 1 TO 1000 (Cont.) N 1 2 3 4 . 5 6 7 8 9 D 167 168 169 169 22- 22- 22- 23- 2716 5309 7887 2976 5568 8144 3236 5826 8400 3496 6084 8657 3755 6342 8913 4015 6600 9170 4274 6858 9426 4533 7115 9682 4792 7372 9938 5051 7630 0193 259 258 257 2 c ifi 170 171 172 173 173 23- 23- 23- 23- 24r- 0449 2996 5528 8046 0704 3250 5781 8297 0960 3504 6033 8548 1215 3757 6285 8799 1470 4011 6537 9049 1724 4264 6789 9299 1979 4517 7041 9550 2234 4770 7292 9800 2488 5023 7544 0050 2742 5276 7795 0300 255 253 252 251 250 174 175 176 177 177 24- 24- 24- 24- 25- 0549 3038 5513 7973 0799 3286 5759 8219 1048 3534 6006 8464 1297 3782 6252 8709 1546 4030 6499 8954 1795 4277 6745 9198 2044 4525 6991 9443 2293 4772 7237 9687 2541 5019 7482 9932 2790 5266 7728 0176 249 248 246 246 245 178 179 180 181 182 183 184 185 186 25- 25- 25- 25- 26- 26- 26- 26- 26- 0420 2853 5273 7679 0071 2451 4818 7172 9513 0664 3096 5514 7918 0310 2688 5054 7406 9746 0908 3338 5755 8158 0548 2925 5290 7641 9980 1151 3580 5996 8398 0787 3162 5525 7875 1395 3822 6237 8637 1025 3399 5761 8110 1638 4064 6477 8877 1263 3636 5996 8344 1881 4306 6718 9116 1501 3873 6232 8578 2125 4548 6958 9355 1739 4109 6467 8812 2368 4790 7198 9594 1976 4346 6702 9046 2610 5031 7439 9833 2214 4582 6937 9279 243 242 241 239 238 237 235 234 ?34 186 27- 0213 0446 0679 0912 1144 1377 1609 233 187 188 189 190 27- 27- 27- 27- 1842 4158 6462 8754 2074 4389 6692 8982 2306 4620 6921 9211 2538 4850 7151 9439 2770 5081 7380 9667 3001 5311 7609 9895 3233 5542 7838 3464 5772 8067 3696 6002 8296 3927 6232 8525 232 230 229 ??8 190 28- 0123 0351 0578 0806 ??8 191 192 193 194 195 196 197 198 199 28- 28- 28- 28- 29- 29- 29- 29- 29- 1033 3301 5557 7802 0035 2256 4466 6665 8853 1261 3527 5782 8026 0257 2478 4687 6884 9071 1488 3753 6007 8249 0480 2699 4907 7104 9289 1715 3979 6232 8473 0702 2920 5127 7323 9507 1942 4205 6456 8696 0925 3141 5347 7542 9725 2169 4431 6681 8920 1147 3363 5567 7761 9943 2396 4656 6905 9143 1369 3584 5787 7979 2622 4882 7130 9366 1591 3804 6007 8198 2849 5107 7354 9589 1813 4025 6226 8416 3075 5332 7578 9812 2034 4246 6446 8635 227 226 225 223 222 221 220 219 218 199 30- 0161 0378 0595 0813 218 200 201 202 203 30- 30- 30- 3O- 1030 3196 5351 7496 1247 3412 5566 7710 1464 3628 5781 7924 1681 3844 5996 8137 1898 4059 6211 8351 2114 4275 6425 8564 2331 4491 6639 8778 2547 4706 6854 8991 2764 4921 7068 9204 2980 5136 7282 9417 217 216 215 213 N 1 2 3 4 5 6 7 8 9 D [170J LOGARITHMS OF NUMBERS LOGARITHMS OF NUMBERS FROM 1 TO 1000 (Cont.) N' 1 2 3 4 5 6 7 8 9 D ?04 30- 9630 9843 ?13 ?04 31- 0056 0268 0481 0693 0906 1118 1330 1542 21? 205 206 207 208 209 210 211 212 ?13 31- 31- 31- 31- 32- 32- 32- 32- 32- 1754 3867 5970 8063 0146 2219 4282 6336 8380 1966 4078 6180 8272 0354 2426 4488 6541 8583 2177 4289 6390 8481 0562 2633 4694 6745 8787 2389 4499 6599 8689 0769 2839 4899 6950 8991 2600 4710 6809 8898 0977 3046 5105 7155 9194 2812 4920 7018 9106 1184 3252 5310 7359 9398 3023 5130 7227 9314 1391 3458 5516 7563 9601 3234 5340 7436 9522 1598 3665 5721 7767 9805 3445 5551 7646 9730 1805 3871 5926 7972 3656 5760 7854 9938 2012 4077 6131 8176 211 210 209 208 207 206 205 204 ?04 213 33- 0008 0211 ?03 214 215 216 217 ?18 33- 33- 33- 33- 33- 0414 2438 4454 6460 8456 0617 2640 4655 6660 8656 0819 2842 4856 6860 8855 1022 3044 5057 7060 9054 1225 3246 5257 7260 9253 1427 3447 5458 7459 9451 1630 3649 5658 7659 9650 1832 3850 5859 7858 9849 2034 4051 6059 8058 2236 4253 6260 8257 202 202 201 200 ?00 218 34- 0047 0246 19P 219 220 221 222 223 223 34- 34- 34- 34- 34- 35- 0444 2423 4392 6353 8305 0642 2620 4589 6549 8500 0841 2817 4785 6744 8694 1039 3014 4981 6939 8889 1237 3212 5178 7135 9083 1435 3409 5374 7330 9278 1632 3606 5570 7525 9472 1830 3802 5766 7720 9666 2028 3999 5962 7915 9860 2225 4196 6157 8110 0054 198 197 196 195 194 1-* 4176 4251 4326 4400 4475 4550 4624 4699 4774 4848 75 ;S82 76H 4923 4998 5072 5147 5221 5296 5370 5445 5520 5594 75 583 76- 5669 5743 5818 5892 5966 6041 6115 6190 6264 6338 74 584; 76- 6413 S6487 6562 6636 6710 6785 6859 6933 7007 7082 74 M g> M t (Per Cent) II J3 *3 13 *3 *si |o1 feol E4HM 1 Up to 5. ( 3 over. 5 under }l2 15 18 21 24 .. .. .. 5 inclusive to 7| exclu- sive.. tt 10 12 14 16 18 20 22 24 7^ inclusive to 10 exclu- sive K 8 10 11 12 13 14 15 16 (b) PLATES 10 POUNDS PER SQUARE FOOT AND OVER ALLOWABLE UNDERGAUGE AT EDGE (Per Cent) Allowable I |s If |s |s s m WEIGHT ORDERED (Pounds per Square Foot) Varia- tion in Weight (Per Cent) h sj l| e H ^ }j| ll s IJ ssl 1 |l fcol (J+il-t id n*" 13 |o| i o o 10 inclusive to 12| exclusive \ 3 over... 5 under. . } 10 11 12 13 14 18 -. 12| inclusive to 15 exclusive, j 2 over . . . 3 under. . I 8 9 10 11 12 14 16 15 inclusive to 17| exclusive . . u 6 7 8 9 10 11 13 17 inclusive to 20 exclusive. . . tt 5 5 6 7 8 9 10 20 inclusive to 25 exclusive . . . " 4 5 5 5 6 7 8 25 inclusive to 30 exclusive . . . it 3 3 3 4 5 5 6 30 inclusive to 40 exclusive. . . " 3 3 3 3 3 4 5 40 and up " 2 2 2 3 3 3 4 STEEL SHAPES FOR HULLS AND HULL CONSTRUCTION NAVY DEPARTMENT 1. General Requirements. "General Specifications for Inspection of Steel and Iron Material, General Specifications, Appendix I," issued June, 1912, shall form a part of these specifications, and must be complied with in all respects. 2. Finish. All shapes shall be true to section, free from injurious defects, and shall have a workmanlike finish. 3. Physical and Chemical Requirements. (a) All shapes shall be of uniform quality. The physical and chemical requirements of the various grades of material for shapes shall be in accordance with the following table: [310] STEEL SHAPES FOR HULLS AND HULL CONSTRUCTION Grade Material Minimum Tensile Strength per Square Inch Minimum Elonga- tion in 8 Inches (b) MAXIMUM AMOUNT OF Cold Bend P. S. Pounds Per Ct. Per Ct. Per Ct. Soft or flange steel f Open -hearth \ carbon I steel 1 48,000 30 {Acid 0.05 Basic .04 i 0.05 180 flat on itself. 1 For test pieces below f inch in thickness, 180 flat on itself. Medium steel ( Open -hearth ] carbon I steel i 60,000 25 f Acid 1 0.05 ] Basic ,/\ J ). 0.05 For test pieces f . inch or more in thickness the I .04 bends will be 180 to a diam- eter of one thickness. Open - hearth i {Acid ("180 to a diam- High ten- sile steel carbon nickel, or silicon steel 80,000 20 0.05 Basic .04 0.05 I eter of one and | one-half thick- l nesses. Common steel (c) f Open - hearth j or Besse- l mer steel i 56,000 22 ( No chemical an- \ alysis required ("180 to a diam- | eter of one I thickness. (b) ELONGATION. For shapes, the legs or webs of which have a nominal thickness | inch or less, elongation will be measured in 2 inches; over inch nominal thickness, to and including ^ inch, in 4 inches; over & inch nominal thickness, to and including J inch, in 6 inches; and over \ inch nominal thickness, in 8 inches. 4. Tensile Tests (Except for Common Steel). Shapes shall be tested by lots (or singly) ; a lot consisting of all the shapes rolled from a particular melt at a continuous rolling into sections, the nominal gauges of the webs or legs of which do not vary more than \ inch from the maximum to the minimum gauge. Four longitudinal test pieces shall be prepared from each lot, each specimen being from a separate shape, and, if practicable, from different ingots. All of these specimens must meet the requirements for the grade of steel specified. No lot will be accepted if there is a difference of more than 10.000 pounds in tensile strength between any two of the four specimens. 5. Bending Tests (Except for Common Steel). Two cold-bend specimens shall be taken from each lot, each from a different shape. These specimens shall meet the requirements of the specified grade of steel without sign of fracture on the outer curve. If one of these specimens fail, each shape rolled from the lot must pass the cold-bending test before being cut to ordered length. 6. Physical Tests for Common Steel. Common steel may be rolled from any stock on hand, but all information! required by these specifications, such as melt and charging records, etc., shall be supplied to the inspector to enable him to select test specimens. Two specimens shall be taken from each melt of finished material one for tension test and one for bending test. 7. Opening and Closing Tests. Opening and closing tests will be made at the option of the inspector on individual angles, Zee bars, Tee bars, I beams and channels which show evidence of mechanical defects or overheating, if in the opinion of the inspector the nature and extent of the defects need confirmation by such tests. The opening test shall consist of opening the section out flat while cold and the closing test [311] BLACK AND GALVANIZED SHEET STEEL shall consist of closing the section down flat on itself while cold. Under these tests the material shall not crack or tear. 8. Test of a Single Shape. In case of a single shape one tensile and one cold- bending test will be made. These tests must meet the requirements for the grade of steel specified. 9. Tolerances. Shapes of 6 pounds per linear foot or less will be accepted if the weights vary 3 per cent above and 5 per cent below the specified weight. Shapes over 6 pounds per linear foot will be accepted if the weights vary 2 per cent above or 3 per cent below the specified weights. 10. Marking Common Shapes. Common shapes shall, in addition to the other marks prescribed, have painted conspicuously on each shape the word "Common." All invoices or "Reports of Material Shipped," covering this class of material, shall be plainly marked with the word "Common." BLACK AND GALVANIZED SHEET STEEL NAVY DEPARTMENT 1. General Instructions. General instructions or specifications issued by the bureau concerned shall form part of these specifications. 2. These specifications cover sheets of 0.141 inch in thickness and thinner. 3. General Requirements. Sheets shall be made of the very best soft sheet steel; to stand double-seam purposes. 4. (a) To be free from all injurious defects, and to be free also from excessive scale and to be commercially flat and reasonably free from waves and buckles. (b) To be of the finest working quality and meet the allowances for thickness and weights given below. (c) BUNDLING. Sheets 0.063 inch thick or thicker, weighing 60 pounds each or over, are not to be bundled. All other sheets to be delivered in commercial bundles fastened with three iron or steel straps not to exceed 1 j inches in width and not thicker than | inch. When sheets exceed 120 inches in length, an extra strap may be required by the inspector. (d) PAYMENT. Gross weight will be paid for. (e) MARKING. Outside surface of the top sheet of each bundle (or single sheet when not bundled) shall be plainly marked to show the number and size of sheets, weight per square foot, and gross weight. (f) Tolerances. When not otherwise specified, allowance over the width and length ordered will be permitted, as shown in the table below. Sheets required to be closer in dimensions will be ordered as "resquared." (g) The agreement with thickness ordered is to be established by the weight. Each sheet shall be of practically uniform thickness. (h) A variation in weight of sheets of 5 per cent, plus or minus, will be allowed. 5. Regular Sizes. (a) Regular sizes of sheets are as follows, those italicized being most used. Thickness, in Inches Width Length Maximum Variation in Length (Plus) Maximum Variation in Width (Plus) 141 to 063, inclusive Inches 24, 26, 28, Inches 72, 84, 96, Inch i Inch 4 0. 056 to 0.025, inclusive 30, 36, 40, 42, 48 24, 26, 28, 120, 144 72, 84, 96, i 1 . 022 to . 016, inclusive 30, 86 24, 26, 28, 120, 144 72, 84, 96, I J . 014 to . 013, inclusive 30 24, 26, 28, 120, 144 72, 84, 96, | 1 30 120 [312] BLACK AND GALVANIZED SHEET STEEL (b) MAXIMUM SIZES. Maximum sizes of sheets are as follows: BLACK GALVANIZED, AND BLACK THINNER THAN 0.063 INCH Thickness Dimensions Thickness Dimensions Inch 141 Inches 24 x 240 or 66 x 180 24 x 228 or 66 x 180 54 x 156 54 x 156 Inch 0.141 to 0.038, inclusive 0.034 to 0.025, inclusive 022 and 019 Inches 48x144 28 x 144 or 48 x 120 28 x 144 or 44 x 120 28 x 144 or 42 x 120 28 x 144 or 36 x 120 0.125 and 0.109... 0.094 and 0.078... 0.070 and 0.063... 017 0.016 to 0.013, inclusive 6. Weights for black and galvanized sheets: (a) These weights are the weights adopted commercially for sheets of corresponding thicknesses and are approximate weights. Thick- ness, in Inches WEIGHT PER SQUARE FOOT Thick- ness, in Inches WEIGHT PER SQUARE FOOT Galvanized Black Galvanized Black Us. Ozs. Lbs. Ozs. Lbs. Ozs. Lbs. Ozs. 0.141 (5.781) 92.5 (5.625) 90 0.034 (1.531) 24.5 (1.375) 22 .125 (5.156) 82.5 (5.00 ) . 80 .031 (1.406) 22.5 (1.25 ) 20 .109 (4.531) 72.5 (4.375) 70 .028 (1.281) 20.5 (1.125) 18 .094 (3.906) 62.5 (3.75 ) 60 .025 (1.156) 18.5 (1.0 ) 16 .078 (3.281) 52.5 (3.125) 50 .022 (1.031) 16.5 ( .875) 14 .070 (2.968) 47.5 (2.812) 45 .019 ( .906) 14.5 ( -75 ) 12 .063 (2.656) 42.5 (2.50 ) 40 .017 ( .843) 13.5 ( .687) 11 .056 (2.406) 38.5 (2.25 ) 36 .016 ( .781) 12.5 ( .625) 10 .050 (2.156) 34.5 (2.00 ) 32 .014 ( -718) 11.5 ( .562) 9 .044 (1.906) 30.5 (1.75 ) 28 .013 ( .656) 10.5 ( .50 ) 8 .038 (1.656) 26.5 (1.50 ) 24 NOTE FOR GENERAL STOREKEEPERS. Requisitions should state the material desired, black or galvanized, the width, length, and weight per square foot. In ordering material, where possible, regular sizes will be asked for, and where special sizes are required the maximum limits will not be exceeded. 7. Galvanized Sheets, Freedom from Defects. Galvanized sheets must be thor- oughly and evenly galvanized, of a bright appearance, devoid of blisters, ragged edges or other defects, reasonably free from buckles, and commercially flat. The zinc coating must not flake or peel off when scraped with a knife or when the sheet is bent sharply at right angles. [313] CORRUGATED GALVANIZED SHEET STEEL 8. Thickness.- Thickness, in Inches Maximum Sizes Minimum Zinc Coating per Square Foot for Galvanized Plates 141 to 0. 038, inclusive Inches 48 x 144 Ounces 1 65 0. 034 to . 025, inclusive /28xl44\ 1ff\ 022 and 0.019 \48x 120 / / 28 x 144 \ .ou 1Af\ 017 1 44 x 120 / / 28 x 144 \ .4U IOC 016 to 013, inclusive . . . \42xl20J / 36 x 120 \ .OO Ioe \28xl44J .OO 9. Samples from Galvanizing Bath. No rerolling of sheets after leaving the gal- vanizing bath will be permitted, except for the purpose of straightening. The galvanizing material must show 98 per cent pure zinc, determined from a sample taken at random by a Government inspector from the upper half of the galvanizing bath. These samples may be taken at any time, provided the manufacturer agrees to have the sample repre- sent the galvanizing for the order; otherwise, when the inspector has been unable to secure a sample of the bath used for the order, the purity of the bath may be established by a Government laboratory from a sample of galvanized sheet taken at random from the order. 10. Determination of Amount of Zinc Coating. The determination of the amount of coating per square foot to be obtained by establishing the practice of the firm at convenient intervals, by weighing plates, as follows: First, weight in bulk of selected plates in the black, after pickling. Secondly, weight of the same selected plates after galvanizing. If this course cannot be pursued, the following method may be used : A selected sample from a galvanized sheet for the order, of two square feet of surface, will be sent to a Government laboratory at the expense of the manufacturer, where determi- nation will be made of the amount of zinc coating per square foot. CORRUGATED GALVANIZED SHEET STEEL NAVY DEPARTMENT 1. General Instructions. General instructions or specifications issued by the bureau concerned shall form part of these specifications. 2. General Quality. Corrugated sheet steel to be of a good grade of steel. Sheets to be thoroughly and uniformly galvanized and of a bright appearance; to be free from ragged edges, deep pits, or other defects. Gross weight, including steel straps for bundling, will be paid for. Weight of flat plates after galvanizing to conform to table following, with a tolerance of 5 per cent either way, provided the weight of coating is not reduced. 3. Types of Corrugation. Corrugations will be of three types, A, B, or C, as re- quired, in accordance with sketch incorporated in and forming a part of these specifica- tions. Corrugations shall be approximately parallel to each other and to edges of sheet, and ends of sheet shall be approximately square. Requisitions must state type of corrugation required. (a) For type A, width of sheet shall be sufficient to allow 9 full corrugations, covering width of 24 inches, finishing both edges down, as shown on sketch. (b) For type B, width of sheets shall be sufficient to allow 9| corrugations, covering width of 24 inches, finished one edge up and one edge down, as shown on sketch. [314] CORRUGATED GALVANIZED SHEET STEEL (c) For types A and B, depth of corrugations to be from \ to f inch, inclusive, pitch center to center of corrugations being between 2 and 2H inches. (d) For type C, the width stated should be in multiples of 8 inches, measured between TYPE- A 9 CORRUGATIONS , COVERING WIDTH ABOUT 24 ]" SHEET WIDTH- ABOUT Z6' (lO CORRUGATIONS LESS ABTif ON EACH EDGE) 4 TYPE-B 9 CORRUGATIONS , COVERING WIDTH ABOUT 24! SHEET WIDTH ABOUT Z7% (\Ok CORRUGATIONS LESS ABT. a-"oN EACH EDGC) the centers of the outside corrugations. This type is to be used only where absolutely necessary. 4. Sizes and Variations Allowed. All sheets to be cut full to length specified and not to exceed this length by more than f inch. 5. Data for Preparing Requisition. Sheets should be specified by type, length, and weight per square foot of flat galvanized plate, as given in the second column of the following table. Standard lengths are 5, 6, 7, 8, 9, and 10 feet. Maximum length 12 feet. The third column of the following table gives approximate weights per square foot of corrugated galvanized sheets, types A and B corresponding to the weights of flat sheets noted: United States Gauge No? WEIGHT PER SQUARE FOOT, POUNDS Minimum Zinc Coating per Square Foot, Ounces United States Gauge No? WEIGHT PER SQUARE FOOT, POUNDS Minimum Zinc Coating per Square Foot, Ounces Flat, Galvanized Corrugated, Galvanized Flat, Galvanized Corrugated, Galvanized 12 4.531 4.88 1.65 23 1.281 1.38 1.50 14 3.281 3.54 1.65 24 1.156 1.24 1.50 16 2.656 2.86 1.65 25 1.031 1.11 1.40 18 2.156 2.32 1.65 26 .906 .98 1.40 20 1.656 1.78 1.65 27 .844 .91 1.35 21 1.531 1.65 1.50 28 .781 .85 1.35 22 1.406 1.51 1.50 ..... 6. Samples from Galvanizing Bath. The galvanizing material must show 98 per cent pure zinc, determined from a sample taken at random by a Government inspector from the upper half of the galvanizing bath. These samples may be taken at any time, provided the manufacturer agrees to have the sample represent the galvanizing for the order; otherwise, when the inspector has been unable to secure a sample of the [315] FLOOR PLATES bath used for the order, the purity of the bath may be established by a Government laboratory from a sample of galvanized sheet taken at random from the order. 7. Determination of the Amount of Zinc Coating. The determination of the amount of coating per square foot to be obtained by establishing the practice of the firm at convenient intervals, by weighing plates, as follows: First, weight in bulk of selected plates in the black, after pickling. Secondly, weight of the same selected plates after galvanizing. If this course cannot be pursued the following method may be used: A selected sample from a galvanized sheet for the order, or 2 square feet of surface, will be sent to a Government laboratory at the expense of the manufacturer, where determination will be made of the amount of zinc coating per square foot. FLOOR PLATES NAVY DEPARTMENT 1. Floor plates to be made from steel plates of domestic manufacture. They will be free from surface defects and conform to dimensions ordered. Unless ordered with planed edges, plates will be shop sheared, and a variation of | inch in dimensions will be allowed. 2. They will be of ribbed pattern. 3. Ribs will be symmetrical, well denned, approximately flat tops, and the axes of patterns shall be parallel with longest dimensions. The ribs shall cover approximately half the surface. 4. The under side of the plates shall be flat and reasonably free from marks of rolls. TABLE V Thickness at Bottom of Pattern: Minimum Height of Rib Weight: Maximum per Square Foot Thickness at Bottom of Pattern: Minimum Height of Rib Weight: Maximum per Square Foot Inch Inch Pounds Inch Inch Pounds \ A 9 t & i7i i 4 A i is' i A 22f 6. Plates exceeding weight in table by not more than 5 per cent may be accepted, but excess weight will not be paid for. A minus variation in height of rib will be allowed as follows: Plates up to 36 inches wide 0.01 inch. Plates 36 inches wide and over 0.03 inch. No upper limit is placed on the height. 7. Inspection will be made at place of manufacture. [316] TERNEPLATE ROOFING TIN TERNEPLATE ROOFING TIN NAVY DEPARTMENT All roofing tin to be made of best quality soft open-hearth steel as a basis, plates resquared, 112 sheets to the box, unless otherwise specified. 1C 14 by 20 Inches 1C 28 by 20 Inches IX 14 by 20 Inches IX 28 by 20 Inches Black. plate from which made to weigh per 1 12 sheets net in the black Pounds 100 to 107 Pounds 200 to 2 14 Pounds 125 to 135 Pounds 250 to 270 Tin when finished to weigh per 112 sheets net 120 to 127 240 to 254 145 to 155 290 to 3 10 1. Coating on all roofing tin to be a mixture of pure new tin and pure new lead thoroughly mixed, and having a proportion of not less than 20 per cent of tin and the remainder lead; coating to be thoroughly amalgamated with the black plate by the palm-oil process. 2. This coating must be applied so that the sheets be evenly and equally coated on both sides and the coating distributed equally over each sheet. 3. After the plate has been cleansed in a weak acid solution it is to be thoroughly washed with water, after which nothing is to be brought in contact with the black plate but pure palm oil, pure new tin, and pure new lead. 4. Every sheet so coated must be free from all defects, blisters, bad edges and corners, and bare or imperfectly coated spots. Each sheet to be stamped with the brand, thickness of the plate, and name of the manufacturer. 5. The weight of coating in pounds per 112 sheets of 20 inches by 28 inches net shall not be less than 40 pounds. 6. Terneplate (Roofing Tin) with Charcoal-Iron Base. In case a plate with a charcoal-iron base is specified, the foregoing specifications shall apply as regards weights of coatings and the process of manufacture. The base or black plate shall be rolled and made from absolutely genuine charcoal iron, and no steel in the form of scrap or otherwise, or any other foreign matter, shall enter into the manufacture of the base or black plate. 7. An affidavit to the above must be furnished by the contractor, which affidavit must accompany the delivery of the roofing tin. 8. Tinned Plate (Bright Tin). All tin to be made of best quality soft open-hearth steel as a basis, 112 sheets to the box, unless otherwise specified. 1C 14 by 20 Inches IX 14 by 20 Inches IXX 14 by 20 Inches IXXXX 14 by 20 Inches Black plate from which made to weigh per 112 sheets net in the black Pounds 102 to 107 Pounds 129 to 135 Pounds 148 to 156 Pounds 187 to 197 Tin when finished to weigh per 112 sheets net 107 to 112 134 to 140 153 to 161 192 to 202 9. The coating shall weigh not less than 5 pounds per 1 12 sheets of 14 by 20 inch size. 10. The tin is to be of the best quality of commercially pure pig tin. If other size sheets are required the same proportions of black plate and tin should be observed. 11. The coating is to be thoroughly amalgamated with the black plate. This coating must be applied so that the sheets be evenly and equally coated on both sides and the coating distributed equally over each sheet. Every sheet so coated must be free from all defects, blisters, bad edges, and corners, and bare or imperfectly coated spots. [317]' WEIGHT OF RECTANGULAR STEEL PLATES WEIGHT OF RECTANGULAR STEEL PLATES PER LINEAL FOOT Reduction factor: 1 cubic inch of steel = 0.283333 pound WIDTH, IN INCHES Thick- 12 13 14 15 16 17 18 19 ness, in Six- AREA, IN SQUARE FEET teenths of an Inch 1.000 1.083 1.167 1.250 1.333 1.417 1.500 1.583 WEIGHT, IN POUNDS & 2.55 2.76 2.98 3.19 3.40 3.61 3.83 4.04 1 5.10 5.53 5.95 6.38 6.80 7.23 7.65 8.08 & 7.65 8.29 8.93 9.56 10.20 10.84 11.48 12.11 I 4 10.20 11.05 11.90 12.75 13.60 14.45 15.30 16.15 & 12.75 13.81 14.88 15.94 17.00 18.06 19.13 20.19 ! 15.30 16.58 17.85 19.13 20.40 21.68 22.95 24.23 A 17.85 19.34 20.83 22.31 23.80 25.29 26.78 28.26 k 20.40 22.10 23.80 25.50 27.20 28.90 30.60 32.30 & 22.95 24.86 26.78 28.69 30.60 32.51 34.43 36.34 1 25.50 27.63 29.75 31.88 34.00 36.13 38.25 40.38 tt 28.05 30.39 32.73 35.06 37.40 39.74 42.08 44.41 I 30.60 33.15 35.70 38.25 40.80 43.35 45.90 48.45 tt 33.15 35.91 38.86 41.44 44.20 46.96 49.73 52.49 1 35.70 38.68 41.65 44.63 47.60 50.58 53.55 56.53 H 38.25 41.44 44.63 47.81 51.00 54.19 57.38 60.56 i 40.80 44.20 47.60 51.00 54.40 57.80 61.20 64.60 I* 43.35 46.96 50.58 54.19 57.80 61.41 65.03 68.64 li 45.90 49.73 53.55 57.38 61.20 65.03 68.85 72.68 l* 48.45 52.49 56.53 60.56 64.60 68.64 72.68 76.71 ii 51.00 55.25 59.50 63.75 68.00 72.25 76.50 80.75 i& 53.55 58.01 62.48 66.94 71.40 75.86 80.33 84.79 if 56.10 60.78 65.45 70.13 74.80 79.48 84.15 88.83 1* 58.65 63.54 68.43 73.31 78.20 83.09 87.98 92.86 li 61.20 66.30 71.40 76.50 81.60 86.70 91.80 96.90 i& 63.75 69.06 74.38 79.69 85.00 90.31 95.63 100.94 11 66.30 71.83 77.35 82.88 88.40 93.93 99.45 104.98 itt 68.85 74.59 80.33 86.06 91.80 97.54 103.28 109.01 H 71.40 77.35 83.30 89.25 95.20 101.15 107.10 113.05 Ill 73.95 80.11 86.28 92.44 98.60 104.76 110.93 117.09 if 76.50 82.88 89.25 95.63 102.00 108.38 114.75 121.13 itt 79.05 85.64 92.23 98.81 105.40 111.99 118.58 125.16 2 81.60 88.40 95.20 102.00 108.80 115.60 122.40 129.20 [318] WEIGHT OF RECTANGULAR STEEL PLATES WEIGHT OP RECTANGULAR STEEL PLATES PER LINEAL FOOT (Cont.) WIDTH, IN INCHES Thick- 20 21 22 23 24 25 26 27 ness, m Six- AREA, IN SQUARE FEET teenths of an Inch 1.667 1.750 1.833 1.917 2.000 2.083 2.167 2.250 WEIGHT, IN POUNDS & 4.25 4.46 4.58 4.89 5.10 5.31 5.53 5.74 i 8.50 8.93 9.35 9.78 10.20 10.63 11.05 11.48 A 12.75 13.39 14.03 14.66 15.30 15.94 16.58 17.21 \ 17.00 17.85 18.70 19.55 20.40 21.25 22.10 22.95 A 21.25 22.31 23.38 24.44 25.50 26.56 27.63 28.69 i 25.50 26.78 28.05 29.33 30.60 31.88 33.15 34.43 A 29.75 31.24 32.73 34.21 35.70 37.19 38.68 40.16 \ 34.00 35.70 37.40 39.10 40.80 42.50 44.20 45.90 A 38.25 40.16 42.08 43.99 45.90 47.81 49.73 51.64 I 42.50 44.63 46.75 48.88 51.00 53.13 55.25 57.38 tt 46.75 49.09 51.43 53.76 56.10 58.44 60.78 63.11 1 51.00 53.55 56.10 58.65 61.20 63.75 66.30 68.85 H 55.25 58.01 60.78 63.54 66.30 69.06 71.83 74.59 1 59.50 62.48 65.45 68.43 71.40 74.38 77.35 80.33 II 63.75 66.94 70.13 73.31 76.50 79.69 82.88 86.06 i 68.00 71.40 74.80 78.20 81.60 85.00 88.40 91.80 l* 72.25 75.86 79.48 83.09 86.70 90.31 93.93 97.54 i| 76.50 80.33 84.15 87.98 91.80 95.63 99.45 103.28 1A 80.75 84.79 88.83 92.86 96.90 100.94 104.98 109.01 i| 85.00 89.25 93.50 97.75 102.00 106.25 110.50 114.75 1A 89.25 93.71 98.18 102.64 107.10 111.56 116.03 120.49 H 93.50 98.18 102.85 107.53 112.20 116.88 121.55 126.23 1A 97.75 102.64 107.53 112.41 117.30 122.19 127.08 131.96 U 102.00 107.10 112.20 117.30 122.40 127.50 132.60 137.70 1A 106.25 111.56 116.88 122.19 127.50 132.81 138.13 143.44 H 110.50 116.03 121.55 127.08 132.60 138.13 143.65 149.18 iH 114.75 120.49 126.23 131.96 137.70 143.44 149.18 154.91 if 119.00 124.95 130.90 136.85 142.80 148.75 154.70 160.65 iH 123.25 129.41 135.58 141.74 147.90 154.06 160.23 166.39 if 127.50 133.88 140.25 146.63 153.00 159.38 165.75 172.13 itt 131.75 138.34 144.93 151.51 158.10 164.69 171.28 177.86 2 136.00 142.80 149.60 156.40 163.20 170.00 176.80 183.60 [319] WEIGHT OF RECTANGULAR STEEL PLATES WEIGHT OP RECTANGULAR STEEL PLATES PER LINEAL FOOT (Cont.) WIDTH, IN INCHES Thick- ness, 28 29 30 31 32 33 34 35 in Six- AREA, IN SQUARE FEET teenths of an Inch 2.333 2 An 2.500 2.583 2.667 2.750 2.833 2.917 WEIGHT, IN POUNDS A 5.95 6.16 6.38 6.59 6.80 7.01 7.23 7.44 I 11.90 12.33 12.75 13.18 13.60 14.03 14.45 14.88 A 17.85 18.49 19.13 19.76 20.40 21.04 21.68 22.31 23.80 24.65 25.50 26.35 27.20 28.05 28.90 29.75 A 29.75 30.81 31.88 32.94 34.00 35.06 36.13 37.19 1 35.70 36.98 38.25 39.53 40.80 42.08 43.35 44.63 A 41.65 43.14 44.63 46.11 47.60 49.09 50.58 52.06 i 47.60 49.30 51.00 52.70 54.40 56.10 57.80 59.50 A 53.55 55.46 57.38 59.29 61.20 63.11 65.03 66.94 I 59.50 61.63 63.75 65.88 68.00 70.13 72.25 74.38 tt 65.45 67.79 70.13 72.46 74.80 77.14 79.48 81.81 1 71.40 73.95 76.50 79.05 81.60 84.15 86.70 89.25 H 77.35 80.11 82.88 85.64 88.40 91.16 93.93 96.69 i 83.30 86.28 89.25 92.23 95.20 98.18 101.15 104.13 89.25 92.44 95.63 98.81 102.00 105.19 108.38 111.56 i 95.20 98.60 102.00 105.40 108.80 112.20 115.60 119.00 1A 101 . 15 104.76 108.38 111.99 115.60 119.21 122.83 126.44 H 107.10 110.93 114.75 118.58 122.40 126.23 130.05 133.88 1A 113.05 117.09 121.13 125.16 129.20 133.24 137.28 141.31 If 119.00 123.25 127.50 131.75 136.00 140.25 144.50 148.75 1A 124.95 129.41 133.88 138.34 142.80 147.26 151.73 156.19 U 130.90 135.58 140.25 144.93 149.60 154.28 158.95 163.63 ITS 136.85 141.74 146.63 151.51 156.40 161.29 166.18 171.06 If 142.80 147.90 153.00 158.10 163.20 168.30 173.40 178.50 1A 148.75 154.06 159.38 164.69 170.00 175.31 180.63 185.94 U 154.70 160.23 165.75 171.28 176.80 182.33 187.85 193.38 til 160.65 166.39 172.13 177.86 183.60 189.34 195.08 200.81 l| 166.60 172.55 178.50 184.45 190.40 196.35 202.30 208.25 if! 172.55 178.71 184.88 191.04 197.20 203.36 209.53 215.69 if 178.50 184.88 191.25 197.63 204.00 210.38 216.75 223.13 iff 184.45 191.04 197.63 204.21 210.80 217.39 223.98 230.56 2 190.40 197.20 204.00 210.80 217.60 224.40 231.20 238.00 [320] WEIGHT OF RECTANGULAR STEEL PLATES WEIGHT OP RECTANGULAR STEEL PLATES PER LINEAL FOOT (Cont.) WIDTH, IN INCHES Thick- ness, 36 37 38 39 40 41 42 43 in Six- AREA, IN SQUARE FEET teenths of an Inch 3.000 3.083 3.167 3.250 3.333 3.417 3.500 3.583 WEIGHT, IN POUNDS A 7.65 7.86 8.08 8.29 8.50 8.71 8.93 9.14 i 15.30 15.73 16.15 16.58 17.00 17.43 17.85 18.28 A 22.95 23.59 24.23 24.86 25.50 26.14 26.78 27.41 i 30.60 31.45 32.30 33.15 34.00 34.85 35.70 36.55 38.25 39.31 40.38 41.44 42.50 43.56 44.63 45.69 I 45.90 47.18 48.45 49.73 51.00 52.28 53.55 54.83 ft 53.55 55.04 56.33 58.01 59.50 60.99 62.48 63.96 ^ 61.20 62.90 64.60 66.30 68.00 69.70 71.40 73.10 A 68.85 70.76 72.68 74.59 76.50 78.41 80.33 82.24 t 76.50 78.63 80.75 82.88 85.00 87.13 89.25 91.38 tt 84.15 86.49 88.83 91.16 93.50 95.84 98.18 100.51 i 91.80 94.35 96.90 99.45 102.00 104.55 107.10 109.65 u 99.45 102.21 104.98 107.74 110.50 113.26 116.03 118.79 i 107 . 10 110.08 113.05 116.03 119.00 121.98 124.95 127.93 H 114.75 117.94 121.13 124.31 127.50 130.69 133.88 137.06 i 122.40 125.80 129.20 132.60 136.00 139.40 142.80 146.20 IT 130.05 133.66 137.28 140.89 144.50 148.11 151.73 155.34 U 137.70 141.53 145.35 149.18 153.00 156.83 160.65 164.48 I* 145.35 149.39 153.43 157.46 161.50 165.54 169.58 173.61 If 153.00 157.25 161.50 165.75 170.00 174.25 178.50 182.75 1A 160.65 165.11 169.58 174.04 178.50 182.96 187.43 191.89 if 168.30 172.98 177.65 182.33 187.00 191.68 196.35 201.03 175.95 180.84 185.73 190.61 195.50 200.39 205.28 210.16 H* 183.60 188.70 193.80 198.90 204.00 209.10 214.20 219.30 iA 191.25 196.56 201.88 207.19 212.50 217.81 223.13 228.44 H 198.90 204.43 209.95 215.48 221.00 226.53 232.05 237.58 1H 206.55 212.29 218.03 223.76 229.50 235.24 240.98 246.71 U 214.20 220.15 226.10 232.05 238.00 243.95 249.90 255.85 IT! 221.85 228.01 234.18 240.34 246.50 252.66 258.83 264.99 If 229.50 235.88 242.25 248.63 255.00 261.38 267.75 274.13 1 237.15 243.74 250.33 256.91 263.50 270.09 276.68 283.26 2 244.80 251.60 258.40 265.20 272.00 278.80 285.60 292.40 [321 WEIGHT OF RECTANGULAR STEEL PLATES WEIGHT OF RECTANGULAR STEEL PLATES PER LINEAL FOOT (Cont.) WIDTH, IN INCHES Thick- ness, 44 45 46 47 48 49 50 51 in Six- AREA, IN SQUARE FEET teenths of an Inch 3.667 3.750 3.833 3.917 4.000 4.083 4.167 4.250 WEIGHT, IN POUNDS A 9.35 9.56 9.78 9.99 10.20 10.41 10.63 10.84 i 18.70 19.13 19.55 19.98 20.40 20.83 21.25 21.68 A 28.05 28.69 29.33 29.96 30.60 31.24 31.88 32.51 i 37.40 38.25 39.10 39.95 40.80 41.65 42.50 43.35 A 46.75 47.81 48.88 49.94 51.00 52.06 53.13 54.19 I 56.10 57.38 58.65 59.93 61.20 62.48 73.75 65.03 A 65.45 66.94 68.43 69.91 71.40 72.89 74.38 75.86 i 74.80 76.50 78.20 79.90 81.60 83.30 85.00 86.70 A 84.15 86.06 87.98 89.89 91.80 93.71 95.63 97.54 f 93.50 95.63 97.75 99.88 102.00 104.13 106.25 108.38 H 102.85 105.19 107.53 109.86 112.20 114.54 116.88 119.21 i 4 112.20 114.75 117.30 119.85 122.40 124.95 127.50 130.05 H 121.55 124.31 127.08 129.84 132.60 135.36 138.13 140.89 1 130.90 133.88 136.85 139.83 142.80 145.78 148.75 151.73 H 140.25 143.44 146.63 149.81 153.00 156.19 159.38 162.56 i 149.60 153.00 156.40 159.80 163.20 166.60 170.00 173.40 1A 158.95 162.56 166.18 169.79 173.40 177.01 180.63 184.24 if 168.30 172.13 175.95 179.78 183.60 187.43 191.25 195.08 iA 177.65 181.69 185.72 189.76 193.80 197.84 201.88 205.91 U 187.00 191.25 195.50 199.75 204.00 208.25 212.50 216.75 1A 196.35 200.81 205.28 209.74 214.20 218.66 223.13 227.59 if 205.70 210.38 215.05 219.73 224 .40 229.08 233.75 238.43 1A 215.05 219.94 224.83 229.71 234.60 239.49 244.38 249.26 H 224.40 229.50 234.60 239.70 244.80 249.90 255.00 260.10 1* 233.75 239.06 244.38 249.69 255.00 260.31 265.63 270.94 H 243.10 248.63 254.15 259.68 265.20 270.73 276.25 281.78 itt 252.45 258.19 263.93 269.66 275.40 281.14 286.88 292.61 U 261.80 267.75 273.70 279.65 285.60 291.55 297.50 303.45 1H 271.15 277.31 283.48 289.64 295.80 301.96 308.13 314.29 if 280.50 286.88 293.25 299.63 306.00 312.38 318.75 325.13 1H 289.85 296.44 303.03 309.61 316.20 322.79 329.38 335.96 2 299.20 306.00 312.80 319.60 326.40 333.20 340.00 346.80 [322]" WEIGHT OF RECTANGULAR STEEL PLATES WEIGHT OP RECTANGULAR STEEL PLATES PER LINEAL FOOT (Cont.) WIDTH, IN INCHES Thick- 52 53 54 55 56 57 58 59 ness, in Six- AREA, IN SQUARE FEET teenths of an Inch 4.333 4.417 4.500 4.583 4.667 4.750 4.833 4.917 WEIGHT, IN POUNDS A 11.05 11.26 11.48 11.69 11.90 12.11 12.33 12.54 22.10 22.53 22.95 23.38 23.80 24.23 24.65 25.08 A 33.15 33.79 34.43 35.06 35.70 36.34 36.98 37.61 i 44.20 45.05 45.90 46.75 47.60 48.45 49.30 50.15 A 55.25 56.31 57.38 58.44 ^59.50 60.56 61.63 62.69 I 66.30 77.58 68.85 70.13 71.40 72.68 73.95 75.23 77.35 78.84 80.33 81.81 83.30 84.79 86.28 87.76 f 88.40 90.10 91.80 93.50 95.20 96.90 98.60 100.30 A 99.45 101.36 103.28 105.19 107.10 109.01 110.93 112.84 f 110.50 112.63 114.75 116.88 119.00 121.13 123.25 125.38 ft 121.55 123.89 126.23 128.56 130.90 133.24 135.58 137.91 f - 132.60 135.15 137.70 140.25 142.80 145.35 147.90 150.45 ft 143.65 146.41 149.18 151.94 154.70 157.46 160.23 162.99 154.70 157.68 160.65 163.63 166.60 169.58 172.55 175.53 ft 165.75 168.94 172.13 175.31 178.50 181.69 184.88 188.06 i 176.80 180.20 183.60 187.00 190.40 193.80 197.20 200.60 1JL 187.85 191.46 195.08 198.69 202.30 205.91 209.53 213.14 U 198.90 202.73 206.55 210.38 214.20 218.03 221.85 225.68 209.95 213.99 218.03 222.06 226.10 230.14 234.18 238.21 H 221.00 225.25 229.50 233.75 238.00 242.25 246.50 250.75 Ml 232.05 236.51 240.98 245.44 249.90 254.36 258.83 263.29 H 243.10 247.78 252.45 257.13 261.80 266.48 271.15 275.83 254.15 259.04 263.93 268.81 273.70 278.59 283.48 288.36 if 265.20 270.30 275.40 280.50 285.60 290.70 295.80 300.90 iA 276.25 281.56 286.88 292.19 297.50 302.81 308.13 313.44 if 287.30 292.83 298.35 303.88 309.40 314.93 320.45 325.98 iff 298.35 304.09 309.83 315.56 321.30 327.04 332.78 338.51 if 309.40 315.35 321.30 327.25 333.20 339.15 345.10 351.05 iif 320.45 326.61 332.78 338.94 345.10 351.26 357.43 363.59 il 331.50 337.88 344.25 350.63 357.00 363.38 369.75 376.13 iif 342.55 349.14 355.73 362.31 368.90 375.49 382.08 388.66 2 353.60 360.40 367.20 374.00 380.80 387.60 394.40 401.20 [323] WEIGHT OF RECTANGULAR STEEL PLATES WEIGHT OP RECTANGULAR STEEL PLATES PER LINEAL FOOT (Cont.) WIDTH, IN INCHES Thick- 60 61 62 63 64 65 66 67 ness, in Six- AREA, IN SQUARE FEET teenths of an Inch 5.000 -5.083 5.167 5.250 5.333 5.417 5.500 5.583 WEIGHT, IN POUNDS & 12.75 12.96 "13.18 13.39 13.60 13.81 14.03 14.24 i 25.50 25.93 26.35. 26.78 27.20 27.63 28.05 28.48 A 38.25 38.89 39.53 40.16 40.80 41.44 42.08 42.71 i 51.00 51.85 52.70 53.55 54.40 55.25 56.10 56.95 A 63.75 64.81 ,65.88 66.94 68.00 69.06 70.13 71.19 I 76.50 77.78 79.05 80.33 81.60 82.88 84.15 85.43 A 89.25 90.74 92.23 93.71 95.20 96.69 98.18 99.66 i 102.00 103.70 105.40 107.10 108.80 110.50 112.20 113.90 * 114.75 116.66 118.58 120.49 122.40 124.31 126.23 128.14 i 127.50 129.63 131.75 133.88 136.00 138.13 140.25 142.38 ft 140.25 142.59 144.93 147.26 149.60 151.94 154.28 156.61 i 153.00 155.55 158.10 160.65 163.20 165.75 168.30 170.85 H 165.75 168.51 171.28 174.04 176.80 179.56 182.33 185.09 1 178.50 181.48 184.45 187.43 190.40 193.38 196.35 199.33 H 191.25 194.44 197.63 200.81 204.00 207.19 210.38 213.56 i 204.00 207.40 210.80 214.20 217.60 221.00 224.40 227.80 i* 216.75 220.36 223.98 227.59 231.20 234.81 238.43 242.04 H 229.50 233.33 237.15 240.98 244.80 248.63 252.45 256.28 i& 242.25 246.29 250.33 254.36 258.40 262.44 266.48 270.51 H 255.00 259.25 263.50 267.75 272.00 276.25 280.50 284.75 i* 267.75 272.21 276.68 281.14 285.60 290.06 294.53 298.99 if 280.50 285.18 289.85 294.53 299.20 303.88 308.55 313.23 14 293.25 298.14 303.03 307.91 312.80 317.69 322.58 327.46 H 306.00 311.10 316.20 321.30 326.40 331.50 336.60 341.70 i* 318.75 324.06 329.38 334.69 340.00 345.31 350.63 355.94 if 331.50 337.03 342.55 348.08. 353.60 359.13 364.65 370.18 1H 344.25 349.99 355.73 361.46 367.20 372.94 378.68 384.41 U 357.00 362.95 368.90 374.85 380.80 386.75 392.70 398.65 iff 369.75 375.91 382.08 388.24 394.40 400.56 406.73 412.89 if 382.50 388.88 395.25 401.63 408.00 414.38 420.75 427.13 in 395.25 401.84 408.43 415.01 421.60 428.19 434.78 441.36 2 408.00 414.80 421.60 428.40 435.20 442.00 448.80 455.60 [3241 WEIGHT OF RECTANGULAR STEEL PLATES WEIGHT OF RECTANGULAR STEEL PLATES PER LINEAL FOOT (Cant.) WIDTH, IN INCHES Thick- ness, 68 69 70 71 72 73 74 75 in Six- AREA, IN SQUARE FEET teenths of an 1 Inch 5.667 5.750 5.833 5.917 6.000 6.083 6.167 6.250 WEIGHT, IN POUNDS A 14.45 14.66 14.88 15.09 15.30 15.51 15.73 15.94 1 28.90 29.33 29.75 30.18 30.60 31.03 31.45 31.88 A 43.35 43.99 44.63 45.26 45.90 46.54 47.18 47.81 i 57.80 58.65 59.50 60.35 61.20 62.05 62.90 63.75 A 72.25 73.31 74.38 75.44 76.50 77.56 78.63 79.69 I 86.70 87.98 89.25 90.53 91.80 93.08 94.35 95.63 A 101.15 102.64 104.13 105.61 107.10 108.59 110.08 111.56 1 115.60 117.30 119.00 120.70 122.40 124.10 125.80 127.50 A 130.05 131.96 133.88 135.79 137.70 139.61 141.53 143.44 I 144.50 146.63 148.75 150.88 153.00 155.13 157.25 159.38 H 158.95 161.29 163.63 165.96 168.30 170.64 172.98 175.31 i 4 173.40 175.95 178.50 181.05 183.60 186.15 188.70 191.25 H 187.85 190.61 193.38 196.14 198.90 201.66 204.43 207.19 1 202.30 205.28 208.25 211.23 214.20 217.18 220.15 223.13 ** 216.75 219.94 223 . 13 226.31 229.50 232.69 235.88 239.06 i 231.20 234.60 238.00 241.40 244.80 248.20 251.60 255.00 i* 245.65 249.26 252.88 256.49 260.10 263.71 267.33 270.94 H 260.10 263.93 267.75 271.58 275.40 279.23 283.05 286.88 I* 274.55 278.59 282.63 286.66 290.70 294.74 298.78 302.81 li 289.00 293.25 297.50 301.75 306.00 310.25 314.50 318.75 1* 303.45 307.91 312.38 316.84 321.30 325.76 330.23 334.69 if 317.90 322.58 327.25 331.93 336.60 341.28 345.95 350.63 l* 332.35 337.24 342.13 347.01 351.90 356.79 361.68 366.56 11 346.80 351.90 357.00 362.10 367.20 372.30 377.40 382.50 1A 361.25 366.56 371.88 377.19 382.50 387.81 393.13 398.44 if 375.70 381.23 386.75 392.28 397.80 403.33 408.85 414.38 tit 390.15 395.89 401.63 407.36 413.10 418.84 424.58 430.31 u 404.60 410.55 416.50 422.45 428.40 434.35 440.30 446.25 i 419.05 425.21 431.38 437.54 443.70 449.86 456.03 462.19 H 433.50 439.88 446.25 452.63 459.00 465.38 471.75 478.13 1H 447.95 454.54 461 . 13 467.71 474.30 480.89 487.48 494.06 2 462.40 469.20 476.00 482.80 489.60 496.40 503.20 510.00 [325] WEIGHT OF RECTANGULAR STEEL PLATES WEIGHT OF RECTANGULAR STEEL PLATES PER LINEAL FOOT (Cont.) WIDTH, IN INCHES Thick- ness, 76 77 78 79 80 81 82 83 in Six- AREA, IN SQUARE FEET teenths of an 1 Inch 6.333 6.417 6.500 6.583 6.667 6.750 6.833 6.917 WEIGHT, IN POUNDS & 16.15 16.36 16.58 16.79 17.00 17.21 17.43 17.64 i 32.30 32.73 33.15 33.58 34.00 34.43 34.85 35.28 A 48.45 49.09 49.73 50.36 51.00 51.64 52.28 52.91 i 64.60 65.45 66.30 67.15 68.00 68.85 69.70 70.55 A 80.75 81.81 82.88 83.94 85.00 86.06 87.13 88.19 I 96.90 98.18 99.45 100.73 102.00 103.28 104.55 105.83 A 113.05 114.54 116.03 117.51 119.00 120.49 121.98 123.46 * 129.20 130.90 132.60 134.30 136.00 137.70 139.40 141.10 A 145.35 147.26 149.18 151.09 153.00 154.91 156.83 158.74 i 161.50 163.63 165.75 167.88 170.00 172.13 174.25 176.38 H 177.65 179.99 182.33 184.66 187.00 189.34 191.68 194.01 I 193.80 196.35 198.90 201.45 204.00 206.55 209.10 211.65 H 209.95 212.71 215.48 218.24 221.00 223.76 226.53 229.29 1 226.10 229.08 232.05 235.03 238.00 240.98 243.95 246.93 H 242.25 245.44 248.63 251.81 255.00 258.19 261.38 264.56 i 258.40 261.80 265.20 268.60 272.00 275.40 278.80 282.20 1* 274.55 278.16 281.78 285.39 289.00 292.61 296.23 299.84 U 290.70 294.53 298.35 302.18 306.00 309.83 313.65 317.48 1A 306.85 310.89 314.93 318.96 323.00 327.04 331.08 335.11 H 323.00 327.25 331.50 335.75 340.00 344.25 348.50 352.75 1A 339.15 343.61 348.08 352.54 357.00 361.46 365.93 370.39 if 355.30 359.98 364.65 369.33 374.00 378.68 383.35 388.03 1A 371.45 376.34 381.23 386.11 391.00 395.89 400.78 405.66 U 387.60 392.70 397.80 402.90 408.00 413.10 418.20 423.30 1A 403.75 409.06 414.38 419.69 425.00 430.31 435.63 440.94 if 419.90 425.43 430.95 436.48 442.00 447.53 453.05 458.58 1H 436.05 441.79 447.53 453.26 459.00 464.74 470.48 476.21 H 452.20 458.15 464.10 470.05 476.00 481.95 487.90 493.85 i 468.35 474.51 480.68 486.84 493.00 499.16 505.33 511.49 if 484.50 490.88 497.25 503.63 510.00 516.38 522.75 529.13 itt 500.65 507.24 513.83 520.41 527.00 533.59 540.18 546.76 2 516.80 523.60 530.40 537.20 544.00 550.80 557.60 564.40 [326] WEIGHT OF RECTANGULAR STEEL PLATES WEIGHT OP RECTANGULAR STEEL PLATES PER LINEAL FOOT (Cont.) WIDTH, IN INCHES Thick- ness, 84 85 86 87 88 89 90 91 in Six- AREA, IN SQUARE FEET teenths of an Inch 7.000 7.083 7.167 7.250 7.333 7.417 7.500 7.583 WEIGHT, IN POUNDS & 17.85 18.06 18.28 18.49 18.70 18.91 19.13 19.34 I 35.70 36.13 36.55 36.98 37.40 37.83 38.25 38.68 A 53.55 54.19 54.83 55.46 56.10 56.74 57.38 58.01 i 71.40 72.25 73.10 73.95 74.80 75.65 76.50 77.35 A 89.25 90.31 91.38 92.44 93.50 94.56 95.63 96.69 1 107.10 108.38 109.65 110.93 112.20 113.48 114.75 116.03 ft 124.95 126.44 127.93 129.41 130.90 132.39 133.88 135.36 i 142.80 144.50 146.20 147.90 149.60 151.30 153.00 154.70 A 160.65 162.56 164.48 166.39 168.30 170.21 172.13 174.04 I 178.50 180.63 182.75 184,88 187.00 189.13 191.25 193.38 H 196.35 198.69 201.03 203.36 205.70 208.04 210.38 212.71 i 214.20 216.75 219.30 221.85 224.40 226.95 229.50 232.05 H 232.05 234.81 237.58 240.34 243.10 245.86 248.63 251.39 1 249.90 252.88 255.85 258.83 261.80 264.78 267.75 270.78 H 267.75 270.94 274.13 277.31 280.50 283.69 286.88 290.06 i 285.60 289.00 292.40 295.80 299.20 302.60 306.00 309.40 i* 303.45 307.06 310.68 314.29 317.90 321.51 325.13 328.74 H 321.30 325.13 328.95 332.78 336.60 340.43 344.25 348.08 I* 339.15 343.19 347.23 351.26 355.30 359.34 363.38 367.41 li 357.00 361.25 365.50 369.75 374.00 378.25 382.50 386.75 1ft 374.85 379.31 383.78 388.24 392.70 397.16 401.63 406.09 U 392.70 397.38 402.05 406.73 411.40 416.08 420.75 425.43 I* 410.55 415.44 420.33 425.21 430.10 434.99 439.88 444.76 H 428.40 433.50 438.60 443.70 448.80 453.90 459.00 464.10 lA 446.25 451.56 456.88 462.19 467.50 472.81 478.13 483.44 if 464 . 10 469.63 475.15 480.68 486.20 491.73 497.25 502.78 i 481.95 487.69 493.43 499.16 504.90 510.64 516.38 522.11 if 499.80 505.75 511.70 517.65 523.60 529.55 535.50 541.45 1H 517.65 523.81 529.98 536.14 542.30 548.46 554.63 560.79 li 535.50 541.88 548.25 554.63 561.00 567.38 573.75 580.13 1H 553.35 559.94 566.53 573.11 579.70 586.29 592.88 599.46 2 571.20 578.00 584.80 591.60 598.40 605.20 612.00 618.80 [327] WEIGHT OF RECTANGULAR STEEL PLATES WEIGHT OF RECTANGULAR STEEL PLATES PER LINEAL FOOT (Cont.) WIDTH, IN INCHES Thick- 92 93 94 95 96 97 98 99 ness, in Six- AREA, IN SQUARE FEET teenths of an Inch 7.667 7.750 7.833 7.917 8.000 8.083 8.167 8.250 WEIGHT, IN POUNDS & 19.55 19.76 19.98 20.19 20.40 20.61 20.83 21.04 i 39.10 39.53 39.95 40.38 40.80 41.23 41.65 42.08 * 58.65 59.29 59.93 60.56 61.20 61.84 62.48 63.11 i 4 78.20 79.05 79.90 80.75 81.60 82.45 83.30 84.15 A 97.75 98.81 99.88 100.94 102.00 103.86 104.13 105.19 t 117.30 118.58 119.85 121.13 122.40 123.68 124.95 126.23 A 136.85 138.34 139.83 141.31 142.80 144.29 145.78 147.26 1 156.40 158.10 159.80 161.50 163.20 164.90 166.60 168.30 A 175.95 177.86 179.68 181.69 183.60 185.51 187.43 189.34 I 195.50 197.63 199.75 201.88 204.00 206.13 208.25 210.38 H 215.05 217.39 219.73 222.06 224.40 226.74 229.08 231.41 1 234.60 237.15 239.70 242.25 244.80 247.35 249.90 252.45 H 254.15 256.91 259.68 262.44 265.20 267.96 270.73 273.49 * 273.70 276.68 279.65 282.63 285.60 288.58 291.55 294.53 if 293.25 296.44 299.63 302.81 306.00 309.19 312.37 315.56 i 312.80 316.20 319.60 323.00 326.40 329.80 333.20 336.60 i& 332.35 335.96 339.58 343.19 346.80 350.41 354.03 357.64 H 351.90 355.73 359.55 363.38 367.20 371.03 374.85 378.68 1A 371.45 375.49 379.53 383.56 387.60 391.64 395.68 399.71 II 391.00 395.25 399.50 403.75 408.00 412.25 416.50 420.75 1A 410.55 415.01 419.48 423.94 428.40 432.86 437.33 441.79 if 430.10 434.78 439.45 444.13 448.80 453.48 458.15 462.83 1ft 449.65 454.54 459.43 464.31 469.20 474.09 478.98 483.86 li 469.20 474.30 479.40 484.50 489.60 494.70 499.80 504.90 1* 488.75 494.06 499.38 504.69 510.00 515.31 520.63 525.94 if 508.30 513.83 519.35 524.88 530.40 535.93 541.45 546.98 1H 527.85 533.59 539.33 545.06 550.80 556.54 562.28 568.01 H 547.40 553.35 559.30 565.25 571.20 577.15 583.10 589.05 1H 566.95 573.11 579.28 575.44 591.60 597.76 603.93 610.09 If 586.50 592.88 599.25 605.63 612.00 618.38 624.75 631.13 itt 606.05 612.64 619.23 625.81 632.40 638.99 645.58 652.16 2 625.60 632.40 639.20 646.00 652.80 659.60 666.40 673.20 [328] WEIGHT OF CIRCULAR STEEL PLATES WEIGHT OP CIRCULAR STEEL PLATES Reduction factor: 1 cubic inch of steel = 0.283333 pound DIAMETER, IN INCHES LThick- ness, 12 13 14 15 16 17 18 19 in Six- AREA, IN SQUARE INCHES teenths of an Inch 113.10 132.73 153.94 176.72 201.06 226.98 254.47 283.53 WEIGHT, IN POUNDS ft 2.00 2.35 2.73 3.13 3.56 4.02 4.51 5.02 i 4.01 4.70 5.45 6.26 7.12 8.04 9.01 10.04 JL 6.01 7.05 8.18 9.39 10.68 12.06 13.52 15.06 1 8.01 9.40 10.90 12.52 14.24 16.08 18.02 20.08 10.01 11.75 13.63 16.65 17.80 20.10 22.53 25.10 1 12.02 14.10 16.36 18.78 21.36 24.12 27.04 30.13 14.02 16.45 19.08 21.91 24.92 28.14 31.54 35.15 | 16.02 18.80 21.81 25.03 28.48 32.16 36.05 40.17 A 18.02 21.15 24.53 28.16 32.04 36.18 40.56 45.19 I 20.03 23.50 27.26 31.29 35.60 40.19 45.06 50.21 B 22.03 25.86 29.99 34.42 39.17 44.21 49.57 55.23 f 24.03 28.21 32.71 37.55 42.73 48.23 54.07 60.25 H 26.04 30.56 35.44 40.68 46.29 52.25 58.58 65.27 I 28.04 32.91 38.16 43.81 49.85 56.27 63.09 70.29 30.04 35.26 40.89 46.94 53.41 60.29 67.59 75.31 i 1 * 32.04 37.61 43.62 50.07 56.97 64.31 72.10 80.33 DIAMETER, IN INCHES Thick- ness, 20 21 22 23 24 25 26 27 in Six- AREA, IN SQUARE INCHES teenths of an Inch 314.16 346.36 380.13 415.48 452.39 490.88 530.93 572.56 WEIGHT, IN POUNDS ft 5.56 6.13 6.73 7.36 8.01 8.69 9.40 10.14 I 11.13 12.27 13.46 14.71 16.02 17.39 18.80 20.28 16.69 18.40 20.19 22.07 24.03 26.08 28.21 30.42 i 22.25 24.53 26.93 29.43 32.04 34.77 37.61 40.56 A 27.82 30.67 33.66 36.79 40.06 43.46 47.01 50.70 f 33.38 36.80 40.39 44.14 48.07 52.16 56.41 60.83 ft 38.94 42.93 47.12 51.50 56.08 60.85 65.81 70.97 1 44.51 49.07 53.85 58.86 64.09 69.54 75.22 81.11 T$ 50.07 55.20 60.58 66.22 72.10 78.23 84.62 91.25 1 55.63 61.33 67.32 73.57 80.11 86.93 94.02 101.39 H 61.20 67.47 74.05 80.93 88.12 95.62 103.42 111.53 1 66.76 73.60 80.78 88.29 96.13 104.31 112.82 121.67 it 72.32 79.74 87.51 95.65 104.14 113.00 122.22 131.81 i 77.89 85.87 94.24 103.00 112.16 121.70 131.63 141.95 H 83.45 92.00 100.97 110.36 120.17 130.39 -141.03 152.09 i 89.01 98.14 107.70 117.72 128.18 139.08 150.43 162.22 [329] WEIGHT OF CIRCULAR STEEL PLATES WEIGHT OF CIRCULAR STEEL PLATES (CW.) DIAMETER, IN INCHES Thick- ness, 28 29 30 31 32 33 34 35 in Six- AREA, IN SQUARE INCHES teenths of an Inch 615.75 660.52 706.86 754.77 804.25 855.30 907.92 962.11 WEIGHT, IN POUNDS A 10.90 11.70 12.52 13.37 14.24 15.15 16.08 17.04 1 21.81 23.39 25.03 26.73 28.48 30.29 32.16 34.07 A 32.71 35.09 37.55 40.10 42.73 45.44 48.23 51.11 i 43.62 46.79 50.07 53.46 56.97 60.58 64.31 68.15 A 54.52 58.48 62.59 66.83 71.21 75.73 80.39 85.19 I 65.42 70.18 75.10 80.19 85.45 90.88 96.47 102.22 A 76.33 81.88 87.62 93.56 99.69 106.02 112.54 119.26 * 87.23 93.57 100.14 106.93 113.94 121.17 128.62 136.30 A 98.14 105.27 112.66 120.29 128.18 136.31 144.70 153.34 f 109.04 116.97 125.17 133.66 142.42 151.46 160.78 170.37 tt 119.94 128.66 137.69 147.02 156.66 166.61 176.86 187.41 1 130.85 140.36 150.21 160.39 170.90 181.75 192.93 204.45 H 141.75 152.06 162.73 173.75 185.15 196.90 209.01 221.49 1 152.66 163.75 175.24 187.12 199.39 212.04 225.09 238.52 H 163.56 175.45 187.76 200.49 213.63 227.19 241 . 17 255.56 l 174.46 187.15 200.28 213.85 227.87 242.34 257.24 272.60 DIAMETER, IN INCHES Thick- ness, 36 37 38 39 40 41 42 43 in Six- AREA, IN SQUARE INCHES teenths of an Inch 1017.87 1075.21 1134.11 1194.59 1256.64 1320.25 1385.44 1452.20 WEIGHT, IN POUNDS A 18.02 19.04 20.08 21.15 22.25 23.38 24.53 25.72 * 36.05 38.08 40.17 42.31 44.51 46.76 49.07 51.43 A 54.07 57.12 60.25 63.46 66.76 70.14 73.60 77.15 i 72.10 76.16 80.33 84.62 89.01 93.52 98.14 102.86 A 90.12 95.20 100.42 105.77 111.27 116.90 122.67 128.58 I 108.15 114.24 120.50 126.93 133.52 140.28 147.20 154.30 A 126.17 133.28 140.58 148.08 155.77 163.66 171.74 180.01 * 144.20 152.32 160.67 169.23 178.02 187.04 196.27 205.73 A 162.22 171.36 180.75 190.39 200.28 210.42 220.81 231.44 1 180.25 190.40 200.83 211.54 222.53 233.79 245.34 257.16 H 198.27 209.44 220.92 232.70 244.78 257.17 269.87 282.88 I 216.30 228.48 241.00 253.85 267.04 280.55 294.41 308.59 tt 234.32 247.52 261.08 275.01 289.29 303.93 318.94 334.31 1 252.35 266.56 281 . 17 296.16 311.54 327.31 343.47 360.03 H 270.37 285.60 301.25 317.31 333.80 350.69 368.01 385.74 i 288.40 304.64 321.33 338.47 356.05 374.07 392.54 411.46 [330] WEIGHT OF CIRCULAR STEEL PLATES WEIGHT OF CIRCULAR STEEL PLATES (Cont.) DIAMETER, IN INCHES Thick- ness, 44 45 46 47 48 49 50 51 in Six- AREA, IN SQUARE INCHES teenths of an Inch 1520.53 1590.43 1661.90 | 1734.94 1809.56 1885.74 1963.50 2042.82 WEIGHT, IN POUNDS A 26.93 28.16 29.43 30.72 32.01 33.39 34.77 36.18 53.85 56.33 58.86 61.45 64.09 66.79 69.54 72.35 A 80.78 84.49 88.29 92.17 96.13 100.18 104.31 108.53 I 107.70 112.66 117.72 122.89 128.18 133.57 139.08 144.70 A 134.63 140.82 147.15 153.61 160.22 166.97 173.85 180.88 I 161.56 168.98 176.58 184.34 192.27 200.36 208.62 217.05 A 188.48 197.15 206.01 215.06 224.31 233.75 243.39 253.23 i 215.41 225.31 235.44 245.78 256.35 267.15 278.16 289.40 A 242.34 253.48 264.87 276.51 288.40 300.54 312.93 325.58 1 269.26 281.64 294.30 307.23 320.44 333.93 347.70 361.75 H 296.19 309.80 323.73 337.95 352.49 367.33 382.47 397.93 t 323.11 337.97 353.15 368.68 384.53 400.72 417.24 434.10 H 350.04 366.13 382.58 399.40 416.58 434.11 452.02 470.28 1 376.97 394.30 412.01 430.12 448.62 467.51 486.79 506.45 H 403.89 422.46 441.44 460.84 480.67 500.90 521.56 542.63 i 430.82 450.62 470.87 491.57 512.71 534.29 556.33 578.80 DIAMETER, IN INCHES Thick- ness, 52 53 54 55 56 57 58 59 in Six- AREA, IN SQUARE INCHES teenths of an Inch 2123.72 2206.18 2290.22 2375.83 2463.01 2551.76 | 2642.08 2733.97] WEIGHT, IN POUNDS A 37.61 39.07 40.56 42.07 43.62 45.19 46.79 48.41 1 75.22 78.14 81.11 84.14 87.23 90.38 93.57 96.83 A 112.82 117.20 121.67 126.22 130.85 135.56 140.36 145.24 i 150.43 156.27 162.22 168.29 174.46 180.75 187.15 193.66 A 188.04 195.34 202.78 210.36 218.08 225.94 233.93 242.07 I 225.65 234.41 243.34 252.43 261.70 271.13 280.72 290.48 A 263.25 273.48 283.89 294.50 305.31 316.31 327.51 338.90 \ 300.86 312.54 324.45 336.58 348.93 361.50 374.30 387.31 A 338.47 351.61 365.00 378.65 392.54 406.69 421.08 435.73 I 376.08 390.68 405.56 420.72 436.16 451.88 467.87 484.14 H 413.68 429.75 446.12 462.79 479.77 497.06 514.66 532.56 I 451.29 468.81 486.67 504.87 523.39 542.25 561.44 580.97 H 488.90 507.88 527.23 546.94 567.01 587.44 608.23 629.38 7 I 526.51 546.95 567.79 589.01 610.62 632.63 655.02 677.80 H 564.11 586.02 608.34 631.08 654.24 677.81 701.80 726.21 i 601.72 625.09 648.90 673.15 697.85 723.00 748.59 774.63 [331] WEIGHT OF CIRCULAR STEEL PLATES WEIGHT OF CIRCULAR STEEL PLATES (Cont.) DIAMETER, IN INCHES Thick- ness, 60 61 62 63 64 65 66 67 in Six- AREA, IN SQUARE INCHES teenths of an Inch 2827.44 2922.47 3019.07 3117.25 3216.99 3318.31 1 3421.20 3525.66 WEIGHT, IN POUNDS ft 50.07 51.75 53.46 55.20 56.97 58.76 60.58 62.43 i 100.14 103 50 106.93 110.40 113.94 117.52 121.17 124.87 150.21 155.26 160.39 165.60 170.90 176.29 181.75 187.30 i 200.28 207.01 213.85 220.81 227.87 235.05 242.34 249.73 ft 250.35 258.76 267.31 276.01 284.84 293.81 302.92 312.17 I 300.42 310.51 320.78 331.21 341.81 352.57 363.50 374.60 350.49 362.27 374.24 386.41 398.77 411.33 424.09 437.04 , .* 400.55 414.02 427.70 441.61 455.74 470.10 484.67 499.47 450.62 465.77 481.17 496.81 512.71 528.86 545.26 561.90 V 500.69 517.52 534.63 552.01 569.68 587.62 605.84 624.34 H 550.76 569.27 588.09 607.22 626.64 646.38 666.42 686.77 1 600.83 621.03 641.55 662.42 683.61 705.14 727.01 749.20 H 650.90 672.78 695.02 717.62 740.58 763.90 787.59 811.64 700.97 724.53 748.48 772.82 797.55 822.67 848.17 874.07 if 751.04 776.28 801.94 828.02 854.51 881.43 908.76 936.51 i 801.11 828.04 855.41 883.22 911.48 940.19 969! 34 998.94 DIAMETER, IN INCHES Thick- ness, 68 69 70 71 72 73 74 75 in Six- AREA, IN SQUARE INCHES teenths of an Inch 3631.68 3739.28 3848.46 3959.20 4071.51 4185.39 4300.85 4417.87 WEIGHT, IN POUNDS * 64.31 66.22 68.15 70.11 72.10 74.12 76.16 78.23 128.62 132.43 136.30 140.22 144.20 148.23 152.32 156.47 ft 192.93 198.65 204.45 210.33 216.30 222.35 228.48 234.70 257.24 264.87 272.60 280.44 288.40 296.47 304.64 312.93 % 321.56 331.08 340.75 350.56 360.50 370.58 380.81 391.17 1 385.87 397.30 408.90 420.67 432.60 444.70 456.97 469.40 * 450.18 463.52 477.05 490.78 504.70 518.82 533 . 13 547.63 514.49 529.73 545.20 560.89 576.80 592.93 609.29 625.87 & 578.80 595.95 613.35 631.00 648.90 667.05 685.45 704.10 I 643.11 662.17 681.50 701.11 721.00 741.16 761.61 782.33 H 707.42 728.38 749.65 771.22 793.10 815.28 837.77 860.57 771.73 794.60 817.80 841.33 865.20 889.40 913.93 938.80 tt 836.04 860.82 885.95 911.44 937.30 963.51 990.09 1017.0 900.36 927.03 954.10 981.55 1009.4 1037.6 1066.3 1095.3 H 964.67 993.25 1022.2 1051.7 1081.5 1111.7 1142.4 1173.5 l 1029.0 1059.5 1090.4 1121.8 1153.6 1185.9 1218.6 1251.7 [332 WEIGHT OF CIRCULAR STEEL PLATES WEIGHT OF CIRCULAR STEEL PLATES (Cont.) DIAMETER, IN INCHES Thick- ness, 76 77 78 79 80 81 82 83 in Six- AREA, IN SQUARE INCHES teenths of an Inch 4536.47 4656.63 4778.37 4901.68 5026.56 5153.00 5281.02 5410.62 WEIGHT, IN POUNDS ft 80.33 82.46 84.62 86.80 89.01 91.25 93.52 95.81 i 160.67 164.92 169.23 173.60 178.02 182.50 187.04 191.63 A 241.00 247.38 253.85 260.40 267.04 273.75 280.55 287.44 1 321.33 329.85 338.47 347.20 356.05 365.01 374.07 383.25 A 401.67 412.31 423.09 434.00 445.06 456.26 467.59 479.07 I 482.00 494.77 507.70 520.80 534.07 547.51 561.11 574.88 ft 562.33 577.23 592.32 607.61 623.09 638.76 654.63 670.69 1 642.67 659.69 676.94 694.41 712.10 730.01 748.15 766.51 ft 723.00 742.15 761.55 781.21 801.11 821.26 841.66 862.32 I 803.34 824.61 846.17 868.01 890.12 912.51 935.18 958.13 H 883.67 907.07 930.79 954.81 979.13 1003.8 1028.7 1053.9 i 964.00 989.54 1015.4 1041.6 1068.1 1095.0 1122.2 1149.8 H 1044.3 1072.0 1100.0 1128.4 1157.2 1186.3 1215.7 1245.6 1 1124.7 1154.5 1184.6 1215.2 1246.2 1277.5 1309.3 1341.4 H 1205.0 1236.9 1269.3 1302.0 1335.2 1368.8 1402.8 1437.2 l 1285.3 1319.4 1353.9 1388.8 1424.2 1460.0 1496.3 1533.0 DIAMETER, IN INCHES Thick- ness, 84 85 86 87 88 89 90 91 in Six- AREA, IN SQUARE INCHES teenths of an Inch 5541.78 5674.51 5808.81 5944.69 6082.13 6221.15 6361.74 6503.89 WEIGHT, IN POUNDS & 98.14 100.49 102.86 105.27 107.70 110.17 112.66 115.17 1 196.27 200.97 205.73 210.54 215.41 220.33 225.31 230.35 A 294.41 301.46 308.59 315.81 323.11 330.50 337.97 345.52 i 392.54 401.95 411.46 421.08 430.82 440.67 450.62 460.69 A 490.68 502.43 514.32 526.35 538.52 550.83 563.28 575.87 I 588.82 602.92 617.19 631.62 646.23 661.00 675.94 691.04 ft 686.95 703.40 720.05 736.90 753.93 771.17 788.59 806.21 * 785.09 803.89 822.92 842.17 861.64 881.33 901.25 921.39 A 883.22 904.38 925.78 947.44 969.34 991.50 1013.9 1036.6 ! 981.36 1004.9 1028.6 1052.7 1077.0 1101.7 1126.6 1151.7 H 1079.5 1105.3 1131.5 1158.0 1184.8 1211.8 1239.2 1266.9 I 1177.6 1205.8 1234.4 1263.2 1292.5 1322.0 1351.9 1382.1 H 1275.8 1306.3 1337.2 1368.5 1400.2 1432.2 1464.5 1497.3 1 1373.9 1406.8 1440.1 1473.8 1507.9 1542.3 1577.2 1612.4 H 1472.0 1507.3 1543.0 1579.1 1615.6 1652.5 1689.8 1727.6 i 1570.2 1607.8 1645.8 1684.3 1723.3 1762.7 1802.5 1842.8 [333 WEIGHT OF CIRCULAR STEEL PLATES WEIGHT OF CIRCULAR STEEL PLATES (Cont.) DIAMETER, IN INCHES Thick- ness, 92 93 94 95 96 97 98 99 in Six- AREA, IN SQUARE INCHES teenths of aii Inch 6647.62 6792.92 6939.79 7088.23 7238.24 7389.80 7542.96 7697.68 WEIGHT, IN POUNDS 117.72 120.29 122.89 125.52 128.18 130.86 133.57 136.31 | 235.44 240.58 245.78 251.04 256.35 261.72 267.15 272.63 A 353.16 360.87 368.68 376.56 384.53 392.58 400.72 408.94 i 470.87 481.17 491.57 502.08 512.71 523.45 534.29 545.25 A 588.59 601.46 614.46 627.61 640.89 654.31 667.87 681.57 1 706.31 721.75 737.35 753.13 769.06 785.17 801.44 817.88 tV 824.03 842.04 860.25 878.65 897.24 916.03 935.01 954.19 I 941.75 962.33 983.14 1004.2 1025.4 1046.9 1068.6 1090.5 A 1059.5 1082.6 1106.0 1129.7 1153.6 1177.8 1202.2 1226.8 1 1177.2 1202.9 1228.9 1255.2 1281.8 1308.6 1335.7 1363.1 H 1294.9 1323.2 1351.8 1380.7 1410.0 1439.5 1469.3 1499.4 f 1412.6 1443.5 1474.7 1506.3 1538.1 1570.3 1602.9 1635.8 H 1530.3 1563.8 1597.6 1631.8 1666.3 1701.2 1736.5 1772.1 i 1648.1 1684.1 1720.5 1757.3 1794.5 1832.1 1870.0 1908.4 H 1765.8 1804.4 1743.4 1882.8 1922.7 1962.9 2003.6 2044.7 l 1883.5 1924.7 1966.3 2008.3 2050.8 2093.8 2137.2 2181.0 <, DIAMETER, IN INCHES Thick- ness, 100 101 102 103 104 105 106 107 in Six- AREA, IN SQUARE INCHES teenths of an Inch 7854.00 8011.84 8171.28 8332.29 8494.87 8659.01 8824.73 8992.02 WEIGHT, IN POUNDS A 139.08 141.88 144.70 147.55 150.43 153.34 156.27 159.23 1 278.16 283.75 289.49 295.10 300.86 306.67 312.54 318.47 417.24 425.63 434.10 442.65 451.29 460.01 468.81 477.70 1 556.33 567.51 578.80 590.21 601.72 613.35 625.09 636.94 A 695.41 709.38 723.50 737.76 752.15 766.68 781.36 796.17 1 834.49 851.26 868.20 885.31 902.58 920.02 937.63 955.40 973.57 993.14 1012.9 1032.9 1053.0 1073.4 1093.9 1114.6 i 1112.7 1135.0 1157.6 1180.4 1203.4 1226.7 1250.2 1273.9 ^ 1251.7 1276.9 1302.3 1328.0 1353.9 1380.0 1406.4 1433.1 f 1390.8 1418.8 1447.0 1475.5 1504.3 1533.4 1562.7 1592.3 H 1529.9 1560.6 1591.7 1623.1 1654.7 1686.7 1719.0 1751.6 1669.0 1702.5 1736.4 1770.6 1805.2 1840.0 1875.3 1910.8 tt 1808.1 1844.4 1881.1 1918.2 1955.6 1993.4 2031.5 2070.0 1 1947.1 1986.3 2025.8 2065.7 2106.0 2146.7 2187.8 2229.3 H 2086.2 2128.2 2170.5 2213.2 2256.5 2300.1 2344.1 2388.5 1 2225.3 2270.0 2315.2 2360.8 2406.9 2453.4 2500.4 2547.7 [334] WEIGHT OF CIRCULAR STEEL PLATES WEIGHT OF CIRCULAR STEEL PLATES (Cont.) DIAMETER IN INCHES Thick- ness, 108 109 110 ill 112 113 114 115 in Six- AREA, IN SQUARE INCHES teenths of an Inch 9160.88 9331.32 9503.32 9676.89 9852.03 10028.75 10207.03 10386.89 WEIGHT, IN POUNDS A 162.22 165.24 168.29 171.36 174.76 177.59 180.75 183.93 i 324.45 330.49 336.58 342.72 348.93 355.19 361.50 367.87 A 486.67 495.73 504.87 514.09 523.39 532.78 542.25 551.80 i 648.90 660.97 673.15 685.45 697.85 710.37 723.00 735.74 A 811.12 826.21 841.44 856.81 872.32 887.96 903.75 919.67 1 973.35 991.46 1009.7 1028.2 1046.8 1065.6 1084.5 1103.6 & 1135.6 1156.7 1178.0 1199.5 1221.2 1243.2 1265.2 1287.5 4 1297.8 1321.9 1346.3 1370.9 1395.7 1420.7 1446.0 1471.5 A 1460.0 1487.2 1514.6 1542.3 1570.2 1598.3 1626.7 1655.4 I 1622.2 1652.4 1682.9 1713.6 1744.6 1775.9 1807.6 1839.3 H 1784.5 1817.7 1851.2 1885.0 1919.1 1953.5 1988.2 2023.3 3 4 1946.7 1982.9 2019.5 2056.3 2093.6 2131.1 2169.0 2207.2 H 2108.9 2148.2 2187.7 2227.7 2268.0 2308.7 2349.7 2391.2 1 2271.1 2313.4 2356.0 2399.1 2442.5 2486.3 2530.5 2575.1 H 2433.4 2478.6 2524.3 2570.4 2617.0 2663.9 2711.2 2759.0 i 2595.6 2643.9 2692.6 2741.8 2791.4 2841.5 2892.0 2943.0 DIAMETER, IN INCHES Thick- ness, 116 117 118 119 120 in Six- AREA, IN SQUARE INCHES teenths of an Inch 10568.32 10751.32 10935.88 11122.02 11309.73 WEIGHT, IN POUNDS A 187.15 190.39 193.66 196.95 200.28 i 374.30 380.78 387.31 393.91 400.55 A 561.44 571.17 580.97 590.86 600.83 i 4 748.59 761.55 774.63 787.81 801.11 A 935.74 951.94 968.28 984.76 1001.4 1 1122.9 1142.3 1161.9 1181.7 1201.7 & 1310.0 1332.7 1355.6 1378.7 1401.9 i 1497.2 1523.1 1549.3 1575.6 1602.2 A 1684.3 1713.5 1742.9 1772.6 1802.5 I 1871.5 1903.9 1936.6 1969.5 2002.8 H 2058.6 2094.3 2130.2 2166.5 2203.0 2245.8 2284.7 2323.9 2363.4 2403.3 H 2432.9 2475.0 2517.5 2560.4 2603.6 1 2620.1 2665.4 2711.2 2757.3 2803.9 H 2807.2 2855.8 2904.9 2954.3 3004.2 i 2994.4 3046.2 3098.5 3151.2 3204.4 [335] WEIGHTS OF SQUARE AND ROUND STEEL BARS WEIGHTS OF SQUARE AND ROUND STEEL BARS. Reduction Factor : 1 cubic inch of steel = 0.28333 pound. Size SQUARI 3 BARS ROUND BARS Size SQUARI 3 BARS ROUND BARS in Inches Per Foot Per Inch Per Foot Per Inch in Inches Per Foot Per Inch Per Foot Per Inch 1 .213 018 167 .014 21 25 71 2 14 20 20 1 68 A.. .332 .028 .261 .022 2*|.. 26 90 2 24 21 12 1 76 478 040 376 031 21 28 10 2 34 22 07 1 84 A. .651 .054 .511 .043 2r!.. 29 34 2 45 23.04 1 92 .850 .071 .668 .056 3 30.60 2.55 24.03 2.00 JL 1.076 .090 .845 .070 SJL 31 89 2 66 25.05 2 08 [f 1.328 .111 1.043 .087 3| 33.20 2.77 26.08 2.17 11 1 607 134 1 262 105 3A 34 54 2 88 27 13 2 26 1.913 .159 1.502 .125 3i . 35.91 2.99 28.21 2.35 T 2 245 187 1 763 147 3JL 37 31 3 11 29 30 2 44 1 2 603 .217 2.044 .170 31 . 38.73 3.23 30.42 2.53 if.. 2.988 .250 2.347 .195 3;& 40.18 3.35 31.55 2.63 1 3 40 28 2 67 .22 3| . 41 65 3 48 32.71 2 72 ITS.. 3.84 .32 3.02 .25 3^ 43.15 3.60 33.89 2.82 li . 4.30 .35 3.38 .28 3f 44.68 3.72 35.09 2.92 1A.. 4.79 .40 3.77 .31 3H-. 46.23 3.85 36.31 3.02 11 ITS 5.31 5 86 .44 49 4.17 4 60 .35 .38 31 3H.. 47.81 49.42 3.98 4.12 37.55 38.81 3.13 3.23 H 6.43 .54 5.05 .42 3f 51.05 4.25 40.10 3.34 ITS 7 03 59 5 52 .46 3H.. 52.71 4.39 41.40 3.45 11 7 65 64 6 01 50 4 54 40 4 53 42.73 3.56 ITS 8 30 69 6 52 .54 4tv . 56.11 4.68 44.07 3.67 If 8 98 .75 7.05 .39 4| 57.85 4.82 45.44 3.78 iii 9.68 .81 7.60 .63 4^ 59.62 4.97 46.83 3.90 1 1 10 41 87 8.18 .68 4x . 61.41 5.12 48.23 4.01 IT! 11 17 93 8 77 .73 4A 63.23 5.27 49.66 4.13 11 11 95 1 00 9 39 78 41 65 08 5 42 51.11 4 25 1*1, 12.76 1.06 10.02 .83 4^ 66.95 5.58 52.58 4.38 2 13 60 13 10 68 .89 4 68.85 5.74 54.07 4.50 2rir 14 46 .21 11.36 .94 4& 70.78 5.90 55.59 4.63 24 15 35 28 12.06 .00 4f 72.73 6.06 57.12 4.75 2rV 16 27 36 12 78 .06 4H. . 74.71 6.23 58.67 4.88 2 17 21 43 13 52 13 41 . 76.71 6 39 60.25 5.01 2A 18 18 52 14 28 .19 4f.. 78.74 6.56 61.85 5.15 21 19 18 60 15 06 25 4* 80 80 6 73 63.46 5.28 2tk. . 20.20 .68 15.87 .33 4H 82.89 6.91 65.10 5.42 2l 21 25 .77 16.69 .39 5 85.00 7.08 66.76 5.56 2JL. 22 33 86 17 53 46 Si 1 *.. 87.14 7.26 68.44 5.70 21 23.43 .95 18.40 .53 5i 89.30 7.44 70.14 5.84 2H.. 24.56 2.05 19.29 .61 5fV 91.49 7.62 71.86 5.98 [336] WEIGHTS OF ROUND STEEL BARS WEIGHTS OF SQUARE AND ROUND STEEL BARS (Cont.) Size SQUARI 2 BARS ROUND BARS Size SQUARI 3 BARS ROUND BARS in Inches Per Foot Per Inch Per . Foot Per Inch in Inches Per Foot Per Inch Per Foot Per Inch 61 93 71 7.81 73.60 6.13 81 . 231.41 19.28 181.75 15.15 5^- 95 96 8.00 75.36 6.27 81 . 238.48 19.87 187.30 15.61 51 98 23 8 19 77 15 6 42 81 245 65 20.47 192.93 16 08 100 53 8 38 78 95 6.57 8| . 252.93 21.08 198.65 16 55 51 102 85 8.57 80.78 6.72 81 . 260.31 21.69 204.45 17.04 105 . 20 8 77 82.62 6.88 81 . 267.80 22.32 210.33 17.55 gi 107 58 8.97 84.49 7.03 9 275.40 22.95 216.30 18.03 gfi 109 98 9 17 86 38 7 19 91 283 10 23 59 222 35 18 53 51 112 41 9 37 88 29 7.35 91 . 290.91 24.24 228.48 19.04 5H 114.87 9.57 90.22 7.51 91 . 298.83 24.90 234.70 19.56 51 117 35 9 78 92 17 7.67 94 . 306.85 25.57 241.00 20.08 119 86 9.99 94.14 7.84 91 . 314.98 26.25 247.38 20.62 6 122 40 10 20 96 13 8 00 91 323 21 26 93 253 85 21.15 61 127 55 10 63 100 18 8.34 91 . 331 . 55 27 63 260.40 21.87 61 . 132.81 11.07 104.31 8.68 10 340.00 28.33 267.04 22.25 61 138 18 11.52 108 53 9.03 101 348 . 55 29.05 273.75 22.81 143 . 65 11.97 112.82 9.39 101 . 357.21 29.77 280.55 23.38 61 149 23 12 44 117 20 9 76 101 365 98 30 50 287 44 23 95 61 154 91 12 91 121 67 10.14 374 85 31 24 294 41 24.53 61 . 160.70 13.39 126.22 10.52 101 . 383.83 31.99 301.46 25,12 7 . . 166 60 13 88 130 85 10 90 101 392.91 32 74 308 59 25.72 71 . 172.60 14.38 135 . 56 11.30 101 . 402.10 33.51 315.81 26.32 71 178 71 14 89 140 36 11 70 11 411 40 34 28 323 11 26 93 71 184 93 15 41 145 24 12 10 111 420 80 35 07 330 50 27.54 191.25 15.94 150.21 12.52 111 . 430 . 31 35,86 337.97 28.16 71 . 197 68 16 47 155 26 12 94 439 93 36 66 345 52 28.79 71 204 21 17 02 160 39 13 37 m. . 449 65 37 47 353 16 29 43 71 210 85 17 57 165 60 13 80 459 48 38 29 360 87 30 07 8 217 60 18 13 170 90 14 24 Ill 469 41 39 12 368 68 30 72 81 . 224.45 18.70 176.29 14.69 479 45 39 95 376 56 31.38 m. . 12 489.60 40.80 384.53 32.04 STRENGTH OP ROUND STEEL BARS Breaking Strength, 51,000 Pounds per Square Inch. Proof Strength, One-half Ultimate Strength. Working Loads Are Percentages of the Proof Strength. WORKING LOAD AT Diam., Inches Area, Sq. In. Breaking Strength, Pounds Load, in Pounds 25% 30% 35% 40% 45% 50% 1 0.049 2,499 1,250 313 375 438 500 563 625 A .077 3,927 1,964 491 589 687 785 884 982 I .110 5,610 2,805 701 842 982 1,122 1,262 1,403 A .150 7,650 3,825 956 1,148 1,339 1,530 1,721 1,913 1 .196 9,996 4,998 1,250 1,499 1,749 1,999 2,249 2,499 [337] STRENGTH OF ROUND STEEL BARS STRENGTH OF ROUND STEEL BARS (Cont.) Diam., Inches Area, Sq. In. Breaking Strength, Pounds Proof Load, in Pounds WORKING LOAD AT 25% 30% 35% 40% 45% 50% A .249 12,699 6,350 1,588 1,905 2,223 2,540 2,858 3,175 f .307 15,657 7,829 1,957 2,349 2,740 3,131 3,523 3,914 H .371 18,921 9,460 2,365 2,838 3,311 3,784 4,257 4,730 i .442 22,542 11,271 2,818 3,381 3,945 4,508 5,072 5,636 H .519 26,469 13,235 3,309 3,970 4,632 5,294 5,956 6,617 1 .601 30,651 15,326 3,832 4,598 5,364 6,130 6,897 7,663 if .690 35,190 17,595 4,399 5,279 6,158 7,038 7,918 8,798 i .785 40,035 20,018 5,005 6,005 7,007 8,007 9,008 10,009 1^ .887 45,237 22,619 5,655 6,786 7,917 9,048 10,179 11,310 H .994 50,694 25,347 6,337 7,604 8,871 10,139 11,406 12,674 1A 1.108 56,508 28,254 7,064 8,476 9,889 11,302 12,714 14,127 H 1.227 62,577 31,289 7,822 9,387 10,951 12,516 14,080 15,645 1ft 1.353 69,003 34,502 8,626 10,351 12,076 13,801 15,526 17,251 H 1.485 75,735 37,868 9,467 11,360 13,254 15,148 17,041 18,934 i& 1.623 82,773 41,387 10,347 12,416 14,485 16,555 18,624 20,694 H 1.767 90,117 45,059 11,265 13,518 15,771 18,024 20,277 22,530 ift 1.918 97,818 48,909 12,227 14,673 17,118 19,564 22,009 24,455 H 2.074 105,774 52,887 13,222 15,866 18,510 21,155 23,799 26,444 1H 2.237 114,087 57,044 14,261 17,113 19,965 22,818 25,670 28,522 if 2.405 122,655 61,328 15,332 18,398 21,465 24,531 27,598 30,664 itt 2.580 131,580 65,790 16,448 19,737 23,027 26,316 29,606 32,895 U 2.761 140,811 70,406 17,602 21,122 24,642 28,162 31,683 35,203 1H 2.948 150,348 75,174 18,794 22,552 26,311 30,070 33,828 37,587 2 3.142 160,242 80,121 20,030 24,036 28,042 32,048 36,054 40,061 2& 3.341 170,391 85,196 21,299 25,559 29,819 34,078 38,338 42,598 2* 3.547 180,897 90,449 22,612 27,135 31,657 36,180 40,702 45,225 2& 3.758 191,658 95,829 23,957 28,749 33,540 38,332 43,123 47,915 2i 3.976 202,776 101,388 25,347 30,416 35,486 40,555 45,625 50,694 2A 4.200 214,200 107,100 26,775 32,130 37,485 42,840 48,195 53,550 21 4.430 225,930 112,965 28,241 33,890 39,538 45,186 50,834 56,483 2A 4.666 237,966 118,983 29,746 35,695 41,644 47,593 53,542 59,492 2* 4.909 250,359 125,180 31,295 37,554 43,813 50,072 56,331 62,590 2& 5.157 263,007 131,504 32,876 39,451 46,026 52,602 59,177 65,752 2! 5.412 276,012 138,006 34,502 41,402 48,302 55,202 62,103 69,003 2H 5.673 289,323 144,662 36,166 43,399 50,632 57,865 65,098 72,331 2! 5.940 302,940 151,470 37,868 45,441 53,015 60,588 68,162 75,735 2H 6.213 316,863 158,432 39,608 47,530 55,451 63,373 71,294 79,216 n 6.492 331,092 165,546 41,387 49,664 57,941 66,218 74,496 82,773 2& 6.777 345,627 172,814 43,204 51,844 60,485 69,126 77,766 86,407 3 7.069 360,519 180,260 45,065 54,078 63,091 72,104 81,117 90,130 3A 7.366 375,666 187,833 46,958 56,350 65,742 75,133 84,525 93,917 H 7.670 391,170 195,585 48,896 58,676 68,455 78,234 88,013 97,793 3ft 7.980 401,880 200,940 50,235 60,282 70,329 80,376 90,423 100,470 31 8.296 423,096 211,548 52,887 63,464 74,042 84,619 95,197 105,774 3A 8.618 439,518 219,759 54,940 65,928 76,916 87,904 98,892 109,880 [338] STEEL HULL RIVETS AND RIVET-RODS STRENGTH OF ROUND STEEL BARS (Cont.) Breaking Proof WORKING LOAD AT Diam., Inches Area, Sq. In. Strength, Pounds in Pounds 25% 30% 35% 40% 45% 50% at 8.946 456,246 228,123 57,031 68,437 79,843 91,249 102,655 114,062 3A 9.281 473,331 236,666 59,167 71,000 82,833 94,666 106,500 118,333 3* 9.621 490,671 245,336 61,334 73,601 85,868 98,134 110,401 122,668 3A 9.968 508,368 254,184 63,546 76,255 88,964 101,674 114,383 127,092 3| 10.321 526,371 263,186 65,797 78,956 92,115 105,274 118,434 131,593 3H 10.680 544,680 272,340 68,085 81,702 95,319 108,936 122,553 136,170 3! 11.045 563,295 281,648 70,412 84,494 98,577 112,659 126,742 140,824 3H 11.416 582,216 291,108 72,777 87,332 101,888 116,443 130,999 145,554 31 11.793 601,443 300,722 75,181 90,217 105,253 120,289 135,325 150,361 3H 12.177 621,027 310,514 77,629 93,154 108,680 124,206 139,731 155,257 4 12.566 640,866 320,433 80,108 96,130 112,152 128,173 144,195 160,217 STEEL HULL RIVETS AND RIVET-RODS NAVY DEPARTMENT 1. General Instructions. The latest issue of " General Specifications for Inspection of Steel and Iron Material" shall form a part of these specifications, and must be com- plied with as to material, methods of inspection, and all other requirements therein. 2. Physical and Chemical Requirements. The physical and chemical requirements for- each grade of material shall be in accordance with the following table: Tensile Strength, Minimum Elonga- MAXIMUM AMOUNT Grade Material Pounds per tion (b) OP~~* Square Inch p. s. P. Ct. P. Ct. Medium steel Open-hearth carbon. 58,000 28 per cent in 8 inches ; 0.04 0.04 to 30 per cent in 2 68,000 inches when type 1 specimen is used. High - tensile Open-hearth carbon, 75,000 23 per cent in 8 inches ; .04 .04 steel. silicon, or nickel to 25 per cent in 2 steel. 90,000 inches when type 1 specimen is used. RIVET RODS 3. Elongation. For rods f inch or less in thickness or diameter, the elongation shall be measured on a length equal to eight times the thickness or diameter of section tested; for sections over \ inch and less than \ inch in thickness or diameter, the elonga- tion shall be taken on a leng'h of 6 inches. In both the preceding cases the required percentage of elongation shall be that specified for the type 3 test piece. 4. Type of Test Piece. Type of test piece to be type 1 or type 3, depending on size of rod; type 1 will be used only when capacity of testing machine prevents the use of type 3. 5. Tensile Tests. Bars rolled from any melt shall be tested by sizes, one tensile test to be taken from each ton or less of each size. If the results of such tests from the various sizes indicate that the material is of uniform quality, not more than eight such specimens shall be taken to represent the melt. In such cases the eight specimens shall be fully representative of the various sizes in the melt offered for test. [339] STEEL HULL RIVETS AND RIVET-RODS 6. Bending Tests for Medium Steel. From each size of each melt one cold-bend test shall be taken as finished in the rolls, but not less than two such bends shall be made from any melt. These cold-bend specimens shall be bent 180 flat on themselves without showing any cracks or flaws in the outer round. TYPE 1 TEST PIECE A BO in 18 IN- OVERALL 8 INCHBS 1 1 1 1 Mf/i 5 t/ftJAf c FONTS, \ 1 2 o 1 , (* W> -Jjj-o* i 7 K 9 INCHES 1 TYPE 3 TEST PIECE 7. Upsetting Tests for Medium Steel. Specimens shall be cut about one and one- fourth times the diameter of the round in length, and shall be required to stand ham- mering down cold in a longitudinal direction to about one-half the original length of the specimen without showing seams or other defects which would, in the judgment of the inspector, tend to produce defects in the manufactured rivet. The number of upsetting-test pieces shall equal the number of tensile-test pieces, but in no case shall it be less than two for each size. 8. Tolerances in Diameter Under the Nominal Gauge Ordered. Up to and including | inch 0.010 inch. Over I inch, up to and including inch 014 inch. Over inch, up to and including f inch 016 inch. Over | inch, up to and including 1 inch 020 inch. Over 1 inch, up to and including 1| inches 024 inch. Over U inches 030 inch. MANUFACTURED RIVETS 9. Manufactured Rivets, Form and Surfaces. (a) Rivets shall be true to form, concentric, and free from scale, fins, seams, and all other injurious or unsightly defects. Tap rivets shall be milled under the head if necessary. They shall conform to the dimensions and form as shown on table incorporated in and forming a part of these specifications. 10. Medium Steel Rivets, Hammer Tests. (a) From each lot of rivets of each size kegged and ready for shipment there shall be taken at random 6 rivets, to be tested as follows: ^, '(b); Three riyets shall be flattened out cold under the hammer to a thickness of one-half' the diameter of the part flattened without showing cracks or flaws. Rivets of over an inch' in diameter shall >be flattened to three-fourths of the original diameter. i- (c) Three rivets shall be flattened out hot under hammer to a thickness not exceeding on^-fourth of the original diameter of part flattened without showing cracks; heat to - be ordinary driving heat. 11. High-Tensile Steel Rivets. High-tensile steel rivets shall be made of rivet rods [340] STEEL HULL RIVETS AND RIVET-RODS conforming to the requirements of these specifications for high-tensile steel rods and shall in addition meet the following requirements: 12. Shearing Strength. From each lot of each size kegged and ready i or shipment there shall be taken at random three rivets for shearing test. These rivets shall be driven hot for test under double shear. The shearing strength when so tested shall not be less than 64,000 pounds per square inch, computed on the actual shearing area of the rivet as driven; i.e., the area corresponding to the area of the rivet hole, not the nominal diameter of the rivet. 13. Quality Test. When for any reason the shearing test described above cannot be made, the following test shall be made: From each lot of each size kegged ready for shipment there shall be taken at randon three rivets. These rivets shall be heated to the driving temperature, when the point shall be quickly hammered down to a thickness of | inch and the rivet immediately cooled by quenching in cold water. It will then be hammered over the edge of an anvil in an effort to bend the flattened portion. The rivet shall break short without appreciable bend. 14. Marking and Packing. (a) Medium rivets shall be marked on top or side of head with a plain cross f by f inch for larger sized rivets, suitably reduced for the smaller rivets. This cross is to be in relief. (b) High-tensile pan or button-head rivets shall have fluted heads. (c) Unless otherwise specified, to be delivered in 100-pound boxes or kegs, marked as given below. (d) All boxes or kegs to be strongly made and plainly marked with the manu- facturer's name and contract number. Boxes or kegs to be neatly stenciled on one end only with the net weight, size, and name of contents, as 100 pounds High-Tensile Steel Button-Head Rivets. zi *5 STANDARD RIVETS FOR SHIP AND TORPEDO-BOAT WORK. NAVY DEPARTMENT K s-* Type A. Pan Head. Straight Neck f \ "t Rivet, Diam. D. . i A 1 I f f i 1 H if r \! v Hole, Diam. A. . . A H. A A tt. H if 1A 1A 1H c \>L 1 M Head, High B... Head, Diam. C. . A i A A 1 H A i 1A 1A f H H if f 1H Head, DiamD... i A t i f f 1 l H 2 [341 STEEL HULL RIVETS AND RIVET-RODS STANDARD RIVETS FOR SHIP AND TORPEDO-BOAT WORK. NAVY DEPARTMENT (Continued) vf Type B. Pan Head. Conical Neck Rivet, Diam. D.. Neck, Diam. Dl . Neck, Cone E . . . Head, High B . . . J A f t A f f A A i f 1 f 1A f 1 if A A 1A 1 1 1A f H i H 1A A H if it H 1A 1 f 1H H a > -^4 m T ^ Head, Diam. C. . Head, Diam. D.. ZSs ^P^ Type C. Button Head. Straight Neck Rivet, Diam. D. . Hole, Diam. A. . . Head, High B... Head, Diam. C.. i 4 & A A t f A A A i A f if f H A i 1 1A 1 if A 1A i 1A f l* H i& H if H IB f IB m, -A : * P-> ^^ **T*^ m & C I \' Type D. Button Head. Conical Neck Rivet, Diam. D . Neck, Diam. Dl . Neck, ConeE... Head High B . * " f A f f B A A i if f 1A I if A A 1A i 1A * f It H 1A A B if it 1A f f IB W.SJP tiSs Head, Diam. C.. - r^'-i,. Type E. Countersunk Head a Rivet, Diam. D. . Head, Diam. Kl. Head, Cone Bl . . Cone Angle i 4 f 60 \ 60 f f A 60 \ I A 60 f 1A f 60 f i& A 45 7 8 li f 45 i IB 37 H iff 7 8 37 ft IB 1 37 ^ The cone angle of 45 in sketch is for f and rivets only. k Kl _* Type F. Countersunk Head ik li Rivet, Diam. D. . Head, Diam. K2 Head, Cone B2. . Cone Angle * * f t f if 60 f It A 45 1 1H A 45 1 H f 37 H it \ * \ / \ / V ^^^^ The cone angle of 45 in sketch is for f and | rivets only. [342 STEEL HULL RIVETS AND RIVET-RODS STANDARD RIVETS FOR SHIP AND TORPEDO-BOAT WORK. NAVY DEPARTMENT (Continued) to_t Type G. Countersunk Head Rivet, Diam D. . Head, Diam K3 Head, ConeB3.. Cone Angle *; A t * 1 i 4 1 45 7 8 H A 45 1 If 37 !!. r4 im. .!. ^^^ The cone angle of 45 in sketch is for f and 1 rivets only. I Type H. Tap Rivets .%1 Rivet, Diam. D. . Head Diam . K4 . Head, Cone B4. . 1 A t If A 60 1 i f If 60 A f i 4 1A 1 45 f 7 8 1H A 45 If 1 Iff H 37 if If 1 37 f if H 1H 1 37 H H HL 1 J! \ t-A ** -45* t r&-+ \ 1 -*& ^ -> 3 Stud, Square R Stud, Height S The cone angle of 45 in sketch is for f and f rivets only. ! -K5- "t" CO Type K. Tap Rivets Rivet, Diam. D . Head, Diam. K5 Head, Cone B5 1 A f i f f 1 U A 45 A If 1 If 37 f If If If f 37 f If H is 1 M Cone Angle * _ / $ ^ jDr V ^p -*SS / V/ -> S T to Stud, Square R Stud, Height S. The cone angle of 45 in sketch is for | rivets only. Studs for Tap Rivets Rivet, Diam Stud, Square R. . Stud, Heights... 1 A 1 f f A f f If 1 A If 1 1 If If f If U H If 3 / K I M n i^ .1 Template for Countersink Rivet, Diam. . . . Angle * 60 2f 3^ A 60 2f "Ff f 60 i 60 2f "64 1 f 60 1 45 3 f 1 45 3 21 f 1 37 3 If 37 3 2f H 37 3 Height L Width M . .. Width N . . . . [343] STEEL HULL RIVETS AND RIVET-RODS STANDARD RIVETS FOR SHIP AND TORPEDO-BOAT WORK. NAVY DEPARTMENT (Continued) g ^fT22> p Snap Points *- 3>-> Rivet, Diam.D.. Point, Height B. Point, Diam.C. . I A A A i f A A i 1 H 1 A i f 1A 1 A 1A 1 1 H H H if 11 f !t- 42 w / p Hammered Points. F-| D Rivet, Diam.D.. Point, Height F . Point, Diam.G.. * A A 1 1 A f i i f A U a 4: f 1A 1 7 T6 1 If A H f llTJ 1 1*- <3>?^ Q^*-^ , Countersunk points to be the same taper and depth as count- ersunk heads, but are to be driven with slightly convex tops. ri trD > i Liverpool Points. Y-2 D Rivet, Diam. D. . Point, Height T. Point, Diam. Y . i A 1 i i 1 i U * A 1 1 If 1 A 2 H 1 ii *-> *- ^J Countersunk Liverpool points to be the same taper as count- ersunk heads, but to be only one-half the thickness of plate. ' / < \ r~j_ \ T\ /T\ /T 1 \ / j j, ^ ^r?7l <&& ^f*& . I LJ ICMGTH OP RIVETS ANOTAPS MEASURED SMALL RIVETS, FLAT OR COUNTERSUNK, FOR SHEET-METAL WORK NAVY DEPARTMENT 1. "General Instructions and Specifications, General Specifications, Appendix I. for Iron and Steel Material," issued June, 1912, shall form a part of these specifications and must be complied with. 2. To be soft steel, black or tinned, as specified. The flat-head rivets shall conform in size and weight to the following table: [344] SMALL RIVETS Size Limit Size of Wire Length Under Head Diame- ter of Head Thick- ness of Head 4 OUI1C6S 072 0.068 | 0.156 0.020 6 ounces .083 .078 & .180 .024 8 ounces 095 .090 & .206 .027 10 ounces .090 .094 ii .214 .029 12 ounces .106 .100 TS .230 .031 14 ounces .110 .104 A .239 .032 1 pound .115 .109 H .249 .033 lj pounds 1| pounds .120 .126 .113 .120 & tt .260 .273 .034 .036 If pounds 2 pounds .134 .144 .128 .136 1 H .290 .312 .038 .041 2 4 pounds .148 .141 & .323 .043 3 pounds. .160 .151 & .346 .046 gi pounds - 165 .156 n .357 .047 4 pounds . . . .176 .167 & .381 .050 5 pounds 189 .180 | .409 054 6 pounds . ... .205 .195 H .444 .058 7 pounds .221 .211 H .479 .063 8 pounds .229 .219 A 496 065 9 pounds .238 .227 H .515 .068 10 pounds 241 .230 522 070 12 pounds .254 .242 .550 .074 14 pounds .284 .272 M .616 .081 16 pounds .300 .288 H 650 086 3. The countersunk rivets shall conform to the sizes given in the following table: Size of Rivet, Diameter of Wire Diameter of Head Angle of Counter- sink Lengths Size of Rivet, Diameter of Wire Diameter of Head Angle of Counter- sink Lengths Inch Inch Degrees Inch Inch Inch Degrees Inch A 0.189 0.345 80 1 and! A -144 .259 80 *, t, and * & .160 .287 80 i, *, and * 1 .125 .230 80 &, i, and & 4. The rivets to be put up in packages of 1,000 rivets, or in boxes of not less than 50 pounds each, as required. TESTS FOR SOFT-STEEL RIVETS 5. A number of rivets, at the discretion of the inspector, shall be selected from each size of each delivery, enough to satisfy the inspector of the quality of the entire lot. 6. Cold Test. One-half of these shall be flattened to one-eighth of their original diameter, and then bent through 180 flat on themselves, and shall show no signs of cracks, flaws, or any other defects. 7. Hot Test. The remaining rivets shall be heated to a red heat and flattened, then reheated and bent through 180 and flattened on themselves without showing any signs of flaws, cracks, or any other defects, [345] SCREW THREADS Previous to the action of the Franklin Institute in 1864 there had been no uniformity in the diameters of taps and dies or in the number of threads per inch, for bolts and studs. Bolt iron was seldom rolled strictly to gauge; in consequence, taps and dies j$ inch over size were in general use. Aside from variation in diameter, there was a lack of uniformity in number of threads per inch. The shape of screw threads then in use was the sharp or V-thread as in the illustration. Screw threads with sharp edges are objected to because the threads are liable to injury in the ordinary course of handling. The sharp edges of taps and dies soon disappear in service, making it difficult to maintain interchangeable work. Formula pitch No. thrds. per in. d = depth = p X .866 An occasional American manufacturer adopted the Whitworth standard for screw threads, but this was exceptional. An investigation of the whole subject was made by William Sellers, of Philadelphia, and presented to the Franklin Institute in a paper read by him in April, 1864. Mr. Sellers disapproved the V-thread; his objections to the Whitworth thread were, first, that the angle of 55 is a difficult one to verify; secondly, the curve at the top and bottom of the thread of the screw will not fit the corresponding curve in the nut, and the wearing surface on the thread will be thus reduced to the straight sides merely. Thirdly, the increased cost and complication of cutting tools required to form this kind of thread in a lathe. The necessity of guarding the sharp edge of a V-thread from accidental injury was a fact recognized by sometimes finishing such bolts with a small flat on the top of the thread. The flat angular sides being necessary, there remained to choose between a rounded or a flat top. As the sides of a thread are the only parts to be fitted, the cutting tool employed having an angle of 60, the width of flat at top of thread will be determined by the depth to which the thread is cut. The flat at the top of the thread serves to -A 7 W A f \ / 6 \f R Formula P = pitch = No. thrds. per in d = depth = p X .6495 /^> protect it from injury, a similar shape at the bottom gives increased strength to the bolt by increasing its diameter at the root of thread. The angle of thread is 60, the same as the sharp thread, it being more easily obtained than 55. Divide the pitch, or, which is the same thing, the side of the thread, into eight equal parts, take off one part from the top and fill in one part in the bottom of the thread, then the flat top and bottom will equal one-eighth of the pitch, the wearing [346] FRANKLIN INSTITUTE SCREW THREADS surface will be three-quarters of the pitch, and the diameter of the screw at bottom of the thread will be expressed by the formula diameter = ~- '- rr-r- - These No. threads per inch proportions will give the depth of the thread almost precisely the same as the English, and as the wearing surface on all screws will be confined practically to the flat sides, this will be 36 per cent greater than on the English. FRANKLIN INSTITUTE STANDARD SCREW THREAD Constants for finding diameter at bottom of thread 1.299 Sellers' formula: Diam. bolt = No. threads per inch Threads per Inch Constant Threads per Inch Constant Threads per Inch Constant Threads per Inch Constant 20 18 16 14 13 .06495 .07217 .08119 .09279 09992 10 9 8 7 6 . 12990 . 14433 . 16238 . 18557 21650 4 4 3* 31 3 .28867 .32475 .37114 .39969 43300 2f 2 2| 21 .49486 .51960 .54695 .57733 12 10825 51 - 23618 21 45183 11 .11809 5 .25980 2| .47236 Example. To find the diameter at bottom of a Franklin Institute thread for a bolt 1 inches diameter we have: 1 m ch diameter = 6 threads per inch. The constant for 6 threads is .21650. Then: 1.50000 - .21650 = 1.2835 = 1& inch nearly. Mr. Sellers also presented a system of uniform dimensions for bolt heads and nuts. The committee of the Institute to whom this paper was referred handed in their final report December 15, 1864, and offered in part the following resolution, which was adopted. " RESOLVED, That the Franklin Institute of the State of Pennsylvania recommend, for the general adoption by American engineers, the following forms and proportions for screw threads, bolt heads, and nuts, viz.: "That screw threads shall be formed with straight sides at an angle to ach other of 60, having a flat surface at the top and bottom equal to one-eighth of the pitch. The pitches shall be as follows, viz. : Diameter of bolt. . . . 1 A i A i A f f 1 1 u 11 If H If H H Threads per inch . . . 20 18 16 14 13 12 11 10 9 8 7 7 6 6 5* 5 5 Diameter of bolt. . . . 2 21 2 21 3 31 3* 3f 4 41 4 4| 5 51 5* 51 6 Threads per inch. . . 4* 4 4 4 3 3 31 3 3 2| 21 2f 2 2* 2| 2f 21 "Bolt Head and Nut. The distance between the parallel sides of a bolt head and nut, for a rough bolt, shall be equal to one and a half diameters of the bolt plus one-eighth of an inch. The thickness of the heads for a rough bolt shall be equal to one-half the distance between its parallel sides. The thickness of the nut shall be equal to the diameter of the bolt. The thickness of the head for a finished bolt shall be equal to the thickness of the nut. The distance between the parallel sides of a bolt head and nut, and the thickness of the nut, shall be one-sixteenth of an inch less for finished work than for rough." The foregoing is what is known as the Franklin Institute Standard, or as the Sellers' Standard, so named after its originator. [347] BOLTS AND NUTS U. S. NAVY STANDARD United States Standard. The Navy Department appointed a Board to recommend a standard gauge for bolts, nuts, and screw threads for the United States Navy. On May 15, 1868, the Chief of Bureau of Steam Engineering submitted to the Secretary of the Navy the report of the Hoard indorsing the Sellers' system, but recommending certain modifications. Its recapitulation expresses the formula thus: Let D = nominal diameter of bolt. d = effective diameter of bolt = diameter p = pitch of thread. under root of thread, n = number of threads per inch. s = depth of thread. H = depth of nut. h = depth of head. d n = short diameter of hexagonal or square dh = short diameter of head, nut. Then p = 0.24 VD + 0.625 -0.175. H = D. n = (No. of threads per inch)"^ d n = f D + |" s =0.65 p. d h = |D + |" d = D 2s =D~ 1.3p. h = 10 + ^" It then gives a table of screw threads the same as that recommended by the Franklin Institute, with the one difference and that regarding the size of finished or unfinished bolt heads and nuts. The Navy report makes no difference in the size of either that is, for finished work the forgings must be made larger than for rough; their idea being to use the same wrench on either black or finished work. In reference to their tables: The only instance where the values in the table differ from those given by the formula is in the number of threads per inch, which is so far modified as to use the nearest convenient aliquot part of a unit, so as to avoid, as far as practicable, troublesome combinations in the gear of screw-cutting machines. The Secretary of the Navy, in a communication to the Chief of Bureau of Steam Engineering, May 16, 1868, writes: "The standard for the dimensions of bolts and nuts, as determined by the Board, is, upon your recommendation, authorized for the naval service." This constitutes what is known as the United States Standard ; it corresponds in all respects to the Franklin Institute Standard for screw threads, but no difference in dimensions as between rough and finished bolt heads and nuts is made, one wrench serving for both. This is the standard now in general use in the United States, but attention is drawn to the table of Standard Dimensions of Bolts and Nuts for the United States Navy, as given below. It will be observed that, beginning with 3 inches diameter of screw, the threads do not follow the authorized standard of 1868, inasmuch as all screw threads for bolts are uniformly 4 threads per inch from 3 inches up to and including 12 inches diameter. [348] BOLTS AND NUTS U. S. NAVY STANDARD BOLTS AND NUTS c- Standard Dimensions for United States Navy DIAMETERS Effective Area Sq. Inches Threads Inch Long Diam. Hex. Nut and Bolt-head Long Diam. Sq. Nut and Bolt-head Short Diam. Hex. & Sq. Nut and Bolt-head Bolt- head, Depth Nut, Depth Out- side, Ins. Root of Thread, Inches A B C D E F G H i 0.185 0.026 20 A M i I 4 1 4 A .240 .045 18 tt if M H A I .294 .067 16 If H H f A .345 .093 14 If i& M H A i .400 .125 13 1 li i. 7 T5 f A .454 .162 12 H if M M A f .507 .202 11 IA U 1A H f I .620 .302 10 IA U H f f 1 .731 .419 9 m 2^ 1A If 1 i .837 .550 8 u 2A H M i if .940 .694 7 2& 2A m If U U 1.065 .891 7 2A 2M 2 i U 1! 1.160 1.057 6 2H 3^ 2^ 1A if II 1.284 1.294 6 2f 3M 2f 1A l| if 1.389 1.515 5i 2M 3| 2& i* if 1! 1.491 1.746 5 3& 31 2! if if 11, 1.616 2.051 5 3M 4^ 2M 1H U 2 1.712 2.302 4 3M 4M 3i 1A 2 2i 1.962 3.023 41 4^ 4H 3^ if 2| 2| 2.176 3.719 4 4M 5M 31 lit 2f 2f 2.426 4.622 4 4|f 6 4 21 2f 3 2.676 5.624 4 5& 6H 4f 2A 3 3i 2.926 6.724 4 5 7^ 5 2^ ai 31 3.176 7.922 4 6& 7H 5f 2H 3| 31 3.426 9.219 4 ' 6f si 51 21 3f 4 3.676 10.613 4 7^ 8fi 61 3^ 4 41 3.926 12.106 4 7* 9A 6 3| 4i 4* 4.176 13.696 4 7H 9|| 61 3A 41 4f 4.420 15.635 4 81 10J 7| 31 4f 5 4.676 17.173 4 8H IOH 7f 3H 5 64 4.926 19.058 4 91 HA 8 4 51 5 5.176 21.042 4 9H 1W 8f 4^ 5 51 5.426 23.123 4 10^- 12| H 4f 5f 6 -5.676 25.303 4 IOH 12ft 9i 4A 6 [349] BOLTS AND NUTS U. S. NAVY STANDARD BOLTS AND NUTS Standard Dimensions for United States Navy. Sizes Over 6 Inches DIAMETERS Aresir Sq. Inches Threads per Inch Long Diam. Hex. Nut and Bolt-head Long Diam. Sq. Nut and Bolt-head Short Diam. Hex. & Sq. Nut and Bolt-head Bolt- head Depth Depth Out- side, Ins. Root of Thread, Inches A B C D E F G H 61 5.926 27.58 4 10H 13** 91 .. 43 61 6.176 29.95 4 HH 14 91 4 if 65 6! 6.426 32.43 4 ill* 14* 101 51 6! . 7 6.676 35.00 4 121 15| lOf 5^ 7 71 6.926 37.68 4 12** 15** 11 5* 71 7 | 7.176 40.44 4 131 161 lit 5H 71 7! 7.426 43.30 4 13* 16** ii! 51 7! 8 7.676 46.27 4 14 17f 12| 6rS 8 81 7.926 49.35 4 14* 17*f 12* 61 81 8.176 52.52 4 14** 188 121 6A 81 8! 8.426 55.76 4 15* w* 131 6* 8! 9 8.676 59.90 4 15** 19** 13f 6H 9 91 8.926 62.57 4 16* 19** 14 7 91 9.176 66.13 4 16H 20^ 14f 7* 91 9! 9.426 69.77 4 17* 20H 14! n 9! 10 9.676 73.52 4 17H 21| I 5 i 7& 10 101 9.926 77.38 4 17! 21! 15* 7H 101 10* 10.176 81.33 4 18** 22^ 151 7 if 10i 10! 10.426 85.34 4 18 161 81 10! n 10.676 89.52 4 1ft* 23 16f 8A n ill 10.926 93.76 4 19f 24& 17 8* Hi 11.176 98.10 4 20^ 24* 171 8ii 11} ill 11.426 102.53 4 20^ 25& 17! 81 n! 12 11.676 107.07 4 21* 25H 181 91 12 MAXIMUM WORKING LOAD FOR TABULAR TENSILE STRENGTH UNITED STATES NAVY Forgings. High grade. Minimum tensile strength 95,000 Forgings. High grade Class A. Minimum tensile strength 80,000 Forgings. High grade Class B. Minimum tensile strength 60,000 Bolts and boiler braces. Bolts and boiler braces. Class A. Minimum tensile strength 75,000 Class B. Minimum tensile strength 58,000 Rolled manganese and Tobin bronze and naval brass. Minimum tensile strength . 50,000 Phosphor bronze and Muntz metal. Minimum tensile strength 40,000 [350] BOLTS AND NUTS U. S. NAVY STANDARD MAXIMUM WORKING LOAD FOR TABULAR TENSILE STRENGTH UNITED STATES NAVY BOLT DETAILS MAXIMUM WORKING LOAD FOR TENSILE STRENGTH F = Factor of Safety Out- side Diam., Ins. Diam. at Root of Thread Effec- tive Area, S.q. Ins. 40,000 50,000 58,000 60,000 75,000 80,000 95,000 I 0.185 0.026 111 138 160 166 206 221 261 9.4 * .240 .045 198 247 287 297 370 396 470 9.1 1 .294 .067 301 376 435 451 560 601 714 9.0 ft .345 .093 415 519 600 623 775 830 986 8.9 i .400 .125 564 704 818 845 1,055 1,125 1,340 8.9 & .454 .162 730 912 1,060 1,095 1,370 1,460 1,730 8.9 f .507 .202 913 1,140 1,300 1,370 1,700 1,870 2,170 8.8 i .620 .302 1,380 1,725 2,000 2,070 2,580 2,760 3,280 8.8 1 .731 .419 1,930 2,410 2,800 2,900 3,600 3,860 4,580 8.7 i .837 .550 2,530 3,170 3,670 3,800 4,700 5,060 6,010 8.7 if .940 .694 3,190 3,990 4,600 4,790 5,980 6,380 7,570 8.7 ii .065 .891 4,140 5,180 6,000 6,210 7,760 8,280 9,830 8.6 If .160 1.057 4,890 6,110 7,080 7,330 9,150 9,780 11,600 8.7 H .284 1.294 6,040 7,540 8,760 9,060 11,300 12,050 14,300 8.6 If .389 1.515 7,060 8,820 10,200 10,600 13,200 14,100 16,750 8.6 If .491 1.746 8,120 10,150 11,770 12,200 15,200 16,200 19,250 8.6 II .616 2.051 9,600 12,000 13,900 14,400 18,000 19,200 22,800 8.5 2 .712 2.302 10,750 13,400 15,500 16,100 20,100 21,500 25,500 8.6 21 .962 3.023 14,200 17,800 20,600 21,400 26,700 28,500 33,800 8.5 3i 2.176 3.719 17,500 21,900 25,300 26,300 32,800 35,000 41,500 8.5 2f 2.426 4.622 22,000 27,500 31,900 33,000 41,200 44,000 52,200 8.4 3 2.676 5.624 26,800 33,500 38,800 40,200 50,200 53,600 63,600 8.4 3| 2.926 6.724 32,200 40,200 46,700 48,400 60,400 64,400 76,400 8.3 3 3.176 7.922 38,100 47,600 55,100 57,200 71,200 76,200 90,400 8.3 3f 3.426 9.219 44,500 55,600 64,300 66,700 83,200 89,000 105,500 8.3 4 3.676 10.613 51,400 64,200 74,500 77,000 96,400 102,800 122,000 8.3 41 3.926 12.106 58,700 73,400 85,100 88,100 110,000 117,400 139,300 8.2 4) 4.176 13.696 66,600 83,200 96,500 100,000 124,900 133,000 158,000 8.2 4| 4.420 15.635 75,000 93,700 108,400 112,000 140,200 150,000 178,000 8.2 5 4.676 17.173 83,800 105,000 121,500 126,000 157,100 167,500 199,000 8.2 5| 4.926 19.058 93,200 116,500 135,000 140,000 174,800 186,000 221,000 8.2 51 5.176 21.042 103,000 129,000 149,000 154,500 193,100 206,000 244,500 8.2 51 5.426 23.123 113,500 142,000 164,000 170,000 212,600 227,000 269,000 8.2 6 5.676 25.303 124,000 155,000 179,800 186,000 232,500 248,000 295,000 8.1 [351 WEIGHT OF BOLT-HEADS AND NUTS WEIGHT OP HEXAGON BOLT-HEADS AND NUTS United States Standard Dimensions BAR HEAD NUT Diam. A Area Weight Sh't Dia. B Area Hexagon Square In. Hgh, Content Cubic Inch Weight Head Sh't Dia. B Hght. Hole Dia. Weight Inch Foot i .049 .014 .167 i .217 1 .054 .015 i 1 A .014 A .077 .022 .261 ft .305 H .091 .026 II A i .022 f .110 .031 .375 ft .409 H .141 .040 H f R .036 A .150 .043 .511 If .529 If .207 .059 If A IF .053 i .196 .056 .667 1 .663 A .290 .082 1 i If .075 A .249 .070 .845 ii .813 ft .394 .112 H A If .100 f .307 .087 1.043 IA .979 H .520 .147 1A f H .139 \ .442 .125 1.502 u 1.353 f .846 .240 H f fi .223 i .601 .170 2.044 i* 1.791 ft 1.287 .365 IA 1 H .353 l .785 .222 2.670 if 2.287 H 1.858 .526 if i M .490 li .994 .282 3.379 itt 2.847 H 2.580 .731 itt I* M .676 li 1.227 .348 4.173 2 3.464 i 3.464 .981 2 n 1^ .962 11 1.485 .421 5.049 2& 4.156 1A 4.546 1.288 2^ u 1A 1.220 1.767 .501 6.008 21 4.885 1A 5.801 1.644 21 H 1A 1.515 if 2.074 .588 7.051 2A 5.689 1A 7.289 2.065 2A If iff 1.852 if 2.405 .681 8.18 2f 6.549 If 9.005 2.551 2f If H 2.272 H 2.761 .782 9.39 2M 7.475 itt 10.979 3.111 m if if 2.817 2 3.142 .890 10.68 3| 8.457 1A 13.214 3.744 3f 2 IB 3.333 2* 3.976 1.127 13.52 3 10.609 if 18.566 5.260 3 21 Hi 4.823 2* 4.909 1.391 16.69 31 13.004 itt 25.195 7.138 31 2 2& 6.549 2! 5.940 1.683 20.20 4J 15.642 2| 33.239 9.418 4| 2f 2^ 8.552 3 7.069 2.002 24.03 4| 18.524 2& 42.837 12.137 4f 3 2H 10.924 31 8.296 2.350 28.20 5 21.650 2 54.125 15.335 5 31 2H 13.695 3| 9.621 2.726 32.71 5f 25.019 2H 67.239 19.051 5f 3* 3^ 16.897 3| 11.045 3.130 37.56 5f 28.632 2| 82.317 23.323 5f 3f 3^ 20.560 4 12.566 3.561 42.73 6| 32.488 3^ 99.495 28.190 6| 4 3H 24.715 [352 ROUND SLOTTED NUTS ROUND SLOTTED NUTS NAVY DEPARTMENT Diam. Bolt A B c D Diam. Bolt A B C D 1 If A 1 f 5f 9f H 1 5f 1 U A i 1 6 101 11 i 6 1 2 f & 1 61 10f 11 \ 61 11 2f f A li 6* 11 If A 61 u 2| I A If 61 HI If A 6f If 2| A A if 7 HI If A 7 i| 21 ft A t| 71 121 II A 71 l! 31 A A if 7| 12f II 7| if 3| i A H *i 13 H 1 7f if 31 1 i 4 If 8 I3| U f 8 2 3f i i 2 81 131 if f 81 21 4i A I 4 21 8^ 141 if H 8| 21 *i f i 2 8| 14| if H 81 2| 41 f A 2| 9 15J U H 9 3 51 ii A 3 91 15| if H 91 3i 5f f A 81 9i 16 if f 9| 3 61 f A 3* 91 16| H 3 4 9f 3f 61 H f 31 10 161 H f 10 4 61 1 f 4 101 17| H if 101 41 7f tt f 41 i(H 17| 11 if 10| 4| 71 i f 4 10| 18 2 if lOf 41 81 i A 41 11 18f 2 7 8 11 5 8* if A 5 1H 191 21 1 11* si 9 if A 51 12 20 21 1 12 5 9f H 7 16 5 [353] BOX WRENCHES BOX WRENCHES FOR HEXAGON AND ROUND SLOTTED NUTS NAVY DEPARTMENT Tprv D deaTcmc e , r f Diam. Bolt A B c D E F G H I K L M I U * 2| U 1 f f 12" A A 11 If 1 H 1 2A If 1 f f 13$" A A 1A 1H 1 2 A 2| Ii 1 f A 15 7/ A f if 2 If 21 A 21 if 1 f A 16*" A f lit 2i 11 2* A 3 U 1 7 8 A 18" A f 2 2f If 2| A 3f if 1 7 8 i 19*" A A 2A 2f ii 21 I 3| il 1 1 i 21" A 7 IT 2f 21 H 3i I 3! H 1 1 A 22*" A A 2A 3 it 3i A 4| 2 u H A 24" i * 2| 31 ii 3* A 4f 2 H H f 2'!*" i * 2M 3* 2 31 } 4| 2* ii H f 2'3" i * 31 3f 21 41 i 5 2i u U f 2'6" - i 4 A 3* 4 2* 41 A 5* 2f it ii H 2'9" i f 31 4f 2| 41 f 6 2 it if f 3'0" i f 4i 4f 3 5i ii 6f 2f it if H 3'2" A H 4f 51 31 5f H 7 21 H ii 1 3'5" A f 5 5f 3* 6| I 7* 3 H 2 1 3'8" A f 5f 6 3f 6| i 4 7| 31 ii 2i if 3'10" A H 5f 61 4 61 1 81 if 2i i 4'1" f 1 61 61 41 71 1 9 3| if 2f i* 4'4" f if 6* 71 4f 7| 1 9f 31 if 2^ H 4'6" f i 61 7f 4f 81 1 10 3f if 2i M 4'9" f i 7i 8 5 8| i* 10f 31 H 2| 1A 5'0" A H 71 81 51 9 I* 11 4 if 2f ii 5'3" A ii 8 81 5| 9| 1* 11* 4* 2 21 ii 5'6" A a 8f 91 [354] BOX WRENCHES BOX WRENCHES FOR HEXAGON AND ROUND SLOTTED NUTS (Continued) NAVY DEPARTMENT Diam. Bolt A B C D E F G H I K L M 5! M M Hi 4* 2 3 1A 5'9" A H 81 9f 6 lot U 12f 4| 2f 3f if 6'0" i it 91 101 8| 10f it 13 4f 2| 3t 1* .... i it 91 101 6* 11 if 131 4f 2| 3f 1* .... i if 91 101 6| Hi if 14 5 2i 8| l \ i if lot lit 7 111 i* 141 si 21 3f i* A if 10f 111 9 121 i* 151 51 21 3f if A *i 11 12| 7* 12f i* 15f 5| 21 81 if A tf HI 13J 7| 13 1* 16 5f 21 31 1H A u HI 121 8 13* if 161 5f 2| 4 if f ii 12| 131 9f 13| if 17 5f 21 41 1H f if 121 131 if 141 if 171 6 21 4t 1H f if 12| 14| 8f 14| if 18 6t 21 4f if f if 131 14| 9 15| if 181 6f 2f 41 iH H if 131 15 w 15| if 191 ei 2| 41 2 H if 14 151 H 16 1H 19f 6f 2f 4f 2 H if 141 15f 9f 16| i 20 6f 2f 4f 2^ H if 141 161 10 161 2A 201 7 3 5 21 H 151 161 1(4 tn 2A 211 7i 3 5f 2A I if 151 17 10| m si 211 7t 31 5t 21 i 4 if 151 17f 10| 18 21 22 71 31 5f 2| f 2 161 17| 11 181 21 221 7f 3t 5* 2& .... H 2 161 181 111 19i 2A 231 7f 31 5f 2f H 21 171 19 12 20 2A 241 81 3^ 6 2| f 21 18| 191 [355] LOCK NUTS LOCK NUTS AND SPLIT PINS NAVY DEPARTMENT CQPl /* *\ * ^* ^--^v^ %. ft Diam. Bolt B c D E F G H K L M i 1 i i A 4 1 8 i 4 A f 4 i 8 i 16 A 8 4 1 8 \ 1 6 A i 4 i 8 i 1 6 A o 1 2f ii H 1 IA f A 4 1 4 8 1 16 \ H 21 it H 1 iA f A 1 1 A H 2B it ! A iA f A f A f if 3 2| it A if A A f A H ii 8J 21 if H ii A A f A f if 3 2| 1 f if A A | A if 3H 2| 7 8 1 if A A A 1 ii 3| 2H if if U i A I A if 2 41 3 if 1* 2 i A A 1 i 21 4A 3f 1 H 21 1 1 A i 4 H 2 5 3| ii H 2| A 1 A 1 4 H 21 5A 4| H if 2f A i 4 i A if 3 51 4| H if. 3 f i \ A H 31 6| 41 H 2 31 f A \ A if 31 6tt 51 H 21 3 f A \ A if 3f n 5f if 2| 3f f A f f H | ^ I I * .!_ I 1 P= pitch = :r= -i j : r No. threads per inch d = depth = | +.010 f =flat = p X .3707 Each side of an Acme thread is at an angle of 14|, or 29 in the included angle between threads. The screw itself is measured by standard, or any given outside diameter suited to the work. Whatever the diameter, the thread hi the nut is 0.02 inch over the standard or given diameter, to provide a clearance space at the top of the screw thread ; similarly a reduction in diameter of 0.02 is provided at the bottom of the screw thread as clearance for the nut. The depth of thread is nominally the same as for a square thread screw of equivalent diameter, to which is added 0.01 inch on each side, for clearance. This allowance for clearance at both top and bottom of HIT thread is shown in the accompanying ^ N U 1 sketch. As compared with a square thread screw, greater strength results from the Acme form of thread be- cause its bottom is much wider than that of a square thread of equal pitch. Recapitulation. The various parts of the 29 Screw Thread, Acme Standard, are obtained as follows: Width of point of tool for screw or tap thread = ^ jr 1 -5 : t No. of threads per inch Width of screw or nut thread = ^ ^ = J 3 : r No. of threads per inch Diameter of tap = diameter of screw + .020. Diameter of tap or screw at root - .0052. diameter of screw \No. of li linear threads per inch + .020. Depth of thread = ' XT j-r ^ r 7 + .010. 2 X No. of threads per inch TABLE OF THREAD PARTS No. of Thds. per In. Linear Depth of Thread Width at Top of Thread Width at Bottom of Thread Space at Top of Thread Thickness at Root of Thread 1 .5100 .3707 .3655 .6293 .6345 H .3850 .2780 .2728 .4720 .4772 2 .2600 .1853 .1801 .3147 .3199 3 .1767 .1235 .1183 .2098 .2150 4 .1350 .0927 .0875 .1573 .1625 5 .1100 .0741 .0689 .1259 .1311 6 .0933 .0618 .0566 .1049 .1101 7 .0814 .0529 .0478 .0899 .0951 8 .0725 .0463 .0411 .0787 .0839 9 .0655 .0413 .0361 .0699 .0751 10 .0600 .0371 .0319 .0629 .0681 [359] BASTARD THREAD SCREWS BASTARD THREAD SCREWS NAVY DEPARTMENT BOLT SCREW THREADS Nut Depth Outside Diam. Area Sq. In. Threads Per Inch Pitch P Depth d Width f Diam. at Root of Thread Effective Area Sq. In. i 0.196 6 .167 .083 .042 0.333 0.087 I I .307 5 .200 .100 .050 .425 .142 1 3. 4 .442 5 .200 .100 .050 .550 .238 1 .601 4 .222 .111 .056 .653 .335 if 1 .785 4 .250 .125 .063 .750 .442 U H .994 4 .250 .125 .063 .875 .601 ii H 1.227 3f .286 .143 .071 .964 .730 if if 1.485 31 .286 .143 .071 1.090 .933 H if .767 3 .333 .167 .083 1.167 1.070 2 if 2.074 3 .333 .167 .083 1.290 1.307 2| if 2.405 3 .333 .167 .083 1.417 1.577 2f if 2.761 ?| .400 .200 .100 1.475 1.709 3 2 3.142 2* .400 .200 .100 1.600 2.011 2| 2i 3.976 21 .400 .200 .100 1.850 2.688 3 2 4.909 2 .500 .250 .125 2.000 3.142 31 2| 5.940 2 .500 .250 .125 2.250 3.976 3f 3 7.069 2 .500 .250 .125 2.500 4.909 4 3| 8.296 2 .500 .250 .125 2.750 5.940 41 81 9.621 2 .500 .250 .125 3.000 7.069 41 3f 11.045 2 .500 .250 .125 3.250 8.296 5 4 12.566 1J .667 .333 .167 3.335 8.736 51 41 14.186 1| .667 .333 .167 3.580 10.066 51 4| 15.904 H .667 .333 .167 3.830 11.520 6 4| 17.721 H .667 .333 .167 4.080 13.074 6| 5 19.635 li .667 .333 .167. 4.330 14.725 61 5* 23.758 1J .667 .333 .167 4.580 16.475 7f 6 28.274 11 .667 .333 .167 4.830 18.323 81 BASTARD THREAD SCREWS As the name implies, these screws are somewhat irregular, therefore, difficult of standardization. In general, they serve as substitutes for square thread screws. A coarse pitch of thread gives rapid movement, and the tapering sides of thread facilitate the operation of a closing and disengaging nut. [360] SQUARE THREAD SCREWS The proportions are always assumed by the designer, who adapts each screw to the service for which it is intended. The accompanying table, prepared for the use of the Navy Department, is intended to supply its own needs without reference to commercial application. SQUARE THREAD SCREWS NAVY DEPARTMENT BOLT SCREW THREADS Nut Depth Outside Diam. Area Sq. In. Threads per Inch Pitch P Depth d Width Diam. at Root of Thread Effective Area Sq. In. \ 0.196 6 .167 .083 .083 0.333 0.087 1 1 .307 5 .200 .100 .100 .425 .142 1 .442 5 .200 .100 .100 .550 .238 H ! .601 4 .222 .111 .111 .653 .335 U i .785 4 .250 .125 .125 .750 .442 11 U .994 4 .250 .125 .125 .875 .601 if If 1.227 81 .286 .143 .143 .964 .730 U H 1.485 31 .286 .143 .143 1.090 .933 2 U 1.767 3 .333 .167 .167 1.167 1.070 2* if 2.074 3 .333 .167 .167 1.290 1.307 2| if 2.405 3 .333 .167 .167 1.417 1.577 2f H 2.761 2| .400 .200 .200 1.475 1.709 2f 2 3.142 2| .400 .200 .200 1.600 2.011 3 *\ 3.976 2 .400 .200 .200 1.850 2.688 3| 2| 4.909 2 .500 .250 .250 2.000 3.142 3f 2f 5.940 2 .500 .250 .250 2 . 250 3.976 4* 3 7.069 2 .500 .250 .250 2.500 4.909 4 3J 8.296 2 .500 .250 .250 2.750 5.940 41 3| 9.621 2 .500 .250 .250 3.000 7.069 5i 3| 11.045 2 .500 .250 .250 3.250 8.296 5f 4 12.566 H .667 .333 .333 3.335 8.736 6 4* 14.186 if .667 .333 .333 3.580 10.066 6| 41 15.904 If .667 .333 .333 3.830 11.520 6f 4| 17.721 i* .667 .333 .333 4.080 13.074 71 5 19.635 H .667 .333 .333 4.330 14.725 7 5% 23.758 H .667 .333 .333 4.580 16.475 8i 6 28.274 li .667 .333 .333 4.830 18.323 9 [361 SQUARE THREAD SCREWS SQUARE THREAD SCREWS This form of screw thread is much used in machine construction by reason of the large bearing surface presented by the sides of the screw; its coarser pitch, than a standard screw, permits rapid motion to the piece requiring to be moved. The absence of oblique pressure tending to burst a solid nut, or to open a disengaging nut, is in its favor. The number of threads per inch is commonly half that of a standard screw of the same diameter, but this proportion is not closely followed; see table of Square Thread Screws, Navy Department. The thickness of thread and width of face are generally half the pitch, but this is subject to modification, for the required pitch may be greatly in excess of these proportions. Rules for square thread screws for ordinary service as given by Unwin are: Pitch =p =0.16 + 0.08 Threads per inch = n = ~ Diameter at bottom of thread Depth of thread = ^ d 1= d = 0.85d 0.075 n To protect the sharp corners of square thread screws from injury, they are some- times slightly rounded, varying with the amount of protection afforded by the machine in which the screw is to be used. Some designers give the side of thread a slight angle; this facilitates manufacture, as also the entrance of jaws of a disengaging nut. The bearing pressure allowable on a square thread is subject to wide variation. In general the problem is not one of strength of material, as it is of lubrication. Slow moving screws, intermittent in action, well lubricated, may carry a pressure of 1,000 pounds per square inch. If the service is continuous, the speed moderately high, say 300 feet per minute, the pressure should in no case exceed 150 pounds per square inch of surface contact. Thrust bearin s for torpedo boats are analogous in some respects to square thread screws; the allowable pressure for naval vessels approximates 50 pounds per square inch of collar surface. MULTIPLE THREAD SCREWS Screws having double or triple threads are chiefly used to transmit motion. When the pitch of a screw is required to be much greater than the customary proportions a serious loss of strength may result through an unnecessary reduction of its diameter. |<-prr^^jy ' 'fot^Jy ' '^^^/^ in the sketch, serves only to make '?/9w' ''%&/ 4%W" the screw symmetrical in appear- ance, inasmuch as the bottom of a screw thread is not liable to injury. Threads per inch are commonly the same as for square thread screws of corresponding diameter. KNUCKLE THREADS AREA IN SQUARE INCHES Diameter Threads Diameter Depth in Inches Imsh at Bottom of Thread Bottom Outside of Nut of Thread Diameter 2 2 1.60 2.01 3.14 3 2* 2 1.85 2.69 3.98 3| 2* 2 2.00 3.14 4.91 31 2i 2 2.25 3.98 5.94 41 3 2 2.50 4.91 7.07 ii 8i 2 2.75 5.94 8.30 41 31 2 3.00 7.07 9.62 5J 3* 2 3.25 8.30 11.05 5f 4 ti 3.34 8.74 12.57 6 [363 SHARP V-THREAD SCREWS SHARP V-THREAD SCREWS These screws are not in general use and are not standardized. The following table relating to V-thread screws indicates the number of threads per inch for taps and dies meeting ordinary commercial requirements. The dimensions of bolt heads and nuts are Manufacturers' Standard. No. threads per inch d = depth = p X .866 SHARP V-THREAD SCREWS This Table is not United States standard Diam. Screw A Thds. Im:h C Thread Const. Diam. at Root of Thread B SQUARE HEAD AND NUT HEXAGON HEAD AND NUT Long Diam. E Short Diam. F Head Thick. C Nut Thick. H Long Diam. Short Diam. Head Thick. Nut Thick. 1 20 .0866 .1634 ft I ft ft ft t ft ft & 18 .0962 .2163 If it H i H H M i I 16 .1083 .2667 Ii ft ft ft Ii ft ft ft ft 14 .1236 .3139 tt li fi f f Ii H 1 ' i 12 .1443 .3557 i& i t ft 1 f f ft ft 12 .1443 .4182 ift H H 1 B M H i 1 11 .1575 .4675 an H H ft 1ft M if ft I 10 .1732 .5768 m 11 ft H Ml H ft H i 9 .1924 .6826 iff ift Ii H II! i* Ii H i 8 .2165 .7835 2| ii I H m U 1 if i| 7 .2474 .8776 2H 1H H H iii 1H M H it 7 .2474 .0026 2ft H H n 2H U H U H 6 .2887 .0863 2H 2ft ift If 2|f 2ft Ift H ii 6 .2887 .2113 3ft 21 H H 2M 21 H ii it 5 .3465 .2785 3*i 2ft 1ft l| 2H 2ft 1ft If 1! 5 .3465 .4035 3ff 2f ift l! 3^ 2| 1ft If 11 4i .3849 .4901 3ft 2H 1H II 31 2M 1H Ii 2 4* .3849 .6151 41 3 H 2 3M 3 H 2 2i 4i .3849 .7401 4i 3ft 1H 21 3H 3ft IH a* 21 4| .3849 .8651 4ff 3| 1H 21 3H 31 iH 21 2f 4| .3849 1.9901 5^ 3^ 1M 2f 4^ 3ft iff 2| 2i 4 .4330 2.0670 5H 31 H 21 4H 3f if 2| 2f 4 .4330 2.1920 5ft 3H IB 2f 4ff m i 21 2! 4 .4330 2.3170 5H 41 2ft 21 4H 4i 2ft 2f 2| 4 .4330 2.442 6& 4A 2A 21 4H 4ft 2& 21 3 3| .4949 2.5051 6H 41 21 3 6M 4i 21 3 [364] S. A. E. STANDARD SCREWS S. A. E. STANDARD SCREWS The form of screw thread adopted by the Society of Automobile Engineers is the same as in the Franklin Institute Standard, that is, the contained angle of the flat sides of the thread is 60, with a flat top and flat bottom equal to one-eighth of the pitch. The number of threads per inch is greater than in the Franklin Institute Standard. The threaded portion of the bolt equals one and a half times the diameter of screw. Bolts and nuts to be made of steel, not less than 100,000 pounds tensile strength, with an elastic limit of 60,000 pounds per square inch. Screw threads, bolt heads, and plain nuts are to be left soft; castle nuts are to be case-hardened. Standard details and corresponding dimensions relating to head, nut, and castle nut are given in the accompanying illustration and table. S. A. E. STANDARD SCREWS SCREW BOLT HEAD AND NUT DETAILS Diam. A Thds. per Inch B c D E F G H K L M Diam. Drfi t I 28 A I A & & A A A A ^6 A A 24 i li H A A B li ft X A H 1 24 A & A A 1 li H 1 i A li & 20 I -B li A i 1 i 1 1 A t i 20 I H I A 1 A * A 1 A A & 18 1 IA li A 1 li M A A 1 i I 18 H IA H A 1 If ft i & l li 16 i 1* H A 1 B I i A i If 1 16 1A l& A A 1 B H i A 1 H 1 14 li 1A B A 1 If If i A 1 If l 14 IA IB i A 1 1 l i A i If li 12 if u H & A H 1A A A li 1A if 12 1 IA H A & IA li A A H 1A H 12 2 1A IA A L 4 IB IB 1 i H IB M 12 2& IB II A i 1A li f 1 H IB WfflTWORTH STANDARD THREADS The form of thread proposed by Sir J. Whitworth and adopted by English engineers is one with flat sides, at an angle to each other of 55, with a rounded top and bottom. The proportions for the rounded top and bottom are obtained by dividing the depth of a sharp thread having sides of 55 into six equal parts, and within the lines formed by [3651 WHITWORTH STANDARD SCREW THREADS the sides of the thread and the top and bottom dividing lines, inscribing a circle, which determines the form of top and bottom of thread, thus: p = pitch = 1 No. threads per inch d = depth = pX .6403 r = radius = p X .1373 WHITWORTH STANDARD SCREW THREADS, NUTS, AND BOLTS Diameter of Bolt HEAD AND NUT OVER Height Nut Height of Head for Bolts Threads Inch Area at Bottom of Thread Thick, of Check Nut Size of Split Pin L. S. G. Flats Angles i 4 \ 1 i A 20 0.027 A No. 14 I H if 1 A 16 .068 1 13 \ if 1ft i ft 12 .121 f 12 I If t| f 11 .203 ft 11 I ift II i H 10 .303 A 10 i It Hi 1 i 9 .421 f 9 1 lit IH 1 7 1 8 .554 f 8 U H 21- li 1 7 .697 H 7 H 2ft 2f H & 7 .894 H 6 if 2ft 2ft H 1& 6 1.059 Ift 5 ri 2ft 2H If Ift 6 1.300 H 4 it 2ft 3 H tft 5 1.471 11 3 if 21. 3A U i* 5 1.752 i& 2 11 3 3^ U if 4* 1.986 if 1 2 3i 3f 2 if 4 2.311 H 1 2* 3ft 4^ 2| 2 4 2.925 A 2* 31 ^ 2i 2A 4 3.732 A 21 4ft 4H 2f 2^ 3* 4.463 . . . f 3 4 54 3 2f 3| 5.449 f 31 41 5f 31 2H 31 6.406 ... f 3* 5ft 6 3^ 3^6 31 7.572 A 3f 5ft 6f 3| 31 3 8.656 A 4 5H 61 4 3^ 3 10.026 . . . 1 41 61 7f 41 3f 21 11.370 i 4| 6M 71 4^ 3H 21 12.913 ... ft 4f 71 8& 4! 4| 2f 14.413 ft 5 7H 9 5 4f 2f 16.145 ... f The above table is from Seaton and Rounthwaite's " Pocket-Book of Marine En- gineering," as is also the following table on the strengths of studs and bolts. The table is based on the relation: Working stress per sq. in. = (Area at bottom of thread)^ X C; where C = 5,000 ,for iron or mild steel, and 1,000 for Muntz or gun-metal. For iron or steel bolts above [366] WHITWORTH STANDARD SCREW THREADS 2 inches diameter, and gun-metal or bronze ones above 3 inches diameter, the moment of the twisting stress is so small, proportionately, that it may be neglected. Studs and bolts may be loaded to the figures given in the table whether the load is daad (as in the case of a joint), or live (as in the case of a connecting-rod bolt), as in the latter case mild steel will always be used, and the shearing stress due to tightening up is practically absent. Mild steel studs and bolts should always be fitted with iron nuts, as steel ones have a much greater tendency to seize, and so greatly increase the twisting stress; for the same reason Muntz metal or naval brass studs should always have iron nuts if possible. Gun-metal and the various bronzes are unsatisfactory materials for small studs and bolts, not because of any lack of tensile strength which is often high but because of their very low elastic limit under a shearing stress. When iron or steel studs are used in connection with gun-metal steam or water valves, etc., they must not be allowed to penetrate into the steam or water space, or they will apidly corrode and come loose. The part of a stud that is screwed into the work should be: Not less than 1 diame- ters long when screwed into cast iron, and 1| diameters when not inconvenient. Nor less than 1 diameter long when screwed into gun-metal, wrought iron, or cast steel. STRENGTH OF STUDS AND BOLTS. WHITWORTH THREADS Diameter Stud or Bolt IRON OR MILD STEEL MUNTZ OK GUN-METAL Working Stress in Pounds per Square Inch Effective Strength of 1 Bolt or Stud in Pounds Working Stress in Pounds per Square Inch Effective Strength of 1 Bolt or Stud in Pounds f 2,000 250 400 50 I 2,500 500 500 100 1 3,000 900 600 180 1 3,400 1,450 680 290 1 3,900 2,150 780 430 tj 4,300 3,000 860 600 t| 4,700 4,200 940 840 If 5,100 5,400 1,020 1,080 1* 5,500 7,100 1,100 1,420 H 5,800 8,500 1,160 1,700 H 6,300 11,000 1,260 2,200 if 6,600 13,100 1,320 2,620 2 7,000 16,100 1,400 3,220 2i 7,000 20,400 1,560 4,560 2| 7,000 26,100 1,730 6,450 2f 7,000 31,200 1,860 8,300 3 7,000 38,100 2,030 11,000 3i 7,000 44,800 2,170 13,900 3| 7,000 53,000 2,350 17,800 3! 7,000 60,500 2,500 21,600 4 7,000 70,100 2,500 25,000 4J 7,000 79,500 2,500 28,400 4* 7,000 90,300 2,500 32,200 4| 7,000 100,800 2,500 36,000 5 7,000 113,000 2,500 40,300 51 7,000 124,600 2,500 44,500 5 7,000 138,000 2,500 49,200 [367] BRITISH ASSOCIATION SCREW THREADS BRITISH ASSOCIATION STANDARD THREAD This standard has been adopted in England by manufacturers of small screws used by electrical and other instrument makers. The form of thread is similar to Whitworth's, the angle of the V is 47|, the top and bottom of threads are rounded off to two-elevenths of the pitch thus: I p = pitch = No. thrds. per mm. depth = p X .6 2 Xp r = radius 11 From Unwin: Let d = diameter of screw, and p = pitch in millimeters. Then for screws less than 6 mm. in diameter a series of pitches are assumed 0.9, 0.9 1 , 0.9 2 . . . and each screw pitch is characterized by a number which is the index of 0.9 in that series. For each of these pitches a standard diameter is selected, given by the equation d = 6 pf . The rounding at top and bottom of threads is j 2 T of the pitch; the depth of thread is | of the pitch. The dimensions being in millimeters. BRITISH ASSOCIATION STANDARD SCREW THREADS DIMENSIONS i NT MILLIMETERS DIMENSIONS IN INCHES Threads Number Diameter Pitch Diameter Pitch per Inch 6.0 1.00 .236 .0394 25.4 1 5.3 .90 .209 .0354 28.2 2 4.7 .81 .185 .0319 31.4 3 4.1 .73 .161 .0287 34.8 4 3.6 .66 .142 .0260 38.5 5 3.2 .59 .126 .0232 43.0 6 2.8 .53 .110 .0209 47.9 7 2.5 .48 .098 .0189 52.9 8 2.2 .43 .087 .0169 59.1 9 1.9 .39 .075 .0154 65.1 10 .7 .35 .067 .0138 72.6 11 .5 .31 .059 .0122 81.9 12 .3 .28 .051 .0110 90.7 13 .2 .25 .047 .0098 101.0 14 .0 .23 .039 .0091 110.0 15 .90 .21 .035 .0083 121.0 16 .79 .19 .031 .0075 134.0 17 .70 .17 .028 .0067 149.0 18 .62 .15 .024 .0059 169.0 19 .54 .14 .021 .0055 181.0 20 .48 .12 .019 .0047 212.0 21 .42 .11 .017 .0043 231.0 22 .37 .098 .015 .0039 259.0 23 .33 .089 .013 .0035 285.0 24 .29 .080 .011 .0031 317.0 25 .25 .072 .010 .0028 353.0 [368] INTERNATIONAL STANDARD SCREW THREADS p - pitch - NQ threads per inch d = depth = p X .6403 r = radius = p X .1373 Diameter, Inches Threads per Inch Diameter, Inches Threads per Inch Diameter, Inches Threads per Inch Diameter, Inches Threads per Inch i 25 u 9 2 7 3f 4* & 22 1A 9 2| 7 3| 4* 1 20 11 9 2i 6 4 4* & 18 1A 9 2| 6 4* 4 1 16 H 8 2| 6 4| 4 & 16 l* 8 2| 6 4| 4 I 14 l| 8 2| 6 5 4 H 14 1A 8 2| 6 5* 3| ! 12 U 8 3 5 5* 3* H U HI 8 3* 5 51 H i 11 If 7 3* 5 6 3* if 11 in 7 31 5 l 10 u 7 3* 41 l& 10 IH 7 3f 4* INTERNATIONAL STANDARD SCREW THREADS SYSTEM INTERNATIONAL The form of thread used is similar to the Franklin Institute Standard; that is, the thread has flat sides, the contained angle between any two threads is 60; the width of flat at top and bottom of thread is one-eighth of the pitch. A clearance at the bottom of thread not exceeding one-sixteenth of the height of the original triangle is included in the specifications and it is recommended that the clearance occurring at the bottom of the screw shall be rounded. The clearance is obligatory, but the bottom of the screw may or may not be flat, inasmuch as the rounded bottom is left to the discretion of the manufacturer. This standard differs in some respects from the French Standard, and the later French Standard differs from that formulated by Armengaud. In the following table the standard dimensions are in terms of the Metric System; English equivalents are supplied in parallel columns for reference only. INTERNATIONAL AND FRENCH STANDARD THREAD (Metric System) J/V T^ / \ S-i / \ i z=4 a _/ \ / 6 8 v~ 8 ^ /->> pitch No. threads per inch d = depth = p X .6495 f=flat =| r 369 INTERNATIONAL STANDARD SCREW THREADS INTERNATIONAL STANDARD SCREW THREADS System International Dimensions in millimeters and inches OUTSIDE Pitch Root Diameter Root Area Diameter Area Mm. Inches Mm. Inches Mm. Threads per Inch Mm. Inches Mm. Inches 3 0.1181 7.07 0.011 0.55 46.18 2.29 0.090 4.12 0.006 4 .1575 12.57 .019 .70 36.29 3.09 .122 7.50 .012 5 .1968 19.63 .030 .85 29.88 3.90 .153 11.95 .019 6 .2362 28.27 .044 .00 25.40 4.70 .185 17.35 .027 7 .2756 38.48 .060 .00 25.40 5.70 .225 25.52 .040 8 .3150 50.27 .078 .25 20.32 6.38 .251 31.97 .050 9 .3543 63.62 .099 .25 20.32 7.38 .290 42.78 .066 10 .3937 78.54 .122 .50 16.93 8.05 .317 50.90 .079 11 .4331 95.03 .147 .50 16.93 9.05 .356 C4.33 1.100 12 .4724 113.10 .175 1.75 14.51 9.73 .383 74.36 .115 14 .5512 153.94 .239 2.00 12.70 11.40 .449 102.07 .158 16 .6299 201.06 .312 2.00 12.70 13.40 .528 141.03 .219 18 .7087 254.47 .394 2.50 10.16 14.75 .581 170.87 .265 20 .7874 314.16 .487 2.50 10.16 16.75 .660 220.35 .342 22 .8661 380.13 .589 2.50 10.16 18.75 .738 276.12 .428 24 .9449 452.39 .701 3.00 8.47 20.10 .792 317.31 .493 27 1.0630 572.56 .887 3.00 8.47 23.10 .910 419.10 .650 30 1.1811 706.86 1.096 3.50 7.26 25.45 1.002 508.71 .789 33 1.2992 855.30 1.326 3.50 7.26 28.45 1.120 635.70 .985 36 1.4173 1017.88 1.578 4.00 6.35 30.80 1.213 745.06 1.155 39 1.5354 1194.59 1.852 4.00 6.35 33.80 1.331 897.27 1.391 42 1.6535 1385.44 2.147 4.50 5.64 36.15 1.423 1026.38 1.591 45 1.7716 1590.43 2.465 4.50 5.64 39.15 1.541 1203.80 1.866 48 1.8898 1809.56 2.805 5.00 5.08 41.51 1.634 1353.31 2.098 52 2.0472 2123.72 3.292 5.00 5.08 45.51 1.792 1626.69 2.521 56 2.2047 2463.01 3.818 5.50 4.62 48.86 1.924 1874.99 2.906 60 2.3622 2827.43 4.383 5.50 4.62 52.86 2.081 2194.55 3.402 64 2.5197 3216.99 4.986 6.00 4.23 56.21 2.213 2481.52 3.846 68 2.6772 3631.68 5.629 6.00 4.23 60.21 2.371 2847.27 4.413 72 2.8346 4071.50 6.311 6.50 3.91 63.56 2.502 3172.92 4.918 76 2.9921 4536.46 7.032 6.50 3.91 67.56 2.660 3584.84 5.557 80 3.1497 5026.55 7.791 7.00 3.63 70.91 2.792 3949.17 6.121 [370] CASTLE NUTS CASTLE NUTS Diatn Bolt A Threads Inch Short Diam. B Long Diam. C Depth D Depth E Width F Diam. G Diam. Hole in Blank Nut H i 13 8 1 I A i i If A 12 ft H | 1 6 A H I 11 I* i* H A A A If f 10 H iA H A A If 7 8 9 1A ill i* If A A ti 1 8 U if U A i 1 If U 7 ill 2& m 1 A A If i\ 7 2 2A 1A A A A 1A if 6 2& 2H iff If H H IA i* 6 2| 2| if H 1 1 1A if 5* 2& 2ft 2^ If H H i|f if 5 2f 3A 2A If A A if if 5 2H 3M 2^ H H H if 2 4| 3* 3M 2^ 1 i i m 2i 4| 3 4^ 2M i A A m 2* 4 31 4M 3| it ! 1A CAP NUTS A B c D E F G H i K Diam. Hole U. S. Th. \ A f 1 H IA U 1A l II IA IA ift 7 1 1A H 1A A A \ A i A f f 1 ? H 7 8 1 A A A A A 1 H 1A H i^ H H H U iH If If If If H [371 STEEL BOLTS AND NUTS CAP NUTS (Continued) A B c D E F G H i K Diam. Hole U. S. Th. 1 H ii iH H 1 H 1 if 2A H U iH 2& H 1 H U I if 21 H H 2 2A 2A H It if A ' lit 2^ iA if 2A- 2M 2i 1 if H A 2A 2f 1A H 2f 2| 2A if l| IH A 2A 3 iA if 2A 2& 2f 1 if IH A 2A 31 lit H 2| 3A 2H 1A if 1 H 2f 3A ii i| 2H 3H aft 1A if 2f H 2H 3H if 2 3i 3H 3i H 2 21 f 3 31 iff STEEL BOLTS AND NUTS NAVY DEPARTMENT BOLTS Bolts shall be made of a good quality of medium steel, and shall conform to the United States standard for both heads and threads, unless otherwise specified as given in Table I below. All threads are to be United States standard, and where blanks are not specially called for bolts will be threaded, and nuts will be tapped and fitted thumb-tight to the bolt. The length of the bolt will be measured from under the head to the first thread at the end of the bolt. Heads of bolts will be square, hexagonal, or button head, and plain or chamfered, as specified in requisition. The nuts will be square or hexagon, either plain or cupped, or double-cupped, as specified in requisition. Unless otherwise specified, to be delivered in 100-pound boxes. All kegs, boxes, or commercial packages to be plainly marked with the manufac- turer's name and contract number. Boxes to be made of new pine or spruce, planed on the outside, f inch when finished. Boxes to be exactly 17 inches long, 10 inches high, 11 inches wide, outside measurements, and must be securely put together. Boxes to be neatly stenciled on one end only with the net weight, size, and name of contents, as: 100 pounds | by 1| inches Bolts and nuts, steel Hexagon heads and nuts. The manufacturer's name, contract number, and any other marks to be on one only; one side, one end, top, and bottom to be free from marks. [372J STEEL BOLTS AND NUTS TABLE I STANDARD DIMENSIONS OF BOLTS AND NUTS FOR THE UNITED STATES NAVY Diameter Area Thrds Long Diam. Short Diam. Depth Diam- eter of Holes In Blank Nuts Norn. Eflf. Eflf. No. Hex. Sq. W. Head Nut I 0.185 0.026 20 A ft .i 1 1 A A .240 .045 18 H tt H if A 1 f .294 .067 16 If H H H f H A .345 .093 14 f* ** M If A H i .400 .125 13 i H f A 1 If A .454 .162 12 i| H B H A H f .507 .202 11 1* H ia H f H .620 .302 10 1* if H f f M 1 .731 .419 9 m 2^ i* H 1 H l .837 .550 8 n 2A If if i If IJ .940 .694 7 2& 2A iH M H H U 1.065 .891 7 2A 2M 2 i 11 1A if 1.160 1.057 6 2M 3& 2A I* if i& IJ .284 1.294 6 2| 3H 2f !A If 1* if .389 1.515 51 m 3f 2A 1* if iff U .491 1.746 5 3A 31 2| if H H H .616 2.051 5 3 ft 4& 2H Itt H if 2 .712 2.302 4 OJJ 4M 3* 1* 2 m 21 .962 3.023 4i 4& 4H 3* if 21 1H 2* 2.176 3.719 4 m 5M 31 m 2| i* 2| 2.426 4.622 4 4ff 6 41 2| 2f 2A All bolts 3 inches in diameter and above to have four threads per inch of standard form, except in special cases, which will be submitted for approval. Variations of Blank Bolts. The variations in size of blank bolts shall not exceed that allowed under Table II below: TABLE II Nominal Diam. Maximum Diameter Minimum Diameter Maximum Variation Nominal Diameter Maximum Diameter Minimum Diameter Maximum Variation Inch Inch Inch Inch Inches Inches Inches Inch A 0.1925 0.1825 0.010 tt .9465 .9285 0.018 1 .2550 .245 .010 1 1.0095 .9905 .019 A .3180 .307 .011 14 1.1350 1.115 .020 f .3810 .369 .012 U 1.2605 1.2395 .021 ft .444 .431 .013 if 1.3855 1.3645 .021 i .507 .493 .014 II 1.5105 1.4895 .021 A .570 .555 .015 if 1.6355 1.6145 .021 f .633 .617 .016 if 1.7605 1.7395 .021 H .6955 .6795 .016 H 1.886 1.864 .022 f .7585 .7415 .017 2 2.011 1.989 .022 H .821 .804 .017 21 2.261 2.239 .022 1 .8840 .866 .018 2* 2.511 2.489 .022 [373] STEEL BOLTS AND NUTS Form and Surface. Bolts must be true to form, concentric, and free from scale, fins, seams, and all other injurious or unsightly defects. Tests. A number of bolts, at the discretion of the inspector, will be taken from each size of each delivery, enough to satisfy the inspector as to the quality of the entire lot, and will be subjected to the following tests: One-half of these bolts shall be bent cold on unthreaded portion through 180 around a diameter equal to one-half the diameter of the bolts, and they must stand this test without breaking, and only a slight fracture of the skin on one side will be allowed. The remainder of the. bolts will be tested hot. They will be heated to redness and hammered out flat to one-half their original thickness. They will then be reheated to redness and bent around flat to an angle of 180, and they must stand this test without breaking off. When bolts are not of sufficient length in the plain part to admit of being bent cold, the threaded part must stand bending cold without fracture as follows : If of inch diameter or less 35 If above inch diameter and under 1 inch 30 If 1 inch diameter or over 25 Bolts and Nuts Ordered Together. When bolts and nuts are ordered together the nuts shall conform to the requirements for medium steel or wrought-iron nuts, as stated hereinafter. The threads must be clean and sharp; the nuts must fit thumb-tight, and be delivered on bolts. NUTS Nuts shall be hot pressed or cold punched and of a good quality of medium steel or wrought iron. They shall conform, unless otherwise specified, to the United States standard dimensions as given in Table I under "Bolts." The allowable variations from these dimensions shall not exceed those given in Table II. When nuts are ordered separately they shall be threaded unless otherwise specified in the contract. Form and Surface. Nuts shall be true to form, concentric, and free from scale, fins, seams, and all other injurious or unsightly defects. Hammer Test. A number of nuts, at the discretion of the inspector, to be taken from each size of each delivery, enough to satisfy the inspector as to the quality of the entire lot. One-half of these shall be placed on their sides and hammered out cold, so that they break. The fracture on steel nuts must indicate medium steel of good quality. The fracture in the case of wrought-iron nuts must show the grain to run normally to the plane through the hole. The remaining nuts shall be heated to redness and hammered under a power hammer to one-sixth their original thickness, and there must be few cracks around the edges, and no signs of large splits or flaws. TENSILE TEST OF BOLTS AND NUTS COMBINED When practicable, tensile test of bolts and nuts combined shall be made. In making the tensile test, the head and nut shall, without previous reduction of sectional area of bolt, be held in opposite jaws of the testing machine and pulled to fracture. Bolts so tested, to be satisfactory, must in every case fracture at threads, and not at juncture with head, and shall withstand a tensile stress of at least 58,000 pounds, find have an elastic limit of not less than 30,000 pounds per square inch sectional area. [374 BOLTS AND NUTS WEIGHT BOLTS AND NUTS. ROUGH SIZES United States Standard Weight in pounds per 100 bolts Length in Inches SQUARE HEADS AND SQUARE NUTS HEXAGON HEADS AND HEXAGON NUTS 1 I i i l i I 1 1 1 2 27 45 67 101 144 24 40 63 93 132 a* 30 49 74 109 155 27 45 69 101 143 3 33 54 80 117 167 30 49 75 109 154 3 35 58 86 126 178 33 54 82 118 165 4 38 62 92 134 189 35 58 88 126 176 4| 41 66 98 142 198 38 62 94 134 186 5 43 71 104 151 209 41 66 100 143 197 51 46 75 111 159 220 44 71 106 151 208 6 49 79 117 168 232 46 75 112 160 219 6* 52 84 123 176 243 49 79 119 168 230 7 55 88 129 185 254 52 84 125 177 241 7* 57 92 136 193 265 55 88 131 185 252 8 60 97 142 202 276 58 92 137 194 264 8* 63 101 148 210 287 60 96 143 202 274 9 65 105 154 218 298 63 100 149 210 285 9* 68 110 161 227 309 66 105 156 219 296 10 71 114 167 235 320 68 109 162 227 307 10| 74 118 173 244 331 71 114 168 236 318 11 77 123 180 252 343 74 118 174 244 329 iH 79 127 186 261 354 77 122 181 253 341 12 82 131 192 269 364 80 127 187 261 352 13 88 140 205 285 387 85 135 199 278 374 14 93 148 217 303 409 91 144 212 295 396 15 99 157 230 320 432 96 152 225 312 418 16 104 165 242 337 451 102 161 237 329 441 17 110 174 255 354 476 107 170 250 346 463 18 116 183 267 371 499 113 177 262 364 485 19 121 192 280 388 521 119 187 275 381 507 20 127 200 292 405 543 124 196 287 398 530 21 132 209 305 422 565 130 205 300 415 552 22 138 218 317 439 588 136 213 313 432 575 23 143 226 330 456 610 141 222 325 449 597 24 149 236 342 473 632 147 231 338 466 619 [375] BOLTS AND NUTS U. S. NAVY SPECIFICATIONS MACHINERY BOLTS AND NUTS AND MATERIAL FOR THE SAME NAVY DEPARTMENT NOTE. These specifications are to be used only when finished or semi-finished bolts and nuts are required, as around machinery or for flanges. 1. Machinery bolts and nuts to be of two grades: Semi-finished (faced under head and nut, body trued); finished (machined throughout). Material to be of domestic manufacture. For use on machinery, Class A rods; for minor purposes, Class B rods; for anti-corrosive purposes, rolled naval brass, manganese bronze, or monel metal rods, as stated on the order. STEEL RODS 2. The physical and chemical characteristics of steel rods for bolts are to be in accordance with the following table: Class Material Mini- mum Tensile Strength Mini- mum Elastic Limit Mini- mum Elonga- tion^ Maximum Amount of Bends' P. s. Pounds Pounds Per Cent per per in 8 Sq. In. Sq. In. Inches A.... Open-hearth 75,000 40,000 23 0.04 0.035 Cold bend 180 about nickel or an inner diameter carbon equal to one-half the steel. thickness of the test piece for diameters up to and including 1 inch, and equal to the thickness for di- ameters over 1 inch; quench bend 180 about an inner di- ameter equal to the thickness of the test piece for diameters up to and including 1 inch, and equal to 1 times the thick- ness for diameters over 1 inch. B.... Open-hearth 58,000 30,000 28 0.04 0.035 Cold bend flat back carbon through 180; quench steel. bend 180 through an inner diameter equal to one-half the thickness of the test piece for diameters up to and including 1 inch, and equal to the thickness for di- ameters over 1 inch. 1 Elongation for rounds J inch and less in diameter shall be measured in an original length equal to 16 times the diameter of the test piece; for material over i inch up to and including 1 inch in diameter, the elongation shall be measured in a length of 8 inches; and for material over 1 inch in diameter up to and including 2 inches in diameter, the required percentage of elongation, measured in a length of 8 inches, shall be reduced by one for each increase in diameter of \ inch or a fraction thereof above 1 inch. 2 Quench test pieces to be heated to a dark cherry red, as seen in daylight, and plunged into fresh, clean water of 80 to 90 F. [376] BOLTS AND NUTS U. S. NAVY SPECIFICATIONS 3. If the contractor desires, and so states on his orders, or if inspection at the place of manufacture of the rods is considered impracticable to the bureau concerned, the bureau will direct that the inspection of the rods be made at the place of manufacture of the bolts, instead of at the place where the rods are rolled. 4. Surface and Other Defects. The rods must be true to form, free from seams, hard spots, brittleness, injurious sand, or scale marks, and injurious defects generally. 5. Tensile Test. One tensile-test piece shall be taken from each ton or fraction thereof of rods rolled from the same heat. If, however, the rods in one heat are not of the same diameter, then the inspector will take such additional test pieces as he may consider necessary according to the number of different sizes of rods in the heat. When practicable, but one piece will be cut from each rod selected for the test. Should any test piece be found too large in diameter for the testing machine, the piece may be prepared for test in the manner prescribed for forgings. 6. Bending Tests. If the total weight of the rods rolled from the same heat amounts to 6 tons or more, four cold-bending test pieces and four quench-bending test pieces will be taken; but if the weight is less than 6 tons, one-half that number of test pieces will suffice. 7. Upsetting Tests. From each heat of rounds as rolled there shall be cut six test specimens about H inches long, which shall stand hammering down cold, longitudinally, to one-half their original length without showing seams or other defects which would tend to produce imperfections in the finished product. FINISHED BOLTS (CLASSES A AND B) 8. After the rods to be made up into bolts have been tested as previously described, the finished articles shall be tested by lots of 500 pounds or fraction thereof, one piece being taken to represent the lot. The failure of 10 per cent of the lots of 500 pounds to stand the specified tests in a satisfactory manner will render the whole of any delivery liable to rejection. 9. When the bolts are of sufficient length in the plain part to admit of being bent cold, they must stand bending double to a curve of which the inner radius is equal to the radius of the bolt without fracture. 10. When bolts are not of sufficient length in the plain part to admit of being bent cold, the threaded part must stand bending cold without fracture as follows: If of | inch diameter or less . . 35 If above ^ inch diameter and under 1 inch 30 If 1 inch diameter or over , . 25 11. Where the bending tests cannot be applied the two following hammer tests must be substituted: (a) The test piece to stand flattening out, cold, to a thickness equal to one-half its original diameter without showing cracks. (b) The test piece to stand flattening out, while heated to a cherry-red heat in daylight, to a thickness equal to one-third its original diameter without showing cracks. 12. (1) All bolts shall be free from surface defects. (2) All bolts are to be headed hot, and the heads made in accordance with the United States standard proportions unless otherwise specified. The head must be concentric with the body of the bolt. (3) The threads must be of the United States standard unless otherwise specified, and must be clean and sharp. The threads of classes A and B bolts may be either chased or cut with a die, but the threads of body-bound bolts must be chased and must extend far enough down so that when the nut is screwed home there will be not more than one and one-half threads under it. The plain part of body-bound bolts must be turned in a lathe to fit accurately in the bolt hole. STEEL AND IRON NUTS (TO BE USED WITH CLASSES A AND B BOLTS) 13. One tensile and one bending test bar from each lot of 1,000 pounds of material or less from which nuts are to be made shall be selected by the inspector for test. [377] BOLTS AND NUTS U. S. NAVY SPECIFICATIONS 14. The material, whether steel or iron, shall show a tensile strength of at least 48,000 pounds per square inch and an elongation of at least 26 per cent in 8 inches. A bar inch square or \ inch in diameter shall bend back, cold, through an angle of 180 without showing signs of fracture. 15. The nuts must be free from surface defects, and the threads clean, sharp, and well fitting. 16. The dimensions of threads must be in conformity with the United States standard unless otherwise specified. STANDARD DIMENSIONS OF BOLTS AND NUTS FOR THE UNITED STATES NAVY Diameter Area Thrds. Long Diameter Short Diam. Depth. Diam- eter of Holes in Blank Nuts Norn. Eff. Eff. No. Hex. Sq. W. Head Nut 1 4 0.185 0.026 20 A M * \ i A A .240 .045 18 H H tt H A i 1 .294 .067 16 If M H H I H * .345 .093 14 H i& If H A H i .400 .125 13 l 11 1 ft ^ M & .454 .162 12 U H H M A H f .507 .202 11 1A i* ift 8 f If f .620 .302 10 i* rt i\ f f M 1 .731 .419 9 m 2& l& H 1 H l .837 .550 8 11 2& if H l If H .940 .694 7 2& 2& 1H H U H 1$ 1.065 .891 7 2& 2fJ 2 1 H l* if 1.160 1.057 6 m 3& 2& 1* H I* a 1.284 1.294 6 2f 3& 21 1* H i& if 1.389 1.515 $ m 3f 2^ 1ft if ill H 1.491 1.746 5 3& 31 2f U U M II 1.616 2.051 5 3M 4& 2H 1H H if 2 1.712 2.302 41 3$ 4H 3i l* 2 m 2* 1.962 3.023 H 4& 4H 3^ U 2i ifi 2* 2.176 3.719 4 4M 5H 31 m 2* ift 2f 2.426 4.622 4 41! 6 4i 2i 2f 2& 17. The nuts must be hot-pressed or cold-punched, the latter to be reamed before threading, the holes to be central and square with the faces. All nuts must fit on the bolts without shake. 18. Nuts to be used about machinery must fit so tight that it will be necessary to use a wrench to turn them. All other nuts must be at least thumb-tight. 19. For the purpose of test all nuts which fulfil the preceding requirements will be divided into lots of 500 pounds or less, and two nuts from each lot selected by the inspector for test as follows: (a) One of the two shall stand flattening out, cold, to a thickness equal to one-half its original thickness without showing cracks. (b) The other shall stand flattening out, when heated to a cherry-red in daylight, to a thickness equal to one-third its original thickness without showing cracks. 20. (a) The failure to stand these tests will subject the lot represented by them to rejection. The failure of 10 per cent of the lot to pass the tests will render the whole order liable to rejection. [378] BOLTS AND NUTS XT. S. NAVY SPECIFICATIONS NON-CORROSIVE RODS 21. The composition must be made of such materials as will give the required chem- ical analysis. Scrap will not be used except such as may result from the process of manufacture of articles of similar composition. Let- ter Name COMPOSITION BY PERCENTAGE Miscellaneous Cop- per Tin Zinc Lead, Maxi- mum Iron, Maxi- mum Mn-r. Mo-r . N-r... Manganese bronze Monel metal. 57-60 Rem. 0.5-1.5 37-40 0.0 .2 2.5 3.5 .06 Manganese, 0.30. Nickel, 60 (min.) ; alu- minium, 0.5 (max.). Rolled naval brass. . 59-63 .5-1.5 Rem. 22. One test piece for every lot of 400 pounds or less shall show the following results: Name Ultimate Let- ter Tensile Strength per Square Inch Yield Point (Minimum) Elongation in 2 Inches (Minimum) (Minimum) Pounds Per Cent N-r Naval brass 1 inch and below 62,000 2 ultimate 25 Above 1 inch 60,000 ^ ultimate 28 Mn-r. Manganese bronze, 1 inch and below 72,000 \ ultimate 28 Above 1 inch 70,000 3 ultimate 30 Mo-r . Monel metal, 1 inch and below 84,000 47,000 25 Above 1 inch 80,000 45,000 28 23. If the contractor desires, and so states on his orders, or if inspection at the place of manufacture of the rods is considered impracticable to the bureau concerned, the bureau will direct that the inspection of the rods be made at the place of manufacture of the bolts instead of at the place where the rods are rolled. 24. Test pieces are to be as nearly as possible of the same diameter as the rounds, or else they are to be not less than inch in diameter and taken at a distance from the circumference equal to one-half the radius of the rounds. 25. Test specimens for rounds and bars, or N-r, Mn-r, Mo-r, will stand: (a) Being hammered hot to a fine point. (b) Being bent cold through an angle of 120 and to a radius equal to the diameter or thickness of the bars. (c) The bending bar may be the full-sized bar, or the standard bar of 1 inch width and \ inch thickness. In the case of bending test pieces of rectangular section, the edges may be rounded off to a radius equal to one-fourth of the thickness. Fractures of specimens must show throughout uniform color and grain. 26. Various composition materials, otherwise conforming to the specifications, but manufactured under proprietary processes or having proprietary names, will be accepted as rolled naval brass provided the ingredients are approved by the bureau. 27. The rods must be free from all surface defects, clean and straight, of uniform color, quality, and gauge. 28. All requirements of the specifications for steel bolts that are applicable in regard to surface, material, and threading shall apply to non-corrosive bolts. 29. Non-corrosive nuts shall be made of the same material as the bolts. NOTE. All requirements for steel bolts and nuts that are applicable, such as surface, threads, and fitting, shall apply to non-corrosive bolts and nuts. [379] IRON BOLTS AND NUTS 30. Should it be impracticable for the bureau concerned to inspect the rods before the manufacture of the bolts, the test specified for the stock shall be made on the finished article as far as practicable. 31. Note for General Storekeepers. Requisitions will state the material, size, length over all, whether bolts and nuts are to be semi-finished or finished. If nuts are to be case-hardened, and if nuts are to fit wrench-tight, it will be so noted on the requisi- tion. Length of bolt to be measured from under side of the head to the first thread at the end of bolt. Requisitions should state whether bolts and nuts are to have hexagon heads or square heads. 32. Correspondence relative to interpretation or modification of specifications should be addressed to the bureau concerned, via the naval inspector of .material of the district. IRON BOLTS AND NUTS NAVY DEPARTMENT NOTE. This specification to be used only when steel bolts and nuts are considered unsuitable for the purpose. 1. To be of best quality neutral iron and to be bought in three grades, as follows, viz. : (a) Blanks (not machined). (b) Semi-finished (face under head and nut, body trued). (c) Finished (machined throughout). 2. These must conform to the dimensions of the table marked "I," except such small variations as are allowed by the table marked "II." The value of both hexagon and square nuts and heads is compiled from the following: Nuts, Blank or Semi-finished. D equals one and one-half tunes diameter of bolt plus | inch. B equals diameter of bolt. Nuts, Finished. D equals one and one-half times diameter of bolt, plus ^ inch. B equals diameter of bolt, less ^ inch. Heads, Blank or Semi-finished. D equals one and one-half times diameter of bolt, plus | inch. B equals one-half short diameter of head. Heads, Finished. D equals one and one-half times diameter, plus ^ inch. B equals diameter of bolt, less ^ inch. The long diameter of a hexagon nut may be obtained by multiplying the short diameter by 1.155 and the long diameter of a square nut by multiplying the short diameter by 1.414. 3. All threads are to be United States standard, and, where blanks are not specially called for, bolts will be threaded, and nuts will be tapped and fitted thumb-tight to the bolt to within three threads of the shank. 4. The length of the bolt will be measured from under the head to the first thread at the end of the bolt. 5. Heads of bolts will be square, hexagonal, or button head, and plain or chamfered. The nuts will be. square or hexagon, either plain or cupped, or double-cupped. All nuts to be cold punched or hot pressed as required. 6. All kegs, boxes, or commercial packages to be plainly marked with the manufacturer's name. MATERIAL AND TEST FOR MACHINE BOLTS AND NUTS OF WROUGHT IRON 1. The material to be known as a good commercial grade of American refined iron. 2. Tensile Strength. Material to be tested in full size when practicable. Specimen bars of not less than ^ square inch sectional area must show an ultimate strength of not less than 48,000 pounds per square inch, and an elongation of not less than 26 per cent in 2 inches. 3. Test of Bolts. From each lot of bolts of the same diameter the inspector will select a sufficient number of test specimens to determine the quality and uniformity of the material used, and the lot will be accepted or rejected according to the results obtained [380] IRON BOLTS AND NUTS 4. Fiber Test. One-half of the test specimens thus selected shall be nicked with a sharp chisel about 20 per cent of the diameter of the specimen, and bent back flat at this point to an angle of 180, the fracture showing clean fiber for at least 60 per cent of the area. 5. Cold Short Test. A number of the remaining test specimens shall be bent 180 to a radius of one and one-half times the radius of the hole, without showing a sign of fracture on outer curve. When the specimens are not of sufficient length in the plain part of the bolt to admit of the above test, the following will be substituted: Break the specimen through the threaded parts without nicking, the result to be the same as required for fiber test. TABLE I Diame- ter of Finished Bolt Nearest Size Drill for Use in Blank. (Blank Nuts Must Not Be Smaller) Exact Dimen- sions at Root of Thread Threads per In. on U.S. Stand. HEXAGON OR SQUARE NUTS HEXAGON OR SQUARE HEADS Blank or Semi-finished Finished Blank or Semi-finished Finished D B D B D B D B 7ns. Inches Inches Inches Inches Inches Inches Inches Inches Inches Inches A No. 25 .1469 32 H A H i H if H i 1 A .1850 20 \ i & & 1 i A A A i .2403 18 H A M i H if H i 1 H .2936 16 H 1 f A H H f A A H .3447 14 If If f If If If f 1 H .4001 13 I H tk 1 & H A A H .4542 12 & A If 1 H li If \ f H .5069 11 1A f l & IA H i A U fi .5694 11 IA H i& f i* li t* f f f .6201 10 ii i 1A H H f 1A H H tt .6826 10 li* H i& i 4 itt If 1A f 1 li .7307 9 iA 1 U H 1A M if H tt li .7932 9 Ui H 1M 1 1H If 1H 1 1 H .8376 8 if i 1A H if H IA H U li .9394 7 m H U i^ iff If if IA H ** .0644 7 2 H 1H 1A 2 1 lil IA H itt .1585 6 2A if 2i 1A 2fV i& 2| 1A li lit .2835 6 521 H 2A 1^ 2f 1A 2^ IA H iff .3888 5 2A if 2f 1A 2& i& 2 IA if U .4902 5 2f H 2H 1H 2f if 2H 1H U if .6152 5 2H U 21 1H 2H 1H 21 1H 2 iff .7113 4* 31 2 3A Itt at IA 3^r iH 2i Ift .9613 4* 3f 2i 3^ 2A 3* H 3^ 2A 2* 2A 2.1752 4 31 2* 3H 2^ 31 1H 3H 2A 6. Hot Test. A number of the samples shall be heated to redness and flattened out to one-half the original thickness, and then reheated to red heat and bent to an angle of 180, and the bend must show no sign of fracture. 7. Test of Nuts. A number of nuts, at the discretion of the inspector, to be taken from each size of each delivery, to determine the quality and uniformity of the material The surface of the nuts should be free from defects; the nuts to be of correct [381] DECK BOLTS AND NUTS size and proper finish, and the lot will be accepted or rejected according to the results obtained. 8. Cold Tests. A number of nuts, at the discretion of the inspector, shall be tested cold as follows: The nuts shall be placed on their sides and hammered out so they will break; the fracture must show the grain or fiber to run normally to the plane through the hole. The following table, marked "II," gives the variations in gauge allowed for blank nuts and bolts: TABLE II Nominal Diam. Maximum Diameter Minimum Diameter Maximum Variation Nominal Diameter Maximum Diameter Minimum Diameter Maximum Variation Inch Inch Inch Inch Inches Inches Inches Inches A- .1925 .1825 0.010 H .9465 .9285 0.018 \ .2550 .245 .010 i .0095 .9905 .019 A .3180 .307 .011 U .1350 1.115 .020 I .3810 .369 .012 U .2605 1.2395 .021 A .444 .431 .013 H .3855 1.3645 .021 i .507 .493 .014 H .5105 1.4895 .021 A .570 .555 .015 H .6355 1.6145 .021 i .633 .617 .016 U .7605 1.7395 .021 H .6955 .6795 .016 if 1.886 1.864 .022 i .7585- .7415 .017 2 2.011 1.989 .022 it .821 .804 .017 21 2.261 2.239 .022 1 .8840 .866 .018 2| 2.511 2.489 .022 DECK BOLTS AND NUTS NAVY DEPARTMENT All deck bolts and nuts to be made of the best quality of neutral iron or mild steel. The bolts shall be well and evenly galvanized to insure a good fit for the nut; to be square necked, with round heads, and to have hexagon nuts, galvanized and fitted thumb-tight to bolts which will be threaded for one-third of their length; bolts and nuts to conform to the following table of dimensions; lengths of bolts to be measured over all: Diameter of Bolt Length of Bolt Over All Diameter of Head Thickness of Head Diameter of Nut Thickness of Nut Inch Inches Inches Inch Inch Inch i 3 1 A H A A 3 1 \ ft A 3* 1 \ ft \ 1 4 li I 1 A TESTS OF BOLTS AND NUTS A number of bolts, at the discretion of the inspector, will be taken from each size of each delivery, enough to satisfy the inspector as to the quality of the entire lot, and will be subjected to the following tests: 1. Cold Tests. One-half of these bolts shall be bent cold through 180 around a diameter equal to one-half the diameter of the bolts, and they must stand this test without breaking, and only a slight fracture of the skin on one side will be allowed. -[382] ' BOLTS FOR ORDNANCE WORK 2. Hot Test. The remainder of the bolts will be tested hot. They will be heated to redness and hammered out flat to one-half their original thickness. They will then be reheated to redness and bent around flat to an angle of 180, and they must stand this test without breaking off. HOLDING-DOWN BOLTS FOR GUN MOUNTS, TORPEDO TUBES, AND TURRET TRACKS NAVY DEPARTMENT 1. The "Specifications for Inspection of Steel and Iron Material, General Speci- fications, Appendix I," issued June, 1912, shall form a part of these specifications, and must be complied with as to material, methods of inspection, and all other requirements therein. 2. Holding-down bolts and their nuts for gun mounts, torpedo tubes, upper and lower turret roller tracks and holding-down clips, shall be made of either forged or rolled bafs, and shall conform to the physical and chemical requirements of the following table. All material shall be free from injurious surface defects and have a workmanlike finish: M?^rial Treatment Mini- mum Tensile Strength Mini- mum Yield Point Mini- mum Elonga- tion in 2" MAXIMUM AMOUNT OF Cold Bend Without Cracking P. s. O.H. nickel steel. Annealed, oil temper- ing optional Lbs. per Sq. In. 80,000 Lbs. per Sq. In. 50,000 Per Cent 25 PerGt. .05 PerCt. .05 180 to inner diameter of inch. In 8" 20 Per Cent 3. At least two test pieces for tensile test and one test piece for bending shall be tested from different bars from each lot of 50 bars or less made from the same heat and subjected to the same treatment. 4. Finished bolts shall conform also to the following requirements: (a) Where the bolts are not turned down from the solid rod, but when the rod is upset to form the head, the bolts are to be annealed after such working. (b) In all cases bolts are to have small fillet under head and not to be cut sharp. (c) Bolts are to have the head rounded by a radius equal to about H diameters of bolt to insure striking directly over the center of the bolt when driving the same in position. (d) The United States standard thread to be used unless otherwise ordered; care to be taken that the threads shall be slightly flattened at root and point, as required by said standard. (e) Threads to be chased, and, in finishing, care to be exercised that the depth of any one cut taken by the finishing tool shall not be sufficient to injure the bolt. 5. Turret-track bolts shall be body-bound turned bolts, with points rounded to radius equal to the diameter of the bolt, and must be a driving fit. The thickness and diameter of turret-track bolt-heads shall be the same as that of the nut; the head to be faced underneath in all cases. [383] STEEL OR COMPOSITION BOLTS AND NUTS BOLTS OF STEEL OR COMPOSITION METALS, AND NUTS OF IRON, STEEL, OR COMPOSITION METALS; STUDS AND NUTS AND BARS FOR BOLTS AND NUTS NAVY DEPARTMENT SPECIFICATIONS 43B9 September 1, 1914 NOTE. These specifications do not refer to machine bolts and nuts which are covered by Specification 43B5 of latest issue. 1. General. The General Specifications for inspection of material shall form part of these specifications. BARS FOR BOLTS AND NUTS 2. Material. The material from which bolts are manufactured shall be medium or commercial steel, rolled naval brass, monel metal, manganese bronze, etc., as may be specified. 3. Tests of Bars for Steel Bolts when Bars are Ordered. To be in accordance with the following requirements: (a) PHYSICAL AND CHEMICAL CHARACTERISTICS: MAXIMUM Material Minimum Tensile Strength Minimum Yield Point Minimum Elongation AMOUNT OF Purpose for Which Used P. s. Lbs. per Lbs. per Per Cent Open - hearth car- bon medium steel Commercial steel. Sq. In. 58,000 Sq. In. 30,000 in 8 In. 1 28 0.04 0.045 JFor general structu- | ral and machine work. f For miscellaneous I work where strength 1 is not important. 1 NOTE. For bars over li inches in diameter add two (2) units of per cent to figures stated for two- inch gauge length and type one test specimen; for bars 1 } inches in diameter or less type three test speci- mens shall be used. (b) TENSILE TESTS. Bars rolled from any melt shall be tested by sizes, two tensile tests to be taken from each ton or less of each size. If the results of such tests from the various sizes indicate that the material is of uniform quality, not more than eight such specimens shall be taken to represent the melt. In such cases the eight specimens shall be fully representative of the various sizes in the melt offered for test. The tensile strengths specified shall be based on the effective sectional area in the threaded portion of the bolt given in Table I. (c) BENDING TESTS FOR MEDIUM STEEL. From each size of each melt one cold- bend test shall be taken as finished in the rolls, but not less than two such bends shall be made from any melt. These cold-bend specimens shall be bent 180 flat on themselves without showing any cracks or flaws in the outer round. COMPOSITION RODS 4. General. (a) All bars shall be clean and straight, of uniform quality, color, and size, and shall meet the requirements of the latest issue of the leaflet specifications for the material ordered, i.e., rolled manganese bronze, rolled naval brass, rolled monel metal, etc. (b) Bars will not be tested when bolts are ordered. All tests shall be then be made of the finished product as required by paragraph 6 except when length of bolt is less than three diameters when tests in the bar shall be made. [384] STEEL OR COMPOSITION BOLTS AND NUTS MANUFACTURED BOLTS 5. Material. To be manufactured from medium or commercial steel, rolled naval brass rod, rolled manganese bronze rod, rolled monel metal rod, etc., as specified, and shall conform to the following: 6. Physical Tests. (a) BENDING. From each lot of bolts medium steel having the same diameter and ready for final inspection, there will be selected not less than two specimens or one for every 500 pounds or portion thereof. One-half of this number selected shall be bent cold 180 to an inner diameter equal to one-half the diameter of TABLE I DIMENSIONS OF BOLTS AND NUTS HEADS NUTS Nominal Diameter Number of Threads per Inch Effective Area of Threaded Portion Wrench Width of Square and Hexagonal Head and Depth of Head Depth of Nut Wrench Width of Square and Diameter at Bottom of Thread of Bolts and Diameter Hexagonal of Hole of of Round Nuts Blank Nuts Head a b c d e f g h Inches Sq. In. Inches Inches Inches Inches Inches i 20 0.037 f A & A 0.185 18 .060 H if H .240 f 16 .088 A A iV f .294 14 .119 li f M .344 i 13 .159 f A H .400 A 12 .203 ii H i If .454 f 11 .252 H H * i .507 f 10 .368 H TS !A .620 7 8 9 .506 1A f^ If if .731 1 8 .662 f H 1A .837 M 7 .836 itt ft H lit .940 li 7 1.051 U U 2 .065 if 6 1.261 2rs 1^ if 2& .160 U 6 1.522 2 H ii 2f .284 if 5 1.784 2A 1A if 2^ .389 if 5 2.061 2f 1A if 2f .491 li 5 2.392 2H IH if 2if .616 2 41 2.705 3 H 2 3| .712 21 4* 3.483 3f Hi 2i 3^ .962 2| 4 4.293 3f H 2^ 31 2.176 4 5.260 4* 2^ 2f 4 * . 2.426 J|. FORMULA V _j_ "* HH T^ \ S- "c? ^ | ^ V + ^ + i 3 {oi llli 37 |T 1 II a M ^ M NOTE. The dimensions given in Table I are commercial sizes; they are not United States standard. [385] STEEL OR COMPOSITION BOLTS AND NUTS the bolt, without fracture on the convex side of the bend. If the bolt is too short to permit this test to be made on the unthreaded portion of the shank, the bolt shall bo flattened hot to a thickness equal to one-fourth of its diameter and, when cold, this specimen shall be bent 180 flat on itself transversely to the direction of the length of the bolt without fracture. (b) TENSILE. The remaining specimens selected as specified in paragraph 6 (a) shall be subject to a tensile tess with the nut in place, unless the length of the bolt is less than three diameters the stress to be applied on the bearing faces of the head and nut. The bolt must meet the tensile strength specified in paragraph 3 (a) and fracture must in all cases occur in the threaded portion of the bolt. Specimens selected for tensile test but which are too short to permit this test to be made must satisfy the bending test specified for short bolts under paragraph 6 (a). Bolts larger than 1 inches in diameter shall be tested by turning therefrom If -inch studs. These studs shall be tested in a like manner as specified for testing bolts by fitting a If -inch nut at each end. 7. Heads. The heads will be plain, chamfered, faced on their lower side, or faced and chamfered as specified in the requisition. Chamfering must be at an angle of 30 with the prolongation of the upper face of the head, leaving a circle on its face, whose diameter must be equal to the wrench width as illustrated in the sketch accompanying these specifications. The heads will conform to the dimensions of Table I and must be concentric with the body of the bolt, and square with the body of the bolt. 8. Dimensions. Bolts shall conform to the dimensions given in Table I and shall have United States standard threads. The length of the bolts is to be measured from under the head to the first thread at the point, and to the end of the cylindrical shank in blank bolts. 9. Threading. (a) Unless blanks are specifically called for in the order, the length of the threaded portion of the shank must be in accordance with Table II, if possible, and if not, the shank is to be threaded to the head. (b) Bolts over 20 inches in length and over 1 inches in diameter are to be threaded for a length equal to three tunes the diameter, if not otherwise specified. (c) Bolts shall be provided, unless otherwise specified, with clean, sharp, and well- fitting tlnited States standard threads, which may be either chased or cut with a die. Nuts to be used on machinery shall fit wrench-tight. Other nuts must be either thumb- tight without shake, or a spinning fit, as specified. 10. Workmanship. Bolts must be hot forged or upset cold; all bolts made by cold upsetting process must be annealed after the heading operation; all bolts must be free from scales, abnormal fins, or other unsightly defects and must have clean, smooth threads, fitting as specified in the requisition. 11. Finish. Bolts will be specified as rough, semi-finished, or finished. (a) Semi-finished bolts and nuts require machining only on the under side of the bolt-head and nut, and the under side of the head shall face square with the body of the bolt. [386] STEEL OR COMPOSITION BOLTS AND NUTS TABLE II LENGTH OF THREADED PORTION OF BOLTS Length of Bolt DIAMETER OP BOLT (Inches) i A I A i A l to H | | 1 i i If to 2 | 1 1 1 i i 21 to 2| . . 1 i 1 1 i l 2f to 3 1 1 1 1 i l 3ito4 4| to 8 1 1 i 1 it if H 11 H li 11 11 8| to 12 1 i 11 u l| li 12i to 20 1 i 11 H 2 2 Length of Bolt DIAMETER OP BOLT (Inches) f 3 A 7 I 1 H H 1 to H H If to 2 u U If 2i to 1\ 2f to 3 11 li H H U if U 2 21 ' 3i to 4 u u 11 2 24 24 4| to 8 8i to 12 12|to20 4 H 2 if 2 2 2 21 2| 21 2* 3 21 3 31 3 31 31 (b) Finished bolts and nuts require machining throughout. 12. Variations of Blank Bolts. The Variations in size of blank bolts shall not exceed that allowed under Table III below: TABLE III Nominal Diameter Maximum Diameter Minimum Diameter Maximum Variation Nominal Diameter Maximum Diameter Minimum Diameter Maximum Variation IncH Inch Inch Inch Inches Inches Inches Inch A 0.1925 0.1825 0.010 H .9465 .9285 0.018 1 .2550 .245 .010 l .0095 .9905 .019 A .3180 .307 .011 H .1350 1.115 .020 t .3810 .369 .012 11 .2605 1.2395 .021 A .444 .431 .013 U .3855 1.3645 .021 i .507 .493 .014 A .5105 1.4895 .021 A .570 .555 .015 if .6355 1.6145 .021 .633 .617 .016 if .7605 1.7395 .021 \ i .6955 .6795 .016 if .886 1.864 .022 .7585 .7415 .017 2 2.011 1.989 .022 1 .821 .804 .017 21 2.261 2.239 .022 .8840 .866 .018 2J 2.511 2.489 .022 [3871 STEEL OR COMPOSITION BOLTS AND NUTS NUTS 13. Manufactured Nuts. The nuts for use with steel bolts may be either steel or iron as specified, and shall conform to the following: 14. Workmanship. Nuts shall be either hot pressed or cold punched from a solid bar. They must be free from scales, fins, seams, or other injurious or unsightly defects and must have cleanly and smoothly threaded holes of nominal size, square to the end faces of the nuts. All cold-punched nuts, whether blank or tapped, must be reamed square to their endjaces before tapping; this reaming process may be omitted in hot- pressed nuts. 15. Dimensions. Nuts shall conform to the dimensions given in Table I above and shall have United States standard threads, unless blanks are specifically called for. They shall be square or hexagonal, either plain or chamfered, or double chamfered, or faced on their lower sides, or counter-bored (recessed), as specified in the requisition. The chamfering to be as specified in paragraph 7. 16. Tests. From'each lot of steel or iron nuts having the same size and ready for final inspection there will be selected not less than two specimens or one for every 200 pounds or fraction thereof. One-half of the number selected shall be drifted cold until they break, the fracture to indicate either homogeneous steel or wrought iron. If fracture indicates wrought iron, the fibers must run at right angles to the axis of the hole. The remaining specimens shall be heated to redness and flattened to one-sixth of their thickness. Under this test, flaws or splits, due to defective steel or badly welded wrought iron, must not develop. 17. Composition Nuts. To be made of the same material as required for com- position rods under paragraph 4 and to conform as far as applicable to the requirements for steel nuts, including surface, threads, and fit. STUDS 18. General. The length ~of threads on studs, including taper, shall be 1 times the diameter of the stud. The length of the taper shall not exceed two threads. The thread on one end of the stud shall be a steam-tight fit and the end of the stud shall be faced square with the axis; the thread on the other end of the stud shall be a thumb- tight nut fit and the end shall be rounded to a radius approximately equal to the diameter of the bolt. When specified for use on machinery, the nut on the stud shall be a wrench fit. 19. Split Pin. When a split pin is required, the diameter and the material of the pin will be specified. MISCELLANEOUS REQUIREMENTS 20. Fit. When bolts and nuts are ordered together, one nut shall be delivered on each bolt, which must fit the bolt as specified in the requisition (see paragraph 22). Bolts ordered separately must fit a nut of standard, nominal size, as specified in the requisition. Nuts ordered separately must be of standard, nominal size. 21. Packing. Unless otherwise specified, all bolts and nuts must be packed in 100-pound boxes, made of new, sound boards of f-inch thickness, well nailed together and strapped at both ends with -inch flat band iron. The boxes must have mill- dressed outside surfaces. Each box must be clearly stenciled on one end only, show- ing the net weight, the size, and name of the contents. The manufacturer's name, contract number, and any other marks may appear on one side only. One side, one end, the top, and bottom of the box shall be left free from marks. 22. Instructions to General Storekeepers. The requisition for bolts and nuts should specify: (a) The kind and class of material required. (b) The form of the head, whether square, hexagonal, round, plain, chamfered, etc. (c) Whether or not the nut, when semi-finished or machined, is to be counter-bored (recessed). This expression should be used in lieu of the word "cupped." (d^ Whether the bolts are to be threaded or blank. [388] STANDARD TAPER BOLTS STANDARD TAPER BOLTS C American Locomotive Practice FOR NEW WORK FOR REPAIR WORK Bolt No. Length C Diam. Under HeadB Bolt No. Length C Diam. Under HeadB 4 4 in. and less D _i_ JL j n 4i 4 in and less D _|_ ^L i n 8 8 in. to 4 in. not including 4 in D 4. JL. j n 8* 8 in. to 4 in. not including 4 in D _L JL in 12 12 in. to 8 in. not including 8 in D _i_ s i n 12* 12 in. to 8 in. not including 8 in D _i_ j_ m> 16 16 in. to 12 in. not including 12 in D + | in 16J 16 in. to 12 in. not including 12 in D _i_ . ^ 20 20 in. to 16 in. not including 16 in D _j_ J& in. 20| 20 in. to 16 in. not including 16 in D _i_ ii in. This table relating to standard taper bolts for locomotives is an adaptation of dimensions given on drawings in the Locomotive Dictionary. The dimensions in table of reamers, given below, apply to the above table of taper bolts. As a standard this table has its limitations, inasmuch as other tapers are in use, notably the bolts in main and side rods for certain locomotives, Lehigh Valley design, the taper = ^ in. in 12 inches; for similar rods | in. in 12 inches is employed by the American Locomo- tive Co., and other variations could be given. [389] STANDARD TAPER REAMERS STANDARD TAPER REAMERS L- American Locomotive Practice D L A B c E F G s T Mark Reamer i 8 i f ft \ i a 4 \ \ *No. 4 i 12 \ f A i i f ' \ \ \ " 8 I 8 f 1 4 A i i ! \ i 1 " 4 1 12 ! 1 A i i f \ \ f " 8 i 8 f ift H i i i I \ f " 4 i 12 1 ift H 1 i i f i I " 8 i 16 f ift ii i i i 3. 4 \ f " 12 i 20 i ift H 1 i i f 1 I " 16 i 8 i if if i i H f \ 1 " 4 i 12 i H H \ i 11 1 \ 1 " : 8 i 16 i H if \ \ H 1 \ 1 " 12 i 20 i H if i i H 1 \ 1 " 16 i 8 i H if \ i H 1 \ 1 " 4 i 12 i H if \ 1 11 1 \ 1 " 8 i 16 i 11 if 1 1 H 1 \ 1 " 12 i 20 i H if 1 i U 1 \ 1 " 16 li 8 H H 1ft i 1 U 1 \ H " 4 ii 12 H ii ift i i U 1 \ H " 8 H 16 H ii 1ft i 1 H 1 i li " 12 li 20 ii H ift 1 } 11 1 1 li " 16 it 8 11 ii Wk i \ U 1 \ H " 4 H 12 H ft ift i i U 1 \ 11 " 8 U 16 H ii ift i i H 1 \ 11 " 12 H 20 li Ii ift i i H 1 \ 11 " 16 H 8 if Ii i& 1 ^ 11 1 \ If " 4 if 12 if li ift i i H 1 \ If " 8 if 16 if ti ift i i n 1 \ If " 12 if 20 if H ift i i 11 1 \ If " 16 Si 8 li H ift i i U 1 i H " 4 i* 12 11 Ii ift \ i 11 1 i H " 8 li 16 li li ift \ i U 1 1 li " 12 H 20 If ift i i H 1 \ li " 16 . NOTE.- 1 inch reamers taper ^ in. per foot. To allow for grinding, each reamer is made 4 in. longer than longest bolt of its class. When a No. 12 reamer has been reduced ^ in. in diameter and goes in up to the top of flutes when reaming for longest bolt of its class, by cutting 4 in. from the small end it can be used as a No. 8 reamer, and afterwards as a No. 4. [390] WEIGHT OF BOLTS AND NUTS MACHINE BOLTS WITH SQUAKB HEADS AND SQUARE NUTS Manufacturer's Standard Average weight per hundred Lgth. in Ins. DIAMETERS i A I 1 I l H ?M 3 26 38 45 72 106 157 211 286 3* 29 42 49 78 115 167 226 303 4 31 46 53 83 123 176 240 320 4 34 50 57 89 131 18. 255 337 5 37 54 60 95 139 196 269 354 51 39 58 64 101 148 206 284 371 6 42 61 68 106 156 216 298 388 6| 45 65 72 112 164 225 313 405 7 47 69 75 118 172 235 327 422 7| 50 73 79 124 181 245 342 439 8 53 77 83 129 189 255 356 456 9 58 84 90 141 205 274 385 490 10 63 92 98 152 222 294 414 524 11 69 100 105 164 238 314 443 558 12 74 107 113 175 255 333 472 592 13 79 115 120 187 271 352 501 626 14 84 122 128 198 288 372 530 660 15 89 129 135 210 304 391 559 694 16 95 137 143 221 320 410 588 728 17 100 144 150 233 336 429 617 762 18 105 152 157 244 353 448 646 796 19 110 159 165 256 369 468 675 830 20 115 166 172 267 385 487 704 864 BOLTS OF UNIFORM STRENGTH The effective area of a bolt is that corresponding to its diameter at the bottom of thread. A bolt that is subject to repeated shock or stress suffers a slight temporary elongation every time the shock occurs. In a solid bolt the smallest area which is under stress is at the base of the threads between the nut and the body of the bolt and the slight elongation due to each shock is largely localized at this point, causing the metal to crys- tallize and give way. By reducing the area of the body of the bolt until it is equal to or less than the area at the base of the threads the elongation distributes itself more uniformly through the entire length of the bolt, and thus the strain on each particle of metal is less than when it is all located between the nut and the body of the bolt. The area of the bolt can be reduced either by drilling out the center or by turning off the outside, but as the latter method weakens the bolt more torsionally the drilling is preferable. C. L. Thompson. When computing the table on page 392, the nearest ^-inch drill was selected; in ordinary shop practice a drilled hole is slightly larger than the drill used to make it, the net area of a hollow bolt at E (see sketch) may, therefore, be slightly less than given. 391 BOLTS OF UNIFORM STRENGTH BOLTS OF UNIFORM STRENGTH United States Standard Threads SCREW HOLE WEIGHT PER INCH Outside Root of Thread length Net Neck C Diam. Area Area of Solid Solid Hollow Section Dia. A Area Diam. B Area D Bolt at E A B E 1 .785 .837 .550 \ H .222 .563 .222 .156 .160 It .994 .940 .694 i I .307 .687 .282 .197 .195 U 1.227 1.065 .891 A H .338 .889 .348 .252 .252 If 1.485 1.160 1.057 A 1 .442 1.043 .421 ^299 .296 H 1.767 1.284 1.294 A If .479 1.288 .501 .367 .065 If 2.074 .389 1.515 ! H .559 1.515 .588 .429 .429 If 2.405 .491 1.746 1 If .645 1.760 .681 .495 .499 II 2.761 .616 2.051 I H .690 2.071 .782 .581 .587 2 3.142 .712 2.302 I i .785 2.357 .890 .652 .668 2i 3.976 .962 3.023 1 II .994 2.982 1.127 .857 .845 2* 4.909 2.176 3.719 ! 1A 1.108 3.801 1.391 1.054 1.077 2! 5.940 2.426 4.622 I 1* 1.353 4.587 1.683 1.310 1.300 3 7.069 2.676 5.624 I I* 1.623 5.446 2.000 1.594 1.543 3i 8.296 2.879 6.509 I H 1.767 6.529 2.351 1.844 1.850 8| 9.621 3.100 7.549 I if 2.074 7.547 2.726 2.139 2.138 31 11.05 3.317 8.641 I H 2.405 8.64 3.131 2.448 2.448 4 12.57 3.567 9.993 i Itt 2.580 9.99 3.562 2.831 2.831 [392] HEADLESS SET SCREWS COLLAR SCREWS WITH SQUARE HEADS SCREW WRENCH Counter Diam A B C Square D E F G H i K L bore M i 1 i f i f li f 1 1 H H f 1ft A f A 1ft 1ft H i A 1 H i 11 A H f ii 1ft f if f H f f 1ft f M H fft H i 4 f i* i i H f Ift f li 1 H if ft U H H 1H ft 1ft H m ft 1 1ft i if n a 2 A 1ft 1 H 2f H 1ft i 3tft ift if 2A i 1ft H 2 3ft i if Vk Jft tft ii 2f i 11 1 2i 21 i if f If i| HEADLESS SET SCREWS A set screw with projecting head, such as sometimes seen in a collar or hub of a wheel fixed upon a revolving shaft, is always to be regarded as a hazard because of the con- stant liability of the projecting head engaging the clothing of an attendant; to eliminate this hazard is the purpose of the headless and non-projecting set screw. NOTE. By slightly rounding the corners in a square socket a shortening of its long diameter is had without materially affecting the action of the wrench, provided the latter snugly fits the socket. Wrenches for hollow set screws are usually furnished by the manufacturers of the screws. [393] CAP SCREWS HEADLESS SET SCREWS United States Standard Threads SCREW HOLE SLOT Outside Diam. Root of Thread Diameters A Area Diam. Area Thds. K Min. Length Square Hexagon Depth F G H Short Long Short Long D E D E * .049 .185 .027 20 A & & 7 T* i A ft i ft .077 .240 .045 18 A A A A A ft A 1 .111 .294 .068 16 I A H A A A A A ft .150 .335 .093 14 A & H i if i 4 ft A I .196 .400 .126 13 i i If A If A A tt A .249 .454 .162 12 A A if H H A ft ft I .307 .507 .202 11 I A ft 1 A i i A 1 .442 .620 .302 10 I t H n H A A A 1 .601 .731 .419 9 1 * H if H f A i i .785 .838 .550 8 i I H H H H H if H .994 .939 .694 7 H A tt If If f if A if 1.227 1.065 .891 7 H t H f tt H A A if 1.485 1.159 1.057 6 if H H H H 1 & A U 1.767 1.284 1.294 6 If I Ift If ift i i 1 CAP SCREWS Threads, in general, follow the United States Standard; in the case of half-inch screws, however, there seems to be a preference for 12 threads, rather than 13, the standard number. Cap screws are, ordinarily, milled from square or hexagon bars of the dimensions given for heads in the table. Square and hexagon heads requiring to be finished are ground and polished from the rough; they are not milled to size, hence, the dimensions given are approximate only. Length of thread is ordinarily cut three-fourths of the length under the head for cap screws 1 inch and less in diameter, when not over 4 inches in length; when longer than 4 inches, the threads are commonly half the length. [394] CAP SCREWS Round head cap screws are milled to dimensions given in the table; the heads are therefore true to size and accurately centered. Flat and button head cap screws are milled from bars slightly larger than the diameter of head; they are not upset heads. CAP SCREWS Commercial sizes. Not United States Standard SCREW SQUARE HEAD HEXAGON HEAD ROUND AND FILJSTER HEAD Slot Diam. A Thds. Inch Short Diam. B Long Diam. C Height D Short Diam. B Long Diam. C Height Diam. B Height C Width Depth D E I 4 20 1 ii i & i i 1 i ^ i A 18 & f A i H A A A ft A I 16 i H f A li 1 A 1 A A * 14 A li & I H A f A A A 12 f H i f 1 i 1 i A ii A 12 tt li A H if A H A A A ! 11 f l& f 1 I* 1 1 f i A f 10 1 HI f i t* f l 1 A A 1 9 H i 1 U 1H 1 li 1 A i i 8 ii i H 1& i H i H H 11 7 it 1H ii if lit ii U H if A t| 7 H 2i li 11 iti H H H * A CAP SCREWS FLAT HEAD NEAJLFSI Commercial Sizes. Not United States Standard SCREW FLAT HEAD BUTTON HEAD Slot Slot Diam. A Threada per Diam. B Height Diam. Height Inch Width D Depth Width D Depth E i 40 i A & A if A A A A 24 1 A & A 4 A A A i 20 if i A i A if A IT A 18 f A A A A i A 64 f 16 f A A f if A & A 14 if A A A f If A A 12 I i A ii if H A A A 12 1 A A if If A A 11 H A i A l i i if f 10 H 1 A A li m A i 395] SET SCREWS SET SCREWS Commercial set screws do not have upset or forged heads. The diameter of screw, the short diameter of head, and the height of head are the same or nearly so. When DOG OVAL CUP FLAT CONICAL the short diameter of head exceeds that of the screw diameter by more than & inch, it is not then classed as a set screw but as a cap screw. Points of set screws vary in shape, depending upon the uses to which the screws are to be put; the leading varieties of points are shown in the accompanying sketches. Cup and oval point set screws are regular; others are special and made to order. Heads are commonly square; should hexagon heads be required they will be made to order at about 25 per cent advance over the square head net prices. SET SCREWS Commercial Sizes. Not United States Standard SCREW SQUARE HEAD HEXAGON HEAD Diam. A Threads per Inch Short Diam. B Long Diam. C Height D Short Diam. B Long Diam. C Height D 1 20 1 H i i H i A 18 A H A & if A I 16 1 H 1 1 A 1 & 14 A ! A ft \ ' A i 12 * tt i i H i A 12 A ft A A B A I 11 ! H f 1 H f f 10 f 1* 1 f 1 f 1 9 1 a 1 1 l* 7 8 1 8 l itt i i l* 1 If 7 a 1H H H 1H H H 7 H iff H a 1ft U [396J STUDS STUDS \ VAVvW / \ i/VWWA I Commercial Sizes. United States Standard Thr ads AREAS Diameter A Threads per Inch Diameter at Root of Thread B Length of Tap End C Blank D Length of Nut End E Length of Stud F Outside Diameter Root of Thread A B j 13 .400 .196 .125 i 1 If Jfe 12 .454 .249 .162 H H iff | 11 .507 .307 .202 H H iff I 10 .620 .442 .302 H I* 2rs 1 9 .731 .601 .419 1A 1A 2ff 1 8 .837 .785 .550 H If 2| i| 7 .940 .994 .694 1H 1H 3^ n 7 1.065 1.227 .892 i& if 3^ if 6 1.160 1.485 1.057 iff 2j^ 3ff il 6 1.284 1.767 1.294 H 21 4i The distance D in the table is zero, and F = C + O + E. As F is the working distance, whatever length is added to F is also to be added to D. HOOK BOLTS Diam. A SQUARE NECK HEAD 1 H if if H [397] COACH AND LAG SCREWS COACH AND LAG SCREWS Manufacturers' Standard "POINT J4-C-* Average weight per 100 screws Diameter A 1 i 7 s * I 9 e I * i 1 Threads per Inch 8 i 6 6 5 5 4 4 Length Length of Thread C Head Axffe Head Hxf Head IfA Head K* Head HxH Head U*f Head lAxf Head Hx| 2 H 8 11 15 23 25 2| H 9 13 18 26 29 43 3 H 11 15 19 29 33 48 75 3* 2 12 17 22 33 37 54 79 90 4 2i 14 19 24 36 41 60 82 99 4 2 15 21 27 39 45 66 86 108 5 2f 17 23 29 43 49 72 90 118 5* 3 18 25 32 46 53 78 98 128 6 31 20 27 34 50 57 84 106 138 7 3f 31 39 56 65 96 123 158 8 41 v. 35 44 63 73 108 139 178 9 4f 49 70 81 120 156 198 10 5 . . . . 54 77 89 131 172 219 11 5 . . t . . V v 84 97 143 189 240 12 5 :.. V 91 105 156 205 261 BOLT-HEADS, LENGTH FOR UPSET BOLT-HEADS Length oi Bar for Upset. United States Standard Heads BAR HEXAGON HEADS SQUARE HEADS Diam. A Area Short Diam. B Long Diam. C Area Square Inches Height of Head D Length of Bar E Short Diam. B Long Diam. C Area Square Inches Height of Head D Length of Bar E i .049 f iV .217 1 Mk f If .250 A 1& ft .077 If H .305 1A if If .353 If 1 .110 ft If .409 if l^ ii ff .473 H If ft .150 If If .529 H if If .610 n m i .196 1 l .663 iV H 1 if .766 TV m A .249 If H .813 !! iff If If .938 ft 1H f .307 Ift i& .979 ift 1.129 iff f .442 ft iiV 1.353 t lM ft If 1.563 i 1 .601 Ift 1.791 if ift 2.066 if 2ff i .785 If i! 2.287 i! 2f if 2A 2.641 i! 2f H .994 113 2^. 2.847 If 2 i| IT! 2 ^ 3.285 If 3 U 1.228 2 2j\ 3.464 l 2if 2 2 4.000 l 3 V if 1.485 2i^ 2if 4.146 l^ 3ir 2& 4.785 i& H 1.767 2f 2f 4.885 ift 3^ 2f 9 3H 5.641 iiV 3 if 2.074 2& 2ff 5.689 3 3f 6.566 i& if 2.405 2f 3A 6.549 if 3f 2f s 31 7.563 if 4iV 11 2.761 2H 3|f 7.475 iff 4 8.629 iff 4|f 2 3.142 3| 3|f 8.457 1ft 4^- 3f 4ff 9.766 i& 41 3 21 3.976 3 4y? 10.609 if 4H 3f 4if 12.250 if s 2| 4.909 31 4H 13.004 IM 5& 31 5M 15.016 5il 2f 5.940 41 4ff 15.642 2i 5|| 41 6 18.063 21 6M 3 7.069 4f 5H 18.524 2j^ 61^ 4f 6ff 21.391 7 3| 8.296 5 5M 21.650 2f 6|f 5 7iV 25.000 1\ 7|f 3 9.621 5f 6^- 25.019 2ii 7 5| 7ff 28.891 2H 8y^ 3| 11.045 5| 6f 28.632 21 7ff 5f 8i 33.063 21 8f s 4 12.566 61 7^ 32.489 7tt 8|f 37.516 [399] SCREW ENDS, LENGTH FOR UPSET SCREW ENDS UPSET ROUND AND SQUARE BARS American Bridge Co. Standard C * C United States Standard Threads SCREW ROUND BARS UPSET FOR A SQUARE BARS UPSET FOR A Diameter Length Weight Weight Area at Area Area Root of Diam. of Side of A Root of Thread B Thread B Round C Square D Round Bar Screw End 1st Ft. Round Bar per Foot Square Bar Screw End 1st Ft. Square Bar per Foot 1 .84 .55 4 | .44 2.00 1.50 H 94 69 4 l .56 2.55 1 91 U 1.06 .89 4 4 1 .60 2.89 2.04 1 .77 3.36 2.60 1 16 1 05 4 1 79 3.57 2.67 M 1.28 1.29 4 4 U .99 4.51 3.38 1 1.00 4.53 3.40 H 1.39 1.52 4 4 u 1.23 5.57 4.17 U 1.27 5.56 4.30 If 1.49 1.74 4 if 1.48 6.74 5.05 u 1.62 2.05 1 u 1 56 7.30 531 2 1.71 2.30 4* *i H 1.77 6.95 6.01 If 1.89 8.57 6.43 V\ 1 84 2.65 4* if 2 07 9.41 7.05 2i 1.96 3.02 5 5 i! 2.41 10.91 8.18 If 2.25 10.84 7.65 2f 2.09 3.42 5 5 li 2.76 12.51 9.39 if 2.64 12.34 8.98 2* 2.18 3.72 5* 5* 2 3.14 14.24 10.68 if 3.06 14.31 10.41 21 2.30 4.16 5i 2i 3.55 15.58 12.06 2f 2.43 4.62 5* t| 3.52 16.93 11.95 2J 2.55 5.11 6 6 2J 3.98 18.60 13.52 2 4.00 19.27 13.60 3 2.63 5.43 6 6 2| 4.43 20.71 15.07 2i 4.52 21.11 15.35 3i 2.88 6.51 6* 6* 2* 4.91 24.34 16.69 2J 5.06 25.11 17.21 3* 3.10 7.55 7 7 2i 5.94 29.45 20.20 2| 5.64 29.57 19.18 3* 3.32 8.64 7 7 2| 6.49 33.10 22.07 2| 6.25 33.65 21.25 4 3.57 9.99 7* 7* 3i 7.67 39.11 26.08 2f 7.56 39.63 25.71 [400] UPSET SCREW END DETAILS UPSET SCREW END DETAILS American Bridge Company Standard United States Standard Threads ROUND BARS SCREW SQUARE BARS SCREW Diameter Area tAddi- Diameter Area Addi- A.' _ Diam. A Area Out- side B Root of Thd. Root of Thd. Ex. over BarA Lgth. c tion. Lgt. for Upset Side A Area Out- side B Root of Thd. Root of Thd. Excess over BarA Lgth. C tion. Lgt. for Upset 4-10% f .44 1 .84 .55 24.7 4 4 4 1 .56 lj .94 .69 23.2 4 4 1 .60 U 1.06 .89 48.0 4 5 1 .77 U 1.06 .89 16.2 4 31 1 .79 U 1.16 1.05 34.2 4 4 1 1.00 U 1.28 1.29 29.4 4 4 li .99 li 1.28 1.29 30.2 4 4 U 1.27 If 1.39 1.52 19.7 4 31 H 1.23 If 1.39 1.52 23.5 4 4 11 1.56 U 1.62 2.05 31.1 4* 4i if 1.49 H 1.49 1.74 17.5 4 4 If 1.89 2 1.71 2.30 21.7 41 4 li 1.77 2 1.71 2.30 30.2 41 41 U 2.25 21 1.96 3.02 34.3 5 5 if 2.07 21 1.84 2.65 27.7 41 4 If 2.64 2f 2.09 3.42 29.5 5 4* if 2.41 21 1.96 3.02 25.6 5 4 If 3.06 2.18 3.72 21.3 51 41 U 2.76 2f 2.09 3.42 23.8 5 4 U 3.52 2f 2.43 4.62 31.4 51 5 2 3.14 21 2.18 3.72 18.3 51 4 2 4.00 21 2.55 5.11 27.7 6 5 2f 3.55 2f 2.30 4.16 17.2 51 31 21 4.52 3 2.63 5.43 20.2 6 41 21 3.98 21 2.55 5.11 28.4 6 21 5.06 31 2.88 6.51 28.6 61 51 2f 4.43 3 2.63 5.43 22.5 6 41 2f 5.64 31 3.10 7.55 33.8 7 6* 2* 4.91 31 2.88 6.51 32.6 61 51 21 6.25 3J 3.32 8.64 38.3 7 7 2f 5.41 31 2.88 6.51 20.3 61 41 2f 6.89 3f 3.32 8.64 25.4 7 51 2f 5.94 31 3.10 7.55 27.1 7 51 2f 7.56 4 3.57 9.99 32.1 71 61 21 6.49 3f 3.32 8.64 33.1 7 6 21 8.27 41 3.80 11.3 37.1 8 71 3 7.07 3f 3.32 8.64 22.2 7 5 3 9.00 41 3.80 11.3 25.9 8 6 31 7.67 4 3.57 9.99 30.3 71 6 31 9.77 41 4.03 12.7 30.5 81 7 31 8.30 4 3.57 9.99 20.5 7* 5 31 10.6 4.26 14.2 34.6 81 71 [401] TURNBUCKLES TURNBUCKLES United States Standard Threads Diam. of Screw A LENGTH Diam. E WIDTH SECTION Thread K Weight v- Thread C Overall D F G H i | 6 f 7| 1 1* f l f 4 1 A 6 if 7H 1 H A f 4 Ii f 6 H 71 I* 1^ H A f 4 Ii f 6 ii 81 11 7 If 1ft ii 1 4 2 1 6 1A 8f 2 t 1 4 3 i 6 ii 9 If 2JL i& JL H 4 4 Is 6 m 9| ijf 2^ 1A i U 4 5 11 6 H 2 2 A 1ft ^ ii 4 6 If 6 2A 10| 2j^ 2H 1 if 4 7 ii -6 2i 2| 3 if f if 4 8 if 6 2A 101 2A 31 2 f H 4 10 if 6 2f HI 2f 3| 2i f 2 4 11 il 6 2H Hf 2ft 3A 2A H 21 4 12 2 6 3 12 3| 3f 2f 21 4| 14 2i 6 3A 12f 3A 3H II 4i 17 21 6 ' 3| 12f 31 4A 2H H 2 5 20 2f 6 3A 131 31 4| 2 1 2f 5 22 2* 6 3f 13? 31 II 3 5 25 2f 6 4? 141 41 5i 31 H 31 5 33 21 6 4| 141 41 6f 31 if 31 5i 33 21 6 4A 14f 4| Bi 3 JL 1* 31 6 36 3 6 4| 15 4| 5H M: lX 3* 6 40 31 6 41 15f 5 6 31 4 6i i 50 31 6 51 16j 5f 6-H 41 1* 4 7 65 ii 6 5f 171 5f 1* 5 7 95 4 6 6 18 7^ 4| 5 7| 108 [402] SLEEVE NUTS SLEEVE NUTS United States Standard Threads SCREW ENDS Diam. Bar D Thread E Length F DIAMETERS Weight Diameter A Threads per In. Length C Short G L Inside I 1 9 4 f If 7 If 11 H 3 1 8 4 1 if 7 If 11 u 3 H 7 4 f if 7 2 2A If 4 H 7 4 1 if 7^ 2 2^ If 4 If 6 4 1 2 8 2| 21 If 5 if 6 4 H 2 8 2f 2f If 6 if 5* 4 H H 81 2f 3^ H 8 if 5 4 if 21 8* 2f 3^ H 9 il 5 4 if 2| 9 3i 3f 2| 10 2 4* 41 if 2| 9 31 3f H 11 2i 4* 4* if 2f 91 3* 4^ 2| 14 2* 4* 5 if 2f 9* 3* *& 2f 15 2| 4* 5 if 3 10 31 4* 2f 18 2| 4 5* 2 3 10 31 4^ 2f 19 2f 4 51 2i 31 10* 4i 4H 21 23 21 4 6 2| 31 10| 4i 4H 21 23 21 4 6 2| 3* 11 4f 5f 3| 27 3 3* 6 2f 3* 11 4f 5f 3i 28 31 31 6* 2* 3f HJ 5 5M 3f 35 3* 31 7 2f 4 12 5f 61 3| 40 31 q 7 2| 41 12* 5f 6H 31 47 4 3 n 3| 4* 13 6| 7A 4i 55 [4031 PLATE WASHERS SPECIFICATIONS FOR WASHERS NAVY DEPARTMENT 1. Washers to be made of wrought iron or mild steel and to be of the best commercial grade and quality, and to be so certified to by the manufacturer. 2. Each commercial package to be plainly stamped with the name of the manufacturer. 3. The diameter of the hole is the necessary requirement, and a slight variation of the gauge or outside diameter will be tolerated in the discretion of the board of inspection. TABLE I PLATE WASHERS Diam- eter Thick- ness, Wire Gauge Size of Hole Size of Bolt Approx- imate Number in 100 Pounds Diam- eter Thick- ness, Wire Gauge Size of Hole Size of Bolt Approx- imate Number in 100 Pounds Ins. No. Inches Inch Inches No. Inches Inches & 18 (3-64) I A 44,075 2| 9 (5-32) If H 520 i 16 (1-16) A i 13,900 3 9 (5-32) If H 400 I 16 (1-16) 1 A 11,250 si 8 (11-64) a if 320 1 14 (5-64) A t 6,570 3 8 (11-64) if H 275 14 (5-64) i A 4,300 3| 8 (11-64) if if 245 H 12 (3-32) A i 2,680 4 8 (11-64) If H 220 H 12 (3-32) I A 2,250 4i 8 (11-64) 2 U 200 i! 10 (1-8) H 1 1,300 4* 8 (11-64) 2i 2 180 2 10 (1-8) H 1 1,010 4f 6 (7-32) 2f 21 110 2i 9 (5-32) H 1 860 5 6 (7-32) 2f 21 91 2* 9 (5-32) 1A i 625 TABLE II PLATE WASHERS (ADDITIONAL SIZES) Diam- eter Thick- ness, Wire Gauge Size of Hole Size of Bolt Approx- imate Number in 100 Pounds Diam- eter Thick- ness, Wire Gauge Size of Hole Size of Bolt Approx- imate Number in 100 Pounds In*. No. Inch Inch Inches M>. Inches Inches F 18 i A 45,500 li 12 f A 3,900 f 16 A i 21,500 If 12 f A 3,000 f 16 f A 16,500 li 12 H f 4,100 1 14 A f 11,500 If 12 H f 3,200 1 14 * A 7,400 11 10 ii f 2,150 a 14 *. A 5,450 H 10 if i 4 2,200 a 12 A \ 4,800 if 10 H f 1,400 H 12 A \ 3,650 2 9 M 1 1,150 if 12 A \ 2,000 2i 9 1A 1 940 [404] &RASS WASHERS TABLE III PLATE WASHERS (EXTRA SIZES) Diam- eter Thick- ness, Wire Gauge Size of Hole Size of Bolt Diam- eter Thick- ness, Wire Gauge Size of Hole . : i Size of Bolt Inches No. Inches Inches Inches No. Inches Inches i & 16 T6 I 2 9 1ft 1 f 16 ft f 2 9 H 1| 1 14 i A 2j 9 it 1 14 * i 2| 9 U u 1ft 12 i 2| 9 H i^ it 12 H 1 2f 9 if ii. 10 H f 3or3i 9 H if 10 it f 3 8 if li 10 f 3^ or 3 8 if 10 H 1 3* 8 M U 10 H 1 3f 8 H if if 10 1ft i 4 8 2i 2 TABLE IV SQUARE WASHERS Approx- Approx- imate imate Wide Thick. Hole Bolt Number Wide Thick. Hole Bolt Number in 100 in 100 Pounds Pounds 7ns. Inch Inches Inches Inches Inch Inches Inches li i ft f 1,300 4 f n H 65 If i i 7 TF 1,100 4| f H U 48 2 A ft 1 500 5 f if H 40 21 i H f 315 6 f U U 28 21 i H f 250 6* f if if 24 3 -i Ii 1 165 7 1 2i 2 21 3| f 1A 1 87 BRASS WASHERS NAVY DEPARTMENT 1. To be made from sheet brass, smoothly punched, without burrs. 2. Sizes to be as specified. The following sizes are those most commonly used: Outside Diameter Inside Diameter Thickness Outside Diameter Inside Diameter Thickness Inches Inch Inch Inches Inch Inch 1 ft 0.065 H . ft .083 ft i .042 If f .083 f A .053 If H .106 1 f .053 2 f .103 H i .063 2* 7 8 .115 [405] CAST IRON WASHERS 3. To be packed in well-made wooden boxes, one size of washer per box, each box marked with the name of the material, the quantity, size, and the name of the manufacturer. 4. Each delivery to be marked with the name of the material, the name of the con- tractor, and the requisition or contract number under which the delivery is made. CAST IRON WASHERS C Diameter of Bolt A Diameter Hole B Diameter Top Diameter Bottom D Area Bottom D Thickness E Approx. Weight Each Approx. Number in 100 Pounds i f H 2 3.14 \ 0.20 500 I f if 2| 4.91 f .40 250 I 1 2 3 7.07 f .69 144 1 1 2i 31 9.62 1 1.10 91 1 U 21 4 12.57 1 1.64 61 U 11 2| 4| 15.90 U 2.33 43 U if 3 5 19.64 n 3.20 31 H ii 3i 5* 23.76 If 4.25 23 M if 3* 6 28.27 Ii 5.52 18 if if 3f 6* 33.18 If 7.02 14 H if 4 7 38.48 If 8.76 11 U 2 4| 71 44.18 U 10.79 9 2 2| 4* 8 50.27 2 13.10 7 [406] FOUNDATION BOLTS AND WASHERS FOUNDATION BOLTS Upset Screw and Cotter Heads, and Cast Iron Washers SCREW Bar B Dia. D LENGTH Wdt. I COTTER WASHER Diam. A Lgth. E F G H K L M Dia. N Dep. Th'k P Dia. Q * 1| 4 H If 6 2 2| 2 A 2 3f, 21 H 3 * 3! 9 U 4 14 H 61 21 2f 2| 2T 4 2| .'2 31 * 4 10 if 4 if 21 71 21 21 21 i 2f 41 2f 21 31 A 41- 11 3 4* if 21 7f 2| 3 2! A 2| 41 2| 2| 34 A 4| 11 2 41 H 2| 8i 2* 31 2K A 2f 4| 3 24 3! f 4f 12 2| 4* U 24 81 2| 31 2i 1 21 41 31 2| 31 f 41 13 21 5 U 2| 8f 2f 3* 2f I 3 5 31 21 4 H 5 14 2| 5 H 2f 94 2f 3f 2| H 3| 51 31 21 41 H 51 14 2* 5 2 21 91 2f 3f 2f H 31 51 34 3 41 i 4 64 15 2f 5* 24 3 9f 21 4 21 f 31 5f 3f 3i 4| f 5f 16 2} 5| 24 34 101 3 41 3 f 3! 51 31 31 44 f 51 17 2| 6 2* 3J 10f 34 4| 31 H 3f 64 4 3| 4| H 64 17 3 6 2f 34 ill 31 4f 31 1 4 61 41 31 4f if 61 18 31 6 21 3f 11! 3f 5 31 if 41 6f 44 31 5 1 6f 20 31 7 2f 4 12* 31 51 3f 1 4f 74 41 4J 5f 1 61 21 3f 7 2| 41 isi 3f 5! 3f i& 5 71 51 4f 54 1 71 22 4 7| 3* 41 14 4 6 4 14 51 8 54 4f 6 1 8 24 FOUNDATION BOLTS Foundation bolts for heavy machinery should not be leaded into cap stones if it can be avoided, even though the cap stones be of considerable depth or weight and anchored to foundation below. If such bolts are required merely to fix a self-contained machine in position, no vibratory strains being transmitted to the bolts, there is no objection to their use, but foundation bolts proper should extend to bottom of masonry or concrete. The illustration at top of page 408 shows a bolt with tapering head much wider at the bottom than at the neck. The cavity in the stone cap is similarly widened at the bot- tom. The bolt-head is jagged to secure a firmer hold on the lead filling which is poured into the cavity and around the bolt after the latter has been correctly located* (407) FOUNDATION BOLTS AND WASHERS FOUNDATION BOLTS Diam. i i i i i U H Square U i U it H if 2 D 2 2* 3 3 4 5 6 1 u u i 11 H if H 21 2| U H H 2 21 2| 2f FOUNDATION BOLTS AND CAST IRON WASHERS United States Standard Bolts SCREW BOLT-HEAD WASHEK Diam. A 1*2* Short Diam. E Thick. F Side of Square G Side of Square Depth Thickness Diam. Hole M Side of Square K L I fc| 11 1 H 6 U 1 f 1 21 1 2* i* I Ift 6* H 1 H 1 2A 1 3 U H 11 7 H f f H 2| U 31 i U 2A 7* U i H H 2H tl 3* 2 i 2i 8 H f 1 if 31 U 3i 2& U 2A 81 li f If ii 3* U 4 2| iH 2| 9 2 i i if 3f II 4 2A IA 2H 10 H i 1* H 3H U 4 at if 3 11 21 i H H 4 if 4* 2H II 3& 11 2f i I* 2 4& 2 41 31 IA 3f 12 a* i U 2| 4f [408] EYE BOLT HEAD EYE BOLT HEAD BAR SCREW EYE BOLT HEAD Dia. A Area Diam. Root of Thread B Area Diam. Th'k- ness E Width F Area EXF Diam. Th'k- ness I Width K Area IXK C D G H 1 .196 .400 .125 A 1 A f .137 A 1 ft f .137 A .249 .454 .162 1 H i H .172 f 1 4 H .172 I .307 .507 .202 1 U A H .254 H 1A A f .234 I .442 .620 .302 1 if I H .352 H 1A f if .352 7 8 .601 .731 .419 1 11 & 11 .492 1 i! A 11 .492 1 .785 .837 .550 H 2| f H .625 1 2 1 H .625 11 .994 .940 .694 1A 2A A if .773 U 21 A if .773 u 1.227 1.065 .891 1A 2if ii U .031 11 2| H U 1.031 If 1.485 1.160 1.057 1A 3A f 1H .266 if 21 i itt 1.266 u 1.767 1.284 1.294 H 3f H 1H .473 11 3| itt 1H 1.473 i! 2.074 1.389 1.515 U 3! 1 ill .695 if 31 1 1H 1.695 if 2.405 1.491 1.746 2 31 H 21 .992 if 3f if 2| 1.992 l| 2.761 1.616 2.051 2A 4A 1 2i 2.250 U 31 i 21 2.250 2 3.142 1.712 2.302 2A 4A i& 2| 2.523 2 41 1A 2f 2.523 21- 3.976 1.962 3.023 2f 5| U 2f 3.281 21 41 U 2| 3.281 2* 4.909 2.176 3.719 21 5f if 3 4.125 2* 51 if 3 4.125 2f 5.940 2.426 4.622 3i 6* H 31 4.875 2f 5f U 31 4.875 3 7.069 2.676 5.624 3| 6f U 3* 5.688 3 61 if 3* 5.688 [409] EYE BOLT PINS EYE BOLT PINS IN DOUBLE SHEAR Without end thrust Diameter A B c D E F G H i K f A t ' \ f i i f 1 f 1 A A i 1 i i f i 1 4 1 i 4 i A 1 1 A H A 1 *A If A A 1A 1 A 1A A 1 1A A 1 f 1A A A H f H |A A ! f IA A A if f H fA 1 f H 1A A A H f H if f f H if A A itt 7 Iff ii U A f f H A A 1H A H 2 A 1 f 2 A 3^ 2 i U 2| A 1 H ii A i 2| f H 21 i i H 2i A i 2i i 2 2f 1 i I 2| A i 2A A tl 2H A H if 2H A A 2f I 2 2H 1 H i 2H A A 3 f 2f 3i H if 1A 31 i H 3f f 3 3J I 1* H 3^ i f 3| f [410] BOLTS FOR FLANGES EYE BOLTS FOR FLANGES B. VR SCR EW HE AD c !ASTIN< 3 Over Diam. A Area Root of Thread B Area C D E F G H I K L All M 1 .196 .400 .126 A 1 A f tt i } f f Itt I .307 .507 .202 H 1A A f H A H H f Itt f .442 .620 .302 H 1A f H l f H tf H 21 1 .601 .731 .419 1 H A H 1A tt H 1A 1A 2& 1 .785 .838 .551 1 2 i li if f 1A H 1A 21 H .994 .939 .693 H 21 A if H H 1A 1A 1A 31 li 1.227 1.064 .890 li 2| H li if 1 1A 1A 1A 3f H 1.485 1.158 1.054 if 21 f itt 1H tt 1A if 1A 3tt H 1.767 .283 1.294 H 31 H 1H 1H i if H itt 3H If 2.074 .389 1.515 if 3f 1 1H 2A 1A if 2 H 4A U 2.405 .490 1.744 if 3f H 2| 21 H itt 2A 2 4| H 2.761 .615 2.049 li 3f 1 21 2| 1A 2 2| 2i 4f 2 3.142 .711 2.300 2 i| 1A 21 2* H 2i 2^ 21 5 [411] BOLT ENDS WITH SLOT AND COTTER BOLT ENDS WITH SLOT AND COTTER Rigid Connection BAR COLLAR SHANK SLOT CAST Boss Diam. A Area Dia. B Thick- ness C Dia. D Length Width H Depth F Dia. K Length E p G L M N 1 .785 H H H 1 li 1 A li 2i H li f li .994 2| 1 li 1 itt li A if 2^ li Itt f U 1.227 2i 1 If If H li f IA 21 1A 1H A H 1.485 2| H 11 H 2^ if f l|i 3| IA 2 i li 1.767 21 1A 1 IA 2i H A il 3| 1H 2i i if 2.074 21 If lit 1A 2A if A 2 3f H 2A A if 2.405 3i if 1 1A 2f if i 2& 4 2 2^ A if 2.761 31 i& 2^ iH 2M H i 2A 4| 2i 2f A 2 3.142 3* 1A 2| if 3 2 A S 4^ 21 2| f 21 3.976 4 if 2 2 3f 2J f 2H 5| 2A 3^ H 2* 4.909 41 H 2f 2& 3f 2 H 31 51 2H 3f H 2f 5.940 41 2i 3& 2& 2f f SA 6i 3i 3H f 3 7.069 Si 24 3A 2f 4| 3 If 31 6f 3f 4 if 31 8.296 5| 21 31 21 41 3J H 4^ 71 3f 4& 1 3| 9.621 6* 2| . 31 3 5i 3^ 1 4f 71 3H 4f if 3f 11.05 6* 21 4f 3i 5f 3f H 4H 8| 4^ 4H i 4 12.57 7 3 4 3* 6 4 i 5 9 *i 51 i Proportions in this table are based on diameter of bar A and corresponding upset screw ends, for which see special table. [412] BOLT ENDS WITH SLOT GIB AND KEY BOLT ENDS WITH SLOT GIB AND KEY FOR RESISTING TENSION ONLY 'US T BAR Diam. B C D E F G H I K L M Diam. A Area 1 .785 if 1 if A 1 2f If If f U i It .994 u If in A if 2f If Itt A If 1 U 1.227 it it i! f tf 2| If H f 1* i if 1.485 if if 2^ f if si if 2^ 1 1 A tt 1.767 Hi if 2i A if 3f 1H 21 A U A if 2.074 1H if 2^ A if 31 iff 2A f 2 f if 2.405 Iff tf 2f 1 U 4 l 2f H 2^ f if 2.761 2^ U 2H 1 if 4i 2^ 2M H 2^ f 2 3.142 2| 2 3 ft 2 4* n 3 1 2| A 2| 3.976 2f 2f 3f f 2j 5| 2^ 3f 1 2H A 2 4.909 2| 2i 31 B 2| 5f 2| 3f H 3| f 81 5.940 3^ 2f 4f i 4 2f 61 3^ 4i 1 3A f 3 7.069 3& 3 4 ft 3 6f 3A 4f ii 3| A af 8.296 3f 3f 4| H ai 7i 3f 41 ii 4^ f 3f 9.621 3| 3* 51 1 31 71 31 5f 1A 4f ii 3f 11.05 41 3f 5f 3f 8f 4f 5f t 4H H 4 12.57 4f 4 6 1 4 9 *f 6 If 5 f WRENCHES The open-end wrench sketched for accompanying table of dimensions has the long diameter of nut in line with the center of the handle; this is a common but not universal practice. To meet service requirements, open-end wrenches are made with the center line of opening ranging from 15 to 45, as shown in the accompanying sketches; what- ever the angle, the proportions for the head are not changed. An open-end wrench, with head at 45, is frequently used in place of a hammer during erecting operations, thereby subjecting it to distortion or breakage. The ordinary proportions are such that the little surplus strength a wrench may have is quickly dissipated by usage wholly foreign to its design. A wrench to withstand such service must be more liberal in its dimensions than indicated in the table, and should be specially forged. Reference may be here made to those special wrenches (sometimes called flogging wrenches) that are employed in setting with a sledge such nuts as cannot be properly tightened by means of a standard wrench. In general, such wrenches have the same dimensions as given in the table for open-end wrenches, excepting only that no H131 WRENCHES reduction is made in the thickness of handle; that is, thickness of head C continues and takes the place of G. This added thickness presents a larger surface for the face of the sledge when driving a nut to its final adjustment. The handle is always short, seldom more than half the tabular length. A wrench with an opening at each end is much used, especially for medium and small bolts and nuts, but for large work such wrenches are too heavy and otherwise inconvenient. For extra heavy work box wrenches are best; a sketch and table of proportions are given. The eye at the end of handle provides for the use of a rope enabling several men to assist by pulling, or for the insertion of a tackle hook, if unusual tension is required. Framed structures requiring dimensioned timber in the larger sizes, such as com- monly used in the construction of bridges, trestles, framed roofs of wide span, seldom have other than square nuts; an efficient wrench, easily forged in the field, is shown in accompanying sketch together with table of working dimensions. PROPORTIONING A WRENCH FOR A HEXAGON NUT Describe a hexagon corresponding in size to that of the nut, A being its short diameter. Draw a line K, from the center through one corner of hexagon. With the corner L as a center and B as a radius, describe a short arc inside the hexagon. Lay off the width D (in the accompanying table D approximates 0.5 A), and with B as a radius, describe a short arc inside the hexagon intersecting the first one at M. With M as a center and B as a radius, describe the outer curve of the jaw to the line K; the distance from this intersection to center of hexagon is the radius E for the lower connecting curve. [414] WRENCHES WRENCHES Diameter Bolt A B c D E F G g H I I i i 1 i ti \ \ A i i .4 A if A i A H A A & i A 5 1 H I A & f f f i & 6 ft H A f f H H H A & A 7 i 7 8 1 A A if f i 4 A A \ 8 A & A i 1A M M H A A 9 1 1A f A H 1A H if H & f 10 f H I f f 1A H 7 f i f Hi 1 1A H H If 1A 1A H A & 1 13i 1 if If if H if H i A A i 15 H 1H 1A 7 8 1! 1M if i A A H 17 U 2 H H 1 2^ 1H 1A H A H 19 if 2A H 1 1A 2f m U * H if 21 H 2| if 1A 1A 2A 2| H H H H 22 if 2A H 1A H 2f 21 1A A H if 24 if 2| 1A H if 3 2A H A f if 26 H 2H iH 1A 1A 3| 2A 1A H f H 28 2 3i 1H if 1A 3f 2f if f f 2 30 2i 3* 2 H if 3f 21 1A & f 2| 32 2* 31 2i if m 4A 3 H B M 2i 34| 2f 4i 2A 1M 2i 4A 3A 1A f if 2f 36f 3 4f 2f 1H 2i 4H 3f Hi H A 2i 39 3i 5 2| 2 2A 5f 3 if M A 2f 41 3* 5f 3A 2i 2f 5f 3H Hi ft if 2f 43| 3| 5f 3A 2f 21 6A 3H H & H 21 45f 4 6i 3* 2^ 3 6A 4 2 i i 3 48 [415] WRENCHES WRENCHES FOR STRUCTURAL WORK For structural work, whether in the mill or in the field, open-end wrenches with a tang for bringing the bolt holes into line are used to the practical exclusion of every other kind. When the wrench is flat it is called a Construction Wrench; when the handle is offset it is called a Structural Wrench. The opening for nut may be either straight or at an angle; if the latter, the angle is commonly 15 degrees. A table of working dimensions for sizes in general use is given. WRENCHES FOR STRUCTURAL WORK Dia. Bolt A B c D E p G H i K L M 1 1 * A A H 1 A i 1 4 1 12 I 1A f A A 1A i 1 1 i 4| 1| 14 ! 11 If 1 f iH a f i f 5 U 15 i 1A H f f 1A a A H f 5J If 16 1 if H 1 H U a i H 1 6 If 18 a iH 1A i i iH if i H 1 6i If 20 a 2 1A ii l 2A U A U i 7 If 22 [416] WRENCHES FIELD WRENCH FOR SQUARE NUTS For United States Standard Nuts Boll, Diam. A Side of Nut B c D E F G H K 1 H H 1 E M 1 H A 15 1| 1H 1 f 1 1 f & 17 if 2 l f 1 1 i A 19 H 2^ H H H i A 21 if 2f H i H H i f 22 if 2& If H H i f 24 if 2| if f if U H f 26 U 2H if f if U H 28 2 3i H f H if U 1 30 21 3^ H f H if H f 32 2| 3| 2 f 2 H H f 34 2| 4i 2 1 2 H H f 36 3 4f 2 1 2 if H f 39 [417] WRENCHES Box WRENCHES FOB HEXAGON NUTS Diam. Bolt A B c D E p G H i K L 1 H 1 f H i f l f 15 li 1H A i 4 If 1 f 1 A 16 H 2 f 1 H A 1 . . M A 18 if 2A f 1 U A i H A 20 li 21 f 1 2 & H U i 22 if 2& 7 T6 1 2| -i 1A . . il i 24 if 2| A if 2i f if il 1 26 11 2M A H 2f 5 8 n if i 28 2 3| 11 2| ii If if A 30 21 31 1 if 2f H H A 33 21 31 i H 21 f 2 2 1 2 A 36 2| 41 A if 3 H' 21 2 1 2 A 38 3 4f A if 3i 1 2f 21 1| 21 f 40 31 5 f 11 3f 7 I 2f 21 H 21 f 42 31 5f H 2 3f If 2H 21 U 21 f 44 3f 5| H 2i 3! if 3 21 li 21 f 46 4 6i i 4 2i 4 1 31 21 If 21 1 48 41 6 f 2f 41 1 3f 21 li 21 f 51 4| 61 H 2i 4f 1 3f 21 H 21 f 54 41 7f if 2f 4i 1 31 21 ii 21 f 57 5 7f 1 2| 4f 1 4f 2* il 2* H 60 51 8 1 2| 4f 1 41 2* il 2| H 63 5 8f 1 21 5 1 4i 2| il 2i H 67 51 8| H 3 5 1 4f i H 2 H 70 6 9i 1 3 51 1 41 2f if 2f f 72 61 9 1 3i 5i 1 5i 2f if 2f f 72 8 91 1 3i 5f 1 5f 2| if 2| f 72 61 101 1 3f 51 1 5 2| if 2f f 72 7 10| 1 3| 6 1 5f 2f If 2i f 72 7* 11 i 3f 61 1 6 2| if 2| f 72 n 111 1 3f 6| 1 61 2f 11 2f i 4 72 71 Hf i 31 6f 1 6f 2| U 2} f 72 8 12| H 4 6f 1 6f 3 1} 3 1 4 72 8i 12i H 4i 7 1 61 3 H 3 f 72 81 121 H 4i 71 H 7 3 H 3 1 4 72 81 131 H 4f 7f H 71 3 H 3 1 4 72 [418] WRENCHES Box WRENCHES FOB HEXAGON NUTS (Cont.) Diam. Bolt A B c D E F G H i K L 9 13| 1A 7| ii 7f 3 li 3 1 72 9i 14 IA 4f 71 ii 7f 3 u 3 I 72 9 14| n 4| 8 ii 7| 3 3 3 1 72 9| 14f li 4| 8i H 8 3 li 3 t 72 10 15| I* 5 8f if aft 3 li 3 1 72 10i 15i 1* 5| 81 li 81 3 ii 3 1 72 10* 15| 1* 5i 8| It 8f 3 H 3 1 72 lOf 16i If 5f 9 H 81 3 H 3 1 72 11 16f If 5 9* li 9f 3 II 3 1 72 III 17| n 5! ft li w 3 XI 3 f 72 12 18| li- 6 10 li 10 3 H 3 I 72 SOCKET WRENCH When a nut or tap bolt is situated so that an ordinary open-end or box wrench can not be used, a socket wrench as shown in accompanying sketch may be employed. The design permits preliminary adjustment of nut by means of an ordinary wrench applied to the square provided at the free end, the final tightening being accomplished by means of a long bar inserted in one or other of the holes provided in the square head. A table of working dimensions is given. SOCKET WRENCH Bolt Dia. A B C D E P H I K L M N 1 If 2| 11 11 2^ 1 If H 7 8 If 3i 1 l H Itt w H m 2^ 1 If if f If 3i 1 1 u 2 2| ii 1H 3 H 2 l 1 li 3^ H u H 2& 2H if 2 3i li 2 l 1 If 3^ H li H 2f 3^ if 2i 3A 11 2i li if 3i u U if 2& 3& 2 2A 3M H 24 ii li if 3f u if if 2f 31 2| 2^ 4^ ii 2* ii li If 4i li U H 2ft 3! 1 2f 4f if 2| 1A ii if 4f li H 2 31 4 2f 2f H if 2f if if If 4f If U 2i 31 4^ 2f 3 51 ii 2f if if H 4f If If [419] BLACK, GALVANIZED AND COMPOSITION SPIKES SOCKET WRENCH (Cant.) Bolt Dia. A B c D E F H I K L M N o H N" i-iN H Hi CM CM CO CO CO CO r* 31 41 4f 5 5f 5f 6| 41 5f 5H 61 6| 7& 7f 21 3i 3f 3f 4 41 4* 3f 3H 4 4& 4f 5 51 5f 6& 6f 71 7f 8& 8H 2 2| 21 2* 2f 2f 3 3] 3 31 31 3* 3f 4 U If U H if H if H H if if if U 2 2i 2| 21 21 2* 2f 2f 41 41 51 51 5f 61 61 H H if if if H 2 i 2 2i 21 2i 2f 2f 3* BLACK, GALVANIZED, AND COMPOSITION SPIKES NAVY DEPARTMENT BLACK AND GALVANIZED SPIKES 1. Material. To be well made of wrought iron or mild steel, and clean-cut. 2. Galvanizing. Galvanized spikes shall be properly protected by a uniform and smooth coating of zinc applied by the hot galvanizing process. 3. Heads. To have diamond-shaped heads l /i inch wider than the width of the spike. 4. Tests. Spikes shall be capable of being bent through an angle of 180 to a diam- eter equal to the thickness of the spike without showing signs of cracking. COMPOSITION SPIKES 5. Material. To be cast from a good grade of brass and be free from blow-holes, sand-holes, slag, and dirt. 6. Heads. To have square countersunk heads with a slightly convex top. Heads to be % inch wider than the widths of the spike. 7. Tests. Spikes shall be capable of being bent through an angle of 60 without showing signs of cracking. When broken, the fracture shall show a homogeneous structure. " GENERAL 8. Points. All spikes shall be made with wedge-shaped points. 9. Sizes. The following list shows the various lengths of commercial spikes for the different sizes of stock: Square Dimension Length Over All, Inches Square Dimension Length Over All , Inches Inch Inch 1 3, 3i 4, 4|, 5, 5J, 6, 7, 8 i 6, 7, 8, 9, 10, 12, 14,16 & 4, 4|, 5, 5|, 6, 7, 8 I 10, 12, 14, 16 t ' 4*, 5, 5i, 6, 7, 8, 9, 10, 12 f 14, 16 & 6, 7, 8, 9, 10, 12 10. Packing and Marking. All spikes to be packed in kegs containing 100 pounds net. Each keg to be marked with the name of the manufacturer, the name of the material, the size, and net weight contained. 11. Deliveries. All deliveries to be marked with the name of the material, the quantity, the name of the contractor, and the requisition or contract number under which delivery is made. [420J SECTION 6 GENERAL SPECIFICATIONS FOR INSPECTION OF MATERIAL NAVY DEPARTMENT 1. General Specifications. These general specifications form part of leaflet specifi- cations (when so stated in the leaflet) issued by the Navy Department. Further instructions to govern special cases may be issued by the bureau concerned. 2. General Inspection and Test Requirements. All material for which tests are prescribed shall be inspected and tested by an inspector representing the bureau con- cerned, subject to restrictions mentioned herein or in the leaflet specifications, before being finally accepted by the Navy Department, attention being invited to paragraph 57. Shipment in advance of authority from the inspector will be at the risk of the manufacturer. GENERAL QUALITY 3. Uniform Quality to be Supplied. All material shall be of uniform quality through- out the mass of each object, and free from all injurious defects. The discarding of inferior portions of ingots, treatment, and manufacture generally shall be so conducted as to insure uniformity in the quality of the metal of each heat, lot, or object submitted for inspection. 4. Testing. All material for which tests are prescribed shall, when practicable for the bureau so to arrange, be tested and inspected at the place of manufacture, and shall be passed by the inspector, subject to the restrictions mentioned herein, as having complied with the particular specifications under which the material was ordered, before acceptance at the navy-yard or ship-yard. 5. Special Material or Treatment. With the approval of the bureau concerned, special material or special treatment, or both, may be used to obtain the qualities speci- fied in the leaflet specifications. CHEMICAL PROPERTIES 6. Chemical Analysis Analysis by Manufacturer. Drillings, turnings, or cuttings for chemical analysis must be fine, clean, and dry, and must be so taken as to repre- sent fairly the heat, lot, ingot, or other object for which the analysis is taken. The inspector representing the bureau concerned may have these drillings, turnings, or cuttings taken from test coupons, or from any part or parts of the material represented by the analysis, provided in the latter case that by so doing the material will not be rendered unfit for use. Part of each sample for analysis shall be furnished the manu- facturer if he desires it, the part retained by the inspector to be sufficient for three analyses. The inspector may require the manufacturer to furnish him with a chemical analysis of each sample with satisfactory evidence that such analysis has been prop- erly and carefully made. A certificate from the party representing the manufacturer in making this analysis may be required. 7. Analysis by Government. Chemical analyses which are made at the expense of the Government will be made as directed by the bureau concerned. 8. All metals of a proprietary nature shall be subjected to a chemical analysis. In case they differ from the specifications for standard mixtures they shall not be accepted unless authorized by the bureau concerned. PHYSICAL TESTS AND TEST PIECES 9. Care and Calibration of Testing Machines. Tensile tests should be made by the use of a testing machine of standard make, kept in good condition. All knife edges [421] GENERAL SPECIFICATIONS should be kept sharp and free from oil and dirt. Such a machine should be sensitive to a variation of load of one two-hundred-and-fiftieth of the load carried. Testing machines should be calibrated once in twelve months, and at such other times as may be considered necessary by the inspector representing the Navy Department. 10. Pulling Speed. Each tensile test piece shall be subjected to a direct tensile stress until it breaks, running at a pulling speed of not less than 1 inch and not more than 6 inches per minute for 8-inch test pieces and not less than inch and not more than 3 inches per minute for 2-inch test pieces. Increasing or decreasing the speed on the testing machine while the test piece is under stress will not be permitted. 11. Interpretation of Terms. The elastic limit may be determined by observing the yield point as found by the drop of the beam or the halt of the gauge of the testing machine. The elongation is that determined after fracture. In the case of test pieces of rectangular section the reduction of area is to be measured by the product of the average width and thickness of the reduced area and not the minimum width and thickness. 12. Types of Test Pieces. Tensile test pieces shall have the dimensions shown in the following figures, which are the standard test pieces. If the manufacturer desires, he may be permitted to use the turned specimen unthreaded if a proper method of gripping the test piece is used. When specimens of Type 2 cannot be obtained from TYPE 1. JMBT.3l*.->; 1T03)MRAD^ MASURl/Y T 1 ~W~O **{ i ^ 1* TYPE 3. shapes whose sizes do not permit of making other than straight-sided pieces, the use of Type 3 may be authorized by the inspector. 13. Boiler Plates and Steam Pipes, Standard Size for Test Pieces. The width of tensile test pieces from plates and steam pipes over ^ inch in thickness will be \\ inches, the thickness the same as the plate or steam pipe, and the length between measuring points 8 inches; under & inch the width will be not over 2 inches, the thickness the same as the boiler plate or steam pipe, and the length between measuring points 2 inches. [422] GENERAL SPECIFICATIONS 14. Full Size Test Pieces. All tests, when practicable, shall be made with pieces of the full size, thickness, or diameter of the material represented by such, test specimens. 15. Length of Test Pieces Between Measuring Points. Test pieces from blooms, large rolled bars exceeding 2 inches in diameter, forgings, and castings are to have a length between measuring points of 2 inches, as shown in figure 1 of paragraph 12. Other test pieces are to have a length between measuring points of 8 inches, as shown in figure 2 of paragraph 12, except as otherwise directed in these, or in the Navy Department leaflet specifications. 16. Uniform Section of Test Pieces. Tensile test pieces shall be uniform in cross- section between measuring points. 17. Variation of Area. A variation of 5 per cent above or below the standard area will be allowed in test pieces. 18. Location of Test Pieces. All test pieces of forgings, and of rolled bars which are too large to be pulled in their full size, shall, unless otherwise specified, be taken at a distance from the longitudinal axis of the object equal to one-quarter of the greatest transverse dimension of the body of the object, not including palms and flanges. 19. Test Pieces for Groups or Lots. Test pieces which represent heats or lots shall be taken, as nearly as the case will permit, so as to represent the metal which was nearest the top and bottom of the ingot; when practicable test pieces shall be taken from dif- ferent ingots of a melt. Generally speaking, test pieces representing groups of lots should represent, as nearly as the case will permit, the worst material in that lot. 20. Flaws in Test Pieces. Test pieces which show defective machining or which show flaws after breaking may be withdrawn at the request of the manufacturer and others taken under the direction of the inspector; also, new test pieces may be selected and tested to replace any which fail by breaking within a distance from the end measuring points equal to 25 per cent of the length over which the elongation is measured. N 21. Bending Test Pieces Edges Rounded. Bending test pieces for blooms, large rolled bars (exceeding 2 inches in diameter), forgings and castings, shall be 1 inch wide by ^ inch thick. Specimens for cold bends for plates and shapes shall be rectangular in cross-section of the thickness of the material from which taken, and, when practi- cable, 12 inches long and of a width of 1^ to 2 inches. The sheared edges will be removed to a depth of at least one-eighth of an inch, and the sides will be made smooth with a file, but no rounding of the edges will be permitted, except the removal of the feather edge. In the case of heavy ship plates of 60 pounds per square foot and over, specimens machined to | inch square section, center of section being half-way between outer sur- faces, will be used for bends. 22. Treatment of Test Pieces. Test pieces shall be subjected to the same treat- ment and processes as the material they represent and no other, except machining to size. They shall not be cut off until the plate or object shall have received final treat- ment and shall have been stamped by the inspector, except in cases which are specially mentioned in these or in the Navy Department leaflet specifications. 23. Extra Material for Test Pieces Required Where Special Treatment Is Given. In the case of material which may require one or more retreatments, the objects must have attached sufficient material to enable the cutting of test pieces after each treat- ment. The manufacturer will be allowed only three official tests. In all cases where the test specimens fail to meet the requirements on the third test, the material repre- sented by the specimens shall be rejected, except where the inspector recommends to the bureau concerned that further treatment or testing be authorized. In special cases general exceptions to the above may be made by the bureau concerned. 24. Other Special Heat Treatment. If the material is to be subjected to any special or general heat treatment to secure physical properties required, the inspector will make such additional tests as may be required to show that the treatment has left the material of uniform quality throughout. 25. Material Which May Be Exempt from Tests. Material called for in Navy Department leaflet specifications specified to be of ordinary commercial quality will not be subject to tests or analysis unless there is reason to doubt that it is of suitable quality. If doubt should arise as to the quality of the material the inspector may [423] GENERAL SPECIFICATIONS make such tests as he deems necessary to determine the equality, either at the works of the manufacturer or at the point of delivery. 26. All Material Subject to Inspection. Material exempt from tests shall be in- spected for injurious defects, workmanship, and for accuracy of dimensions. This inspection will be made either at the point of shipment or at point of delivery, as may be designated. 27. Tests for Special Material. Tests may be prescibed by the bureau concerned for the inspection of material for which tests are not specified in the leaflet specifications. 28. Tests for Uniformity of Material. The inspector may require from time to time such additional tests as he may deem necessary to determine the uniformity of the material and to insure material of the desired quality. 29. When Heat Number Is Doubtful. Manufacturers of steel material desiring to avail themselves of melt tests for acceptance of material must so arrange their working and handling of the material that the inspector may at all times identify with perfect certainty any portion of the melt which is offered for inspection. In case the inspector cannot definitely determine the identity of the melt from which a plate, forging, casting, or other object is made, such plate, forging, casting, or other object shall be tested singly, and, before acceptance, must conform to the chemical and physical requirements specified for its class. 30. Annealing. The whole of an object specified to be annealed shall be subject to the same proper degree of heat at the same time, or, when necessary, to a uniformly graded degree of heat which will produce a uniform degree of anneal. The number of hours requisite for raising the object to sufficient temperature, the length of time during which it shall be soaked at its maximum heat, and the period for slow cooling in the furnace may be prescribed by the bureau. 31. Treatment of Lots. Objects tested as a lot after being treated shall be from the same melt. 32. Weights. The weights of all materials shall be obtained before shipment and shall be accurately entered upon the proper invoices. Accurate standard scales which have been frequently tested shall be used, and an inspector will witness testing and weighing when possible. 33. Methods of Weighing. Weighing will be done by one of the following methods: (a) Weighing each individual piece. (b) Weighing lots or parts of lots of material of same size which is inspected by lots. 34. Methods of Checking. Checking of weights will be done frequently, when practicable, or when ordered by the bureau, by the following methods: (a) Reweighing individual pieces. (b) Reweighing lots or parts of lots of material weighed individually or by lots. (c) Gauging and measuring. (d) Weighing full car. 35. When the method of checking by weighing the full car is used, the manufacturer shall furnish the inspector for each carload a statement showing the gross, tare, and net weights of the car, and the total weights of the individual pieces on the car if it is practicable to obtain same. If the net weight of the car varies by more than 1 per cent from the weight obtained by totaling the weight of individual pieces or of the lots, if weighed by lots, the material, if ordered by the department, shall be paid for on the basis of the lesser weight, or the manufacturer may run down the error by removing the material from the car and reweighing, or by other means which will satisfy the inspector as to the actual weight of the material. 36. Contractors' and Other Orders for Inspection of Material. At a ship-building yard the ship-builder shall furnish the bureau's representative at his ship-yard with quadruplicate copies of every order to manufacturers for all materials which are to be inspected at the plant of the manufacturer by an inspector representing the bureau concerned. 37. Material Which Is To Be Inspected Without Instructions. Any material which a manufacturer may present to a naval inspector shall be inspected, provided it is with- out doubt material that is intended for the Navy Department. In such cases the inspector shall call upon the manufacturer to exhibit the original orders or contracts, [424] GENERAL SPECIFICATIONS or true copies of such orders or contracts, from the representatives of the Navy De- partment, showing the object, quantity, specifications, and other details descriptive of the material. If inspection has not been authorized by the bureau, it should be reported to the bureau concerned, together with copies of the correspondence involved. 38 (a). Subletting. A contractor when subletting a part or whole of his contract shall notify the bureau concerned through the local inspector; shall give the sub- contractor full information as to the fact that the material is subject to naval inspection, and the number and the date of the specifications. 38 (b). The subcontractor shall fully comply with all the requirements of the contract specifications concerning quality, dimensions, method of inspection, rejection, replacement, shipment, etc. 38 (c). Orders from Contractors to Subcontractors and Manufacturers. Con- tractors and subcontractors shall furnish the inspector representing the bureau con- cerned in their district quadruplicate copies of all orders placed with manufacturers for materials, stating, when possible, the purpose of each item ordered and the specifica- tions for the same. Such orders shall state explicitly what treatment, other than machining, is to be given the material after leaving the manufacturers' works. In all cases these orders shall contain the number of the original contract of which these constitute suborders. 39. Inspection During Manufacture. The inspector should keep in touch with the work throughout its manufacture and should make such efforts as are practicable to secure delivery within the contract time. If at any time it should appear that prefer- ence is given to commercial work, thereby causing delay in Government work, a special report of the circumstances should at once be made direct to the bureau concerned. ORDERS, LISTS, AND INVOICES 40. Contractors to Supply Blue- prints. Blue-prints or sketches forming part of contractors' or subcontractors' orders shall be supplied by contractors in triplicate. 41. Matters to be Referred to Inspectors. Correspondence relating to material should be carried on directly with the inspector having cognizance of the inspection. When in cases of rejection contractors consider it necessary to appeal to the bureau concerned, the correspondence should be forwarded via the inspector. 42. Information to be Furnished by Manufacturer. Manufacturers shall furnish the inspector copies of mill orders, which shall be given separately for each vessel and which shall state the following: (a) The order or schedule number and name or designation of vessel. (b) The leaflet number and date of the department's specifications under which the material is ordered. (c) The kind or grade of material of each object. (d) The purpose for which intended, if practicable. (e) The ship-yard's location mark. (f) The number and quantity of each item and the essential dimensions. (g) The estimated weight of each plate, lot of shapes, forgings, castings, or other objects. (h) Information as to marking and arranging ingots (the marking to be such as to make identification easy). (i) The amount of discard at top and bottom of ingots (when required by inspector), (j) The number and height of heads and risers (when required by inspector). 43. Shipment of Material. No material shall be shipped by a manufacturer or sub- contractor except by direction of the inspector or other authorized representative of the bureau concerned. 44. Invoices to be Promptly Prepared by Manufacturers. The manufacturer shall furnish the inspector, immediately after a shipment of material, with invoices in quadruplicate covering each shipment. The information called for below may be sub- mitted on a form furnished by the bureau or inspector concerned, or on a manufac- turer's approved form. Manufacturers should furnish this information promptly, [425] GENERAL SPECIFICATIONS as any delay in so doing will cause delay in acceptance of material at destination and in the preparation of vouchers incident to the payment for the same. Invoices or shipping reports should contain the following information: The name of the manufacturer. The name and location of the navy-yard or ship-yard ordering or receiving the material. The name or designation of the vessel or stock concerned, the date of shipment, car initials, and number. The order, schedule number, or item number. The grade or kind of material of each object. The location marks designated by the navy-yard or ship-yard. The name of road, car number local, line or steamer, truck, etc. The number of articles on the item and dimensions of each object in inches, the gauge for plates in pounds per square foot, and for shapes in pounds per linear foot. The actual and estimated weight of each plate or lot of like shapes, rivets, or other objects, and the melt and serial number of each plate or forging, the melt number only for other objects. 45. Date of Shipping Report. The date of a shipping report should be the date of shipment. 46. Inspection Stamps. Each object accepted shall be clearly and indelibly marked with four separate stamps: (1) The private stamp of the inspector; (2) stamp of the manufacturer; (3) identification number; (4) the regulation Government pass stamp. The last shall not be stamped on any material until it has been inspected and passed ready for shipment. In case of small articles passed and packed in bulk the above- mentioned stamps shall be placed on the boxing or packing material of the object. If the objects are bundled these stamps will be placed on tags securely wired to the bundles. Exceptions to the above may be made, when considered necessary, at the discretion of the inspector. 47. Sealing of Cars. In special cases, where material is shipped in carload lots, in sealed cars, the inspector will witness the loading of the car and place the regulation pass stamp on the seals which seal the car. Where the material is of such a nature that stamping would injure it, the marking will be done with stencils bearing the initials of the inspector and the regulation pass stamp. 48. Acceptance of Material. No material will be received at a naval station, navy- yard, or ship-building yard unless it bears, either on its surface or that of its packing, these stamps as evidence that it has passed inspection, nor shall it be finally accepted until after the receipt of a duly certified report of the inspector by whose office the inspection was made. 49. Removal of Stamps Without Authority. The removal of any Government stamp from material without authority of the inspector will be sufficient reason for the rejection of that material. 50. Stamps on Large, Rough Work. Each object which has passed inspection shall be clearly marked with the necessary stamps, and these stamps, on large, rough work, shall be encircled by a ring of paint. 51. Marking Ingots, Etc. Ingots, blooms, and other material intended to be cut up shall have the stamps above-mentioned put on in three places, viz., near each end and near the middle, and encircled by paint marks. 52. Stamps on Boxes. In the case of small articles passed and packed in bulk, or in the case of material which would be injured by stamping, the above-mentioned stamps shall be applied to the boxing or packing material of the articles, or may be done with stencils bearing the inspector's initials and the regulation pass stamp. REJECTION AT DESTINATION 53. Rejection After Having Passed Inspection. Material may be rejected at a navy-yard or other place of delivery for defects either existing on arrival or developed in working or storage for which the contractor is clearly responsible, even though such [426]. GENERAL SPECIFICATIONS GENERAL SPECIFICATIONS FOR INSPECTION OF MATERIAL UNDER THE COGNIZANCE OF THE BUREAUS OF CONSTRUCTION AND REPAIR, STEAM ENGINEERING, AND ORDNANCE Issued by the Navy Department, October, 1913 INDEX OF GENERAL SPECIFICATIONS FOR INSPECTION OF MATERIAL PARAGRAPH Acceptance of material 48 Access to work 56 Analysis, chemical 6 Annealing 30 Area, variation of 17 Bending test pieces 21 Blue-prints, contractors to supply. ... 40 Boiler plates, standard size test pieces 13 Boxes, stamps on 52 Checking, methods of 34 Chemical analysis 6 Contractor, orders to subcontractor . . 38c Contractors to supply blue-prints. ... 40 Date of shipping report 45 Expense 54 Flaws in test pieces 20 Furniture, office, for inspector 58 General requirements 2 Groups, test pieces for 19 Handling material 54 Heat number, when doubtful 29 Information given by manufacturer. . 42 Information and facilities for inspector 57 Ingots, marking 51 Inspection, all material subject to ... 26 Inspection,contractor'sandotherorders 36 Inspection during manufacture 39 Inspection, rejection after passing.. . . 53 Inspection requirements 2 Inspection stamps 46 Inspector 56 Inspectors, matters to be referred to . 41 Invoices, orders, and lists 42 Invoices prepared by manufacturers. . 44 Lists, orders, and invoices 42 Lots, test pieces for 19 Lots, treatment of 31 Machines, testing 9 Manufacture, inspection during 39 Manufacturer, information from 42 Manufacturers, invoices prepared by . 44 Manufacturers, orders from contrac- tor to 38c Marking ingots. . 51 Material, acceptance of 48 Material, extra, for test pieces 23 Material exempt from tests 25 Material, handling 54 Material inspected without instruc- tions . . .37 PARAGRAPH Material, inspection of orders for .... 36 Material, shipment of 43 Material, special 5 Material, special, tests for 27 Material, subject to inspection 26 Material, tests for uniformity of 28 Orders from contractor to subcontrac- tors and manufacturers 38c Orders for inspection of material .... 36 Orders, lists, and invoices 42 Physical tests 10 Properties, chemical 6 Pulling speed 10 Quality to be supplied, uniform 3 References 60 Rejection 53 Removal of stamps without authority, 49 Report, shipping, date of 45 Sealing cars 47 Shipment 43 Shipping report, date of 45 Specifications, where obtainable 59 Special heat treatment 24 Special material 5 Special material, tests for 27 Special treatment 5 Special treatment, extra mat'l for test 23 Stamps 52 Steam pipes, standard size test pieces 13 Subcontractors, orders from con- tractor 38c Subletting 38 Tests 27 Tests, making 55 Tests, material exempt from ........ 25 Tests, physical 10 Test pieces 10, 22 Test pieces, boiler plates and pipes. . . 13 Test pieces, full size, etc 14 Test pieces, treatment of . 22 Test pieces, types of 12 Test requirements 2 Testing 4 Testing machines, calibration of 9 Treatment 22 Treatment, lots 31 Treatment, special 5 Types of test pieces 12 Uniformity of material, tests for 28 Weighing, methods of 33 [427] INSPECTION OF RUBBER MATERIAL material may have passed previous inspection by the inspector at the place of manu- facture. In such cases the manufacturer must make good any material rejected. EXPENSE 54. Handling Material. All handling of material necessary for purposes of in- spection shall be done at the expense of the contractor. 55. Making Tests. All test specimens necessary for the determination of the qualities of material shall be prepared and tested at the expense of the contractor. OFFICE AND INSPECTORS 56. Access to Work. The department shall have the right to keep inspectors at the works, who shall have free access at all times to all parts thereof and be permitted to examine the raw material and to witness the processes of manufacture. 57. Information and Facilities. Contractors and manufacturers shall furnish all the information and facilities the inspector may require for proper inspection under these specifications. The department is at liberty at any time to require additional information. 58. Office and Furniture. Inspection and tests shall be made when practicable at the place of manufacture, and any firm doing work for the Navy that requires inspection shall furnish the inspectors, free of expense, with such facilities as may be necessary for the proper transaction of their business as the agents of the Government. When requested by the bureau, inspectors shall be supplied free with suitable office and laboratory room, and such plain office and laboratory furniture as may be necessary for the proper transaction of their business. 59. Specifications, Where Obtainable. NOTE. Copies of the above specifications can be obtained upon application to the various Navy pay offices or to the Bureau of Supplies and Accounts, Navy Department, Washington, D. C. 60. References. (Ord., C. & R., and S. E.) C. & R., SPS, May 5, 1913. S. & A., 380-5. GENERAL SPECIFICATIONS FOR INSPECTION OF RUBBER MATERIAL NAVY DEPARTMENT September 1, 1914 1. Temperature of Room. All tests of the rubber parts shall be made in a room the temperature of which is not below 65 F., and the range of temperature not to vary beyond the limits of 65 F. to 90 F., if practicable; the tests shall not be made in the cold, nor shall any tests be made until the article to be tested has been standing 48 hours after vulcanization. 2. Tests of Adhesion of Rubber Parts to Cotton or Fabric Parts. (a) APPARATUS. A standard testing table suitable for the purpose shall be used. (b) PREPARATION OF TEST PIECE. In making the test a section of the article shall be cut. In testing hose the section shall be cut transversely, unless the diameter of the hose is too small to be practical for this test, in which case it shall be cut longitudinally. When testing belting, packing, or gasket material, it may be cut in any direction. When testing cotton rubber-lined hose the test piece shall be prepared by cutting directly through the section, so as to lay out upon the table a piece measuring the full length of the circumference of the hose and 2 inches in width. On this piece two parallel cuts 1 inches apart shall be made by cutting through the lining only and not injuring the cotton cover. This strip shall be started at one end to the extent of about 1 inches. The cotton cover only shall be fastened in the clamps. [428] INSPECTION OF RUBBER MATERIAL When testing a fabric-plied hose the section shall be 1 inch in width. The piece shall be separated until the part next to the rubber cover shall be loosened. The section shall then be placed on a mandrel whose diameter is the same as that of the inside of the hose to be tested. When testing packing, the piece shall be prepared as in the case of cotton rubber- lined hose, unless the thickness of rubber is greater than | inch, under which conditions the piece shall be prepared in such a way that the rubber part is to be clamped at the top and held immovable while the weight, as described below, is to be clamped to the fabric. When testing belting, the test strip is to consist of 2 plies of fabric only, one ply being held in the stationary grip, with weights suspended freely from the other ply. Square Tuck's packing shall be tested in the same manner as is specified for testing the friction between the plies of a belt. The friction hi round Tuck's packing shall be tested by the same method as is used in fabric-plied hose, the core being drilled out to permit the insertion of a mandrel. Whenever the core is & inch or less in diameter it shall be tested in its original shape. When it is over & inch in diameter a piece 6 inches long shall be separated from the fabric and cut and buffed on four opposite sides to form a square section i by | inch in the center of the test piece. The | inch square shall be at least 1 inch in length. In testing the friction of belting the load should be applied at right angles to the plane of separation, or the test strip should consist of only 2 plies of fabric, 1 ply being held in the stationary grip with the weight suspended freely from the other ply. By this means the effect of the thickness of the belt may be eliminated. (c) PERFORMANCE OF THE TESTS. Having thus fastened the test piece, the clamp ring shall be slipped upon the mandrel, or in the case of fabric-plied hose, the test piece shall be slipped upon the mandrel. The free-moving clamp shall be tightly fastened to the free end and the weight supported upon a movable table hooked over the hook in the clamp. The weight and the clamp together shall be exactly equal to the weight called for in the specifications. The weight then supported by the movable table of the testing machine shall be lowered until the clamp and free end of the hose are just taut. An indelible pencil mark shall be placed upon the separating layers of the test piece, and by quickly loosen- ing the thumb-screw supporting the table, it shall be allowed to fall, leaving the weight freely suspended. In every case this shall be done without a jerk. The time shall be read at the moment of freeing the weight and at the moment of re-marking. The weight shall be allowed to act upon the test piece for ten minutes, at the end of which time an indelible pencil mark shall be placed again upon the separating layers of the test piece. The movable table shall then be brought up to hold the weight, the test piece removed and laid upon the table, and the distance between the pencil marks shall be measured by means of a certified rule accurately graduated in decimals of an inch. The distance between the marks shall be recorded as the number of inches of separation in ten minutes, from which shall be computed the rate in inches per minute. 3. Tests of Rubber Parts. (a) TEST PIECE PREPARATION. For hose, a section 1 inch in width shall be cut. For belting, packing, and sheet gaskets a piece 1 inch in width and 6 inches in length shall be cut in any direction. The rubber parts shall be carefully separated from the fabric of this piece, using benzine in small amount if necessary. The benzine used in this case shall always be 76 Baume, free from oil. In case of articles to be tested, such as washers, ferrules, and moulded gaskets, which are of such peculiar shape that the above methods do not apply, small sample pieces shall be sent with each delivery. These sample pieces shall be 8 inches in length, 1 inches in width, and | inch in thickness, unless otherwise specified. These sample pieces shall be guaranteed by the manufacturer to truly represent the average com- position and cure of the article delivered. Test pieces shall be cut from these samples as described below. From these 1-inch sections, or from sample pieces thus prepared, a test piece shall be cut by a die. The dimensions of the test piece shall be indicated in each specification. It is the intention to have the cross-section area at the con- stricted part approximately ^j square inch. The backing or cloth impression shall be removed from the test piece by buffing for determining the cross-section area. No [429] INSPECTION OF RUBBER MATERIAL test shall be performed until the piece has been allowed to stand for one hour after removal from the article, if it has in any way been in contact with benzine. (b) Testing Machine. JAWS. The jaws must tighten automatically and exert a pressure proportionate to the applied tension. The rate of speed of separation of the jaws is to be uniformly 20 inches per minute. The jaw must exert a uniform pressure across the width of the test piece, regardless of any variation in the thickness of the rubber. The test machine should be suitable to carry out the necessary tests, and should be standardized in accordance with the latest approved designs so far as practicable. (c) Making of the Measurements. TAKING OF TIME. All measurements of time shall be taken by means of a stop watch. The fundamental methods of testing are so made throughout the entire rubber specifications that the following procedure shall be uniform: After placing any test piece in the machine ready for stretching the piece shall be drawn just taut and the stop watch started at the instant of the beginning of the stretch. The piece shall then be held for ten minutes at a specified distance and the time shall be again noted at the moment the piece is released. This moment is simul- taneously the beginning of the period of rest. The measurement is then to be taken at the instant of expiration of the second ten minutes. (d) MEASUREMENT OF ELONGATION. Marks 2 inches apart shall be placed on the test piece by means of a marker. These marks shall be at right angles to the direc- tion of pull of the piece in the machine. Great care shall be taken: (1) That the marks are not too wide, and that (2) at the time of marking the piece shall have been lying for a sufficiently long time to be completely at rest on a wooden table which has been at the temperature of the room mentioned in paragraph 1 herein. The marks shall be placed on the smooth side; that is, in no case on the side which is corrugated due to its impression taken from the fabric. After clamping the test piece in the jaws of the machine the movable jaw shall be so adjusted with the pointer reading zero on the scale that the test piece is just taut, but not under tension. The operator shall throw on the current to start the screw and when ready throw in the engaging lever to start the jaws. He shall keep the elongation scale pointers opposite the outside edges of the marks on the piece. To stop the motion at the desired elongation or upon the break of the piece, the jaws shall be disengaged from the screw. The accuracy with which the elongation measurements are made will depend upon the accuracy with which the operator keeps the two pointers opposite the outside edge of the marks on the test piece. The elongation shall be reported in inches, including the original 2 inches; that is, if the rupture occurs at 11 inches, or 12 inches, or 13 inches, it will indicate that the stretch has been 2 to 11, 2 to 12, or 2 to 13. After the piece has been removed from the machine, the permanent elongation or recovery shall be measured by laying it upon a wooden table, which is of the temperature of the room, and allowing it to rest for ten minutes. Immediately upon the expiration of the ten minutes, a rule graduated to yj inch shall be laid upon the piece and the elongation read in ^ of an inch, measuring the outside of the marks. The per cent of elongation of the test piece above the original 2 inches shall represent its permanent elongation. (e) TensUe Strength. The tensile strength shall be determined by stretching a test piece not previously tested in the tensile machine until it breaks. If the test piece breaks outside the marks, or in the wider portions of the piece, and the tensile is much below that called for in the specifications, it is probable that this piece is faulty and that another would meet the requirements. If the piece breaks outside the marks and yet shows a tensile above that called for in the specifications, it is probable that the piece is faulty and that its true tensile strength is higher than indicated. Since its recorded tensile strength exceeds that called for in the specifications, however, it shall not be necessary to retest. Before any tests are made, the width of the test piece shall be determined at 3 points, equidistant between the marks. The backing or irregularities of fabric im- pression shall be stripped or buffed off and the thickness measured with the backing [430] INSPECTION OF RUBBER MATERIAL removed. It shall be determined at 3 points equidistant between the marks on the test piece, by means of a standard spring gauge micrometer, the disks of which are inch in diameter. The measurements used in the computation of tensile strength shall be those read nearest the point of break. The disk of the micrometer shall be inch in diameter when measuring thickness of the tube of all hose which has an inside diameter of 1 inch or under. (f) INITIAL STRESS. During the elongation and recovery test the initial stress shall be taken by connecting a spring balance with the piece under test. The number of pounds read on the balance at the maximum stretch shall then be computed in pounds per square inch, and expressed as "initial stress." 4. Pressure Tests. (a) The hose shall be stretched out for inspection, connected to the pump, and filled with water, leaving the air cock open to allow the air to escape. The air cock shall then be closed and a pressure of 10 pounds per square inch applied. The test is then begun by taking original measurements without releasing the pressure. (b) All pressure tests shall be made by using a hand or power water pump standard- ized gauge. The increase in pressure shall be made at the rate of 100 pounds per minute, and the hose under test shall be held for measurement not more than 2 minutes, unless otherwise called for in the specifications. 5. Composition. (a) FRICTION. Wherever, in the detail specifications, friction is mentioned, it is understood that it should be made from a compound which will neither yield to acetone any organic constituent foreign to Hevea rubbers nor contain more sulphur than is necessary for vulcanizing, so that the percentage of sulphur in the rubber layers shall not be raised beyond the permissible amount. (b) MATERIAL. The shall be properly vulcanized, and be made (Article.) from and have all the characteristics of a compound containing not less than per cent of washed and dried, fine Para rubber, not more than per cent of sulphur, with the remainder suitable, dry, inorganic, mineral fillers. The mineral fillers may contain barytes, but shall be practically free from sulphur in other forms and from any substance likely to have a deleterious effect on the rubber compound. The sulphur in barytes will not be included in the allowable sulphur content. (c) SAMPLE FOR CHEMICAL ANALYSIS. A sample taken for chemical analysis shall be free from backing. 6. Average Reading. Since the physical properties of rubber vary noticeably in any given product, it may occasionally happen that tests are made upon a sample which will be of poor quality. The hose, belting, or packing will, as a whole, meet the require- ments of the standard, but the particular piece taken may fall somewhat below it. To reject or accept a lot of hose because of its failure to meet one test under specifications would therefore be unfair. For this reason acceptance or rejection of an item offered for delivery shall be based on the average of at least four determinations for each quan- tity. In arriving at these averages no weight shall be given to tests which are obvi- ously in error, and do not represent true average conditions, e.g., cases in which the tensile strength is low on account of a small flaw in the article or the friction is low on account of a small flaw in the friction part. In other words, the intent of the specifica- tions is to insure a high-grade article in every particular, and the intent of the methods of testing is to see that the article as a whole is of this high standard. Deliveries of hose, packing, etc., which regularly meet certain provisions of the specifications, but quite as regularly fail to meet others, are obviously improperly made and should be rejected. 7. Rejections and Replacements. All rubber materials shall be inspected and tested, so far as practicable, at the point of manufacture. In case of rejection the con- tractor shall be allowed ample opportunity to test the rejected articles before replacing them. Articles found to be defective within the guaranteed time required in the specifications under which they were purchased may be examined and tested by the contractor before replacements are made. [431] TESTING OF RUBBER GOODS THE TESTING OF MECHANICAL RUBBER GOODS BUREAU OF STANDARDS The principal sources of crude rubber are South America, Central America, Africa, and Asia. The Amazon district of South America is noted for the excellent quality of its rubber. In addition, much rubber is secured from plantations where rubber- bearing trees are cultivated according to scientific principles. This is generally known as "plantation rubber." Briefly stated, rubber is obtained in the following way: Incisions are made in the bark of the trees, and receptacles are placed under the incisions to collect the gradual flow of latex. The custom usually followed by natives is to coagulate or dry the latex by means of smoke or merely by exposure to the ah*. "Plantation latex" is coagulated by the addition of acid, after which the rubber is washed, sheeted, dried, and sometimes smoked. The smoking process has been adopted in an attempt to secure the valuable properties possessed by the wild rubbers, which are coagulated by smoking. Crude rubber is greatly affected by changes in temperature, becoming stiff when cold, and soft and sticky when warm. Vulcanizing. Goodyear discovered, in 1839, that if crude rubber to which sulphur had been added was heated to a temperature above the melting point of sulphur it combined with the sulphur, became very much less susceptible to temperature changes, and at the same time gained both in strength and elasticity. This important discovery may be said to mark the practical beginning of the rubber industry, although crude rubber had been previously used to a limited extent as a waterproofing material. The process is popularly known as "vulcanizing." Rubber Substitutes. No true rubber substitute that is, no material possessing all the properties of rubber has yet been produced on a commercial scale. There are a number of so-called substitutes, however, that may be mixed with rubber to advantage in the production of certain articles. Such materials are produced from vegetable oils, by processes of vulcanization or oxidation. Reclaimed Rubber. On account of the large amount of waste vulcanized rubber or scrap available, and the high cost of crude rubber, the reclaiming of rubber has assumed such proportions as to constitute an industry in itself. By "reclaimed rubber" is not meant devulcanized rubber, although in some cases the free sulphur is removed. No process has yet been developed by which the process of vulcanization can be reversed and crude rubber reclaimed. The old method of reclaiming consisted in grinding the scrap and removing the fibers and particles of metal, and other waste material, after which the rubber was mixed with oil, heated in ovens, and sheeted. In a more modern process, the fibrous materials are destroyed by treatment with acid, after which the scrap is heated in ovens. A third method, known as the alkali process, which is carried out on an extensive scale, may be briefly outlined as follows: Old rubber is ground between rollers, particles of iron are removed by magnets, and the ground material is screened. The rubber is then heated in iron vessels containing an alkali solution, by which means free sulphur is removed and the fibrous matter destroyed, after which it is thoroughly washed to remove the alkali and dried by steam coils. It is then mixed between rollers without the addition of oil, and sheeted. It is said that rubber reclaimed by this process from carefully selected scrap is superior to some of the lower grades of crude rubber. Manufacture. Crude rubber as received at the factory is in the form of lumps of irregular shape and size, and contains varying amounts of impurities which have to be removed. These lumps are placed in a vat containing water, and boiled in order that they may become sufficiently soft to be handled by the washing rolls. Breaking Down and Washing. The washing rolls consist of two steel cylinders, about 12 to 18 inches in diameter, which revolve in opposite directions and at different speeds, their axes being parallel and in the same horizontal plane. These rolls are corrugated, and as the crude rubber is fed between them their action is such as to [432] TESTING OF RUBBER GOODS masticate the soft lumps and expose the impurities, which are washed out by a series of water jets and collected in a pan under the rolls. Two sets of rolls are used in this process. The first set breaks down the lumps while a large part of the impurities is washed out, and the second set, in which the rolls are closer together, completes the process of washing. After a sufficient number of passages through the rolls, the washed rubber has the form of a rough sheet of irregular shape, and contains considerable water, which must be removed before vulcanization. Drying. There are two methods in use for removing the water from washed rubber. The first is to hang the rubber sheets in a warm dry place usually the attic steam- heated pipes being used to maintain the proper temperature during cold weather. This method is usually employed, as less skill is required than in the second and quicker method, in which vacuum heaters are used. The rubber having been dried as described above, is "broken down" or worked through smooth steam-heated rolls, by which process it is rendered soft and plastic. Compounding and Mixing. The rubber is now in condition to be compounded or mixed with sulphur and mineral matter, and with reclaimed rubber or rubber sub- stitutes, if such are used. The ingredients required for a batch having been weighed out in the definite pro- portions to produce a compound of the desired quality, the mixing is done with FIG. l. DIAGRAM SHOWING OPERATION OP CALENDER ROLLS. smooth rolls operated as in the washing process. Both steam and water connec- tions are provided so that the temperature of the rolls may be regulated to suit the condition of the rubber as it is being worked. The rubber gradually absorbs the sul- phur and fillers which are added by an attendant. Such material as passes through without being incorporated with the rubber is collected in a pan and returned to the rolls. The temperature of the rolls is so regulated that as the operation of mixing proceeds the compound sticks to one of them in the form of a sheet. This sheet is cut with a knife, folded upon itself, and passed through the rolls again, the operation being repeated until the material shows a uniform color and is as nearly homogeneous as it is practicable to make it. Sheeting. The next step in the process of manufacture depends upon the purpose for which the rubber is intended. If sheet rubber is being made, as for packing or for the tubes and covers of hose, the compound coming from the mixing rolls : [433] TESTING OF RUBBER GOODS through calender rolls. The calender consists of three steam-heated rolls, one above the other, which are so geared together that the middle roll revolves in the opposite direction from that of the other two. The rolls may be adjusted to form sheets of different thickness. The skeleton diagram in Fig. 1 shows the method of operation. Rubber is fed between the top and middle rolls, and by a proper regulation of tem- peratures the sheet adheres to the middle one while the top one remains clean. A strip of cloth is taken from the reel 1 and passed between the middle and bottom rolls to the reel 2. The sheeted rubber as it passes between the middle and bottom rolls is received by the cloth and carried to the reel 2, upon which they are wound together, the cloth preventing the layers of rubber from adhering. The sheet may be cut into strips of any desired width by knives which press against the middle roll. Sometimes several calendered sheets are rolled together to form a single sheet. The rubber is now ready to be vulcanized or worked into hose or other fabricated articles. " Friction." What is known as "friction" in the case of rubber hose, rubber belt- ing, and other articles, which are made up with superimposed layers of canvas, is the soft rubber compound which is applied to the canvas and by means of which the differ- ent layers or plies are held together. The canvas is first dried by being passed over steam-heated rolls, after which the friction is applied by means of rolls which are operated in the manner just described, and illustrated in Fig. 1. In the case of the friction calender, the bottom roll revolves at about two-thirds the speed of the middle roll, thus causing a wiping action which forces the friction well into the meshes of the canvas. Cutting the Canvas. Canvas for use in making rubber hose is usually cut on the bias from strips 40 to 42 inches wide, into pieces long enough so that when placed end to end and lapped, the resulting strip is just wide enough to produce the necessary number of plies on the hose. There is no waste when cutting on the bias, and the finished hose is more flexible than when the canvas is cut straight. On the other hand, when the canvas is cut straight there is more or less waste on account of the last strip, which is often too narrow to be used. This method of cutting, however, produces the stronger hose, and a hose which will not expand as much, and which will elongate under pressure, avoiding the objectionable feature of longitudinal contraction which is noticed in hose made with bias-cut duck. RUBBER HOSE The ordinary "plied" hose with rubber tube and cover is manufactured as follows: 1. Tubes and Covers. For low-grade water hose of small diameter it is usual to form the tubes by passing the rubber compound through a die which may be adjusted to produce a wall of any desired thickness. The rubber coming from the mixing rolls must be at a sufficiently high temperature to make it plastic, in which condition it is forced through the die by means of a worm. The operation is similar to that of a "soft mud" brick machine, and the tube as it comes from the die is carried away on an end- less belt. These tubes are placed on steel mandrels by a rather ingenious process, as follows: The mandrel, which is about 52 feet long, is placed on an endless belt and held stationary. Powdered talc is blown into the tube to act as a lubricant and to prevent it from sticking to the mandrel during vulcanization. One end of the tube having been placed over the mandrel, air pressure is applied at the other end, sufficient to ex- pand the tube slightly. The belt is now set in motion, and the tube as it is fed onto the belt floats over the mandrel on a cushion of air. In the case of high-grade hose and hose of large diameter, the tube is made from a strip of sheet rubber, cut with a "skive" or tapering cut, which is wrapped over the mandrel by hand, the edges being lapped and pressed flat by means of a small hand roller. In either case, the cover is made from a strip of sheet rubber just wide enough to pass once around the hose and form a narrow lap. To ensure firm adhesion between the tube and canvas, the former is cleaned with gasoline, preparatory to receiving the frictioned canvas. 2. " Making up " the Hose. Water hose of small diameter is usually wrapped by [434] TESTING OF RUBBER GOODS machinery consisting of three rolls about 2 inches in diameter and slightly more than 50 feet long. The two bottom rolls lie in the same horizontal plane and the top roll, which is just above and between the other two, may be raised while the mandrel carrying the tube to be wrapped is being placed on the bottom rolls. The top roll is now lowered onto the tube, which is held firmly between the three rolls. A rotary motion imparted to the rolls causes the tube to revolve, and the canvas and rubber cover are wrapped on in a few seconds. This method has the advantage of consuming very little time, but unfortunately, it is not applicable to the construction of best-quality hose, which are made up by hand with the assistance of small rollers having a concave face. The rollers are run up and down the hose and serve to press each ply of frictioned canvas onto the next. Before going to the vulcanizer the hose is wrapped with cloth. First, a long strip is wrapped lengthwise on the hose, and over this a narrow strip is wrapped spirally. This is done very rapidly by causing the hose to revolve in roller bearings while the narrow strip of cloth is held under tension and guided by hand. The operation requires only a few minutes. 3. Vulcanizing. The vulcanizer consists of a long cylinder provided with steam and drip connections, and a pressure gauge. The pressure and time necessary for vul- canization depend upon the composition of the rubber compound, the thickness, and the use for which the hose is intended. After vulcanization the wrapping cloth is stripped off, and the hose is removed from the mandrel by means of compressed ah*, in the same way that the tube was put on. The couplings are now put on and the hose is ready for shipment. 4. Cotton Rubber-lined Hose. In the manufacture of woven cotton hose with rubber lining, the tube is made in the usual way and partially vulcanized, in order that it may develop sufficient strength to be drawn through the cover. A long slender rod is passed through the cover, carrying with it a stout cord. This cord is attached to the end of the rubber tube, and the rod is withdrawn. The cord is now drawn through the cover, bringing the tube with it, the tube having been coated with rubber cement. The hose is now filled with steam under pressure, which expands the tube, thus forcing the cement well into the meshes of the woven cover, and at the same time vulcanizes the rubber. 5. Braided Hose with Rubber Tube and Cover. A form of braided hose which is claimed to have, and appears to have, decided merit, is made as follows: The rubber tube passes first through a bath of cement and then to the braiding ma- chine, where the first ply of fabric is braided over the fresh cement. This operation is repeated until the desired number of plies have been formed, r/hen the rubber cover is put on and the hose is vulcanized in a mold. While being vulcanized the hose is sub- jected to air pressure from within, which forces the rubber well into the meshes of the loosely braided fabric. RUBBER BELTING Duck for rubber belting is passed over steam-heated rolls to remove the moisture, and frictioned as described in connection with the manufacture of rubber hose. The frictioned duck is cut lengthwise into strips, the width of which depends not only upon the size of belt, but also upon the method of manufacture, which is not the same in all factories. These strips are cut by passing the canvas over a drum against which knives are held at points necessary to produce the desired widths. One method is to make the inner plies of the belt with strips which are equal in width to that of the belt. These strips, stacked one above the other, are placed in the center of a strip of double the width, and in this position they are drawn through an opening with flared edges which folds the bottom strip over the top strips and forms a butt joint on the top face of the belt. The belt then passes between rolls which press the plies firmly together and at the same time lay and press a narrow strip of rubber over the joint. When the belt is to have a rubber cover, as is usually the case, this is calendered onto the outside ply or layer of the canvas before it is put on the belt. Some of the most expensive belts, however, are made without a rubber cover. Another method is to cut each strip of canvas twice as wide as the belt. The first [435] TESTING OF RUBBER GOODS strip is folded upon itself, as described above, so that its edges form a butt joint. This folded strip is placed with its joint down upon the next strip, which is in turn folded to form a butt joint on the back of the first strip. In this way, the belt is built up with the desired number of plies, the last joint being covered with a narrow strip of rubber, which is rolled flush with the surface. The belt is now ready to be vulcanized. In this process there are two steps. First, the closely coiled belt is wrapped so that only its edges are exposed, and in this condition it is put in the vulcanizer. After the edges have been vulcanized the belt is stretched and held under heavy pressure between the steam-heated faces of a long hydraulic press. This drives the friction into the pores of the duck and vulcanizes the belt throughout. As regards the advantage of using a high-grade rubber cover for belting, the con- sensus of opinion seems to be that the expense thus incurred, except in the case of conveyor belting, had better be devoted to increasing the quality of friction between the plies of canvas. MECHANICAL RUBBER GOODS The term "rubber," as 'commonly employed, does not refer to the commercially pure gum, but to a vulcanized compound as already described, which consists of gum, mineral matter or pigments and sulphur, mixed in various proportions, according to the purpose for which it is intended. Mineral matter or the so-called fillers serve a very useful purpose, both in cheapening the product and in adding certain desirable properties which could not otherwise be obtained. Their presence, therefore, should not be looked upon as an adulteration. There is a limited demand for pure gum by the medical profession and a very con- siderable amount is used in the manufacture of stationery bands, elastic thread, etc., but the amount of rubber thus consumed is insignificant as compared with the enormous quantity used in the manufacture of mechanical rubber goods, such as automobile tires, hose, packing, and footwear. A properly vulcanized compound of high-grade rubber which is suitable for the best hose and packing, may be stretched to about seven times its original length and has a tensile strength of about 2,000 pounds per square inch. The properties that are desirable in rubber depend in a great measure upon the use for which it is intended. For example, rubber intended for steam hose or steam packing should be of a composition to withstand high temperatures, while rubber for the tread of an automobile tire should offer great resistance to abrasion. The real value of rubber in any case depends upon the length of time that it will retain those properties which are desirable, and it is a matter of common observation that rubber often deteriorates less rapidly when in use than when lying idle. Deteriora- tion, as indicated by loss of strength and elasticity, is considered to be the result of oxidation, which action is accelerated by heat and very greatly by sunlight. Other things being equal, the better grades of rubber possess greater strength and elasticity, and may be stretched to a greater extent than the poorer grades, and they also deteriorate less rapidly. The physical properties of rubber, however, are subject to variation within wide limits, depending upon the proportion of gum present, the materials used as fillers, and the extent of vulcanization. PHYSICAL TESTING OF RUBBER Rubber testing in the present stage of its development is not susceptible of very great refinement as regards measurement. The nature of the material is such that refinement seems of less importance than uniformity of methods, which is absolutely essential where the work of different laboratories is to be compared. Tension Test. Tension tests in various forms are used to determine the more important physical properties, such as tensile strength, ultimate elongation, elasticity, and reduction in tension when stretched to a definite elongation. Recovery. Recovery as applied to rubber is in a way synonymous with elasticity, and is measured by the extent to which the material returns to its original length after having been stretched. The term "set," as commonly employed, refers to the extension remaining after a specified interval of rest following a specified elongation for a given period of time. [436] TESTING OF RUBBER GOODS Friction. In the case of such materials as rubber hose and rubber belting, which are built up with layers of duck cemented or frictioned together with rubber, it is customary to determine the friction or adhesion between the plies of duck as well as the quality of rubber. It is also usual to subject hose (particularly fire hose and air hose) to a hydraulic pressure test, in order to detect any imperfections in materials or workmanship. Steam Pressure. An important test in the case of steam hose consists in passing steam at about 50 pounds pressure through a short length of the hose in order to deter- mine if the rubber is of suitable composition to withstand the effects of service conditions. This test usually lasts for about six days, the steam being turned off at night to allow the rubber to cool. A decided hardening or softening of the rubber, or a large decrease in the value of friction, as a result of steaming, is an indication of inferior quality. Packing. No absolutely reliable test (other than an actual service test) has been devised for rubber steam packing, but in many cases valuable information may be obtained by clamping a piece of the packing between metal plates and subjecting it to the action of steam at a pressure equal to or slightly above that under which it is to be used. A more satisfactory method is to clamp the packing in the form of a gasket between pipe flanges and apply the desired steam pressure from within. The test should last several days, the steam being turned off at night to see if the joint has a tendency to leak as a result of the cooling effect. This, however, practically constitutes a service test. Tires. The testing of tires, or rather the materials used in their construction, ia done almost exclusively by manufacturers. Manifestly it would be too expensive for the consumer, or even the dealer, to sacrifice whole tires for the purpose of securing test pieces. The tests which have been outlined above will, in the majority of cases, enable one to form a fairly accurate judgment as to the quality of rubber. Tension Test. When the material is made up with layers of fabric, as in the case of rubber hose, the first step in preparing specimens for the tension test is to separate the rubber from the fabric. Unless the frictioning is very poor, this will necessitate the use of a solvent. If there is more than one layer of fabric, the easiest way is to remove the first layer along with the rubber. The rubber is then separated from the adjoining layer of fabric by means of gasoline blown from a wash bottle. Narrow strips are more easily handled than larger pieces, and there is less danger of injuring the rubber. The rubber should be allowed to rest for several hours in order that it may recover from the stretching it has received and that the gasoline may thoroughly evaporate. Test Piece. The central portion of the test piece cut with a metal die is straight for a distance of 2 inches, and the ends are enlarged to prevent tearing in the grips of the testing machine. The width of the contracted section is usually made either one-fourth inch or one-half inch. It is impossible to obtain satisfactory specimens one- half inch wide from hose of small diameter. Parallel lines 2 inches apart are placed on the specimens, and by means of these gauge marks elongation and permanent extension are measured. A stamp consisting of parallel steel blades enables one to mark very fine lines with ink, without cutting the rubber, and in this way much time is saved and all chance of error eliminated. Influence of Speed on Tensile Strength and Elongation. The speed at which rubber is stretched probably affects the results to a less extent than is often supposed, though doubtless different rubbers are not equally affected. Influence of Temperature on Strength, Elongation, and Recovery. It is generally recognized that the physical properties of rubber are affected by changes in temperature, though, of course, to a less extent after vulcanization than before. The results of tests at 50, 70 and 90 F., in a room maintained at the specified temperature for three hours before the tests were made. It was observed that the rubbers were not all affected to the same extent by equal differences in temperature, but there was a marked tendency in each case toward decreased strength, decreased set (increased elasticity), and increased elongation as the temperature is raised. It was noted that in nearly every case, greater differences were secured between 50 and 70 than between 70 and 90. '[437f TESTING OF RUBBER GOODS The set in each case was measured after one minute stretch and one minute rest, Of five specimens, Nos. 1 and 2 were stretched 350 per cent, Nos. 3 and 4, 300 per cent, and No. 6, 250 per cent. TABLE 1 SHOWING STRENGTH AND ELONGATION OF RUBBER WHEN STRETCHED AT THE RATE OF 30 AND 120 INCHES PER MINUTE [Gauge length = 2 inches.] Rubber No. 2 3 4 5 6 Speed in Inches per Minute 30 120 30 120 30 120 30 120 30 120 Tensile strength (pounds per square inch) . . 1,740 1,690 990 1,100 1,710 1,790 750 920 930 1,030 Ultimate elonga- tion (per cent) 665 670 510 530 460 460 430 430 375 380 These results would indicate that elongation is not appreciably affected by speed, and that for the lower-grade rubbers greater tensile strength is secured at high speed. Influence of Cross Section on Tensile Strength and Elongation. Tensile strength and ultimate elongation are theoretically independent of sectional area, but as in other materials there is a tendency for small test pieces to develop higher unit values than large ones. Complete data on this subject is not at hand, but it is thought that test pieces one-fourth inch and one-half inch wide will show but little difference in unit strength and elongation, provided the snrface is uniform and the wider specimens are sufficiently enlarged at the ends to prevent tearing in the grips. Influence of the Direction in which Specimens are Cut on Strength, Elongation, and Recovery. The tensile properties of sheet rubber are not the same in all directions. Specimens cut longitudinally or in the direction in which the rubber has been rolled through the calender show greater strength and (at least for the better grades of rubber) less elongation than specimens cut transversely or across the sheet. The recovery, however, is greater in the transverse direction. TABLE 2 SHOWING THE RELATIVE STRENGTH, ELONGATION, AND RECOVERY OF RUBBER WHEN TESTED IN THE LONGITUDINAL AND TRANSVERSE DIRECTIONS . Rubber No. 1 2 3 4 5 6 Tensile strength 1 (pounds per square inch) : Longitudinal . .... 2,730 2,070 1,200 1,850 690 880 Transverse 2,575 2,030 1,260 1,700 510 690 Ultimate elongation (per cent) : Longitudinal 630 640 480 410 320 315 Transverse 640 670 555 460 280 315 Set 1 after 300 per cent elongation for 1 minute with 1 minute rest (per cent) : Longitudinal 11.2 6.0 22.1 34.0 27.5 34.3 Transverse 7.3 5.0 16.3 .24.0 25.0 25.9 The set and tensile strength were determined with different test pieces. [438] TESTING OF RUBBER GOODS Influence of Previous Stretching on Strength, Elongation, and Recovery. Previous stretching seems not only to increase the ultimate elongation, as is generally known, but also the tensile strength, at least in the case of high-grade compounds. Table 3 gives the tensile strength and ultimate elongation obtained in testing six samples of rubber, first, with a single stretch, and, second, by repeated stretching, beginning with 200 per cent and increasing each stretch by 100 per cent until failure. The recovery after a definite elongation is usually greater if the rubber has been previously stretched than if determined in the usual way. This is illustrated by the results shown in Table 4, in which the columns marked " Repeated, stretch " show the set after repeated stretching, beginning with 100 per cent and increasing 100 per cent for each subsequent stretch. The results in columns marked "Single stretch" were TABLE 3 THE INFLUENCE OP REPEATED STRETCHING ON TENSILE STRENGTH AND ULTIMATE ELONGATION Rubber No. 1 2 3 4 5 6 Tensile strength (pounds per square inch) : Single stretch 2,470 1,740 990 1,710 750 930 Repeated stretch 2,610 1,960 1,180 1,790 790 920 Ultimate elongation (per cent) : Single stretch 645 665 510 460 430 375 Repeated stretch 765 780 645 555 440 465 obtained in the usual way, each specimen being stretched but once. In each case, the set was measured from the original gauge marks, after one minute stretch and one minute rest, the tabulated results being the average of a number of observations. TABLE 4 THE INFLUENCE OF REPEATED STRETCHING ON THE RECOVERY OF RUBBER Si 3T AFTER BEING >TKETCHI 3D No. Method of Testing 100 % 200 % - 300 % 400 % 500 % / Repeated stretch 1 4 5 9 5 16 25 1 \ Single stretch 11 7 19 8 29 / Repeated stretch 1.8 4 7.7 13 7 21 2 2 \ Single stretch 8 14 7 21 5 / Repeated stretch 3 7 9 17 7 27 37 3 \ Single stretch 21.7 34 47.0 ( Repeated stretch 4 12 3 28 7 48 7 4 \ Single stretch 14 3 33 56 / Repeated stretch 8 1 19 4 34 \ Single stretch 19 3 33 / Repeated stretch 4 3 16 3 34 6 \ Single stretch 17 35 3 It will be noted that the effect of previous stretching is very marked in the case of Nos. 1, 3, and 4; that it is very slight hi the case of Nos. 2 and 6; and that in the case of No. 5 the set is slightly increased by previous stretching. Influence of the Form of Test Specimen on the Results of Tension Tests. There is a wide difference of opinion in regard to the relative merits of the straight and ring- [439] TESTING OF RUBBER GOODS shaped test specimen. The ring, which is highly recommended by some, undoubtedly possesses certain advantages as regards convenience in testing, and uniform results may be obtained by this method. Ring specimens, however, do not show the full tensile strength of rubber, on account of the uneven distribution of stress over the cross section. This fact is evident from a simple analysis, and may be verified by comparative tests with straight and ring shaped test pieces, provided the straight test pieces are sufficiently enlarged at the ends to prevent failure in the grips, and provided further that the change in width is not made too abruptly. Friction Test. The "friction" or adhesion between the plies of canvas on rubber hose and between the canvas and the rubber tube and cover, is of great importance; B FIG. 2. Two METHODS OP TESTING THE "FRICTION" OF RUBBER BELTING. in fact, the life of hose depends in great measure upon the efficiency of this adhesion. The same is true and to an even greater extent in the case of rubber belting. The friction of "plied" hose is determined in the following manner: In preparing test pieces, a short length of hose is pressed tightly over a slightly tapered mandrel. The mandrel is put in a lathe, and 1-inch rings are cut with a pointed knife. Beginning at the lap a short length of canvas is separated and the ring is pressed snugly over a mandrel which is free to revolve in roller bearings. The rate at which the canvas strips under the action of a specified weight suspended from its detached end is taken as a measure of the friction. The "friction" of rubber-lined fire hose is usually determined as follows: A 1-inch strip is cut and a portion of the tube separated from the jacket. The detached end of the jacket is clamped in a stationary grip and the weight is suspended from the rubber tube. The "friction" between the plies of duck in rubber belting is sometimes measured in the same way (Fig. 2, B), but some prefer to apply the load in a direction at right angles to the plane of separation, as in the case of "plied" hose. This is done by cutting the belt about halfway through along parallel lines 1 inch apart. The belt rests on horizontal supports just outside of the strip which has been cut, and the weight is sus- pended from the detached end of the duck (Fig. 2, A). It is found that for a given weight the rate of stripping is decidedly greater by the former method than by the latter. Table 6 gives comparative results obtained by the two methods in the case of a six-ply belt. Hydraulic Pressure Test. The pressure test as usually made consists simply in subjecting a short length of the hose to water pressure created by a force pump of any [440] TESTING OF RUBBER GOODS convenient type. When testing a full length of hose, or even a short length of large diameter, a pet cock should be provided to release the air as the hose is being filled. TABLE 6 SHOWING COMPARATIVE VALUES OF "FRICTION" BY DIFFERENT METHODS [Inches stripped per minute.] Weight (Pounds) 12 15 18 21 First ply: Tested as in Fig. 2, B 08 26 1 26 3 56 Tested as in Fig. 2, A 0.11 Second ply: Tested as in Fig. 2, B 07 48 2 18 7 65 Tested as in Fig. 2, A 0.15 Third ply : Tested as in Fig. 2, B 04 32 1 33 7 00 Tested as hi Fig. 2, A 0.16 Requirements of specifications as regards the pressure test vary according to the kinds of hose, but, as a rule, the test is made, not with a view to developing the ultimate strength of the hose, but rather to detect defects in workmanship, which are usually noticeable at a pressure well below that necessary to rupture the hose. In the case of fire hose, it is usual to specify a certain pressure when the hose is lying straight or when bent to the arc of a circle of given radius; and the hose must stand a specified pressure when doubled upon itself. It must not show excessive expansion, elongation, or twist under pressure, and the twist must be in a direction tending to tighten the couplings. THE CHEMISTRY OF RUBBER Although rubber has been extensively used for a number of years, it is only recently that we have known very much about its chemical nature. The synthesis of rubber shows that it belongs with the terpenes, having the formula of (Ci Hi 6 ) w , but so far all attempts to show the actual size of this molecule have been unsuccessful. The synthesis is accomplished by the polymerization of the simple terpene, isoprene, which has the formula CsHg. Additional proof of the correctness of the above formula is obtained by means of the various addition products which have been formed, such as the tetrabromide, nitrosite, ozonide, etc. These latter show that in the rubber molecule, each group of CioHie is capable of combining with two atoms of sulphur. It is this adding of sulphur during the process of vulcanization which transforms the crude, sticky gum into a tough, elastic material. The crude rubbers, however, contain other substances than the pure rubber just mentioned; they contain varying proportions of proteids, resins, hydrocarbons, etc. The mechanical impurities and water-soluble constituents are removed by washing. The resins remain behind and form one impurity which must be determined by chemical analysis. The amount and character of these resins are of great assistance in determin- ing the nature of the rubber used in compounding. In some cases the percentage of resins is exceptionally high and then the crude rubbers must be subjected to a deresiniz- ing process before they can be used. The acetone extraction for the purpose of determining the quantity of such resins is made by taking a weighed sample of the finely ground material and extracting it with acetone for a period of from 8 to 15 hours. The acetone is removed by distillation, the residue weighed, and the latter, consisting of the rubber resins, subjected to a very careful examination. If the extraction is made on a vulcanized compound, the acetone also extracts the [4411 TESTING OF RUBBER GOODS free sulphur and any mineral oils or waxes that may have been used. The free sulphur can be readily determined by any of the methods given in the test books, and the amount so determined must be deducted from the total extract. This gives a corrected figure called "organic extract" or, sometimes, simply "corrected acetone extract." For the best grades of Para rubber, this figure should not exceed 5 per cent of the rubber present. A higher percentage of resins would indicate the presence of other rubbers than Para, while the presence of mineral oil indicates the possibility of reclaimed rubber having been used, inasmuch as practically all the reclaimed rubbers are com- pounded with more or less mineral oil to make them work easier. The acetone extraction is one of the most promising tests for the examination of rubber goods. The process of vulcanization consists simply in the chemical combination of sulphur and rubber. Varying amounts of sulphur, depending upon the nature of the crude gum as weil as upon the properties desired in the finished product, are added to the compound, and, after heating, varying amounts of the sulphur will be found to have combined chemically with the rubber, giving thus a new chemical compound with new and desirable properties that are not possessed by the crude material. It is often desirable to limit the amount of sulphur in a compound, and this calls for a method of determining the total amount of sulphur present. In addition to the sulphur combined with the rubber, and the free sulphur already mentioned, sulphur may be present in the mineral fillers. Barytes is one such com- pound, and it is permitted in practically all compounds where the amount of sulphur is specified. Sublimed lead (largely a basic sulphate of lead, of varying composition) does not yet fulfil the conditions just mentioned, but it is quite probable that we shall soon be able to determine it accurately, and it will then be merely a question of deciding whether it is a desirable filler in high-grade compounds. [442] SECTION 7 IRON AND STEEL CASTINGS FOUNDRY PIG IRON Pig iron is the metal reduced from iron ores in a blast furnace. It is the crudest form of iron in the market and seldom or never used without remelting. It is often referred to as an impure iron because there are always contained in the pig metal cer- tain elements such as carbon, silicon, manganese, sulphur, phosphorus, etc. The effect of each of these when combined with iron is substantially as follows: Carbon. This element is always present in pig iron either as free graphite in which thin flakes of graphite are mechanically present between the crystals of iron, as in soft gray iron; or it may be chemically combined as in white iron, which is much harder. The quantity of carbon in cast iron is largely dependent upon the temperature of the furnace. It has been commonly understood that the highest amount of carbon that can be taken up by pure iron is 4.50%, and at 1100 C. (2012 F.) this percentage is correct, but E. Adamson found on raising the temperature to 2200 C. (4992 F.), 9.50% carbon could be absorbed. He further states that iron containing 4.50% carbon when cooled down under normal conditions made white iron; but with the higher percentage it was impossible to secure a white iron, because a certain amount of graphite separated out and made it gray or mottled. An important point is the time during which the iron is left in contact with the hot coke in a foundry cupola, also the temperature of melting, as this latter decides the total amount of carbon taken up. On remelting pig or cast iron, the primary condition of the carbon is important in influencing the grade and strength of the material pro- duced. The quicker the cooling, the more closely compacted the form of the carbon, and therefore the greater the strength and durability of the metal. Foundry Irons. The total carbon in No. 1 pig iron is about 3.60%, of which 0.10% will be combined. In No. 2 pig iron the total carbon is about 3.50%, of which about 0.20% will be combined. In No. 3 pig iron the total carbon is about 4.00%, of which about 1.00% will be combined. In No. 4 pig iron the total carbon is about 4.00%, of which about 2.00% will be combined. Silicon. This element diminishes the power of carbon to unite with iron, and tends to cause the separation of carbon as graphite, especially when the metal is slowly cooled from a white heat. It increases the fluidity of cast iron, while decreasing its strength. As compared with carbon, the silicide FeSi dissolves readily in the iron, and, like the carbide, hardens the metal, but to a much less extent than the carbide, approximately 5% silicon being the same as 1% carbon, so that if silicon be added to iron, there being no other constituents present, the tendency is to give a hard metal, but silicon has an indirect influence which is of much greater importance in that it expels the carbon from combination and throws it into the graphitic form. Gray iron castings, having moderately large crystals, therefore, rich in graphitic carbon, are commonly those of high silicon content, cast in sand, and slowly cooled. Silicon in moderate quantity added to cast iron diminishes the hardness, increases the tensile strength, increases the resistance to crushing, increases the density, prevents the formation of blow holes, and diminishes the shrinkage. Shrinkage appears to closely follow the hardness of cast iron, and as both hardness and shrinkage depend on the proportion of combined carbon they may be regulated by the addition of silicon. [443] PROPERTIES OF PIG IRON Silicon in No. 1 pig iron will average 2.50% and upwards. No. 2 pig iron will range between 2.25% and 2.75%, averaging about 2.50%. No. 3 pig iron will range between 0.75% and 200%, averaging about 1.60%. No. 4 pig iron will range between 0.80% and 2.00%, averaging about 1.60%. Silicon Pig. This alloy when made in the blast furnace is from highly silicious ores, at a temperature much higher than for ordinary foundry irons; the blast must be much stronger to quickly burn the excess of fuel supplied. Silicon is not reduced by carbonic oxide or incandescent carbon alone except in the presence of molten iron, with which it readily enters into combination, the resulting product being a silicon pig, containing from 3 to 10% silicon, depending upon the quality of the ores. According to Turner the maximum resistance to tension, bending, and crushing pig iron is attained by proportions of silicon varying from 1.5 to 3%. Pig iron containing 2 to 3% of silicon is softer than other irons, hence silicon iron is used in admixture with other brands of pig iron in the foundry to produce soft gray castings. Manganese. This element is always present in pig iron; it increases the power of carbon to combine chemically with iron at high temperatures, the effect of which is to change the characteristic coarse grain of gray iron to a finer grain; the percentage of combined carbon will be greater, the iron will be much harder, and if the percentage of manganese be sufficiently increased a white iron will result. Manganese is more readily oxidized than is iron, it therefore unites with oxygen in the liquid iron and acts as a deoxidizer, it also counteracts the bad effects of sulphur, thus preventing red shortness, but it does not prevent the cold shortness due to phosphorus. The compounds of iron and manganese are limited in composition as shown by the crystalline forms so charac- teristic of spiegeleisen, but with increase in manganese the crystals are greatly modified, they are much smaller and less brilliant. Sulphur present as iron sulphide in pig iron will undergo decomposition by manganese and a manganese sulphide formed, thus liberating the iron which was in combination with the sulphur. The bad effects of sulphur, which are to render iron red short hard and brittle, as also its power of reducing oxide of iron, are thus counteracted by the manganese sulphide which, not being as soluble in iron as in iron sulphide, passes into the slag. Spiegeleisen. Manganese combines with iron in nearly all proportions, the two best known alloys are spiegeleisen and ferro-manganese. This alloy much used in steel making is not used in foundry practice, except in special cases. Foundry irons do not often contain more than 4.0% total carbon; spiegeleisen will have 5.0 to 6.0% total carbon; the manganese content will approximate 15.0% in combination with 5.0% carbon up to 30.0% with 6.0% carbon. Ferromanganese. This alloy differs from spiegeleisen in its having a much higher percentage of manganese, of which the lower limit is 25 to 30%; its higher limit extends to 85 or, in some instances, to 90%. Commercial needs cover nearly all pro- portions up to 80% manganese, in combination with 5 to 7% of iron. An alloy with 40% manganese will have a carbon content of 4.5 to 5.0%, which is more carbon than ordinary pig iron contains. This higher carbon content over that of ordinary pig iron is due to the influence of the manganese present which increases the power of the iron to absorb more carbon. Silicon-spiegel. Silicon is always present in ferromanganese as it is a constant constituent in pig iron; it has a marked effect upon steel in promoting the solubility of gases and by reducing a part of the iron oxide. In silicon-spiegel, which is an alloy of iron, manganese, silicon and carbon, notwithstanding the presence of a large amount of manganese, the silicon prevents carbonization taking place by expelling the carbon from combination and throwing it into the graphitic form. This alloy is seldom used in the foundry, but it is useful in the manufacture of steel and steel castings. Oxygen and Manganese. Manganese prevents the oxidation of iron when in the molten state, but as manganese is more oxidizable than iron, the more readily does it combine with oxygen, passing into the slag with silica, thus protecting the other con- stituents in the iron from oxidation. Manganese is reduced from its oxide at a white heat, while silica is unaffected, showing that manganese has a lower affinity for oxygen than silicon. Sulphur. This element is always present in pig iron; its tendency is to make the [444] PROPERTIES OF PIG IRON metal hard, brittle, and weak. The indirect action of sulphur is exactly opposite to that of silicon; that is, it tends to retain the carbon in the combined condition. When sul- phur is present in pig iron it lowers the temperature at which solidification begins, and as the cooling progresses the iron sulphide separates and forms layers or films between the crystals, preventing them from coalescing and from breaking up into ferrite and graphite. These sulphide films are very thin, and a very small quantity of sulphur thus present will make iron brittle. Dr. Moldenke states that, taking the three arbitrary divisions of gray iron castings, the light, medium and the heavy, a limit should be placed in the sulphur at 0.08, 0.10, 0.12 respectively. Sulphur has a well-known influence in increasing the depth of " chill " in solidifying cast iron against a metal wall, that is the thickness of metal free from graphitic carbon produced by the cooling action of that wall. Its other influences are harmful as it increases shrinkage, causes the molten metal to be sluggish and induces unsoundness. Phosphorus. When present in iron ores occurs chiefly as phosphate of lime; as but little phosphorus is oxidized in the blast furnace, nearly all that contained in the ores finds its way into the pig iron. Phosphorus combines with a carbonless iron to form a phosphide Fe 3 P, which is soluble in iron up to 1.7%; beyond this, free phosphide separates out and forms an eutectic, and this is the form in which it occurs in cast iron. The percentage of carbon in pig iron containing much phosphorus is lower than in that containing no phosphorus. Owing to the low melting point of the phosphide, eutectic iron high in phosphorus is extremely fluid and gives fine castings, but the metal is brittle. For fine castings in which strength is not important 1.50% phosphorus may be employed, the metal will not only be very fluid, but the phosphorus lessens the shrinkage of the castings. The presence of a large amount of carbon in cast iron is a means of liberating phos- phorus held in solution, causing it to pass into an eutectic condition in gray cast iron, even if the metal contains less than the 1.7% phosphorus needed to saturate the iron. Phosphorus has little effect on the condition of the carbon, but it makes the metal harder and diminishes the color of gray iron. When phosphorus does not exceed 1.7% the metal is comparatively strong but an addition of 0.35% reduces the strength. For strong castings the phosphorus should not materially exceed 0.50%. The general influence of phosphorus is to increase the fluidity of iron and thus insure castings accurate as to size, because phosphorus lessens the shrinkage on solidifying, it also produces a sounder casting; but phosphorus in excess of about 1.50% has another influence, and that is to weaken iron, to diminish its hardness, and to render it cold short. As a rule pig irons should not, in a cupola mixture, average more than 1.0% phosphorus for the ordinary run of machinery castings, below 0.50% the iron will not be sufficiently fluid, and with more than 1.50% medium and small castings will be too brittle. Foundry Irons. Phosphorus in No. 1 pig iron ranges from 0.50 to 1.25%, often higher. No. 2 pig iron ranges from 0.40 to 1.00%. No. 3 pig iron ranges from 0.40 to 0.80%. -No. 4 pig iron contains about 0.40%, or less. United States Navy specifications require 0.50 to 0.80% in Nos. 1 and 2 pig irons, and 0.50 to 0.90% in No. 3 iron. For No. 4 charcoal iron the maximum phos- phorus is 0.30%. Grading Pig Iron. Pig iron is sold in the market in five grades, Nos. 1, 2, 3, 4 and 5. Besides there are special grades established recently but used extensively, namely: Low phosphorous and sulphur iron used in the open-hearth and Bessemer process. Silicized iron containing 4 to 7% of silicon is also made to soften other irons and to make them run liquid. The following chemical analysis and physical characteristics of Pennsylvania pig irons are by John Hartman. [445] GRADES OF PIG IRON ANALYSIS OF STANDARD No. 1 Pig Iron. Iron. 92.37% Gray. A large, dark, open grain iron, softest Graphitic Carbon ..... 3 . 52 of all the numbers and used exclusively in Combined Carbon 0.13 the foundry. Tensile strength, low. Elastic Silicon 2 . 44 limit, low. Fracture, rough. Turns soft Phosphorus 1 . 25 and tough. Sulphur 0.02 Manganese 0.28 No. 2 Pig Iron Iron 92.31% Gray. A mixed large and small dark grain, Graphitic Carbon 2.99 harder than No. 1 iron and used exclusively Combined Carbon 0.37 in the foundry. Tensile strength and elastic Silicon 2.52 limit higher than No. 1. Fracture, less Phosphorus 1.08 rough than No. 1. Turns harder, less tough Sulphur 0.02 and more brittle than No. 1. Manganese ' . 72 No. 3 Pig Iron Iron 94.66% Gray. Small, gray, close grain, harder than Graphitic Carbon ..... 2.50 No. 2 iron, used either in the rolling mill Combined Carbon 1 . 52 or foundry. Tensile strength and elastic Silicon 0.72 limit higher than No. 2. Turns harder, less Phosphorus 0.26 tough and more brittle than No. 2. Sulphur Trace Manganese . 34 No. 4 Pig Iron A B Iron. . 94.48% 94.08% Mottled. White background, dotted closely Graphitic Carbon 2.02 2.02 with small black spots of graphitic carbon, Combined Carbon 1 . 98 1 . 43 little or no grain. Used exclusively in the Silicon 0.56 0.92 rolling mill. Tensile strength and elastic Phosphorus 0.19 0.04 limit lower than No. 3. Turns with dif- Sulphur . 08 . 04 ficulty, less tough and more brittle than Manganese 0.67 2.02 No. 3. The manganese in this (B) pig iron replaces part of the combined carbon, making the iron harder and closing the grain notwithstanding the lower combined carbon. Iron. . 94.68% Combined Carbon 3 . 83 Silicon 0.41 Phosphorus . 04 Sulphur 0.02 Manganese . 98 Malleable iron contains . Steely iron contains .... Steel contains Hard steel contains .... No. 5 Pig Iron White. Smooth, white fracture, no grain, used exclusively in the rolling mill. Tensile strength and elastic limit much lower than No. 4. Too hard to turn and more brittle than No. 4. Per Cent Combined Carbon 0.25 0.35 0.50 . 1 to 1.50 [416] GRADES OF PIG IRON Taking the sum of the graphitic and combined carbon in each quality of pig iron they are practically the same, the softness of pig iron is dependent on the amount of graphitic carbon in it. Separating the iron in the No. 1 pig from the graphitic carbon it is a nearly pure iron embedded in the graphitic carbon, and in the absence of combined carbon, gives it the softness and flexibility that makes it desirable for machinery and other purposes. The grains of iron are crude crystals. When the iron is nearly pure and allowed to cool very slowly, regular octahedral crystals of iron are formed. No. 1 Pig Iron may be defined as being composed of grains of wrought iron con- nected together but embedded in graphite. No. 2 Pig Iron has more combined carbon, which converts the wrought iron into a soft steel harder to the tool working it. No. 3 Pig Iron has more combined carbon, and the iron portion is a crude steel harder to the tool working it. Nos. 4 and 5 are virtually crude, high-combined carbon steel. The numbers here given, 1, 2, 3, 4, 5, are the old standard. If the impurities in pig iron were uniform, which would be the case if there were only one kind of ore and fuel, the proper plan would be to buy iron by chemical analysis on a basis of graphitic and combined carbon, but the impurities so change the character that the eye is found to be the best guide so far hi fixing the grade. In running the end of the fingers over a fracture of a pig of iron, if the ends of the grains tear the fingers the iron is strong. The analysis (B) of No. 4 Pig Iron shows low in combined carbon, but the manganese hardens the iron and changes it from gray to mottled iron. No. 1 Hot-blast Charcoal Iron Grand Rivers, Ky. Silicon 1.955% Sulphur .029 Phosphorus 488 Manganese . 213 Graphitic Carbon 3 . 310 Combined Carbon 460 Iron 93.545 The pigs of this iron bend before breaking. The ends of the grain are sharp and tear the fingers. On breaking this iron the pig when it strikes the breaking blocks emits a dull thud like lead. It is an iron of high tensile strength and well adapted for making car wheels. The bending of pigs is not confined to charcoal iron. Coke and anthracite irons do the same when using good stock and running the furnace at the proper temperature. [447] FOUNDRY PIG IRON FOUNDRY PIG IRON NAVY DEPARTMENT 1. General Instructions. General instructions or specifications issued by the bureau concerned shall form part of these specifications. 2. Grades. There shall be four grades of pig iron conforming to the requirements stated below. 3. Chemical Requirements. The chemical requirements shall be as follows: Grade Carbon (Mini- mum) Silicon Sulphur (Maxi- mum) Phosphorus Manganese Remarks Per Ct. Per Cent Per Ct. Per Cent Per Cent No. 1. 3.50 2. 75 to 3. 25 0.04 0.50 to 0.80 0.50 to .90 No. 2. 3.25 2.00to2.50 .05 .50 to .80 .50 to .90 No. 3. 3.25 1.25 to 1.75. .06 .50 to .90 .50 to .90 No. 4. 3.25 1.50to2.00j .03 .30 max. .75 to 1.25 Charcoal iron 4. Purpose for Which Used. Grade 1 is suitable for general foundry purposes. It may be used for either heavy or light castings which are to be machined. Grade 2 is suitable for marine engine cylinders, turbine casings, and work of similar character. Grade 3 is suitable for hard, close-grained castings, which are to be machined, where great strength is required. It may also be used with Grades 1 and 2 in varying propor- tions as the work requires. Grade 4 is suitable for use with Grades 1, 2, and 3 where castings of great strength or high finish are desired. 5. Sampling. The sample is to be taken as follows: One pig shall be taken for every 4 tons in the lot, chosen from different locations so as to represent as nearly as possible the average quality of the iron. The pigs selected for sampling shall each be drilled with two ^-inch holes, spaced about \ the length of pig from each end. The holes shall run from bottom to top of the pig, the drillings of the first j inch to be discarded, and the drill to be stopped about f inch from the top of the pig. All drillings from the same lot to be thoroughly mixed, and analysis made from this sample; no resampling to be allowed. 6. Method of Analysis. The inspector at the place of manufacture shall forward to the navy-yard requiring the pig iron not less than 6 ounces of the sample, taken and mixed as above, for analyses and recommendation as to acceptance. In case the first analysis shows that the material does not conform to the specifications a check analysis shall be made. The average of these analyses shall be considered final. Analyses shall be made according to the standard method of the American Foundry- men's Association, the gravimetric method being used for determination of sulphur. Each bidder shall state in his proposal the composition of the pig iron he proposes to furnish if awarded the contract. 7. Penalties. SILICON. For each 0.01 per cent below minimum content specified a penalty of $0.02 per ton to be exacted. If the silicon content is below the specified content by more than 0.10 per cent the pig iron will be rejected. SULPHUR. For each 0.002 per cent above maximum content specified, a penalty of $0.10 per ton to be exacted. If the sulphur content exceeds the specified content by more than 0.01 per cent, the pig iron will be rejected. 8. Locality. When it becomes necessary for a navy-yard to obtain pig iron from a particular locality to insure the best results in the foundry, the requisition should state whether Northern, Virginia, or Southern iron is desired. 9. Sow Iron. Not more than 12 per cent of sow iron will be allowed, and this must be of size to be easily handled. [448] CHEMICAL CHANGES IN CUPOLA CHEMICAL CHANGES IN THE CUPOLA The foundry cupola is a melting and not a refining furnace. The chemical changes which take place in it are of secondary importance to results sought by melting and mixing irons to produce a metal having properties suited to the work in hand. Pig irons contain carbon, silicon, manganese, sulphur, phosphorus, which are chemi- cally combined with the iron, and these must be dissociated before any oxidation be begun. In the combustion zone opposite the tuyeres is a mass of burning coke into which the blast is projected, combustion is quickened, and the heat thus generated melts the charge of pig iron immediately above. As the metal melts it passes down through the combustion zone and accumulates in the hearth below. The falling metal is in small globules or drops, and when these drops pass the tuyeres, where there is always an abundant supply of free oxygen, there must be more or less of oxidizing action upon the iron and its contained elements in solution. Carbon in foundry irons is mostly in the graphitic state and as sucji easily oxidized. But any such oxidation is offset by the drops of iron coming in contact with red hot coke and thus taking up additional carbon, so that, instead of diminishing the total carbon, it happens that the iron flowing from the cupola contains quite as much carbon as was present in the pig iron, and possibly more. Silicon undergoes oxidation during the melting process, it is to be expected, there- fore, that the iron as cast will contain less silicon than the pig, because 0.25 to 0.40% will have been burned out of it during the melting of the iron, and proper allowance for this wastage must be allowed for in the charge. Manganese is more oxidizable than iron, it more readily unites with oxygen and thus retards the oxidation of iron; during the process of cupola melting manganese volatilizes to some extent, but the quantity present in foundry pig iron is never large and its in- fluence in the cupola is not important. Its tendency is, however, to counteract the bad effects of sulphur, and to increase the solvent power for carbon at high temperatures and to prevent the separation of graphite at lower ones. It also assists in making a more fusible slag by the readiness with which it unites with silica. Sulphur is always present in pig iron. Irons high in silicon are usually low in sulphur; the latter is always present as ferrous sulphide which is readily soluble in molten iron. The tendency of sulphur is to keep the carbon in the combined condi- tion, the effect of which is to make castings hard and brittle. Coke always contains sulphur and during the process of combustion it unites with oxygen forming sulphurous oxide, which passes off with the other products of combustion into the open air. Sul- phur in the pig iron as charged is not reduced; during the process of cupola melting, in fact, the iron may take up 0.02 to 0.03% sulphur from the coke ; castings from pig irons containing . 08 % sulphur may contain 0. 10% sulphur, especially during the first of the heat. Phosphorus passes through the melting process in the cupola unoxidized; whatever phosphorus is contained in the pig iron as charged will be present in the molten iron flowing from the cupola. Foundry Coke. An excellent quality of coke for foundry use is such as made in the Connellsville region, Pennsylvania; its characteristics are: steel-gray color, a metallic luster, columnar, very strong, dense, slightly puffed on the surface, burns free under a strong blast, and will support any necessary weight of iron above it, in a cupola, without crushing. Such a coke, after expulsion of moisture, averages about 90.0% fixed car- bon, no volatile matter, 10.0% ash; the latter consisting of about 58.0% silica, 35.0% alumina, 2.0% sesquioxide of iron, 1.5% lime, 2.0% sulphur, 1.0% other constituents, such as magnesia, potash, soda, phosphoric acid, etc. The quantity of sulphur in the ash will depend largely upon the quantity of pyrites in the coal before coking. Pyrites is also the probable source of the oxide of lime in ashes; the greater part of the sulphur being expelled by heat during the process of coking, its equivalent of oxygen unites with the iron, with which hydrogen also combines, forming the sesqui- oxide of iron. Alumina present in ashes is in the form of a clay or a mixture of the two simple [449] CHEMICAL CHANGES IN CUPOLA earths, alumina and silica, generally tinged with iron, it is infusible in the cupola. Silica is decomposed at a red heat by carbon in presence of iron and at white heat by carbon monoxide, CO, a metallic silicide being formed ; it plays a very important part in the formation of slags, and fusion is not necessarily required to produce combination. The bases which most frequently occur in slags are lime, magnesia, oxide of iron, potash in small quantity, and alumina. Calorific Value of Coke. The total heat obtained by the combustion of 1 pound of carbon, in oxygen to carbon dioxide CO 2 , as determined by calorimeter test, varies in a slight degree from 14500 B.t.u., that value may, therefore, be accepted as a fan* average. If the coke is 90.0% carbon we have 14500 X 0.9 = 13050 B.t.u. as the total calorific value of 1 pound of coke. A result such as this is never realized in practice, instead of the carbon being burnt to carbon dioxide CO 2 , yielding 14500 B.t.u., it may be burnt to carbon monoxide CO, the calorific value of which is 4450 B.t.u., approxi- mately one-third of the former. Gases escaping from the cupola show about equal volumes of CO 2 and CO, the calorific value of the carbon suffers loss to the extent of: (14500 X .5) + (4450 X .5) = 9475 B.t.u., equivalent to 65% thermal efficiency. The temperature at the melting zone in the cupola may be estimated thus: For perfect combustion 1 pound of carbon will require 2 . 67 pounds of oxygen, yielding 3 . 67 pounds carbon dioxide CO 2 . In addition there will be 8.94 pounds of nitrogen left after the separation of the oxygen from the air. The specific heat of carbon dioxide CO 2 is . 216, and that of nitrogen . 244. We have then : Specific Heat Products Pounds Heat Units Carbon dioxide CO 2 3.67 X .216 = .794 Nitrogen 8.94 X .244 = 2. 181 12.61 2.975 heat units absorbed in raising the temperature of the products of combustion of 1 pound of carbon, 1 F. The combined weights of the two products are 12.61 pounds. Then: 2.975 -J- 12.61 = 0.236, their mean specific heat. Dividing the total heat of combustion of 1 pound of carbon by the heat units absorbed, as above, we have: 14500 -T- 2.975 = 4874 F.; the highest theoretical temperature attainable by 11.61 pounds of air, the minimum theoretical limit. This temperature occurs only opposite the tuyeres and at the time of combination. As the carbon dioxide CO 2 rises in the cupola it passes through a bed of incandescent coke, some of the gas takes up another equivalent of carbon and carbon monoxide CO is formed. Upon analyzing the gases escaping from the cupola it is found that carbon dioxide CO 2 and carbon monoxide CO escape in practically equal volumes. The temperature is greatly affected thereby, and may be estimated per pound of carbon thus: \ Specific Heat Gas Pounds Heat Units Carbon dioxide C0 2 1.84 X .216 = .397 Carbon monoxide CO 1.17 X .243 = .284 Nitrogen 6.71 X .244 = 1.637 2.318 The total heat of 1 pound of carbon burnt: 0.5 Ib. burnt to CO 2 = 14500 -J- 2 = 7250 0.5 Ib. burnt to CO = 4450 ^ 2 = 2225 9475 Then: 9475 -h 2.318 = 4087 F., about 16% less than in the earlier example. [450] CHEMICAL CHANGES IN CUPOLA The heat required to raise 1 pound of iron to its melting point and melt it, and im- part sufficient heat to the molten metal to keep it fluid for pouring, is about 625 B.t.u., or 2240 X 625 = 1,400,000 B.t.u., per ton. The melting of iron is always accompanied by the production of slag consisting principally of silica and alumina, each having a higher melting point than iron. The percentage of slag will vary, but we may for the purpose of illustration take the very low limit of 3.5% of the weight of pig iron melted, or 78 pounds of slag per ton. The total heat required to melt 1 pound of slag at furnace temperature approximates 750 B.t.u. Then: 78 X 750 = 58500 B.t.u., to be added to 1,400,000 = .1,458,500 total B.t.u. required per ton of pig iron melted. In estimating the calorific value of coke, it was assumed to be 90.0% carbon, therefore 14500 X 0.90% = 13050 B.t.u. per pound. There would be required for 2240 pounds of iron 1,458,500 * 13,050 = 111.7 pounds of coke. This corresponds to the melting of 20 pounds of iron per pound of coke. No such rate of melting occurs in any cupola; reference has already been made to the fact that the escaping gases consist in practically equal volumes of CO 2 and CO, and that the B.t.u. had been reduced from 14,500 to 9,475 per pound of carbon. We have then 9,475 X 90.0% = 8,527 B.t.u. per pound of coke, and 1,458,500 -5- 8,527 = 171 pounds of coke per ton of iron melted, or 13 pounds of iron melted per pound of coke, on the carbon basis alone. Excess of Air. In estimating the calorific value of 1 pound of carbon in which 14,500 B.t.u. were obtained, it was stated that 11.61 pounds of air were used, a much smaller quantity than obtains in practice. Probably no less than 18 pounds of air are blown into the cupola for each pound of coke burnt; this air has to be heated to the temperature of the escaping gases, and one bad feature about it is that the abstraction of heat occurs in the melting zone, thus depriving the furnace of heat which otherwise would be usefully employed in melting iron. This dilution of gases in the cupola re- duces its efficiency and is one of the reasons for its lower melting capacity, reducing the ratio of 13 to 1 as given above to 10 to 1, a good working ratio and much better than obtains in many foundries. Temperature of Escaping Gases. This will vary with each cupola; beginning with the temperature of the melting zone, the gases lose heat in their passage upward through the successive layers of iron and coke, constituting the cupola charge. A reduction in temperature occurs during the inevitable breaking down of carbon dioxide CO 2 and the formation of carbon monoxide CO. There is also an excess of air in the cupola which carries with it a temperature corresponding to that of the fuel gases, this excess of air maybe anywhere from 50 to 100% of that necessary for combustion. The presence of moisture in the air; in the coke; on the surface of the iron to be melted; the melting of the several constituents which form the slag; the radiation of heat from the cupola itself, all these tend to reduction of temperature of escaping gases, which for a well proportioned cupola may, in the absence of pyrometer test, be reckoned at 1600 F. Slag. This is a fused compound of silica in combination with lime, or other bases; slag produced in the cupola will vary in composition with the irons being melted. Silicon is easily oxidizable and forms silica. Most pig irons are cast in sand and a certain amount of sand, say 1.0% attaches to the outer surface of the pig; this sand is nearly all silica. Coke consists of about 50.0% ash, and this ash contains about 50.0% silica. When iron is oxidized ferrous oxide is formed, and this oxide combines with silica forming silicate of iron, or slag. Flux. In order to promote the fusion of non-metallic substances during the process of melting iron in a cupola a flux is employed. For foundry use calcium carbonate CaCO 3 , or carbonate of lime is commonly used, chiefly as limestone, gray in color, more or less impure, containing clay, sand, and other substances. If procurable, the white marble refuse chips from a stone yard are preferable, on account of their greater purity. When calcium carbonate CaCOa is heated it yields calcium oxide CaO, or lime, a white amorphous infusible substance, and carbon dioxide CO 2 , or carbonic acid gas. Pure carbonate of lime CaO 3 = 56% lime CaO -j- 44% carbon dioxide C0 2 . The carbon dioxide passes off into the open as a gas ; the lime passes into the slag. Limestone should not contain much silica because of its affinity for lime, forming a silicate of lime, which reduces the fluxing value of the limestone and increases the [451] CHEMICAL CHANGES IN CUPOLA quantity of slag. When the melting has begun, the molten iron is in an atmosphere containing free oxygen and oxidation of iron takes place; some of the silicon in the iron is also oxidized, and silica is formed. The oxide of iron will combine with the silica, and a silicate of iron or slag is formed. The fluid slag finds its way down through the burn- ing coke and in its course it takes up any ash present in the coke, as well as the sand which adhered to the pig iron, these, and other impurities, combine in a fluid mass which floats upon the molten iron at the bottom of the cupola. If white marble chips are used, the quantity may be, for reasonably clean pig, about 20 pounds per ton of iron. For ordinary limestone the quantity may be 40 pounds or more to the ton. Much depends upon the purity and cleanliness of the iron and the quantity as well as the quality of the ash from the coke. If the iron is clean, the weight of the slag will be about the same as that of the limestone charged. For each 56 parts of lime that can be put into the slag, 72 parts of iron oxide, or 56 parts of iron will be liberated. Slag from a cupola contains from 5.0 to 8.0% of iron, partly as oxide, and partly in small particles held in mechanical suspension. Fluorspar. This substance derives its name from its power to effect the liquefaction of earthy substances. It is a combination of 1 part calcium Ca with 2 parts fluorine F, the formula being CaF 2 . This compound occurs in large quantities in nature in crys- tallized cubes; it is insoluble in water. If it be strongly heated in contact with silica, the latter takes up the fluorine to form the gas silicon fluoride SiF 4 , whilst the calcium and oxygen unite to produce lime, which combines with another portion of the silica to form a silicate of lime. The silicate of lime would not easily fuse into a slag by itself, but when clay and oxide of iron are present, a slag is readily produced. It is used in metallurgical operations for the reason that it melts readily into a transparent liquid which does not act upon other substances easily; it serves as a liquid medium in which reactions take place at high temperatures. For foundry use it serves no useful purpose that cannot be had by the use of white marble chips or first quality limestone except perhaps to increase the fluidity of the slag. FUEL EFFICIENCY OF THE CUPOLA FURNACE The heat balance in melting 80,000 pounds of pig iron in a 60-inch cupola is thus given by John Jermain Porter, Trans., Am. Inst. Mining Engrs., 1912. The cupola selected operated under fairly efficient conditions; the data are as follows: Cupola, 60 inches in diameter, 15 feet high to the charging door, with a 9-inch lining. Bed charge, 2,000 pounds of coke and 4,000 pounds of iron. Subsequent charges, 400 pounds of coke and 4,000 pounds of iron. Total number of charges, 20. There was 800 pounds of coke recovered from the drop, hence the total coke burned is 8,800 pounds, or 0.11 pound of coke per pound of iron. Coke contains 90 per cent fixed carbon and 2 per cent of moisture. 300 pounds of kindling wood is used in lighting. 80 pounds of limestone (95 per cent CaCOs) is used per charge, 0.02 pound per pound of iron. Melting loss 4 per cent; distributed thus: Fe, 3.5; Si, 0.25; Mn, 0.25 per cent. Aver- age analysis of top gases: CO 2 , 15.1; CO, 10.0 per cent. Average temperature of top- gases, 1,600 F. Temperature of air and stock charged 60 F. Dew-point of air, 50 F. The items entering into the total heat balance and their calculation are as follows: 1. Heat of Combustion of Fuel. Total heat evolved = 14,580 X lb. of carbon burned + 7,200 X lb. of wood burned. Hence B.t.u. per pound of iron charged = 8,800 X 0.9 X 14,580 + 300 X 7,200 80,000 = M7 ' 4 2. Oxidation of Iron to FeO. B.t.u. per pound of iron charged = 0.35 X 2,112 = 74.0 3. Oxidation of Silicon to SiO 2 . B.t.u. per pound of iron charged = 0.0025 X 12,600 = 31.5 4. Oxidation of Manganese to MnO. B.t.u. per pound of iron charged = . 0025 X 2,975 = 7.4 5. Sensible Heat in Coke. B.t.u. per pound of iron charged =0.11X60X0.16 = 1.1 6. Sensible Heat in Iron. B.t.u. per pound of iron charged = 1X60X0.12 = 7.2 [452] FUEL EFFICIENCY OF CUPOLA 7. Sensible Heat in Limestone. B.t.u. per pound of iron charged = 0.02 X 60 X 0.21 = 0.252 8. Sensible Heat in Blast. From the gas analysis, 9 pounds of air is used per pound of carbon burned, hence B.t.u. per pound of iron charged = 0.11 X 0.9 X 9 X 60 X 0.235 = 12.6. 9. Heat of Formation of Slag. This is a matter of some uncertainty but is of minor importance. The heat of formation of CaO + SiO 2 is 278 B.t.u. per pound, and of FeO + giO 2 121 B.t.u. per pound, and if we assume that the slag consists of equal parts of each, and that . 06 pound of slag is made per pound of iron, the heat of the forma- tion of the slag is in B.t.u. per pound of iron charged 0.06 X 200 = 12.0. la. Heat in Molten Iron. B.t.u. per pound of iron charged = 0.96 X 450 = 432.0. 2a. Heat in Molten Slag. B.t.u. per pound of slag = 1 X (t X (0. 17 + 0.00004t) + latent heat of fusion + (t/ t) X 0.35), where t = the melting point of the slag or say, 2,000 F., and t' = the temperature at which it issues from the cupola or, say, 2,250 F. Hence B.t.u. per pound of iron charged = 0.06 (2,000 X 0.25 -f- 160 -f 250 X 0.35) = 44.8. 3a. Heat to Decompose Limestone. B.t.u. per pound of iron charged = 0.02 X 0.95 X 813 = 15.4. 4a. Heat to Evaporate Moisture in Coke. B.t.u. per pound of iron charged = 11 X 0.02 X 966 = 2.1. 5a. Heat Stored up in Lining. The weight of the lining below the charging door figures out approximately 27,400 pounds. Estimating its average temperature to be 1,000 F., the B.t.u. per pound of iron charged = 27,400 X 1,000 X (0.193+0.000043 X 1,000)-= 80.9. 80,000 6a. Heat to Decompose Moisture of Blast. A dew-point of 50 F. corresponds to 0.0075 pound of water per pound of moist air. Hence the B.t.u. per pound of iron charged = 9 X 0.9 X 0.11 X 0.0075 X 5,800 + 38.8. 7a. Heat Sensible in Gases. The weight of the gases per pound of carbon burned works out as follows: CO 2 , 2.200; CO, 0.933; N, 6.910; H, 0.007; total, 10.050 pounds. The average specific heat is 0.23 + 0.000023t. Hence the B.t.u. per pound of iron charged = 0.11 X 0.9 X 10.05 X 1,600 X 2,668 = 424.7. 8a. Heat Potential in Gases. B.t.u. per pound of iron charged = 0.11 X 0.9 X 0.933 X 4,370 = 403.7. 9a. Heat Lost by Radiation Plus Error and Unaccounted For. This amount is found by difference to be 174.2 B.t.u. per pound of iron charged. Summarizing these items, we get the following heat balance expressed in B.t.u. per pound of iron charged: Sources of Heat Heat Used and Lost 1. Combustion of fuel. . . 1470.4 2. Oxidation of iron 3. Oxidation of silicon .... 4. Oxidation of manganese , 5. Sensible in coke 6. Sensible in iron 7. Sensible in limestone ... 8. Sensible in blast . . .. 74.0 .. 31.5 7.4 1.1 7.2 0.3 .. 12.6 9. Formation of slag 12.0 1616.5 la. In molten iron 432 . 2a. In molten slag 44 . 8 3a. To decompose limestone .... 15 . 4 4a. To evaporate moisture 2.1 5a. To heat up lining 80 . 8 6a. To decompose moisture 38.8 7a. Sensible in gases 424.7 8a. Potential in gases 403 . 7 9a. Radiation and error. . 174.2 1616.5 The great source of wasted heat in the cupola is in the gases escaping at the top. If these losses could be eliminated it should be possible to charge some 22 pounds of iron for each pound of coke, have the gases come off from the top perfectly cold and containing no CO, and the iron satisfactorily melted. Actually this cannot be done. [453] IRON CASTINGS In the cupola there is a deep bed of carbon (coke) which is being replenished from above as fast as it is consumed. Under these conditions, with carbon always in excess, the products of combustion depend upon the temperature and time of contact of the gases with the excess carbon. The tendency is towards the formation of CO at high temperatures and CO 2 at lower temperatures. Now in the cupola there is a zone im- mediately in front of the tuyeres which is cooled by the inrushing blast of cold air and in which CO 2 is formed, this formation of CO 2 being also aided by the fact that in this space oxygen is supplied faster than the surface of the coke present can combine with it. Further in and up in the cupola the temperature is much higher and conditions are such as to favor the reduction of the CO 2 to CO, according to the reaction CO 2 + C = 2 CO. Time, however, is necessary for this reaction to take place, and since the velocity of the gases is very great and they are in contact with the hot carbon for only an instant, more or less CO 2 invariably passes through unchanged. On the other hand, it is im- possible to make the velocity of the gases so great as to prevent entirely the reduction of CO 2 without creating intensely oxidizing conditions inside of the cupola and, hence, destroying its usefulness as a melting furnace. The temperature of the top gases depends on the amount of heat absorbed by the stock in proportion to the total amount generated in the zone of combustion. More heat is generated when carbon is burned to CO 2, and the rapid rate of blowing necessary to the formation of a large percentage of CO 2 increases the velocity of the gases and gives less opportunity for the absorption of heat by the stock. IRON CASTINGS NAVY DEPARTMENT 1. General Instructions. General instructions or specifications issued by the bureau concerned shall form part of these specifications. 2. Physical Properties. The physical characteristics of cast iron are to be in accordance with the following table: Grades of Iron Cast- ings Tensile strength (pounds per square inch) Length of test piece not less than 2 inches Transverse breaking load (for bar 1 inch square loaded at mid- dle and resting on sup- ports 1 foot apart) Purposes for which intended 20,000 (min.).... . 2,200 (min.). 2,800 (max.) 20,000 (min.) 2,500 (min.), 20,000 (min.) 2,200 (min.) To be inspected to see if they are in all respects suitable for the purposes for which they are intended. Steam cylinder and valve-chest cas- ings. Steam turbine casings, steam turbine parts. Gas-engine cylinder and valve-chest casings. Internal-combustion engine cylinders and valve-chest casings. Cylinder liners and valve-chest liners. Steam, gas and internal-combustion engines. Cylinder and valve-chest liners, small gas engines, and internal-combus- tion cylinders when cast in one piece. Other important parts, such as main and auxiliary engine parts, etc. Minor parts, such as furnace fittings, etc. [454 MALLEABLE CAST IRON 3. Placing of Order. The grade and quality of the metal will be specified on the order. 4. Hardness Requirement. Great care must be taken to determine that the ma- chinery specifications for hardness of cylinders, liners, and valve-chest liners are complied with, and a test piece from the casting should be machined in order to show the degree of hardness. 5. Quality of Material. The castings must be of uniform grain, smooth, free from blow-holes, porous places, shrinkage, and other cracks or defects, and must be well cleaned. TESTS 6. Number of Tests. Sound test pieces shall be taken in sufficient number to exhibit the character of the metal in the entire piece from all castings requiring physical test. 7. Additional Tests. The inspector may require from time to time such additional tests as he may deem necessary to determine the uniformity of the material. 8. Rejection on Delivery. Iron castings may be rejected at the place of delivery for surface or other defects either existing on arrival or developed in working or storage, even though the material may have passed the required inspection at the place of manufacture. FINISH 9. Surface Inspection. The scale shall be removed from the unfinished parts of the inside of all cylinders, cylinder covers, and valve-chest covers, and from the un- finished parts of all cylinder and valve-chest liners, and from ports and passages of cylinders and valve chests, either by pickling or other approved process as may be required. 10. Finished Size. All engine castings must finish to blue-print size. 11. Marking and Stamping. Each casting, if large enough, shall be stamped with heat number, figures to be not less than \ inch long, and shall have size and order number plainly marked with white paint. 12. Inspection Stamps. Castings which have passed inspection must show the U. S. anchor and other stamps necessary for identification, encircled by white-paint marks. MALLEABLE CAST IRON The following is an abstract of a paper read by Dr. Richard Moldenke before the Am. Foundrymen's Ass'n., 1903. While nominally the composition of a good malleable casting is but little different from that of a car wheel, the fact that it can be twisted, bent and hammered out hot or cold and has double the tensile strength shows that the constitution of the casting is quite different. This difference may be traced to the condition of the carbon. In the ordinary gray casting we may have some 3 to 3| per cent graphite present. In malleable castings we have the same amount as graphite in the analysis, but radically different in characteristics. This form of carbon due to the annealing process has been called temper carbon by Professor Ledebur, who first described it in connection with the malleable (Ger. " temper ") process. The tensile strength of malleable castings should run between 42,000 and 47,000 pounds per square inch; castings showing only 35,000 pounds are serviceable for ordinary work. It is not advisable to run beyond 54,000 pounds per square inch, for the resilience is reduced, and one of the most valuable properties of the malleable casting impaired. The elongation of a piece of good "malleable" will lie between 2| and 5%, measured between points 2 inches apart. The thicker the piece the smaller the elongation. In making the transverse test, the deflection of an inch square piece, resting upon supports 12 inches apart, should be over \ inch, the breaking weight being at least 3,500 pounds. Very soft iron often deflects 1\ inches under the test, but this is exceptional and may not be reproduced continuously. [4551 MALLEABLE CAST IRON The high resilience, or resistance to shock, in "malleable" is its most useful char- acteristic. Only where an exceedingly high tensile strength is required, as in the car couplers for the heavy modern trains, is the malleable casting being gradually replaced by steel castings. Composition and Structure. Originally cast to be perfectly chilled that is, with the carbon all combined and a contraction of some 1 inches to the foot, the annealing process serves to expel the carbon from its state of combination, depositing it between the crystals of the iron, not in the crystalline graphite of the gray iron, but as an amor- phous form not unlike lampblack. At the same time an expansion equal to half of the original contraction takes place, the net result being a shrinkage allowance for the pattern identical with that for gray iron castings of similar shape and thickness. Besides this expulsion of the carbon from its combination, there is a removal of some of it from the outer portions of the casting. This amounts to nearly all in the skin to nothing inch inward. It will be noted that owing to the removal of varying amounts of carbon from the skin to the interior no carbon determination of a malleable casting is of any value, unless the sample is taken before the anneal, and even then it is only good for the total carbon. For an annealed piece of sample taken from the center of the fracture with at least f inch untouched around the drill would give a fair indication of the carbon contents, but cannot claim accuracy. Formerly charcoal iron about 4% carbon was the rule in malleable castings; in these days of coke irons and steel additions to reduce the carbon this may run as low as 2.75% before trouble ensues in the anneal, if not already in the foundry through excessive cracking and shrinkages. With the modern demand for a high tensile strength it is well to place the lowest limit at 2.75%, and the upper limit for common work would be found in the saturation point of this grade of iron, or 4.25%. It is absolutely neces- sary that the hard casting be free from graphite; even a small amount of this indicates an open structure with consequent ruin to the work in the anneal from penetrating oxygen. To keep the carbon in the combined state is the function of the silicon per- centage arranged for in the mixture, the rate of cooling due to the cross section, the pouring temperature, sand, etc. The sulphur content is quite important, the percentage should not be allowed to go over 0.05, and it is wise to hold the pig iron below 0.04, and to see that the fuel used is not too rich in sulphur. Manganese is seldom troublesome, as it does not often exceed 0.40 in the mixture, which means 0.10 to 0.20 in the casting. Above 0.40 in the casting it begins to give trouble in the anneal, therefore, manganese should be kept low. Phosphorus should not exceed 0.225, and is better kept below this. Silicon. In general the thicker the casting the lower the silicon allowable in order to get a white iron in the sand. Thus for the heaviest class of work the silicon of the casting should not exceed 0.45. For ordinary work 0.65 is the point to be sought for. Agricultural work may run up to 0.80, while the lightest casting may have 1.25% without danger, though it is not advisable to exceed this limit for anything. American practice differs from the European in several respects; we have a com- paratively short anneal that is, we aim at a conversion of the carbon rather than its removal. Over there it is desired to get all carbon out, so that a wrought iron casting, if it may be so called, may result. The common American practice is to use the reverberatory, or air-furnace, either with or without the top blast over the bridge to hasten the melting. While not many malleable establishments have the open-hearth furnace it is undoubtedly an economical melter, provided it be kept busy. It also means a man who will push the pigs into the bath as quickly as they can be cared for, mix his iron well and fire sharp and quick so that the process becomes one of melting only rather than a refining or burning out of large quantities of silicon and carbon. Under fan- conditions, with three heats daily from a 10-ton open-hearth furnace using producer gas as fuel, the ratio is about one of coal to six of iron. In the rever- beratory furnace the fuel ration is one to four at best, and often only one to two. It is not advisable to make larger heats than 15 to 18 tons, as the time consumed in melting, [456] MALLEABLE CAST IRON and especially in pouring from the small ladles after tapping, becomes so great that the bath is seriously damaged by undue oxidation and overheating. For making malleable castings, the open-hearth furnace should be pushed very hard for a time, obtaining a short, sharp heat. The silicon of the heat may be cal- culated for a loss of 20 to 25 points, whereas from 35 upward is the rule in other processes. The cupola still turns out a considerable tonnage of malleable castings, but this process will be gradually superseded by the furnace method, chiefly on account of the better grade of work turned out by the latter. Cupola iron requires some 200 F. more than furnace iron to anneal it properly. It seems strange that it should be so, possibly the structure of cupola iron is so close that it requires more effort to get the crystals apart and to effect the liberation of the carbon from its state of combination. Whether this is due to the contact of the metal with the fuel as it trickles down in thin streams and drops is hard to say, but the difference certainly exists and must be provided for in the anneal. In the annealing process we find two extremes leading to about the same results: A short anneal at a very high heat is as effective as a comparatively long anneal at a much lower temperature. That is to say, we can change the carbon in a casting, by placing it overnight in a melting furnace which has cooled below the melting point of iron, or do the same thing in the annealing oven at a much lower temperature, but giving it a week's time. Of the two methods the latter is preferable, as it not only permits the change in the carbon but also gives the carbon time to get out. The result is a good, reliable casting, while in the hurry-up processes one never knows whether they are annealed at all. The annealing process may be described by a curve which runs up quickly, remains horizontal for a short time and then drops very gradually. That is, a sharp heating up, in the shortest safe time possible, then a shutting off of the dampers and maintaining of the temperature evenly for a period of, say, two full days at least, and then a gradual cooling down to at least a black heat before dumping. Furnace iron of average thickness must have received over 1,250 F. after coming up, until cutting off the heat, to be safely annealed. Perhaps even then some of the work must be put back for another anneal. A safer limit is 1,350 F., and no more is necessary. This temperature must exist in the coldest part of the furnace, or usually at the lower part of the middle in the front row pots. As a rule the upper space of an oven is some 200 F. higher than this. Translating these temperatures, we find that 660 C. (1,220 F.) is the lowest point for successful annealing of furnace iron, while 780 C. (1,436 F.) is the safest one. For cupola iron the temperature should be about 850 C. (1,562 F.). SPECIFICATIONS FOR MALLEABLE IRON CASTINGS Malleable iron castings may be made by the open-hearth, air furnace or cupola process. Cupola iron, however, is not recommended for heavy nor for important castings. Chemical Properties. Castings for which physical requirements are specified shall not contain over .06 sulphur nor over .225 phosphorus. Physical Properties. (1) Standard test bar shall be 1 inch square and 14 inches long, without chills and with ends perfectly free in the mold. Three shall be cast in one mold, heavy risers insuring sound bars. Where the full heat goes into castings which are subject to specification, one mold shall be poured two minutes after tapping into the first ladle, and another mold from the last iron of the heat. Molds shall be suitably stamped to insure identification of the bars, the bars being annealed with the castings. (2) Of the three test bars from the two molds required for each heat, one shall be tested for tensile strength and elongation, the other for transverse strength and deflection. The other remaining bar is reserved for either the transverse or tensile test, in case of the failure of the two other bars to come up to requirements. The halves of the bars broken transversely may also be used for tensile strength. (3) Failure to reach the required limit for the tensile strength with elongation, as [457] MALLEABLE IRON CASTINGS also the transverse strength with deflection, on the part of at least one test rejects the castings from that heat. (4) Tensile Test. The tensile strength of a standard test bar for castings under specification shall not be less than 42,000 pounds per square inch. The elongation measured in 2 inches shall not be less than 2J%. (5) Transverse Test. The transverse strength of a standard test bar, on supports 12 inches apart, pressure being applied at center, shall not be less than 3,000 pounds, deflection being at least % of an inch. Test Lugs. Castings of special design or of special importance may be provided with suitable test lugs at the option of the inspector. At least one of these lugs shall be left on the casting for his inspection upon his request therefor. Annealing. (1) Malleable castings shall neither be over nor under annealed. They must have received their full heat in the oven at least sixty hours after reaching that temperature. (2) The Saggers shall not be dumped until the contents shall at least be black hot. Finish. Castings shall be true to pattern, free from blemishes, scale or shrinkage cracks. A variation of j\ of an inch per foot shall be permissible. Founders shall not be held responsible for defects due to irregular cross sections and unevenly dis- tributed metal. MALLEABLE IRON CASTINGS NAVY DEPARTMENT 1. General Instructions. General instructions or specifications issued by the bureau concerned shall form a part of the specifications. 2. Open-Hearth or Air- Furnace. The malleable iron castings for which physical requirements are specified may be made either by the open-hearth or air-furnace process. 3. Physical and Chemical Properties. The physical and chemical characteristics of malleable iron castings are to be in accordance with the following table: Material Tensile Strength per Square Inch (Min.) Elonga- tion in 2 Inches (Min.) Transverse Breaking Bar 1 Inch Square, 12 Inches long, loaded at Center Deflec- tion MAXIMUM Sul- phur Phos- phorus Open-hearth or air- furnace process. . . Pounds 36,000 Per Ct. 3 Pounds 3,000 Inch $ Per Ct. 0.08 Per Ct. 0.225 4. Freedom from Defects. Castings must be true to pattern, free from scale, blemishes, shrinkage cracks, or other defects. 5. To Have Sufficient Anneal. Castings must be neither "over" nor " under" an- nealed. They must have received their full heat in the oven at least 60 hours after reaching that temperature, and shall not be dumped until they are at least "black hot." 6. Test Bars; How Cast and Number. Test bars to be cast accurately 1 inch square, not less than 14 inches long, and of sufficient number to insure sound ones for all test purposes. 7. Appearance After Machining. The castings when machined should show the annealing process has changed the carbon from the combined carbon to graphite carbon. 8. Pipe Flanges. For pipe flanges the castings should be made sufficiently malleable to permit of steel tubing being satisfactorily expanded into them without distorting the shape or cracking the castings. If more than one casting of any size ordered will not stand the expanding, they must be replaced with satisfactory castings. 9. Specifications for Malleable- Iron Pipe Fittings. These specifications are inde- pendent of Specifications for Malleable-Iron Pipe Fittings, Black or Galvanized, issued by the Navy Department. [458] SEMI-STEEL CASTINGS SEMI-STEEL CASTINGS Melting steel with iron in a cupola adds strength to the resultant casting; to what extent this is so, and the best proportion of steel to use are not clearly understood. To ascertain definitely in regard to these and to trace if possible the connection between percentage of total carbon in the iron and its tensile strength, Mr. H. E. Biller made the tests summarized in the accompanying table: PROPERTIES OF SEMI-STEEL CASTINGS JJlCdlkUJg MlCHgUI OICCI i .-! :__ Phos- Man- 'Com- ~V^al ULMI Graph- Trans- mixture. No. Silicon. Sulphur. phorus. ganese. bined. itic. Total. Tensile. verse, percent. I 1-43 0.047 0.564 0.82 0.67 3-H 3 .8l 23,060 2,550 o 2 1.50 .065 >532 33 .64 344 3-08 30,500 2,840 25 3 1.76 .062 .488 53 .51 3.12 3.63 22,l8o 2,440 4 1.76 139 .515 57 43 2.94 3-37 27,090 2,770 \2 1 A 5 1.77 .069 339 .49 .56 2.87 343 32,500 3,120 12% 6 1.83 .IOO .610 55 51 2.44 2.95 36,860 3,280 25 7 1-75 .089 .598 35 .74 2.12 2.86 30,160 3,130 37K 8 1.96 .104 .446 63 3-18 3-8i 21,950 2,230 o 9 2.12 037 .410 .26 38 3-26 3-64 21,890 2,470 12^ 10 2.16 .060 .315 .20 i. 06 2.30 3.36 26,310 2,670 \2y t II 1.97 093 .470 48 57 2.83 340 32,530 3,050 37/4 12 2-35 .061 .515 .56 54 340 3-94 21,990 2,200 o 13 2-53 .104 .490 54 .60 2.56 3-16 33,390 2,850 25 14 2. 3 6 .064 .327 .24 i. 08 2.15 3-23 31.560 3,200 25 The tensile and transverse strengths given in the table are the average of two, and in some cases three test bars. For tensile strength a l|-inch round bar was used. The transverse strength was obtained from a 1-inch square bar placed on supports 12 inches apart. The object sought in classification into sets was to have the silicon about equal in the tests of each set; the other elements being as nearly alike in quantity as it was possible for him to get them. Set 1. Test Nos. 1 and 2 show comparatively little difference in chemical content, except in manganese and graphite. As the manganese in No. 1 should be beneficial to the strength of the bar, the only way to account for the greater strength of the iron from No. 2 is the lower percentage of graphite, or the molecular structure resulting from the 25% of steel in the mixture. Set 2. Comparing Nos. 3 to 7 the strength increases with percentage of steel used and decrease of total carbon, with the exception of No. 7; in this 37^% of steel was used, and the total carbon was less than in any other test, but it is weaker than either Nos. 5 or No. 6. This being a solitary case it can hardly be used as proof that 37 % of steel is more than it is well to melt in a cupola. But test No. 11, which also con- tained 37^% of steel and more carbon, was only a little stronger. Test No. 4 was considerably weaker than No. 5, but its higher percentage of sulphur with its lower combined carbon would seem to indicate that these bars were either cooled slower, or poured from duller iron than were the bars from No. 5, which may account for their being weaker than the No. 5 bars. Set 3. Nos. 8 to 11 we note that No. 9, although containing 12|% of steel is no stronger than No. 8, in which there was no steel. And No. 10 with 1.06 combined carbon, and 12% of steel, gives less strength than might be expected. As these tests are so much lower in manganese than Nos. 8 and 11, it may be that their weakness is due either to the lower manganese or to the conditions of melting, which reduced the percentage of manganese so much more than in Nos. 8 and 11. The four charges each contained about 50% manganese before melting. [459] STEEL CASTINGS Set 4. Nos. 13 and 14, each from charges containing 25% of steel, show a marked increase in strength over No. 12. All the tests from charges containing 25% of steel are stronger than those from charges containing but 12%, with the exception of No. 5, which is stronger than two of the tests which had 25% of steel in the mixture. These tests were made with pig iron, ferro-silicon, and steel scrap, no cast-iron scrap being used. This, in order to better control the percentage of the elements in the iron. In some cases when a large percentage of steel was added, it was necessary to use ferro-silicon to get the desired amount of silicon, in the charge. Two tests were taken from No. 13, which contained 1,000 pounds of steel, 400 pounds of ferro-silicon (8.5% silicon), and 2,600 pounds of pig iron. The charge was tapped from the cupola into a ladle, and the tests taken at different times, as the iron was being poured from the ladle. The one sample contained 2.53 and the other 2.54% of silicon. Two tests, taken in the same way from No. 14, contained 1.97 and 1.94% of silicon. This charge was made up of 1,500 pounds steel, 450 pounds ferro-silicon, and 2,050 pounds of pig- iron. Similar tests from charge No. 2, which was made up of 1,000 pounds steel and 3,000 pounds pig iron, contained 1.50 and 1.52% silicon. These three cases offer pretty strong proof that the pig iron, steel, and ferro-silicon mixed thoroughly. Although of a limited number, the tests given seem to indicate that 25% of steel will add about 50% to the strength of the iron; and 12|% of steel, approximately 25%. The tests containing 37|% of steel were hardly as much improved in strength as those with 25% of steel, from which we may infer that the limit of the amount of steel it is beneficial to melt with iron in a cupola, is between 25 and 37|%. STEEL CASTINGS Steel castings combine in large measure the convenience of gray iron castings with a strength approximating that of forgings. In structural material construction, such as bridges, blast furnaces, mills, large buildings, etc., the engineer is specifying steel rather than iron castings. Maritime construction turns out a vessel composed entirely of steel plates and castings. Castings are commonly of open hearth steel which may be produced by the acid or by the basic process. A resume and condensation of the two processes would be as follows: The furnace is, in each instance, practically the same, the difference being in the lining of hearth of furnace. The acid process eliminates manganese, silicon and carbon only, the phosphorus and sulphur being practically unchanged from the initial charge. The basic process eliminates all the ingredients above specified, except silicon, which is very deleterious to this process. But silicon is a subject for the blast furnace treatment, and can there be kept low. Steel is now being produced of such chemical and physical structure that no chemical or physical determination will demon- strate by which process it was made, whether it is a product of an acid or basic open- hearth furnace. This, then, completely obviates the pertinency of the question by which process was the steel produced. In a regenerative or open-hearth furnace, the charge is exposed to the direct action of the reducing flame, and, when melted, the carbon is also eliminated; to the resultant bath manganese is added, and the molten iron is recarbonized, thus producing steel. To obtain the requisite heat, regeneration is practiced; the general practice is with producer gas and air. The regenerators play a specific part, and that is to preheat the ingoing gases and air; to accomplish this end the chambers or regenerators should contain 60 to 100 cubic feet per ton of steel. L. L. Knox. SPECIFICATIONS FOR STEEL CASTINGS Ordinary castings, those in which no physical requirements are specified, shall not contain over 0.40% of carbon, nor over 0.08% of phosphorus. Castings which are subjected to physical test shall not contain over 0.05% of phosphorus, nor over 0.05% sulphur. Tested castings shall be of three classes: Hard, Medium, and Soft. The minimum physical qualities required in each class shall be as follows: [460] STEEL CASTINGS Hard Castings Medium Castings Soft Castings Tensile strength, Ibs. per sq. in 85,000 70,000 60,000 Yield point, Ibs. per sq. in 38,250 31,500 27,000 Elongation, per cent in two ins 15 18 22 Contraction of area, per cent . **) 25 30 A test to destruction may be substituted for the tensile test, in the case of small or unimportant castings, by selecting three castings from a lot. This test shall show the material to be ductile and free from injurious defects and suitable for the purpose intended. A lot shall consist of all castings from the same melt or blow, annealed in the same furnace charge. Large castings are to be suspended and hammered all over. No cracks, flaws, defects, nor weakness shall appear after such treatment. A specimen one inch by one-half inch shall bend cold around diameter of one inch without fracture on outside of bent portion through an angle of 120 for soft castings and 90 for medium castings. The standard turned test specimen one-half inch diameter and two inch gauged length, shall be used to determine the physical properties specified. It is shown in the following sketch: The number of standard test specimens shall depend upon the character and im- portance of the castings. A test piece shall be cut cold from a coupon to be molded and cast on some portion of one or more castings from each melt or blow or from the sink-heads, in case heads of sufficient size are used. The coupon or sink-head must receive the same treatment as the casting or castings, before the specimen is cut out, and before the coupon or sink-head is removed from the casting. One specimen for bending test one inch by one-half inch shall be cut from the coupon or sink-head of the casting or castings. The bending test may be made by pressure, or by blows. The yield point specified shall be determined by the careful observation of the drop of the beam or halt in the gauge of the testing machine. Turnings from the tensile specimen, drillings from the bending specimen, or drillings from the small test ingot, if preferred by the inspector, shall be used to determine whether or not the steel is within the specified limits in phosphorus and sulphur. Castings shall be true to pattern, free from blemishes, flaws or shrinkage cracks. Bearing surface shall be solid, and no porosity shall be allowed in positions where the resistance and value of the casting for the purpose intended will be seriously affected thereby. STEEL CASTINGS NAVY DEPARTMENT 1. General Instructions. General instructions or specifications issued by the bureau concerned shall form part of these specifications. [461] STEEL CASTINGS 2. Process of Manufacture. Castings shall be made by a process approved by the bureau concerned. 3. Chemical and Physical Properties. The physical and chemical requirements of steel castings shall be in accordance with the following table: Class Symbol CHEMICAL COMPOSI- TION PHYSICAL REQUIREMENTS Not Over Minimum Tensile Strength Minimum Yield Point Mini- mum Elonga- tion Mini- mum Reduc- tion of Area Bending Test; Cold Bend (Not Less Than) P. s. Special... A 0.04 .05 .06 .06 0.04 .05 .05 .05 Pounds per Sq. In. 90,000 80,000 [ Maximum 80,000 ! Minimum { 60,000 Pounds per Sq. In. 57,000 35,000 30,000 Per Ct. in 2 7ns. 20 17 22 Per Ct. 30 20 25 90 about an inner diameter of 1 inch. 90 about an inner diameter of 1 inch. 120 about an inner diameter of 1 inch. B c 4. Class C. Class C castings will not be tested unless there are reasons to doubt that they are of a quality suitable for the purpose for which they are intended. Tests, if required, may be made at the building yards. The inspector will select a sufficient number of castings and have them crushed, bent, or broken, and note their behavior and the appearance of the fracture. 5. Treatment. (a) All castings shall be annealed. All annealing shall be done in a properly constructed pit or furnace. The furnace must be held at the annealing temperature long enough to insure that all of the interior of the casting or castings being annealed have been brought to that temperature. After the castings have been soaked at the proper annealing temperature they must be allowed to cool slowly in the furnace, carefully protected from drafts of air. Unless otherwise directed by the inspector, castings must not be removed from the furnace until they have been cooled down to the temperature at which the color dies (about 700 F.). The number of hours requisite for raising the castings to the proper temperature, the length of time during which they should be soaked at that temperature, and the period required for glow cooling in the furnace or in the air, may be prescribed by the bureau concerned, if it is so desired. (b) ADDITIONAL OR SUBSEQUENT TREATMENT. Castings shall not be subjected to additional annealing or subsequent treatment without the knowledge and consent of the inspector, and when this is done the inspector will make such additional tests as will satisfy him that the retreated castings meet the requirements. (c) Castings that have received any treatment without the consent of the inspector shall be rejected. (d) CLEANING. All castings shall be thoroughly cleaned before inspection, after final treatment. 6. Test Specimens, Number, and Location. (a) Coupons from which test speci- mens are to be taken shall, whenever practicable, be cast on the body of the casting. The number and location of the coupons shall be such as to thoroughly exhibit the character of the metal throughout the casting. When the use of these cast-on coupons is not practicable, the test bar shall be taken from a coupon cast with and gated to the casting, or with small runners to the gate. If necessary, coupons may be cast separ- [462] STEEL CASTINGS ately, but in all such cases the approval of the inspector must first be obtained. Coupons shall not be detached from the casting until it has received its final treatment. (b) Particular care will be exercised with castings estimated to weigh 200 pounds or over that the test specimens taken from the castings shall be in sufficient number and so located as to thoroughly exhibit the character of the metal of the entire casting. (c) TESTS, INDIVIDUAL AND LOT. Castings, the estimated weight of which is 200 pounds or over, will be tested by individual tests. Other castings shall be tested by lots as follows: A lot shall consist of castings from the same heat and annealed in the same furnace charge. From each lot two tensile and one bending specimen shall be taken, and the lot shall be passed or rejected on the results shown by these specimens. Manufacturers, for their own safety, will provide enough coupons for extra tests in case of flaws showing in the test specimens. (d) In the case of castings tested by lots, the test pieces may be taken from the body of a casting from the lot if so desired by the manufacturer. When a number of small castings have been cast on the same heat with two or more larger castings carrying test coupons, the small castings may, at the discretion of the inspector, be represented by the test bars from the large castings. A casting from which an unsound test speci- men has been taken shall receive particular care to detect porosity or other unsoundness in the casting itself. (e) A "lot" or "heat test," provided for in the preceding paragraphs, will not be permitted unless the manufacturer complies with the instructions hereafter relative to identification. 7. Rejection After Delivery. The acceptance of any casting by the inspector will not relieve the makers thereof from the necessity of replacing the casting should it fail in proof test or trial or in working or exhibit any defect after delivery. 8. Percussive Test. (a) Large castings shall be subjected to hammer tests as follows: (b) The castings are to be suspended and hammered all over with a hammer weighing not less than 7 pounds. If cracks, flaws, defects, or weakness appear after such treat- ment, castings will be rejected. 9. Surface Inspection. (a) All castings shall be thoroughly cleaned and, where practicable, have the gates and heads removed before being submitted to the inspector for inspection in the green. The removal of heads and gates by burning will not be permitted. All castings shall be submitted in the green that is, before they have received any treatment other than cleaning. (b) Castings shall be sound and free from all injurious defects. Particular search will be made at the points where the heads or risers join the castings, as unsoundness at this jpoint may extend into the castings. (c) The closing of cracks and cavities by hammering and plugging will not be tolerated. (d) WELDING WHEN PERMITTED. Minor defects that do not impair the structural value of the casting may be welded up by an approved process if, in the judgment of the inspector, they are unimportant, but no such burning in or welding the defects will be permitted except after an inspection by the inspector of the casting in the green, with the defect thoroughly cleaned out to show its extent. Such welding should always be performed before annealing, and in no case shall welding be done without being subsequently annealed. The castings shall be inspected by the inspector after the defect has been welded up and before being annealed. Surface defects and cavities which are of more than minor importance shall not be so welded up except by permission of the inspector in charge of the district or of the bureau concerned. In no case will any welding be allowed on steam piping or any other casting used in connection with steam piping or subjected to steam pressure, nor in the following ordnance castings: Gun yokes and slides in region of the trunnions, elevating gear lugs, and recoil cylinder and spring cylinder bearings for same. White-lead marks shall be placed about defects which have been welded up, before shipment, in order that during any machining or other treatment at the manufacturing plant where used, special attention may be given this point. 10. Chemical Analysis. Manufacturers shall furnish a chemical analysis of each [463] PLUMBAGO heat made in an approved manner, the process of analysis to be open to the inspector. The Government check analysis must show the heat to be in accordance with the specifications. 11. Casting Record. (a) For the purpose of identifying castings inspected under these specifications the manufacturer shall, upon request, furnish the inspector with true copies of his shop order sheet, molding and pouring record, and a detailed list of the castings to be inspected, cast in each heat, showing manufacturer's analysis of the heat, name, pattern number, heat number, serial number, and estimated weight of each casting. (b) ANNEALING RECORD. For castings annealed a "Report of annealing" shall be furnished the inspector, showing the heat and serial number of each casting to be inspected in the annealing furnace charge, together with the time of raising to the soaking temperature, the time of soaking, the time of cooling, and the temperature at which soaking was done. The record cards shall be exhibited to the inspector upon request. (NOTE. Steel castings for hawse pipe, turret tracks, and all important parts sub- ject to crushing stresses or surface wear only shall be Class A castings, and those for stern post, rudder frames, and all parts subject to tension or vibratory strains shall be Class B castings, unless the bureau concerned otherwise directs.) SPECIAL PROVISIONS FOR ORDNANCE CASTINGS 12. Patterns. Patterns for all large ordnance castings contracted for will be fur- nished by the Government, but the responsibility shall rest upon the contractors to supply castings that will finish to the drawing dimensions within the tolerances specified. The contractor shall report to the Government any alterations in the patterns that he may deem necessary to insure castings coming to the finished drawing dimensions, and shall, H required by the Government, make such alterations of the patterns. The actual cost of such alterations shall be borne by the Government. PLUMBAGO FOR FOUNDRY USE NAVY DEPARTMENT Plumbago for foundry use shall be finely powdered, dry, free from coal dust or grit, and conform to the following requirements as to chemical composition: Volatile Matter. Not over 5 per cent. Ash. Not over 40 per cent. Graphite Carbon. Not less than 55 per cent. For Foreign Shipment. It must be delivered in good, well coopered, oak barrels, such as are used in the transportation of oil. Each barrel to be completely filled and to contain about 400 pounds of material. Barrels must have the bodies lined with elastic crinkled paper tubes and have sheets of ordinary strong paper properly fitted in tops and bottoms. The name of material, quantity, and name of manufacturer must be neatly stenciled on the heads. At least 10 per cent of the barrels must be opened at random for inspection of contents. For Domestic Shipment. It must be delivered in No. 1 flour barrels, completely filled and containing about 250 pounds each. Top and bottom heads to be reinforced. The bodies of the barrels must be lined with elastic crinkled paper tubes and have sheets of strong ordinary paper properly fitted in bottoms and heads. The name of material, quantity, and name of manufacturer must be neatly stenciled on the heads. At least 10 per cent of the barrels must be opened at random for inspection of contents. [464] SECTION 8 IRON AND STEEL FORCINGS. CARBON AND HIGH-SPEED STEELS. HEAT TREATMENT, FORGE EQUIPMENT Wrought Iron. From time immemorial wrought iron has been the principal, al- most the only, metal employed by the smith at the forge. Its extended use in the arts has been due to its inherent properties being at once a malleable, ductile, weldable material of high tensile strength, high elastic limit, and of great reliability under per- manent and alternating stresses. In recent years it has been, in great measure, super- seded by mild steel, but only in articles which do not require welding. Wrought iron is made from white cast iron by a process of elimination known as puddling, the purpose of which is to eliminate the graphite entirely and the combined carbon so far as to leave less than 0.20%, a quantity which does not wholly prevent welding but is sufficient to increase the strength, rigidity, and hardness of the iron. Puddling by hand is commonly done in a reverberatory furnace. The pigs of white iron are broken up and placed in the hearth of the furnace, being ultimately mixed with scales of oxide of iron obtained from the rolling mill. This mixture of iron and scale is subjected to an oxidizing flame, the temperature of the furnace being so regulated as to reduce the iron to a pasty condition; while in this condition the iron and the molten scales or cinder are constantly stirred by hand tools until the whole is thoroughly mixed, it is then formed into a ball as large as can be conveniently gotten through the furnace door. This newly converted mass of viscous iron and cinder or slag is then worked under a hammer, or placed in some form of squeezer, the slag with its contained im- purities being driven out by pressure; the resulting bloom is then rolled into a muck bar, which is cut into short pieces, piled into a bundle, reheated to the welding point, and again hammered and rolled to further cleanse the iron of its impurities, the product being known as single refined iron; if subjected to a second piling, heating, hammering, or rolling it is known as double refined iron. This process of piling, reheating, and roll- ing may be repeated until the desired quality of iron is attained. Chemistry. As a chemical process it consists essentially in the elimination of carbon from pig iron in the action of the furnace flame upon the molten oxide of iron, the oxygen of which unites with the carbon in the pig iron, carbon dioxide is formed which passes off as a gas. The quantity of carbon remaining in the puddled iron is very small, usually between . 05 and . 10%, an amount insufficient to harden the iron by rapid cooling from a red heat. The silicon in the pig iron unites with any free oxygen in the furnace, a basic silicate of iron is formed which passes off with the slag. Manganese is readily removed from iron by oxidation; while restraining the oxida- tion of iron it permits oxidation of other elements combined with the iron, thus: Man- ganese present in pig iron, in which sulphur is also present as iron sulphide, changes the latter into manganese sulphide, liberating the iron. Manganese sulphide not being as soluble in iron as iron sulphide readily passes into the slag. Phosphorus exists in pig iron as phosphide of iron. During the process of refining or puddling it is reduced to phosphate of iron which may be removed from iron by strong bases, such as oxide of iron, oxide of manganese, alkaline earths, such as lime, and by basic silicates in a strongly oxidizing atmosphere, passing oft 7 with the other impurities in the slag. When oxide of iron is reduced in the presence of an earthy phosphate, phosphorus is separated, and unites with the iron; 0.3% phosphorus in wrought iron makes it hard and diminishes its tenacity; 0.5% makes the iron cold-short but not red-short; 1.0% makes iron brittle. Phosphorus imparts to iron a coarse, crystalline structure, diminishes its strength, increases its fusibility, and makes it cold-short. [465] WROUGHT IRON In the accompanying table a chemical analysis of an average sample of white iron, such as used in the puddling furnace, is given, together with analysis of plate iron of 55,000 pounds tensile strength. The plate analysis shows 0.80% cinder, of which only 0.04% is carbon. Pig Iron Per Cent. Wrought Iron Per Cent. Iron 89 . 44 99 20 Carbon-graphite 87 Combined 2 45 04 Manganese 2 71 17 Silicon 1.11 .15 Sulphur 2.51 .03 Phosphorus. .91 .21 Oxvgen. . .20 100.00 100.00 Wrought iron as distinguished from mild steel is traceable to its method of manu- facture. Steel is of molten origin, wrought iron is of plastic origin, that is, it is made by stirring into an intimate mixture white pig iron heated to a pasty but not a molten condition in a bath of molten cinder, mechanically working it with a rake and after removal from the furnace squeezing out of the puddled mass much of its contained cinder, and not separating the molten metal by fusion as in the case of steel. Nearly all the carbon and most of the other impurities in the pig iron are taken up by the cinder leaving comparatively pure iron. Texture of Wrought Iron. Irons are said to be either fibrous or granular in texture. When worked directly from a bloom the forging presents a granular appearance; in large forgings, this grain, is coarser at the center and finest near the surface. Should the process of hammering be continued, the forging will become, when considerably reduced in area, uniformly fine grained. If, however, instead of this continued hammer- ing, the original forged billet be elongated by running it through a train of rolls the texture of a section cut longitudinally from the bar will have changed from granular to fibrous; but if the section be cut transversely or at right angles to this direction, the section will have a wholly different appearance. This is due, as explained by Sauveur : In longitudinal section the ground mass of the metal consists of ferrite, similar in every respect to the crystalline grains of pure iron. The ferrite of wrought iron is not pure iron but rather a solution of iron in which are dissolved small quantities of silicon, phosphorus, and other minor impurities. Slag which has assumed the shape of fibers, or streaks, running in the direction of the rolling, imparts a fibrous appearance to the metal. In transverse section there is a polygonal network indicating that the metal is made up of crystalline grains of ferrite. The slag, which in the longitudinal section occurred as fibers running in a direction parallel to the rolling, here assume the shape of irregular dark areas, corresponding to the cross-sections of the slag fibers. In both the longitu- dinal and transverse sections the f errite grains are equi-axed, and show no sign of having been elongated in the direction of rolling. Certain peculiarities noted by A. L. Hass in connection with Yorkshire iron show that, if the iron is nicked % inch deep around, say, a 1-inch bar, with a sharp set, and broken short over the anvil with a single blow, it shows a fracture in which the bar breaks dead short and square; the fracture is coarsely granular, resembling badly burned steel, only the granular structure is coarser. The bar nicked on one side only, and carefully bent with the nick a couple of inches from the edge of the vise or anvil, shows a beautiful gray, silky, fibrous structure, free from crystals and perfect in every way. This peculiarity, so perplexing to many iron-workers, is fully covered in the preceding explanation of the fibrous texture of wrought iron by Professor Sauveur. [466] WROUGHT IRON Iron when pure presents but a single texture, and that the granular one. Puddling, as already explained, consists in stirring a mass of viscous iron in a bath of cinder; the latter prevents intimate contact of the particles of iron, it opposes thorough welding, and favors the production of fibrous texture, since during subsequent working the grains of iron accompanied by cinder can slide over each other in layers, and this gives to iron its fibrous texture. Malleability. So far as engineering work is concerned there are no restricting limitations to forgings of wrought iron, either as to size or shape, but soft fibrous irons are more malleable, that is, more easily worked than are hard granular irons. Tensile Strength. Wrought iron bars or plates, as delivered from the mill, should have a tensile strength not less than 48,000 pounds per square inch, and this should be accompanied by not less than 15% elongation in an 8-inch specimen. The fracture should be 90% fibrous. Plates and bars should bend cold without fracture through 135 over two thicknesses of plate and two diameters for bars, in order to meet the U. S. N. specifications. Bar irons of good quality should have a tensile strength of about 53,000 pounds per square inch with an extension of about 20% in 8 inches; such irons must have good welding qualities; therefore the carbon and the phosphorus should each be less than 0.20%. Irons which do not require to be welded may have a tensile strength of 60,000 pounds per square inch, with elongation of 18% in 8 inches. Such irons are apt to ,be hard, steely, and difficult to weld; they should, therefore, be restricted to uses direct from the bar or simple forging. When tested across the fiber wrought iron plates and wide bars show a diminution in tensile strength of about 10% as compared with tests made in the direction of the fiber. Ductility. This property enables a material to be drawn out without breaking. It is also called elongation or extension in reports on the mechanical tests to which plates or bars are subjected. Elongation occurs when a ductile material is subjected to a tensile stress higher than its elastic limit, after which a permanent change of form takes place. It may be measured in a tensile testing-machine in two ways by the actual amount of elongation in inches and parts of an inch, and by reducing the amount so found to percentage extension of its original length. Wrought iron plates under 45,000 pounds tensile strength should show a reduction of area of not less than 12%; 45,000 to 50,000 pounds, 15%; 50,000 to 55,000, 25%; 55,- 000 pounds and over should show 35% reduction of area. The following data were obtained from Government tests of wrought-iron plates, which it will be observed are of very high quality. These were short specimens: Thickness Tensile Strength Pounds Reduction of Area Per Cent. j inch with the grain 58373 38 j inch across the grain 53,333 9 Y inch with the grain 62,195 43 YS inch across the grain . 60202 10 f inch with the grain 56,270 25 f inch across the grain 56461 17 The behavior of wrought iron under tension will greatly depend upon its inherent hardness or softness; a hard specimen will elongate but little, while a softer specimen will be drawn out considerably, the middle part becoming gradually smaller, and fracture will ultimately take place at the smallest section, and probably at a lower strain than with a specimen of harder iron. The stretching of wrought iron is seldom taken into account in engineering work, and the reason for selecting the softer iron is that it can be used with greater safety, [467] WROUGHT IRON since when subjected to jar or sudden strain it is more likely to be drawn out than broken asunder, and thus gives timely warning before fracture. Elastic Limit. Wrought iron bars rolled, 4 inches diameter, having a tensile strength of about 46,000 pounds per square inch, will have an elastic limit averaging 50%. Bars of 2 inches diameter, tensile strength about 48,000 pounds per square inch, will have an elastic limit about 65%. Bars of 1-inch diameter having a tensile strength of about 51,000 pounds will have an elastic limit of about 70%. The above are adaptations from Beardslee's tests which were intended primarily to show the effect of continued working of wrought iron from a comparatively large area through successive operations to small bars. For wrought iron, the following physical properties are taken as representing ac- ceptable material in engineering work: Bar iron in tension : 50,000 pounds tensile strength, elastic limit 26,000 pounds = 52%, with 18% elongation in 8 inches. Shape iron in tension: 48,000 pounds tensile strength, elastic limit 26,000 pounds = 54%, with 15% elongation in 8 inches. Safe Load. Wrought-iron bars subject to varying stresses, such as screw bolts in engineering structures, should have a factor of safety of not less than 8, on the net area. For chains the proof load up to 2.5 inches diameter is: Proof load in tons = 18 X (diameter in inches). 2 The breaking strengths are placed at 40% above the proof loads. Thus the proof load on a 2-inch chain would be 18 X 2 2 = 72 tons (161,280 pounds). The area of a 2-inch bar is 3.14 square inches, then 161,280 -r- 3.14 = 51,363 pounds per square inch. The safe working load is one-half the proof load, or 25,681 pounds per square inch of sectional area of bar; accepting this, we have: Working load in 2 1 6 X D 2 for close link tons of 2240 pounds = , T t. - I 4 X D 2 for ordinary chains In which D = diameter of bar in inches. Compression. Of 10 specimens of wrought iron, cut from forgings of high quality, the softest began to yield with 22,800 pounds, and the hardest with 31,000 pounds, the average being 26,900 pounds. In each case weight was added until the specimen became shorter, by the i .063 = 1& .638 .425 2.2578 12750 15938 21250 VA 2.188 =2& .094 = 1& .656 .438 2.3927 13125 16406 21875 8 1 A 2.250 = 2% .125 = iy 8 .675 .450 2.5313 13500 16875 22500 m 2.313 = 2A .156 = 1^ .694 .463 2.6739 13875 17344 23125 9 2.375 = 2% .188 = 1A .713 .475 2.8203 14250 17813 23750 [570] MACHINE DETAILS RELATING TO STEAM ENGINES KEYWAYS AND SUNK KEYS Continued SHEARING RESISTANCE OF KEY PER INCH OP LENGTH,, FOR WORKING VALUES PER Shaft Area of SQUARE INCH OF Diam. B T ti tz Key D 6000 7500 10,000 Pounds Pounds Pounds VA 2.438 = '2& .219 = 1& .731 "."488 2.9708 14625 18281 24375 $ 1 A 2.500 = 2 l / 2 ,250 = 1M .750 .500 3.1250 15000 18750 25000 &A 2.563 = 2& .281 = 1& .769 .513 '3.2833 15375 19219 25625 10 2.625 = 2% .313 = 1A .788 .525 3.4453 15750 19688 26250 10M 2.688 = 2H .344 = 1H .806 .538 3.6115 16125 20156 26875 10^ 2.750 =2^ 1.375 = l^g .825 .550 3.7813 16500 20625 27 500, IOM 2.813 = 2H 1.406 = 1H .844 .563 3.9552 16875 21 094 28125 11 2.875 = 2^ 1.438 = 1& .863 .575 4.1328 17250 21563 28750 IIJ4 2.938 = 2H 1.469 = 1H .881 .588 4.3146 17625 22031 29375 11^ 3.000 =3 1.500 = 1H .900 .600 4.5000 18000 22500 30000 11M 3.063 =3^ 1.531 = 1H .919 .613 4.6896 18375 22969 30625 12 3.125 = 3H 1.563 = 1& .938 .625 4.8828 18750 23438 31 250 Length of Key. Apart from resistance to crushing, a key should have length enough to hold it securely in place under any conditions of service. Pulley hub proportions are influenced by those of the rim, but in any case the length of hub is seldom less than twice the diameter of shaft; this provides a little more length than is needed to resist crushing of key. Short hubs, for any service, are seldom less than one shaft diameter in length; if a key is proportioned D -r 4 + .125 in., the shortest limit of length is reached when the length of key equals the diameter of shaft for which it is proportioned, as above. The proper length closely approximates 1.6 diameter of shaft. Square Sunk Key Largely used in machine construction in resisting shearing strains only, any tendency to lateral movement being prevented by one or more set screws in the hub, as shown in the illustration. A common proportion for square keys is one-fourth the diameter of the shaft for sizes from 2 to 4 inches, for smaller shafts ibsssssss^l _?_ D -f- 4 + .0625 is often used. In general, square keys are simply cut to length from cold drawn polished rods, and used without further preparation, unless it may be case- hardening. Two set screws are shown in hub; except for hubs of unusual length this is not always necessary. The screw should have a flat point and casehardened to prevent distortion of thread. Special Keys. Key on a flat, Fig. 1, has the same breadth B for shaft diameter A as has a sunk key. The flat should be parallel to the axis of shaft and a little wider than the key. Its thickness C, measured at the small end is one-third its breadth; the taper is commonly one-eighth inch per foot, for which allowance is made in the hub, [571] MACHINE DETAILS RELATING TO STEAM ENGINES If the piece to be keyed is in a confined space, the key should have a gib head to facilitate its withdrawal. Saddle Key This key, Fig. 2, is wholly included in the hub, no preparation of shaft being necessary for its use. In breadth D it follows the same proportions relative to shaft diameter as for a sunk key. Thickness E, measured at the small end, is one- third its breadth. The usual taper is one-eighth inch per foot, for which a correspond- ing taper is included in the hub. The under side of key is made concave to fit the shaft. To facilitate its removal, the key should have a gib head. As this key lies wholly outside the circumference of shaft, and drives by friction only, it is not well adapted for important power transmission. Round Key. This method of fastening, Fig. 3, is sometimes employed instead of a sunk key. For practical reasons it is limited to fastening a hub at the end of a shaft. The diameter of pin may be one quarter the shaft diameter; the hole reamed for either a straight or taper pin. The location oHiole is such that one-half the pin is in the hub, the other half in the shaft. A pin key resists working stresses in the same manner as a sunk key, that is, by resistance to shearing. Pin keys are occasionally used in large work, but their use is practically confined to small details in machine construction. Taper Pin Key In fastening a hub other than at the end of a shaft a pin is mode to pass diametrically, or nearly so, through the hub and shaft as shown in sketch. In this case a taper pin is used, the usual taper being | inch per foot. The pin is in double shear. TAPER PINS AND REAMERS Commercial Sizes Alf F " ; Taper of pins PIN REAMER SHAFT HUB Trade Number Diameter Large End B Longest Length c Inches Diam. Small End E Length Cutting Edge F Diam. Large End G Diameter A Diameter D Pin X3 Pin X 4 Pin X 3 Pin X4 Dee. Frac. 1 .172 .193 .219 .250 .289 .341 .409 .492 .591 .706 it A & H if tt H H tt H 1H m IK 2 VA *y* 4 4^ 5 1 A 6 .146 .162 .183 .208 .240 .279 .331 .398 .482 .581 m 2 VA VA 3 &A 1 A VA VA 7 181 204 230 260 303 355 425 507 610 727 .516 .579 .657 .750 .867 1.023 1.227 1.476 1.773 2.118 .688 .772 .876 1.000 1.156 1.364 1.636 1.968 2.364 2.824 1.02 1.20 1.41 1.56 1.81 2.09 2.35 2.73 3.15 3.62 1.19 1.41 1.63 1.88 2.16 2.49 2.89 3.34 3.86 4.45 2 3 4 5, 6 7 8 9 . . 10 [572 MACHINE DETAILS RELATING TO STEAM ENGINES Taper pin dimensions coincide with those of the reamer used in fitting the hole. Certain sizes of pins are commonly accepted as standard, the larger sizes of which are tabulated herewith. Shaft diameters are given in the table merely to show what diameters result from multiplying the several pin diameters by 3 and 4 respectively. The tabular sizes for shafts are exact multiples of the standard pin diameter, these are to be changed to the nearest common fractional measurement the design may suggest. The designer must determine how much of the shaft area can be allotted to the pin. Suppose a design calls for a shaft about 1J inches diameter; the nearest shaft diameter in the table under Pin X 3 is 1.227, for which a No. 7 pin will be required. In the column Pin X 4 the choice lies between 1.156 and 1.364 for shaft diameter, the former calls for a No. 5 pin, the latter a No. 6 pin, which size would probably be selected together with an average shaft diameter of lj inches. Shaft diameters as given in the table are subject to increase or decrease in diameter, to conform to the next nearest working unit, suited to the standard parallel reamer used for the hub; thus, 1.227 inches would be increased to 1.25 inches, similarly 1.156 inches would be advanced 1.1875 inches. Reamer flutes, as well as overall lengths of standard taper pins, are of sufficient length that a moderate increase in shaft diameter is permissible. Gib Head Key. This form of key is useful in supplying a fixed projection, or an abutment, against which a wedge may be driven in order to loosen a key preparatory to its withdrawal. A table of sizes up to and including 4 inches in breadth is given. The breadth and thickness follow Unwin's proportions for sunk keys; knowing the breadth of a key, suitable working dimensions for a gib head may be taken from the table. TAPFRflNCH PFR FOOT k- A* GIB HEADS FOR KEYS H /8 A K H 4 IK IK IK A % tt 7* 1 1A ?4 H H H 3^ M H H K A K y* H H B % H l IK 1A 1A 2 2M 1 1A 1A 1A 3^ 4 1H 1A 1*1 2M H K K l l l IK IK IK 1M IK 2 2K 2K 3K [573] MACHINE DETAILS RELATING TO STEAM ENGINES Sliding Keys. When a rotating hub in a fixed bearing is required to rotate a shaft passing through it, the shaft having an end movement as well, the driving key included in the hub is then provided with gib heads, or other form of fastening, to prevent the key sliding out of place. A sliding key, such as included in the feed works of a machine tool, has but little work to do, and one key will suffice; but if, as in the case of a large boring machine spindle, it may be required to transmit nearly the whole power of the machine, two keys are recommended, to be placed diametrically opposite each other in the spindle. For light and medium work the breadth of key may be one-fourth the shaft di- ameter; the thickness of key following, usually, 0.25 shaft diameter + 0.125 inch. For heavy work the breadth of key diminishes somewhat, because two keys are commonly employed, the proportionate rate for thickness of key remaining as above. To increase the surface of key subject to wear, 0.4 of the key may be placed in the hub and 0.6 in the keyway in shaft. The gib head details for a sliding key will depend upon the clearance at end of traverse. Should the hub have little or no clearance the gib will be included within the hub as in Fig. 2, if plenty of clearance, the ends may then project as in Fig. 3. SLIDING KEYS A B c D E F G H i 1 H H .150 .225 % H A H 1M A & .175 .263 1 A H A l /s m % .200 - .300 ft a K A 1% A A .225 .338 A A H A 2 1 A H .250 .375 H A A A VA A H .275 .413 1 A A A A VA M X .300 .450 H A A A &A H H .325 .488 X H H H 3 Z A H .350 .525 A H y* 1 A 3^ if ft .375 .563 A I A y* H &A % i .400 .600 A li A 1 A 3M tt l* .425 .638 A M A 1 A 4 i 1H ,450 .675 H A A A To facilitate fitting, the hub at F G, Fig. 2, can be notched through; the gib ends at G to extend to outside of hub and finished with it. Maximum Load on Key Crank pin pressures in automatic cut-off engines will vary from that due to full boiler pressure at the beginning, to a fourth or less at the end of stroke. In cross compound engines the high pressure steam is confined to one cylinder [5741 MACHINE DETAILS RELATING TO STEAM ENGINES the crank and reciprocating mechanism of the low-pressure side is commonly a duplicate of the high-pressure side, the crank keys are somewhat larger than necessary for the work but need not be considered here. Starting a single or compound engine from a state of rest, the crank pin being at or near half stroke it may, and probably does, receive the maximum load due to full boiler pressure upon piston area which may equal 1,500 pounds per square inch of projected crank pin area, the crank shaft, meanwhile, being at a state of rest. The maximum effort of the steam is transmitted through the crank directly upon the crank shaft keys which, in turn, must resist the shearing effort and permit rotation of shaft. Mean effective pressures cannot be used in determining key proportions. Keys forged from medium steel have a tensile strength from 65,000 to 70,000 pounds per square inch; 7,500 pounds per square inch of section subject to shearing stress is taken as the working load for a sunk key. Example. Crank keys for steam engine. 20 inch cylinder = 314.16 sq. in. area. Steam pressure = 160 Ibs. per sq. in. P = 50,266 pounds = 314.16 X 160. R = 18 inches, r = 5 inches. 2 keys. B If inches. L = 6f inches. D = 10 inches. Then P XR 50,266 X 18 r 5 2B X L X 7500 180,958 180,469 The pressure exerted by the steam piston upon the crank pin is 180,958 pounds. The resistance of the two keys in the crank shaft is 180,469 pounds, they thus practically balance each other. Example. Pulley driving a shaft. P = 4,000 pounds. R = 24 inches, radius of pulley. r =2 inches, radius of shaft. B = 1| inches, key breadth. L = 6 inches, key length. D = 4 inches, shaft diameter. Then B X L X 7500 = 1.125 X 6 X 7500 = 50,625. In this example there is a margin of 2625 pounds in favor of the key. The breadth of key is by Un win's formula: B = + i inch. Keyways for Minor Attachments. Keyways in engine shafts are much too large for the needs of minor attachments sometimes carried by it, such as pulleys, gears, eccentrics, etc., transmitting but a fraction of the total power. No general rule can be given for such minor fastenings other than to select a hub suited to the pulley or gear and employ its corresponding size of key for which an additional keyway should be made in the shaft. A small pulley thus placed on an engine shaft would in all prob- ability be made in halves, in which case the small keyway in shaft need not be longer than the pulley hub. [575] MACHINE DETAILS RELATING TO STEAM ENGINES Double Keys. A limit so the breadth of a single key is quickly reached in large shafts transmitting full power. By Unwin's formula the breadth of a single key for a 24-inch shaft would be 6| inches, its depth STS inches. The shearing resistance of a key varies as its breadth; we can, therefore, divide this breadth into two or more keys without loss of strength. Referring to the accompanying table of double keys, a 24-inch shaft would have two keys 4 inches in breadth. Two thicknesses are given for double keys according to the severity of service. For a crank the key thickness would be 3 inches; for a pulley the thickness would be 2 inches. The crank would have its keys placed 90 apart; the pulley would have its keys diametrically opposed, one key in each half of the hub. The liberal proportions of double as compared with single keys is to favor the exacting conditions under which double keys are commonly used. The stresses upon a crank and shaft are, in general, more severe than those in a pulley or gear so that, for the same breadth of key, its thickness may be increased for the crank connection, thereby pre- senting a larger area opposing deformation of key and keyway through crushing. Double keys are commonly set at an angle of 90 when placed in cranks and solid hubs. An incidental advantage, outside the real function of a key, occurs in the 90 keyways in a pulley hub, in making three points of support, thus taking up any lost motion between the shaft and hub, should the bore of pulley be sufficiently large to make a loose fit. Keys and keyways are placed diametrically opposite when employed in split hubs, driving each half separately; the bolts passing through a hub will securely clamp it to the shaft. Kennedy Double Keys. These keys have been satisfactorily used in rolling mills for the transmission of heavy loads subject to periodical reversal. Key dimensions for any shaft may be found thus: Draw a semicircle in which the diameter A is the same as that of the shaft for which the key is desired. From its center draw 45 angle lines beyond the circumference as at B and C. Bisect each half diameter as at D and E. From each of these points D and E erect a perpendicular extending to the circumference as at E G. Where the perpendicular crosses the 45 diagonal as at F draw F H parallel to A. Then F H and F G being equal represent two sides of a square key F H B G. Dimensions for keys suited to shafts from 6 inches to 24 inches diameter are given in table of Double Keys for Cranks and Engine Pulleys. The keyways in the hub and the upper side of the key are tapered | inch per foot. The sides of key are parallel and closely fitted into shaft and hub. It will be noted that the key is wholly in compression. Peters' Double Key This key is designed to have its breadth of bearing located on a radial line in the shaft, and to transmit the rotary motion of the shaft to a diag- onally opposite bearing in the hub; or, the reverse, in case motion is to be transmitted through the hub to the shaft. In either case an equal breadth of key is had in both shaft and hub. The working stresses upon the key tend to compression. In designing a key of this kind, lay down that portion of hub and shaft in which the keys are to be located, as in the accompanying diagram, in which A is equal to the shaft diameter. From the shaft center, draw two opposite radial lines at an angle of 22 each, above the horizontal, the complemental angle being 135. From the cir- cumference of the projected shaft, lay off on one of the diagonal lines the desired breadth of key B, and erect a perpendicular C, intersecting the shaft circumference. The lines B C form two sides of a parallelogram which, when completed, represents the key area. Repeat for the opposite side. The keyways in both shaft and hub are parallel. Each key, as shown in the diagram, is made up of two halves with central inclined faces; the outer faces of the key are parallel and machined to slide freely into place in the keyways. After the preliminary adjustment each pair of keys is firmly fixed in place, by driving the tapering keys to the desired tension. Any increase of breadth B has the effect of lengthening C, there- [576] MACHINE DETAILS RELATING TO STEAM ENGINES DOUBLE KEYS FOB CRANKS AND ENGINE PULLEYS Sunk Key Kennedy Key SUNK KEY KENNEDY ** For Cranks For Pulleys g?iS Shaft rQ Shearing Shearing SJSo ^ Diam. '^ Area Load per Area Load per Inch on A B C Area 1 Key Ijs 1 A 1 C IKey 1 Key at C IKey 1 Key at i^^ w W 7500 Lbe 7500 Lbs O ft perSqln perSqln 6 ... Ik K 1.09 9375 k 0.94 9375 6 1A 3 1.13 7968 6K... 1A H 1.23 9844 k .98 9844 6K IK 3k 1.27 8441 7 ... IK l 1.38 10313 H 1.12 10313 7 ik 3K 1.56 9375 7K... i& l 1.44 10781 It .17 10781 7K i& 3k 1.72 9844 8 ... IK i& 1.59 11250 K .31 11 250 8 1A 4 2.07 10781 8K... i& IK 1.76 11 719 K .37 11719 8K IA 4k 2.44 11719 9 ... IK IK 1.83 12188 H .52 12 188 9 IK 4K 2.64 12 187 9K... 1H 1A 2.00 12656 if .58 12656 9K ik 4k 3.06 13 125 10 ... IK 2.19 13 125 1 .75 13 125 10 IK 5 3.52 14062 IOK... 1H l& 2.38 13594 1 .81 13594 IOK 1H 5k 3.75 14531 11 ... IK m 2.58 14063 l 1.88 14063 11 2 5K 4.00 15000 UK... 1H 2.66 14531 1A 2.06 14531 UK 2K 5k 4.52 15937 12 ... 2 l p 2.88 15000 iA 2.13 15000 12 2k 6 5.06 16875 13 ... 2K 3.19 15938 IK 2.39 15938 13 2K 6K 5.64 17812 14 ... IK 3.76 17344 1A 2.75 17344 14 2K 7 6.89 19687 15 ... 2 JL 1H 4.11 18281 ik 3.05 18281 15 2M 7K 7.56 20625 16 ... 2K 1H 4.76 19688 1A 3.45 19688 16 3 8 9.00 22500 17 ... 1H 5.45 21 094 IK 3.87 21094 17 3K 8K 9.77 23437 18 ... 3 1 2K 6.38 22500 IK 4.50 22500 18 3K 9 11.39 25312 19 ... 3K 2k 7.03 23438 1A 4.88 23438 19 3K 9K 12.25 26250 20 ... 3rV 2K 7.87 24844 1H 5.38 24844 20 3k 10 14.06 28125 21 ... 3K 2A 8.97 26250 6.13 26250 21 3K IOK 15.02 29062 22 ... 2 ii 9.74 27 188 *T* 6.57 27188 22 4K 11 17.02 30937 23 ... 3H 2K 10.96 28594 7.15 28594 23 4k UK 18.06 31875 24 ... 4 3 12.00 30000 2 8.00 30000 24 4K 12 20.25 33750 fore B must be kept down to a close working limit. As the crushing strength of steel is practically the same as its tensile strength, 7,500 pounds per square inch gives a safe working value to the key, [577] MACHINE DETAILS RELATING TO STEAM ENGINES T t> B = shaft radius. PETERS' DOUBLE KEY C = nearest shop measurement. Graphic Determination KEY Com- pression Load per KEY Compres- sion Load per Inch Shaft Area Inch on Shaft Area on 1 Key A 1 Key 1 Key at 7500 A 1 Key at 7500 Lbs. per B c Lbs. per Sq. In. B c Square Inch 4 N 1* 0.66 3750 7 y 2 if 2K 2.34 7031 4M H iy* .73 3985 8 1 2% 2.63 7500 4/^ A I'M .84 4219 8^2 llV 2{f 2.99 7969 4^ $ iA .93 4454 9 l/^ 3 3.38 8438 5 1% 1.02 4688 9K 14 3H 3.71 8906 5M Jl W 1.15 4922 10 IK 3A 4.14 9375 5^ H ^ 1.25 5156 10H i 3K 4.59 9844 5% 1.35 5391 11 i/^ 3% 4.98 10313 6 M 2 1.50 5625 11^ i^ 3H 5.48 10781 1 A H 2A 1.78 6094 12 iH 4 6.00 11250 7 2A 2.02 6563 Keys for Screw Propellers These are always subject to violent changes of load through racing of mam engines in a rough sea, not overlooking the frequent and full powered reversals which occur during maneuvers. To meet this service the outboard end of tail shaft is tapered, the propeller boss is bored to fit the tapered shaft, the keys are thicker to resist crushing, and extend the whole length of boss. Single key proportions by Seaton and Rounthwaite are: Breadth of key = 0.22 X largest diameter of shaft + 0.25. Thickness of key = 0.55 X breadth. The thickness of a single key is limited to about one-eighth the shaft diameter; should this thickness be insufficient, two keys must be used. The breadth of key is less than in stationary practice by reason of the greater length and consequent area which the key offers in resisting compression or shearing. The breadth of key need not greatly exceed once and a half its total thickness. The length of a propeller boss may vary according as the propeller is cast in one piece or whether the boss and blades are cast separately. The former will include all small propellers, especially those of cast iron, for which Seaton and Rounthwaite's rule = 2.7 X diameter of tail shaft. Thus an 8-inch tail shaft would have a taper and boss with key 21.6 inches long. A boss having separate blades will vary between 2.25 and 2.5 diameters in length, averaging the latter figure nearly; in this case, the keyway of the taper end of a 16-inch tail shaft would be 40 inches long. A propeller shaft of carbon steel will have an elastic limit of about 35,000 pounds [578] MACHINE DETAILS RELATING TO STEAM ENGINES per square inch. If the maximum working stress be fixed at one-half this, a maximum working limit is reached at 17,500 pounds per square inch. When this limit is reached two keys must be used, and these should be placed diametrically opposite each other. The bearing surface of a key is important in preventing deformation. The shearing "of a key of ordinary proportions is quite unlikely to occur. In general, the depth of keyway in a propeller shaft is 0.0625 that of its diameter. The aggregate area of two keys for a given shaft diameter is greater than for a single BOLT END WITH COLLAR AND COTTER For Rigid Frame Connection BAR COLLAR SHANK SLOT Kf Diam. A Area Diam. B Thickness C Diam. D Length Width E Depth F 1 .785 H f U 1 A Ii H II .994 1H H H 1& A m 1* t| 1.227 2 f if H f H if If 1.485 2A H H H f 2& lit ii 1.767 2| 1 Hi if A 2i 2 u 2.074 2^ 1 Itt I& & 2^r 2i if 2.405 21 H 1H H i 2f 2A H 2.761 2H 1 2^ if 1 2H 2^ 2 3.142 3| 1A 2i m A 3 2H 2i 3.976 3* 1A 2^ H f 3f 3 2| 4.909 31 !& 2! 2 H 31 3f 2f 5.940 *i I* 3^6 2i 1 4i 3! 3 7.069 4| ii 3A 2A H 41 4i H 8.296 5 U 3f 2^ H 41 4^ 3 9.621 5f H 31 2H 5i 4H 3f 11.05 5| H 4i 21 If 5f 5i 4 12.57 61 2 4^ 3 i 6 5| [579] MACHINE DETAILS RELATING TO STEAM ENGINES key, a result of greater thickness, relatively, of double keys over a single one. When the thickness of a double key is determined, its breadth may be one and a half times that thickness. The central core in a propeller boss is commonly one-third of its length, therefore only two-thirds of the tapered length of a tail shaft is available for driving through the key. No taper is given the keys used in fastening a propeller boss on the tapered end of a tail shaft. The boss slides over the key or feather (both terms are in use) until taper surfaces are in contact; the boss is followed up by a nut on the outer end of the tail shaft. Taper of tail shaft in the boss of propeller = 1 inch per foot. BOLT EXD FOE RIGID FRAME CONNECTION Countersunk Head and Cotter BAR COLLAR SHANK K fy FRAME Dia. A Area Diam. B Thick- ness C Diam. D Length Slot Width H K L M E F G 1 .785 If f 1| 1 H 1 A H 1| 11 2| U .994 m H H it I *ft A i* 2A 1H 2f H 1.227 2 1 if H H U f if 2J H 3 H 1.485 2& H H if 2^ H f lit 2A 2A 81 il 1.767 2f 1 1H H 21 if A 2 2f 2i 8| if 2.074 2& 1 Itt If 2A 1* A 2| 2H 2A 31 i! 2.405 21 if IJt If 2f H i 2& 3 2f 3f U 2.761 2H l 2A if 2H if i 2* 3A 2H 4 2 3.142 31 1& 2* 2 3 1H A 2H 3f 3 4i 2i 3.976 8f 1A 2| 2i 3f U f 3 3H 8| 4f 2* 4.909 3| I* 2| 2| 3f 2 H 8| 4A 3f 5 21 5.940 4* 1* 8& 2| 4| 2i f 8| 4A *t 5| 3 7.069 4f U 3A 3 4| 2A H 4i 5 4f 51 3i 8.296 5 U 3f 3| 41 2^ H 4A 5f 41 6t 3* 9.621 5f U 31 3* 5i 2H 1 4H 51 5i 6f 3f 11.05 51 if 41 3f 5f 21 if 5| 6i 5f 71 4 12.57 6* 2 4* 4 6 3 l 5^ 6^ 6 n 580] MACHINE DETAILS RELATING TO STEAM ENGINES VALVE ROD END WITH BUSHING IK IK K K H K IK IK IK 2 2K 2K 2K 2K 2K 3K 3K 3K IK IK 2 2K 2K H K IK H 2 2K 2K 2K 3 4 2K 2K 3 3K 4K 4K 5K 2K 2K 2K 3 3K IK H K H if 1 IK VALVE ROD END WITH COUPLING 1 IK IK IK IK IK 2 2K 1K2K \N\QO\Tf\00 -H\ 10\ C0\ t-\ ^- 4K 4K 4K 5K H IK IK IK i-t K M N K IK IK 2 [581 MACHINE DETAILS RELATING TO STEAM ENGINES VALVE ROD END WITH COUPLING (Continued) A B C D IX IK 2 2K 2K 2K 2K 2K K 2 2K 2K 2K 2K 3 3K 3K 3K 3K 3K 3x 4 4K 4K 5K 5K H 2K 2K 2H 2H IK 1A 1A IK IK K l i^ IK 1A i& IK 1A IK itt IK IA IA IK ^ IK l& l& itt l^ l^ IK l& 1A IK IK 1A 1A IK M N K if l 1^ IK IA 1M IA IA IK 1A IK if if K if l l i^ IK 1A IK 2K 2K 2K 2K 3 3K M Valve rod socket and key taper Y^, in. per foot. g = K + L + N + 0.125. VALVE ROD END. GUN METAL BOXES WITH SET SCREW ADJUSTMENT AND LOCK NUT K M 1 IK IK IK 2 2K 2K 2K 2K 2K 2K 3 IK 1A 1A IK IK 2 2K 2A 2A 2A 2if 3 3K 3K 3K 2K 2M 2K 2K 3K 3K 3K 3K 4K 4M 1 IK IK IK 2 2 2K 2K 2K 2K 2K K H if K IK IK IK iA IX IK 2K A K H if K if if l 1A 1A IK 3K 3K 4K 4H 5K 5K IK IK IK IK 2 2K 2K 2K 2K 3 3K 3K 1A 1A IK IK IK 2 2 2M 2K 2K IX IK 2 2A 2K 2K 2K 3 3K 3K 4 K K 3// X K K K l l l IK IK IK IX 3K 4 4K 5 4 6K ^ if 1A IK 1A IX IK 1A IK IK itt IX itt IK 2 [582] MACHINE DETAILS RELATING TO STEAM ENGINES VALVE ROD END. GUN METAL BOXES WITH KEY ADJUSTMENT PTQ IK IK IK IK 2 2K 2K 2K 2K 2K 2K 2K 3 B IK 1A 1A IK IK IK 2 2K 2A 2K 2if 3 3K 3K 3K IK IK 2 2K 2K 2K 2K 2K 1A IK 1A 1A 1A itt IK A IK IK 2 2K 2K 2K 2K 2K 2K 3 3K 3K 3K K if K if 1A IK 1A IK 1A 1A IK 1 P IK IK 2 1H 2K 3K 3K 3tt 3K 4K 4K 4H 4K 5K 3 3K 3K 3H 4K 4K 4tt 5K 5K 6K 6K 6tt IK itt 2K 2K 2K 3K 4K 4K 4K 4K u IK K K tt tt K K if if K K if l l 1A 1A IK N K K K A K K K K K K K K K if K l 1A IK 1A IK IK 1A IK IK itt IK itt IK 2 Key tapers 1 in. per foot. [583] MACHINE DETAILS RELATING TO STEAM ENGINES VALVE ROD KNUCKLE ii 1 IN IN IK IK IN ill 2 3 3K N K ift ift IK K tt H i ift ift H % if ift IN lit 2N N K N H H H i ift ift IK ift 1H 2 N A N K K H l l l l l ift ift ift i* ift ift lit 2M ^e \ 6 X K K K N [5841 MACHINE DETAILS RELATING TO STEAM ENGINES VALVE ROD KNUCKLE 1 IK IK 9 IK 2 2A 2K 2K 2K 3K IK 2 2K 3 3K 4 4K 6K 7 8 K K A H H K l IK IK IK IK K K H H K H K IK IK 2K 3K l IK 2K 2A 2K 2H K A A A A K K A A K A H l IK IK IK 1A lil 2 2A 4 4A A A A A K K K 8 A A A A [585] MACHINE DETAILS RELATING TO STEAM ENGINES STRAP JOINT WITH GUN METAL BODY AND STEEL STRAP For operating balanced parts. Not suitable for heavy work M K. l IK IK 2A 2K 2A 2K 3 3A 3H 4K 1 IK 1H Ij 2 2K K A H K A IK IK 2 4 2% 3 3K ft ii i IK ift ift ift IK if l IK ift ift IK l IK ift IK IK itt itt 5* K H if IK ift ift ift IK IK IK ift ift i 3 ^ IK y* y 8 7 T6 K A ift IK 1M IK IK K K K K K A 1ft 1K1K 1ft IK IK 2 2> 2K 1 1 IK H IK IK IK [586] MACHINE DETAILS RELATING TO STEAM ENGINES ROD COUPLING WITH COLLAR AND COTTER ROD B c D E F G H I J K L M N o Diam. A Area 1 .785 li i H 3 4 11 7 8 H i 2| 1 1J 1 f 3f li .994 itt A H 1 1A 1 li A 2 1 1A 1 H 41 H 1.227 if f 1A if 1A u ll 3 . A 21 U 1A H f 4A if 1.485 2^ H 1A 1A U 1A 1A f 3| H if H H 5A I| 1.767 2j i 1H H H 1A itt f 3f if 11 if 1 5^ if 2.074 2A H lit H 2^ H 11 A 31 li 2A 11 i 6A if 2.405 2f 1 1H 1A 2A li 2 A 4 if 2^ 1A 1A 6^ 11 2.761 2H if 2^6 1A 2| H 21 i 4| H 2| 1H H 6H 2 3.142 3 i 2i li 2i 1H 2| i 4^ itt 2| 1H 1A 7A 21 3.976 3f 11 2i 1H 2H U 2A 9 5| 2^6 2H 2A 1A 8i 2 4.909 3! U 2f if 3| 21 2H f 5| 2A 3| 2A 1A 9A 2| 5.940 *i H 3A 2^ 3A 2& 3| H 6 2A 3A 2| if 10i 3 7.069 4* H 3A 2| 3f 2 3f i 4 6f 2| 3f 2f if 11 ROD COUPLING WITH SINGLE TAPER SOCKET AND COTTER Diam. A B c D E F G H i j K L M N 1 H H 1 2tt 2i 1 f H f 1A If li i 3A H f 1A 1A 3i 2| 1 1 1A H if 2 H A ^ H 1 1A 1A 3f 2| H 1 1A f H 2A if A 4A if if if U 3H 21 H 1A if 1 21 2A 1A A 4H H IA H if 4A 31 if 1A 11 if 21 2f 1H f 5A [587] MACHINE DETAILS RELATING TO STEAM ENGINES ROD COUPLING WITH SINGLE TAPER SOCKET AND COTTER (Continued) Diam. A B C D E F G H I J K L M N o If U 2A ii 4H 31 ii H 2^ 1 2& 21 1H f 51 If 1A 2A 1A 4H 3| if If 2T% IA 21 2rs 2 T6 6fk U n 2f if 4 if 1A 1A 2H 3A 2| A 6f 2 1A 2* if 5& 41 1H IA 2$ H 3i 3| 21 1 7A 21 ii 2H 11 6& 41 2^ if 2H if 3^ 3H 2^ A 8A 2* 1H 3* 21 6H 5f 2A 1H 31 1A 3 1A 4f 2H f 9 21 1H 3A 21 71 51 2A 2i 3^ if 4f 2H H 9H 3 2 31 2* 81 6* 2f 2f 3f H 4f 51 3f f 101 ROD COUPLING WITH Two ABUTTING ENDS AND COTTERS ROD B c D E F G H I K L M Diam. A Area 1 .785 f U 1 21 2 1 If 11 1 2| 5f H .994 H If 1 3A 21 1 11 H A 2f 6f H 1.227 if IA H 3f 2i H i if A 3| 71 if 1.485 IA if tA 4 21 iA nf 1A A 3A 8 If 1.767 ii H 1A 4A 3 Ub 2 m f 3f 8| if 2.074 H 2^ iA 4f 31 iA 21 1H 1 4^ 9* if 2.405 1A 2A 1A 5A -3* 1A 21 2 A 4f 101 U 2.761 1A 2f if 5A 31 if 2^ 21 A 4H 101 2 3.142 n 2^ if 5f 4 if 2A 21 i 5 HI 2i 3.976 itt 2H 2 6^ 4^ 2 21 2| A 5f 13 2* 4.909 H 3| 2A 7A 5 2A 3A 2H f 61 14| 2f 5.940 2A 3A 2f 71 5i 21 3A 31 H 61 151 3 7.069 21 3f 21 ;f 6 21 3f 31 f 7^ 171 [588] MACHINE DETAILS RELATING TO STEAM ENGINES ROD COUPLING WITH Two ABUTTING ENDS. GIB AND KEY Dia. A B C D E F G H I j K L M N 1 1 If 1 3 ! 11 1 If f f I 21 A 1 4 61 li 1 1A H 2f H H ii H A 3A f 7f 11 H if U H 2f H 1H f f A 3f f A 8i if 1A 11 if 2f if 11 1 1 A 4 * A 81 M 1A H 41 21 H if if f 4& f 91 if i^ 2 i if 5 jL 3i if 2i 1 i f 41 i f 10f if i& %TS if 51 3f if 2f 1A i^ iSr A A Hi U if 2& H U 2A 1A i& 7 5^ A A 12i 2 if 2f 2 65 3yf 2 2f U U i 51 f 1 13 21 2 3A 2i 7& 4& 2i 3f if if A 61 H A 14f 2 i 2 JL 3 JL 2 i 81 4f 2| 3 JL 1A i& f 7A 1 f 16* 2f 2f 3f 2f 81 5* 2f 3H if if H 71 H 171 3 2f 4i 3 9f 5f 3 4f 11 H 3 4 8f 1 4 19| ROD COUPLING WITH Two TAPER ENDS AND COTTERS J RODS TAPER* IN. PER WOT ROD B c D E F G H i K L M Diam. A Area 1 .785 f 11 f 2f 2 f 11 i i 4 21 5 11 .994 H H 2f 21 1 1* H A 2f 5f U 1.227 f Ift 3 2* H H A 3 61 If 1.485 if 1A 1 3f 2f 1A 1H if A 3| 7 2 1.767 if if 1A 3H 3 H U H f 3H 71 [589] MACHINE DETAILS RELATING TO STEAM ENGINES ROD COUPLING WITH Two TAPER ENDS AND COTTERS (Continued) ROD Diam. A Area B c D E F G H I K L M If 2.074 1 if lA 4 31 H 2A If i 4 81 if 2.405 1* 2 H 4fV 31 1A 21 If & 4^ at If 2.761 i| 2A i* 4f 3f ii 3 * 2A H A 4f 9f 2 3.142 iA 2A if 4M 4 1J 2A 2 i 4H 10 2t 3.976 iA 2| 1A 5& 4^ lit 2H' 21 A 5& 111 2* 4.909 It 2| 1H 6A 5 3A 2| f 6A m 2f 5.940 U 3A if 6| 51 2iV 3| 2f H 6| 13f 3 7.069 if 81 2 n 6 2J 4 3 f 71 15 SCEEW COUPLING. ADJUSTABLE WITH LOCK NUTS Right and left hand threads. United States Standard A B c D E F G H I K L M N o P i f 1 1 1 1 H 1 f H -t i f f it f M kA A A f itt B if 1A A 1 f if if f H H H H f 1A H It itt f i f i 2i 1 1A i 1 f 1 iff if 1A if i 4 A 1 It 2f 1 U if H M 1 2 1A It 2| if A It 1A 3 It itf itt It M It 2& 1A 1H 2A if A H H 3f H U 2 f i U 2A if U 2A 1 1 if if 3f U 2^ 2A if A If 2it it*. 2^ 2| 1A i 4 It 1H 4i It 21 2| H H It 21 1H 21 3 It 1 if 2 ' 4t U 2& 2A i f If 31 lit 2^ 31 H A if 2t 4f 1! 2f 2f ifc H If 3A 1H 2| 3& 1A A U 2& 51 if 2H 2M 1A H If 3A 2t 2tt 3f if A 2 2^ 5f 2 3 3t H f 2 3f 21 3 3f U f 2t 2f 6 [590] MACHINE DETAILS RELATING TO STEAM ENGINES CRANKS. CAST IRON Suitable for Steam Engines up to 24 In. Diameter of Cylinder; Steam Pressures No More than 125 Pounds. For Higher Pressures Steel Castings Should be Used. CKANK PIN END IK IK 2K 2K 2K 2K 3K 4K 4K 5K 6K 6K 6M 7 IK 2K 2K 3K 4K 5K 6K 6K 6& IK IK IK IK IK 3% 4K 4K 4K 4K 5K 6 6K SHAFT END 3 3K 4K 5 6 7 8 9 9K 10 11 UK 12 3% 4K 4K 5K 6 6K 7 7K 8K 8K 6K 7K 9 10K 12 12K 13K 16 16K 17K 18K 20 2K 3K 7K 8 K IK IK 2 2K 2K 3K 4K 4K 5 6K 6K 7K K H 1 IK 1A 1A IK lii IK itt 2 2K M A tt ft 1A IK 1A IK 1H 1H IK 1H 2K 2K 2K N H A ft tt tt i it 1A IK 1A [591] MACHINE DETAILS RELATING TO STEAM ENGINES CRANK PINS 3 , J , H-'T^ 1 M*-"-* S....- * f .?. m 3 I i - F >* * For Stationary Engines Diam. A Area A Length B Project- ed Area Sq. In. Pressure on Pin at 1500 Lbs. Sq. In. Diam. C Area C Length D E F G H I 1 .7854 IK 1.375 2063 K .601 IK IK X K N H IK .994 IK 1.688 2532 1 .785 IN IK X K H H IN 1.227 IN 2.031 3047 IN .994 IK itt M K % H IN 1.485 1% 2.406 3609 IN 1.227 IN 1H A A K H IK 1.767 IK 2.813 4220 IN 1.485 IK 2 K A K ft IN 2.074 2 3.250 4875 m 1.767 2 2K K K l A IN 2.405 2K 3.719 5579 l 5 /8 2.074 2K 2M K K 1 A IK 2.761 2N 4.219 6329 IN 2.405 2M 2^ K K 1 A 2 3.142 2K 4.750 7125 IK 2.761 2K 2A A A IK ft 2K 3.547 2K 5.313 7970 2 3.142 2K 2H A A IK ft 2N 3.976 2% 5.906 8859 2K 3.547 2K 2K A A IK ft 2K 4.430 2N 6.531 9797 2M 3.976 2^ 3 K A IK ft 2K 4.909 2K 7.188 10782 2M 3.976 2K 3K K K IN H 2K 5.412 3 7.875 11813 2K 4.430 3 3A K K IN H 2N 5.940 3K 8.594 12891 2^ 4.909 3K 3* K K IN H 2K 6.492 3N 9.344 14016 2% 5.412 3M 3^ 3^ K IN H 3 7.069 3K 10.500 15 750 2M 5.940 3^ 3M A IK K 3N 8.296 3N 12.188 18282 3 7.069 3^ 4 K N IK K 3^ 9.621 4K 14.438 21657 VA 8.296 4K 4A H N IK K 3N 11.045 4K 16.406 24609 V/2 9.621 4K 4K N N IK K 4 12.566 4N 19.000 28500 3% 11.045 4^ 4K N K IN If 4N 14.186 5 21.250 31 875 4 12.566 5 5K N K IN If 4K 15.904 5N 23.625 35438 4M 14.186 5Ji 5K N K IN ft 4^ 17.721 5^ 26.125 39188 4^ 15.904 5^ 5K H K IN B 5 19.635 5K 29.375 44063 4M 17.721 5K 6 H K 1% ft 5N 21.648 6^ 32.156 48234 5 19.635 6K 6^ H K IN H 5^ 23.758 6^ 35.063 52594 5^ 21.648 6^ 6K H K IN H 5N 25.967 6^ 38.813 58 219 5^ 23.758 6M aK K K IN ft 6 28.274 7 42.000 63000 5M 25.967 7 7K K l 2 H 6N 30.680 7M 45.313 67970 6 28.274 7^ 7K K l 2 H 6K 33.183 7N 49.563 74345 6M 30.680 7K 7K K 1 2 H 6N 35.785 7-N 53.156 79734 6^ 33.183 7K 8 K l 2 H 7 38.485 8^ 56.875 85313 6M 35.785 8K 8^ K 1 2 H 7N 41.282 8K 61.625 92438 7 38.485 8^ 8K H l 2 H 7K 44.179 8M 65.625 98438 7^ 41.282 8M 8K H l 2 H [592] MACHINE DETAILS RELATING TO STEAM ENGINES CRANK PINS. For Stationary Engines (Continued) Diam. A Area A Length B Project- ed Area Sq. In. Pressure on Pin at 1500 Lbs. Sq. In. Diam. C Area C Length E F G H I 7% 47.173 9 69.750 104625 7H 44.179 9 9% tt 1 2 H 8 50.265 9% 75.000 112500 7% 47.173 9% 9% 1 1% 2% H 8% 53.456 9% 79.406 119 109 8 50.265 9% 9% 1 1% 2% If % 1 A 56.745 10 85.000 127 500 8% 53.456 10 10 1 1% 2% If 8% 60.132 10% 89.688 134 532 &A 56.745 10% 10% 1 1% 2% H 9 63.617 10^ 94.500 141 750 8% 60.132 10% 10% 1 1% 2% If 9% 67.201 10% 99.438 149 157 9 63.617 10% 10% 1 1% 2% If VA 70.882 11% 105.688 158532 9% 67.201 11% 11% 1 1% 2% If 9% 74.662 11% 110.906 166 359 VA 70.882 11% 11% 1 1% 2% If 10 78.540 11% 116.250 174 375 9% 74.662 11% 11% 1 ,1% 2% 1 10% 82.516 12 123.000 184 500 10 78.540 12 12 1 1% 2% IOH 86.590 12^ 128.625 192 938 10% 82.516 12% 12% 1 1% 2% 10% 90.763 12% 134.375 201 563 10% 86.590 12% 12% 1 1% 2% 11 95.033 12% 141.625 212 438 10% 90.763 12% 12% 1% 1% 2% 11% 99.402 13% 147.656 221 484 11 95.033 13% 13% 1% 1% 2% 11% 103.869 13% 155.250 232 875 11% 99.402 13% 13% 1% 1% 2K 11% 108.434 13% 161.563 242 345 ny 2 103.869 13% 13% 1% 1% 2% 12 113.097 14 168.000 252000 11% 108.434 14 14 1% 1% 2^ CONNECTING ROD STUB END, FOR CRANK PIN. Box END WITH WEDGE ADJUSTMENT A B C D E P G H i j K 1 i% 1% 1% i% 2% 2% 2& 2% 3 IA 1% i% 1% 1H % A A % % ljf 2% 2% 2% 2H A 1 A A A H 3 3% 3H 3% 4% % 1 IA 1A 1% A A % % % H % if % H IA W l% 1^ 1H [593] MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END, FOR CRANK PIN. Box END WITH WEDGE ADJUSTMENT (Continued') A B c D E F G H I J K 1 3M lit A 3rV H 4K IK TV 1 IK i& 3A 2A N 3A % 4H 1* TV IK 3A i% 3K 2M N 3K % 5K IK A 1A 2K 2 3K 2K H 3M tt 5K IK K 1H 2K 2K 4A 2K N 4 K 5H 1M K if\ 2K 2K 4M 2K K 4H H 6 1H K IK 2K 2K 4K 2M H 4^ H 6M IK K IK 2^ 2K 4* 2K K 4^ i 6A 2 K liV 2K 2K 4% 3 y 8 4% l 6^t 2K K IK 3 2^ 4K 3K H 5 IT\ 7 2A K IK 3K 2K 5* 3^ H 5 l /8 1ft 7rV 2M K ifV 3M 3 5M 3K 1 V/S IK 7K 2K A IK 3K 3M 5M 3K IrV &A IH 8M 2K A 1M 3K 3K 6K 4 IfV &A IK 8K 2H A IK 4 3M 6K 4J4 1M &A IK 9K 3 A 2 4M 4 7 4H 1 7M IK 10H 3M K 2K 4K 4M 7K 4M IrV 7^ iH 10K 3K K 2M 4M 4K 7K 5^ iH 8^ 1H UK 3% K 2K 5K 4M 8K 5^ i 8^ itt 12M 3K K 2K 5K 5 8M 5^ 1 9 2rV 12K 4K K 2K 5K VA 9K 5^ 1M W .2K 13K 4K K 2M 5K 5K 9K 6M iff 9^ 2K 14K 4K k 2K 6M 5% 10 6^ IK 10M 2K 14^ 4M s 3 6K 6 10K 6^ 2 10% 2K 15K 5 % 3K 6^ 1 A L u N p Q R s ; T u 1 K m 2A A A A IK K A 1 A IK A IK 2H A A A 1ft 1 A y IX K IK 2H A K A 1M IK H A IK H 1H 3K A K A IK 1A M A IK H IK 3K A K A 2A 1A M K IK H 2 3K A 'A A 2M 1A A K 1% K 2K 3H M A 1 A 2A 1A A A IK H 2^ 4K K A H 2A IK K A 2 2K 4K K K M 2M 1% K K 2K 1 2K *A A K K 2K IK K K 2% IK 2K 4% A K M 3A 1H K K 2K IK 2M 4K A A H 3A 2 K K 2K 1% 2K 5A A A M 3A 2K A K 2K 1% 3 5K A A A 3K 2K A K 2% IK 3K 5K A K A 3K 2A A K [594 MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END, FOR CRANK PIN. Box END WITH WEDGE ADJUSTMENT (Continued) A L M N p Q R s T u 2K 3 3K 4 4K 5 5K f> IK IK IK 2 2K 2K 2K 2K 3 3K 3% 4K 4K 5 5K 5K 6K 6K 7 5H 5K 6K 6K 10 11 8 UK K K tV K K X K H H K K H K H i IK IK IK * K K K K A K K K 3K 4K 4K 5K 5K 5K 6K 6K 6% 7K 7K 2K 2H 2K 3K 3K 4 4K 4K 5 K K K K K M H % if K i 6 IK IK CONNECT .7 X _1 TING ROD STUB END, FOR CRANK PIN . STRAP JOINT -^ 1 WITH GlB AND KEY T 0. il: J-^NK-- -f - 9 Wm &3 ^ V ,/ \ ) h '. L. -0- i ' * r- M-* O K-U^ o J _vil ] '.'^xl 1 L -1; ^ i_ H / I i ,.* ^i< S *; A^ >|" t r> J >' ^ c^ II 1 f i 1 ' h 1 VU 1 * 1 1 w-i U r )!i > *~~ ^*"i ^ i ^^l^i 1 . H :*si i L 1 Jr 1 1 i r~*~ A B c D E F G H I j K L 1 IK IK IK IK IK 1H 2 2K 2A iA 1A IA IK 1^ 2 2^ SIA 2A 2H IK IK IK iX IK A A K A K K K A K K IH 2^ 2^ 2K 23^ 1 IK 1A 1A IK K A K H M K 1 IK i.k IK ;A A K K A [595] MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END, FOR CRANK PIN. STRAP JOINT WITH GIB AND KEY (Continued) B E IK IX IK 2 2K 2K 2K 2K 2K 3 3K 3*A 5K 2K 3 1 3H 3K 4 6K 6K 7 7K 2 2K 2tt 3 3K 3K 3H 4K 4K 5 4H tt $ tt 10 1A 1A IX IK 2 2M H M M H itt 2 3H 3H 5H Itt Itt Itt 2K 2K 2K 3 3^ 4 4K 4K 5K H K tt IK IK IK IK 2 2K 2K 2K 2K 2K 3 i* lit 2K 2K 3 3K 4 4K 4K 5K 5K 5K A M. N P Q R s T u V 1 1 A 2H 3 1 4A A A K X IK IK A 2H 3K IK 4K K K l H 1M 1M 1 A 3& 3^ IA 5K K K IA K IK IK 1 A 3K 4K 1H 5K K A IA l IK IK A 3^ 4K IK 6K K A i& p IK IK A 4K 4K IK 6K K K IK IK IH I9K K 4K 5K IA 7 K H IK IA IK IK K 4K 5K itt 7^ K H IK iK 2 2 A 5A 6 i 7H K N 1H IA 2K 2K K 5^r 6K IK 8K K K 1H iA 2K 2M K 5A 6M 2 8H K K itt IK 2K 2K K 5M 7K 2K 9K K K 2 IA 2^ 2K K A 7K 2K 9K K 1 2K itt 2K 2K A 6K 7K 2K IOK K 1 234 IH 2H 2^ A 6K 8M 2& ion K 1 2K itt [596] MACHINE DETAILS RELATING TO STEAM ENGINES STRAP JOINT WITH GIB AND KEY (Continued) A M N p Q R s T U V 2K 3 3% 3K 3% 4 4% 4K 4% 5 5% 5K 5% 6 2K 3 3% 3K 3% 4 4% 4K 4% 5 5% 5K 5% 6 5 /s 7 K 7K F 7 H it 8% K 9K if 10% 1^ 12K IK 12K IK 13K 1A 14 1% 14% 9 9% IOK 12 13K 15 16K 18 4 2K 2K 3K 3K 3K 4 4% 4K 4K 15K 17% 18% 19% 23K K K K K K l IK 2 IK 2 1A 2 1A 2 1% 2 IK s IK ? 1 11 ^ 1% 2 IK 4 2 4 2K ^ 2% 4 A IK A 2 '% 2K 'K 2^ K 2K K 2^ K 2% % 2H K 3K t 3% t% 3K tK 3K tK 3K t% 3% CONNECTING ROD STUB END, FOR ^4 CRANK ^^ PIN. -^ STRAP JOINT WITH GIB AND KEY tj y i ^ i i <^ P 1 L''/7^^ iOr $fc IT- V V* F / -^N- F * L < i H 3 : f-i- i : ; ; % M < - 1 *! 1 1 -A- 1 ! 1 ^s ^ 7. ^- i -T, r-\ J j 1 >! Kei^s taper %in.pvrfoo&. ( ! i i ! A t 1 >:: \ v Si U m. A B C D E IF G H I J K L, M N O 1 IK IK IK 2 1 2K 1A IK i& lA IK 1H 1A IK IK IK 1% 2 1% IK 2K 1 IK IK K p i* K l IK IK 1 IK L% K l 1A H K if 1A 3 2% 3K 3 3K 3K 4% 3A 4% 3H 2 IK 2% 1% 2K IK 2H IK 2H IK [597] MACHINE DETAILS RELATING TO STEAM ENGINES STRAP JOINT WITH GIB AND KEY (Continued) 2K 3 3A 3K 3A 3tt 3K 4 4A 4K 4M 5 5K 5H 7 7K 7H 2 2K 2H 3 3H 3H 6M E 2A 2K 2K 3K 3A 3M 3K 4 4K 4H 5 5K 5K 6K 7K 7K 1A Itt IK 2 2K 2A 2K 2g 3K 3K K IK l p 1A IK IK IK IK 2 2K 2K 2K 2K 3 IA 2K 2K 2% 3K 4K 4M 4K 5K 5K 5K IK IK 2 2K 2K 2K 2K 2K 3 3K 3M 4 4^ 5 5% IK 1A 1A IK 1A IK 2 2K 2K 2H 3K 3K 3K 3K l p 1A IK 1A IK IH IK 2K 2K 2H 2H 3K 3A 3H 3H 3H 5K 5K 6 7 7K 10 10; UK 13 14K 15K 16 17 M 4H 5K 5K 5K IOA HA HH 12K 14 15K 3H 4 4K 4K 4H 5 S 6K 8H 9K 9K I 10K 10K UK UK IK IK 2 2K 2K 2K 2K 2K 3K 3K 3H 4 5K 5K 2A 2M 3 4A 4A 5^ 6 2 2A 3 3A 4 * tt 7 1 H' 1 1A : 1A 1A 1A IK IK A A K K A A K A A K K H K K K 2K 3K 3H 5 5K 6K u 1 IK 1A IK IK itt 2 2K 2K 2A 2K 2K 3 7598 IK IA IK 2A 2% 2K 3A 3K 3K 3K 4K w A H K K K K K K K K K K K K K K H K K if l l 1A IK IK IK K A K K K IK IK IK IK IK IK IK IK K 5^; 4K 4ft 5K 5K 7tt 9ft IOA 11 tt UK 12K 14K MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END FOR CRANK PIN. STRAP JOINT WITH GIB AND KEY (Continued) u w 4 4K 5 8 8K 9 9K 10 11 UK 12 4K 5K 6 6K 2 2K 2M 2K 2K 2K 3 IK IK IK IK 7M 7% Itt 111 2^ K i i 1A 1A istt 16tt 20^ 22H 23% CONNECTING ROD STUB END FOR CRANK PIN WITH BOLTED STRAP, WEDGE BLOCK AND KEY Adapted from American Locomotive Practice A B b C D E F G H i j K L [M m N n 1 IK H I* A A IK 1 A K A 2 IK 1 A K A K A IK 1.81 .91 1.33 .34 .10 W, IK A K .20 2.21 Itt y* K K H K IK 2.00 1.00 1.47 .38 .11 IK 1A 3*2 K .21 2.42 Itt A K K % K IK 2.19 1.09 1.61 .41 .12 IK 1A A K .23 2.65 2 A A A H A 1H 2.38 1.19 1.75 .44 .12 IK IK K K .24 2.86 2K A -h A K K 599] MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END FOR CRANK PIN WITH BOLTED STRAP, WEDGE BLOCK AND KEY Continued A B b C D E p G H i j K L M m N n IK 2.56 1.28 1.89 .47 .13 2 IK M K .26 3.08 2M K A K & H i% 2.75 1.38 2.03 .50 .14 2K IK M A .27 3.29 2A K K H 1 H IK 2.94 1.47 2.17 .53 .15 2M Itt A A .28 3.50 2K K K A IK M 2 3.13 1.56 2.31 .56 .16 2K 1H & A .30 3.73 2% K K ^ 1A H 2K 3.31 1.66 2.45 .59 .16 2K itt A A .31 3.93 2tt A K ^ 1H H 2M 3.50 1.75 2.59 .63 .17 2K 2 A A .32 4.14 3A A H H 1A K 2K 3.69 1.84 2.73 .66 .18 2% 2K A A .34 4.37 3^ A K H 1^ H 2K 3.88 1.94 2.88 .69 .19 2K 2M A K .35 4.58 3K H H M 1A if 2K 4.06 2.03 3.02 .72 .20 3 2K A M .37 4.80 3A K A M 1H 1 2% 4.25 2.13 3.16 .75 .20 3K 2A H M .38 5.00 3tt 1 A A H 1% 1A 2% 4.44 2.22 3.30 .78 .21 3M 2A H K .39 5.22 3K A A H itt 1A 3 4^ 2A 3A tt A 3K 2K A M H 5A 4 A 1 A K 1% l l /8 A P P Q q R T s 8 T t u u V w X Y z 1 m 5 /8 A K 2A K A K A A 2M IK 5K 1 5 /8 K A IK 2A H K K 2.33 M K K A K 2K 1M 5H IK M H A IK 2M tt K K 2.47 l A K K K 2H IK 6H i% if M A IK 2K K A K 2.74 l K K 7 T6 A 2H IK 7K IK if M A 1H 2K H A K 2.88 l 5 /8 K A A 3K IK 7A IK 1A if M IK 2K 1 K K 3.14 1 H K K K 3K IK 7K IK 1A K M I5i 3A 1A H K 3.41 l Z A K K K 3A IK 8K 1% 1H K M IK 3A IK K K 3.67 i H K A A 3H IK 8K IK IK if H 2 3A 1M H M 3.94 IK K A A K 4A IX 9A 2 IK l M 2K 3H 1A H K 4.08 IK K A K K 4M 1M 9K 2K 1A IK K 2M 4 IK K K 4.34 IK H A K H 4K IK IOK 2M 1A 1A M 2K 4K 1A H K 4.61 IK tt A H H 4^ IK 10% 2K IK 1A K 2K 4K IK K 4.88 IK l A H M 4tt IK HA 2K itt 1A A 2K 4A IK i K 5.02 IK l A H M 5A IK UK 2K l% 1A A 2^ 4H 1H 1A 1 5.29 IK IK A H if 5K 2K 12A 2% 1M itt A 2K 5 1^ 1A 1 5.43 IK 1A A H if 5K 2K 12K 2K m 1% A 3 5A 1H IK l 5H IK 1M A H K 5tt 2K 12K 3 IK IK A Distance U is subject to slight correction due to fractional quantities being expressed in the nearest working fraction. In no case will the difference exceed V inch. Fractional differences in column V may be adjusted in column U. [600 MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END FOR CRANK PIN, WITH BOLTED STRAP, WEDGE BLOCK, AND KEY Adapted from American Locomotive Practice 5M 6 2H 2K 3 3H 1A 7M 2H 3 3H 4 ft 1 1 1A [601 A 6% 10 11 4M 5H M H H 1 A tt 1A 1A 1A 1A 1A 2M 2K MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END FOR CRANK PIN, WITH BOLTED STRAP, WEDGE BLOCK, AND KEY Continued 6% 7 7% 7K 7% 8 9K lOK UK UK 4H 5^ 5% 7% 7K 8% 9 1A 1A IK IK 1H itt 7K 8K 8K 8% 9 5K 5K 6% IK IK 1A 1A 1M 1A 12% 12% 12% 13% 8% 8K 8% 9K 9K 9% M IK IK K N IK 1H 1% itt 3K 4 4K 4% 2% 2A 2K 2H 2% 2K 12 12% 12% 8% 9 10 14 10% 14% 10% 11 11% 11% 15% 12 16 14% 6% 7% 7A 7H 9% 9% 10 10% UK 11% 12% 12% 12% 13 13% Itt 1% 1% ill Iff 2 2 A 9% 10 10% 10% UK 11% 12 12% 12% 12% 13% 13% 13% 14 7% 8% 9% IK IK IK 1A 1A 1A 13% 14 14% 14% 14% 15% 15% 15% 10 10% 10% 10% UK 11% 12 16% |12% 16% 12% 16% 17% 1A 17% 1% 1% 17% 12% 13% 13% 13% 18% 14 18% 14% IK IK l% 1% IK IK IK IK 2 2 1% 111 2 2 2% 2K 2% 2% 2K 2K 2K 4K 2^ 4% 3 4K 5 5K 5% 5K 5% 5% 6% 6K 3% 3K 3% 3% 3K 3H A p p Q q R r s 8 T t u u V W X Y z 3 5A lit IK % 5H IK 1% A H K 5K 1% 13A 3 IK IK A 3% 5K 2^ 1% K ! 6% IK l% A K K 6 IK 14% 3% 2 2 A 3K 6 2%1A Ki 6K IK 1A % if H 6% IK 15% 3K 2& 2fV K 3% 6K 2K >1A i 7K iK 1A % i if 6K 2K 16% 3% 2K 2K K 4 6% 2K IK i 7K IK IK % 1A l 7 2K 17% 4 2K 2K K 4% 7 2H |l% IK 7% 1% IK A 1% 1. 7A 2K 18tt 4% 2K 2K % 4K 7K 2*1 1A IK 8% 1% 1A A 1A. 1A 7H 2K 19A 4K 2% 2% A 4% 7K 2H 1H 1% 8% IK 1A K 1% 1A 8 2K 20A 4% 2K 2K & 5 8K 3% 1H 1% 9% IK IK % 1% iK 8K 2K 20K 5 3 3 A 5% 8K 3% 1H IK 9K 2K IK A IK, IK 8H 2K 22K 5% 3K 3K A 5K 9 3A itt IK 10 2K 1A A 1A i& 9K 2K 23^ 5K 3% 3% K 5% 9K 3A itt 1% 10% 2% 1A K IK tA 9& 3 24K 5% 3K 3K 1 A 6 9% 3% 2 IK 10% 2% IK K 1A 1% 9% 3 24% 6 3K 3K y 2 6% 10 3K 2^ IK UK 2K IK K IK 1% 10% 13% 26^ 6% 3K 3K 1 A 6^ 10% 4A 2K IK 11% 2K 1% K IK 1A '10% '3% 26K 6K 3% 3% 'A [602] MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END FOR CRANK PIN, WITH BOLTED STRAP, WEDGE BLOCK, AND KEY Continued 7 7% 7% 8 11% 11% 12% 12** 12% 4% 4H 5 2% IK IK 2 2 12 12% 13% 13; 14 2K 3 3 2 2 2V 1% lit 1H lit 2 1A 1% 1A u 12A 12% 3% 3% 3% 3% 3K 3K 27H 28% 29K 31% Slit W 6% 7 7% 7% 7% 8 3K 4 4K 4H 3K 4 4K 4% 8% 8% 8% 9 9M 10 10% 11 11% 11% 12 13 24 15% 16% 17% 17% 18% 5A 5A 5^ 6% 7K 7% 2A 2tt 2% 2H 3 3 3K 3% 3% 2 2% 2% 2% 2% 2K 2% 2% 2% 2% 2% 2% 3 3 3 14** 14% 15 15% 16** 17 18% 18% 19% 20 3% 3% 3% 3% 4K 4% 4K 4K 4% 4% S 2K 2% 2^ 2% 2% 2K 2K ** 2 2 2% 2% 2% 2% 2% 2K 2K 3 1A 1A itt itt 1% 1% itt itt IK 2 2 U 12tt ISA 14 14% 14% 15 ISA 16% 16** 16% 17% 17% 18 3K 4% 4% 4% 4% 5% 5% 5% 5% 5% i 5% 32% 34M 35^ 35M 38A 41A 41% 42^ 42H 45^ 45& 46 W 8% 8% 8% 9 9% 9K 9% 10 10% 10% 11 11% 11% 12 4% 5 5% 5% 5% 5K 6 6% 6% 6% 6% 6K 7 4% 5 5% 5% 5% 5% 5K 6 6% 6% 6% 6K [603] MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END FOR CRANK PIN. FORKED DESIGN WITH BACK BLOCK, ADJUSTING WEDGE AND LINER Adapted from American Locomotive Practice M 3M 7K 8 2i i 3 3H 4 4K 4% 634 7 1A 1A 1A itt lit 2 2H 3M 3A 4A 4H ?4 N 8H IK IN IK IN 2 2 2K 2H 3 3H 4 4A 2A 3A 3A [604] MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END FOR CRANK PIN. FORKED DESIGN WITH BACK BLOCK, ADJUSTING WEDGE AND LINER Continued 9 9% 9^ 9K 9K 10 4.K 4A 4tt 4H 4tt 7% 8 8% 8K 8% 8K 8K 8% 9 9K 6 7 /8 7K 7% 7K 8% 10% 10% 11 11% 6% 7 7% 7% 9 9% 9% 10 10% IOK 2A 2% 2A 2% 2A 6 6A 6A IK 2% M 4% 5 N W 3% 4 5% 6 6% 7 7% 8 4% 5 3% 5% 6 7K 4% 4H 5% 5% 7% Itt Itt 2K 2A 2% 2K 2% 2H 2H 2K 3 3% 3% 4K 4K 5K 5% 7 7K 8 8K 9 * 1 IK IK 1A 2% 2K 3% % tt 1 1 IK 1A 1% IK itt itt 1% 2 2K 2K 6 6K 6K 7K 8K 9K 9K 11% 12% 13% 13K 14 14K 14% 15% 4% 6K 6H 10% IOA lOtt "A ntt 12 12% 12% 8% 10% 10% 12A 13 14tt 15% 16 A 17% 18 18% 19A 20K 21tt 22% 23 4 4% 4A 4H 4K 5K 5% 6 6% 6% 7 7% 7K 7% 8 IK 2% 2% 2tt 3K 3% 4K 4% 4K 4K 4% 4% 2% 2% 2% 2% 3 3K 3^ 3A 3% 4K 4K [605] MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END FOR CRANK PIN. FORKED DESIGN WITH BACK BLOCK, ADJUSTING KEY AND LINER Adapted from American locomotive Practice 53^ 6 7^ 8 83/1 2H 3 3H 3H 3 33^ 3M 3^ 43^ H i 1^1 33^ 6 43/4 5? 6 7^6 8H 33^ 3H 4H 6M 9% 19?4 1034 UK 11 12 12A Itt 4H 3 3% 43^ 43^ 5 4M 5% 63^ M 3K [606] MACHINE DETAILS RELATING TO STEAM ENGINES CONNECTING ROD STUB END FOR CRANK PIN. FORKED DESIGN WITH BACK BLOCK, ADJUSTING KEY AND LINER Continued 7 7% 7% 7% 8 10 10% 4H 5 5K 5A 5K 7% 7K 8K 8K 8% 6% 7K 8% 8K 8% 9 1H 6% 7 7% 10% 11% 11% 12 12% 12% 5A 5% 5A 12 12K 13 13% I2tt 13A 13% 14% 14tt 15% 2A 2H 2% 2K 3 3K 8A 8K 8M 7% M 4K 4% 4K 5K 5% 6 6% 7 N 11 11% 12% 13% 14% 14% 15% 16% 17% 18% 18% 19% 20K 20K IK IK 1% IK 4H 5% 6 6% 10% 10% 11 11% UK 5 6 6K 7% 10 10% 10% 11% UK 11% 12% 12% 13% 2H 2K 3% 3% 4H 4K 5%' H IT 4 4% 6 6% 7% 8 8 8% 9 9% 10 10% if l 1A 1% 1A 1% 1A 1H itt lit 2 2A 2A 2% H l 1A IK IK 1A 1% 1A 1A 1A IK 1A 1H w 3 3% 3K 3% 4 4% 4K 4% 5 5% 5% 6 6% 6% 7 7% 7K 7% 8 2 2A 2A 2K 2H 3 3K 3A 3K 3H 4 1 4K 4% 4K 4K 4K 5 IK 2% 2K 2% 2K 3 3K 3^ 3A 3% 4% 4A 4K [607] INDEX Acceleration, 7 Acetylene, properties,, 199 Acid open-hearth furnace, 230 oxides, 200 properties^ 199 Acidic oxides, 510 Acme thread screws, 358 Activity, C. G. S., 5 Admiralty metal, A, U. S. N., 551, 558. Aich's metal, 558 Air as a standard, 12 properties, 200 specific heat, 14 Ajax bronze, 562 Alabama pine, 298 Alcohol, industrial, 201 properties, 201 Alkali metals, 509 properties, 202 Alkaline-earthy metals, 508 Allotropic theory, hardening steel, 482 Allotropy, 202 Alloy, non-oxidizable, 558 properties, 202 Alloy-steels, 245 Alloy-steels, heat treatment, 263 Alloys, aluminum, 517 chemical nature of, 511 copper, tin, zinc, U. S. N., 539 copper, uses, U. S. N., 539 eutectic, 512 fusibility, 512 liquation in, 512 non-ferrous, 510 non-ferrous, porosity of, 514 occlusion in, 512 physical properties, 511 specific gravity, 511 specific heat of, 512 used in engineering, 558 Aluminum alloys, 516, 558 alloys improved by zinc, 518 and chromium, 517 and copper, 518 and manganese, 517, 559 and nickel, 518, 559 and tin, 517 and titanium, 517 and tungsten, 518 Aluminum alloys, brass, Cowles, 558 bronze, 558 copper, 558 fluxes for, 516 ingots, properties, U. S. N., 525 magnesium alloys, 508 melting point, 517 physical properties, 516 properties, 203, 508 working and annealing, 517 Amalgams, 205, 518 American wire gauge, 73 Ammonia, properties, 206 Angle, 7 Angular velocity, 7 Annealing carbon tool steel, 494 mild steel, 494 wought iron, 469 Anti-friction metal, U. S. N., 559 Admiralty, 559 Comp. W, U. S. N., 541, 554 Antimony, properties, 207 Apothecaries' weight, 43 Arc of a circle, 124, 126 Arcs, circular, lengths of, 126 Area, 7 of circles, 94 of irregular figure, 135 of segment of circle, 125, 129 Areas of circular segments, 129 Argentan, composition, 559 Armor plate, 255 Arsenic, bronze, 559 properties, 207, 506 Asbestos, properties, 207 Attraction, intensity of, 8 Austenite, 208 Avoirdupois weights, 42 Babbitt metal, 559 Barium chloride bath, disadvantages, 490 bath for steel, 490 properties, 208, 508 Basic Bessemer process, 211 open-hearth furnace, 230 oxides, 510 Bastard thread screws, U. S. N., 360 Baths for heating steel, 489 Bell, David, 478 [609] INDEX Bell metal, composition, 559 Belting, rubber, testing, 435 Benedict nickel, Comp. Be-r, 535 Bessemer process, 208 Billets and blooms, classed, 474 Binary alloys, melting point, 55? Birmingham wire gauge, 74 Bischof's refractory quotient, 290 Bismuth amalgam, 519 properties, 214,. 506 Blister steel, 214 Blooms and billets, classed, 474 Board measure, 40 Boiler braces, strength, U. S. N., 350, plates for U. S. Navy, 304 tubes, nickel steel, 253 Bolt end for rigid connection, 580 end with collar and cotter, 579 end with gib and key, 413 end with slot and cotter, 412 head and nut, Frank. Inst., 347 head and nut, U. S. Std., 348 head, length for upset, 399 Bolts and nuts, deck, tests, 382 and nuts, dimensions, 385 and nuts, dimensions, U. S., 381 and nuts, iron, U. S. N., 380 and nuts, steel, U. S. N., 372 and nuts, tensile test, 374 and nuts, U. S. Std., 349, 350 and nuts, weight per 100, 375 and washers, foundation, 408 composition rods for, 384 eye, proportions, 409, 411 for gun mounts, U. S. N., 383 heads and nuts, weight, 352 hook proportions, 397 length of thread, 386 manganese, strength, 350 non-corrosive rods, 379 of composition, U.'S. N., 384 of uniform strength, 391 square head weight, 391 steel, nickel or carbon, 376 strength of, 350 taper, Loco. Std., 389 Tobin bronze, strength, 350 working load for U. S. N., 351 Bone for case hardening, 501 Borax properties, 215 Boron, properties, 215, 509 Box wrench for hex. nuts, 418 Brass castings, B-c., U. S. N., 549 BE, U. S. N., 550 chem. prop., 549 elec. work, 550, 560 porosity of, 513 U. S. Navy, 560 Brass castings, yellow, 560 Brass, commercial, 560 condenser tubes, 560 fluxes for, 515 high, rolled, 561 inspection of, U. S. N., 536 low, rolled, 561 Naval, Admiralty, 561 naval, properties, U. S. N., 545 pipe fittings, U. S. N., 561 pipe, hydraulic tests, 543 pipe, seamless, tests, 544 pipe, seamless, weight, 544 red, commercial, 561 rods, B-r, U. S. N., 549 rolled rods for bolts, 379 sheets, B-p, U. S. N., 549 spring wire, composition, 561 tubes, British standard, 561 washers, U. S. N., 405 with aluminum, 559 with lead, 560 with manganese, 560 with tin, 561 yellow, composition, 561 Brasses, constituents, 505 Brazing aluminum bronze, 561 metal, 562 metal, F., U. S. N., 551 metal, F., U. S. N. uses, 540 Brick, fire, 285 British Ass'n Std., screw, 368 thermal unit, 6 Bronze, acid resisting, 562 Ajax, 562 arsenic, 559 carbon, 562 castings, Admiralty 5j62 deoxidized, 562 fluxes for, 515 inspection of, U. S. N., 536 journal, H., U. S. N., 527 journal, U. S. N., 562 manganese, Mn-c, 528 phosphor, P-r, U. S. N., 530 plates and bars, spec., 532 plates, tensile tests, 532 Torpedo, U.S. -N., 528 valve, Comp. M., U. S. N., 527 Bronzes, constituents, 505 proprietary, 529 Bushel, legal weights, 80 U. S. standard, 42 Cadmium, properties, 215, 507 Calcium carbide, properties, 216 oxide in alloys, 509 properties, 216, 508 [610] INDEX Calcium sulphate as a flux, 510 Calorie, major and minor, 5 Calorific value of coke, 450 Camelia metal, 562 Cap nuts, 371 screw, 394 Capacity, measures of, 41 Car bearings, Penna. R. R., 562 Carbon and alloy steels, Comp., 498 and alloy steels, heat treatment, 498 and low-tungsten steel, hardening, 496 bronze, 562 chrome-nickel steel, 498 chrome-vanadium steel, 499 in alloys, 509 in pig iron, 443 properties, 216 steel for forgings, 471 steel, heat treatment, 480 steel, other than tool, 495 steel, tempering and annealing, 481 steel tools, color scale, 485 steel, requirements, 275 theory of hardening steel, 482 tool steel, 484 tool steel, quenching of, 493 tool steel, U. S. N. requirements, 284 Case-hardening, 500 carburizing gas, 501 carburizing materials, 500 chrome steel, 500 cooling, reheating, 503 cyanide process, 503 effect of nitrogen, 501 for colors, 504 method of, 502 mild steel, 500 mixture, 503 nickel steel, 500 queching, 502 temperatures, 502 Cast iron for U. S. N. properties, 267 malleable, 455 washers, 406 Castings, chrome-nickel steel, 256 iron and steel, 443 iron comp. and structure, 456 iron, physical properties, 454 iron, silicon in U. S. N., 456 iron, tensile strength, 454 iron, tests, U. S. N., 455 iron, transverse strength, 454 manganese steel, 249 semi steel, 459 steel, 460 Castle nuts, 371 Cementation process, 216 Cementite, 217 C. G. S. Mechanical units, 4 C. G. S. System, defined, 2 Charcoal pig iron, 447 Charred leather for case-hard, 501 Chemical changes in the cupola, 449 requirements, pig iron, 448 Chemistry of rubber, 441 Cheval, C. G. S., 5 Chrome-nickel carbon steel, 498 steel, case-hardening, 500 vanadium carbon steel, 499 Chromium hardens aluminum, 517 in steel, 259 properties, 217 steel, 246 vanadium steel, 261 Circle, length of arc, 124 Circles, properties of, 91 table, Dia., Cir., Area, 94 Circular arcs, length of, 126 steel plates weight, 329 Circumference of circles, 94 Clay, melting point, 287 plastic, 288 Clays, general properties, 286 refractory, nature of, 286 Coach and lag screws, 398 Coals, weight of American, 22 Cobalt in steel, 260 properties, 217, 507 Coins, values of foreign, 45 Coke, calorific value, 450 foundry, characteristics, 449 Cold-rolled or drawn steel, 276 Collar screws, proportions, 393 Color scale, hardening steel, 485 Colors in case-hardening, 504 of heated steel, 492 Composition A, U. S. N., 551 B-c, U. S. N., 549 B-p, U. S. N., 549 B-r, U. S. N., 549 BE, U. S. N., 550 Be-r, U. S. N., 535 Cu-p, U. S. N., 522 Cu-r, U. S. N., 520 Cu-si, U. S. N., 522 D, U. S. N., 541 D-c, U. S. N., 547 D-r, U. S. N., 547 F, U. S. N., 540, 551 G, U. S. N., 525 G-Ag, U. S. N., 536 H, U. S. N., 527 M, U. S. N., 527 Mn-c, U. S. N., 528, 541 Mn-r, U. S. N., 541 Mo-c, U. S. N., 533 [611] INDEX Composition Mo-r, TJ. S. N., 534 N-c, U. S. N., 540 N-r, U. S. N., 540, 545 P, U. S. N., 541 P-c, U. S. N., 529 P-r, U. S. N., 530 rods for bolts, 384 S, U. S. N., 540 T, U. S. N., 541 Vn-c, U. S. N., 531 W, U. S. N., 541, 554 Zn-r, U. S. N., 524 Condenser tubes, brass, 560 Conductivity, 10 Cone, mensuration, 155 Connecting rod ends, 593, 607 Constantin, composition, 562 Copper alloys, melting point, 552 alloys, uses, U. S. N., 539 amalgam, 519 and hydrogen, 513 and oxygen, 513 castings, porosity, 513 deoxidizing, 513 fluxes for, 514 for sheathing, 521 for U. S. N. alloys, 543 hardens aluminum, 518 in steel, 260 ingot, for U. S. N., 519 inspection of, U. S. N., 536 lead alloys, melting point, 553 non-ferrous ; Cu-r, 520 phosphor, properties, 522 pipes, hydraulic test, 543 pipes, material, 543 pipes, physical tests, 543 pipes, strength of, 543 plates, English std., 562 properties, 218, 505 refined, cartridge cases, 522 rods, English std., 562 rods, properties, 520 sheets, properties, 520 sheets, weight, 521 silicon, properties, 522 tin alloys, melting point, 553 tubes, British std., 562 zinc alloys, melting point, 553 Corrugated sheet steel, 314 Corrugation types for U. S. N., 315 Cosecants and secants, 139 Cosines, sines, 139 Cotangents and tangents, 139 Couplings for valve rods, 587-8-9 Crank phi stub ends, 593, 607 pins, table, 592 Cranks, cast iron, table, 591 Crankshafts, steel, test pieces, 475 Crucible furnace, tilting, 556 steel, 218 Crucibles, sizes, 555 Cube, mensuration, 153 roots of numbers, 102 Cubes of numbers, 102 Cubic measure, 41 Cupola, chemical changes in, 449 excess of air in, 451 flux to promote fusion, 451 fuel efficiency in, 452 heat of combustion, 452 slag, 451 temp, melting zone, 450 temp, escaping gases, 451 wasted heat, 453 Cupro-nickel, cartridge cases, 562 Curvature, 8 Cyanide bath for steel, 489 process, case-hardening, 503 Cyanides for case-hardening, 501 Cycloid, area of, 133 length of arc, 133 Cylinder, mensuration, 154 Cylindric rings, mensuration, 163 Darcet's fusible alloys, 563 Decimal wire gauge, 74 Deck bolts and nuts, U. S. N., 382 Delta metal composition, 562 Density, 7 Deoxidized bronze, 562 Deoxidizing copper, 513 Dodecahedron, mensuration, 161 Douglas fir, 299 Douglas spruce, 299 Dry measures, 41 Ductility of wrought iron, 467 Duralumin, composition, 562 Dyne, unit of force, 4, 5 Elastic limit, determination, 422 limit, manganese steel, 249 limit, nickel steel, 252 limit, wrought iron, 468 Elasticity, modulus of, 9 Electric furnace, hardening, 488 hardening, high-speed tools, 492 Elements, melting point, 20 Ellipse, area, 133 Elliptic segment, area, 133 Emissivity, 10 Energy, C. G. S., 5 Engine forgings, 476 forgings, steel, 475 Entropy, 10 Erg, C. G. S., unit of work, 5 [612] INDEX Eutectic alloys, 512 Expansion, coefficient, 10 Eye bolt head, proportions, 409 bolt pins, 410 bolts for flanges, 411 Ferrite, 218 Ferromanganese, 444 properties, 506 Fir, Pacific Coast, 299 Fire brick, 285 analyses, 292 composition, 291 crushing strength, 294-5 hardness, burning, 294 load tests, 291 physical tests, 294 Fire clay, 285 analyses, 292 and alumina, 288 and feldspar, 289 and iron oxide, 289 and line, 290 and mica, 290 and quartz, 288 and titanium oxide, 289 chemical formulas, 293 effect of fluxes, 290 vitrification, 290 Flameless combustion, hardening, 487 Flint clay, properties of, 287 Floor plates, steel, 316 Fluorspar as a flux, 515 used as a flux, 452 Fluxes, effect on fireclays, 290 for copper, 514 non-ferrous alloys, 514 Force, 8 unit of, 4 Forging steel, physical changes, 477 Forgings, iron and steel, 465 steel, engine, U. S. N., 475 steel, heat treatment, 474 wrought iron, 470 Foundation bolts and washers, 408 Foundry coke, characteristics, 449 irons, 443 pig irons, U. S. N., 448 Franklin Institute screws, 346 Furnace, hardening, electric, 488 hardening, flameless, 487 Kroeschell-Schwartz, 556 muffle, 486 oven, 486 tempering, gas fuel, 487 tempering, oil fuel, 487 Furnaces, heating, 486 Fusible alloy, 562 G, value of, 4 Galvanized, corrugated steel, 314 sheet steel, 313 steel plates, 309 Gas, for case-hardening, 501 furnace for tempering, 487 Gases, weight and spec, grav., 24 Gear bronze, hard, 563 medium hard, 563 Geometrical quantities, 3 Georgia pine, 298 German silver, 563 Comp. G-ag, 536 fluxes for, 515 Gillett, H. W., 552 Gold amalgam, 519 properties, 219 Gram-degree, 5 Graphite bearing metal, 563 properties, 219 Gravitation units of work, 5 Gun bronze, Comp. G., 539 Gun metal, Admiralty, 563 Comp. G., 525, 564 English, 564 for bearings, 564 for general use, 564 Hammer, Bell's Steam, 478 Hardening carbon steel, 496 high-speed steel, 491 low-tungsten steel, 496 steel, color scale, 485 steel, critical points, 483 Harvey steel, 220 Headless set screws, 393 Heat treatment, alloy steels, 263 carbon steel, 480 high-speed tools, 263 unit of, 6, 9 units, conversion factors, 12 Heating and hardening high-speed steels, 494 carbon steel, 484 Hemlock, Western, 300 Hexahedron, mensuration, 161 Hibbard, H. D., alloy steels, 245 High-speed steel, quenching, 494 steels, theory, 265 tool steels, 258 tools, elec., hard., 492 tools, hardening, 491 tools, heat treatment, 263 Holding down bolts, gun mounts, 383 Hollow forgings, steel, 477 shaft, steel, 256 Hook bolts, proportions, 397 Horsepower, C. G. S., 5 [613] INDEX Horsepower and kilowatt, 28 Continental, 27 English, 25 unsuitable unit, 28 Horsepowers to kilowatts, 29 Hose, rubber, requirements, 434 steam, pressure test, 437 Hydrogen in alloys, 509 in copper, 513 properties, 221 Hyperbola, area of, 134 Hyperbolic conoid, mensuration, 161 Hyperboloid, mensuration, 160 Icosahedron, mensuration, 162 Inertia, moment, 8 Ingot iron, 221 steel, 222 Inspection of material, index, 427 of material, U. S. N., 421 International standard screw, 369 Invar, 253 Iridium, properties, 222 Iron and steel castings, 443 bolts and nuts, U. S. N., 380 castings, properties, 454 castings, silicon in, 456 castings, structure, 456 forgings, 465 properties, 222, 506 wrought, properties, 465 Joule's equivalent, 6, 10 Journal bronze, Comp. H,, 527, 540 Kaolin, properties, 287 Kennedy Double Keys, table, 576 Key, double, table, 577 gib head, table, 573 length, 569 Peters' double, table, 578 sliding, table, 574 sunk, proportions, 569 taper pin, table, 572 Keys for screw propellers, 578 Keyways and sunk keys, table, 569 Kilogram, calorie, 5 degree, 5 Kilograms per sq. cm. to pounds, 70 Kilometers, miles and knots, 68 Kilowatt as unit of power, 28 C. G. S., 5 Kilowatts to horsepowers, 34 Knot, Admiralty, 39 Knots, miles and kilometers, 68 Kroeschell-Schwartz furnace, 556 Lag and coach screws, 398 Larch, western, 300 Latent heat, 10 Lead amalgam, 518 bath for heating steel, 489 bronze, bearing metal, 564 pig, properties, 525 properties, 222, 506 Legal weights, commodities, 79 Length, measures of, 39 standard, 1 Lime in alloys, 509 Limestone used as a flux, 451 Line measurement, 39 Lipowitz's fusible alloy, 563 Liquation, 223 in alloys, 512 Liquids, weight and spec, grav., 24 Lithium, properties, 223 Loblolly pine, 298 Lock nuts, split pins, U. S. N., 356 Log. sines, cosines, tangents, 146 Logarithms of numbers, 163 Longitude and time, 48 Longleaf pine, 297 Lumen bearing metal, 564 Lune, area of, 134 Macadamite, composition, 564 Machine bolts and nuts, 376 bolts, tests, U. S. N., 380 Magnalium, composition, 564 Magnesia, properties, 223 Magnesite, properties, 224 Magnesium, carbonate, 224 properties, 224, 508 Magnolia metal, composition, 564 Malleable cast iron, 455 iron castings, 457-8 iron pipe flanges, 458 Manganese bronze, 564 bronze castings, 541 bronze, Mn-c, 528, 541 copper, 564 hardens aluminum, 517 in pig iron, 444 properties, 225, 506 rods for bolts, 379 steel, 247 vanadium bronze, 564 Manganin, composition 565 Marble chips used as a flux, 451 Martensite, 226 Mass, 2 Materials, chemical properties, 421 Materials, physical tests, 421 sizes for test, 422 types, test pieces, 422 j Mayari steel, 256 [6141 INDEX Mechanical equivalent of heat, 6 quantities, 3 Medical signs, 43 Melting point, copper alloys, 552 of clay, 287 of elements, 20 Mensuration, 89 of solids, 153 Mercury, properties, 226, 506 Metals, physical constants, 19 specific gravity, 21 Metric and U. S. measures, 50 screw threads, 369 system, 1, 49 Micrometer wire gauge, .74 Mild steel, case-hardening, 500 Miles, knots and kilometers, 68 Mill and foundry products, 267 Modulus of elasticity, 9 Moldenke, Dr. Richard, 455 Molybdenum in steel, 260 properties, 227 Moment of a couple, 8 of inertia, 8 Momentum, 8 Monel metal cast, Mo-c, 553 composition, 534 for bolts, 379 physical properties, 534 rolled, MO-E, 534 U. S. N., 565 Money, U. S., 44 Muffle furnace, 486 Muntz metal, cast, D-c, 547 composition, 565 comp. D, uses, 541 properties, 547 sheets, D-r, 547 Naval brass, cast, N-c, 545 inspection, 542 N-c, 540, 565 N-r, 540 rods for bolts, 379 rolled, N-r, 545 Newton's fusible alloy, 563 Nickel alloys, 505 and aluminum, 518 chromium steel, 253 fluxes for, 515 properties, 228, 507 silver, 565 steel, 250 steel, case-hardening, 500 steel for forgings, 471 steel, properties, 251 Nickelin, composition, 565 Niter, oxidizing agent, 509 Nitrogen in case-hardening, 501 in alloys, 509 properties, 229 Non-corrosive rods for bolts, 379 Non-ferrous alloys, 505, 510 metal, D-r, 565 metals, 505 Non-metals used in alloys, 509 North Carolina pine, 298 Norton, A. B., 552 Norway pine, 300 Nuts, cap, 371 Castle, 371 lock and split pin, 356 round slotted, 353 sleeve, dimensions, 403 steel and iron, 377 Occlusion, 229 in alloys, 512 Octahedron, mensuration, 161 Oil furnace for tempering, 487 Open-hearth carbon steel, 307 process, 230 steel for U. S. N., 305 Oregon pine, 299 Oven furnace, 486 Oxides, 232 Oxygen and copper, 513 and manganese, 444 properties, 233, 510 Parabola, area of, 133 Parabolic conoid, mensuration, 160 Paraboloid, mensuration, 160 Parallelepipedon, solidity, 153 Parallelogram, area, 89 Pearlite, 233 Pennsylvania R. R., car bearings, 562 Penna. R. R. case-hardening mixture, 503 Peters' double key table, 578 Phosphor bronze, inspection, 542 P, uses, 541 P-c, 529, 565 properties, 529 Phosphor copper, properties, 522 Phosphorus, 260 in alloys, 510 in pig iron, 445 properties, 234 Physical constants of metals, 19 prop, iron castings, 454 Pi, (TT) useful functions, 93 Pig iron, analysis, standard, 446 chemical requirements, 448 grading, 445 Norway, 301 Pine, Longleaf, 297 [615] INDEX Pig iron, Shortleaf, 298 Southern yellow, 296 Pipe, brass, requirements, 543 copper, requirements, 543 flanges, malleable iron, 458 Piping in steel ingots, 476 Plane trigonometry, 136 Plaster of Paris, flux, 510, 515 Plastic bronze, composition, 566 Plate washers, dimensions, 404 Platinoid, composition, 566 Platinum, properties, 234 Plumbago for foundry use, 464 Polygon, area, 90 Porosity, non-ferrous alloys, 514 Porter, H. F. J., 476 Potassium cyanide, flux, 510 nitrate, oxidizing agent, 509 properties, 235, 509 Pound-degree, C., 6 F.,6 Pound, unit of mass, 6 Poundal, 4 Pounds per sq. in. to kilograms, 70 Power, C. G. S., 5 or activity, 9 Pressures, pound to kilograms, 70 Prism, solidity of, 153 Prismoid, mensuration, 158 Projectiles, 255 Properties of materials, 199 Protective hull plates, 273 Puddling iron, 465 Pyramid, mensuration, 156 Quenching baths, 493 Reamers for taper bolts, 390 Recalescense, 477 Reciprocals of numbers, 102 Reduction, 236 Redwood, 300 Refractories, manufacture, 288 Reheating steel ingots, 476 Resilience, 9 Rheotan composition, 566 Ring, to find area, 132 Rivet rods, tests, 339 Rivets, manufactured, tests, 340 small, sheet metal, 344 standard, U. S. N., 341 steel, for hulls, U. S. N., 339 Rose's fusible alloy, 563 Rowland, Professor H. A., 6 Rubber belting, requirements, 435 chemistry of, 441 elongation, 438 fabrics, tension tests, 437 Rubber, friction test, 440 goods, compounding, 433 goods, definition, 436 goods, friction, layers, 437 goods, properties, 436 goods, testing of, 432 hose, requirements, 434 hydraulic test, 440 material, inspection, 428 physical testing, 436 repeated stretching, 439 tensile strength, 438 Salt, common, flux for copper, 514 Screw, Acme thread, U. S. N., 358 Bastard thread, U. S. N., 360 British Assn. standard, 368 buttress thread, 363 coupling, valve rod, 590 ends, length for upset, 400 ends, upset, details, 401 International, standard, 369 multiple thread, 362 propellers, key, 578 S. A. E. standard, 365 sharp V-thread, 364 square thread, 361 thread, length, bolts, 386 threads, Metric, 369 threads, Sellers, 346 threads, sharp V, 346 United States standard, 348 Whitworth standard, 365 Screws, cap, proportions, 394 collar, 393 headless, 393 set, sizes, 396 Secants and Cosecants, 139 Second, unit of time, 6 Segment of a circle, 125 Segregation in steel ingots, 476 Sellers, Wm., screw threads, 346 Semi-steel, 236 castings, 459 Set screws, sizes, 396 Shafts, steel, test pieces, 475 Shortleaf pine, 298 Silica, properties, 236 Silicon as a flux, 510 bronze, 566 copper, deoxidizer, 513 copper, properties, 522 effect, yellow brass, 513 in iron castings, 456 in pig iron, 443-4 properties, 236 spiegel, 444 steel properties, 257 [616] INDEX Silver amalgam, 519 properties, 237 Simpson's rule, irregular figures, 135 Sines and Cosines, 139 Sleeve nuts, dimensions, 403 Socket wrench, 419 Sodium amalgam, 519 properties, 237, 509 Solder, aluminum, 566 half and half, 566 hard for copper, 566 nickel silver, 566 spelter, 566 tin-lead, 555 tinmen's, 566 Solids, mensuration of, 153 Solution theory, hardening steel, 482 Sorbite, 483 South Carolina pine, 298 Southern yellow pine, 297 Space, 1 Specific gravity, liquids, 24 of gases, 24 of metals, 21 of minerals, 21 of wood, 23 Specific heat of air, 14 of alloys, 512 Speed, flow, cu. ft. to cu. meters, 72 Spelter solder, 554, 566 Sperry, E. S., 561 Sphere, mensuration, 158 Spherical triangle, mensuration, 158 Spheroid, mensuration, 159 Spiegeleisen, 444 Spikes, black and galv., 420 Spring cotters, U. S. N., 357 steel for U. S. N., 280 Spruce, 301 Square thread screws, U. S. N., 361 roots of numbers, 102 Squares of numbers, 102 Steam hammer, 478 hose, pressure test, 437 metal, brass, 566 Steel, allotropic theory, hardening, 482 annealing, 494 annealing mild, 494 as wrought iron substitute, 277 bars for concrete, 267 bars, strength of round, 337 bars, weights, 336 Bessemer, for hulls, 311 boiler plates, U. S. N., 304 boiler plating, U. S. N., 267 bolt rods, U. S. N., 376 bolts and nuts, U. S. N., 372 carbon and alloy, comp., 498 Steel, carbon chrome-nickel, 498 carbon chrome-vanadium, 499 carbon, color scale, 485 carbon, heating, 484 carbon nickel for hulls, 311 carbon, other than tool, 495 carbon, requirements, 275 carbon theory, hardening, 482 carbon tool, 484 carbon tool, U. S. N., 284 casting specifications, 460 castings, 239, 460 castings, chemical and physical prop- erties, U. S. N., 462 castings, composition, 462 castings, heat treatment, 462 castings, tensile strength, 462 castings, U. S. N., 461 castings, U. S. N. properties, 267 castings, welding, 463 chromium-vanadium, 261 cold-rolled or drawn, 276 colors of heated, 492 common for hulls, 311 common, properties, 307 corrugated sheets, 314 crankshafts, test pieces, 475 double hardening, 494 drill rod, U. S. N., 274 extra soft for U. S. N., 277 for forgings, process, 471 for forgings, properties, 471 for forgings, tests, 472 for miscell. forgings, 278 for rivets, properties, 267 for springs, 280 for tools, 281 for U. S. N. requirements, 267 forgings, 465 forgings, hollow, 477 forgings, U. S. N., 471 galvanized, 309 galvanized sheet, 312 hardening carbon and low-tungsten, 496 heat treatment, alloy, 263 heating, barium chloride bath, 490 heating in cyanide bath, 489 heating in lead bath, 489 high-speed, theory, 265 high-speed tool, 258 high tensile, 307 hull plating, 267 ingots, defects, 476 ingots for U. S. Navy, 303 ingots, piping, 476 ingots, reheating, 476 ingots, segregation, 476 [617] INDEX Steel, ingots, specifications, 474 manganese, 247 Mayari, 256 nickel-chromium, 256 nuts for U. S. N., 377-8 open-hearth carbon for hulls, 311 other than carbon, 482 overweight allowance, 306 plates, circular, weight, 329 plates for hulls, 306 plates, rectangular weight, 318 plates, shapes and bars for U. S. properties, 267 plates, special treatment, 273 properties, 239 quenching baths, 493 reheating boiler, 305 rivets for hulls, 339 shafts, test pieces, 475 shapes for hulls, 310 sheet, black and galv., 312 silicon, 257 silicon for hulls, 311 simple chromium, 246 simple nickel, 250 simple tungsten, 246 slabs, blooms, billets, 474 soft or flange, 307 solution theory, hardening, 482 terms relating to, 245 tests for hull plates, 308 tungsten tool, requirements, 284 variation in weight, 268 wire gauge, 73 Sterro metal, composition, 566 Strap joint, bolts, key, 599, 601 light, table, 586 round end, 597 square end, 595 Strength of round steel bars, 337 uniform, bolts, 391-2 Stress, intensity of, 9 Strontium, properties, 508 Structural timbers, 296 Stub end, box pattern, 593 , forked, table, 604 strap, gib and key, 597 strap joint, table, 595 strap, key, 599, 601 Studs, commercial sizes, 397 length of thread, 388 Sulphur, 260 in alloys, 510 m pig iron, 444 properties, 239 Surface measure, 40 Surveyors' measure, 39 Talbot process, steel, 231 Tamarack, 301 Tangents and Cotangents, 139 Tantalum, properties, 239 Taper bolts, Loco., Standard, 389 reamers, for bolts, 390 Temperature, case-hardening, 502 Tempering and annealing steel, 481 Tensile strength, malleable iron, 455, 458 phosphor bronze, 529, 530 steel castings, 462 N., wrought iron, 467 Terneplate roofing tin, 317 Test of material, U. S. N. std., 421 rubber materials, 428 Testing rubber fabric, 437 rubber goods, 432 Tests, timber, 302 Tetrahedron, mensuration, 161 Therm, C. G. S., 5 Thermal capacity, 10 Timber, New England, 301 Structural, 296 tests, 302 Timbers of Pacific Coast, 299 Time, 1 and longitude, 48 " between two dates, 47 measures, 44 Tin amalgam, 519 and aluminum, 517 ingot, properties, 523 phosphor, 523 properties, 240, 506 terneplate roofing, 317 Titanium and aluminum, 517 properties, 241 Tobin bronze, composition, 566 T, uses, 541 Tool steel, carbon, 484 requirements, 281 tempering furnace, 486 Torpedo bronze, U. S. N., 528, 567 Torque or twisting, 8 Tortuosity, 8 Trapezium, area, 89 Triangle, area, 89 Trigonometrical formula, 137 Trigonometry, plane, 136 Troy weight, 42 Tungsten and aluminum, 518 in steel, 259 properties, 242 steel, 246 tool steel requirements, 284 Turnbuckles, dimension, 402 Unit of energy, C. G. S., 5 (618] ' INDEX Unit of force, 4 heat, 6 Mass, 2 momentum, 5 power, C. G. S., 5 time, 1 work, C. G. S., 5 Units and standards, 1 and standards, U. S. A., 12 fundamental and derived, 11 geometric and dynamic, 11 Useful alloy steels, 245 Valve bronze, comp. M, 527, 540 bronze, U. S. N., 567 rod couplings, tables, 587 rod end, adjustable, 582 rod end, bushed, 581 rod end, key adjustment, 583 rod knuckle, 584, 585 Vanadium bronze, 567 bronze, Vn-c, 531 in steel, 260 properties, 242 Velocity, 7 Virginia pine, 299 Vitrification, fire clay, 290 Volume, 7 measure of, 41 Washers, brass, U. S. N., 405 cast iron, 406 dimensions, U. S. N., 404 Water as a standard, 15 Watt, C. G. S., 5 Wedge, mensuration, 157 Weight, bolts and nuts, 375 bolts, square head, 391 metals and minerals, 21 of circular plates, 329 of copper sheets, 521 of square and round bars, 336 rectangular plates, 318 steel, variation, 268 Weights and measures, 39 and measures, Metric, 49 per bushel, 80 Welding steel castings, 463 Western hemlock, 300 larch, 300 White brass, 567 metal, Admiralty, 567 metals for bearings, 505, 567 Whitworth standard threads, 365 Wire gauge, U. S. standard, 77 gauges, American, 73 gauges in use in U. S., 75 Wood, structural timber, 297 weight and spec, grav., 23 Wood's fusible alloy, 563 Work and energy, 9 Work-rate, C. G. S., 5 Wrench, box, hex. nuts, 355, 418 field, square nuts, 417 socket, 419 Wrenches, box, round nuts, 354 open end, 413 Wrought iron, analysis, 466 annealing, 469 blacksmith grade, 470 chemical and physical requirements, 470 chemistry of, 465 compression, 468 ductility, 467 elastic limit, 468 for blacksmith use, 470 for U. S. N., 267 forgings, 470 low temperature, 469 proof load, 468 safe load, 468 special grade, 470 stiffening of, 469 tensile strength, 467 texture, 466 Wulfenite, properties, 244 Yard, unit of length, 6 Yellow brass, S., uses, 540 pine, 297 Zinc amalgam, 518 chloride, flux, aluminum, 516 for boilers, U. S. N., 524 for hulls, U. S. N., 524 for salt water piping, 524 improves aluminum alloys, 518 plates, Zn-r, U. S. N., 524 properties, 244, 507 slab, for U. S. N., 523 [619] Engineering UNIVERSITY OF CALIFORNIA LIBRARY